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An Econometric Model of the US Economy
John J. Heim
An Econometric
Model of the
US Economy
Structural Analysis in 56 Equations
John J. Heim
University at Albany-SUNY
Albany, New York, USA
ISBN 978-3-319-50680-7 ISBN 978-3-319-50681-4 (eBook)

DOI 10.1007/978-3-319-50681-4
Library of Congress Control Number: 2017940494
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This book is dedicated to
Susan
who has given me so much
P REFACE
I left academic life in 1972, after getting my Ph.D. At that time large-scale
econometric modeling of the economy was the rage; everyone thought it
would be just a matter of time before we had “done enough science” to
allow economists to discuss economics in the classroom, not in terms of
the alphas and betas of theoretical models, but in terms of the real-world
coefficients they represent. Economics would become the next branch of
engineering, or so many thought.
Much to my surprise, when I returned to academic life 25 years later
things had not much progressed. Most economists were still using alphas
and betas to describe how one variable affects another in economics. For
lack of vigorous, concerted effort over those 25 years to pursue the hard
numbers underlying the theories, and their statistical significance, econom-
ists were still just discussing theories with the best “numbers” we had – the
abstract alphas and betas of pure theoretical discourse. Because we hadn’t
disciplined our presentation of theories to those scientifically proven to
work, even more theories abounded than was the case in 1972. Worse, the
overriding emphasis in economic theory was not on “what works?”, but
on “what’s new?”.
My engineering students knew the difference. When I tried to describe
macroeconomics as real science, and then described the coefficients that
connect one variable to another in alphas and betas, instead of real num-
bers, they just snickered. “Yes, but what is the real relationship?” they
would ask, meaning what are the real numbers? “And if you don’t have
them, why do you call this science?” they would ask. Certainly in their
vii
viii PREFACE
engineering courses, where every equation describes what actually works,

they were getting real numbers.
This book attempts to meet that very standard by focusing on what
works. It attempts to move forward the empirical efforts of Tinbergen,
Goldberger, Klein, Eckstein, and Fair the past 80 years to determine what
works. That is, the effort to convert economics from just theory to hard
(by which I mean reliable) science. Doing so requires three things.
First, it requires that the postulates we test have some economic mean-
ing, and not be just some collection of variables we are “running up the
flagpole,” to see what happens.
Second, it requires that the theory-based postulates we test are struc-
tured loosely enough so that the data determine what is real, i.e., the exact
shape and content of the theory being tested. It is not for us to say a
priori by how we structure the model we test, whether Keynes’ consump-
tion function, whose principal determinant is current income, is correct,
or whether Freidman’s, whose principal determinant is average income
(permanent income) is correct.
Third, it is not for us to claim some empirical result proves some theory
is correct, simply because it explains some variation in the economy, in some
time period, in some economic model. To be correct, it should explain most
variance, in most or all time periods, in most or all models.
This book tries to adhere to these three rules, we think successfully.
To meet the first condition, its model is built around the theory that we
found most consistent with the data. To meet the second, the shape (and
inclusion) of each equation in the model is data-determined, e.g., there are
no predetermined assumptions about what drives consumer or investment
spending. Third, a large-scale econometric model is needed to capture
all the sources of economic variation, and that’s what is used. Extensive
robustness testing was used to prove that any initial statistical finding was
real and not just some spurious artifact of the time period or particular
model tested.
I hope the reader will agree that the models developed in this book
adhere to these rules for good engineering science.
SUNY, Albany John J. Heim

A CKNOWLEDGMENTS
Most of all, I am indebted to Nobel Laureate Robert Solow for providing

review comments and suggestions on an earlier draft, as did David Colan-
der and Ray Fair. They were a source of inspiration and without their
involvement and support, especially Robert Solow’s, this book probably
would not have been finished.
I am also indebted to distinguished econometrician, Kajal Lahiri, for
bringing me to SUNY Albany and providing a place where I could work
on this book with a minimum of other distractions. He has provided a
very supportive and intellectually stimulating atmosphere within which to
work, and provided guidance on econometric issues through his careful
review of an earlier draft.
I would also be remiss if I did not mention the long line of earlier
economists who toiled long and hard as both macroeconomists and
econometricians to turn macroeconomics from philosophy into science.
These economists include Jan Tinbergen, Lawrence Klein, Frank deLeeuw,
Arthur Goldberger, and, more recently, Ray Fair. Fair has had the doubly
difficult job of keeping the strongly scientific Cowles tradition alive during
recent decades, when many economists turned to different, less scientific
approaches. We owe him much.
For similar reasons, we owe Greg Mankiw much. His 2006 article in
the Journal of Economic Perspectives convinced many that the detour in
the 1980s away from Cowles modeling and toward DSGE has proven
unproductive, and helped resurrect interest in Cowles modeling again.
Solow’s (2010) testimony to Congress reached the same conclusion about
DSGE and helped in the same way.
ix
x ACKNOWLEDGMENTS
Nor could the book have been written without the strong support of
my wife Sue. This book required 2 years full-time work, and before that,
considerable part-time work. The problems to be resolved required endless
long hours at work, and endlessly preoccupied my mind, even at home.
Sue was always willing to make the sacrifices necessary to cope with all
that.
Finally, I must acknowledge the secretarial assistance provided by
Annemarie Hebert. She has helped pull together, duplicate, and send out
endless drafts of this work.
C ONTENTS
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Modern Macroeconomics: Moving from
the Methods of Economic Philosophy to Those of
Economic Science 5
1.2 Summary of Ways in Which This Large-
Scale Econometric Model Improves on Past Work 9
1.3 The 56-Equation Model: 30 Behavioral Equations,
15 Identities (Product Side of National Income
and Product Accounts (NIPA)), and 8 Behavioral
Equations, 3 Identities (Income Side of NIPA) 14
1.4 The 38 Behavioral Equations: Coefficients,
Significance, R2 , and Durbin Watson Tests:
(Summary of Results: Detailed Explanations of
Findings Presented in Chapters 4–20) 16
Part I Production of the GDP
2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1 General Methodological Issues 40
2.2 Choosing Between VAR, DSGE, and
Cowles Commission Models 48
3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3.1 Lawrence Klein and Michael Evans (1968): The
Wharton Econometric Forecasting Model 116
xi
xii CONTENTS
3.2 Otto Eckstein’s (1983) The DRI Model of the U.S. Economy 125
3.3 Ray Fair’s Estimating How the Macroeconomy Works (2004) 131
3.4 Federal Reserve Board/U.S. Model (1996) 140
3.5 Literature Review Summary 144
4 The Consumption Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4.1 Total Consumer Spending on Both Domestically
Produced and Imported Consumer Goods 151
4.2 Spending on Imported Consumer Goods – OLS Estimates 157
4.3 Spending on Imported Consumer Goods – 2SLS Estimates 161
4.4 Consumer Spending on Domestically Produced
Consumer Goods (OLS) 162
4.5 Determinants of Consumer Borrowing – OLS Estimates 166
4.6 Determinants of Consumer Borrowing – 2SLS Estimates 168
4.7 Modeling the Major Components of Total Consumption 171
4.8 Determinants of Spending on Consumer Durables (OLS) 172
4.9 Determinants of Spending on Consumer Durables (2SLS) 172
4.10 Determinants of Spending on Consumer
Nondurables (OLS) 176
4.11 Determinants of Spending on Consumer
Nondurables (2SLS) 177
4.12 Determinants of Spending on Consumer Services (OLS) 180
4.13 Determinants of Spending on Consumer Services (2SLS) 181
5 Models Identifying the Determinants of Investment

Spending and Borrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.1 OLS Estimates of the Determinants of Total
Investment Spending 188
5.2 2SLS Estimates of the Determinants of Total Investment 189
5.3 OLS Estimates of the Determinants of Domestically
Produced Investment Goods 192
5.4 2SLS Estimates of the Determinants of
Domestically Produced Investment Goods 193
5.5 OLS Estimates of the Determinants of Imported
Investment Goods 197
5.6 2SLS Estimates of the Determinants of Imported
Investment Goods 198
5.7 An Alternative Method of Calculating Coefficients
in the Investment Imports Model 201
CONTENTS xiii
5.8 OLS Estimates of the Determinants of Investment

Borrowing 203
5.9 Determinants of Spending on Fixed Plant and
Equipment Investment (OLS) 207
5.10 Determinants of Spending on Fixed Plant and
Equipment Investment (2SLS) 208
5.11 Determinants of Spending on Residential
Investment (OLS) 212
5.12 Determinants of Spending on Residential
Investment (2SLS) 215
5.13 Determinants of Spending on Inventory
Investment (OLS) 215
6 The Exports Demand Equation . . . . . . . . . . . . . . . . . . . . . . 221

6.1 OLS Model of Export Demand 225
7 Statistically Estimated Real GDP Determination

Functions (“IS” Curves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.1 The GDP as a Function of the Determinants of
Domestically Produced Consumer and Investment
Goods and Services, Government Spending and
Exports (GDP = CD + ID + G + X) 230
7.2 The GDP as a Function of the Determinants of
Total Consumer and Investment Goods
and Services, Government Spending, and
Exports Minus Imports (GDP = CT + IT + G + X – M) 236
8 Real GDP Determination Function (“IS” Curve)

Coefficients Aggregated from Parameter
Estimates Obtained by Statistically Estimating the
Subcomponent Functions Comprising the GDP . . . . . . . . . 239
8.1 Using the GDP Determination Model
GDP = CD + ID + GD + X 239
8.2 Using the GDP Determination Model
GDP = CT + IT + GT + (X – M) 246
9 Determinants of the Prime Interest Rate: Taylor

Rule Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9.1 OLS Estimates 254
9.2 2SLS Estimates 255
xiv CONTENTS
10 Determinants of the Prime Interest Rate – LM

Curve Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
10.1 OLS Models of the LM Curve 259
10.2 2SLS Models of the LM Curve 260
11 Determinants of Inflation – The Phillips Curve Model . . . . 265

11.1 Reconciling the Money Supply Variable
in the Taylor Rule and LM Equation Interest Rate
Models with the Money Supply Variable in the
Inflation (Phillips Curve) Equation 269
12 Determinants of Unemployment . . . . . . . . . . . . . . . . . . . . . . 273

12.1 A Simple OLS Model Based on Okun’s Law 273
12.2 The 2SLS Okun Model 276
12.3 The OLS Technological Change Model 279
12.4 The 2SLS Technological Change Model 280
13 The Savings Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

13.1 The Corporate Savings Function 285
13.2 The Depreciation Allowances Savings Function 291
13.3 Personal Savings 296
14 Determinants of Government Receipts . . . . . . . . . . . . . . . . . 303

14.1 Contributions to Explained Variance 304
14.2 Robustness Over Time 304
14.3 Robustness to Model Specification Changes
(1960–2010 Data Set) 307
15 Endogeneity of Government
Spending Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
15.1 The Model for Total Government Spending for All
Purposes: Goods, Services, and Transfers 309
15.2 The Model for Government Spending on Goods
and Services Only 313
16 Capacity of the Model to Explain Behavior

of the Macroeconomy Beyond the Period Used to
Estimate the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
16.1 Model #1 Treating All Determinants of C, I, and X
as Exogenous 318
CONTENTS xv
16.2 Model 2: Treating C, I, and X Model Determinants

for Which We Have Explanatory Functions as Endogenous 322
17 Converting the Older Keynesian IS-LM Model to

the More Modern AS-AD Interpretation of the
Keynesian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
17.1 Short- and Long-Run Aggregate Supply Curves 331
17.2 The Aggregate Demand Curve and the Role of
Velocity In Aggregate Demand 332
17.3 OLS Tests of M1 Velocity’s Determinants 338
17.4 2SLS Tests of M1 Velocity’s Determinants 342
17.5 OLS Tests of M2 Velocity’s Determinants 346
17.6 Which Determinants of GDP Are Also
Determinants of Velocity 352
17.7 Stationarity Issues 359
17.8 Alternative Method: Calculating Impact of
Determinants of GDP on Velocity Using
Regression Coefficients Obtained Estimating
Consumption, Investment, and Export Functions 359
18 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
18.1 Introduction 363
19 Summary and Conclusions (Production Side of the

NIPA Accounts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
19.1 Other Major Findings 376
Part II Income Side of the NIPA Accounts
20 Determinants of Factor Shares . . . . . . . . . . . . . . . . . . . . . . . 381

20.1 Introduction, Theory of Factor Shares, and
Summary of Findings 381
20.2 Literature on Factor Shares 394
20.3 Methodology 397
20.4 Determinants of Labor, Profits, Rent, and Interest
Factor Shares and Income Levels 400
20.5 Summary and Conclusions (Income Side
of the NIPA Accounts) 441
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
L IST OF F IGURES
Fig. 4.1.1 Actual consumption compared to levels

calculated from Model 4.1.T 1960–2010 . . . . . . 153
Graph. 6.1.1 Equation 6.1 Graphed . . . . . . . . . . . . . . . . . . . . . 225
Graph. 12.2.1 The augmented Okun model (Eq.
12.4) model for explaining variation in
unemployment 1960–2010 . . . . . . . . . . . . . . . . . 276
Graph. 12.4.1 Technological change model of
determinants of unemployment (Eq. 12.4.1) . . . . 281
Graph. 13.1.1 Fifty years annual variation in corporate
saving (calculated from Eq. 13.1.1, then
compared to actual) . . . . . . . . . . . . . . . . . . . . . . 287
Graph. 13.2.1 Explained and actual depreciation
allowance savings the past 50 years . . . . . . . . . . . 293
Graph. 13.3.1 The explanatory power of the Eq. 13.3.1 model . 299
Graph. 17.4.1 Actual and fitted V1 values 1960–2010
(taken from Eq. 17.4.1.TR) . . . . . . . . . . . . . . . . 345
Graph. 17.5.1 Actual and fitted V2 values 1960–2010
(taken from Eq. 17.5.2.TR) . . . . . . . . . . . . . . . . 352
Graph. 20.1.2.1 MPK and MPL curves – constant slopes . . . . . . . 387
Graph. 20.1.2.2 MPK and MPL curves – varying slopes . . . . . . . . 389
Graph. 20.1.2.3 MPK and MPL curves – non – market wages . . . 390
xvii
xviii LIST OF FIGURES
Graph. 20.4.1.1 Model of only variables robust in at least

three of four sample periods (Eq. 20.4.1.2.TR) . . 407
Graph. 20.4.3.1 Graph of the initial profit’s share model
(Eq. 20.4.3.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
L IST OF TABLES
Table. 1.4.1 Determinants of consumption . . . . . . . . . . . . 18

Table. 1.4.2 Determinants of investment . . . . . . . . . . . . . . 21
Table. 1.4.3 Determinants of GDP (Cptr.8;
arithmetically calculated from IS curve
components) . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Table. 1.4.4 Is the prime interest rate determined
by the Taylor rule? . . . . . . . . . . . . . . . . . . . . . 25
Table. 1.4.5 Is the prime interest rate determined
by traditional Keynesian “LM” theory? . . . . . . 25
Table. 1.4.6 Determinants of savings . . . . . . . . . . . . . . . . . 26
Table. 1.4.7 Determinants of government receipts
and spending . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Table. 1.4.8 Determinants of unemployment and inflation . 29
Table. 1.4.9 Determinants of export demand . . . . . . . . . . . 31
Table. 1.4.10 Determinants of velocity robust
models only (where V1or2 = Y(P/M1or2) . . . . . . 32
Table. 1.4.11 Determinants of labor’s total income
and percentage share of NI . . . . . . . . . . . . . . . 33
Table. 1.4.12 Determinants of profits’ total income
Table. 1.4.13 Determinants of rent’s total income
xix
xx LIST OF TABLES
Table. 1.4.14 Determinants of interest total income

Table. 2.2.3.1.1 DSGE model inflation forecast accuracy . . . . . 53
Table. 2.2.3.1.2 DSGE model GDP growth forecast accuracy . . 54
Table. 2.2.3.2.1(1) Current and four future year annual
changes in income
(real GDP) (Billions of 2005 Dollars) . . . . . . . 61
Table. 2.2.3.2.2(1) Yearly variation in consumer spending
1960–2010. Explained by yearly
variation in TFP compared to other
determinants of consumption . . . . . . . . . . . . . 64
Table. 2.2.3.2.3(1) Robustness over time: (2SLS
detrended model; subsamples of
1960–2010 data set) . . . . . . . . . . . . . . . . . . . . 66
Table. 2.2.3.2.3(2) Robustness over time: (2SLS model
5.2, 1960–2010 data) . . . . . . . . . . . . . . . . . . . 67
Table. 2.2.3.2.4(1) Forecasts of observable variables . . . . . . . . . . . 71
Table. 2.2.3.2.5(1) Error of fit of a model similar
to FRB/US’S nondurables and
nonhousing services consumption
model compared to Cowles model
(yearly change in ND&S consumption
as a % of total ND&S consumption) . . . . . . . . 79
Table. 2.2.4.3.1 Comparison of % error of GDP
estimates of VAR with structural
models for the 10 years after their
1960–2000 estimation period
(absolute value of error % used) . . . . . . . . . . . . 92
Table. 2.2.4.4.1 Time period robustness of SVAR
model results . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Table. 2.2.4.4.2 Out-of-sample fit comparisons:
Structural models vs. SVARs . . . . . . . . . . . . . . 101
Table. 4.0.1 Determinants of consumption
assumed endogenous when applying
endogeneity tests . . . . . . . . . . . . . . . . . . . . . . 148
LIST OF TABLES xxi

or investment initially assumed
exogenous or lagged, and used as
regressors in the first-stage regression
in Hausman of endogeneity tests
(subscripts denote lags) . . . . . . . . . . . . . . . . . . 149
Table. 4.1.1 Explained variance – total consumption . . . . . . 154
Table. 4.1.2 Robustness over time – (2SLS
detrended model, Eq. 4.1.T) . . . . . . . . . . . . . . 155
Table. 4.2.1 Explained variance – consumer imports . . . . . . 159
Table. 4.2.2 Robustness over time – consumer imports . . . . 160
Table. 4.4.1 Explained variance – domestically
produced consumer goods . . . . . . . . . . . . . . . 163
Table. 4.4.2 Robustness over time – domestically
produced consumer goods . . . . . . . . . . . . . . . 164
Table. 4.6.1 Explained variance – consumer borrowing . . . . 169
Table. 4.6.2 Robustness over time – consumer
borrowing, 2SLS Model 4.6 . . . . . . . . . . . . . . 169
Table. 4.9.1 Explained variance – consumer durables . . . . . 174
durables, 2SLS Model (Eq. 4.9) . . . . . . . . . . . 174
Table. 4.11.1 Explained variance – nondurables . . . . . . . . . . 178
Table. 4.11.2 Robustness over time – nondurables,
2SLS Model (Eq. 4.11) . . . . . . . . . . . . . . . . . . 179
Table. 4.13.1 Explained variance – consumer services
(Eq. 4.12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
services, 2SLS model (Eq. 4.12) . . . . . . . . . . . 182
and investment initially assumed
endogenous when applying
endogeneity tests . . . . . . . . . . . . . . . . . . . . . . 186
and investment initially assumed
xxii LIST OF TABLES
exogenous or lagged in their effect

when applying endogeneity tests . . . . . . . . . . . 187
Table. 5.2.1 Explained variance – total investment . . . . . . . 190
Table. 5.2.2 Robustness over time – total
investment, 2SLS Model 5.2 . . . . . . . . . . . . . . 190
Table. 5.4.1 Explained variance – domestically
produced investment goods . . . . . . . . . . . . . . 194
Table. 5.4.2 Robustness over time: (domestically
produced investment goods, 2SLS
Model 5.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Table. 5.6.1 Explained variance – imported
investment goods . . . . . . . . . . . . . . . . . . . . . . 199
Table. 5.6.2 Robustness over time: – investment
imports, 2SLS . . . . . . . . . . . . . . . . . . . . . . . . . 200
Table. 5.8.1 Explained variance – business borrowing . . . . . 205
Table. 5.8.2 Robustness over time – business
borrowing, 2SLS . . . . . . . . . . . . . . . . . . . . . . 206
Table. 5.10.1 Explained variance –
plant and equipment
investment . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Table. 5.10.2 Robustness over time – plant and
equipment, 2SLS Model 5.10 . . . . . . . . . . . . . 210
Table. 5.11.1 Explained variance – residential investment . . . 213
Table. 5.11.2 Robustness over time – residential
investment, OLS Model 5.11 . . . . . . . . . . . . . 213
Table. 5.13.1 Explained variance – inventory investment . . . 216
Table. 5.13.2 Robustness over time – inventory
investment 2SLS Model 5.13 . . . . . . . . . . . . . 217
Table. 6.0.1 Import/export relationships among
U.S. trading partners . . . . . . . . . . . . . . . . . . . . 223
Table. 6.1.1 Explained variance – exports . . . . . . . . . . . . . . 226
Table. 6.1.2 Robustness over time – exports . . . . . . . . . . . . 227
LIST OF TABLES xxiii
Table. 7.1.1 Comparison of PR –2 effects in GDP,

C, I, G, and (X–M) functions (i.e., all
components of GDP) . . . . . . . . . . . . . . . . . . . 234
Table. 9.2.1 Explained variance – Taylor rule
model, using 2SLS . . . . . . . . . . . . . . . . . . . . . 256
Table. 9.2.2 Robustness over time – Taylor rule
model: 2SLS model 9.2 . . . . . . . . . . . . . . . . . . 257
Table. 10.2.1 Explained variance LM curve interest
rate model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Table. 10.2.2 Robustness over time: LM curve
interest, 2SLS model . . . . . . . . . . . . . . . . . . . . 262
Table. 11.1 Explained variance – Phillips curve . . . . . . . . . 267
Table. 11.2 Robustness over time: Phillips curve . . . . . . . . 268
Table. 12.2.1 Explained variance – Okun
unemployment model . . . . . . . . . . . . . . . . . . . 277
Table. 12.2.2 Robustness over time: (Okun
unemployment 2SLS model) . . . . . . . . . . . . . . 277
Table. 12.4.1 Explained variance – technological
progress unemployment model . . . . . . . . . . . . 281
Table. 12.4.2 Robustness over time: (tech. progress
unemployment, 2SLS model) . . . . . . . . . . . . . 282
Table. 13.1.1 Explained variance – corporate savings
(as % of GDP) . . . . . . . . . . . . . . . . . . . . . . . . . 288
Table. 13.1.2 Robustness over time – corporate
savings, Eq. 13.1.2 2SLS Model . . . . . . . . . . . 289
Table. 13.2.1 Explained variance depreciation
allowance savings . . . . . . . . . . . . . . . . . . . . . . 293
Table. 13.2.2 Robustness over time – depreciation
allowance savings . . . . . . . . . . . . . . . . . . . . . . 294
Table. 13.3.1 Explained variance – personal savings model . . 300
Table. 13.3.2 Robustness over time – Personal
savings model . . . . . . . . . . . . . . . . . . . . . . . . . 301
Table. 14.1 Explained variance – government receipts . . . . 304
xxiv LIST OF TABLES
Table. 14.2 Robustness over time – government

receipts (assumes 1993 tax increase
repealed by 2001 tax cut) . . . . . . . . . . . . . . . . 305
Table. 14.3 Alt robustness over time (assumes
1993 tax increase continues through 2010) . . . 306
Table. 15.1.1 Explained variance – total government spending 311
Table. 15.1.2 Robustness over time – total
government spending . . . . . . . . . . . . . . . . . . . 311
Table. 15.2.1 Explained variance – government
spending model (goods and services only) . . . . 314
Table. 15.2.2 Robustness over time – government
spending (goods and services only) . . . . . . . . . 315
Table. 16.1.1 Model 1 How well the model fits the
data for the 10 periods following the
1960–2000 period used to estimate
the modela (billions of 2005 dollars) . . . . . . . . 321
Table. 16.2.1 How well models 1 and 2 fit the
1960–2000 estimation period (billions
of 2005 dollars) . . . . . . . . . . . . . . . . . . . . . . . 327
Table. 16.2.2 How well models 1 and 2 fit the
1960–2000 estimation period (nine
additional equations substituted for
variables treated as exogenous in
Model 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Table. 17.4.1 Explained variance – V1 velocity . . . . . . . . . . . 343
Table. 17.4.2 Robustness over time – M1 velocity,
2SLS Eq. 17.4.1 . . . . . . . . . . . . . . . . . . . . . . . 344
Table. 17.5.1 Explained variance – V2 velocity . . . . . . . . . . . 349
Table. 17.5.2 Robustness over time – M2 velocity,
2SLS Eq. 17.5.1.2 . . . . . . . . . . . . . . . . . . . . . 350
Table. 17.7.1 Variables significant in stepwise models . . . . . . 360
Table. 18.1 Dynamic Effects of Stimulus Programs
on the GDP . . . . . . . . . . . . . . . . . . . . . . . . . . 368
LIST OF TABLES xxv
Table. 18.2 Dynamic Effects of Stimulus Programs

on the GDP (Detailed effects on other
key economic variables after 33 periods) . . . . . 369
Table. 19.1 Determinants of consumption,
investment, government spending,
interest rates, and exports . . . . . . . . . . . . . . . . 374
Table. 20.1.1.1 Index of real profit and labor income
growth 1929–2010 (1960 = 1.00) . . . . . . . . . . 384
Table. 20.1.1.2 Nominal income levels and shares for
labor, profit, rent, and interest 1930–2010 . . . 385
Table. 20.4.1.1 Stepwise estimate of individual
variable’s contributions to total
explained variance . . . . . . . . . . . . . . . . . . . . . . 405
Table. 20.4.1.2 Coefficient stability in Eq. 20.4.1.2:
2SLS labor share model . . . . . . . . . . . . . . . . . . 405
Table. 20.4.1.3 Comparisons of GDP and labor
productivity growth rates . . . . . . . . . . . . . . . . 411
Table. 20.4.1.4 Effects of counterfactuals on labor’s share . . . . 412
explained variance in profit’s share . . . . . . . . . . 419
Table. 20.4.3.2 Determinants of profit’s share of
national income coefficient stability
over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420
Table. 20.4.3.3 Simulation of effects on profit’s share
of counterfactuals . . . . . . . . . . . . . . . . . . . . . . 425
Table. 20.4.4.1 Summary of factors affecting profit’s %
share and level of real national income . . . . . . . 428
explained variance in interest share
model 20.4.5.1 . . . . . . . . . . . . . . . . . . . . . . . . 430
Table. 20.4.5.2 Determinants of rent’s share of
over time in Eq. 20.4.5.1 . . . . . . . . . . . . . . . . 430
xxvi LIST OF TABLES
Table. 20.4.6.1 Summary of factors affecting profit’s %

share and level of real national income . . . . . . . 433
explained variance in interest share
model 20.4.7.2 . . . . . . . . . . . . . . . . . . . . . . . . 435
Table. 20.4.7.2 Determinants of interest’s share of
over time in Eq. 20.4.7.2 . . . . . . . . . . . . . . . . 436
explained variance in interest level
model 20.4.8.2 . . . . . . . . . . . . . . . . . . . . . . . . 439
Table. 20.4.8.2 Determinants of interest’s share of
over time in Eq. 20.4.8.2 . . . . . . . . . . . . . . . . 439
Table. 20.4.9.1 Summary of factors affecting interest’s
% share and level of real national income . . . . . 440
S UMMARY
The book has two parts: Part I contains 45 equations describing in detail
the “product side” of the National Income and Product Accounts (NIPA).
It contains tested models of the GDP and its major components, and the
determinants of their level of production (Chapters 4–19). Part II provides
11 additional equations describing how the value of the product generated
producing the GDP is distributed among the factors of production. For
each factor of production there are two equations. The first describes the
variables that were found to determine each factor’s percentage share of
national income. The second describes the variables found to determine
the total amount (the level) of each factor’s total income. These models
describe the variables whose own changes cause the distribution of income
among factors to shift from one factor to another over time (Chapter 20).
Chapter 19 provides a summary of the substantive findings as to the
determinants of GDP and its components. Chapter 20, Section 20.5,
summarizes the determinants of factor shares and levels of income.
THE PRODUCTION SIDE MODEL

Production is treated as a response to aggregate demand (AD). Hence
the key determinants of GDP production are expressed as determinants
of AD. Supply shortages can also affect the level of production, but the
empirical evidence indicates that demand is far more commonly the driv-
ing factor. Fully 85–95% of the variation of GDP over the 50-year period
1960–2010 appears to stem from variation in AD. Demand-driven models
are commonly thought of as Keynesian models, and to that extent this is
xxvii
xxviii SUMMARY
a Keynesian model. However, when a variable to measure “crowd out” is

added to standard Keynesian consumption and investment equations, this
model’s conclusions about the effectiveness of fiscal policy in stimulating
the economy are just the opposite of Keynes’. Its conclusions about mon-
etary policy conclusions are also not the same. The model indicates the
stimulus effects of changes in the money supply to be modest at best.
The 45-equation first part (the production side) includes 30 behavi-
oral equations and 15 identities. The identities connect the behavioral
equations into a comprehensive model of the real U.S. economy. The
behavioral equations were generally estimated applying strong instrument
2SLS to 1960–2010 data. The model includes eight consumption and nine
investment equations, including three for personal, corporate, and depre-
ciation allowance savings. Two interest rate determination models based
on the Taylor rule or the Keynesian LM curve are included. Also included
are two unemployment determination models, a Phillips curve model, one
export function, and two “IS” curve functions determining GDP. Other
behavioral models are provided for taxes and government spending, recog-
nizing that part of these variables levels is endogenously determined by the
state of the economy. Two functions describe the determinants of M1 and
M2 velocity. These are included to show mathematically how fiscal policy
can shift the AD curve. Extensive efforts were made to ensure that all iden-
tification issues were resolved by replacing Hausman-endogenous variables
with Wald-strong instruments which were Sargan-tested to ensure they
also were not endogenously determined.
There are 75 variables (or different lags of the same variables) in the
45 equations. Robustness testing, a non-negotiable requirement of good
science, was exhaustive. All models were tested in four different time peri-
ods to ensure estimated effects were consistent over time, i.e., immune to
Lucas critique. All coefficients were also tested for robustness to changes in
the model being tested, i.e., to see how additions and subtractions of vari-
ables from the model affected the remaining variables estimated effects.
Because of the pervasiveness of the multicollinearity problem, this type
of robustness testing is also a non-negotiable requirement of good sci-
ence. Finally, almost all were tested using OLS as well as 2SLS techniques
to allow comparisons with literature of an earlier day, which sometimes
used OLS.
DSGE and VAR methodologies are currently more popular methodolo-
gies for macroeconomic modeling. Therefore, a lengthy section is included
in Chapter 2 discussing the advantages of the older Cowles methodology
SUMMARY xxix
and why it is used here. Chapter 2 is literally a paper within a paper. It

deals with what may be the most pressing unresolved methodological
issue facing macroeconomic modelers today: how to successfully model
the macroeconomy the way it actually works, so that models can be reliably
used by policy makers to predict consequences of decision-making. Early
models designed to do this were referred to as Cowles Commission mod-
els and were very good at explaining the data, though not always 100%
successful. Cowles models dominated model building from the advent of
the econometric revolution up to the mid-1980s. However, in the last 30
years, many economists have turned away from Cowles types of modeling
in favor of DSGE and VAR.
Which of these three methods for discerning economic reality is to be
preferred? To shed some light on this question, the statistical perform-
ance of several VAR and DSGE models are compared with Cowles-type
structural models. Comparisons are made, or reported from other studies,
and include comparisons with a Sims (1980) VAR model, the Smets-
Wouters model, FRB/US, and a simplified version of the FRB/NY model.
These tests overwhelmingly indicate the more Keynesian (Cowles) struc-
tural models outperform the others in accurately modeling the actual
year-to-year fluctuations of the economy. Therefore, they should become
the models of choice in future macroeconomic studies analyzing the
consequences of changes in economic variables.
Nobel Laureate economist Robert Solow (2016) concurs; he has said
Cowles models far better explain the data than DSGE or VAR models:
after reviewing this paper’s analysis of the three methods, Solow wrote
. . . Your arguments in favor of Cowles-type models as against VAR and

DSGE models have real weight . . . I think that you get across that whatever
can be said for DSGE models . . . they are inferior at explaining the facts
. . . You do the same for general VAR models
After Keynes himself, Solow is arguably the greatest economist of the

twentieth century.
THE INCOME SHARES MODEL

Part II of this book (Chapter 20) describes how the income generated
producing the GDP is distributed. Four equations describe the variables
found to determine the level of income received as labor, profit rent, and
xxx SUMMARY
interest income. An additional four equations describe the variables found

to affect the percentage share of national income received by each of these
factors, that causes factor shares to vary from decade to decade. A summary
of findings is presented at the beginning of Chapter 20. The econometric
methodology used, including exhaustive robustness testing, was the same
as used in Part I of the book.
METHODOLOGY
Good science requires replicability of results. This chapter’s goal was to
provide, to the best extent possible, models whose results meet the rep-
licability standard. Largely, this goal appears to be achieved, though in
some areas more remains to be done. Hopefully, future generations of
researchers will find it worthwhile to take up where this study leaves off.
In particular, in some equations we were not able to fully resolve the “left
out” variables and multicollinearity problems that affects the credibility of
parameter estimates in any economic model.
In most models 85–95% of the variance is explained. However, in some
models, there are definitely some “left out” explanatory variables remain-
ing to be found. Less of the total variance in the model than we would
like is explained by the variables. Models with this problem are identified
in the text.
In addition, the problem of multicollinearity needs to be better
resolved. It is perhaps the most serious impediment to doing good science
in economics today. To mitigate the problem in this study, we use first dif-
ferencing, and careful selection of combinations of explanatory variables
used. In addition, we do extensive robustness testing, by adding and sub-
tracting explanatory variables to a model, to ensure (reasonable) model
changes do not cause marked changes in other parameter estimates. For
most of our parameter estimates we are able to show these techniques
achieved the desired level of stability, but not for all. For some models,
parameter estimates are still sensitive to exactly what other variables are
included in the model (these models are identified in the text). Economists
needs to develop better scientific methods for dealing with this problem.
CHAPTER 1
Introduction
The econometric model of the U.S. economy developed in this

chapter follows the demand-driven structural modeling approach used by
Lawrence Klein, and for which he received a Nobel Prize, as well as by
other major structural models developed by Eckstein, Goldberger, and De
Leeuw in the 1940–1980 period. This modeling tradition is carried on
today by Ray Fair, and by this model. This type of model is a modern ver-
sion of the “old” non-micro foundations Keynesian (i.e., demand driven)
model. It incorporates additional equations and variables to address issues
not dealt with in Keynes’ original work: for example, the crowd out prob-
lem resulting from government deficits, cost push inflation corrections to
the Phillips curve, the Samuelson accelerator, and the Taylor rule version
of the LM function. We show that these “Cowles Commission” models
can easily be extended to allow calculation of sector, industry, or even
individual product demand curves. That is, Cowles models can be struc-
tured to allow analysis of microeconomic as well as macroeconomic issues.
Hence, the description of “old” Keynesian models as not having micro
foundations seems somewhat inaccurate.
The production-side model contains 45 equations. Thirty are behavior
equations whose determinants describe what drives the demand for con-
sumer goods (8 equations), investment goods (9 equations), exports (1
equation), and the demand for government goods, services, and trans-
fers, and the supply of government receipts (3 equations). Two other
“IS curve” equations combine the preceding equations to determine the
© The Author(s) 2017 1

J. J. Heim, An Econometric Model of the US Economy,
DOI 10.1007/978-3-319-50681-4_1
2 1 INTRODUCTION
Gross Domestic Product (GDP). Other behavioral equations describe the

factors which determine a key interest rate (two equations), the unem-
ployment rate (two equations), inflation (one equation), and the velocity
of money (two equations). The other 15 equations are identities tying the
various behavioral equations together.
The eight consumer goods equations express the determinants of
demand for
Total consumption Consumer savings
Domestically produced consumer goods and services Durable consumption goods

Nondurable consumption goods
Imported consumer goods and services Consumer services
Consumer borrowing
The nine investment goods equations express the determinants of demand

for
Total investment Corporate savings
Domestically produced investment goods Depreciation savings

Imported investment goods Plant and equipment investment
Business borrowing Residential housing investment
Business inventory investment
There are 75 variables (or different lags of variables) in the 45 equations.

A list is provided further below.
The models are presented in traditional Investment, Savings – Money
Demand, Money Supply (IS-LM) equation form in Chapters 4–16. But
this format for presenting Keynesian models is being replaced in some texts
by the AD–AS system. However, none of these texts presents a system of
equations that show how the Keynesian system translates into the AS –
AD model. The exceptions are those that show how, by shifting previously
calculated IS or LM curves, you can shift the AD curve, producing Keyne-
sian results. But this makes AS–AD only a series of deductions derived
from previously calculated IS–LM curves, not the simpler, more intuitive,
alternative to it, which was its original objective.
To deal with this deficiency, Chapter 17 develops an AD model for
showing a full Keynesian system of fiscal and monetary policy effects. It
is derived from Fisher’s equation of exchange. It is easy to develop an
AD curve to show monetary policy effects directly from Fisher’s equation.
Econometric estimation of the determinants of velocity makes it just as
easily using Fisher’s equation to model the Keynesian stimulus effects of
INTRODUCTION 3
fiscal policy (with or without crowd out effect variables included). This
reconciles a major formulation of the neoclassical model with Keynesian
mechanics. It shows that under the right assumptions, Keynesian results
obtain from this neoclassical model.
This chapter chooses to use Cowles Commission structural mod-
eling techniques, yet today most macroeconomic models use either
Vector autoregression (VAR) or Dynamic, Stochastic, General Equilib-
rium(DSGE) techniques. One can ask why the Cowles technique was
chosen. The answer is Cowles-type models are both good economics
(based on recognizable economic theory) and good science (use the best
econometric methods available for presenting and testing the enormous
detail in such large models). By comparison, VAR is usually thought of
as good science, but bad economics (atheoretical, so results can be hard
to interpret), and DSGE is generally considered good economics, but bad
science (key parameters calibrated, not estimated). These deficiencies have
been widely criticized during the past decade by major economists. A sum-
mary of those criticisms is presented below. They suggest that a better
alternative is needed. Cowles modeling, by combining good economics
and good science, is not only better, it is really the only alternative available
for large-scale modeling of the economy’s multitudinous determinants.
DSGE criticisms
Cooley (1997) Calibration too informal compared to econometric methods . . .

Fernandez-Villaverde (2010) Calibration approach unsatisfactory; econometrics needed
Solow (2010) “DSGE assumptions do not reflect reality . . . has nothing useful
to say about antirecession policy . . . There are other traditions
with better ways to do macroeconomics.”
Solow (2016) “Whatever can be said for DSGE models . . . they are inferior in
explaining the facts . . . the same for general VAR models.”
Colander (2010) DSGE models don’t explain the data very well
Fair (2004) Tests lead to rejection of rational expectations hypothesis
Edge and Gurnayak (2011) Smets-Wouters DSGE model only explains 8–13% of the variance
Mankiw (2006) DSGE “failed as a way of replacing Keynesian theorizing . . . New
classical and new Keynesian research has had little impact on
practical macroeconomists, . . . the work of the past several
decades looks like an unfortunate wrong turn”
VAR criticisms
Eckstein (1983) (Cowles) structural model forecasts better than VAR models tested
Gale and Orszag (2004) (∼Cowles) structural model forecasts better than VAR models tested
Fair (2004) (Cowles) structural model forecasts better than VAR models tested
4 1 INTRODUCTION
Earlier criticisms of Cowles models, particularly the Lucas critique, have

simply been wrong. Our tests for this model, presented later in this
chapter, as well as tests by earlier Cowles modelers like Eckstein (1983)
and Fair (2004) have shown the Lucas critique largely unfounded when
applied to Cowles models. Another major criticism was that in Cowles
models identification problems were difficult to discover and address. This
seems fully resolved with the development of modern tools for discerning
and resolving identification problems (see methodology section). The last
major criticism was that Cowles models lacked micro foundations, which
we noted above does not seem completely true. Cowles is certainly a bet-
ter methodology than DSGE for determining, through scientific testing,
what drives the demand for a specific product, like carrots, and how sensit-
ive that demand is to the prices of other goods. And this, we would argue,
is the type of microeconomic issue most economists need to know how to
resolve in order to practice their trade.
The goal of this book is substantial: it is to develop a reliable engineer-
ing manual for the macroeconomy, presenting in great detail the structure
of the macroeconomy and how it operates. There are endless parameter
estimates calculated. Since we desire to elevate this work to the status of
an engineering manual, the reliability of each parameter estimate is actu-
ally more important than the initial estimate itself. To determine reliability,
each estimate in the model has its robustness is tested three ways:
• Testing the same model in four different sample periods (i.e., can the
experimental results be replicated?)
• Using three different variants of each model to test the stability of
each variable’s parameter estimates when variables are added to or
subtracted from the model. (Do our estimates avoid multicollinearity
problems?)
• Using two different regression tools (Ordinary Least Squares [OLS]
and 2 Stage Least Squares [2SLS]), and sometimes a third (stepwise
regression) to determine consistency over time and importance of
results with older studies
Results of all these reliability tests are presented in the sections dealing with
each of the 30 behavioral equations. This information provides readers
with an unprecedented level of knowledge regarding the robustness of
parameter estimates presented in the model.
Our objective is to develop a model whose parameter estimates can be
used by economists and policy makers with confidence in their reliability.
In most cases, we feel this objective is adequately achieved.
1.1 MODERN MACROECONOMICS: MOVING FROM. . . 5
1.1 MODERN MACROECONOMICS: MOVING FROM

THE METHODS OF ECONOMIC PHILOSOPHY
TO THOSE OF ECONOMIC SCIENCE
Over eighty years ago, Keynes (1936) put forth a theory of how the
macroeconomy operates. Its fundamental assumption was that the eco-
nomy is demand driven, and that absent supply constraints, modeling the
determinants of demand is to model the determinants of supply. Because
it was so testable, Keynes’ theory served as a good basis for develop-
ing macroeconomics into a science whose purpose was to discover the
actual, measurable causes of fluctuations in observable economic behavior,
rather than just offer philosophical statements of the fundamental factors
that underlie humans’ economic behavior. His theory provides a basis for
good science because all its basic assertions are directly testable (e.g., is
current income the principal determinant of current consumption? Is it
more important than interest rates? Are interest rates or is the acceler-
ator the key determinant of investment?). There simply is no equation in
Keynesian theory that cannot be directly tested (and each is tested in this
study). This is an absolute requirement for good science. As Nobel Laur-
eate Adam Riess has emphasized, “Historically, this method (the scientific
method) has required that hypotheses should be directly testable by new
experiments or observations.” Riess, awarded a Nobel Prize for his part
in discovering that the universe was expanding, also noted that accepting
hard to test hypotheses would signify the end of the scientific method as we know
it (Riess and Livio 2016).
By comparison, philosophical inquiry as a way of discerning the nature
of reality is not generally testable. It is a pre-scientific methodology
developed in the age of the Enlightenment before the scientific revolution.
It involves identification of universal or self-evident truths, and deduc-
tion of conclusions about the nature of the world or human (economic)
behavior from them. The complex of self-evident assumptions usually is
not testable directly. However, when they, or a deduction from them, are
found consistent with some specific fact or incidence from economic his-
tory, are taken to prove the philosophy’s accuracy, e.g., the rise of interest
rates in the war of 1812 coincident with government deficit spending may
be taken as proof deficits cause interest rates to rise. DSGE models tend
to be more philosophically than scientifically based in this respect. Their
conclusions derive from assumptions about human behavior (e.g., rational
expectations, intertemporal utility, and profit maximization), rather than
6 1 INTRODUCTION
from empirical findings. For scientists, an asserted theory (philosophy)

can only be considered valid if holds in all instances (ceteris paribus),
and testing is done to assure it is. In our example, science requires com-
monly held theoretical hypotheses about interest rates and deficits to
hold for all instances in which deficits occur, controlling for other factors
which can also affect them (they don’t as our Taylor rule interest rate
model below shows). Tests of “old” Keynesian (non-micro foundations)
structural models are scientific in this way.
Philosophy becomes science only when all basic assumptions of theory
(its priors) can be tested directly, so that we know that the assumptions
from which policy conclusions are derived are themselves empirically true
(and not, perhaps, one of several sets of priors which might be consistent
with observed results). Keynesian structural models allow for this. DSGE
models don’t (e.g., how do we empirically test the hypothesis that con-
sumers successfully maximize utility intertemporally? And if we find the
data do not support the hypothesis, do we scrap DSGE theory?). DSGE
typically states that if such and such a condition holds (e.g., successful
intertemporal utility maximization), then such and such a result should
obtain (consumption spending, except for unforeseeable shocks, will be
constant from period to period).
The econometric revolution, starting at about the same time Keynes’
theory was introduced, handed macroeconomists tools with which they
could scientifically test that theory’s precepts for consistency with the real
world.
Thanks to the statistical stability of the average performance of large
numbers of people, parameters governing the relationship between people
and their economic behavior could be stable over long periods of time,
eliminating much of the distinction between the stability of parameter
estimates in fields of “social science” and “science,” at least for econom-
ics. Kuznets’ (1952) finding of a (0.88) coefficient for the relationship
of consumption to national income for the 1867–1929 period, and (0.86)
separately for the 1867–1948 period, and Heim’s (2008) finding of (0.82)
for the same relationship for the 1960–1990 period is a case in point.
Hence, as science, macroeconomics seems more like geology than soci-
ology: parameters may shift, but at a glacial pace. In the meantime, they
are perfectly adequate for assessing the impact of one economic variable
on another (ceteris paribus).
With the advent of econometrically based macroeconomic modeling,
it seemed only a matter of time before the “alphas” and “betas” used in
classroom exposition of key economic relationships like the consumption
1.1 MODERN MACROECONOMICS: MOVING FROM. . . 7
function could be replaced by hard, empirically verified numbers, turning

economics from a branch of natural or moral philosophy into a legitimate
branch of science and engineering. Cowles-type models were intended to
provide engineering models describing in great detail the structure of the
economy and how it operates.
This led to efforts in the 1950s and 1960s, building on Jan Tinber-
gen’s work (1939), to develop large-scale econometric models providing
inductively (not deductively) determined parameter estimates for all the
key parameters in this new demand-driven macroeconomics.
On the supply side, Leontief’s (1952) models were performing a sim-
ilar function, allowing us to provide scientifically inductive, not deductive,
answers to supply questions such as “If we expect demand in the aggregate
to be this much, what demands will this place on individual industries? Are
they reasonable or will there be supply constraints?”
Earlier large-scale econometric models of the macroeconomy, such
as Klein and Evans (1968) and Eckstein’s (1983), achieved remarkable
results in moving toward this goal, but not without problems. These
problems kept their models from explaining the economy as well as they
would have liked. Some problems only became obvious retrospectively,
after further developments in the field of econometrics. Problems such as
multicollinearity, stationarity, and identification were not tractable (or even
fully recognized) in some of those early models.
Today, we have methods which can eliminate the identification and
nonstationarity problems. We can substantially reduce the multicollinearity
problem by using data in first differences rather than levels.
In addition, computerization has made it easy to test alternative models
and evaluate the stability of parameter estimates by “tinkering” with model
specification changes, varying sample periods tested, and by varying the
type of regression technique used.
The econometric models developed here test for parameter estimate
stability by reporting results for at least two other specifications of the
same model with some additional variables added or subtracted to validate
reliability of the initial parameter estimate results. Adding and subtracting
variables generally did not significantly affect estimates of parameters of the
most important explanatory variables remaining in the model, provided
the variables deleted were not themselves major explanatory variables
whose elimination would cause a “left out variables” problem, i.e., just
another form of multicollinearity.
In addition, consistency and reliability of test results when sample peri-
ods were changed was an issue with older models. Little if any effort was
8 1 INTRODUCTION
made to ensure the robustness of regression results to different sampling

periods (i.e., to ensuring the results were replicable). The econometric
model developed here eliminates this problem by reporting results for sev-
eral sample periods to validate reliability of the results. Parameters initially
estimated here using a 50-year sample period were retested using three
other separate samples each covering only part of the larger 50-year test
period initially used. Generally, the job of obtaining reliable parameter
estimates in the initial sample was done well enough so that retesting on
other sample periods confirmed the initial results, i.e., the models explain
as well in one period as another.
Computerization has also simplified the process of reevaluating land-
mark models estimated in earlier times using methods now considered
inadequate. At virtually no marginal cost, computer programs can provide
OLS and 2SLS estimates for the same problem to allow reevaluation of
results using older techniques with new methods better able to deal with
identification (and other) problems.
For all models in this study, robustness testing extends to comparing
results derived from OLS as compared to 2SLS results for the same model.
This has indicated results are much the same for most variables, provided
the models tested are well constructed to start with, i.e., contain enough
explanatory variables to explain 85% or more of the variance, and provided
the instruments used in 2SLS models are strong, i.e., very good proxies
for the variable they are replacing, explaining most of their variance. And
of course, the instruments themselves must not be endogenous. We typ-
ically provide both sets of results (OLS and 2SLS) to allow evaluation of
sensitivity of this chapter’s results to method used.
Structural modeling has been replaced in recent decades by VAR
and DSGE modeling. Neither of these alternatives tells us much about
structure, particularly any detailed assessment of demand’s multitude of
different determinants. If the questions an economist/researcher is inter-
ested in are structural in this sense, there does not seem to be an alternative
to using Cowles-type structural models. And many, if not most, questions
of interest to most economists are structural.
Economists need structural models of the economy for the same reason
astronomers need structural models of the solar system: to explain how
the solar system will operate over long periods of time. They can’t fit a lin-
ear curve to last month’s path a planet followed and project a linear trend
forward for the rest of the year (the VAR method). Nor can astronomers
be content relying on philosophical “self-evident” truths about how the
1.2 SUMMARY OF WAYS IN WHICH THIS LARGE-SCALE ECONOMETRIC. . . 9
universe operates. That was the methodology the natural philosophers of

the Enlightenment (and medieval theologians) had to rely on before the
scientific revolution. It is an outdated method of discerning empirical real-
ity today in astronomy. Similar methods for evaluating economic questions
would seem as outdated.
1.2 SUMMARY OF WAYS IN WHICH THIS

LARGE-SCALE ECONOMETRIC MODEL
IMPROVES ON PAST WORK
• Currently, there is only one large-scale Cowles Commission-type

structural model available for economists to use for guidance on what
makes the economy work. It is Yale economist Ray Fair’s (2004)
large-scale econometric model (29 behavioral equations, 71 iden-
tities), though some parts of Eckstein’s 1983 Data Resources, Inc.
(DRI) model, which is proprietary, may still be in use by DRI. This
book advances the field by adding a second model of the same type, a
56-equation model containing 38 behavioral equations and 18 iden-
tities. It is the first new Cowles Commission-type model since Fair’s
last major revision in 2004, which itself was the first new model since
Eckstein (1983).
• This model builds on Fair’s model by identifying additional determ-
inants of consumption and investment required to fully explain
variation in these variables in economic terms. These new variables
include
Additional consumption determinants Additional investment determinants
Government deficit (crowd out) Government deficit (crowd out)

Prime interest rate Prime interest rate
Exchange Rate Exchange rate
Consumer confidence index Capacity utilization rate
Past savings levels Depreciation
Consumer borrowing Tobin’s q (proxy)
Substitution effects of a change in demand Profit levels
for one type of consumption
Population levels (some models)
(D, ND, S) on another Business borrowing
The wide range of variables used also builds on the more limited
number typically used in VAR and DSGE analysis.
10 1 INTRODUCTION
• It also builds on Fair’s work by providing separate behavioral models

of demand for domestically produced and imported consumer and
investment goods. It also adds models for exports, personal and cor-
porate savings, and the Keynesian LM function. All models are tested
in first differences rather than levels to help address stationarity and
multicollinearity issues.
• This model is different from most past structural models in that it
does not use lagged values of an equation’s dependent variable on
the right-hand side of the equation. Many past Cowles models use
lagged values of the dependent variable to explain variation in the
current value of the dependent variable in some models. They can be
useful in forecasting models, where definitionally the present cannot
be predicted except from the past.
• The reason they are not used in this 56-equation model is because
this model is intended to be an explanatory, not a forecasting model
extrapolating foreword from past trends. This model’s goal is to
develop equations that accurately identify the fundamental determ-
inants of each endogenous variable in the model. Given this goal, to
use lagged values of the dependent variable on the right-hand side
would seem self-defeating. We would then need to model the vari-
ables that determine the lagged value of the dependent variable and
substitute them in for the lagged in order to find out what drives
the dependent variable’s current value. In models whose principal
objective is to accurately describe the determinants of endogenous
variables, backward substitution is always required to eliminate any
lagged dependent variables from the model’s right-hand side, oth-
erwise we just obfuscate the true causes of variation in endogenous
variables. It is like the difference between forecasting and explain-
ing in astronomy; you can vector forward linearly from your present
position by adding a few percent to its current location and speed
and reasonably accurately predict where you will be, but if you want
to explain why the orbit will eventually vary in elliptical fashion as a
body circles the sun, you better scrap the linear forecasting approach
in favor of a fundamentals description of what causes heavenly bodies
to move, like Newton’s and Kepler’s gravitational formulae.
• By extension of this argument we can say that if a lagged value of
the dependent variable does seem to explain variance in a depend-
ent variable for causal, rather than inertial, reasons, it is because the
dependent variable’s lagged value is causally determined by lagged
values of other variables. Our approach in this model is to include the
lagged values of those other variables directly to clarify what exactly

drives the dependent variable, and with what lags.
• By comparison, lags of the explanatory variables are used in this
chapter’s models. Some variables only affect a dependent variable
after a lag. The effect of consumer confidence on consumer spend-
ing and the effect of interest rates on construction spending are
examples. Both were found systematically related to their dependent
variable, but only after an adjustment period, and there are theoretical
foundations for the findings.
• This model tests far more exhaustively for robustness of results
than prior large-scale econometric models, and this may be its most
important contribution to strengthening economics’ reputation as a
science. Three different kinds are robustness testing are employed:
(1) modifying model variables to test the stability of parameter estim-
ates for variables in both the original and modified models, (2)
requiring models to be replicable in different sample periods, and (3)
using different statistical methods and comparing results for consist-
ency. Findings for all variables are subjected to robustness tests using
four sample periods, three different model specifications, and two dif-
ferent estimation methods (2SLS and OLS). Testing in both OLS and
2SLS simplifies comparisons of current results with historical studies
examining the same thing, but which only used OLS methods preval-
ent at the time. Similarly, testing different time periods allows a way
of determining if different results obtained in earlier studies differ
because of period sampled. Robustness testing is hugely important
for any study, like this one, desiring its results to have engineering
manual levels of reliability. How else can one ensure that the next
study done on the same topic won’t come up with different results?
Robustness testing is the economist’s equivalent of replicating exper-
imental findings in the natural sciences and is just as necessary to
establish the credibility of findings.
• Another contribution this chapter makes is that it tests the Lucas cri-
tique to determine its validity. The chapter’s robustness tests over
different sample periods generally show the Lucas critique not valid.
Roughly the same coefficients on tax and government spending
stimulus effects are found over time, removing one of the major cri-
ticisms of Cowles structural modeling in the 1980s which led to its
replacement by DSGE.
12 1 INTRODUCTION
• Some of this study’s most important findings show key assumptions

underlying rational expectations theory are simply not valid. This
is particularly true for the notion that consumers rely on accurate
expectations of long-term future income as the key determinant of
current consumption. This finding implies any DSGE micro found-
ations model that relies on the correctness of this assumption for
its own correctness, is not valid. Tests in this chapter indicate con-
sumption is driven by current, not by accurately estimated averages
of current and future income. Our tests also find that consumption
is not constant from year to year except for unexpected technology
shocks, as DSGE models suggest would result from the intertemporal
utility maximization implied by the rational expectations assumption,
a result typically deduced from Euler equations. A major criticism
of “old” Keynesian structural modeling in the 1980s and 1990s was
that it had no micro foundations of the sort found in DSGE models.
But key assumptions underlying the “old” Keynesian model, such as
consumption’s determinants, seem better supported by the data than
micro foundations model assumptions. This would suggest the “no
micro foundations” criticism of “old” macroeconomics is no longer
reasonable.
• The “old” Keynesian structural Model developed in this chapter
explains the behavior of key economic variables very well for a full
decade after the period used to estimate the test model (1960–2000).
The average yearly error explaining out-of-sample yearly changes in
the 2001–2010 decade following the estimation period (as a % of
GDP) was
GDP ½ of 1%
Consumption ½ of 1%
Investment 3.2%
This model explains yearly variation in the economy in the decade

after the sample period 6 times better than (Sims’ 1980) VAR model
projections, and as much as 30 times better than other VARs tested.
It also explains variation far better than several DSGEs tested. The
model explains yearly variation in the decade after the sample period
two times better than models approximating either the FRB/NY or
FRB/US Federal Reserve bank models.
• Critically important, the model is good enough at identifying the

fundamental underlying structure of the economy that it can explain
changes in GDP, consumption, and investment, in any of the past five
decades about equally well. Graphs showing this tightness of fit are
presented in the text.
• All parameters are econometrically estimated; nothing “calibrated,”
as in DSGE models, hence more reliably reflective of economic
behavior as it actually occurs. It is better science.
• Models are theoretically based, and only lags consistent with theory,
and found statistically significant are included, unlike VAR models.
• Better scientific methods than many earlier models: more up-to-date
econometric techniques used to ensure
° Stationarity issues fully resolved

° Identification (endogeneity) issues fully resolved. only Wald-strong
Instruments used to resolve endogeneity
° Minimize multicollinearity and serial correlation issues
• This chapter is also unique in that it provides a way of unifying micro
and macro different from the micro foundations approach used in
DSGE models. In fact, the approach used is just the opposite of
the micro foundations approach. It is based on the assumption that
macroeconomic variables are the principal determinants of microe-
conomic demand (and therefore production) in a given period,
mitigated to some extent by relative price effects. The approach
starts with a large-scale macro model, whose consumption and invest-
ment functions, when divided into successively smaller parts, can be
reduced to a series of evermore micro-sized models, except with
macro determinants found irrelevant for a specific micro portion of
the macro model deleted (e.g., mortgage interest rates may affect
residential construction, but not inventory investment). When doing
so, the basic macro model stays intact, with a relative prices variable
added to allow estimation of substitution effects between goods in
the micro model and goods that are not. The idea is not new; it
was used in the 1980s by Eckstein in his huge 800-equation model
of the U.S. economy. Eckstein’s model used a “macro foundations of
micro” approach to unifying the two fields. It was similar to that used
in this book to evaluate the demand for domestically produced versus
imported goods: same basic determinants used in both models, but
14 1 INTRODUCTION
with the exchange rate used to measure the effects on demand of

relative prices of imports compared to domestic goods.
• A final way this study improves on other models is by distinguishing
what the model’s parameters say a variable can potentially do, from
what it actually did during a sample period. Stepwise regression is
used to estimate each variable’s actual importance in explaining vari-
ance during a sample period. This is a way of distinguishing between
the potential contribution a variable can have (using β, Sβ ), and the
actual importance it did have during the sample period by measuring
its contribution to explaining variance compared to other variables
in the same model. Explanatory variables that do not move cannot
explain variance, even though if they did move, they would explain
variance.
1.3 The 56-Equation Model: 30 BEHAVIORAL

EQUATIONS, 15 IDENTITIES (PRODUCT SIDE OF
NATIONAL INCOME AND PRODUCT ACCOUNTS
(NIPA)), AND 8 BEHAVIORAL EQUATIONS,
3 IDENTITIES (INCOME SIDE OF NIPA)
1.3.1 Eight Consumption Equations, Econometrically Estimated
1. CT = domestically produced and imported consumer G&S
2. CD = domestically produced consumer G&S
3. CI = imported consumer G&S
4. CDur = durable consumer goods
5. CND = nondurable consumer goods
6. CS = consumer services
7. CBOR = consumer borrowing
8. Csav = consumer saving
1.3.2 Nine Investment Equations, Econometrically Estimated

9. IT = domestically produced and imported investment G&S
10. ID = domestically produced investment G&S
11. IM = imported investment G&S
12. IP&E = investment in plant and equipment
13. IRES = investment in residential housing
14. IINV = investment in inventories
1.3 THE 56-EQUATION MODEL: 30 BEHAVIORAL EQUATIONS, 15 IDENTITIES. . . 15
15. IBOR = business borrowing

16. SC = corporate savings (retained earnings)
17. Dep = depreciation allowance savings
1.3.3 Five Others Related to the GDP Identity,

Econometrically Estimated
18. GG&S = government spending on G&S (economic condi-

tions)
19. GT&I = all government spending (G, S & Trans.) = f (econ.
conditions)
20. X = foreign demand for U.S. exports
21. GDP = f (determinants of C, I), plus G, X-M
22. GDP = f (determinants of CD , ID ), plus G, X
1.3.4 Eight Others Econometrically Estimated: Two Interest Rate,

Two Unemployment, One Inflation, On Taxes, M1 and M2
Velocity Determinants
23. PRT = Taylor rule interest rate model

24. PRLM = Keynesian LM theory interest rate model
25. UNEMo = Okun unemployment determination model
26. UNEMT = tech. progress unemployment determination model
27. INFL = Phillips curve model of determinants of inflation
28. TT = government receipts = f (economic conditions)
29. V1 = determinants of M1 velocity
30. V2 = determinants of M2 velocity
1.3.5 Eight Equations Describing Factor Shares and Total Factor

Income, Econometrically Estimated
31. Labor’s percentage share of national income

32. Labor’s total income
33. Profit’s percentage share of national income
34. Profit’s total income
35. Rent’s percentage share of national income
36. Rent’s total income
37. Interest’s percentage share of national income
38. Interest’s total income
16 1 INTRODUCTION
1.3.6 The 18 Identity Equations

1. Y = CT + IT + GT + NX (t = total)
2. Y = CD + ID + GD + X (D = domestically produced)
3. CT = CD + CM (M = imports)
4. CT = CDUR + CND + CS = total consumer durables, nondurables,
and services
5. IT = ID + IM
6. IT = IP&E + IH + IINV = total plant and equipment, housing and
inventory investment
7. MT = MC + MI = total imports of consumer and investment goods
8. MC = MT – MI
9. MI = MT – MC = imports of capital equipment, industrial S&M
10. NX = (X-M)
11. (M2–M1) = savings components of M2
12. STotal = SCORP + SPERS + SDEPREC
13. GG+S = government spending on goods and services
14. GT = GG+S + GTrans = total government spending
15. MV = PY Fisher’s equation of exchange (using income)
16. GDP = product side = income side
17. GDP = depreciation + indirect taxes + labor income + profit
income + rental income + interest income + proprietor’s income
+ GDP/GNP definition adjustments
18. National income = labor income + profit income + rental income
+ interest income + proprietor’s income
1.4 THE 38 BEHAVIORAL EQUATIONS: COEFFICIENTS,

SIGNIFICANCE, R2 , AND DURBIN WATSON TESTS:
(SUMMARY OF RESULTS: DETAILED EXPLANATIONS
OF FINDINGS PRESENTED IN CHAPTERS 4–20)
Tables 1.4.1–1.4.14 present statistical findings for each of the 38 beha-
vioral equations. Included with each is a list of variable names and the
acronym used for each in the equations. Two models are shown for each
dependent variable. The left column of data for each dependent variable
shows the initial model run, and the regression coefficients and significance
levels for each included variable, and the R2 and Durban Watson serial
correlation results for the model. The second column of data presents
the final, time period and model specification robust model. Typically,
some variables in the initial model will be missing, initial estimates of
1.4 THE 38 BEHAVIORAL EQUATIONS: COEFFICIENTS, SIGNIFICANCE, R2 ,. . . 17
their effect having not proved reliable (robust) when we attempted to

replicate our initial results in other time periods and models. These robust
equations are this chapter’s final model. We hope they will be received
as not “just another model,” but one for which many parameter estim-
ates approach engineering manual levels of reliability, a first-in large-scale
macroeconomic modeling.
The process of moving from initial findings to finalized, robust models
was as follows:
1. An extensive literature review identified variables thought to be

determinants of each dependent variable. Preliminary testing, using
the full 50-year sample, was undertaken using OLS or 2SLS
as appropriate. Variables found significant in preliminary testing
became the “initial” model. For example, total consumption’s initial
model (CT ) in Table 1.4.1 is in the leftmost column under labeled
equation “4.1T.”
2. The initial model was then retested in three additional, though over-
lapping time periods for robustness. Variables not significant in 3 of
4 total time periods tested were discarded as spurious. This became
our semi-final model.
3. The semi-final model was tested by adding and then subtracting
two variables from the semi-final model to determine robustness of
parameter estimates to changes in model specification.
4. The model passing these robustness tests is listed next to its own ini-
tial model with notation “TR” added, e.g., for Ct , the robust model
is designated “4.1T.TR” in Table 1.4.1.
Steps 2–4 were uniformly applied in the development of all 38

stochastic equations. The consumption, investment, and labor share equa-
tions received the most extensive literature reviews when developing the
initial models in step 1. In large part, this was because there is so much
more written in these areas than in the others. The goal was to have
the initial models tested reflect the economic equivalent of the physicist’s
“standard model,” reflecting consensus opinion on what drives key com-
ponents of the economy. For some equations this proved difficult, either
because of lack of consensus, or because of the limited number of previous
studies in the relevant area.
Table 1.4.1 Determinants of consumption
18
CT CT CD CD CM CM CB2 CB2
Equation #: 4.1T 4.1T.TR 4.4 4.4.TR 4.2 4.2.TR 4.6 4.6.TR
Y-T 0.48∗∗∗ 0.49∗∗∗ 0.29∗∗∗ 0.29∗∗∗ 0.09∗ 0.19∗∗∗ 0.57∗∗∗ 0.44∗∗

T 0.56∗∗∗ 0.57∗∗∗ 0.31∗∗∗ 0.34∗∗∗ 0.13∗∗∗ 0.25∗∗∗ 0.70∗∗∗ 0.47∗∗
G –0.39∗∗∗ –0.38∗∗∗ –0.20∗∗∗ –0.23∗∗∗ –0.08∗ –0.18∗∗∗ –0.52∗∗∗ –0.46∗∗
PR –9.98∗∗∗ –9.31∗∗∗ –6.86∗∗ –5.44∗∗ –2.09 –3.06∗ –21.89∗∗∗ –14.62∗∗∗
1 INTRODUCTION
DJ0
DJ–1 –1.65∗∗∗ –1.37∗∗
DJ–2 0.43∗∗∗ 0.44∗∗∗ 0.44∗∗∗ 0.48∗∗∗ 0.11∗
DJAV-2, -3
DJAV-0, -1, -2
XRAV 1.44 –0.33 3.13∗∗∗ 2.22∗∗ 14.06∗∗∗ 13.16∗∗∗
POP16 –418.25 –517.17∗∗∗ –515.07∗∗∗ 239.00∗∗ 68.02
POP 0.018∗∗∗ 0.017∗∗∗ 0.020∗∗∗ 0.020∗∗∗ –0.002 –0.012∗∗
ICC–1 0.37 0.41 0.53∗∗ –14 0.52
M1Real-1
M2AV-2-4 46.31∗∗∗ 44.78∗∗∗ 38.16∗∗∗ 38.00∗∗∗ 7.16 –30.60
(M2-M1)Real –0.14
PERSAV–2 –0.07 –0.07∗∗∗(2)
CB 0.12∗∗∗ 0.13∗∗∗ 0.10∗∗∗ 0.09∗∗∗ +0.12∗∗
X 0.47∗∗∗
IHousing
PHousing
Int.%Mortgage
CNONDUR
CDUR
R2 (%) 95.3 94.8 88.7 87.8 86.7 76.7 59.7 55.3
D.W. 1.6 1.6 2.0 2.2 2.2 1.5 2.5 2.2
Table 1.4.1 (continued)
Y-T 0.14∗∗∗ 0.18∗∗∗ 0.19∗∗∗ 0.24∗∗∗ 0.20∗∗∗ 0.26∗∗∗

T 0.13∗∗∗ 0.24∗∗∗ 0.11∗∗∗ 0.18∗∗∗ 0.35∗∗∗ 0.45∗∗∗
G –0.08∗∗∗ –0.14∗∗∗ –0.08∗∗ –0.12∗∗∗ –0.19∗∗∗ –0.25∗∗∗
PR –0.24 –2.46∗∗ –2.44∗∗ –4.83∗∗ –6.99∗∗∗
DJ0 0.17∗∗
DJ–1
DJ–2 0.28∗∗∗ 0.19∗∗
DJAV-2, -3 0.19∗∗
DJAV-0, -1, -2
XRAV 2.54∗∗∗ 2.40∗∗∗
POP16
POP 0.02∗∗∗ 0.02∗∗∗
ICC–1
M1Real-1 0.015
M1Real-2 0.19∗∗∗ 0.19∗∗
M2AV-2-4 12.36∗∗
(M2-M1)Real 0.08∗∗∗ 0.06
PERSAV–2
CB1
X
IHousing 0.14∗∗ –0.12∗∗∗ –0.19∗∗∗ –0.001∗∗∗
PHousing –0.0004∗∗∗
Int.%Mortgage 8.72∗∗∗ 6.72∗∗∗
(continued)
1.4 THE 38 BEHAVIORAL EQUATIONS: COEFFICIENTS, SIGNIFICANCE, R2 ,. . .
19
CDUR CDUR CNDUR CNDUR CS CS

20
Equation #: 4.9 4.9.TR 4.11 4.11.TR 4.12 4.12.TR
CNONDUR(-1) –0.19∗∗ –0.43∗∗∗

CDUR
R2 (%) 89.0 82.4 89.3 81.8 90.5 85.4
D.W. 2.1 2.3 1.7 1.4 2.0 2.0
Significance levels: ∗ 10%; ∗∗ 5%; ∗∗∗ 1%.

1 INTRODUCTION
1 C can be substituted for I

B Housing and PHousing without significantly changing the coefficients or significance levels of the other variables in the model.
Doing so gives 0.08 (t = 2.8) CB . This indicates the chief use of CB is to purchase housing and the durables in it. However, neither set of variables was robust
except in samples with the 2001–2010 data.
where
Y = real GDP
Y-T = real disposable income
G = real total government spending
PR = real prime interest rate
DJ = NYSE Composite Index
XRAV = real exchange rate, average of current and past three years
POP16 = ratio of population 24 and under to population 65 and over population
POP = population size
ICC–1 = Conference Board’s Index of Consumer Confidence, lagged 1 year
M1Real = real M1; (M2-M1)Real = real M2 money supply – real M1 money supply
M2AV-2- 4 = M2 money supply average for lagged periods 2–4
CB = real consumer borrowing
X = real exports; IHousing = real investment in residential housing
PERSAV = real personal savings
PHousing = real price of residential housing
CM = real consumption – imports
CS = real consumption of services
CB2 = real consumer borrowing
Int%Mortgage = real mortgage interest rate
CDUR = real consumption – durables
CNONDUR = real consumption – nondurables
CT = real total consumption of both domestically produced and imported consumer goods
CD = real consumption of domestically produced consumer goods and services
Table 1.4.2 Determinants of investment
IT IT ID ID IM IM IBor IBor
Equation # 5.2 5.2.TR 5.4 5.4.TR 5.6 5.6.TR 5.8 5.8.TR
ACC 0.30∗∗∗ 0.25∗∗∗ 0.25∗∗∗ 0.26∗∗∗ 0.01 0.52∗∗∗ 0.59∗∗∗

T 0.23∗ 0.30∗∗∗ 0.29∗∗∗ 0.27∗∗∗ 0.08∗∗ 0.045∗∗ 1.62∗∗∗ 1.84∗∗∗
G –0.26∗∗∗ –0.32∗∗∗ –0.31∗∗∗ –0.30∗∗∗ –0.04 –1.07∗∗∗ –1.12∗∗∗
DEP 0.68∗∗ 0.97∗∗∗ 0.08 0.08 0.85
CAP–1 2.28 2.60 2.55∗ 0.03 11.26∗∗ –8.67∗∗
PRReal(-2) –6.89∗∗ –10.53∗∗∗ –3.01∗ –3.00 –3.91∗∗∗ –6.18
PRRealAV0-1
PRReal(AV-1- 2) –4.72∗∗∗
PRRealAV-3- 4
DJAV 0.53∗∗ 0.87∗∗∗ 0.19 0.60∗∗∗ 0.62∗∗∗
DJAV–1 –1.61∗∗∗ –1.43∗∗
DJAV–2
DJAVAV-1- 2
PROF 0.03 0.08 0.16∗∗∗ 0.33
PROFAV-3-6
XRAV0-3 5.89∗∗ 3.18 7.08∗∗ 6.81∗∗∗ 1.63∗∗ 2.43
XRAV-1-4
Pop 0.004 0.011∗∗∗ 0.011∗∗∗
IBOR-1 0.061 0.02 0.06∗
M2AV-2-4
CBOR
M1Real
PHousing
CT
PHousing
Y–1
R2 (%) 91.0 86.6 84.4 83.3 79.9 68.9 71.7 62.7

D.W. 2.2 2.2 2.0 2.0 2.3 1.3 1.8 1.8
21
(continued)
Table 1.4.2 (continued) 22
IP&E IP&E IRes IRes IInv IInv

Equation #: 5.10 5.10.TR 5.11 5.11.TR 5.13. 5.13.TR
(Y-T) 0.10∗∗∗ 0.10∗∗∗

ACC 0.06∗∗∗ 0.06∗∗∗ 0.33∗∗∗ 0.32∗∗∗
GDP–1 0.22∗∗∗ 0.16∗∗∗
T 0.12 0.14 0.21∗∗∗ 0.21∗∗∗
G –0.13∗ –14∗∗ –0.22∗∗∗ –22∗∗∗
1 INTRODUCTION
DEP 0.93∗∗∗ 0.83∗∗∗

CAP–1 3.29∗∗∗ 3.02∗∗∗
CAP0 –1.60∗∗
PRReal(-2)
PRRealAV0-1
PRRealAV-1- 2) –7.15∗∗∗ –7.15∗∗∗ –1.40∗∗∗
PRRealAV-3- 4 –0.67
DJAV 0.21∗ 0.18
DJAV–1
DJAV–2
DJAVAV-1-2
PROF 0.10∗∗∗
PROFAV-3-6 0.06∗∗∗ 0.06∗∗∗
XRAV0-3 0.92
XRAV-2-4 2.41∗∗ 2.41∗∗∗
Pop –0.001
IBOR-1 0.13∗∗ 0.14∗∗
M2AV-2-4
CBOR 0.13∗∗∗ 0.13∗∗∗
M1Real 0.37∗∗∗ 0.37∗∗∗
PHousing –0.001∗∗∗ –0.001∗∗∗
CT –0.32∗∗∗ –22∗∗∗
R2 = 91.6% 91.0% 87.1% 87.1% 88.5% 83.4
D.W. 2.1 2.1 2.2 2.2 2.3 2.1
Significance levels: ∗ 10%; ∗∗ 5%; ∗∗∗ 1%.1 (when residential investment is removed from total investment, this coefficient is 0.10∗ , more consistent with our
IP&E finding (0.13∗ ∗) in the next table. Likewise, the domestic investment coefficient increases from 0.02 to 0.07. Similarly, removing IP&E from ITotal
allows CBOR to have a significant coefficient in this model as it does in the IRES equation in the following table. We conclude the failure of IBOR-1 and
CBor to appear as determinants of IT and IDom is technical, not a sign of inconsistency of results.)
where
IT = real total investment in domestically produced and imported investment goods
ID = real total investment in domestically produced investment goods
IM = real total investment in imported investment goods
IB2 = real business borrowing
IP&E = real investment in plant and equipment
IRES = real investment in residential construction
IInventory = real inventory investment
Disp. Inc. = real disposable income (Y-T)
ACC = real accelerator (YT -YT-1 )
T = real total government revenue
DEP = real depreciation allowances
XRAV0-3 = real exchange rate average0-3
CapUtil% = % of productive capacity utilized
Y = real GDP
PRREAL = real prime interest rate
CBOR = consumer borrowing
DJAV = NYSE Composite Index
M1REAL = real M1
PROF = real corporate profits
PHousing = real price of housing
POP= U.S. population size
CT = real total consumption
IBor = real business borrowing

M2AV-2-4 = M2 money; average 2–4 years ago
23
24 1 INTRODUCTION
Table 1.4.3 Determinants of GDP (Cptr.8; arithmetically calculated from IS

curve components)
(X-M) model GDP = CT + IT + G + (X – M)

(Using Eq. 4.1T for CT and 5.2 for IT )
(X) model: GDP = CD + ID + G + X
(Using Eq. 4.4T for CD and 5.4 for ID )
X model X model (X-M) model (X-M) model
Equation#: 8.1.1.1 8.1.2.1.TR Eq. 8.2.1.1 8.2.2.1.TR
TTotal –0.41 –0.41 –0.92 –0.96

G∗ Total 0.69 0.69 1.04 1.06
TDeficit 0.85 0.86 1.51 1.71
GDeficit –0.72 –0.75 –1.25 –1.37
PR –9.67 7.67 –19.16 –18.25
PR–2 –4.24 –6.66 –13.23 –20.64
DJAV0 –0.27 1.02 1.71
DJAV–2 0.62 0.68 0.83 0.86
XRAV 9.52 9.60 14.07 6.23
POPY/OLD RATIO –729.21 –726.24 –803.04
POP 044 0.044 0.04 0.033
ICC–1 0.75 0.71 0.80
M2AV-2-4 53.81 53.58 88.92 87.77
CBor 0.14 0.13 0.23 0.25
ACC 0.35 0.37 0.58 0.49
DEP 0.11 1.31 1.90
CAP–1 3.67 3.60 4.38
PROF0 0.11 0.06
IBOR(–1) 0.03 0.12
X 1.41 1.41
(X-M) 1.92 1.96
where
TTotal = real total government receipts
G∗ Total = real total government spending (see p. 156 note on coefficient validity)
TDeficit = tax reduction-induced deficit
GDeficit = government spending increase-induced deficit
PR = real prime interest rate
XRAV = real exchange rate average, current and past three years
POP16 = ratio of population 24 and under to population 65 and over population
POP = U.S. population
ICC–1 = Conference Board’s Index of Consumer Confidence
M2AV-2-4 = real M2 money average for period from 2–4 years ago
CBor = real consumer borrowing
ACC = real accelerator (YT -YT–1 )
CAP–1 = capacity utilization percentage, lagged 1 year
PROF0 = real corporate profits
IBOR(–1) = real business borrowing, lagged 1 year
X = real exports
(X-M) = real net exports
Table 1.4.4 Is the prime interest rate determined by the Taylor rule?
Initial model
PRREAL = .42INFL – 1.29UNEM – .008 M1REAL + .012 M1REAL(–1)
(t =) (2.6) (–4.8) (–3.4) (2.8)
(Eq. 9.2)
–.002 Taxes – .001 G.Spend + .44AR(1)
2
(–1.1) (–0.5) (2.4) R = .81 D.W. = 2.
Notes: TDef and GDef included because government deficits thought to affect the economy by raising
interest rates. See text discussion.
Robust model
PRREAL = .42INFL – 1.30UNEM + .44AR(1) R2 = .67 D.W. = 1.9
(Eq. 9.2TR)
(t =) (2.8) (–6.6) (2.4)
Table 1.4.5 Is the prime interest rate determined by traditional Keynesian “LM”
theory?
PRREAL = .002 GDP – .0.27M1REAL + .022 M1REAL AV(–1–2) ) R2 = .22, D.W. = 1.6
(t =) (1.9) (–4.3) (4.0)
(Eqs. 10.2 and 10.2TR)
All three variables were significant in all four time periods tested and robust to model changes, hence
Eq. 10.2 is also our robust Keynesian model 10.2.TR.
Tables 1.4.4 and 1.4.5 Significance levels: 1.7 = 10%, 2.0 = 5% and 2.7 = 1%.
where
PRReal = real prime interest rate
INFL = inflation rate (CPI)
UNEM = unemployment rate
M1Real = real M1 money supply
Taxes = real total government revenue (T)
G.Spend = real total government spending (G)
AR(1) = first-order autocorrelation control
GDP = real gross domestic product
Table 1.4.6 Determinants of savings
26
Personal savings Personal savings Corporate savings Corporate savings Deprec. savings Deprec. savings
Equation #: 13.3.1 13.3.1TR 13.1.2 13.1.2TR 13.2.1 13.2.1.TR
Constant –9.05 –17.89

Disp. Inc. 0.31∗∗∗ 0.22∗∗∗
TDef –0.11∗∗ –0.14∗ 0.85∗∗∗ 0.66∗∗∗
GDef –0.05 –0.93∗∗∗ –0.77∗∗∗
PRReal 3 0.11∗∗∗ 0.14∗∗∗
1 INTRODUCTION
PRReal(–2) 2.72
DJAV0 –.25
DJAV0+(–2) 9 –2.29E-25∗∗∗ –2.27E-25∗∗∗
XRAV0–4 1.80 7.92∗∗∗
POPY/Old Ratio 440.60
POP 0.011∗∗
ICC0.1 –713.64∗∗∗ –725.37∗∗∗
M2AV-2-4 –30.86∗∗∗
CBOR –0.18∗∗∗ –0.16∗∗∗
INFL3 –0.02∗∗ –0.03∗∗∗
Tax Increase93 –32.39∗∗∗
BEA DefnChge99 –195.10∗∗∗ –195.94∗∗∗
Katrina Shock05 –160.05∗∗∗ –176.30∗∗∗
ACC –0.03 –0.17∗∗∗
DEP –0.96∗
CAP–1 –0.39
PROF 0.73∗∗
IBOR 0.10
INV0 0.06∗∗∗ 0.06∗∗∗
INV–1 0.10∗∗∗ 0.10∗∗∗
INV–2 0.10∗∗∗ 0.10∗∗∗
INV–3 0.07∗∗∗ 0.07∗∗∗
INV–4 0.03∗∗ 0.03∗∗
INV–5 0.04∗∗∗ 0.04∗∗∗
INV–6–10 0.03∗∗∗ 0.03∗∗∗
INV–11–17 0.04∗∗∗ 0.04∗∗∗
R2 (%) 84.4 78.7 94.0 78.2 96.6 96.6
D.W. 2.6 2.1 2.2 2.1 2.1 2.1

where
Disp. Inc.1.3 = real disposable ∧ 1.3
T = real total government receipts
PRReal 3 = real prime rate ∧ 3
POP = U.S. population
CBOR = real consumer borrowing
POPY/Old Ratio = ratio of population 24 and under to population 65 and over population
XRAV0–4 = real exchange rate, average of current and past three years
ICC0.1 = Conference Board’s Index of consumer confidence, raised to the 0.1 power
M2AV-2-4 = real M2 money average for period from 2–4 years ago
BEA DefnChge99 = change in treatment of proprietor’s income affecting definition of saving
Tax Increase93 = 1993 tax increase of wealthy
INFL3 = inflation (CPI)
CAP–1 = capacity utilization percentage, lag1
Katrina Shock05 = Hurricane Katrina shock
PROF0 = real corporate profits
ACC = real accelerator (YT -YT–1 )
IBOR = real business borrowing
INV0 = IT = real investment, current period

27
Table 1.4.7 Determinants of government receipts and spending
28
Total government receipts∗ Total government spending Only G&S government spending
Equation #: 14.1 14.1.TR 15.1.1 15.1.1.TR 15.2.1 15.2.1.TR
Constant –4.38 –11.17 61.69∗∗∗ 61.69∗∗∗ 7.47 2.76

GDP 0.30∗∗∗ 0.30∗∗∗ 0.03 0.03
GDP–2 0.09∗∗∗ 0.10∗∗∗
INFL%AV-1-2 12.28∗∗ 13.64∗∗
1 INTRODUCTION
UNEM % –48.59∗∗∗ –50.87∗∗∗ 23.85∗∗∗ 23.85∗∗∗ 1.76

TaxCutShock86 –27.02
Tax Incr. Shock93 31.11
POP–31–21 0.028∗∗∗ 0.028∗∗∗ 0.011
Vietnam Build Up 64.65∗∗∗ 64.65∗∗∗ 34.70∗∗∗ 30.88∗∗∗
R. Mil. Build Up, Iraq 34.85∗∗ 34.85∗∗∗ 29.48∗∗∗ 32.32∗∗∗
Shock08 (Fin.Crisis) 74.56∗∗∗ 74.56∗∗∗ –21.69∗∗∗ –17.43∗∗∗
R2 (%) 72.6 72.0 66.0 66.0 71.0 68.0
D.W. 1.8 1.8 1.8 1.8 1.9 1.8

∗ Changing effectiveness of 1986 tax cut from 1993 to 2010 instead of 2003 changes sign of both 1986 tax cut and 1993 tax increase (see text).
where
GDP = gross domestic product
INFL%AV-1-2 = inflation % (CPI), average of two past years
UNEM % = unemployment %
TaxCutShock86 = 1986 Reagan tax cut shock
Tax Incr. Shock93 = 1993 tax increase on wealthy
POP–31–21 = growth in population from 21 to 31 years ago (proxy for school and infrastructure costs associated with new family formation period for
cohort)
Vietnam Build Up = years of Vietnam military spending build up
R. Mil. Build Up, Iraq = years of Reagan and Iraq military build ups
Shock08 (Fin.Crisis) = 2008 financial crisis
AR(1) = first-order autocorrelation control
Table 1.4.8 Determinants of unemployment and inflation
Okun’s law unemployment Technical change Phillips curve inflation

function unemployment function function
Equation #: 12.2.2.1 12.2.2.1.TR 12.4.1 2.4.1.TR 11.1 11.1.TR
Constant 1.37∗∗∗ 1.27∗∗∗ 1.50∗∗∗ 1.55∗∗∗

%GDPReal –0.38∗∗∗ –.41∗∗∗
%GDPReal-1 –0.04
GDPReal .17 –53.44∗∗∗ –63.53∗∗∗
GDPReal-1 .17 –8.88∗∗
INFL. Rate –0.09∗∗∗ –0.14∗∗∗ –0.08∗∗
OPEC Shock73 0.54∗ 0.57∗ 0.43
OPEC Shock78 0.14 0.06
Katrina Shock05 –0.56∗∗∗ –0.51∗∗∗ –0.41∗∗∗ –0.48∗∗∗
FinanceShock08 0.75∗∗∗ 0.75∗∗∗ 0.47∗
Unem. RateAV0–1 –2.20∗∗∗ –2.20∗∗∗
M1–2 0.009∗∗∗ 0.009∗∗∗
[(M-X)/GDP]AV0–1 –135.67∗∗∗ –135.67∗∗∗
(Forgn.Bor/GDP)–1 13.12∗∗∗ 13.12∗∗∗
(U.S.SavingP,C&D/Y)-1 –46.46∗∗∗ –46.46∗∗∗
(continued)
29
30
Okun’s law unemployment Technical change Phillips curve inflation

function unemployment function function
Equation #: 12.2.2.1 12.2.2.1.TR 12.4.1 2.4.1.TR 11.1 11.1.TR
1 INTRODUCTION
OPECShock73&78 2.73∗∗∗ 2.73∗∗∗

AR(2) 0.52∗∗∗ 0.52∗∗∗
R2 (%) 84.1 84.0 86.0 78.0 78.0 78.0
D.W. 1.7 1.7 1.9 2.2 1.7 1.7

where
%GDPReal = % change in real GDP
GDPReal .17 = real GDP raised to the 0.17 power
INFL. Rate = inflation rate (CPI)
OPEC Shock73 = OPEC oil price shock 1973
OPEC Shock78 = OPEC oil price shock 1978
Katrina Shock05 = Hurricane Katrina shock 2005
FinanceShock08 = finance shock 2008
Unem. RateAV0–1 = unemployment rate, average of current and past years
M1–2 = change in M1 money supply
(M-X)/GDPAV0–1 = size of real trade deficit as a percent of GDP, average of current and past years
(Foreign Bor/GDP)–1 = real foreign borrowing as a % of GDP, lagged 1 year
Total (U.S.SavingP,C&D/Y)-1 = total real U.S. saving (personal, corporate and depreciation allowances, lagged one year)
AR(2) = second-order autocorrelation control
Table 1.4.9 Determinants of export demand
Equation # 6.1 6.1.TR
GDPTRADE PTRS(-2) 0.16∗∗∗ 0.16∗∗∗

XRAV0–3 –9.47∗∗∗ –9.47∗∗∗
IMPORTS0 0.56∗∗∗ 0.56∗∗∗
U.S. Prime RateAV-1-2 14.74∗∗∗ 14.74∗∗∗
U.S.INFLAV-1-2 –11.58∗∗ –11.58∗∗
AR(6) –0.49 –0.49
R2 (%) 87.9 87.9
D.W. 1.6 1.6

where
GDPTRADE PTRS(-2) = trade-weighted real GDP of the U.S.’s trading
partners, lagged 2 years
XRAV0-4 = real exchange rate, average of current and past four years
IMPORTS0 = U.S. real imports, current year
U.S. Prime RateAV-1-2 = real prime interest rate, average of past two
completed years
U.S.INFLAV-1-2 = inflation rate (CPI), average of past two completed
years
AR(6) = sixth-order autocorrelation control
32
Table 1.4.10 Determinants of velocity robust models only (where V1or2 = Y(P/M1or2 )
Determinants of M1 or M2 velocity a Determinants of M1 or M2 velocity a

Variable Using (X-M) model Using (X) model
(M i = M1 or M2) Eq. 17.8.0.TR Eq. 8.1.2.1.TR
(P/Mi )*Gov’t Receipts (TTI ) –0.96 –0.41

(P/Mi )*Gov’t Spending (GT&I ) 1.06 0.69
1 INTRODUCTION
(P/Mi )*Tax Cut Deficit (TDef ) 1.71 0.86

(P/Mi )*Spending Deficit (GDef ) –1.37 –.75
(P/Mi )*Prime Interest Rate (PR) –18.25 –7.67
(P/Mi )*Prime Interest Rate (PR–2 ) –20.64 –6.66
(P/Mi )*Tobin’s q Proxy (DJ0 ) 1.71
(P/Mi )*Wealth (DJ–2 ) 0.86 0.68
(P/Mi )*Exchange Rate (XRAV0 to-4 ) 6.23 9.60
(P/Mi )*Ratio of Young/Old (Pop16 ) –726.24
(P/Mi )*Total Population (Pop) 0.033 0.044
(P/Mi)*Consumer Confidence (ICC–1 ) 0.80
(P/Mi )*M2 (Av.-2 to -4) (M2AV ) 87.77 53.58
(P/Mi )*Accelerator (ACC) 0.49 0.37
(P/Mi )*Depreciation (DEP) 1.90
(P/Mi )*Cap. Utilization (CAP–1 ) 3.60
(P/Mi )*Profits (PROF)
(P/Mi )*C Borrowing (CB2 ) 0.33 0.13
(P/Mi )*I Borrowing (IB(–1) )
(P/Mi )*Net Exports (X-M) 1.96
(P/Mi )*Exports (X) 1.41
a Coefficients calculated from estimates in consumption and investment equations, not by regression of V on these components to avoid confusion of causal
and spurious effects.
Table 1.4.11 Determinants of labor’s total income and percentage share of NI
Labor’s % share of NI Labor’s total income (levels)

Cptr. and equation #: 20.4.1.2 20.4.1.2TR 20.4.2.1 20.4.2.1.TR
(YAV0,–1 ) 0.000019∗∗∗ 0.000027∗ 0.55∗ 0.55∗

EMPL/NI 0.030∗ 0.033∗ 0.13.52
W/NI –1.10 –0.11∗∗ –197.61
%Union 0.001 4.62
Prof ROW /NI –0.74 –0.45∗∗∗∗ –783.18
FinProf/TProf 0.008 63.38∗
(LProd /NI)av-1-2 0.74∗∗∗ 0.406.03
INFL 0.16 153.88
UNEMAV-1,-2 –.007∗ –0.006∗ –23.79∗∗
LPARRATE 0.005∗∗∗ +0.006 42.79∗∗
(T–G) –0.00005∗∗ –0.000033 0.02
(XRAV-1-3 ) 3.50∗∗∗
R2 (%) 83 88 94 90
D.W. 1.5 2.0 1.7 1.8
Significance levels: ∗∗∗∗ 15%; ∗∗∗ 10%; ∗∗ 5%; ∗ 1%.

where
(YAV0,–1 ) = variation in average of current and previous year real GDP
(EMPL/NI) = changes in the ratio of employment to national income
(W/NI) = changes in the real wage/national income ratio
(%Union) = changes in the % unionized
(PROFROW /NI) = changes in real U.S. profits (derived from operations outside the U.S.) as a percent of real national income
(FinProf/TProf) = financial industry profits as a % of total profits
(LProd /NI)av–1,–2 = labor productivity
(Firm<5) = % of firms with 1–4 employees
(UNEMAV-1,-2 ) = unemployment rate
(LPARRATE) = labor force participation rate

(T-G) = the government deficit
33
(XRAv-1-3 ) = real trade weighted exchange rate, average years - 1 to 3

Table 1.4.12 Determinants of profits’ total income and percentage share of NI
34
Profits’ % share of NI Profits’ total income (levels)

Cptr. and equation #: 20.4.3.1 20.4.3.1TR 20.5 20.5.TR
(Y) –0.000006∗∗∗ 0.008∗∗∗ 0.10∗

(ACC) –0.000008∗∗ –0.08
EMPL/NI –0.011∗ –0.003∗∗∗ –35.60
W/NI 0.77 674.58
%UnionAV –0.002∗∗∗ –7.72
1 INTRODUCTION
LProd(–1 /NI–1 7.08∗∗∗ 1.92 56430.86

Prof ROW /NI 4.32∗ 4.76∗ 41221.13∗ 47766.69∗
FProf/TProf –0.43∗ –0.50∗ –4273.90∗ –5077.98
PRAV-3-4 –0.0010∗∗∗∗ –7.44
INFL –0.009 232.06
Cons.Borrowing 0.000013∗ 0.18∗
XRAV0,-1,-2,-2 –0.0006∗ –0.0003∗∗ –4.28
R2 (%) 93 89 88 83
D.W. 1.6 1.6 1.8 1.9

where
(Y) = GDP
(ACC)=(Y-Y–1 ) = the Samuelson accelerator.
(EMPL/NI) = ratio of employment to real national income
(W/NI) = the real wage/real NI ratio
(%Union) = % unionized
(INFL2 ) = the inflation rate (squared)
(LPROD(–1) /NI(–1) ) = ratio of labor productivity growth to real national income growth
(ProfROW /NI) = real U.S. profits derived from operations in the rest of the world as a portion of real national income
(FProf/TProf) = foreign profits as % of total profits
(PRAV-3-4 ) = average of real prime interest rate lagged 3 and 4 years
Cons.Borrowing = consumer borrowing
(XRAv.0,-1,-2 ) = the real exchange rate average for current and past two years
Table 1.4.13 Determinants of rent’s total income and percentage share of NI
Rent’s % share of NI Rent’s total income (levels)

Cptr. and equation # 20.4.5.1 20.4.5.1.TR 20.4.6.1 20.4.6.1.TR
(HPrice /NI) –0.000009∗ –0.000009∗ 0.00027∗ *

(Prop.Inc/NI) 26.83∗ *
Mort.Int.Rate–1 0.025∗∗ 2.60∗ *
Resid.Inv–1–2 –0.108∗ *
LaborInc/NI –488.51∗∗ *
Av.Wage–1 /GDP–1 –19.41∗∗ –3769.09 *
R2 (%) 77 70 78
D.W. 2.0 2.1 1.9

*No variable met robustness standards. See text at Eq. 20.5.
where
(HPrice /NI) = the ratio of real house prices to NI
(Prop/NI, L/NI and Prof/NI) = proprietor’s, labor’s, and profit’s share of real national income
(Resid. Inv.) = investment in residential housing
(Mort) = real mortgage interest rates
(Av.Wage–1 /GDP–1 ) = the ratio of average real wage rates to GDP, lagged 1 year
Resid.Inv–1–2 = residential investment, average of past two years
LaborInc./NI = ratio of labor income to national income
35
36
Table 1.4.14 Determinants of interest total income and percentage share of NI
Interest’s % share of NI Interest’s total income (levels)

Cptr. and equation # 20.4.7.2 20.4.7.2.TR 20.4.8.2 20.4.8.2.TR
DebtC&B 44.91∗∗∗ 54.48∗∗

PRAV–1,–2,–3 /NI 27.17∗ 36.68∗ 30.40∗ 30.97∗
1 INTRODUCTION
UNEM –21.30∗ –29.33∗

(T-G) 0.032∗
Baa/NI 7.24∗∗ 12.57∗∗ 5.19∗∗∗∗
INFLAV0,–1 5669.50∗ 5518.62∗
DJAVAV0,–1 .28∗
(Debt.3
C&I ) –0.39∗ –0.40∗
(T-G)/GDP –0.0005∗ 0.0006
EMPL/NI 0.02∗ 0.014∗ 0.02∗∗
R2 (%) 95 89 74 54
D.W. 2.1 2.0 2.1 2.4

∗ No variable met robustness standards. See text at Eq. 20.5.
where
(DebtB&C ) = total business and consumer real debt levels
(PRAv -1,-2,-3 ) = average real prime interest rates
(Baa/NI) = real Baa bond interest rate/national income ratio
(EMPL/NI) = employment/NI ratio
(DJAV) = NYSE Composite Index
(T-G)/GDP = the ratio of the government deficit to GDP
(Prof/NI) = profit income/NI ratio
(Labor/NI) = labor income/NI ratio
PART I
Production of the GDP

CHAPTER 2
Methodology
The methodology section is divided into two parts. The first part
(Section 2.1) discusses how standard methodological issues like station-
arity, endogeneity, heteroskedasticity, and multicollinearity are dealt with.
Treatment is brief because methods for dealing with most of these
problems are commonly agreed upon.
The second part (Section 2.2) deals with what many economists would
consider to be the first and perhaps most important methodological issue
a large – scale modeler has to deal with: whether to model using DSGE,
VAR, or Cowles Commission methodology. This section is 10 times as
long as the previous methodology section. This is because the issue dis-
cussed remains unresolved, unlike the most issues discussed in the first
section (2.1). Not all economists agree which of these three modeling
methods to use. Therefore, we feel the need to extensively empirically and
theoretically show that the modeling method chosen here (Cowles) is by
far the best at modeling how the actual economy performs, and there-
fore the logical methodological choice for those attempting to develop a
large-scale, detailed model of how the macroeconomy works.
Another reason these lengthy comparisons are important is that large-
scale econometric models have lost credibility in recent decades. They are
no longer routinely relied upon by economists and policy makers for reli-
able guidance, as was the case with, say, Eckstein’s DRI model, 30 years
ago (a Cowles model). The change in the type of models to VARs and

DOI 10.1007/978-3-319-50681-4_2
40 2 METHODOLOGY
DSGEs since then appears to be a large part of the reason. We hope to

show with our comparisons that by returning to Cowles modeling, we can
significantly improve our models’ explanatory power, and therefore the
reliability of the guidance they provide. As the Nobel Laureate economist
Robert Solow (2016) has said, Cowles models far better explain the data
than DSGE or VAR models: After reviewing this paper’s analysis of the
three methods, Solow wrote
Your arguments in favor of Cowles-type models as against VAR and DSGE

models have real weight . . . I think that you get across that whatever can be
said for DSGE models . . . they are inferior at explaining the facts . . . You do
the same for general VAR models
For readers already comfortable with Cowles methodology, and not inter-
ested in reading the full 38 pages devoted to discussing differences in
Cowles, DSGE, and VAR methods, the long second section of the meth-
odology can be skipped. The reader can move on to Chapter 3 (literature
review) or Chapters 4–19 (detailed presentation of the findings for each
equation in the model) without loss of ability to understand what is
presented.
2.1 GENERAL METHODOLOGICAL ISSUES

Parameter estimates for the model were developed using 1960–2010
annual data. All data were obtained from the Economic Report of the Pres-
ident (2002 and 2011) and the Federal Reserve’s; Flow of Funds Accounts
(2011). The Economic Models Used were “Standard Models” in the sense
that all variables commonly cited in the literature as determinants of con-
sumption, Investment, etc. were used in the initial hypotheses tested in this
study. This standard resulted in a need to test many variables. A few vari-
ables cited in other studies, uncovered after work on a particular model
was completed, were not included in the testing. Variables tested were
listed in Section 1.3, summarizing statistical results for each equation in
the model. They are listed again in the appropriate text section detailing
test results for each equation in the model (Chapters 4–16), and in the
summary and conclusions section, Chapters 19.
Some preliminary testing was done to weed out variables only occa-
sionally cited in the literature and found to be statistically insignificant in
2.1 GENERAL METHODOLOGICAL ISSUES 41
our initial tests. However, when variables commonly theorized to be sig-

nificant factors were found insignificant (e.g., interest rates and measures
of consumer confidence in some consumption and investment functions),
they were left in the model even though insignificant. This was done if it
was not clear if the insignificance was a substantive finding, or the result
of a technical problem such as multicollinearity, small sample size, or some
other econometric problem. Here we follow both Otto Eckstein’s (1983)
practical advice (see for example, his multifamily housing demand equa-
tion), but also that of statistician Triola (2011) who notes that in the
absence of statistical significance when evaluating the mean of a sample,
the best estimate is the sample mean, not zero. In addition, it serves as
a reminder that the research agenda for the future must include further
work to determine if the lack of significance is indicating something sub-
stantive about the variable, or only some technical problem with the data
and how it is used.
When dealing with which (if any), lagged values of a variable to use,
economic theory typically provides little if any guidance. In this study, if
theory indicated one variable was a determinant of another, numerous lags
were tested, and we adopted the lag level of the determinant found most
significantly related to the first variable, unless of course, theory specified
a specific lag level, following Tinbergen (1939).
Generally we followed the same process in defining the values to include
when calculating aggregates and averages. We do not use “Life Cycle” or
“Permanent Income” averages of income over time as the definition of
the “right” income variable to use as a determinant of consumption, as
many economists do, since in prior testing of different sized averages made
up of leads and/or lags, evidence strongly indicated that only current
income mattered significantly. The evidence was overwhelming. Similarly,
exchange rate testing indicated that the average of the current rate and the
past 3 years’ rates was the lag combination most systematically (signific-
antly) related to consumption and investment, so that is the rate used in
our models.
All models were initially estimated using OLS. However, testing was
then done to determine if endogeneity was present among the variables
in the model tested. If so, Two Stage Least Squares (2SLS) was used to
develop instruments to replace the endogenous variable(s). This was done
to eliminate simultaneous equations bias caused by identification problems
arising from endogeneity. The process used to identify endogeneity, and
42 2 METHODOLOGY
replace endogenous variables with strong, non-endogenous instruments

was as follows, following a process suggested by Griffiths et al. (2008):
• Hausman endogeneity tests were used to determine what needed to

be instrumented.
• Wald weak instrument tests were used to ensure the instrument was
a reasonable proxy for the variable it replaced, i.e., was not a weak
instrument.
• Sargan “Valid Instrument” tests were used to ensure the chosen
instrument was free of any endogeneity with the dependent
variable.
In addition, a reasonably objective way of arriving at suitable instruments

is needed to ensure instrument components were not picked to ensure the
instrument selected would obtain some desired result, for example, the
right sign on itself or other variables. Here again, the method we have
used reflects Griffiths et al. (2008) and Pindyck and Rubinfeld (1991):
all exogenous and lagged variables in the system are used as the initial
components of the instrument. If tests indicate it is a weak instrument,
additional lagged values of variables already in the instrument are added.
If that is not enough, efforts switch to removing instrument components
that have very low statistical significance as a way of increasing t statistics
on remaining variables and the instrument’s F statistic until the stand-
ard Wald criteria are met (at least one t statistic greater than 3.3 or an
F-statistic greater than 10.0).
All variables were tested for stationarity. If found nonstationary, a vari-
able was detrended unless it was found cointegrated with the dependent
variable in the model in which it was used.
• 75 time series variables (or different lags thereof) tested

• ADF (Augmented Dickey Fuller) unit root tests used to determine
stationarity
• DF (Dickey Fuller) test used to determine if nonstationary were
cointegrated
• Detrending done to those not cointegrated
All models were tested extensively to ensure the robustness of the findings.
This is particularly important when using nonexperimental techniques
like regression analysis where even moderate levels of multicollinearity or
left-out variables can severely bias estimates of a variable’s impact. We test

every model for robustness three different ways
• Robust to Time Period Sampled: Four different time periods tested

• Robust to Model Specification: Test sensitivity to two significant
changes in
• Variables specified in the model tested
• Robust to Regression Technique Used: OLS vs. 2SLS
Generally, the key coefficients in the equations included in this large-scale

model were strong enough to be very robust to time period sampled and
choice of regression technique (we typically find more difference between
weak and strong instrument results than between OLS and strong instru-
ment results). There were occasional exceptions, noted in the testing
sections for each model.
Testing for robustness to model specification is more complicated.
In a model (already) well specified, i.e., explaining 85% or more of the
dependent variable’s variance with theoretically sound variables and lags,
adding or subtracting variables above this level rarely will lead to signi-
ficant changes in other variables’ parameter estimates, except perhaps for
variables making only marginal contributions to the model. In this circum-
stance, most of the possible effects of direct multicollinearity or left-out
variables which are collinear with variables in the model have already been
accounted for.
But, respecifying a model by deleting a variable already in it which
accounts for much variance in the model is to court disaster. The vari-
able dropped is likely to be multicollinear with many other variables in
the model, since many variables tend to move together, at least partially.
Dropping it will change the estimated effect of other variables in the model
on the variable of interest’s coefficient, since each variable’s coefficient is
a function of their collinearity levels with other variables in the equation.
Similarly, adding variables to a model which explains little or only moder-
ate amounts of variance will often significantly change the estimated effects
of variables already in the model, particularly if the variable added adds
much to explained variance. This is because the newly added variable is
likely somewhat collinear with variables already in the model, and when
entered, will be assigned some of their explanatory power.
Hence, our tests for specification robustness will be taken to be success-
ful if variables making minor contributions to explained variance can be
44 2 METHODOLOGY
added or subtracted without changing other variables coefficients much.

However, given the nature of correlational tools, we will actually expect
that removal of major variables in a model, say the income variable in the
consumption function, will result in major distortions to coefficients on
the remaining variables. Hence, we do not test for specification robustness
this way.
Hence, the key criteria for evaluating what belongs in an equation are
the equations ability to explain variance (R2 ), the statistical significance
of a variable’s regression coefficient, and in some tests, comparison of an
equation’s mean square error with that of another equation.
All models are tested in first differences, not levels: This has many
advantages when dealing with time series data. In our case testing in first
differences:
• Reduced by almost half the number of variables found nonstationary

• Raised virtually all Durbin Watson serial correlation statistics to 1.6–
2.2 range
• Reduced multicollinearity effects substantially:
◦ Median correlation coefficient fell from ∼0.80 to ∼0.40.
◦ Regression coefficients far more stable when model changes are
made
Newey–West standard errors are used throughout to address heteroske-

dasticity problems.
GDP determination is done by adding together regression coefficients
of the determinants of domestically produced consumption and invest-
ment, government spending, and the exports function. From an economic
theory perspective (IS curve calculation), this is the way the GDP is
determined. At first blush, this should mean we could simply regress GDP
on all the variables in our consumption, investment, and export models,
plus government spending, and get the same results. It can be shown
that this is true if precisely the same variables are determinants of con-
sumption, investment, and exports. In our models they are not. Using
the same variables as determinants of both consumption and investment
can’t be theoretically justified. Regressing GDP on all the variables that
are determinants of each of the models is equivalent to assuming they are,
and provides a linear summation of the estimated relationship of a given
determinant on all each of the functions. For example, the depreciation
allowances variable is considered a determinant of investment, but not of
consumption, yet including it in the consumption function will typically

give a non-zero parameter estimate of its importance, simply because so
many variables are at least mildly correlated with each other. In the regres-
sion of GDP on depreciation, the coefficient obtained will represent the
sum of this (noncausal) correlation of depreciation on consumption, plus
the (presumed causal) correlation of depreciation on investment. The net
effect is a biased estimate of depreciation’s effect on the GDP. We avoid
this by obtaining our estimated value for GDP by arithmetically sum-
ming the coefficients on only the variables found theoretically important
enough to include in the consumption, investment, and export function
regressions. This, of course, leaves depreciation out of the consumption
function, but in the investment function.
This problem illustrates the importance of only using theoretically – jus-
tified variables in economic models. How else are we to determine from
correlational data, which relationship are causal vs. simply spuriously cor-
relational? Surely a non-zero coefficient or a significant t-statistic is not
enough to distinguish correlation from causation. In Sims-type VAR mod-
els, where every dependent variable is a function of the past values of every
variable in the model, this gives a regression coefficient for (e.g.) depre-
ciation in the GDP function which sums its causal effects on investment
with its noncausal effects on consumption.
Method Used to Develop Robust Models
Each of the 38 stochastic models in this study uses a standard series of
statistical tests to refine initial estimates obtained from a model using one
sample period and one particular combination of explanatory variables into
a final, robust model whose results are reliably consistent over time period
and for variations in the variables included in model tested.
The initial test is an OLS test of variables found to be determinants of
the dependent variable in prior studies reviewed, or cited in theory or dis-
covered in exploratory testing. If endogeneity between the dependent and
an explanatory variable is discovered, a strong, non-endogenous instru-
ment is developed and the initial model is reestimated using 2SLS. Then,
each explanatory variable in the model is tested using stepwise regression
to determine its individual contribution to total explained variance. Then
the model is retested in three other, though overlapping, time periods
to determine which initial results can be replicated in other time peri-
ods. Finally, the model comprised of variables that have proven to be time
period robust are tested for the sensitivity of regression coefficients and
significance levels to multicollinearity in the model. This is done by adding
46 2 METHODOLOGY
and subtracting variables from the time–period robust model to see if the
parameter estimates on remaining variables remain reasonably stable. Vari-
ables’ coefficients’ are considered to remain stable if adding/subtracting
variables from the model does not change their values by more than one
third. Some exceptions are made to this rule depending on particular
model characteristics. Reasons for exceptions are noted in the text.
For those who wish to move more quickly from initial to final fully
robust models, we note at the beginning of each equation’s development
process the initial model we are starting with, and where to find the final
robust model we end up with, so the reader can jump from start to finish.
We also note that Section 1.4 presents all initial and robust models results
for each variable used side by side, with each variable used identified.
Final Comments About the General Methodology

Good science requires replicability of results. This paper’s foremost goal
is to provide, to the best extent possible, models whose results meet the
replicability standard. Largely, this goal appears to be achieved, though
in some areas more remains to be done. In particular, in some equations
we were not able to fully resolve the “left out” variables and multicollin-
earity problems that affects the credibility of parameter estimates in any
economic model.
In most models 85–95% of the variance is explained. However, in some
models, there are definitely some “left out” explanatory variables remain-
ing to be found. Less of the total variance in the model than we would
like is explained by the variables. Models with this problem are identified
in the text.
In addition, the problem of multicollinearity needs to be better
resolved. It is perhaps the most serious impediment to doing good science
in economics today. To mitigate the problem in this study, we use first dif-
ferencing, and careful selection of combinations of explanatory variables
used. In addition, we do extensive robustness testing, by adding and sub-
tracting explanatory variables to a model, to ensure (reasonable) model
do not cause marked changes in other parameter estimates. For most of
our parameter estimates we are able to show these techniques achieved
the desired level of stability, but not for all. For some models, parameter
estimates are still sensitive to exactly what other variables are included in
the model. (these models are identified in the text). Economists need to
develop better scientific methods for dealing with this problem, and are
long overdue doing so.
A Note on the Disposable Income Variable Used in Consumption Models

The variable used to represent disposable income consumption functions
in this study was (GDP – total government revenue), and that this is similar
to the National Income variable used by Kuznets in his path breaking
1940s and 1950s studies of the consumption/income relationship. More
commonly these days, disposable personal income is used as the income
variable in consumption studies. To show the similarity of results using the
two variables, we have used a previously developed model of consumption
given in Heim (2013, p. 72, Eq. 7.1). It was estimated using OLS because
standard Hausman test method indicated no endogeneity.
The disposable personal income variable typically used in other studies
differs from the (Y-TT ) variable used in this study in the following way:
Disposable Personal Income = Personal Income
– (Total Taxes–CIT – ½ FICA Taxes).
This leaves “personal” income taxes defined as the total of PIT, ½ FICA,
Sales, and Misc. taxes. These added to the CIT and the other half of
FICA taxes, equal total government revenue. (See Economic Report of the
President, 2012, Table 83 for government revenue, Table 27 for personal
income)
Results are repeated below for the consumption model using the (Y-TT )
definition, and for exactly the same model using the disposable personal
income definition, also calculated using OLS since the standard method
for calculating Hausman endogeneity indicated no statistically significant
level of endogeneity was present among the right hand side variables.
Model 2.1.1
Consumption Function (Using Y-TT ):
CT = 0.50(Y – TT ) + 0.55(TT ) – 0.26(GT& I ) – 11.81PR
(t =) (11.4) (11.4) (–3.7) (–5.1)
+0.42DJ–2 + 3.42XRAV – 336.65POP16 + 0.012POP
(5.3) (2.3) (–1.3) (2.6)
+0.36ICC–1 + 40.86M2AV + 0.12 CB2
(1.3) (3.8) (3.1)
+0.04 GDPReal(–3) R2 = 94.9% D.W. = 1.8 MSE = 25.45
(1.1)
(2.1.1)
48 2 METHODOLOGY
Model 2.1.1.a
Same Consumption Function as 2.1
(Except Disposable Personal Income Used)
CT = 0.38(YP – TP ) + 0.45(TT ) – 0.33(GT& I ) – 9.35PR

(t =) (6.2) (9.2) (–2.5) (–4.2)
+.47DJ–2 + 3.56 XRAV – 446.88POP16 + 0.02POP
(3.0) (2.2) (–1.6) (3.0)
+0.13ICC–1 + 65.46M2AV + 0.25 CB2
(0.3) (4.2) (5.3)
+0.05 GDPReal(–3) R2 = 90.1% D.W. = 2.4 MSE = 35.49
(1.2)
(2.1.1.a)
Results for all variables in the model are roughly the same as before.
R2 drops 4.8% points when substituting disposable personal income for
(Y-TT ). This may be because not all spending on consumer goods and
services may be out of consumer income. Some may be out of business
income (profits). Profits, when added to Eq. 2.1.a as a separate income
variable was found to be a statistically significant determinant of spend-
ing on consumer goods, in addition to personal income. On the other
hand, when the typical income variable used in this study (Y-TT ) is sub-
stituted for personal income, profits are not found statistically significant
as a second income variable. This suggest the profits variable may be
behind the drop in explanatory power when using personal income. For
example, some of the food bought at grocery stores may be purchased out
of retained business earnings, perhaps for a conference.
2.2 CHOOSING BETWEEN VAR, DSGE, AND

COWLES COMMISSION MODELS
2.2.1 Overview of the Three Methods and Results
Economists who wish to model the macroeconomy have three methodolo-
gical choices: use a neoclassical DSGE structural model, a more Keynesian
Cowles Commission structural model, or a more atheoretical VAR model.
This paper examines which performs better, i.e., explains the economy’s
year-to-year fluctuations most accurately.
2.2 CHOOSING BETWEEN VAR, DSGE, AND COWLES COMMISSION MODELS 49
Cowles Models
Cowles models are structural. They provide answers grounded in both
good science and good economic theory to very detailed questions, such
as “What variables drive year- to – year consumer spending on durables?
Nondurables? Inventory Investment?” How are they different? It is the
only one of the three methods in which you will typically find upward of
a dozen explanatory variable in each equation, and dozens of explanat-
ory equations, richly describing the complexity of relations in a modern
economy. It is one of two reasons some economists prefer Cowles-type
structural modeling. DSGEs are also structural, but typically much smaller
and do not include the large number of variables and relationships need to
answer such detailed questions. Nor do VARs.
The second reason some economists prefer Cowles models, is that such
models when tested, tend to explain the actual behavior of the US macroe-
conomy far better than do VAR and DSGE models. This is the judgment
of many economists, whose comparisons are discussed in detail below. It
is also this study’s finding, based on detailed comparisons of the three
models’ performance, also presented below.
Cowles-type structural models were the standard way the science of
macroeconomics was applied from the until the 1980s. The first Nobel
prize in economics was awarded, in part, to Jan Tinbergen for developing
the first econometric model of the macroeconomy, and in 1980 another
was awarded to Lawrence Klein for the same type of research. The mod-
els tend to be demand driven, and therefore have a decidedly Keynesian
look. Cowles models take a top down, “macro principles first” modeling
approach. They cut the macro model into more and more micro-sized
pieces, adding relative price variables as they go along. In this way they
identify the effects of demand for other products on the demand for the
one being studied, thereby allowing for integration of micro into macro.
Eckstein (1983) provides numerous examples of this. This “macro prin-
ciples first” approach is based on the notion that most year-to-year changes
in demand for products are likely to be caused by macro factors (like busi-
ness cycles), not micro factors like prices, though relative prices do matter.
The Cowles approach is continued today in Ray Fair’s models of the
US and world economies. Cowles models incorporate the multitudinous
variables and relations necessary to describe the detailed structure of the
economy. Many believe macroeconomics parameters are sufficiently stable
to allow macroeconomic relationships to be evaluated as a science.Those
who agree would argue the goal of modeling should be to correctly
50 2 METHODOLOGY
describe how the economy operates at an engineering manual level of

detail, and as closely as possible to engineering manual levels of reliability.
In the 1970s and 1980s, many questions were raised about Cowles
models’ by Lucas, Sims, and others that led to a shift to VAR and DSGE
modeling by most macroeconomists.
DSGE Models
DSGE advocates argued that Cowles models lack a firm micro-foundation
in their explanations of economic behavior, i.e., are not built to show how
profit maximization and utility maximization conduct is actualized from
year to year. DSGE models are constructed and tested on the assumption
this “micro principles first” approach best describes what drives year-to-
year fluctuations in macroeconomic variables.
DSGE models also assume rational expectations characterize the actions
or consumers and businesses, i.e., they are predicated on the notion that
consumers accurately foresee future income, at least in the probability
distribution sense, and armed with this foresight, consumers base cur-
rent consumption decisions on expected future lifetime average income,
not just current income (Keynes) or past income (DeLeuuw/Modigliani).
Basing it on (accurate knowledge of) lifetime income allows (accurate)
maximization of lifetime utility, the consumers’ driving objective in a
DSGE model. Businesses are assumed to operate in similar profit max-
imizing fashion. Though the assumed micro foundations are not directly
testable, it is possible to look at, say, the first-order conditions for inter-
temporal utility maximization implied by the model, and test to see if some
of these results occur. For example, DSGE models assume consumers
can accurately deduce what savings level is required to maximize utility
intertemporally. If so, an implication of the theory that the savings rate
is such that consumption should be constant in all periods, for example,
Ct = Ct+1 = Ct+n except for unexpected shocks.
DSGE models are often parameterized rather than estimated. All theor-
etical concepts underlying a Cowles model are estimated. There is no such
thing as a “non-testable” component of the theory underlying Cowles
models.
VAR Models
The a priori use of theory to decide what relationships to test was
criticized in the 1980s by Sims and others and led to the development of
VAR modeling. VAR is based on the premise that everything (potentially)
may be a function of everything else, at least after one or more lags, and
therefore, everything should be included in tests as potential determinants

of everything else; let the data determine which relationships actually hold
(Sims 1980). Sims argued Cowles models were overly restrictive, because
only variables (and lag levels) previously established in theory were
included in models, and the theory often had not been tested. Hence,
theory often provided no good guide to deciding if important variables
(or the right lag levels for them) were being left out of econometric
testing. If important variables or lags were left out, the model would be
under identified.
As a result, Cowles structural models were thought to have an identi-
fication problem.
VAR modelers let the data decide which variables and what lags are
determinants of the current values of all economic variables. Conceptually,
VAR models assume every dependent variable in the system is predeter-
mined by some combination of its own lagged values and the lagged values
of all other variables in the economy. Test results determine the coefficients
which connect everything to everything else.
In practice, testing such “everything” models requires unreasonably
large amounts of data; there are just too many variables in the economy to
test them all, especially with multiple lags (too few degrees of freedom in
data sets). In practice, VAR models typically include only five or six vari-
ables considered most important. It is often difficult to discern a theory
of how the economy operates that connects these variables, and therefore
difficult to explain their results in economic terms.
The genius of Sims’ system is that it allows the scientific forecast-
ing of future values of key economic variables based on past values. But
accurate forecasts rely on coefficients that are unbiased, are estimates of
non-spurious relationships, and can prognosticate regime changes that
may not occur until the future.
In the Sections 2.2.2–2.2.5, we examine DSGE, VAR, and Cowles/
Keynesian methods in detail. We also conduct head-to-head tests of the
three models’ ability to explain economic activity during the decade fol-
lowing the period in which the models were estimated, 1960–1990, or
1960–2000.
Tests will show Cowles models have greater explanatory power than
VARs or DSGE models. The average error with which the Cowles models
fit the data in the decade after estimation will be only half that of DSGE
models, only and 1/6 that of VARs.
52 2 METHODOLOGY
The VAR error likely results from combining likely causal and spuri-
ous regression coefficients in models, a problem that is unavoidable when
using the same explanatory variables in every equation, and is discussed
in the VAR section below. The error also likely results from failure to
provide any way of adjusting forecasts for unanticipated future regime
change. Out-of-sample performance of Cowles models is better because
they control for variables which might cause regime change in the future.
This allows forecasts of (say) the effect of interest rate changes today on
investment 2 years in the future to be adjusted in the future in prede-
termined ways as specific types of change in the control variables occurs,
changes which were unforeseen at the time the initial forecast was made. In
this sense, the out-of-sample performance record of Cowles models better
describes how well they explain the causes of what actually happed, rather
than how well they forecast it. This is a key difference with VARs.
The DSGE flaws result from use of incorrect theory. Tests indicate using
current year income in consumption functions explains more variance than
estimates of lifetime income. Failure of the lifetime income assumption
casts doubt on the validity of the rational expectations assumption, a key
postulate of DSGE theory. The DSGE assumption of constancy of con-
sumer spending from year to year, except for technological shocks (Romer
1996) was also tested. The data tested did not support this theory. Wide
variation in consumer spending was found, aside from that caused by tech-
nological shocks. It was better explained by factors commonly found in
more Keynesian – looking, demand driven models, like Cowles models.
2.2.2 Previous Performance Comparisons of DSGE,

VAR, and Cowles Models
Several studies have compared DSGE, VAR, or Cowles methods either
against an absolute standard (variance explained) or the relative per-
formance of one compared to the others. These studies are discussed in
detail in the DSGE, VAR, and Cowles methods sections of this paper
(Sections 2.2.3–2.3.5), which follow immediately.
2.2.3 DSGE Modeling

This section of Chapter 2 is divided into three major subsections: (1) a
review of tests by others of the performance of DSGE models compared
to Cowles and VAR models, (2) this paper’s own comparisons, and (3) a
section surveying the widespread criticisms of DSGE models in the recent

literature. This survey is included as a way of examining why DSGE models
seem to perform so badly in this paper’s out-of-sample tests, particularly
compared to Cowles models.
2.2.3.1 Tests by Others of How Well DSGE Models Fit the Data
The test of any theory’s usefulness is its ability to explain or forecast accur-
ately beyond the sample period used to estimate the model’s parameters.
For DSGE, perhaps the most popular model today is the Smets–Wouters
“New Keynesian” DSGE model.
Comparisons with Smets–Wouters
In examining the Smets–Wouters model, Edge and Gurkaynak (2011)
found that it explained very little variance in the data, only 13% or less,
depending on the test. Two tables with their findings are presented below
(Tables 2.2.3.1.1 and 2.2.3.1.2).
Some DSGE advocates have argued that, because of rational expecta-
tions, income should be predictable from year to year except for changes
due to unforeseeable technological progress. It is argued that this means
DSGE’s should not be able to successfully explain much of the variance
in year-to-year changes in consumption. This is a random walk explan-
ation of consumption growth over time. However, tests below indicate,
most of the year-to-year changes in consumption are due to factors other
than year-to-year technological change. Most of the change that Smets–
Wouters can’t explain – which is roughly 90% of it according to Edge
and Gurkaynak, stems from sources other than technological progress,
Table 2.2.3.1.1 DSGE model inflation forecast accuracy
1Q Ahead 2Q Ahead 3Q Ahead 4Q Ahead 5Q Ahead 6Q Ahead
DSGE model
Slope 0.451∗∗ 0.089 0.031 0.209 0.167 0.134
(0.108) (0.149) (0.250) (0.261) (0.216) (0.174)
Intercept 0.261∗∗ 0.421∗∗ 0.446∗∗ 0.363∗∗ 0.386∗∗ 0.398∗∗
(0.051) (0.082) (0.122) (0.128) (0.112) (0.112)
R2 0.13 0.00 0.00 0.02 0.01 0.01
No. of obs 104 104 104 104 104 104
Source: Edge and Gurkaynak (2011), Board of Governors, Federal Reserve System, p. 20
Notes: **/* denotes 1/5% significance levels
54 2 METHODOLOGY
Table 2.2.3.1.2 DSGE model GDP growth forecast accuracy
1Q Ahead 2Q Ahead 3Q Ahead 4Q Ahead 5Q Ahead 6Q Ahead
DSGE model
Slope 0.374∗ 0.485 0.477 0.507 0.495 0.553
(0.174) (0.249) (0.321) (0.303) (0.312) (0.279)
Intercept 0.419∗ 0.313 0.331 0.299 0.320 0.284
(0.206) (0.292) (0.362) (0.346) (0.344) (0.311)
R2 0.08 0.09 0.07 0.08 0.07 0.06
No. of obs 104 104 104 104 104 104
Source: Edge and Gurkaynak (2011), Board of Governors, Federal Reserve System, p. 20
Notes: Standard Errors in Parentheses; ∗∗ /∗ denotes 1/5% significance levels
like business cycle effects. Business cycle effects are in Cowles models, and
may account for why they explain year-to-year variation in consumption
so well.
[Comparisons with Fair]
Fair (2007) compared his Cowles model to a DSGE model presented in
Del Negro et al. (2007), and found the Cowles model performed better.
The average root mean square error of fit were as follows:
Period Tested Fair’s DSGE

Model Model
4 Qtr. Ahead Projection 1.33% 2.62%

8 Qtr. Ahead Projection 1.84% 6.05%
A number of other studies have compared DSGE and VAR models

in terms of their success in explaining or forecasting the economy.
Paccagnini (2011) noted
If the goal of the empirical analysis is to provide an impulse response func-

tion, for example, for an unanticipated change in the target inflation rate, the
Vector Autoregressive model (VAR) (Sims 1980) can be a good estimation
instrument (even though the VAR does not provide a coherent economic
explanation for the responses). Instead, if the aim is to determine the welfare
effect of a change in the inflation target, the VAR s very limited. (p. 1)
And, Sims (2006) noted
VAR models do still fit better than DSGE’s when they are applied to real
data (and not to processed data that has had trend removed by filtering or
regression). (p. 53)
Tovar (2008) found
(VARs) still do better than DSGEs when they are applied to real data (ie
data that has not been processed by removing the trend, either by filtering
or regression)
However, there are other analysts who have found their DSGE models
perform as well as VARs. For example, Christoffel et al. (2010) note:
we examine the forecasting performance of the New Area-Wide Model

((NAWM) that has been designed for use in macroeconomic projections
at the European Central Bank . . . Overall, the empirical evidence indicates
that the NAWM compares quite well with the reduced form models and the
results are therefore in line with previous studies. (pp. 4, 7)
Smets and Wouters (2003, p. 1125) found that their DSGE model
performed as well as VARs.
Wickens (2012) notes:
A review of the literature shows that forecasts from DSGE models are not
more accurate than either times series models or official forecasts, but neither
are they any worse (Abstract of paper).
We found no studies indicating DSGE models performed better than

Cowles models.
Finally, we note that Cowles models such as Eckstein’s DRI model,
were quite widely used by the private sector in the 1960–1980s. VARs,
have been used in the private sector since the 1980s. However, DSGE
models do not seem to have been adopted by the private sector. As
Smith (2014) notes
56 2 METHODOLOGY
As far as I’m aware, private-sector firms don’t hire anyone to make DSGE
models, implement DSGE models, or even scan the DSGE literature . . . As
I see it, this is currently the most damning critique of the whole DSGE
paradigm
2.2.3.2 This Study’s Tests of How Well DSGE Models Fit the Data
In subsections 1 and 2 below, this study tests the DSGE assumption
of (accurate) intertemporal utility maximization. We test whether con-
sumers can foresee lifetime income accurately, and whether consumption
is constant from year to year, except for unexpected technology shocks.
Subsection 3 tests whether the Lucas critique holds, i.e., whether the past
effects of policy variable changes can predict the effects of similar changes
in the future. Subsections 4 and 5 compare the out-of-sample perform-
ance of the FRB/NY and FDR/US DSGE models with Cowles models
during the 2001–2010 period, based on models whose parameters were
previously estimated using the same estimation periods.
2.2.3.2.1. Evaluating DSGE’s “Foresee Lifetime Income

Accurately” Assumption
Consumer behavior collapses from a neoclassical DSGE model to an “old”
Keynesian model if all or most consumers’ spending decisions are based
on current year disposable income only, not expected future lifetime aver-
age income. Similarly, if most consumers are New Keynesian DSGE “rule
of thumb” consumers, rather than rational expectations consumers, New
Keynesian models reduce to old Keynesian models.
Heim (2008) tested various income averages ranging from 0– 4 forward
leads (rational expectations) to 0–4 backward lags (adaptive expecta-
tions), to a combination of four forward leads and four backward lags
to see if both rational and adaptive expectations played a part in con-
sumer behavior. Such average income models are also key to consumption
determination in Modigliani’s Life Cycle and Friedman’s Permanent
Income models.
The power of such DSGE models to explain variation in consumer
spending over time was compared to “current income only” income
model. Testing was for the period 1960–2000. Rational expectations mod-
els were tested by averaging actual future year American income (with or
without present year income included). With rational expectations, that is
what the consumer sees, since by assumption they can foresee their future
incomes accurately. This was used as the income variable in consumption
tests. Results were compared to models using only current income. This
old Keynesian formulation explained more variance in consumer spending
than any of the rational or adaptive expectations models.
We replicate this approach here, using a typical “Old” Keynesian
model consumption function. The new model adds some explanatory
variables not used in the Heim model. For example, prior years’ sav-
ings, and consumer borrowing. Testing also covers a slightly longer time
period (1960–2006). Controls include the government deficit, current
year interest rates, a wealth variable, the exchange rate, and other variables.
Variables used are defined as follows:
CT = real consumer goods and services

(Y-TT ) = real disposable income, defined as GDP minus total government receipts,
which yields estimates nearly identical to the national income variable used
in Kuznet’s (1947) consumption study)
(TT -GT&I ) = real government deficit: total receipts minus total expenditures on
government consumption, Investment, transfers, interest and subsidies.
When tested separately, TT and GT&I used. Growth in the deficit is
measured net of growth in the pool of loanable funds, since what we are
trying to capture with this variable is crowd out
PR = real prime interest rate defined as the nominal rate minus the average of the
past two completed years inflation
DJ–2 = a measure of wealth (NYSE Composite Index), lagged two years (Federal
Reserve/MIT Large econometric model showed stock market activity to
be a major determinant of household wealth, which in turn was a
determinant of consumer spending. See Eckstein 1983, p. 5)
XRAV = the real broad US exchange rate average for current and past 3 years
(foreign currency per dollar)
POP16 = ratio of young (20–24) to old (65+) in population
ICC–1 = Index of Consumer Confidence (Conference Board measure), lagged 1 year
M2AV = real M2 money supply; average of second, third, and fourth past years
M2-M1 = savings components of M2 for the current period
CB , CB2 = consumer borrowing (annual change in consumer debt). (Federal
Reserve/MIT model)
Indicates credit access a major determinant of housing demand
(Eckstein 1983, p. 5)
Econometric testing was done using OLS, since Hausman endogeneity

tests indicated no variables were endogenous at statistically significant
levels. Hence, no 2SLS Models were needed. There were stationarity
issues to resolve. Six variables plus the dependent variable were found
58 2 METHODOLOGY
nonstationary: disposable income, government spending, the wealth vari-

able (stock market average), the ratio of young to old in the population,
population, and the average M2 money supply. Five of the six were
cointegrated with the dependent variable, so no detrending was needed.
The government spending and the dependent variable were detrended to
restore stationarity. (Detrending only the government spending (GT&I )
variable yielded identical or virtually identical results.)
Test results for this “Old” Keynesian-style consumption function are
given in Eq. 2.2.3.2.1.1. We will compare its explanatory power with
several Friedman/Modigliani average income models further below.
CT = 0.55(Y – TT ) + 0.52(TT ) – 0.27(GT& I ) – 13.02PR

(t =) (9.2) (10.4) (–3.6) (–5.3)
+0.44DJ–2 + 3.75XRAV – 383.02POP16 + 0.011POP
(2.8) (2.5) (–1.5) (2.5)
+.42ICC–1 + 41.6M2AV + 0.04 CB2
(1.5) (3.6) (0.7)
R2 = 94.8% D.W. = 1.5 MSE = 23.92
(2.2.3.2.1.1)
By comparison, a more DSGE version the same model, which used the
average of current year and four future year values of disposable income,
yielded the following results:
CT = 0.72(Y – TT )AV + 0.46(TT ) – 0.18(GT& I ) – 3.97PR

(t =) (7.9) (7.6) (–1.5) (–1.1)
+0.22DJ–2 + 1.85XRAV – 162.09POP16 – 0.008POP
(1.5) (1.3) (–0.6) (–0.9)
–0.05ICC–1 + 75.7M2AV + 0.26 CB2
(–0.2) (7.1) (4.0)
R2 = 91.9% D.W. = 2.2 MSE = 29.76
(2.2.3.2.1.2)
Compared to the “old” Keynesian model, this income variable is less
statistically significant and the model explains less variance over time.
(Even these figures overstate average income’s effect. This is due to
compensating errors when calculating the average, as explained below.)
One could argue that using a 9-year average of income (4 years before,
the current year and 4 years into the future) is a better approximation of a
“lifetime” average income, but still produces results inferior to the “Old”
Keynesian model, as shown in Eq. 2.2.3.2.1.3:
CT = 0.56(Y – TT )AV + 0.44(TT ) – 0.29(GT& I ) – 4.89PR

(t =) (6.8) (6.4) (–1.8) (–1.4)
+0.30DJ–2 + 2.90XRAV – 265.62POP16 + 0.01POP
(1.5) (–1.8) (–0.9) (1.4)
+0.14ICC–1 + 56.5M2AV + 0.32 CB2
(0.3) (5.0) (4.1)
R2 = 90.0% D.W. = 2.9 MSE = 33.23
(2.2.3.2.1.3)
Results using a 9-year average of income (the current year and 8 years
into the future) is also a better approximation of a “lifetime” average
income than a 4-year average, but still produces results inferior to the
Keynesian model.
We conclude average, or “lifetime” income variables do not explain
as much variance in consumption as models using the “Old” Keynesian
“current income only” formulation of income.
The fact that DSGE/Modigliani/Friedman-type income averages used
in DSGE models explain any consumption variation at all may be because
of the “errors in variables” problem, not because they are to some degree
correct. The errors in variables problem is that sometimes, a data series
used represents an error-ridden version of the real underlying data series.
If so, test results will understate the relationship that exists in reality, i.e.,
the true relationship between income and consumption. Estimates will
be biased downward (Johnston 1963). The fact that we get any positive
results at all may be because average income may function like an error
ridden approximation of current income.
We can test for errors in variables two ways: (1) We can assume current
income is the real variable driving consumption, and average income is the
imperfect substitute. (2) Alternatively, we can assume average income is
the real variable, and current income the imperfect substitute.
1. If multiyear income averages are an imperfect substitute for current

income, we would expect tests to show the average income variable
explains less variance, and has coefficients on the income variable
with lower levels of statistical significance. That is what results above
show. Hence, we accept this hypothesis.
60 2 METHODOLOGY
2. By comparison, if we hypothesize that average income is the real vari-

able, and current income is just an imperfect substitute, we would
expect a current income variable to explain less variance in consump-
tion than an average income variable. This was not what we found.
Hence, we reject this hypothesis.
Tests using any one future year’s disposable income hugely reduce the
explanatory power, compared to using current year income, no matter
what future year is used. This again leads us to reject the hypothesis that
average income is a better determinant of consumer behavior than current
income. As an example, we show the results for the same model as tested
above, except that we substitute next year’s actual income for this year’s
as the income variable in the test. Results show that this reduces explained
variance from 94.8% (using current income) to 79.7% (using next year’s
income).
CT = 0.19(Y+1 – TT ) + 0.50(TT ) – 0.24(GT& I ) – 5.21PR

(t =) (1.5) (4.9) (–1.2) (–1.2)
+0.50DJ–2 + 3.63XRAV – 355.84POP16 + 0.02POP
(1.2) (1.4) (–0.7) (2.2)
–0.12ICC–1 + 84.3M2AV + .27 CB2
(–0.2) (3.4) (2.5)
R2 = 79.7% D.W. = 1.9 MSE = 47.01
(2.2.3.2.1.4)
Similar results are obtained using other single future years
Using the average of four future years income explains more variance
(See Eq. 2.2.3.2.1.2) than any single future year, which seems like a con-
tradiction since each future year does so badly. But this is a consequence
of compensating errors in averaging. The average of the yearly changes in
the 4-year period is a better proxy for current income, than any one future
year change. For example, the yearly changes for the year 2006 com-
pared to the next four future years are given in Table 2.2.3.2.1(1). This
implies the variance in consumption explained using average income mod-
els (Eq. 2.2.3.2.1.2) actually substantially overstates the extent to which
consumers can accurately determine future income and use it as a basis for
current period consumption decisions. The success seems more related to
compensating errors, i.e., because the average is a less imperfect proxy for
current income alone than anyone of the years is. The rest appears due to
the errors in variables problem discussed above.
Table 2.2.3.2.1(1) Current and four future year annual changes in income
(real GDP) (Billions of 2005 Dollars)
Year Change in GDP
2006 (“Current Year”) $186.4

2007 243.2
2008 277.8
2009 –56.7
2010 231.3
Av. 2007–2010 $173.9
We conclude the Keynesian current income formulations of the con-

sumption function are more accurate than the average income formula-
tions used in DSGE studies.
2.2.3.2.2. Does the Euler Condition Ct = Ct+1 = . . . Ct + n ..+

Technology Shocks Hold?
A standard DSGE model’s conclusion is that if consumers are intertem-
poral utility maximizers, consumption levels will be the same in every time
period, or will not vary more than unpredictable future changes in pro-
ductivity due to technology improvements. Constant consumption levels
were also suggested by Modigliani’s (1963) Life Cycle Hypothesis. How-
ever, tests below show there simply is no econometric support for this
conclusion.
Consumption growth since 1960 has been unrelenting. In real (2005)
dollars it has grown from $1.785 trillion dollars to $9.315 trillion. In per
capita terms, it has grown from $9,880 to $ 30,150 The per capita average
annual growth rate over this 50-year period was 2.24%, a number identical
to the growth in the worker productivity index in the Economic Report of
the President, 2011 and 2013, B-49. If the APC remained constant over
the period, this is what we would expect to see. The earlier comparison of
Kuznets and Heim results indicated relatively little change in APC since
Kuznets’ first 1869–1929 sample.
To determine how well DSGE models fit consumption data, we need to
determine how much of the year-to-year variance in consumption can be
traced to the yearly growth in worker productivity indexed in the Economic
Report of the President (ERP). In DSGE theory, this should explain most
or all changes in consumption. Alternatively, the data may show that on
a year-to-year basis, most of the changes in consumption are explained by
more Keynesian-type determinants such as business cycle fluctuations.
62 2 METHODOLOGY
To estimate what percentage of the year-to-year changes in consump-

tion were actually caused by productivity growth, we will run three tests,
each testing two models.
1. The first test will test the following two models:

(a) A “simple” model of consumption spending as a function of
current year productivity growth and current year disposable
income (minus the part of disposable income attributable to
TFP’s current year increase).
(b) A more sophisticated model in which consumption is a func-
tion of current year productivity growth, disposable income,
and 10 other variables found in this study to be determinants of
consumer spending. These variables include disposable income
(minus the portion associated with productivity growth), the
government deficit variables (taxes and spending), the current
prime interest rate, the NYSE stock index lagged two periods,
the 4-year average of real trade-weighted exchange rates for the
USA, the ratio of young to old people in the population, the
population itself, the Index of consumer confidence lagged one
period, the 3-year average of the savings components (i.e., non
M1 components) of the M2 money supply for the period 2–4
years ago, and real consumer borrowing levels.
2. The second test will be like the first, except done in per capita instead
of aggregate consumption terms. It will also have the same simple
and sophisticated sub-models.
3. The third model will be identical to the per capita models in test two,
except current TFP and its four lagged values are included to test the
possibility that a TFP generated gain in this year’s income might only
slowly over time reflect itself in increased consumer spending
The First Set of Tests

In our first set of tests, we test aggregate consumption using the simple
two variable model. We determine the percentage of variance in con-
sumption the two variables together (productivity and disposable income
minus the part attributable to productivity growth) can explain. Having
established the total amount of variance in consumption both together
can explain, we then test each variable separately using the “First Out”
form of stepwise multiple regression. This allows us to determine what
portion of the variance only the withdrawn variable can uniquely explain.
Withdrawing the productivity index variable from the two explanatory

variable model will reduce our measure of total explained variance by this
unique amount. Similarly, withdrawing only the disposable income vari-
able reduces the total variance (R2 ) explained by the amount that only
disposable income can uniquely explain.
Part of the total variance explained by the two variables is that which
can be explained equally well by either, i.e., the part representing the level
of multicollinearity between the explanatory variables.
Results are presented in Table 2.2.3.2.2(1). Results indicate that total
variance explained by the two variables was 59.1%. The productivity index
uniquely explains 5.3 % of the variation. If all of the variation that could
be explained equally well by either variable (33.7%) was assumed also due
to productivity growth, it still only means 39.0% total of 59.1% of vari-
ance is explained by productivity growth. 20.1% is uniquely explained by
changes in non-TFP induced yearly changes in disposable income. Dis-
posable income can explain as much as 53.8% of the total of 59.1% of
consumption variation attributable to both variables, when the portion
attributable to either variable is included.
This suggests the DSGE theory that consumption over time should
be constant, except for unanticipated changes due to TFP, is based on a
faulty theory (rational expectations) that ignores the year-to-year effects
of the business cycle, consumer confidence, interest rates, etc., which are
not foreseen until they actually occur. To assure that productivity changes
do not impact after a lag, we reran the simple total productivity index/
disposable income model using a lagged value of the index. Lags from (-1)
to (-10) were tested. They caused TFP to become statistically insignificant.
The 11 variable sophisticated model (model #2 of test #1) explained
95.1% of total variance, with current year productivity index uniquely
explaining only 1.4% of the variance. The other determinants accounted
for 56.0% uniquely. Either the productivity index or the other 11 variables
could explain equally well the remaining 37.7%.
The Second Set of Tests
The second set of tests repeats the simple and sophisticated tests done in
test one, except in per capita spending, rather than total spending, terms.
In the simple model, consumption and disposable income (after the por-
tion attributable to yearly productivity growth is deducted) are run in per
64
2 METHODOLOGY
Table 2.2.3.2.2(1) Yearly variation in consumer spending 1960–2010. Explained by yearly variation in TFP compared to
other determinants of consumption
Variance (R2 ) Per Capita consumption Per Capita consumption

Total consumption (Using current TFP only) (Using current TFP and four lags)
Explained by Simple Sophisticated- Simple Sophisticated Simple model Sophisticated
model (%) model (%) model (%) model (%) model (%)
Full model 59.1 95.1 81.5 94.1 67.1% 95.4

TFP uniquely 5.3 1.4 0.3 1.7 23.6% 2.9
Other variables uniquely 20.1 56.0 58.4 89.7 7.1% 48.1
Either TFP or others equally well 33.7 37.7 22.8 2.7 36.4 44.4
capita terms. In the sophisticated model, the deficit, money supply, and
consumer borrowing variables are also measured in per capita terms.
In the simple model 81.5% of the total consumption is explained by the
full model, which includes both the disposable income per capita variable
and productivity index as separate variables. Removing the index reduces
R2 to 81.2%, implying the productivity index can uniquely explain only
3/10 of 1% of consumption’s yearly variation. By comparison, remov-
ing the disposable income variable indicates non-TFP disposable income
changes (such as those due to a recession) uniquely explain 58.4% of the
yearly variation in per capita consumption over the 50-year period. The
remaining 22.8% of the explained variance can be equally well explained
by either variable.
Test two’s more sophisticated model of consumer behavior included
not only (non-TFP) changes in disposable income and TFP’s effect on
income but also interest rates, wealth, exchange rates, the mix of young
and old in the population, the overall population size, the consumer con-
fidence index, savings accumulations in the prior 3 years, and access to
borrowing. All variables together, including TFP, explained 94.1% of the
total year-to-year variation in consumption over the 50-year period tested.
Removing the productivity index indicated productivity growth could only
uniquely explain 1.7% of the year-to-year variation in consumption (4.4%
including the variation that could be explained by either the productivity
index or the other variables). The rest of the variables uniquely explained
89.7% of year-to-year consumption variance, 53 times as much as the
productivity index could uniquely explain. This becomes 92.4% if all the
variance that could be explained by either productivity or the group of
variables equally well was assigned to this group of non-productivity index
variables.
The Third Set of Tests A third set of test results are also in per capita terms.
The models are identical to those in test two, except the current productiv-
ity index and four lagged values of it are included. This was done to test
the possibility that a productivity gain in this year’s disposable income
might only slowly lead to changes in consumer spending. For the simple
model, total explained variance was 67.1%, of which the productivity index
explained 23.6% uniquely. The disposable income variable explained 7.1 %
uniquely. Either variable could explain and additional 36.4% of the vari-
ance. For the sophisticated model, total explained variance was 95.4%, of
which only 2.9% could be uniquely explained by current year and four lags
of the productivity index. Forty-eight percent could be explained uniquely
66 2 METHODOLOGY
by the combined effects of the other determinants of consumption. An

additional 44.4% could be explained equally well by either variable.
The data show that variables other than unexpected changes in techno-
logy account for most variation in consumption. In a rational expectations
world that shouldn’t happen; what should happen is Ct = Ct+1 = . . . , Cn
2.2.3.2.3. Does the Lucas Critique Hold? Testing the Constancy of

Policy Change Effects over Time)
Closely related to DSGE is the Lucas Critique (1976). The Lucas Critique
suggests that if we tested the effects of fiscal (or other) economic policy
changes in the past, tests in different time periods would show different
results. This would prove Lucas’s contention that past results of policy
changes can’t be used to predict the effects of the same type changes
in the future. Our tests of fiscal policy changes provide no support for
Lucas’ assertion. Rather, they show the effects of changing government
tax, spending or interest rate policy are very similar from decade to decade.
For example, our results for the consumption function are shown below
for different time periods, using the Cowles model cited in Section 4.1
(Table 2.2.3.2.3(1)).
Results are quite similar for all periods sampled for most variables. For
government tax cut deficits the stimulus effect (net of crowd out effects)
is consistently slightly negative, for spending increase deficits the negative
effect is larger. Both findings are significant in all periods sampled. The
prime interest rate (monetary policy variable) was significant in all four
Table 2.2.3.2.3(1) Robustness over time: (2SLS detrended model; subsamples

of 1960–2010 data set)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y–T) 0.48∗ 0.43∗ 0.52∗ 0.52∗

T 0.56∗ 0.55∗ 0.41∗ 0.48∗
GT&I –0.39∗ –0.40∗ –0.28∗ –0.31∗
PR –9.98∗ –9.88∗ –8.60∗ –9.39∗
DJ–2 0.43∗ 0.37∗ 0.73∗ 0.64∗
XRAV 1.44 1.88 1.92 1.52
POP16/65 –418.25 45.17 –758.74∗ –502.82∗ ∗
POP 0.018∗ 0.024∗ 0.016∗ 0.016∗
ICC–1 0.37 0.61∗∗ 0.59∗ 0.65∗
M2AV 46.31∗ 49.84∗ 18.64∗ 22.03∗
CBOR 0.12∗ 0.12∗ 0.12∗∗ 0.10∗
Significance levels: ∗ = 1%, ∗∗ = 5%, ∗∗∗ = 10%.

Table 2.2.3.2.3(2) Robustness over time: (2SLS model 5.2, 1960–2010 data)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(ACC) 0.30∗∗∗ 0.30∗∗∗ 0.23∗∗∗ 0.23∗∗∗

(TT ) 0.23∗ 0.23 0.39∗∗∗ 0.29∗∗
(GT&I ) –0.26∗∗∗ –0.27∗∗∗ –0.39∗∗∗ –0.30∗∗∗
(PR–2 ) –6.89∗∗ –7.95∗∗ –4.48∗ –4.74∗
(DJ) 0.53∗∗ 64∗ 0.42 0.58∗∗
(PROF) 0.03 0.00 0.03 0.05
(XRAV ) 5.89∗∗ 6.11∗∗ 2.72 2.26∗∗
(POP) 0.004 0.005 0.008 0.004
(BOR–1 ) 0.06 0.02 0.13∗ 0.15∗∗
Significance levels: ∗∗∗ = 1%, ∗∗ = 5%, ∗ = 10%.
samples, and at similar magnitudes. The magnitude of the exchange rate

effect was nearly identical and significant in all four samples, as was the
M2 measure of past savings and consumer borrowing. The consumer
confidence level was significant in three of the four periods.
Findings for the effects of fiscal policy on investment were also stable
over various time periods. Table 2.2.3.2.3(2), which shows this for
investment spending, using the investment model in Section 5.2.
Generally, results are quite robust for all periods sampled; signific-
ant variables remain significant (though level of significance may vary),
and insignificant variables stay insignificant, but there were exceptions.
The significant determinants of total investment are the accelerator, tax
cut deficits, spending deficits. Interest rates, stock market levels, and the
exchange rate.
Depreciation, capacity utilization, population levels, and business bor-
rowing were not found to be statistically significant determinants of total
investment in at least three of the four samples.
These tests just echo Eckstein’s tests of over 30 years ago. He also found
no empirical support for the Lucas notion that announcing a policy change
is coming allows people to game it, resulting in different effects when
policies are enacted than expected based on past experience:
Policy announcements still seem to be interpreted as carrying little or no

information. Policy is a source of stochastic variation, but no more so than
other sources to which households and businesses must respond. There is
no empirical basis to the assertion that the models are invalid beyond their
usual stochastic risk bands because policies systematically change parameters.
68 2 METHODOLOGY
So far, the evidence suggests that changes in policy regimes are not among
the principal causes of simulation error, that forecast error is largely created
by other exogenous factors and the stochastic character of the economy.
(Eckstein 1983, pp. 50–51)
In addition, Fair’s single equation tests of the rational expectations hypo-

thesis generally reject the hypothesis and notes that if expectations are
not rational, the Lucas critique is not likely to be a problem. (Fair 2004,
p. 206)
2.2.3.2.4. Comparisons with FRB/NY Model

We were able to test a model conceptually similar to the New York Federal
Reserve bank’s DSGE model, though much smaller and simpler, and with
less sectors, developed by Sbordone et al. (2010).
In this simplified model, consumption is the only source of spending.
The Euler equation for the model was given as
1/Ct = Et [βbt+1 /bt ∗ 1/Ct+1 ∗ Rt /(Pt+1 /Pt )] (Sbordone Eq. 3.3)
we can substitute consumption of final good Ct with its output Yt because

in our model consumption is the only source of demand for the final good.
Therefore, market clearing implies Ct = Yt . (p. 28)
A log-linear approximation of the Euler equation (3.3), after some
manipulation, gives (p. 28)
yt = Et yt+1 – (it – Et πt+1 ) – δt (Sbordone Eq. 3.4)
where –δt = Et log(βbt+1 /bt ) is a time-varying factor for discounting future

utility
This DSGE model assumes perfect knowledge of the probability dis-
tribution with which future events will occur. Therefore, we use the
actual value of next year’s future income and inflation as their expec-
ted value when testing the model. The data used in the test below are
annual; the real federal funds rate is defined as the nominal prime rate
minus 3% points, inflation is CPI inflation (not core CPI, as used in the
Sbordone simple DSGE model). Since bt+1 /bt is only an exogenously
determined random variable, we omitted it, which should increase the
explanatory power of the model compared to including it, since it is purely
stochastic, and definitionally it explains nothing over time, but creates
additional unexplained variance from period to period. Estimation is in

first differences, 1951–2009.
Testing the model given in Sbordone’s Eq. 3.4 gave the following
results:
(Estimated 1960–2010 data): yt = 0.78yt+1

(t =) (7.9)
+19.20 (it – 3 – πt+1 ) + e
(1.6)
R2 = –0.03; DW = 1.9
(2.2.3.2.4a)
(Estimated 1984–2007 data,: yt = 0.96yt+1

More similar to Sbordone’s (t =) (14.5)
Sample period) + 26.67 (it – 3 –t πt+1 ) + e
(1.9)
R2 = –0.19; DW = 2.0
(2.2.3.2.4b)
(Estimated 1960–2010 data ct = 0.59 yt+1

Ct used instead of yt , since (t =) (9.4)
this is technically a consump- + 8.84 (it – 3 – πt+1 ) – +e
tion model only) (1.3)
R2 = 0.03; DW = 1.6
(2.2.3.2.4c)
Clearly this particular simplified DSGE model does not explain much vari-
ance. This suggests a fundamentally Walrasian market clearing, perfect
foresight model of human and market behavior does not explain much
of how and why economies fluctuate from year to year in the real world.
The model has much more explanatory power using lagged GDP in
predicting current GDP than does using expected future GDP and infla-
tion. In addition, when using lagged GDP, the interest rate now has the
right sign; it had the wrong sign in the previous models:
(Est. using Lagged Y; yt = 0.85yt–1

1960-2010 data) (t =) (13.4)
–14.42 (it – 3 – πt+1 ) + e (2.2.3.2.4d)
(–1.3)
R2 = +0.22; DW = 2.0
70 2 METHODOLOGY
Using only 1984–1907 data, lagged GDP is more statistically significant,

but its coefficient is essentially the same as with the Sbordone et al. model
for the same period, shown above.
(Est. using Lagged Y; yt = 0.92yt–1

1984-2007 data) (t =) (12.4)
–6.67 (it – 3 – πt+1 ) + e (2.2.3.2.4e)
(–0.4)
R2 = –0.17; DW = 2.2
In both cases the backward-looking adaptive expectations model better

explains the data than the forward-looking rational expectations model
assumed in DSGE models. In natural logs, the model results were similar.
However, to avoid non-positive data, not testable in logs, the interest rate
data used was prime rate data, not prime rate –3 = federal funds rate)
(Est. using logs 1984-2007 data) yt = 1.00 yt+1

(t =) (11.5)
+0.009 (it – πt+1 ) + e
(1.9)
R2 = –0.08; DW = 2.2
(2.2.3.2.4f)
(Est. using logs; Lagged Y; yt = 0.89 yt–1

1984-2007 data) (t =) (12.7)
–0.006 (it – πt+1 ) + e
(–1.0)
R2 = –0.09; DW = 2.2
(2.2.3.2.4g)
To examine out-of-sample performance, the Sbordone model (in first dif-
ferences of levels, not logs) was reestimated using 1957–2000 data, and
produced the following results:
(Est. using Lagged Y; yt = 0.83 yt–1

1960-2000 data) (t =) (9.1)
+9.23 – (it – Et πt+1 ) + e (2.2.3.2.4h)
(0.9)
R2 = 0.03; DW = 2.2
Table 2.2.3.2.4(1) Forecasts of observable variables
Quarter GDP% Qtr Chge Annual Chge DSGE model Forecast vs. actual
Est. forecast
2002:IV 10,095.8
2003: I 10,138.6 0.0042 1.64 1.64 2003 qtr. av.
II 10,230.4 0.0091 3.64 3.64 3.1% DSGE
III 10,410.9 0.0176 7.04 3.6 4.0%Actual
IV 10,502.6 0.0088 3.52 3.55 (9/10 of 1%)
2004: I 10,612.5 0.0105 4.20 3.0 2004 qtr. av.
II 10,704.1 0.0086 3.44 3.0 3.1%DSGE
III 10,808.9 0.0098 3.92 3.0 3.7%Actual
IV 10,897.1 0.0082 3.28 3.3 (6/10 of 1%)
2005: I 10,999.3 0.0094 3.76 3.3
Source of Actual GDP Data: ERP 2006, Table B2.

Note: Annualized Growth Rates at variance with those in Chart 4; DSGE estimates of growth rates on
Chart 4 are visual “guesstimates,” since data for each observation not provided with chart.
Using these estimated model parameters, the model was then used to
calculate estimated values of (yt ) for the out-of-sample period 2001–
2009. The Sbordone et al. model estimate of average yearly change in
GDP was 1.34%, 36% below the actual average change of 2.1% in the
absolute value of yearly changes). By comparison, for the Cowles model
(described below in this paper’s VAR section), the average out-of-sample
error was less than half of one percent (46/100) compared to Sbordone’s
1.34%. The Sbordone DSGE model out-of-sample error is 2.9 times as
large.
Other Tests of the Sbordone et al. (2010) model

Table 2.2.3.2.4(1) from Sbordone et al. (2010, p. 36) shows forecasts
from 2003:1 to 2005:1. Numerical results are only presented graphically;
actual numeric values can only be approximated. Results appear to indicate
the changes in GDP forecast by the model was at considerable variance
with the actual changes in GDP in most quarters.
Error Comparison with Cowles Model:

Model 2003 2004
Cowles 9/100 of 1% 28/100 of 1%

DSGE 90/100 of 1% 60/100 of 1%
72 2 METHODOLOGY
For the Cowles model developed later in this paper (see VAR section
below), the error for 2003 was much smaller: 9/100 of 1% compared
to 90/100 of 1% for the DSGE model above. For 2004, the Cowles error
of fit was 28/100 of 1% compared to 60/100 of 1% for the DSGE model
above.
2.2.3.2.5. Comparisons of a Simplified FRB/US Model to This

Paper’s Cowles Model
The Federal Reserve maintains a large, 375 equation model of the
US economy, the Federal Reserve Bank/US (FRB/US) model, initially
developed by Brayton and Tinsley (1996). Roughly 50 equations are beha-
vioral. It was intended to replace the older Keynesian-style FRB/MPS
model developed by deLeeuw and Gramlich (1968) with a newer general
equilibrium structure that incorporated a forward-looking rational expect-
ations model for making consumption and investment decisions. It was
also designed to address the Lucas critique through built-in consideration
of the rational expectations assumption on decision making (Edge et al.
2010).
The model is generally considered a DSGE model, though one con-
siderably larger than others. The Board itself currently describes it as
“The FRB/US model is a large scale estimated general equilibrium model
of the U.S. economy” (FRB 2015), noting that one distinctive feature
that distinguishes it from (other) DSGE models is “its ability to switch
between alternative assumptions about expectations formation of eco-
nomic agents.” Individual Fed staff have also referred to the model as
a DSGE (Chung 2015), noting:
In this note, I focus on the effects of forward guidance and compare the pre-
dictions of three structural models: FRB/US, EDO and the model of Smets
and Wouters (2007), which is a representative class of dynamic stochastic
general equilibrium (DSGE) models . . . All three models considered here
share a core New Keynesian structure. (p. 13)
Other Fed staff do not consider it such (Wilcox 2015), presumably

because of its unusual size and the flexibility in modeling expectations
either rationally or adaptively noted above. These differences are acknow-
ledged, but considered here as variations in DSGE methodology rather
than a fundamentally different kind of modeling. After all, there are only
three basic methodologies for modeling the macroeconomy – DSGE,

VAR, and Cowles modeling. The FRB/US model more closely fits the
DSGE methodology than a VAR or Cowles methodology though it
contains elements of both.
The key equations in FRB/US represent specific implementations of
a method developed by Tinsley (2002) in an attempt to improve what
he considered the poor ability of rational expectations models to explain
the data successfully. As Tinsley noted: “empirical rejections of rational
expectation restrictions are the rule, rather than the exception, in macroe-
conomics.” The method is referred to as the polynomial adjustment cost
approach (PAC). Each of the key consumption and investment equations
in the model use the following general form for each decision variable
(noted as yt ):
yt = a0 (y∗t–1 – yt–1 ) + k=1,m–1 ak yt–k + Et–1 j=0,∞ dj y∗t+j + εt

(2.2.3.2.5.1)
Where is the first difference operator, Et–1 represents expectations based

on information available at t – 1, and ε is an error term that is assumed to be
serially uncorrelated. The equation decomposes the determinants of y into
three elements:
• The lagged deviation of the decision variable from its target (y∗t–1 –yt–1 )
• Lagged changes in the decision variable (y)
• A weighted sum of expected future changes in the target variable (y∗ )
And for consumption and residential investment, expected income is

defined as
Permanent income. In the PAC equations for components of consump-
tion and for residential investment, the target levels of spending depend
on expectations of future income (the target variable). An important char-
acteristic of these expectations is that they are computed using a 25 percent
annual rate of discount, a value that is based on micro evidence about indi-
viduals’ income uncertainty.(Source: FRB/US Equation Documentation,
2014)
One criticism of the FRB/US model is that not all its parameters were
estimated; some were calibrated. Fair (2004, website version) noted that
74 2 METHODOLOGY
critical parameters in the Federal Reserve Bank/US (FRB/US) model

were imposed, not estimated, and hence their validity could not be
assured:
The FRB/US model . . . has strong interest rate effects . . . In most of the
expenditure equations real interest rate effects are imposed rather than
estimated. Direct tests of nominal versus real interest rates . . . are not done,
and so there is no way of knowing what the data actually support in the
FRB/US expenditure equations. (p. 120)
(Brayton et al. (April 2014) acknowledge as much.)
The consumption function for the FRB/US model (Brayton and

Tinsley 1996, p. 17) is given as:
ct = –0.12(ct–1 – ct–1 ∗ ) + 0.17 lags 1 (ct–1 ) + 0.75 leads∞ (c∗e

t+1 )
+ 0.09yt R2 = 0.54 SEE : 0.0032; (2.2.3.2.5.2)
The data set used to test the model spanned the quarterly periods:
63:1–95:4.
The following definitions are used in this and other consumption
equations below:
c- log consumption (including service flow of stock of durables)

Y – income (labor + transfer + property)
y – log Y
V = Expected wealth = leads∞ (Ye )
v = log V
Strans – transfer wealth/V
Sprop – property wealth/V
Sstock – value of corp. equity/V
So – other net financial and tangible assets/V
X – aggregate output gap
The model explains slightly more than half the variance in total consump-
tion, and even less for subcomponents such as motor vehicles (R2 = 43%),
and other durables (R2 = 34%). For residential construction, R2 = (60%).
For the business investment categories, producer durables (40%) and
inventories (42%) results are also unimpressive. Hence, the model does
not seem to represent a highly accurate representation of what economic

factors shape consumer and investment spending.
The equilibrium relationship, describing desired levels of consumption
as a function principally of wealth, but also of the output gap is given by
C∗ = 1.0v + 0.62strans – 0.15 sprop + 0.52 sstock + 1.28 so

+ 0.013X (no regression information given;
estimates may be calibrated)
The dynamic consumption equation is a weighted average of the behavior

of life cycle and liquidity – constrained households. The share of income
associated with the latter group is about 10 percent, based on the estim-
ated coefficient on contemporaneous income growth. This direct effect of
income growth is in addition to the contribution of income growth in the
VAR forecasting model for expectations of target consumption that was used
in estimation of the dynamic consumption equation. Lifecycle consumers
adjust spending sluggishly, with a mean response to shocks (surprise) of
about two years. (p. 17)
This original model has been updated over the years. The 2014 ver-
sion (for consumer nondurables and nonhousing services only) looks like
this:
ct = +0.11(ct–1 – ct–1 ∗ ) + 0.46 lags 1 (ct–1 ) + 0.748 leads∞ (Y∗e )

(t =) (3.8) (4.8) (2.2)
+0.252yt R2 = 0.35 SEE : 0.0042
(2.2)
(2.2.3.2.5.3)
The data set used to test the model spanned the quarterly periods: 68:3–
2013:4.
A 5 variable core VAR model is used to model forward expectations of
income and consumption, with additional variables added for some sectors
(Brayton et al. 1997).
In addition, some allowance is provided for a small portion of con-
sumers to be New Keynesian “rule of thumb” consumers. In the 2014
version it is 18% of consumers. However, the approximation of FRB/US
tested here allows the data to decide what portion of consumers are “rule
of thumb,” as distinct from rational expectations based decision makers.
76 2 METHODOLOGY
The data indicate that most variation in consumer spending is caused by

rule of thumb consumers.
Estimating the Out-of-Sample Fit of the Simplified

FRB/US Model
We tried to approximate the 2014 nondurables and services consump-
tion model shown above with estimates from 1960 to 1990 data. We
have done this both in logs, and in levels of the data to facilitate com-
parison with the more Keynesian-looking Cowles consumption models
in this paper. We will use the parameter estimates from the tests on the
1960–1990 period to see how well the model estimates actual consump-
tion in the decade after the estimation period 1991–2000. Because of
the leads required for some variables, this is the latest full decade we can
forecast.
To be sure a correlational model’s parameter estimates are truly indic-
ative of the underlying structure of the economy and, not just spurious,
the model must perform (approximately) as well in periods outside the
estimation period as within. The underlying structure of the economy
does not seem to change much from decade to decade (which is what our
Cowles models show – see the Lucas Critique comparisons previously dis-
cussed, and the graphs further below which show the same consumption
and investment models explain each of the 1960–2010 decades perform-
ance about equally well). Since the underlying structure is stable, if our
initial estimates of parameters got it right, they should nearly as accurately
explain how the economy operates in the decade following estimation.
This is particularly important for models that forecast the future values of
economic variables from their behavior in the past.
The actual model definitions for the long-term equilibrium levels of
consumption (c∗ ) and income (Y∗ ) are complex and difficult to model
precisely with available data. However, the equation documentation notes
that the variable for long run expected average income can be expressed
as the expected weighted sum of future y∗ , which is what we use. We
assume future year income expectations are formed with perfect foresight,
i.e., correctly estimated; hence we use actual data on future year income
for the expected value in developing our equilibrium income aggregate.
And since long run equilibrium consumption is a function of long run
equilibrium income, we estimate long run desired (equilibrium) consump-
tion the same way, though with one less future value in the aggregate.
As required for consistency with the PAC method, these equilibrium
aggregates are the sum the first differences of component year’s incomes,
not their levels.
The variable ct–1 ∗ is the sum of five income (GDP) variables. Each of
the five income variables is comprised of the sum of the first differences
of current and five leads values of income; and the same year’s unem-
ployment rate (a proxy for the output gap) is subtracted from the income
aggregate. A lagged version would contain last year’s value, the current
and four lead values. This is our approximation of the consumption equi-
librium condition used in FRB/US. The ct+1 ∗e variable is estimated using
the average of the first differences of seven leads of the variable c∗e (or
Y∗e in the 2014 version). The unemployment rate in the same period is
subtracted from each of the income components. Because the dependent
variable was not stationarity, nor fully cointegrated with the right hand
side variables, a trend variable was added, resolving the stationarity issue,
increasing the reliability of the regression coefficients. It is not needed in
the out of sample projections using these corrected regression coefficients.
Because of the need to use data for leads, the latest out-of-sample full dec-
ade we could test was 1991–2000. The in sample estimation period was
1960–1990.
Using the 1960–1990 data, the model’s parameters were estimated as
ct = 0.0032(ct–1 – ct–1 ∗ ) – 0.06715 (ct–1 ) – 0.1185 leads∞ (ct+1 ∗e )

(t =) (4.3) (–0.6) (–0.7)
+0.56yt – 0.0002 Trend R2 = 0.78; SEE = 0.007; DW = 2.2
(8.9) (–1.7)
(2.2.3.2.5.4)
All variables are in logs, all c values are in real terms and taken from the Eco-
nomic Report of the President (ERP). Unlike the FRB/US model, which
assumes “rule of thumb” (i.e., Keynesian) consumers only account for
18% of consumption, this model allow the data to determine the actual
percentage. The “real” percentage is substantially higher, and as a result,
our approximation of the FRB/US model explains far more variance in
consumer spending than the actual FRB/US model. Hence, it is likely to
overstate the actual FRB/US equation’s ability to explain out-of-sample
variance.
The results indicate the current income variable (yt ) plus the trend
variable explain 70% of the 77% of the variance explained by the
model. By comparison, the three DSGE variables (plus trend) when
78 2 METHODOLOGY
used alone, explain only 15%. About 8% of the total variance can
be explained equally well by either Keynesian or rational expectations
variables.
The same model in levels rather than logs was estimated as
ct = –0.0016(ct–1 – ct–1 ∗ ) – 0.0021ct–1 + 0.3917 leads∞ (ct+1 ∗e )

(t =) (0.4) (–0.0) (2.9)
+0.3219yt R2 = 0.77; SEE = 23.00; DW = 2.1
(8.7)
(2.2.3.2.5.5)
No trend variable was necessary because in levels, the right hand
side variables were cointegrated with the dependent variable. Using
“first out” stepwise regression, the results indicate the current Keyne-
sian “rule of thumb” income variable alone (yt ) can explain 50% of the
77% of the variance explained by the model. By comparison, the three
DSGE variables explain only 37%. About 10% can be explained by
either.
Once estimated, we then evaluated the models ability to correctly estim-
ate the 10 years out-of-sample behavior of actual consumption which
followed. To get the future year out-of-sample estimates, we used the
parameter estimates obtained when estimating the model, and data for
the determinants of consumption for each of the 10 years after the end
of the estimation period that we were testing. The same procedure was
used with the Cowles models used for comparison. Results are given in
Table 2.2.3.2.5(1).
In the Cowles model, the same dependent variable (CND&S ), estima-
tion sample period (1960–1990), and regression technique (OLS) were
used as with the FRB/US model. This was done to ensure the only
differences between the models compared were the DSGE models use
of rational expectations model of consumption determination and the
Cowles model’s more Keynesian consumption function. The Cowles
model was also tested for endogeneity issues to determine if 2SLS was
a more appropriate technique, but none were found.
For comparison, results for this paper’s Cowles model of consump-
tion are also noted above. They are also estimated using 1960–1990
data, and fit to the 10 year out-of-sample period following. The
Cowles model tested on the 1960–1990 data to obtain parameter
estimates was:
Table 2.2.3.2.5(1) Error of fit of a model similar to FRB/US’S nondurables

and nonhousing services consumption model compared to Cowles model (yearly
change in ND&S consumption as a % of total ND&S consumption)
Year DSGE Cowles DSGE Cowles
Log Log Levels Levels
Model Model Model Model
1991 24/100 of 1% 7/100 of 1% 1.31% 1.02%

1992 10/100 11/100 49/100 1.03
1993 3/100 5/100 1.13 76/100
1994 8/100 6/100 37/100 1.34
1995 12100 0/100 93/100 46/100
1996 15/100 1/100 65/100 25/100
1997 2/100 2/100 41/100 14/100
1998 2/100 4/100 1.58 1.24
1999 2/100 4/100 1.90 43/100
2000 2/100 9/100. 2.78 38/100.
Error 9/100 of 1%1 5/100 of 1%1 1.15%1 71/100 of 1%1
10 yr. Avg 11/100 of 1%2 6/100 of 1%2 1.36% 2 82/100 of 1%2
1 Absolute value of error.

2 RMSE.
CT = 0.40(Y – TT ) + 0.29(TT ) – 0.14(GT& I ) – 4.85PR

(t =) (3.5) (2.4) (–1.8) (–1.9)
+0.60DJ–2 – 1.19XRAV – 444.56POP16 + 0.018POP
(1.1) (–0.9) (–1.5) (2.8)
+0.47ICC–1 + 14.52M2AV + 0.06 CB2
(1.7) (1.2) (0.6)
R2 = 87.4% D.W. = 1.2 MSE = 19.85
(2.2.3.2.5.6)
The same model, but where all variables are in log form is
CT = 0.32(Y – TT ) + 0.15(TT ) – 0.13(GT& I ) – 0.0003PR

(t =) (2.5) (2.4) (–2.1) (–0.2)
–0.01DJ–2 + 0.033XRAV – 0.03POP16 + 1.74POP
(–0.7) (0.5) (–0.5) (4.0)
–0.003ICC–1 + 0.212M2AV + 0.05 CB2
(0.2) (2.2) (0.7)
R2 = 79.4% D.W. = 1.9 MSE = 0.008
(2.2.3.2.5.7)
80 2 METHODOLOGY
Variable definitions are as follows:

CT Total consumer spending
Y-TT Disposable income
TT Total government receipts
GT&I Total government spending
PR Real prime interest rate
DJ–2 Stock market index measure of wealth, lagged 2 years
XRAV Real exchange rate, average current and 3 previous years
POP16 Ratio of those over 64 to those under 21 in the population
POP Total population
ICC–1 Index of consumer confidence, lagged 1 year
M2AV M2 average, 2–4 years ago
CB2 Level of consumer borrowing
The actual average change in consumption was 1.92% for 2001–2010;
2.9% per year for 1991–2000
Using even a simpler metric, the consumption equation in the Cowles
model, specified in either levels or logs, also outperformed the FED/US
model. The metric used was the average actual change in consumer goods
spending for the 10 years, divided by the model’s predicted change:
• In levels, the Cowles average error in estimating yearly consumption

growth was $14.3 billion; for the FRB/US model it was $67.5 bil-
lion (2005 dollars). Actual average yearly growth was $190.3 billion.
The FRB/US average error was 4.7 times as large. Clearly the model
does not explain variation in consumption as well as the Cowles
model.
The model we used as a simplified version of the FRB/US explained far

more of the variation in consumption than the Fed’s own consumption
equation (77% vs. 35%); this was because we let the data decide what
portion of consumers were “rule of thumb,” compared to rational expecta-
tions type consumers. Most were Keynesian “rule of thumb,” and specified
this way, the model explains much more variance. Hence, the results above
for the simplified model likely overstate how well the FRB/US equation
actually explains out-of-sample data when used for forecasting. The Fed’s
earlier FRB/MPS model was more similar to a Cowles model than to the
FRB/US model (some would call it a Cowles model), its out-of-sample
forecasts probably were more accurate.
2.2.3.2.6. Factors Explaining the Poor Performance of DSGE

Models
Suppose the goal of a macroeconomic model building exercise was to
develop an engineering manual, reliably useful in identifying the variables
associated with actual year-to-year changes in the economy. Its equations
would extensively detail the structure of the American economy, as its para-
meters would be discerned from the actual performance of the economy
over time.
DSGE models are really not suitable for this. Though structural,
like Cowles models, their structure is arrived at deductively, from a
priori assumptions about consumer and business behavior. Sbordone
et al. (2010, pp. 25–28) noted that key among those assumptions was
that
• Expectations about the future are key determinants of today’s out-

comes; expectations are the main channel through which policy
affects the economy.
• Markets clear every period.
• Households are aware of the kind of future random events or shocks
which may occur and “crucially” knows the probabilities with which
these shocks may occur.
Fair (2012) noted the counter intuitive nature of these key DSGE
assumptions:
To some people, brought up under macro1 . . . (i.e., Cowles Commission

detailed forms of “old” Keynesian modeling) . . . the message . . . (of DSGE
models) . . . seems completely loony. How could one think that one or a
few maximization problems so well approximate how the aggregate data
behave . . . And how could one think that the households and firms know so
much about how the economy works that the assumption of rational expect-
ations is a good approximation? . . . Solow argued it was not worthwhile
engaging new classical economists in debate, arguing that “if the person sit-
ting next to you thinks he is Napoleon Bonaparte, the last thing in the world
you want to do is get into a discussion of cavalry tactics.” (p. 6) (language
in italics added)
Unlike DSGE, the theoretical structure of Cowles models is arrived at

inductively, through testing various hypotheses for consistency with the
real world. The theoretical hypotheses that explain the most variance
(while simultaneously being consistent with some economic theory) are
82 2 METHODOLOGY
taken to define the structure of the economy. For example, whether

current consumption is determined by current income alone, or by some
estimate of average future income, is decided by assumption in a DSGE
model, but by testing in a Cowles model.
DSGE models, like Cowles models, describe the behavior of the eco-
nomy within a theoretical structure, but the DSGE structure is highly
generalized and not easily used to obtain detailed estimates. Typically,
they are highly simplified models whose objective is to model the utility
maximization process, subject to a budget constraint, assuming profit max-
imization, immediate (or eventual) market clearing of the Walrasian type,
and the constraints of the production function. Such models typically do
not show the detail present in Cowles models about what determines the
various components of consumption and investment, exports and imports,
savings, and borrowing.
DSGE models do not answer the type of questions economists typically
like to ask, like:
• How do depreciation allowances affect investment, controlling for

interest rates and profits?
• How do changes in consumer confidence affect consumption, con-
trolling for wealth, income, interest rates and past savings?
• What specific variables drive demand for consumer durables and
how exactly does that compare with what drives the demand for
nondurables, or housing?
Cowles models are always detailed enough to provide answers to questions

like this.
Fair (2012, p. 6) pointed out the limited size and scope of DSGE
model, using one of the best known (Smets and Wouters 2007) as an
example. Fair notes the model has only seven variables, unlike Cowles
models which typically have scores or hundreds. Fair also cites problems
with the data. He notes:
1. Using same deflator for consumption and investment, and assuming

government and private sector workers work the same number of
hours
2. The model is over aggregated. The three components of con-
sumption and investment are driven by different things, yet these
components are not tested individually.
3. Inventory adjustments and imports are not included in the model,

no use of financial wealth data of the household sector, no use of tax
rates and government transfer payments.
Fair also argues it is not realistic to think that agents are sophisticated
enough to have rational expectations, and concludes the Smets–Wouters
model seems highly misspecified.
A more philosophical objection to DSGE methodology is that it is not
a modern way of deciding how the economy operates. It is not scientific
and inductive, but rather based on self-evident truths (“consumers max-
imize utility,” etc.) and deductions from them. This is a throwback to the
nonscientific methods used by the natural and moral philosophers of the
seventeenth and eighteenth centuries to determine what was “true” and
“real.” For example, Sims (2006) described the difference noting
aggregate DSGE models are story – telling devices, not hard scientific
theories. (p. 153)
For example, generally, DSGE models assume consumers can foresee

their economic future accurately (rational expectations), and use this abil-
ity to make accurate intertemporal decisions about how much to consume
in a given period compared to the next in order to maximize lifetime utility.
Such models generally conclude a utility maximizing consumer will con-
sume the same amounts in each period, absent unforeseeable technological
change effecting previous estimates of lifetime income.
DSGE modelers might work backward from an economic phenomenon
that actually occurred in a single or limited number of time periods, to (by
trial and error) pick a precise set of production and utility function para-
meters, which when applied to DSGE theory, produce a result consistent
with the observation. Or, if consumption were different in 2 years, a set of
parameters for production and utility functions which could explain that.
They calibrate the model to replicate the observation.
Fernandez-Villaverde (2010) found calibration unsatisfactory com-
pared to econometric methods, noting some newer models were “leaving
behind the rather unsatisfactory calibration approach.”
By comparison, the scientist would look at decades of, say, consump-
tion data, and empirically test a wide range of variables, put forth by a
wide range of theories, to see which one best explained the variation in
consumption over the whole period studied, and did so as well in one
84 2 METHODOLOGY
decade as the next. Part of how the modeler would decide they got the
model “right” would derive from the model’s ability to explain as well all
2-year variations in consumption, not just the one of special interest.
The scientist (a.k.a. Cowles or VAR modeler) would let the data
decide what variables are best included in a theory of the determinants
of consumption.
In this study, when we let the data decide, we find there simply is no
empirical support for DSGE’s key assumption that today’s consumption is
a function of (accurate) estimates of lifetime average income by consumers.
Without this, the DSGE assumption of consumers being able to accur-
ately estimate future income and therefore successfully be able to maximize
utility intertemporally simply collapses, as well as any policy change implic-
ations subsequently deduced from the theory, whose validity is dependent
on such assumptions.
Fair (2004, website version) has noted the limited empirical underpin-
nings of DSGE models:
The rational expectations (RE) assumption is hard to test and work

with empirically. The widespread use of this assumption has moved mac-
roeconomics away from standard econometric estimation toward calibra-
tion . . . (p. xv) . . . The methodology here is more empirically driven than
the use of calibration, which is currently popular in macroeconomics. (p. 5)
The Handbook of Econometrics describes, Vol. 5 (2001) describes DSGE

modeling in a similar way
DSGE model parameters are typically calibrated, not statistically estimated.

Micro – foundation general equilibrium modelers calibrate models to a
(sometimes) single equilibrium observation . . . . Calibration of an economic
model involves the setting of specified parameters to replicate a bench-
mark data set as a model solution . . . In calibrating a general equilibrium
model, for example, the numerical values of some of the model paramet-
ers are typically set exogenously, while others, the calibrated parameters,
are endogenously determined so as to reproduce the benchmark data as an
equilibrium of the model. (p. 3656)
Cooley (1997) described the difference between econometric and calib-

rated models in the following way:
The econometric approach that dominated research from the 1940s until
the 1980s (and perhaps still dominates) takes the observed data as a given
and uses it to determine the structure of economic models . . . the researcher

conditions on the data and searches for the economic world most likely to
have generated it. The calibration approach, in contrast, views the appro-
priate data or measurements as something to be determined in part by the
features of the theory. Some of the parameter values are chosen based on
the observed features of actual economies, as in traditional methods, but the
determination of others may be based heavily on theory (p. 10) . . . There
is a strong feeling that the methods currently used are too informal com-
pared to standard statistical econometrics. One issue that is frequently raised
about the use of calibrated models is that practitioners do not acknowledge
the uncertainty in their calibrated parameters and do not report sensitivity
analysis. (p. 15)
Nobel laureate Robert Solow (2010) also raised issues about how realist-
ically DSGE theory reflects economic reality. In congressional testimony
he decried the then-current situation in macroeconomics:
I do not think that the currently popular DSGE models pass the smell test.
They take it for granted that the whole economy can be thought about as if it
were a single, consistent person or dynasty carrying out a rationally designed
long-term plan, occasionally disturbed by unexpected shocks, but adapt-
ing to them in a rational, consistent way . . . . One important consequence
of this “representative agent” assumption is that there are no conflicts of
interest, no incompatible expectations, no deceptions. This cannot be an
adequate description of a national economy . . . An obvious example is that
the DSGE story has no real room for unemployment of the kind we see
most of the time . . . the only way DSGE and related models can cope with
unemployment is to make it somehow voluntary, a choice of current leis-
ure or a desire to retain some kind of flexibility for the future or something
like that. But this is exactly the sort of explanation that does not pass the
smell test.
David Colander (2010) has also criticized the policy usefulness of DSGE
models:
The economics profession failed society . . . because it over-researched a par-

ticular version of the dynamic, stochastic general equilibrium (DSGE) model
that happened to have a tractable formal solution, whereas more realistic
models that incorporated purposeful forward looking agents were formally
unsolvable. That tractable DSGE model attracted macroeconomists as a light
attracts moths. More and more macroeconomists are willing to draw strong
policy conclusions from their DSGE model, and hold them regardless of
86 2 METHODOLOGY
what the empirical evidence and common sense might tell them. Some of
the most outspoken advocates of this approach . . . admit the DSGE model
does not fit the data, but state that a model neither “can nor should fit most
aspects of the data” (Chari et al. 2009, p. 243). Despite their agreement
that their model does not fit the data, they are willing to draw strong policy
implications from it, for example, they write “discretionary policy making
has only costs and no benefits, so that if policy makers can be made to
commit to a rule, society should make them do so.”
In the literature review above we noted tests of the Smets–Wouters DSGE

model found it explained only 8% to 13% of the actual changes in the
economy over time.
One might ask: “If Chari, Kehoe and McGratten are right and a good
model neither can nor should fit the data, why is it that Cowles-type
models do it so successfully?” As we show below, Cowles models explains
year-to-year changes in the economy better but they are based on a mod-
ern form of Keynesian demand-driven theory, not DSGE theory. Do we
live in such an “upside down” world that a “bad” model explains reality
so much better than a “good” model?
It seems more plausible that modern Keynesian structural models – like
Fair’s and the model used in this paper for comparison with DSGEs – out-
perform DSGE’s because consumption decisions are more driven by the
variables they explicitly incorporate, like income, interest rates, exchange
rates, and the definition of income they use, compared to those in the
DSGE consumption model, like the form of the utility function chosen
and the consumer’s time preference rate.
The Movement Toward DSGE Modeling

That said, DSGE models do provide a way of incorporating the Lucas
critique into model building. The Lucas critique (1975) raised questions
about whether the response of the economy to past stimulus efforts, like
past tax cuts, could be used to as a guide when estimating the likely
effects of future tax cuts. Lucas thought that econometric estimates of
the effects of tax cuts in the past, even in well-controlled models, would
not provide accurate information on how people would react to future tax
cuts. Thus, it would not be possible for even the best Cowles models to
provide the information on the future effects of future economic policy
changes.
By comparison, Cowles structuralists believe key structural parameters
(like the marginal propensity to consume and save) change only slowly
(if at all) over time. Hence, they would argue next year’s effect of some
change in income on consumption is likely to be the same as last year’s
effect, ceteris paribus.
Fair notes choice of modeling method depends on one’s assumption
about rational expectations, where rational expectations means that, people
can (correctly) forecast their likely economic futures, and therefore make
decisions today about how to save and spend that will accurately maximize
their lifetime utility.
If rational expectations theory holds, when testing, we should explain
more variance in consumption using DSGE’s claim that current consump-
tion is determined by lifetime income, than is explained by the Keynesian
“current income only” hypothesis. Some research indicates this is not the
case. In testing, the more years – forward and/or backward added into the
average representing lifetime average income, the worse it gets at explain-
ing the effect of income on consumer spending (Heim 2008). Without
rational expectations, DSGE collapses to a Keynesian model (i.e., con-
sumption depends on current income only), or an adaptive expectations
model (e.g., the FRB/MPS), where consumer spending depends on both
current and past income.
We showed above that in typically structured consumption functions
C = f (disposable income, wealth, interest rates, etc.), current income
alone always explains more variance in consumption than long-term
income averages of the Modigliani “Life Cycle” or Friedman “Permanent
Income” type. (See section 2.2.3.2.1.). In short, “old” Keynesian models
explain the economy better than their DSGE and adaptive expectations
counterparts.
If so, one can ask why DSGE theory and its less empirical modeling
method still dominate macroeconomic thinking, and not Cowles or VAR
models? This was addressed by Eckstein (1983):
The relationship between the theoretical and empirical branches of eco-

nomics has never been an easy one. Our discipline has not followed the
model of the natural sciences in which theories are a response to previously
unexplained phenomena and enter the body of accepted doctrine only after
empirical testing (p. 29)
Finally, we note that Mankiw (2006), a founder of New Keynesian

DSGE theory, has also found DSGE has not produced useful results. He
88 2 METHODOLOGY
has pronounced the DSGE movement as something of an evolutionary

mistake in the development of macroeconomics:
New classical and new Keynesian research has had little impact on practical
macroeconomists who are charged with the messy task of conducting actual
monetary and fiscal policy . . . From the standpoint of macroeconomic engin-
eering, the work of the past several decades looks like an unfortunate wrong
turn . . . it is clear that the new classical economists promised more than they
could deliver . . . The new Keynesians can be criticized for having taken the
new classicals’ bait, and, as a result, pursuing a research program that turned
out to be too abstract and insufficiently practical. (pp. 39, 44)
David Colander et al. (2008) has recommend abandonment of DSGE and

a return to the structural modeling methods that prevailed during the
1940s–1980s, noting
[p]olicy economists need to go back to the engineering approach that eco-

nomists used up until the 1940s and 1950s . . . . It is time to return to an
engineering approach to macro policy that has long existed in econometrics,
and accept that one can, and should, search for relationships among mac-
roeconomic variables without worrying about the behavioral foundations of
those relations
The Cowles models used in this paper are consistent with Colander’s
recommendation.
2.2.4 VAR Models

This section of Chapter 2 is divided into four parts: (1) a brief introduc-
tion to VAR, (2) this paper’s out-of-sample performance comparison of
VARs and Cowles models, (3) comparisons of VAR performance to DSGE
and Cowles models by others, and (4) a more theoretical critique of VAR
models. This is included as a way of examining why VAR models seem to
perform so badly in this paper’s out-of-sample tests, particularly compared
to Cowles models.
2.2.4.1 VAR Models – Simple and Sophisticated

2.2.4.1.1. The Simple VAR Model
A second methodology for modeling the macroeconomy is the VAR
method. In its simplest form, a VAR is a way of projecting a variable’s
future direction and rate of motion as a linear vector that simply extends
its past direction and rate of motion. For very short future periods, peri-
ods too small for regime change to take place, this is a sound, scientific
approach to forecasting the future. High school physics students use sim-
ilar forms of vector analysis to determine (e.g.) where and when a boat
leaving a dock on one side of a river with a current will reach the other side.
The problem is, if you project far enough into the future, there will
eventually be regime changes (e.g., changes in the water current’s speed).
You must predict those accurately too if your forecasts are to remain accur-
ate. Because we cannot accurately foresee the future, this is not likely. For
this reason, it is not something VAR analysts try to do. Every VAR forecast
is accompanied by a strong ceteris paribus assumption. This limits the util-
ity of the simplest form of VAR to short run forecasting. As an example of
this problem, in structural models, testing may indicate 75 or more differ-
ent variables and lags are necessary to explain movements in the economy.
Changes in many of them are frequent and constitute a “regime change.”
Incorporating each would be important to the accuracy of a VAR forecast,
but would not typically be done in a simple VAR model.
2.2.4.1.2. The More Sophisticated VAR Model

Sims (1972, 1980) is considered the father of VAR modeling. Sims
acknowledges his work builds on Granger’s earlier (1969) work using VAR
methods to determine whether one variable can be considered a “causal”
determinant of another. A Granger model might look like this:
X0 = f (t=–1 to –j X(t) , t=–1 to –j Y(t) (2.2.4.1.1)
Sims (1972) notes that in using such a VAR
Granger has given a definition of a testable kind of causal ordering based on

the notion that absence of correlation between past values of one variable
X and that part of another variable Y which cannot be predicted from Y’s
own past implies absence of causal influence from X to Y. More precisely,
the time series Y is said to “cause” X relative to the universe U (U is a vector
time series including X and Y as components) if and only if, predictions
of X(t) based on U(s) for all s<t are better than predictions based on all
components of U(s) except Y(s) for all s<t. We will give content to Granger’s
definitions by assuming all time series to be jointly covariance – stationary, by
considering only linear predictions, and by taking expected squared forecast
error as our criterion for predictive accuracy. (p. 544)
90 2 METHODOLOGY
Granger’s definition of “causation” is what many economists would define

as the presence of a correlation whose causal, as opposed to spurious,
nature remains undetermined. It encompasses all observed non-zero cor-
relations between Y’s current periods’ values and the current value of X,
after subtracting the correlation of more current Y data with Y’s own past
trends. The remaining correlation with X would include spurious correl-
ations having no causal relationship to Y, or correlations between two
noncausally related variables, which show a correlation because both are
causally driven by a third variable’s motion. As such, to call the remain-
ing relationship Granger “causation” rather than Granger “correlation”
overstates the available evidence, and flies in the face of the old admoni-
tion: “correlation does not imply causation.” As we show below, adherence
to Granger’s notion can cause biased VAR projections of variables like
the GDP.
Sims’s (1980, Econometrica) presents a more sophisticated VAR model
that includes four lagged values of the same six economic variables in each
equation in a six equation model. How these six explanatory variables were
picked is not detailed. The effect of each lag for each variable is estimated
econometrically. Sims’ equation for GDP determination was
GDPReal = f (t=–1 to –4 GDPt , t=–1 to –4 M1Nom(t) , t=–1 to –4 Unemt ,

t=–1 to –4 Av.WageNom(t) , t=–1 to –4 Gen.Price Indext ,
t=–1 to –4 Imports Price Indext )
(2.2.4.1.2)
There are five other identical equations, each using one of the other five
right hand side variables as a dependent variable. Coefficients and standard
errors, of course, for each right hand side variable differ from equation to
equation. Sims does not publish regression coefficients or standard errors
for his models, arguing that
The autoregressive coefficients themselves are difficult to interpret . . . (and)

. . . Because estimated AR coefficients are so highly correlated, standard
errors on the individual coefficients provide little of the sort of insight into
the shape of the likelihood we ordinarily try to glean from standard errors
of regression coefficients. (Sims 1980, p. 18)
2.2.4.2 Tests by Others if How Well VAR Models Fit the Data
Eckstein (1983) tested a Cowles model (the DRI model) and found it
had smaller forecasting errors than optimal ARIMA forecasting formulas
developed for the same period. Eckstein noted that “since ARIMA will not
produce turning points, the method is then guaranteed to fail.”
Comparative forecasting errors for 20 key economic variables indicated
the Cowles model had better 1 quarter ahead forecasts for all 20 variables,
and for 4 quarter ahead forecasts, 17 of the 20 Cowles model forecasts
were better than the ARIMA model.
Gale and Orszag (2004, p. 149), also found VAR projections to be
inferior to others when evaluating the impact of deficits on interest rates,
noting that most studies find a change in interest rates when deficits
increase, but that those that don’t are usually VARs, suggesting VAR-
based may be biased toward showing no effect of deficits on interest rates.
They also noted “VAR–based projections have been shown to be inferior
to those produced by the OMB or by Data Resources, Inc.” (p. 152).
Fair (2004) also found that his structural model performed better than
both a 7-variable VAR model with four lags for itself, and two lags for each
of the other six variables.
In addition, VARs commonly use lagged values of the dependent vari-
able in their models. If there is serial correlation in the error terms, using
lagged dependent variables results in biased and inconsistent parameter
estimates. (Griffiths et al. 2008, 2011), affecting forecast accuracy.
2.2.4.3 Tests of Ability to Explain Variance: Comparing Sims, Mountford,

and Uhlig VAR Models to Cowles Models
Sims argues we should rely more on out-of-sample forecasting error
than on coefficients and standard errors to evaluate VAR models. In
Table 2.2.4.3.1, we do so. We compared estimates of GDP for several
VAR’s, including Sims’ 1980 Econometrica model. All models were estim-
ated using a 1960–2000 data set for the USA. Then, forecasts of GDP for
the decade following the estimation period were made using the estim-
ated models. In addition to Sim’s model, we also included Mountford and
Uhlig’s (2008) well-known VAR model and a general VAR model of our
own construction
VAR forecasts were compared with estimates for the same 10-year
period obtained from a Cowles structural model. The Cowles model is
shown further below.
Results indicate the average yearly error of estimate for the post-
sample period was 6–10 times as large for the VAR models as for the
Cowles model. This might have been expected since the VARs make no
attempt to adjust for regime change after the estimation period, while
92 2 METHODOLOGY
Table 2.2.4.3.1 Comparison of % error of GDP estimates of VAR with structural

models for the 10 years after their 1960–2000 estimation period (absolute value
of error % used)
Year Cowles Sims Montford & Montford & General

structural: Uhlig Uhlig
Model (%) VAR (%) VAR (full model) VAR (partial model) VAR. (%)
(%) (%)
2001 0.9 4.6 2.9 2.6 2.2

2002 0.2 0.2 4.1 0.2 3.0
2003 0.1 0.9 5.3 4.0 6.2
2004 0.3 1.9 0.4 2.2 10.2
2005 0.2 1.3 2.8 9.8 18.1
2006 0.4 2.4 2.2 7.4 16.1
2007 0.2 4.6 4.0 6.8 16.7
2008 0.6 4.6 5.1 1.3 15.1
2009 1.2 2.0 1.3 3.5 6.7
2010 0.5 6.6 7.6 1.3 5.6
Average 0.5 2.9 4.6 3.9 10.0
the Cowles structural models do (Eckstein 1983). The error of estim-

ate for each year was calculated as the absolute value of (GDPActual –
GDPCalculated)/GDPActual. The 10-year average of the yearly errors is
shown in Table 2.2.4.3.1
Average real GDP growth during this period was 2.2%. The Cowles
model’s average error in estimating yearly growth in GDP was 46/100
of 1%. That is equivalent to saying the Cowles model’s estimate of GDP
growth averaged about 80% correct. In the recession-related turn around
years 2001 and 2007–2008, the Cowles model far more accurately estim-
ated GDP than did the VAR models. Sims’ worst projections were for
these turnaround years with his error of prediction about six times as large
as the estimate of the Cowles model, and for the 2007–2008 years, his
model’s projections had errors 10–15 times as large. There is less of a pat-
tern to the Mountford and Uhlig model projections; they just tend to be
larger than the structural model errors in all years, and larger than the Sims
model errors in most years.
Sims’ average yearly error in estimating yearly changes in GDP (2.9%
of GDP) was more than 100% larger than the actual average change
itself (2.2%).
The two Mountford–Uhlig models tested were as follows (all variables

are in real terms):
Full Model
GDP = f (t=–1 to –3 GDPt , t=–1 to –3 Ct , t=–1 to –3 Fixed & Inventory Inv.t ,

t=–1 to –3 Govt. Receipts(t) , t=–1 to –3 Govt. Spendingt ,
t=–1 to –3 Prime Interest Ratet , t=–1 to –3 Wage Levelt ,
t=–1 to –3 Adj.Mon.Baset , t=–1 to –3 Materials Price Indext ,
t=–1 to –3 GDP Deflatort )
(2.2.4.3.1)
Partial Model
GDP = f (t=–1 to –5 GDPt , t=–1 to –5 Ct , t=–1 to –5 Fixed & Inventory Inv.t ,

t=–1 to –5 Govt. Receipts(t) , t=–1 to –5 Govt. Spendingt ,
t=–1 to –5 Prime Interest Ratet , t=–1 to –5 Materials Price Indext )
(2.2.4.3.2)
Because of the limited size of our data set (40 observations, 1960–
2000) available for estimating the model, we could not run Montford
and Uhlig’s full model with more than three lags (they used six). We
also ran a partial model, with seven variables and five lags. Our version
of Mountford and Uhlig’s model, though very similar, was not identical
to their model in several respects. They used a crude materials price index,
while we used a total materials index when recreating their model. Also,
they used the GDP definition of government spending, which excludes
transfer spending, while we used the full amount in our updated ver-
sion of their model. Results indicated the average predicted change in
the GDP in the decade following model estimation for the Montford and
Uhlig models, was about twice as large as the actual average change in
GDP:
A fourth VAR, labeled the “general” VAR model was also tested, used
five lagged values of six variables for current year GDP determinants:
Lagged GDP, consumption, investment, government spending, exports,
and imports. Since GDP is an identity comprised of all of their current
values, we expected applying the VAR method, with absolutely nothing
that actually does determine GDP missing, would yield the best projec-
tions. Instead, it yielded the worst. The model tested is given below (all
variables are in real terms)
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General VAR Model
GDP = f (t=–1 to –5 GDPt , t=–1 to –5 Consumptiont , t=–1 to –5 Investmentt ,

,
t=–1 to –5 Govt. Spendingt , t=–1 to –5 Exportst , t=–1 to –5 Importst ),
(2.2.4.3.3)
Structural Model
The Cowles structural model used in this comparison is a typical
Keynesian-type “IS” curve. It is derived from the GDP identity: GDP =
CD + ID + GD + X = C + I + G + (X – M) where the previously estim-
ated behavioral equation determinants of consumption, investment, and
exports are substituted in and the estimated value of GDP calculated for
each of the 10 years beyond the 1960–2000 period used to estimate the
model’s parameters. The consumption model’s estimated parameters are
CD = 0.35(Y – TT ) + 0.23(TT ) – 0.13(GT& I ) – 4.33PR

(t =) (5.2) (2.3) (–2.0) (–1.8)
+0.32DJ–2 – 1.17XRAV – 508.20POP16 + 0.017POP
(2.0) (–0.8) (–2.8) (4.6)
+0.30ICC–1 + 35.93M2AV + .16 CB2
(1.3) (4.4) (3.1)
R2 = 91.2% D.W. = 1.6 MSE = 21.60
(2.2.4.3.4)
Generally coefficients on significant variables remain reasonably close to
their estimated values in the full 50 year data set (1960–2010) model,
which we would expect since the graph of this equation shows it explains
consumer behavior equally well in each of the five decades included in the
sample. Dropping one decade should not change the coefficients much.
Definitions of these variables are provided below.
The model of domestically produced investment goods, estimated using
1960–2000 data, gives the model results shown in the equation below:
ID = +0.22(ACC) + 0.33(TT ) – 0.34(GT& I ) – 0.18DEP

(t =) (7.3) (3.7) (–4.0) (–0.6)
+2.31CAP–1 – 2.89PR–2 + .22DJ0 – .12PROF–0
(1.9) (–1.7) (1.3) (–.07)
+2.30XRAV + 0.01POP + .11 (BOR–1 )
(0.9) (2.7) (1.5)
R2 = 84.4% D.W. = 2.4 MSE = 24.21
(2.2.4.3.5)
Here again the estimates from the 1960 to 2000 sample are quite sim-
ilar the full 1960–2010 year sample estimates, This was expected, since
the graph of this equation shows the model explains consumer behavior
equally well in each of the five decades included in the sample.
The parameter estimates for the model of domestically produced goods
for export for the 1960–2000 period gives the model results shown in the
equation below:
X = 0.10(WGDPRealTP(0)) – 7.91(XRAV0 to –3 ) + 0.58(M0 )

(t =) (1.8) (–4.7) (9.3)
+13.24(PRRealAV–1–2 ) – 8.56INFLAV–1 to –2 )
(3.9) (–1.9)
–0.38AR(6) R2 = 78.6; DW = 2.0 MSE = 18.19
(–1.5)
(2.2.4.3.6)
Variable definitions are as follows:
CT = Total consumer spending
Y-TT = Disposable income
TT = Total government receipts
GT&I = Total government spending
PR = Real prime interest rate
DJ–2 = Stock market index measure of wealth, lagged 2 years
XRAV = Real exchange rate, average current and 3 previous years
POP16 = Ratio of those Over 64 to those under 21 in the population
POP = Total population
ICC–1 = Index of consumer confidence, lagged 1 year
M2AV = M2 average, 2–4 years ago
CB2 = Level of consumer borrowing
ACC = Accelerator
DEP = Depreciation
CAP–1 = Capacity utilization rate, lagged 1 year
PROF = Profits
BOR–1 = Business borrowing, lagged 1 year
WGDPRealTP(0) = Trade-weighted real GDP of US trading partners
INFLAV–1to–2 = Inflation, average of prior 2 years
AR(6) = 6th order autoregression control
This Cowles model uses a markedly different method to decide which vari-
ables to include in a model for testing. It intentionally limits the variables
96 2 METHODOLOGY
used in test to those consistent with theory (to protect against confus-
ing spurious correlations with those consistent with causality), and uses
established econometric techniques (Hausman endogeneity tests, 2SLS)
to ensure identification issues are resolved.
In classic VAR models, each dependent variable is determined by
numerous lagged values of all economic variables in the larger economic
model, including lagged values of the dependent variable itself. This allows
the regression to determine how much each of several lags matters. It
also avoids what Sims considered to be the identification problem with
structural models, i.e., structural models attempt to define a priori, not
necessarily through scientific testing, precisely which variables are determin-
ants of each specific variable (like consumption or investment), and with
precisely what lags.
Results above indicate the Cowles approach led to better performance
results than the VAR approach.
2.2.4.4 Comparing Cowles Models with Structural VAR Models

Sims’ VAR model was selected for out-of-sample fit testing in the previ-
ous section because it is considered one of the classic VAR models. More
recently, models described as “structural VARs” have been developed
which attempted to integrate a limited number of structural equations
(such as you might find in a Cowles model) into a general VAR structure.
For example, Stock and Watson (2001) offered the following example of
a 3-variable VAR model (interest rate, inflation, and unemployment) with
a structural component inserted into the interest rate determination equa-
tion. The structural relationship inserted was a version of the Taylor rule
model for interest rate determination.
Stock and Watson’s structural VAR (SVAR) has three equations, one for
each of the three current period dependent variables in the model (interest
rate R, inflation rate π, and unemployment rate u). On the right hand side
of all three equations are the standard VAR model lagged values of each of
the three variables and an error term. In addition, a “shock” is added to the
interest rate equation in the form of the Taylor rule equation. A simulated
change in the Taylor rule component creates a simulated change in the
current period value of the interest rate (R), which in subsequent periods
affects future values of all three variables in accordance with relationships
expressed by the standard lagged values of the VAR variables.
Stock and Watson’s equation system for this three-equation SVAR
showing how the Taylor Rule interest rate equation is integrated into the
full VAR model is as follows:
Rt = r∗ + 1.5(πt – π∗ ) – 1.25(ut – u∗ )
+ (lagged values of R, π, u) + ξt(R) (2.2.4.4.1)
π = (lagged values of R, π, u) + ξt(π) (2.2.4.4.2)
U = (lagged values of R, π, u) + ξt(u) (2.2.4.4.3)
where r∗ is the desired real interest rate, πt and ut are the average values
of inflation and unemployment rate over several past periods, π∗t and u∗
are the target inflation and unemployment rates, and ξt is the error term
in the equation.
The theory is that this type of structural VAR avoids the problem of
having to decide what year’s error term in the interest rate equation can
be considered caused by (only) an interest rate shock.
The basic VAR model we tested in the previous section and compared
to a Cowles model was conceptually like the model above, but without the
Taylor Rule structural component included in the interest rate equation.
When separately testing the Structural and VAR pieces of a model nearly
identical to the Stock and Watson model, we found the following using a
1960–2010 data sample:
Structural Only
R = .1.02(486(π – 2) – 1.08(U – 2))

(2.2.4.4.4)
(t =) (9.3) R2 = 0.63, MSE 1.25, D.W. = 1.6
where “2” in the Taylor rule equation is both the desired inflation and
unemployment rate.
VAR Only
R = 0.20R–1 – 0.30π–1 – 0.26U–1 – 0.46R–2 – 0.15π–2 – 0.02U–2

(t =) (0.9) (–1.5) (–0.7) (–2.0) (–0.6) (–0.0)
–0.01R–3 – 0.27π–3
(–0.0) (–1.2)
–0.18U–3 R2 = .47, MSE = 1.64, D.W. = 1.9
(–0.4)
(2.2.4.4.5)
Where the Fed’s desired interest rate was considered a constant, and
therefore does not show in the first difference model above.
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Structural VAR
R = 0.87(486(π – 2) + 1.08(U – 2)) + 0.18R–1 – 0.06π–1 + 0.26U–1

(t =) (6.4) (1.2) (–0.4) (1.0)
–0.22R–2 – 0.11π–2 + 0.05U–2 + .13R–3 – 0.07π–3
(–1.3) (–0.6) (0.2) (0.7) (–0.4)
2
+0.28U–3 R = 0.74, MSE 1.17, D.W. = 2.0
(0.9
(2.2.4.4.6)
Most of the variance (0.63) can be explained by the structural component
alone. Adding the lagged VAR variables does increase explained variance
to (0.74), but does so by adding nine lagged variables, none of which is
found statistically significant, nor whose presence in the model is required
because they are based in a recognized theory of how the prime interest
rate is determined. Therefore, though collectively they explain some vari-
ance in interest rates in the 1960–2010 period, it is difficult to determine
if their contribution merely spurious or if it is real. Also, note some VAR
variable signs were wrong. It is bizarre to find a model that concludes that
over the sample period, typically any current year’s prime rate will be only
18% of last year’s; that increasing inflation rates are associated with declin-
ing prime rates, and that the higher last year’s unemployment, the higher
this year’s prime interest rates. And these bizarre results hold no matter
which of four time periods sampled the model is applied to, as we show
further below.
As we also show further below, the signs on most of these VAR variables
are utterly unreliable: they change with the sample period chosen, and
change with the number of the lag chosen. These unusual results, of course
reflect nothing more than the (nightmarish) problem of multicollinearity
at work. It has been well recognized for half a century that signs, coeffi-
cients, and significance levels of a model’s explanatory variables are highly
unreliable in the presence of high levels of correlation among explanatory
variables. Unfortunately, we often get this when we include several lags of
the same variable in the model. Many economists try to avoid this prob-
lem by structuring their models in ways which avoid the problem, thereby
leaving their test statistics credible (which would seem to be a require-
ment of good science). By comparison, VAR modelers argue that because
these test statistics are unreliable, we should just ignore them, and just
concentrate on the model’s final product: how well the model forecasts.
As noted earlier, another way of testing the spuriousness of statistical

findings is to see if coefficient results can be replicated in other sample
periods. We test the structural VAR discussed above in three additional,
though overlapping sample periods to see if we could replicate our initial
findings.
Table 2.2.4.4.1 Time period robustness of SVAR model results
Variable 1960–2010 1970–2010 1970–2000 1960–2000 High/low

%diff
Taylor rule 0.87∗ 0.92∗ 1.38∗ 1.27∗ 37%

Prime rate (-1) 0.18 0.15 0.55∗∗ 0.54∗ 67
Inflation (-1) –0.06 –0.03 –0.26 –0.27 78
Unemployment (-1) 0.26 0.25 0.81 0.75 65
Prime rate (-2) –0.22 –0.23 –0.24 –0.27 19
Inflation (-2) –0.11 –0.07 0.17 0.13 15
Unemployment (-2) 0.05 0.01 –0.11 –0.12 58
Prime rate (-3) 0.13 0.20 0.24 0.19 32
Inflation (-3) –0.07 –0.11 0.02 0.04 43
Unemployment (-3) 0.28 0.42 0.52 0.47 40
R2 0.74 0.75 0.87 0.84
MSE 1.17 1.30 1.04 0.9
D.W. 2.0 2.0 2.1 1.9
∗ Significant at 1% level; ∗∗ Significant at 5% level.
Note the stability differences between the Structural model variable and
the VAR lagged variables.
1. The only variable significant in all four periods was the Structural
model variable.
2. Only one of the VAR variables was significant at all, and then only in
two test periods.
3. For the structural model variable, the lowest sample estimate was
only 37% below the highest estimate.
4. For the VAR variables, six of the nine variable coefficients were less
stable than the structural variable coefficient
Out-of-Sample Comparisons
How the VAR model performs compared to the structural model in
out-of-sample tests is now examined. Such tests are considered the best
100 2 METHODOLOGY
way of evaluating forecasting models. As Stock and Watson (2001)

noted: “the ultimate test of a forecasting model is its out of sample
performance.”
As was done with our earlier out-of-sample performance comparison
with traditional VAR work, we estimated the Stock & Watson SVAR
interest rate model using 1960–2000 data, and then used those parameter
estimates to calculate how well the model fit the data in the decade after it
was estimated, 2001–2010. The structural model we compared it against
was a simple Taylor Rule model of Prime interest rate determination. The
Prime historically has been set at the Federal funds rate plus 3%, so like the
Federal funds rate, it is essentially an administered rate, set indirectly by
the Federal Reserve Board.
The two models estimated using 1960–2000 data are as follows:
Model 2.2.4.4.7
Cowles Commission – Type Taylor Rule Structural Model
PRREAL = 0.552(INFL – 2%) – 1.322(UNEM – 2%)
(t =) (5.2) (–6.5) (2.2.4.4.7)
R2 = 0.63; MSE 1.25; DW 1.6
Model 2.2.4.4.8
Structural VAR Model
Structural VAR
R = .1.06(.552(π – 2) – 1.322(U – 2)) + 0.56R–1 – 0.26π–1

(t =) (8.0) (3.1) (–1.7)
+0.76U–1 – 0.27R–2 + 0.12π–2 – 0.11U–2 + 0.18R–3
(2.4) (–1.5) (0.7) (–0.4) (1.7)
+0.06π–3 + 0.45U–3 R2 = 0.84, MSE 0.97, D.W. = 1.9
(0.4) (1.6)
(2.2.4.4.8)
These models were then used to calculate estimates of the real prime
interest rate for individual years in the decade following the estimation
period, 2001–2010. The calculated value for each year was compared
to the actual, and the percentage by which the calculated value differed
from the actual value was calculated The average percentage error for the
Table 2.2.4.4.2 Out-of-sample fit comparisons: Structural models vs. SVARs
Model Type Structural SVAR#1∗ SVAR#2∗
Average Error of Fit 0 65% 90% 85%

Mean Square Error 0.74 2.45 0.77
1∗ : Assumes different Taylor Rule Shock each year, based on shocks that actually occurred. Equation 2.36
coefficients used, except coefficient for Taylor rule variable set at 1.00; setting it at the value in Eq. 2.36
increased average error to .94. Using coefficients from a traditional VAR, with the Taylor variable added
with coefficient of 1.00 raised the average error to 119%.
2∗ : Assumes 2001 Taylor shock is reversed in 2002; no additional shocks (Taylor Rule changes) thereafter.
(This leaves some internal inconsistency within the model: U, π held constant in Taylor rule variable, but
allowed to vary from year to year in the VAR component in accordance with the actual changes in the
economy.)
structural and SVAR models for the 10 out-of-sample years was calcu-
lated, and is presented below. Two SVAR models errors were calculated:
(1) assuming the Taylor rule shock changed each year to reflect what actu-
ally happened to inflation and unemployment; and (2) assumed the first
year shock lasted 1 year only. Results are presented in Table 2.2.4.4.2.
In the Table 2.2.4.4.2, the statistics indicate that the Cowles-type struc-
tural equation has a smaller average error of fit and smaller MSE than
either structural VAR tested. We conclude that even when adding a struc-
tural model to a standard VAR equation, the Cowles structural model
outperforms the Structural VAR, i.e., provide a better set of estimates of
out-of-sample data.
Note that with even this small model, it would be impractical to make
each equation a structural VAR. As we show in later chapters with inflation
Model 11.1.TR and unemployment Model 12.4.TR, there are at least five
additional variables driving inflation and unemployment in addition to the
three noted above. Each would need its own equation, and its own three
lags added to each equation, and that undoubtedly would add additional
variables to the model, each of which would need its own equation, and
also need its own three lags added to each equation. Each equation could
end up with 25 or more highly multicollinear explanatory variables.
In short, even if the other problems mentioned did not exist, it does
not seem feasible that the SVARs could be used to construct a large-
scale, detailed model of the economy. Hence, they would not seem to
be a suitable alternative to Cowles models for this purpose.
102 2 METHODOLOGY
2.2.4.5 Factors Which May Explain the Poor Performance of VAR Models
Sims’ equation for GDP determination was
GDPReal = f (t=–1 to –4 GDPt , t=–1 to –4 M1Nom(t) , t=–1 to –4 Unemt ,

t=–1 to –4 Av.WageNom(t) , t=–1 to –4 Gen.Price Indext ,
t=–1 to –4 Imports Price Indext )
(2.2.4.5.1)
There are five other identical equations, each using one of the other five
right hand side variables as a dependent variable. Coefficients and standard
errors, of course, for each right hand side variable differ from equation to
equation. Sims does not publish regression coefficients or standard errors
for his models, arguing that
The autoregressive coefficients themselves are difficult to interpret . . . (and)

. . . Because estimated AR coefficients are so highly correlated, standard
errors on the individual coefficients provide little of the sort of insight into
the shape of the likelihood we ordinarily try to glean from standard errors
of regression coefficients. (p. 18)
The uncertainty in standard errors (and coefficients) caused by multicollin-

earity is a real problem faced by any scientist forced to rely on correlational
methods of analysis to measure economic reality (Fox 1968). Historic-
ally, analysts worked to reduce the multicollinearity as a way of increasing
the reliability of standard errors. They did not just stop using standard
errors to evaluate coefficient significance. Multicollinearity is probably
the greatest unresolved statistical problem economist scientists have to
grapple with when trying to discern relationships between explanatory and
dependent variables.
Sims argues we should assume regression coefficients are informative
enough to use, regardless of significance levels. He notes that statisticians
have long argued that in the absence of statistically significant estimates
of the mean relationship between two variables, our best estimate is the
test’s estimate of the mean effect, regardless of significance levels, not zero.
While true (Triola, 2011), to avoid confusion between causation and cor-
relation, traditionally we do this only for variables (or particular lag levels)
if there is some a priori theoretical reason to expect a non-zero relationship.
In correlational analysis, when assessing statistical findings, this is the only
way to distinguish between mere spurious correlation which can lead to
non-zero parameter estimates and correlations possibly resulting from a

causal relationship.
Sims notes that auto regressive coefficients are difficult to interpret.
This is because they are (definitionally) distorted, often grossly, by the
huge multicollinearity problem accompanying use of several successive lags
as independent variables in a model. It is this that causes the chronically
high standard errors discussed in the paragraph above. Every coefficient is
a function of, and distorted by, the level of multicollinearity among right
hand side variables in an equation (Fox 1968). It is impossible for four
or five successive lags of time series variables commonly used in VAR’s
not to be very highly correlated. Coefficients commonly show the usual
symptoms: one lags’ coefficient has a positive sign, while the lag before
it has a negative sign, and the lag before that may (again) have a positive
sign, etc. In some cases, all lags have theoretically inappropriate signs. For
example, in reestimating Sims’ 1980 Econometrica model, using data for
the 1960–2000 period, using exactly the same variables and lags that Sims’
did, we find all lags of the unemployment rate to be positively related to
the current level of the GDP, not negatively, as even the simplest economic
theory would lead us to expect.
In addition to this distortive effect, coefficients in VARs are hard to
interpret. The variables hypothesized as determinants of (say) GDP are
not, in any obvious way, a hypothesis derived from any known economic
theory. (Can we explain growth in unemployment’s positive relationship
with growth in GDP using Keynesian theory? DSGE theory? Even if we
had the right sign on the unemployment variable, would the direction of
causation assumed by the model be correct?)
The VAR is grounded in the theory that “everything may be a function
of everything, at least with a lag.” It allows the regression to determine
which lags and which variables actually are the most important. In theory,
all variables in the “everything is a function of everything” hypothesis are
included as determinants of each dependent variable, using their regres-
sion coefficients as estimates of marginal effects of each lagged value of a
variable.
This type of initial model specification inevitably results in overfitting.
For any one equation, some variables will be included which are determ-
inants of the dependent variable, and some which are not. This may result
in bad fits in periods beyond the sample period because the projection for-
mula is too much influenced by the use of spurious, noncausal correlations
related to this latter group of variables.
104 2 METHODOLOGY
This opportunity is not given to the variables in structural models.

Some variables are excluded a priori on theoretical grounds from each
equation to be tested in an attempt to eliminate what otherwise might be
spuriously significant test results.
In allowing the data to decide what’s important, some economists
might view the VAR approach as good science (statistically based, rather
than calibrated), but bad economics, e.g., what if statistically, the model
shows some interest rates to have positive signs? Or that depreciation
rates are determinants of consumption? VAR analysts says “let the data
decide.”
Some economists would not even say VAR is good science: in practice, if
VAR analysts don’t like what the data have decided, it is common for VAR
analysts to change statistical results so they match some generally accepted
notion of how the economy behaves (Uhlig 2005, p. 384). This of course
negates the science involved. It is also precisely what Sims charged struc-
tural modelers with doing wrong by including only theoretically acceptable
variables in their models: i.e., not letting the data decide.
Scientific techniques in macroeconomics are generally correlational.
Experimentation – changing one variable controlling for others – and
replication of experiments is usually not feasible. If only correlational tech-
niques are available for discerning reality, not restricting hypotheses tested
to only those consistent with established economic theory is to embrace as
causal, every empirical result showing a correlation between the depend-
ent variable and other variables in a model. It does not matter whether
correlation results from an underlying causal relationship, or whether it is
merely spurious, an artifact of the current data set, and which may not be
present in the next sample.
Consider the role of depreciation in economic theory. Suppose we
wished to show the effects of three explanatory variables: income, the
accelerator and depreciation, on consumption and investment. Suppose
theory tells us that of the three,
• only current income (Y) affects consumption, and

• only current depreciation and the current accelerator affect invest-
ment spending.
Testing these hypotheses on the 1960–2010 data set used in this study, we
obtain the following regression estimates of marginal effects:
C = 0.663 Y (2.2.4.5.2)
I = 0.478 Acc + 1.38 Dep (2.2.4.5.3)
Suppose these are the “real” marginal effects of Y, Acc, and Dep. By
adding them together, we could deduce that
(C + I) = 0.663 Y + 0.478 Acc + 1.38 Dep (2.2.4.5.4)
But separate VAR-type regressions of consumption and investment on Y,

each of which includes all three explanatory variables in the system, would
yield
(C) = 0.526 Y – 0.005 Acc + 1.38 Dep (2.2.4.5.5)

(I) = 0.453 Y + 0.150 Acc – 1.74 Dep (2.2.4.5.6)
By adding C and I, this suggesting that the real total effects of Y, Acc, and
Dep are
(C + I) = 0.979 Y + 0.145 Acc – 0.355 Dep (2.2.4.5.7)
Since the consumption and investment equations have exactly the same
determinants (and only because of this), regression of (C+I) on the three
determinants produces exactly the same results we obtained adding the
parameter estimates in equations Eqs. 2.2.4.5.5 and 2.2.4.5.6.
We assume the effect of Y on investment in the investment equation
is spuriously correlational not causal, because that’s what theory tells us
(though that would not be the case for the accelerator: Y). But in a VAR
model, purely correlational and causal effects are added together when
estimating the effects of income on (C+I), biasing the resulting estim-
ate. In addition, including the depreciation and accelerator variables in the
consumption function biases the estimate of income’s marginal effect on
C in the consumption function. By our assumptions, neither the accel-
erator nor depreciation has any effect on consumption. Yet because the
regression coefficient on income in the consumption function is (in part)
a function of the level of multicollinearity between income and these two
variables (Fox 1968), the estimate in the VAR-type consumption equation
is biased by any non-zero correlation the accelerator and depreciation have
with income. In fact, it is lower (.526) than the estimate provided by the
106 2 METHODOLOGY
structural model (0.663), where only theoretically specified variables are

included, for this reason.
This may cause severe bias in VAR model coefficients used to make
out-of-sample projections.
Consider the GDP equation in a VAR model that included an invest-
ment and consumption equation as well as a GDP equation. Some
variables (depreciation) that enter into one VAR equation (investment),
which are not usually thought to causally enter another, (consumption)
may still be found to be (noncausal) correlates of consumption. If run in a
consumption regression model, they will explain variance in consumption,
and may even be statistically significant. In a VAR model that included
consumption, investment and GDP equations, each containing the same
explanatory variables; adding depreciation’s correlative (but not causal)
effect in the consumption function to its correlative (and causal) effect
from the investment equation will give you a biased parameter estimate
for depreciation in the GDP equation, which will affect forecasts of GDP
from the equation.
To generalize these results, consider a five-equation VAR system in
which each of the components of the GDP in which the GDP and each
of its components (CD , ID , G, X) is a separate regression, each having
the same five explanatory variables. Regressing these five explanatory vari-
ables on GDP gives the same coefficient on any one variable as you obtain
from adding its (spurious or causal) coefficients in the other four VAR
equations. It is true that if the correlation effect is spurious, you could
run, say, 20 VAR analyses on different time periods, and average the res-
ults to check the coefficients expected value. If truly spurious, it should
be approximately zero, but this is not done due to its impractically large
demands for time series data (Where would we get 20 different time period
samples, each large enough to run, say, a 5-variable VAR, with 8 lags
each?)
Thus, the VAR approach is likely to chronically lead to situations where
correlation is confused with causation in simulating the future effects of
past values of variables in the system, and hence, not be good at mak-
ing projections outside the sample period due to the over fitting that has
occurred due to use of coefficients describing the relationship of dependent
variables to noncausally related variables in the model. But if we restrict
the explanatory variables in any equation to those that are theoretically
plausible, as is done in structural models, this is not possible. This is the
approach used in Cowles Commission-type models.
Without this governing mechanism for limiting variables (and lags) in

models to those that are theoretically plausible, you get implausible (or
plain silly) results (e.g., this year’s interest rates are positively related to
this year’s GDP, but negatively related to last year’s; but positively related
to the year before that, etc., or that a variable’s value 6 and 5 years ago has
a statistically significant effect on the some variable today, but not 4 years
ago, though it did 3 years ago, but not since then.
Because of this problem, VARs, acknowledged by many to be poor
economics because they lack a theoretical foundation, may not be good
science either.
There is an additional problem. Multiple lags take up so many degrees
of freedom, VAR analysts are forced to reduce the “everything” that
belongs on the right hand side in VAR models to some manageable num-
ber of variables. Rarely, if ever, are the reasons given why some variables
are deleted, or what empirical tests showed they were less important than
the variables left in. Nor is it explained to what extent leaving some out
may have resulted in “left out variables” bias (Goldberger and Jochems
1961). Most of the variables found by structural analysts to be determin-
ants of GDP, consumption, or investment are left out of VAR models. For
example, elsewhere in this paper, 11 variables were included as determin-
ants of consumption. It seems likely “left out variables bias” creeps into
the marginal effect estimates for the relatively few variables used in VAR
models.
Due to the large number of lags used with each explanatory variable in
a VAR model, commonly such models limit the number of economic vari-
ables they test to – four to six, even though the number of variables in the
system may be much larger since “everything is a function of everything”).
If variables are omitted that are determinants of a dependent variables in
the VAR model, their influence on the dependent variable is captured in
the error term (the “left out” variable problem). If the omitted variable
(i.e., the error term) is correlated with any variable in the equation tested,
the parameter estimate for that variable is biased and inconsistent (Griffiths
et al. Griffiths et al.), p. 275).
In the out-of-sample tests described earlier, Cowles structural models
explained the future better than Sims or Mountford and Uhlig’s VAR
models This is because Cowles models include variables to capture the
effects of specific regime changes on the variable of interest. VAR’s do
not, and therefore, cannot adjust their estimates of the future for such
changes as they occur.
108 2 METHODOLOGY
2.2.5 Cowles Commission Structural Models

A third macroeconomic method available for discerning macroeconomic
reality is the Cowles Commission method. The method is named after the
earliest source of support for these models, an Econometrica-sponsored
research commission at the University of Chicago. Since 1955 it has been
referred to as the Cowles Foundation and located at Yale (Hildreth 1985).
The Cowles method involves developing large-scale econometric mod-
els of the macroeconomy, involving dozens of behavioral equations, each
describing the determinants of one of the economy’s endogenous (or
partially endogenous) variables. Each equation is derived from standard
economic theory, though occasionally the testing process uncovers (and
thereafter includes) variables that should be part of existing theory, but
only now are being discovered important. Parameter estimates for the
determinants, and significance levels, are all estimated using OLS or 2SLS
methods of econometric testing. Fair’s (2004) work is the most mod-
ern of the large-scale econometric models of the macroeconomy of the
Cowles type.
The methodology followed . . . is called here the “Cowles Commission

Approach”. Theory is used to guide the choice of left-hand – side and
right-hand side variables for the stochastic equations in the model. (p. 4)
Fair also notes that unlike equations in DSGE models
It is never the case that all the coefficients in a stochastic equation are chosen
ahead of time and thus no estimation done: every stochastic equation is
estimated. In this sense, the data rule. (p. 4)
This method does not calibrate parameter estimates which best allow a
favored predetermined explanation (i.e., theory) to fit a particular set of
data. It defines as the best explanation, the one theory among many which
best explains the empirical behavior of variables over long periods of time,
under varying economic conditions. To do this, it tests hypotheses directly
expressing an underlying economic theory to help improve the likelihood
their estimated effects are not spurious, selecting the one that fits the data
best. To Cowles modelers, demand-driven models of the economy, like
those described in “old” Keynesian models, seem to best fit this bill. They
explain an uncannily large amount of the total variance of key variables
over time, and do so in a theoretically sensible way, and (when well-

constructed), the same model explains economic change as well in one
decade as another. This is as it should be if the underlying theory accurately
describes how economies work.
Hence, most Cowles hypotheses about consumption, investment,
export and import demand tested have an old-Keynesian look to them,
but a modernized version of it. They include post-Keynes augmentations
that fill in gaps in the original Keynesian model, but sometimes change
the results, including any changes in policy implications of the original
model. Examples include adding accelerator and crowd out variables to
the original Keynesian formulations, adding Taylor Rule formulations of
the interest rate determination equation, making provision for supply push
inflation, and providing adequately for inflation effects as well as liquidity
effects of money supply changes. More traditional Keynesian LM curve
formulations are also shown, but not often used because Taylor rule
formulations explain so much more variance. Some Cowles models go
beyond the core demand side model to examine supply side and other
financial markets issues.
Examples of Cowles-type consumption, investment, and export func-
tions were given earlier in Section 2.2.4.2 of this paper, where performance
levels were compared to VAR models.
A major reason Cowles models are used is because there is no real
alternative if you wish to investigate detailed structural questions like “how
much does a decline in interest rates increase investment compared to an
increase in profits, controlling for all the other factors that affect invest-
ment?” Or, “How are the determinants of the demand for consumer
durables different from the determinants of the demand for services?” The
biggest DSGE and VAR models simply do not control for more than a
fraction of these variables needed to do this, as we have shown in our
tests above. For example, it is difficult to construct and solve most DSGE
models with the kinds of structural detail Cowles modelers desire (per-
haps 8 different consumption functions, 9 different investment functions
depending on the type of consumption or investment of interest (each
with perhaps 11 determinants), for example, durables vs. nondurables vs.
imports).
Another reason the Cowles structural method is used is because tests
performed, including those in this study, on out-of-sample performance
show Cowles models far more successful in explaining variation in the
economy than VARs or DSGE’s. In addition, the tests above show there is
110 2 METHODOLOGY
little empirical support for key assumptions underlying DSGE models that
are required for them to work, for example, current consumption spending
being based on accurate estimates of lifetime income averages, the Lucas
critique’s accuracy, etc. This makes DSGEs bad science, and therefore of
questionable value to modern economics.
In Cowles models each component of the GDP (consumption, invest-
ment, exports, demand for government goods and services) is tested to
find its determinants. Nothing is taken on faith (i.e., there is no use of
“self-evident” truths unless they have been directly tested and verified).
Each component, such as consumption, is divided into its major sub-
components (e.g., consumer durables, nondurables, services, consumer
saving and borrowing). Each subcomponent is tested separately to assess
its hypothesized determinants.
DSGE’s most innovative feature is its attempt to unify macro and
micro theory using the micro foundations method. The Cowles alternat-
ive is a “macro foundations of micro” method of deriving microeconomic
demand models for each firm and industry from a larger macroeconomic
model. A model with macro foundations, from which micro relations are
derived, makes sense because in any given period, changes in demand
for individual products, like cars, are likely to be principally driven by
macroeconomic phenomena, like booms and recessions, not by microeco-
nomic phenomena like price changes. Eckstein (1983) presents a Cowles
model that includes macro equations subsequently cut into smaller more
micro-sized sector and industry pieces, each with relative price variables to
capture microeconomic effects of price change. To the extent the supply
constraints are of interest, modern updates of Leontief’s (1951) input-
output models of the macro economy provide equivalent or greater level
of supply side micro detail, also scientifically estimated. Together they
provide a comprehensive science-based, rather than calibrated, alternative
to DSGE modeling.
In this sense, Cowles modeling provides a simple and straightforward
way of providing macroeconomic foundations for microeconomics, devoid
of the strong types of hypothesizing necessary to allow the build – up
of macroeconomic theory from microeconomic foundations, for example,
consumers and business have perfect knowledge of the future; they are
capable of doing Lagrangian maximizations in their head to determine
lifetime utility maximizations regarding how much to save and spend this
year, etc. It also avoids all the well-known tractability issues micro founda-
tions modelers face in trying to solve their models. Parameter estimates for
all levels of model aggregation can be solved using OLS or 2SLS applied
to mathematically simple hypotheses about how particular determinants
affect some dependent variable.
Past efforts to put a micro foundation under macro have met with very
limited empirical success. As noted earlier, with what some consider the
best of the micro foundations models (Smets–Wouters), a recent Federal
Reserve Board study by Edge and Gurkaynak (2011) indicated its forecasts
only were able to explain 8–13% of the variance in actual movements of
the GDP for periods as small as one to six quarters forward. In Cowles
models, the unexplained variance is more typically like this.
Cowles structural models typically explain about 90% of the variance in
key variables over time, and do so with models that explain what drove
economic behavior the 1960s or any other decade, more or less equally
well. This is true even when the data are tested in 1st differences, where
it is generally harder to explain variance than in levels. Hence, modern
versions of Keynesian structural models are very powerful in explaining
economic behavior. The difference in capacity to explain variance com-
pared to DSGE or VAR models is due to use of a theory that better
explains how consumers and businesses actually behave.
In general in such systems, the level of production is thought to be
demand driven, that human wants are endless, and that as long as people
have the purchasing power to buy more rather than less, they will do so.
We assume profit maximization provides the incentive that drives pro-
ducers to produce more in response to demand, provided there are not
supply constraints. In this sense all the great structural models of the
past including Klein’s, Eckstein’s, Fair’s, etc. are demand-driven models
of what determines the level of production. This and the belief that one
needs to know the essential determinants of demand to explain variation
in production over time accurately, constitute the essential criterion of a
Cowles model (not whether fiscal policy works or not).
Comparing DSGE models with Cowles models is to compare two
different ways of discerning empirical reality: one fundamentally is philo-
sophical and deductive, reaching its conclusions from deductions from
“self-evident” truths about the economic behavior of consumers and busi-
nesses. Deduction from self-evident truths was a methodology used to
determine “truth” and “reality” by natural and moral philosophers before
the scientific method was available. Cowles methods are more modern:
they are inductive and scientific. Consumption and investment functions
used in GDP models are those obtained from testing. Eckstein (1983), an
112 2 METHODOLOGY
early practitioner of scientific macroeconomics, highlighted the difference

noting
. . . Econometricians emphasize the empirical representation of the economic

process through dynamic structures with specific quantitative paramet-
ers and representation of the stochastic elements. Theorists represent the
economic process that can be derived from a minimum of behavioral
assumptions, but are willing to pursue logical ramifications a good deal fur-
ther. Given these differences in method and attitude, it is not surprising that
the conclusions are not always identical. (p. 53)
2.2.5.1 A Note on Fiscal and Monetary Policy Implications

of Cowles Models
Modern versions of “old” Keynesian models do not necessarily reach “old”
Keynesian policy conclusions about how well fiscal (or monetary) policy
works. Fiscal policy conclusions depend critically on whether the crowd
out effects of government deficits are explicitly included and tested as part
of the Keynesian consumption and investment models. If so, this paper’s
Cowles model results indicate fiscal policy does not have a net simulat-
ive effect on the economy. But if the crowd out variable (the deficit)
is omitted, and therefore the negative effects of the government deficit
on private borrowing are not included, theoretically, fiscal policy seems
to work. However, when testing, without adding the crowd out variable
(the deficit) to traditional Keynesian models, the traditional model explains
noticeably less variance and the coefficients on the government spending
and tax cut variables typically have the wrong sign) (Heim 2013). In effect,
what changes in the government spending and tax variables are measuring
is the net of the stimulus and crowd out effects. We conclude deficits have
both measurable stimulus and measurable crowd out effects which should
be included in consumption and investment equations.
Whether monetary policy is accommodating or not does not seem to
matter much in the Cowles models we tested. We have not extended our
research sufficiently to determine why, but suspect it has to do with the
open market method used to increase the money supply, which may skew
most new money issued toward securities markets and securities purchases
not much affecting the GDP, not toward purchases of goods and services
which do.
It may be that most of the money created by open market operations
results from purchases of securities by the Fed from private investors,
investors who merely want to trade in current investments so they can buy
others which currently look more profitable. In doing so, the open market
process causes the market valuation of securities to rise, but aside from the
small mpc out of wealth, or business spending out of proceeds from newly
issued securities, does not affect the real GDP. If this hypothesis is correct,
much of the additional money created by the open market process merely
increases money chasing investments, causing the stock and bond markets
to rise, not in buying goods and services that raise the real GDP. As an
explanation as to why monetary policy fails to stimulate the real economy,
this explanation is considered nearly an article of faith by much of the busi-
ness press. But it is not well researched by economists. It is a topic which
deserves future additional investigation.
Open market purchases of bonds from banks does increase free reserves
held by banks. However, the reserves may just stay in the bank in poor
economic times, failing to result in increased real spending when it is most
needed. This also may be part of the reason we empirically find little rela-
tionship between monetary policy and the real economy. The model tested
in this paper suggest monetary policy principally can affect the real eco-
nomy – consumption and investment – through its effect on the prime
interest rate and the level of consumer borrowing, particularly for housing,
but the measured effects are small.
2.2.6 Conclusions
Our tests indicated the out-of-sample performance of Cowles models was
far better than that of VARs and DSGEs. Out-of-sample performance test-
ing is considered by many to be the gold standard for evaluating the
usefulness of models.
Tests showed Cowles models have greater explanatory power than
VARs or DSGEs. The average error with which the Cowles models fit
the data in the decade after estimation was only half that of DSGE mod-
els, and 1/6 that of VARs. The larger VAR error likely results from two
problems:
• Combining likely causal and spurious regression coefficients in mod-

els, a problem that is unavoidable when using the same explanatory
variables in every equation in a model.
• The error also likely result from failure to provide any way of adjust-
ing forecasts for unanticipated future regime change. Out-of-sample
114 2 METHODOLOGY
performance of Cowles models is better because they control for vari-

ables which might cause regime change in the future. This allows
forecasts of (say) the effect of interest rate changes today on invest-
ment 2 years in the future to be adjusted in predetermined ways as
specific types of future regime change occur. In this sense, the out-
of-sample performance record of Cowles models better describes how
well they explain the causes of what actually happed, rather than how
well they forecast it. This is a key difference with VARs.
• In deciding which type of model is more useful, the analyst may have
to choose between a method which forecasts badly and explains not
at all (VAR), or a model which (in some cases) forecasts not at all, but
explains well how the economy actually operates (Cowles).
The DSGE flaws result from use of incorrect theory.
• Tests indicate using current year income in consumption functions

explains more variance than estimates of lifetime income. Failure of
the lifetime income assumption is casts doubt on the validity of the
rational expectations, a key postulate of DSGE theory.
• The DSGE assumption of constancy of consumer spending from year
to year, except for technological shocks (Romer 1996) is also tested.
The data tested did not support this theory. Wide variation in con-
sumer spending was found, aside from that caused by technological
shocks. It was better explained by factors commonly found in more
Keynesian-looking models, like Cowles models.
For all these reasons we have chosen the Cowles methodology for use in
developing this paper’s large-scale econometric model of the US economy,
presented in Chapters 4–19 below.
CHAPTER 3
Literature Review
Jan Tinbergen was the first economist to develop large-scale economet-

ric models, and during the period of 1960–2004, a number of large-scale
models were developed. Four of these models are reviewed below. The first
three, models by Klein and Evans (1968), Eckstein (1983), Fair (2004),
covering almost 40 years of successive development of the same type
of model, the Cowles Commission (i.e., Keynesian IS-LM) model. It is
important to note that the main reason these are referred to as “Keyne-
sian” is that that their key hypothesis about the economy is that its
principal components are demand driven. It is not that the economy can
be controlled by fiscal or monetary policy actions, a topic on which the
model results can differ considerably. Comparison of these earlier models
with this chapter’s results will be made later in the chapter. In this section,
our objective is just to describe major consumption, investment, interest
rate, export and import equations used in those earlier Cowles models,
and the variables they found to be key determinants in those equations.
The fourth model reviewed is the Federal Reserve Board/U.S. model
(Brayton and Tinsley, 1996). The FRB/U.S. model attempts to use DSGE
theory coupled with VAR methodology to develop testable hypotheses
about what equations are important in driving the U.S. economy. Alas,
this model does not explain the behavior of the American economy during
the past 50-year period nearly as well as the three more Keynesian mod-
els reviewed, explaining only roughly half the variance in consumption

DOI 10.1007/978-3-319-50681-4_3
116 3 LITERATURE REVIEW
and investment spending that the Keynesian models do. Also, because of
its atheoretic VAR approach to some aspects of model building, the eco-
nomic meaning of some equations can be hard to interpret. Nonetheless, it
does reflect dominant current trends in macroeconomic theoretical mod-
eling. Hence, it is important to compare the variables found important in
predicting and explaining consumption and investment in such models, to
those using more traditional methods having greater explanatory power.
3.1 LAWRENCE KLEIN AND MICHAEL EVANS (1968):

THE W HARTON E CONOMETRIC F ORECASTING M ODEL
Based on the earlier Klein–Goldberger model, this model uses quarterly
data for 68 quarters 1948–1964 to estimate the model’s structural regres-
sions. The models are Keynesian (i.e., demand driven) and are generally
referred to as “Cowles Commission”-type models for this reason. This
model, commonly referred to as the Wharton School model, extends
simple Keynesian models to include equations for
• price determination (wage rates plus a markup)

• wage rate determination (driven by Phillips curve unemploy-
ment/inflation relationship)
• aggregate supply (from Cobb-Douglas production function: how
much labor and capital available, capacity utilization indices)
• factor shares (what determines labor, capital’s share of total GDP (the
business cycle in short run, constant shares in long run))
The statistical technique used to estimate the equations was 2SLS if there
was evidence of endogeneity. Instruments developed to replace endo-
genous variables were constructed using factor analysis to develop 12
orthogonal (no multicollinearity) principal components for use in the
instrument instead of using individual variables, as is more common today.
Klein and Even’s model uses Almon and Koyck lags in investment and
consumption models to show lags (e.g., for a construction project which
affects several future years’ GDP). Such lags are commonly used as a way of
avoiding the problem of multicollinearity distorting individual year effects,
when several lagged values of an explanatory variable are required to show
its full influence on the current value of the dependent variable.
Key parts of the complete Klein-Evens model include
Three consumption models
3.1 LAWRENCE KLEIN AND MICHAEL EVANS (1968): THE WHARTON . . . 117
• Durables, except autos

• Autos
• Nondurables and services
Six Investment models
• Manufacturing
• Mining and regulated (utility) industries
• Commercial (office buildings, stores, shopping centers)
• Housing
• Inventory (manufacturing)
• Inventory (nonmanufacturing)
Three models explaining what determines demand for imports
• Food imports
• Raw materials and semi-finished goods
• Manufactures and services
One model explaining total export demand

Two interest rate models
• Short run = f (discount rate, free reserves)

• Long run = f (short-run rate, long-run rate – 1)
All models analyzed below are given in real terms, unless otherwise noted.
3.1.1 (Per Capita) Consumer Demand for Nondurables and

Services (as Cnd&S /Y)
CND& S /Y = 0.227
(t = ) (10)
– 0.46 (WEIGHTED% CHANGE IN DISP.INCOME(YD )FOR YEARS–1,–4 )
(14)
+ 0.72 (CND& S AV–1,–4 )R2 = 0.83, DW = 1.6
The model for nondurables and services basically is an adaptive

expectations model, indicating it takes four periods for consumer spending
to adjust to changes in income. Variables like wealth and interest rates are
not postulated to have an effect on nondurables demand. Four lags of con-

sumer spending are also postulated to have an effect. It is not clear why
these variables are included since adjustments to changes in income are
already accounted for, though it may be an indirect way of picking up the
variation in consumption that wealth, interest rate, etc., cause, that are not
controlled for in the regression simply by controlling for income.
3.1.2 Consumer Demand for Durables (Cd ), Except Autos
CD = – 14.19 + 0.12(Y) – 0.02Kna(–1)

(t =) (3) (.7)
+ 0.06 (MICH INDEX OF CONSUMER EXPECTATIONS (ICS))
(1.7) R2 = .96 DW = 1.3
where Kna = stock of consumer durables except autos and Y = disposable

personal income.
For durables except autos, demand is positively affected principally by
current year income, and to some extent, consumer expectations (but not
as reliably).
3.1.3 Consumer Demand for Autos
Ca = 48.50 + 0.11(Y-TRANSFERS) – 47.54(PA /PALL C ) + 0.12(MICH ICS)

(t =) (4) (10) (2.2)
– 0.10(UNEM RATE)
(4)
+ .90(DUMMY FOR LOAN AVAILABILITY)
(1..2)
– 0.05(STOCK OF AUTOS–1 (KA(–1) )
(2) R2 = .92 DW = 1.1
where Y-Transfers = nontransfers income; Pa/Pc = price index for

autos relative to index for total consumption; DUMMY FOR LOAN
AVAILABILITY = –1 when regulation W was in effect, 0 when not before
1955; 1 when not in 1955 and after.
For autos, demand was positively related to nontransfer income and
the index of consumer sentiment, demand was negatively related to the
unemployment rate, the price of cars relative to other consumer goods,

and the existing stock of autos.
3.1.4 Investment Goods Demand: Manufacturing Industries
IMANU = – 11.43 + 15.62 (CAP UTIL.%)

(t =) (8)
+ 0.09 (ALMON.AV OF MANU.OUTPUT–1,–8 )
(9)
+ 0.11 (ALMON AV CASH FLOW–1,–8 )
(2.5)
– 0.32 (ALMOM AV LONG TERM i–1,–8 )
(–1.5)
– 0.03(ALMON AV CAPITAL STOCK–1,–8 )
(7)
+ 0.40 (INVEST.ANTICIPATIONS INDEX)
(9) R2 = .95; DW = 1.2
Investment demand by manufacturing industries was found positively

related to capacity utilization, growth in output, growth in cash flows,
and growth in the investment anticipations index. It was found negatively
related to interest rates and growth in capital stock value though it is not
clear why this last variable would be negatively related since it serves as a
rough proxy for the Tobin’s q effect.
3.1.5 Investment Goods Demand (Spending) – Mining and Utility

Industries
IM& UTIL = – 0.40 + 0.006 (Priv. Sector SalesAv–1,–2 )

(t = ) (.7)
– 0.008 (ALMON.AV OF MANU.CAPITAL STOCK–1,–8 )
(2.7)
+ 0.04 (ALMON AV PRIV. SECTOR SALES–1,–3 )
(4)
– 1.60 (ALMON AV LONG TERM i–1,–8 )
(–5)
+ 0.40 (INVEST.ANTICIPATIONS INDEX)
(9) R2 = 0.83; DW = 0.8
Mining and utility investment demand was found to be positively related

to private sector sales and the investment anticipation index. It was
negatively related to interest rates and stock values.
3.1.6 Investment Goods Demand – Commercial Industries

(Stores, Offices)
ICOMM = – 35.72 + 0.17(TOTAL C–1 ) – 0.06 (COMM.CAPITAL STOCKS–1 )

(t =) (6) (3)
+ 0.04 (ALMON AV TOTAL CONSUMPTION–2,–9 )
(0.7)
+ 2.40 (ALMON AV:GAP LONG – SHORT TERMi–2,–9 )
(–5) R2 = 0.93 DW = 0.7
Investment demand by retail and other commercial industries was pos-

itively driven by past levels of consumer demand, and the gap between
long and short interest rates (which we interpret as meaning very low
short rates). Again, we see a negative relationship to values of physical
capital.
3.1.7 Investment Goods Spending – Housing

IHOUSING = + 33.65 – 26.48 (PHOUS /PRENT )
(t =) (10)
0.009 (HSE STARTS–1 )
+ 0.26 (i RATELONG – i RATESHORT )–3 +
(1.7) (17)
R2 = 0.96 DW = 1.6
Demand for housing is driven positively by the gap between long-

and short-term interest rates (which may mean that when commer-
cial paper rates are low, banks have an incentive to borrow and make
loans, i.e., this may reflect the supply side) and positively by the level
of housing starts last year (this could represent supply last year or an
indirect measure of the general level of housing demand). Demand
for housing is driven negatively by the cost of housing relative to
renting,
3.1.8 and 3.1.9 Demand for Manufacturing And Nonmanufacturing

Inventories (a Representative Mix of Coefficient
from Both Models)
Iinventory = – 5.03 + 0.07 (M or NonM Sales–1 ) – (0.01, .05) (inventories)–2

(t =) (2.5) (∼ 2.5)
+ 0.42 (Unfilled Orders–1 )
(5)
+..33 (M Output) + 0.42 (Unfilled Orders–2,–4 ), .21 Con.Dur.–1 4
(5) (5) (3.5)
+ 0.43 manuf.price growth + 2.07 Steel Strike
(3.7) (3.3) R2 = 0.61 – 0.77 DW = 1.2 – 1.6
Inventory investment was found to be a positive function of lagged sales,

the level of unfilled orders, and growth of manufacturing output and
prices. It was negatively related to past inventory levels.
3.1.10 Klein’s Calculation of the Real GNP (p.14, eq. g)

X = Xf + Xg + Xh + Xm + Xn = Gross Output of Farm (f) + gov’t (g).+ rental
sector (h) +, manufacturing (m) + nonfarm, nonmanufacturing, nonrental
private sector (n). Xf + Xg are exogenously determined. Xm , Xn , and Xh are
determined as follows:
3.1.11 Manufacturing Output
Xm =– 2.4 + 0.22Cns + .1.13Cd + 0.53 Ip + 0.40Ip + 0.40Ii + 0.39 Gd

(t =) (NA) (5.0) (5.4) (2.6) (2.6) (3.2) (10.1)
2
R = 0.98; DW = 0.63
Ln Xm = 0.645 + 0.75 Ln (#employees in manu.∗ #of hours worked)
(t =) (NA) (8.4)
+ 0.24 Ln (Capital stock in manu.∗ Capacity Util.)
(4.2)
+0.881(Productivity trend)
(23.8)
R2 = 0.98; DW = 0.82 (p. 10, Eq. 14)
Manufacturing output is described two ways: first as a derived demand

function, showing manufacturing output is a function of demand for con-
sumer, investment, and government defense goods and services. Secondly,
as a supply function showing it dependent on the amount of capital and
labor available, capacity utilization, and some allowance for the growth of
productivity over time.
3.1.12 Non manufacturing Output
Ln Xn = 0.27 + 0.99Ln (#nonmanu, nonfarm employees∗ #of hours worked)

(t =) (NA) (4.7)
+ 0.28 Ln (nonmanu,nonfarm, Capital stock)
(7.4)
+ 0.881(Productivity trend)
(1.0)
R2 = 0.98; DW = 0.82 (p. 10, Eq. 14)
And nonmanufacturing output is found to be a function of the same

factors as manufacturing output.
3.1.13 Housing Output
Ln Xn = 0.27 + 0.99Ln (#nonmanu, nonfarm employees∗ #of hours worked)

(t =) (NA) (4.7)
+ 0.28 Ln (nonmanu,nonfarm, Capital stock)
(7.4)
+ 0.881(Productivity trend)
(1.0)
R2 = 0.98; DW = 0.82
Housing output is found to be a function of gross output minus depreci-

ation and disposable income
Alternatively, Klein provides a way of summing the C, I, G, and (X-
M) components of the GDP to get the total. He also provides behavioral
equations (given above for all of these components), so we can sum their
determinants times their parameter estimates to get a GDP estimate based
directly on what we know of its determinants.
X = Cns + Cna + Ca + Ip + Ipf + Ih + Ii + Iif + G + Fe – Fif – Fim – Fic
Behavioral equation definitions of the first eight components are provided

above; and G (government spending on goods and services) is exogenous.
Behavioral equations for real exports and imports are provided below:
3.1.14 Exports (Fe )
Fe = – 38.88 + 0.17 Xwt + 34.33 (Pwt /Pe ) + 0.47(Fe Av–1 to–4 )

(t =) (NA) (13.0) (7.2) (8.7)
R2 = 0.98 DW = 1.3
where Xwt = index of world trade; Pwt = price of world trade, and
Pe = implicit deflator for exports.
Klein’s export demand is defined as a function of the level of world
trade, average prices in world trade relative to our export prices, and the
average level of our exports the past four years. It is not likely these are
causal factors; causally, we would expect exports to be driven more by
our trading partners income levels, exchange rates, and to the extent that
current trade is needed to give foreigners cash to buy U.S. exports, our
import levels may be a factor.
3.1.15 Imports of Crude and Manufactured

Food Products (Fif )
Fif /N = 0.0117 + 0.0064 (Y/N) – 0.0041 (Pif /Pf ) R2 = 0.31; DW = 1.7

(t =) (NA) (4.9) (2.7)
where Y/N = disposable income per capita, Pif = deflator for food
imports, and Pf = prices received by farmers. Demand for crude and food
imports is positively related to disposable income and negatively the price
of these imports relative to domestic prices for agricultural goods.
3.1.16 Nonfood Crude Materials and Semi-Manufactured Goods

Imports (Fim )
Fim = 3.51 + 0.0329Sm + 0.096Iim – 2.14 (Pim /Pm ) R2 = 0.90; DW = 0.76

(t =) (NA) (15.0) (4.9) (2.9)
where Sm = manufacturing sales, Iim = manufacturing inventories,

Pim = deflator for nonfood materials imports, and Pm = deflator for
manufactured goods.
Demand for imported crude materials and semi-manufactured goods is
positively related to manufactured goods sales and inventories and neg-
atively related to the price of these items relative to the price of all
manufactured goods.
3.1.17 All Imports Except Food, Raw Materials, and

Semi-Manufactured Goods
Fic = – 2.57 + 0.0293 Y + 0.60 Fic(AV–1 to –4) – 1.97(Pic /Pm )
(t =) (NA) (4.0) (5.5) (–1.3)
R2 = 0.99; DW = 0.79
where Y = disposable income, Pic = deflator for nonfood, nonmaterial,

non-semi-manufactured imports, and Pm = deflator for manufactured
goods. In short, demand for most imports is a function of dispos-
able income and the relative price of such imports to domestically
produced manufacturing goods, and past trends in importing such
goods.
3.1.18 Concluding Comments on Klein Model

Klein and Evans’ model, one of the earliest, was a huge step forward in
the development of economic science. It represented perhaps the best
of the very early attempts to statistically estimate a demand theory-based
model of the economy successfully. But of course, as an early step, some
equations may include supply as well as demand components. There
are some elements in some equations we might not include today. A
few demand equations have components that seem more like determin-
ants of supply, and there is some use of essentially noncausal variables,
pushing forward past trends into the future without much of a theory-
determined causal relationship, like the Almon distributed lag functions,
which seem somewhat heuristic. Serial correlation problems arise in many
models.
But then again, nobody considers a Copernicus a failure simply because
he thought the path of heavenly bodies was circular. Kepler’s correction
3.2 OTTO ECKSTEIN’S (1983) THE DRI MODEL OF THE U.S. ECONOMY 125
for ellipses is considered an improvement on Copernicus’s work, not a

refutation of it.
Although Klein’s is the best known work from the early era of scientific
model building, other notable work was produced by de Leeuw, Goldber-
ger, Suits, and others. Space is too limited to allow an exploration of their
contributions.
3.2 OTTO ECKSTEIN’S (1983) T HE DRI MODEL OF THE

U.S. E CONOMY
Klein’s work was followed by Otto Eckstein’s (1983) The DRI Model
of the U.S. Economy, a 781-equation model of the U.S. macroeconomy,
using quarterly data for the period 1962:1–1981:4 to obtain parameter
estimates for his models. Eckstein, like Klein, uses a structural model, fol-
lowing the Cowles Commission/Keynesian modeling approach, though
broader in its extensive coverage of financial and sectoral micro mar-
kets. It was originally developed before the advent of rational expectations
modeling, but Eckstein continued to use it after rational expectations the-
ory became well known. Eckstein’s defended doing so for the following
reasons:
. . . The basic rationale for continuing to use structural models in the face
of the rational expectations criticism is this: changes in policy regime seem
to have been among the minor sources of structural change of the eco-
nomy and of forecasting error in the actual historical record. The principal
obstacles to structural consistency and forecast accuracy seem to lie in the
exogenous shocks of wars and OPEC, and in the unpredictability of the
exogenous monetary policy variables. The central assumption of the rational
expectations school, that the forecasts on which businesses and households
make their decisions are free of bias and that markets clear instantaneously,
so far do not seem confirmed by the historical record (Eckstein 1983, pp.
xi–xii) and
. . . the DRI model shows a nervous consumer, subject to the risk
of an unstable environment acting on an exposed financial position,
forming “permanent” expectations rather quickly and acting to a con-
siderable degree in response to short term changes. This is a far
cry. . . from the life-time permanent income theories of stable spending . . . .
(Eckstein 1983, p. 113)
In addition, Eckstein preferred structural to ARIMA (moving-average

VAR) models because his experiments with both showed structural models
to be better at forecasts of the period 1977:4–1980:3, and he provides a
detailed comparison of the forecasts for key variables (p. 27), with struc-
tural models providing better estimates for 17 of the 20 variables tested.
Eckstein also notes
ARIMA is inapplicable for longer forecast horizons. The optimal parameters

produced by the data are always of low degree, implying that ARIMA is
limited to extrapolation of existing trends. As the forecast horizon moves
toward eight quarters, it begins to correspond to the length of the business
cycle, and since ARIMA will not produce turning points, the method is then
guaranteed to fail . . . (Eckstein 1983, p. 28)
Eckstein’s DRI model includes a 212-equation GDP determination sub-

model (64 stochastic, 148 identities) in 84 variables, which will be our
major focus. In addition it includes 193 financial sector equations (112
stochastic), and 94 wage and price equations (57 stochastic). It also
includes 208 industry equations dealing with production, investment cap-
ital stock, and employment, of which 112 are stochastic. There are a few
additional miscellaneous equations. Some equations were estimated using
2SLS. Decisions as to which presumably were made after assessments for
endogeneity in the original variables used in each equation, but the process
is not discussed.
Our focus will be on some of the stochastic equations used to
estimate GDP demand. These will allow us to make some compar-
isons later in the chapter with this chapter’s own equations. Given
the extraordinary size of Eckstein’s model, only some of these equa-
tions can be reviewed, and in fact not all are even presented in Eck-
stein’s book, due to size limitations. The model was re-estimated each
year incorporating the latest data. Key features included the following
equations.
3.2.1 Consumer Demand (Per Capita) for Certain Nondurables

(Clothing and Shoes Only)
LN CS /N = – 2.51 + 0.72 LN (YDisp /N) + 1.26 LN (YDisp/Ydisp-Permanent)

(t =) (–14) (14) (4.4)
– 0.71 LN (PRICES /PRICEALLC )

(–23)
+ .07 LN(NET WORTH–1 /N–1 ) R2 = .99; DW = .8
(3.1)
The model finds per capita clothing and shoes consumption to be a

positive function of per capita disposable income, the ratio of actual
income to permanent income, and net worth. Demand was negatively
related to growth in shoes and clothing prices relative to the price level
for all consumer goods. (The model also shows how structural mod-
els with macro foundations can be used divided into micro models
by adding a relative price variable to the determinants, and adjust-
ing the components of the dependent variable to the desired micro
level.)
3.2.2 Consumer Demand for Durable Goods (Furniture

and Appliances)
LN CF& A /N18–64 = – 4.16 + 1.09 LN(Ydisp-Permanent/N)

(t =) (22) (11)
+ 2.00LN Ydisp /Ydisp-Permanent)
(8)
– 0.57 LN(PRICEFurn& Household Equip /PRICEALL C )
(–5.3)
+ 0.06(Mich.Index Cons.Sent.)
(2.3)
+0.39LN(NetWorth–1 /N–1 )
. – 0.01(irate cons. Credit ) R2 = 0.99 DW = 0.8
(6)
This model finds per capita demand for furniture and appliances to
be positively related to per capita permanent income, the ratio of cur-
rent disposable income to permanent disposable income, the index of
consumer sentiment, and net wealth. Demand was negatively related
to growth in the price of these goods relative to all consumer
prices.
3.2.3 Consumer Demand for Durable Goods (Autos)
LN CA /N18–64 = – 6.99 + 1.09 LN(Ydisp-Permanent/N18–64 )

(t =) (–4) (4)
+ 2.84 LN Ydisp /Ydisp-Permanent)
(4)
– 0.55 LN(PRICEAutos(–1) /PRICEALL C(–1) )
(–5.3)
+ 0.45(Mich.Index Cons.Sent.)
(5.5)
– 1.45 LN(StockCars–1 /N18–84 ) R2 = 0.95 DW = 1.1
This model finds per capita demand for autos to be a positive function
permanent income, the ratio of current income to permanent income, and
the index of consumer sentiment. Demand for autos was negatively related
to the price of autos relative to all consumer goods and the existing per
capita level of car ownership.
3.2.4 Consumer Demand for Single-Family Housing
CHousing = 15.01 + 0.14(Ratio of Houses Sold/Houses For Sale)

(t =) (5) (6)
+ 0.005(Price IndexHSE /iRateMORT )
(4)
– 30.61(StockHousing/N22–64 )
(5)
+ 1.21 (New Mortgage CommittmentsAV–1 to –5 Lags )
(4)
– .14(Price IndexGAS& Elec. ) R2 = .92, DW = 1.3
(–4)
Single-family housing demand and supply is a positive function of how

fast houses are selling relative the number for sale, cost of houses rel-
ative to the mortgage rate (which we interpret to mean the lower rates
are relative to house prices, the more demand, but there is some ambi-
guity in how to interpret this), and financing availability (mortgage
commitments by banks). It is negatively related to the existing stock of
housing, and the cost of major home owner utilities – gas and elec-
tric. (It is surprising that income and wealth variables did not prove
significant.)
3.2.5 Consumer Demand for Multifamily Housing/N
CMultiUnitHsg /N = 0.06 + 0.01(YPerm /N) – 0.01(YTransitory/N)

(t =) (5) (18) (–3)
– 0.004(Price IndexHSE /Price IndexRent )
(–2) R2 = 0.96, DW = .06
Demand for multifamily housing, i.e., rental housing, is a function of both

permanent income (positive effect) and negatively related to transitory
income and the relative price of owning housing compared to renting. The
negative effect of transitory income presumably signals a shift away from
renting to house ownership in the presence of positive windfalls. There
is no reason given for the unexpected negative sign on relative housing
prices. It may be reverse causation. Demand shifts to housing may raise its
prices, lowering rental prices.
3.2.6 Business Demand for Investment Goods (Machinery

and Equipment)
IEquip = – 15.35 – 0.14(Stock of Equip–1 ) + 0.37(Cap Util.∗ Stk.Equip)

(t =) (–3.6) (2) (3.6)
+ 0.01(Cost of Capital–1 ) – 11.87 (Int. Payments/Cash Flow)–1
(1.7) (–1.2)
– 0.15(Koyck Av.Expec.Output–1,–10 ) R2 = 0.996 DW = 1.6
(–7.7)
(Note: Wrong sign on cost of capital, expected private output.)

Demand is principally a function of the size of existing stocks and
utilization level of existing capital. The model suggests it is positively
related to the cost of capital, but there is no good reason for this.
Demand is found negatively related to two other variables, but this prob-
ably spurious, since there is no good reason for the relationship to be
negative.
3.2.7 Business Demand for Investment Goods (Factories,

Other Structures)
IPlant = 105.52 – 0.14(Stock of Bldgs–1 ) + 0.19(Cap Util.∗ Stk of Equip.–1 )

(t =) (1.7) (–1.7) (2.8)
– 13.61 (Int.Payments/CashFlow)–1 + 0.001(Desired Cap.Stock)
(–1.9) (2.5)
– 283.91 (Stk.ofStructures/GDPPotential) R2 = .93; DW = 1.7
(–1.9)
The demand for business buildings is positively related to the level of

utilization of the current stock of buildings and the size of the desired
stock, and negatively related to the interest payment burden and negatively
related to the size of the existing stock of buildings and its size relative to
potential output.
3.2.8 Business Demand for Investment Goods (Inventories)
IInven = –19.58 + 0.08(Sales)+0.13(Expected Sales – Actual Sales)

(t =) (–8) (4) (3.4)
– 0.25(Inventory–1 ) + 88.51(Cap.Util)–1
(–4) (4.3)
+ 9.76(Unfilled Orders–1 ) + Dummy Var. R2 = 0.80; DW = 2.0
(3.1)
Demand for inventory is found positively related to sales, expected sales,

capacity utilization levels, and the speed with which unfilled orders are
being filled (perhaps because the faster orders are being filled, the more
vendors have to sell and are selling, and therefore, the more inventory they
need to replace). They are negatively related to the stock of inventories in
the prior period.
3.2.9 Concluding Comments on Eckstein’s model:

Eckstein’s model has proved to be the largest, most comprehensive model
of the U.S. economy, its financial sector, and hundreds of micro-level
industry offshoots ever produced. It was also commercially viable as
the DRI, Inc. model, and a large step forward in terms of statistical
3.3 RAY FAIR’S ESTIMATING HOW THE MACROECONOMY WORKS (2004) 131
methodology. Eckstein was also aware of the growing interest in VAR and
DSGE modeling, and argued against them. He offered evidence in favor
of his Cowles-type model with arguments commonly still used today when
comparing model strengths and weaknesses the three types of large-scale
modeling.
That said, Eckstein always considered his models a work in progress,
and there are a few remaining equations (though not many) with explan-
atory variables that may confuse directions of causation, whose estimates
have the wrong signs, or use a Koyck distributed lag to push forward
a past empirical trend for which the theoretical basis is not obvious. In
addition he heavily used formulations of permanent income hypothesis
(averages of several year’s income) as the income variable driving con-
sumption, without indicating if this was the result of an empirical finding,
or just an off-the-shelf theoretical argument assumed to be valid. Our
own tests have indicated current income alone explains more variance in
consumption.
Eckstein’s DRI model has export and import sub-models, but they are
not included in his 1983 book describing the model. Also, no models of
interest rates are presented.
3.3 RAY FAIR’S E STIMATING HOW THE MACROECONOMY

WORKS (2004)
Fair’s large-scale model of the economy is the most modern and meth-
odologically sophisticated of the large-scale Cowles Commission-type
structural models. Fair’s equations are regularly updated and re-estimated
using the most recent quarterly data. Our discussion below is taken entirely
from the 2004 book, except the actual regression equations shown for
consumption and investment. Regression data is taken from a 2009 online
update to the regressions in the book. Occasional other quotes are taken
from the online version of the book. Data used in regressions typically
was quarterly data for the period 1954.1–2009.1. Key features of Fair’s
large-scale model include the following:
Expectations: Past conditions assumed to shape expectations for future,
but generally, rational expectations (perfect knowledge of future) not
assumed.
Autoregression variables AR(1), AR(2), etc., used to deal with non-
stationarity issues.
Fair found nominal (vs. real) interest rates explained variation in con-
sumption and investment models better, i.e., interest rate effects were
more statistically significant. His tests were complicated (see p. 71) and
are not repeated here. For comparison, we tested standard consumption
and investment equations in this study’s models two ways; one using the
real prime interest rate, then retesting the exact same model except using
the nominal prime interest rate. Results for OLS first difference models
are presented below:
Consumption (PR0 ) Investment (PR–2 )

Real Nominal Real Nominal
Coefficient –12.15 –9.23 –2.33 –9.06

t-Statistic (–5.2) (–2.8) (–2.2) (–3.4)
R2 (%) 93.3 91.3 93.5 94.3
Real does substantially better for consumption; nominal does better for
investment (more marginally). Our practice will be to use real interest rates
for investment as well as consumption; they are more theoretically sensible
and only give marginally different results in terms of their ability to explain
variance.
Details of Fair’s Model

In the section below, we review and evaluate the specific real consumption,
investment, and GDP equations used in Fair’s model of the U.S. economy.
3.3.1 Demand for Consumer Services

Log(CS/POP) = – 0.03 – –0.22AG1 – 0.54AG2 + 0.68AG3
(t =) (–1.2) (–4.7) (–7.4) (6.4)
+ 0.78Log(CS/POP)–1 + 0.11log(YD/POP∗ PH)
(23.9) (3.6)
.. – .001(RSA) + .03Log(AA/POP) – 1.00042 T
(–6.0) (5.6) (4.7)
R2 = 1.00; DW = 1.8
Demand for per capita consumer services is found to be a function of the

mix of age groups, young (AG1), “middle aged” (AG2), and old (AG3)
in the population (demand for services is greatest when the elderly are
the largest segment), the previous year’s spending on services, per cap-
ita disposable income (YD/POP), the after tax three-month treasury bill
rate-negatively (RSA), per capita wealth levels (AA/POP), and a time
trend.(T).
3.3.2 Demand ffor Consumer Nondurables
Log(CN/POP) = –0.26 + 0.03AG1 + 0.13AG2 – 0.25AG3

(t =) (–4.8) (0.5) (1.8) (–2.1)
+ 0.76Log(CN/POP)–1 + 0.18Log(CN/POP)–1 +
(22.1) (3.0)
+ 0.05log(AA/POP)–1 + 0.11 Log(YD/POP∗ PH)
(5.3) (5.2)
– 0.002RMA.00042T R2 = 0.99; DW = 1.9
(–4.9)
Nondurables per capita are found to be a function of the distribution of

young, middle aged, and old in the population (demand is greatest when
the middle group is largest relative to the others), last year’s demand
for nondurables, the change in demand for nondurables since last year,
wealth(AA/POP), disposable income, and the mortgage interest rate
(RMA).
3.3.3 Demand for Consumer Durables
(CD/POP) = – 0.40 + 0.51AG1 + 0.80AG2

(t =) (–3.6) (2.9) (1.8)
– 1.49AG3.17(DELD(KD/POP)–1
(–3.3)
– 0.02Log(CD/POP)–1 )
(3.6)
– 0.01 (KD/POP)–1 + 0.06 Log(YD/POP∗ PH)
(–3.8) (3.5)
– 0.004RMA∗ CDA + 0.0006(AA / POP)–1
(–2.3) (3.6)
R2 = 0.19; DW = 2.1
Per capita demand for durables is found to be a function of the mix of

young, middle age, and old in the population (greatest the larger the
middle group compared to the others), and per capita values of depre-
ciation of existing stocks of durables, disposable income (YD), and net
wealth (AA). The mortgage interest rate (RMA) was negatively related to
spending on durables.
3.3.4 Demand for Residential Investment
IHH/POP – (IHH/POP)–1 = 0.30 + 0.35 17(DELH(KH/POP)–1

(t =) (4.0) (5.9)
– (IHH/POP)–1 ) – 0.02(KH/POP)–1
(–3.9)
+ .13YD/(POP∗ PH) – .02(RMA∗–1 IHHA)
(4.1) (5.1)
+ .65RHO1 + .26RHO2 R2 = .33;
(8.3) (3.6) DW = 1.9
Demand for residential housing per capita is found to be positively related

to per capita values of the rate of depreciation of the housing stock
relative to last period’s demand for housing, last year’s stock of hous-
ing (KH/POP)–1 , and disposable income. The mortgage interest rate
was negatively related to demand for housing. Autocorrelation controls
(RHO1&2) are added.
Fair Consumer and Residential Housing Equation Variable
Definitions:
CD = consumer durables
CN = consumer nondurables
CS = consumer services
IHH = residential investment
AG1 = % of 16 + population 26–55 minus % 16–25
AG2 = % of 16+ population 56–65 minus % 16–25
AG3 = % of 16+ population 66+ minus % 16–25
POP = noninstitutional population 16+
YD = disposable income
RSA = after tax bill interest rate (% points)
AA = total net wealth
RMA = after tax mortgage interest rate
PH = price deflator for CD, CN, CS, and IHH
KD = stock of durable goods
CDA = peak-to-peak interpolation of CD/POP
KH = stock of housing
IHHA = peak-to-peak interpolation of IHH/POP
RHO = autocorrelation control
DELH = housing depreciation rate
DELD = durables depreciation rate
AA = net wealth
3.3.5 Demand for Fixed Investment
LogKK = – 0.00 – 0.009 log(KK/KKMIN)–1 + 0.95Log KK–1

(t =) (–0.3) (–2.6) (59.5)
+ 0.06LogY + 0.004LogY–1 + 0.002LogY–2
(3.8) (0.7) (0.5)
+ 0.001LogY–3 + 0.002LogY–4 – 0.0002 RBA-pe4–2
(2.9) (0.5) (–2.4)
∗
+ 0.0002(CG–2–4 )/((PX YS)–2–4 R2 = 0.97; SE = 2.0
(0.6)
where KK = stock of capital, LogKK = investment, KKMIN = amount

of capital needed to produce production level Y, Y = private sector pro-
duction, CG = capital gains, and PX∗ YS = price deflator for sales∗ potential
output of the firm sector
Current year fixed investment is postulated to be positively related to
the capital stock relative to output levels (KK/KKMIN)–1 , last year’s level
of capital (KK–1 ), the level of production for the past four years, and the
level of potential output for the firm sector. Demand is negatively related
to the after real tax bond interest rate.
3.3.6 Inventory Investment

Defined as this year production (Y) minus this year’s sales. This year’s pro-
duction is a function of last year’s production, current year sales, last period
inventory, and three dummies. Consolidating, current period inventory
levels (V) are defined as approximately
V = 0.76V–1 + 0.30Y–1
3.3.7 Capital Consumption Allowances (CCF)

LogCCF = 0.003 + 0.06Log((PIK∗ IKF)/CCF–1 ). + 0.06D621
(t =) (1.7) (8.3) (6.40)
+ 0.03 D721N723 + 0.034D9231N924 + 0.04D013
(5.7) (6.0) (4.010.8)
+ 0.06D9411N942 + 0.03D014 + 0.06D043N044 – 0.17D051
() (3.4) (9.3) (17.7)
+ 0.16D053 – 0.14D054 + 0.15D081 + 0.29RHO1
(16.7) (14.9) (15.4) (4.5) R2 = 0.87; DW = 2.1
where PIK = price deflator: nonres. fixed investment; IKF = nonresidential

fixed investment; CCF = capital consumption; D621 = dummy variable =
1 in 1962:1; D721N723 = dummy variable = 1 in 1972:1; –1 in 1972:3.
(Other dummy variables have similar meanings.)
Capital consumption is presented as a function of the ratio of this year’s
fixed investment to last year’s CCFs and a series of dummies reflecting
changes in the law regarding allowable depreciation. A variable is added to
ensure no coefficient bias due to autocorrelation.
3.3.8 U.S. Demand for Imports

Log(IM/POP) = –1.07 + 0.77Log(IM/POP)–1
(t =) (6.4) (21.7)
+ 0.53Log(all consumption., res. & nonres. Invest)
(6.5)
+ .08Log(PF/PIM) – 0.13D691 + 0.13D692

(5.1) (–4.5) (4.3)
– 0.09D714 + 0.09D721 R2 = 0.999 DW = 1.6
(–3.3) 93.1)
where PF = price deflator for (total sales-farm GDP) and PIM = price
deflator for imports.
Demand for imports (per capita) is given as a positive function of last
year’s imports level, total consumption, and investment demand (which
includes demand for imports) and the relative growth in domestic prices
compared to imports. Dummies are used to represent unique events in
1969 and at the end of 1971 and beginning of 1972.
3.3.9 Month Treasury Bill Interest Rate (RS)
RS = 0.67 + 0.92RS–1 + 0.07(100∗(PD/PD–1 )4 – 1) – 10.09UR

(t =) (4.5) (53.2) (4.0) (–3.4)
– 70.15UR + 0.01PCM1–1 + 0.22D794823∗PCM1–1
(–5.4) (2.5) (9.7)
0.26RS–1 – 0.31RS–2 R2 = 0.48; DW = 1.8
(4.9) (–6.2)
D794823 = 1 for the period 1979:4–1982:3

PD = price deflator for total sales – net exports, PD/PD–1 = inflation,
UR = unemployment rate, and PCM1 = annual percentage change in M1
(in % points).
Fundamentally, the variance in the treasury rate is explained principally
by last period’s rate, the change in the rate the past two periods, plus
the Taylor rule variables, with allowance for the Volcker severe money
constraint period 1979–1983.
3.3.10 Real GDP Model (Identity)
GDPR = Y + PIEB + CCB + PSI13(JG∗ HG + JM∗ HM + JS∗ HS + STATP)

where
Y = real private sector production, derived from Log Y
LogY = 0.45 + 0.30LogY–1 + 0.87LogX – 0.24LogV–1 – 0.01D593

(t =) (4.3) (7.7) (18.6) (–7.6) (–2.8)
– 0.004D594 + 0.01D601 + 0.44Rho1 + 0.36Rho2
– (1.2) (2.5) (5.8) (5.0)
2
+ .15Rho3 R = 1.00; DW = 2.0
(2.1)
V–1 = real inventories

Y–1 = real production
X Sales = determined by consumer spending equations described above,
spending on in residential housing and fixed plant and investment
described above as well as residential investment by firms and financial
businesses (exog) plus net exports, government spending of consumer
and investment goods, minus profits (exog) and capital consumption
(exog)
PIEB = real before tax profits (exog)
CCB = real capital consumption (exog)
PSI13 = ratio of gross product of Fed state and local government to
total govt. employees hours (exog)
JG∗ HG = number of civilian federal government employees∗ average #
of hours worked) (exog)
JM∗ HM = number of military federal government employees∗ average
# of hours worked) (exog)
JS∗ HS = number of state and local government employees∗ average #
of hours worked) (exog)
STATP = statistical discrepancy due to using chain type price deflator
(exog)
D593 = dummy variable, valued at 1 in 1959, 3rd qtr., zero otherwise
(other dummies defined similarly)
Rho1 = autocorrelation control for first-order autocorrelation (other
Rho defined similarly)
Fair did not just enter all the variables he found to be determinants
of consumption, investment, and imports into one IS curve regression
model, along with variables representing exports and government

spending, and then estimate it. This would seem to be the simplest stat-
istical estimation method of using the classroom “IS” curve method of
GDP determination we teach students. While mechanically it can be done,
substantive results are not satisfactory.
Chapters 7 and 8 explain why that won’t work, as well as our earlier
Chapter 2, Section 2.2.4 describing why VARs give distorted estimates
when all variables are assumed to be determinants of all dependent vari-
ables. The process of doing just one regression aggregates the spurious
effects of a variable on one component of GDP (e.g., depreciation on
consumption), with its causal effects on another (e.g., depreciation on
investment). The result of adding two such regression coefficients (which
is what the regression does) is to provide results that are sometimes illo-
gically high, low, or having the wrong sign. An additional problem is that
adding so many variables to one equation increases multicollinearity levels,
which also distorts parameter estimates.
We suspect Fair deferred from using this method for similar reasons.
3.3.11 Concluding Comments on Fair’s Model

Fair’s model is uniformly a 2SLS model, without serial correlation prob-
lems. Statistically, it is the most advanced of the three Cowles models
discussed so far. It also clearly uses a coherent “IS curve“ model for GDP
determination. Its models identify some key determinants of consump-
tion and investment, key to its responsibility to explain how the economy
operates. In addition to structuring each equation to include key variables
important for this purpose, Fair’s model uses some trend variables and
some lagged dependent variables to allow the model to also be used for
forecasting purposes.
We have noted earlier in the methodology section that trend variables
don’t add to the (substantive) explanatory power of models, and hence,
though they explain variance, they don’t do so for a theoretically sensible
reason. From the explanatory model point of view, they are, at best, a place
marker reminding us that there is an equation where more remains to be
done before we have fully explained the dependent variable’s behavior.
From the forecasting point of view, they explain some drift that would
otherwise go unexplained.
We noted earlier that multicollinearity can distort estimates of a determ-
inant’s marginal effect on a dependent variable. From the explanatory
model point of view, adding dependent variable lags as explanatory
variables can add to this problem, though they may be useful in forecast-
ing. The lagged dependent variable’s own determinants, lagged one more
year, are the same explanatory variables as are explicitly included in the
current year model along with the lagged dependent variable. Including
the lagged dependent variable as explanatory just indicates the modeler’s
belief that not all changes in an explanatory variable are felt in the year the
change occurs; some are not felt until the following year. This substantive
message may be clearer if these explanatory variable lags were added to the
model, as well as the more current values already included.
Consumption was hypothesized as a determinant of imports; though
imported consumer goods and services are usually counted as part of total
consumption, so while use of the variable explains variance, it does not
explain much about what makes import demand vary. An income variable
might work better since it is generally considered the major determin-
ant of consumer demand. We also noticed the depreciation model did
not include prior years’ investment levels as explanatory variables. Prior
year investment generally determines allowable percentage write offs as
depreciation from year to year.
3.4 FEDERAL RESERVE BOARD/U.S. MODEL (1996)

This newer DSGE/rational expectations model (Brayton, F and
Tinsley, P., ed. 1996) was intended to replace the older FRB/MPS
model which had been used for 25 years and was a more typical
Keynesian/Cowles Commission-type model.
In this model, estimates of current consumption or investment are
typically modeled as partial adjustments of current conditions’ effect
on consumption or investment to long time desired equilibriums. The
long-term equilibriums are determined by estimating how much wealth
individuals will accumulate in their lifetime, including accumulated labor
income, government transfers income, and more normal types of wealth
derived from ownership of stock market and other assets. Desired yearly
consumption is then defined using a Modigliani Life Cycle/Friedman
Permanent income hypothesis. Regressions are then run to estimate the
current period demand for consumer goods as a function of the gap
between last year’s consumption and equilibrium consumption (c–1 – c∗ –1 ),
lags of the change in consumption in past Periods (c–i ), expected changes
in consumption in future periods(c*e +i ), and current year income. Below
3.4 FEDERAL RESERVE BOARD/U.S. MODEL (1996) 141
we present the equations used for three different types of consumption.

Variables in functions described below are typically given in logs, not levels
unless otherwise noted. Data used in estimating regressions is generally
1963:1–1995:4.
3.4.1 Total Consumption of Durables, Nondurables, and Services (C)
Desired equilibrium level of consumption (C∗ ) :

C∗ = 1.0V + 0.62Strans – 0.15Sprop + 0.52Sstock + 1.28So + 0.013X
where V = wealth = leads∞ (Ye ), Strans = transfer wealth/V, Sprop = property

wealth/V, Sstock =stock wealth/V, So = other wealth, and X = aggregate
output gap.
The theory behind this consumption function is fundamentally
Modigliani’s Life Cycle hypothesis: consumers accumulate wealth (includ-
ing wealth from labor earnings) principally to finance consumption. They
are reasonably accurately able to assess their lifetime wealth and desire
to spend it down in relatively equal increments throughout their life.
The output gap variable indicates the extent to which consumer spend-
ing is affected by temporary lapses from full employment levels of income.
Life cycle hypothesis functions rely heavily on the notion that consumer
spending is based on expected lifetime income, not just current year
income. An exhaustive study (Heim 2007. Review of Business Research.
Vol. 7(1). Oct. 2007) of how well such functions explained variance in
consumption over the 1960–2000 period in the U.S. found that they
explained only about half as much variance as current income alone,
and that their capacity to explain variance only increased as less and less
years – either in the past, or going forward – were used in calculating
the income average intended to represent their permanent income. Non-
etheless, this is the approach taken in the FRB/U.S. model and it does
represent the thinking of one of the dominant school in macroeconom-
ics today (VAR being the other), which is why the FRB has replaced its
earlier, more Keynesian MIT, U. Penn., SSRC model (MPS) with this
model.
Key to understanding these models is to understand that consumption
is always in the process of incrementally adjusting current consumption
levels to desired levels (C∗ ), and equations always contain an adjustment

variable of the form (Ci –C∗i ). where i = some designated period.
Dynamic Adjustment:
C = – 0.12(C–1 – C∗ –1 ) + 0.17lags1 (C–i ) + 0.75Leads (C∗e +i ) + 0.09y
R2 = 5.4; (No t-stats.provided)
The model explains slightly more than half the variation in the change in
the log of total consumption. This is considerably less than was the case for
most Cowles structural models examined, where R2 s in the 0.80–0.95 range
are more common not only for total consumption, but for its individual
components including any equations estimated in logs. Estimation in logs
is the standard practice in the FRB/US and other DSGE models, but less
common in Cowles models.
How should we interpret all this? The guide to the FRB/US indicates that
. . . Based on a linear approximation of the logarithmic equilibrium condi-

tion, marginal propensities to consume out of categories of income and
tangible wealth are 0.51 for labor income, 1.05 for transfer income, 0.39
for property income, 0.03 for corporate equities, and 0.075 for other net
tangible assets . . . (A Guide to FRB/US, 1996, p.17)
The fundamental difference here (beside poor explanatory power) with

structural models is that structural models try to explain variation in
consumption (or other variables) on the basis of consumption’s current
(or recent past) determinants: income, wealth, interest rates, etc. The
approach used here attempt to define this year’s consumption as a function
of income’s growth in the past and anticipated growth in the future toward
a desired level, this desired level being related to income and estimates of
lifetime wealth.
Another way of looking at the conceptual difference between this
DSGE and structural models is this: the DSGE model collapses to the
Keynesian (structural) model if the assumption that consumption is driven
by consumer lifetime wealth is incorrect, and that consumption is princip-
ally driven by current year income and recent wealth levels only (or the
assumption that these are the expectations of lifetime average income and
wealth).
3.4 FEDERAL RESERVE BOARD/U.S. MODEL (1996) 143
3.4.2 Consumption of Consumer Durables and Investment in

Residential Construction (Time Span =1963:1–94:4 for Autos,
1963:1–1995:4 for Other Durables and Housing)
Equilibrium relationships: C∗ dv = 1.0c∗ – .46(pdv – pc ) – .41(pgas – pc ) – .03rdv

C∗ do = 1.0c∗ 41(pdo – pc ) – .02rdo + .004t82
i∗ h = 1.0c∗ – .13(rh – pc ) – .003(t47 ) + 003t88
where (pdv – pc ) = log prices of autos – log price of aggregate consumption;

(pdo – pc ) has same meaning for other durables, as does (pgas – pc ) for
gas; rdv ., rdo , rh = costs of capital for, autos, other durables and housing;
t82,47 and 88 = quarterly time trends starting in the year specified.
Dynamic adjustment:
cdv = – 0.30(cdv–1 – c∗ dv–1 ) – 0.28lags1 (cdv–i ) + 3.22Leads (c∗e dv+i )
+ 7.46Lags4 (c∗e dv+i ) R2 = 0.43; (No t-stats.provided)
cdo = – 0.10(cdo–1 – c∗ do–1 ) + 0.17lags1 (cdo–i ) + 2.15Leads (c∗e do+i )
+ 1.12Lags4 (c∗e do+i ) R2 = 0.34; (No t-stats.provided)
ih = – 0.09(ih–1 – i h–1 ) + 0.38lags1 (ih–i ) + 6.10Leads (i∗e h+i )
∗
+ 4.15Lags4 (i∗e h+i ) R2 = 0.60; (No t-stats.provided)
The fundamental difference here (beside poor explanatory power) with

Cowles structural models is that structural models try to explain vari-
ation in consumption (or other variables) on the basis of consumption’s
current (or specific recent lags of) determinants: income, wealth, interest
rates, etc. The approach used here attempts to define this year’s consump-
tion as a function of its growth in the past and anticipated growth in the
future toward a desired level, this desired level being related to anticipated
lifetime income and wealth.
3.4.3 The New FRB/U.S. Model Estimates of Producer’s Durables

and Business Inventory Demand
Equilibrium Relationships : i∗ pd = 1.0Xb – 1.0rpd + 1.0zpd + 19.5Xb

k∗ i = 1.0Xb
where i∗ pd = desired level of producers’ durables; k∗ i = desired level of

inventories; xb = business sector output; rpd = rental cost of producers
durables; zpd = (depreciation rate + mean of xb ).
Dynamic Adjustment of Producer Durables Δipd and Inventories Δki :
Equilibrium Relationships : i∗ pd = 1.0Xb – 1.0rpd + 1.0zpd + 19.5Xb

k∗ i = 1.0Xb
where cf–1 = corporate cash flow
ki = – 0.23(ki–1 – k∗ i–1 ) + 0.47lags3 (ki–i ) + 0.53Leads (k∗e i+i )

R2 = 0.42; (No t-stats.provided)
Both producer durables and inventories are a function, first, of the rate of
adjustment of current levels of them to desired levels. In addition current
period changes are found to be linear projections of past and anticipated
rates of change each quarter in these variables. From a substantive per-
spective, projecting future change from past changes amounts to arguing
that there are no substantive determinants of changes in spending on pro-
ducer durables or inventories, only the inertia of past trends in spending
growth. The role of future changes in investment in determining the cur-
rent period change is not so obvious. The theoretical credibility of the first
term, i.e., that the desired change this period depends on prior decisions
about how quickly to try to move from current levels to desired levels
hangs on how reasonable it is to assume that desired levels of invest-
ment = current output minus current price of producers durables plus
depreciation plus 19.5 times the accelerator. This would seem to be an
empirical question not addressed in the model.
Exports, Imports, and Interest Rates
The new FRB/U.S. model of the economy has export, import, and
interest rate equations, but these were not included in the Federal
Reserve’s “A Guide to FRB/US”: A Macroeconomic Model of the
United States (1996)
3.5 LITERATURE REVIEW SUMMARY

In concluding, we note that currently the only large-scale econometric
models currently in use are Fair’s Cowles Commission model, the FRB’s
DSGE model, and the DSGE models of some regional banks. Eckstein’s
3.5 LITERATURE REVIEW SUMMARY 145
DRI, which is also a Cowles model, is proprietary and appears to continue

to be in use, though undoubtedly in modified form.
The Klein, Eckstein, and Fair models all reach explicit conclusions
about how income, wealth, interest rates, depreciation, etc., affect con-
sumption and investment spending. Findings are relatively similar in the
sense that, e.g., most consumption models contain income, interest rate,
and wealth variables. The capacities of these models to explain variance
in key economic variables are substantial. In a few cases, however, part of
the explanatory power of some equations is derived from variables whose
estimates run counter to theory, or are atheoretical. This raises questions
as to whether part of these models’ capacity to explain variance is perhaps
merely spuriously correlational rather than something from which we can
infer a likelihood of causality. Our goal, after all, with large-scale structural
modeling is to produce something standard that reliably explains fluctu-
ations that occur in the economy; something like the physicist’s standard
model (though not with that degree of precision).
We are struck by the fact that in the more modern DSGE model
examined explanatory power of the regressions is limited at best, and
experience shows that regression coefficients in models whose total explan-
atory power is small or only moderate are notoriously likely to change with
even small modifications to the model. Further, unless we go behind the
values of desired levels of consumption and investment, we cannot get at
the economic variables which ultimately explain why the Fed’s dynamic
adjustment equations explain at least some variation in consumption and
investment, and no empirical verification of the correctness of the para-
meter estimates on determinants of desired consumption or investment
were provided (and may not be possible to empirically verify in DSGE
models; e.g., what data series do we use to represent desired equilibrium
consumption in the FRB/US equation
C∗ = 1.0V + .62Strans – .15Sprop + .52Sstock + 1.28So + .013X
Finally, there were no tests of robustness of parameter estimates in three

of the four models reviewed, and limited testing in the fourth. How much
credibility can we give to an estimate derived from correlational analysis
knowing how sensitive individual estimates are to the period sampled,
regression method used, and the exact combination of variables tested in
a regression equation? Studies should provide estimates for every variable
for different time period samples, different regression techniques, or for
models with different numbers of other variables included in the model.
Robustness testing along these three dimensions is required before a par-

ticular finding can be considered good science, rather than just another
hypothesis tested with “interesting” results. In the sections to follow, this
study hopes to remedy these deficiencies by extensive testing the robust-
ness of parameter estimate findings for every equation included in the
large-scale model presented.
CHAPTER 4
The Consumption Models
What variables should we test to see if they are determinants of consumer

spending? An extensive review of the literature (Heim 2013) indicated
the following variables, or variants of them, have been tested and found
to be determinants of consumer spending (CT ) or borrowing (CB2 ) in at
least one previous study. All these variables were tested in this chapter to
determine if they would be found significant here, too. Testing for their
precise effects was done initially using OLS. Then, all right-hand side
variables were also tested for endogeneity with the dependent variable.
If endogeneity (identification) issues were found, strong instruments for
the endogenous variables were developed, and the hypothesis was tested
using 2SLS.
CT = real consumer goods and services

(Y-TT ) = real disposable income, defined as GDP minus total government
receipts, which yields estimates nearly identical to the national income
variable used in Kuznets (1952) consumption studies)
(TT -GT&I ) = real government deficit: total receipts minus total expenditures on
government consumption, Investment, transfers, interest and subsidies.
To capture any differences in the effects of tax cut and spending defi-
cits, the TT and GT& I components were tested separately. Year-to-year
changes in the deficit are measured net of year to year changes in the
pool of loanable funds (personal, corporate and depreciation savings +
foreign borrowing)

DOI 10.1007/978-3-319-50681-4_4
148 4 THE CONSUMPTION MODELS
PR = real prime interest rate defined as the nominal rate minus the average
of the past two completed years inflation
DJ–2 = a measure of wealth (NYSE Composite Index), lagged two years
(Federal Reserve/MIT Large econometric model showed stock mar-
ket activity to be a major determinant of household wealth, which in
turn was a determinant of consumer spending. See Eckstein 1983, p. 5)
XRAV = the real broad U.S. exchange rate average for current and past three
years (foreign currency per dollar)
POP16 = ratio of young (20–24) to old (65+) in population
ICC–1 = Index of Consumer Confidence (Conference Board measure), lagged
one year
M2AV = real M2 money supply; average of second, third and fourth past years
M2-M1 = savings components of M2 for the current period
CB , CB2 = consumer borrowing (annual change in consumer debt). (Federal
Reserve/MIT model indicates credit access a major determinant of
housing demand (Eckstein 1983, p. 5))
Above, as well as in tests below, current period values are typically denoted
without subscript. Other subscripts indicate periods lagged.
Variables in the consumption model such as disposable income or the
deficit variables (T, G) may be endogenous with consumption since con-
sumption is a part of GDP and GDP is a determinant of all the models
tested. Explanatory variables “suspected” a priori as being endogen-
ous with the dependent variable in consumption spending or borrowing
models are given in Table 4.0.1.
Endogeneity of these “suspect” variables was tested using the Hausman
endogeneity test.
All other explanatory variables beside those listed in Table 4.0.1, used
in either the consumption function or in standard investment models in
Chapter 5, which follows, were assumed to be exogenous, or only affect
Table 4.0.1 Determinants of consumption assumed endogenous when applying

endogeneity tests
• Disposable income
• The government deficit (T, G)
• The exchange rate
• The prime interest rate
• Consumer borrowing
• The exchange rate average
THE CONSUMPTION MODELS 149
consumption after a lag. They were used as first-stage regressors when

applying the Hausman test to “suspect” variables.
When endogeneity was found, the initial instruments were developed
in the standard way described in the methodology section. Each involved
regressing a variable found Hausman-endogenous, on the current period
variables considered exogenous or used only with a lag in the consumption
and investment models, plus the exports variable. If it proved to be a weak
instrument, it was made a strong instrument using procedures described
in the methodology section.
Somewhat surprisingly using these variables for the Hausman first-stage
test, no right-hand side variables were found endogenous with the depend-
ent variable in the total consumption, consumer imports, or domestically
produced consumer goods models.
The initial instruments were developed regressing these variables
on the endogenous variable being replaced. Calculated values of the
dependent variable from the estimated equation replaced the endogenous
variable.
In 2SLS tests, models labeled with an “a,” are 2SLS models that
use the group of exogenous and lagged variables given in Table 4.0.2
as the initial instrument’s components. Generally, these proved to be
weak instruments and were replaced by strong instruments. Strong
instruments, labeled “Alt,” met Wald F or t-statistic criteria by adding
additional lagged values of variables already in the initial instrument,
and occasionally new variables, or removed variables from the initial
instrument whose t-statistics indicated they were not contributing to
strengthening the instrument and were pulling the instrument’s F-
statistic down. Strong instruments labeled “Alt2” also added to the
instrument any of the originally “suspect” variables that proved not
endogenous.
Table 4.0.2 Determinants of consumption or investment initially assumed exo-

genous or lagged, and used as regressors in the first-stage regression in Hausman
of endogeneity tests (subscripts denote lags)
Capacity Utilization Rate–1 Real M2AV(–2 through –4)

Real Prime interest rate–2 Business Borrowing–1
NYSE Composite Index–2 Consumer Confidence–1
Population Size0 Exports
Population Age Distribution0 (20–24 /65+ year olds)
Seven consumption models are tested. They included separate models

for total consumption, durables, nondurables and services consumption,
domestically produced and imported consumer goods, and consumer bor-
rowing. Of the seven dependent variables, four were found nonstationary
(in first differences): total consumption, domestically produced, imports,
and nondurables. A total of 15 variables were hypothesized to be determ-
inants of one or another of these seven dependent variables; and were
tested in these models to determine if such were the case. Nine of them
were found nonstationary, five were cointegrated with the dependent
variable they were used with, so no detrending was done with them.
Four could not be cointegrated with their dependent variable, and were
detrended, which restored their stationarity or at least left them cointeg-
rated with the dependent variable they were used with. Detrending was
done by regressing the nonstationary consumption variable on a constant
and a trend variable, and the detrended version used in the model was
obtained using the following formula:
CDetrended = CNonstationry – α – β(Trend Variable)
where α and β are the results of the detrending regression.
Specific variables found nonstationary are described in the write up of
results for each the seven consumption models below.
Method Used to Develop Robust Models
Each of the 38 stochastic models in this study uses a standard series of
statistical tests to refine initial estimates obtained from a model using one
sample period and one particular combination of explanatory variables into
a final, robust model whose results are reliably consistent over different
time periods and for variations in the variables included in model tested.
The initial test is an OLS test of variables found to be determinants
of the dependent variable in prior studies reviewed or cited in theory or
discovered in exploratory testing. If endogeneity between the dependent
and an explanatory variable is discovered, a strong, nonendogenous instru-
ment is developed and the initial model is re-estimated using 2SLS. Then,
each explanatory variable in the model is tested using stepwise regression
to determine its individual contribution to total explained variance. Then
the model is retested in three other, though overlapping, time periods
to determine which initial results can be replicated in other time peri-
ods. Finally, the model comprised of variables that have proven to be time
period robust are tested for the sensitivity of regression coefficients and
4.1 TOTAL CONSUMER SPENDING ON BOTH DOMESTICALLY PRODUCED. . . 151
significance levels to multicollinearity in the model. This is done by adding

and subtracting variables from the time period robust model to see if the
parameter estimates on remaining variables remain reasonably stable. Vari-
ables’ coefficients’ are considered to remain stable if adding/subtracting
variables from the model does not change their values by more than one
third. Some exceptions are made to this rule depending on particular
model characteristics. Reasons for exceptions are noted in the text.
For those who wish to move more quickly from initial to final fully
robust models, we note at the beginning of each equation’s development
process the initial model we are starting with, and where to find the final
robust model we end up with, so the reader can jump from start to finish.
We also note that Section 1.4 presents all initial and robust models results
for each variable used side by side, with each variable used identified.
4.1 TOTAL CONSUMER SPENDING ON BOTH

DOMESTICALLY PRODUCED AND IMPORTED
CONSUMER GOODS
Findings for the initial model tested, which included all variables we found
significant in at least one previous study we reviewed, are presented in
Model 4.1. The final model, robust to changes in time period sampled
and the number of other variables included in the model, is presented in
Model 4.1T.TR further below.
Model 4.1
OLS Standard Consumer Spending Model, with Borrowing
Included as a Determinant of Consumer Spending (No Variable
Found Endogenous, So No 2SLS Models)
CT = 0.48(Y – TT ) + 0.56(TT ) – 0.39(GT& I ) – 9.98PR

(t =) (10.5) (10.2) (–8.7) (–4.9)
+ 0.43DJ–2 + 1.46XRAV – 419.33POP16 + 0.019POP
(5.0) (0.9) (–1.6) (5.0)
+0.38ICC–1 + 46.87M2AV + 0.12CB2
(1.2) (4.4) (3.0)
R2 = 95.3% D.W. = 1.6 MSE = 24.12
Six variables plus the dependent variable were found nonstationary:

disposable income, government spending, the wealth variable (stock
market average), ratio of young to old in the population, population, and

the average M2 money supply. Five of the six were cointegrated with the
dependent variable, so no detrending was needed. The government spend-
ing and the dependent variable were detrended to restore stationarity.
(Detrending only the GT& I variable yielded identical or virtually identical
results for all variables.) Detrended results are shown in Eq. 4.1.T and are
nearly identical to the OLS results above.
Model 4.1.T
Included as a Determinant of Consumer Spending;
Stationarity Issues Resolved
(No Variable Found Endogenous, So No 2SLS Model Needed)
CT = 0.48(Y – TT ) + 0.56(TT ) – 0.39(GT& I ) – 9.98PR

(t =) (10.6) (10.2) (–8.7) (–4.9)
+ 0.43DJ–2 + 1.44XRAV – 418.25POP16 + 0.018POP
(5.1) (0.9) (–1.6) (4.7)
+ 0.37ICC–1 + 46.31M2AV + 0.12CB2
(1.2) (4.3) (3.0)
R2 = 95.3% D.W. = 1.6 MSE = 24.12
Equation 4.1T is graphed in Graph 4.1.1.

The model explains consumer behavior nearly equally well in each of
the five decades in the sample, an indication of its robustness. The top two
curves are the actual and fitted values for each year in billions of 2005 dol-
lars (right vertical axis values). The bottom curve measures the difference
between actual and fitted values in the top curves for each year. Values for
the bottom curve, in billions of 2005 dollars, are given on the left axis.
Equation 4.1T is repeated below, except using a one variable definition
of the deficit, not two.
Model 4.1.T (1VarDef)
Model 4.1.T(1VarDef)
Included as a Determinant of Consumer Spending (No 2SLS
Models; 1Variable Definition of Deficit Used)
CT = 0.50(Y – TT ) + 0.14(TT – GT& I ) – 0.75PR + 0.15DJ–2

(t =) (5.2) (3.4) (–0.2) (0.7)
– 3.78XRAV – 620.97POP16 + .024POP + 1.74ICC–1

(1.0) (–2.2) (4.1) (4.2)
+ 20.82M2AV + 0.26 CB2 R2 = 95.3% D.W. = 1.6 MSE = 24.12
(1.7) (3.4) (4.1T.1VarDef)
Consumption tests in this study regularly indicate that the effects of a tax
cut deficit on consumption are greater than those of a spending deficit.
Hence, the one variable form’s single coefficient for deficit effects gives
a distorted view of the effect of both and explains markedly less variance
than the two variable form. Our practice throughout the remainder of this
chapter will to specify each type of deficit separately.
Variance Explained and Robustness Tests

Contributions of Individual Variables to Explained Variance
The importance of these variables in explaining variation in total consumer
spending during the 1960–2010 period can be examined using stepwise
regression the on model given in Eq. 4.1T over the 1960–2010 period. By
comparing the R2 for the full model (4.1.T) to the R2 after removing one
400
300
200
100
60 0
40 –100
20 –200
0
–20
–40
–60
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Residual Actual Fitted
Fig. 4.1.1 Actual consumption compared to levels calculated from Model 4.1.T
1960–2010
variable, we can determine the amount of total variation in consumption

over the 50-year sample period was uniquely explained by the left out
variable (the “first-out” stepwise method). The “first-in” method regresses
consumption on just the single variable, and its R2 shows the variance it
uniquely explains as well as the variance it explains that other variables in
the full regression could explain equally well. For example: the change in
disposable income uniquely explains 19% of all explained variance, but can
also explain (0.52 – 0.19) = 0.33 that other variables could have explained as
well were they in the model. Negative R2 result from the particular way R2
is calculated and should be interpreted as meaning the first-in variable is
not found to systematically explain any variance in the dependent variable.
In reality, it may explain a little, but the regression’s ability to discern it
gets lost in the background noise caused by not controlling for the other
variables which influence consumption (Table 4.1.1).
The “first-out” results indicate by how much R2 dropped from its
starting value of 0.95. They indicate that disposable income and tax
cut deficits were the most important factors affecting consumer spend-
ing in the 1960–2010 period, with changes in spending deficits third.
Without these variables in the model, R2 drops the most. The “first-in”
results suggest nearly the same thing: disposable income, the two deficit
types and population growth. First-out stepwise results tend to understate
contributions because the omitted variable typically shares some ability to
explain variance with a remaining variable. Therefore, pulling the variable
Table 4.1.1 Explained variance – total consumption
Variable: First-out stepwise method First-in stepwise method

(R2 = 0.95 to start) (R2 = 0.00 to start)
(Y-T) 0.76 +0.52

T 0.78 –1.07(+0.34 with constant added)
GT& I 0.87 –1.90 (+ .02 “ “ “ )
PR 0.91 –2.1
DJ–2 0.92 –1.9
.94XRAV 0.94 –2.2
POP16/65 0.94 –2.1
POP 0.94 +.05
ICC–1 0.95 –2.1
M2AV 0.92 –.62
CBOR 0.93 –2.1
out does not mean pulling all its influence out. Stepwise is an illumin-
ating, but imperfect, tool. For the same reason, first-in stepwise tends
to overstate contributions. As such, stepwise results can provide some
information on variable importance, but either approach alone is con-
sidered a definitive measurement of a variable’s contribution to explained
variance.
Table 4.1.2 tests Model 4.1.T in four sample periods to determine if
coefficients are stable from sample-to-sample.
Results are quite robust for all periods sampled. The similarity of effect
of fiscal policy variables in different historic time periods strongly contra-
dicts the Lucas critique notion that how the economy reacted to past
policy changes is no guide to how it will react to the same changes in
the future. As the four samples above show, clearly you can use the results
in one sample period as a reliable guide to the likely results in another, for
both fiscal policy and other variables. Eckstein (1983), who also tested the
Lucas critique, also could not find any support in the data for it. Hence,
simulation of policy changes in the future should produce reliable guides
to the actual effects that will occur, at least if the estimate of past effects is
obtained from a Keynesian-style, demand-driven structural model like Eq.
4.1.T above or other similar structural models used in other consumption
models in this study.
Table 4.1.2 Robustness over time – (2SLS detrended model, Eq. 4.1.T)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.48∗ 0.43∗ 0.52∗ 0.52∗

T 0.56∗ 0.55∗ 0.41∗ 0.48∗
GT& I –0.39∗ –0.40∗ –0.28∗ –0.31∗
PR –9.98∗ –9.88∗ –8.60∗ –9.39∗
DJ–2 0.43∗ 0.37∗ 0.73∗ 0.64∗
XRAV 1.44 1.88 1.92 1.52
POP16/65 –418.25 45.17 –758.74∗ –502.82∗∗
POP 0.018∗ 0.024∗ 0.016∗ 0.016∗
ICC–1 0.37 0.61∗∗ 0.59∗ 0.65∗
M2AV 46.31∗ 49.84∗ 18.64∗ 22.03∗
CBOR 0.12∗ 0.12∗ 0.12∗∗ 0.10∗ .

Robustness to Model Specification Changes

Only two variables (POP16/65 and the exchange rate) were not found signi-
ficant in at least three of the four time periods sampled and were dropped
from the model. The remaining model, robust to time period sampled, is
re-estimated and given below as Eq. 4.1T.TR:
Model 4.1.T.TR
Time Period Robust Standard Consumption Model
CT = 0.49(Y – TT ) + 0.57(TT ) – 0.38(GT& I ) – 9.31PR

(t =) (10.8) (11.0) (–7.9) (–4.6)
+ 0.44DJ–2 + 0.017POP + 0.41ICC–1 + 44.78M2AV
(5.4) (4.3) (1.2) (4.3)
+ 0.13 CB2 R2 = 94.8% D.W. = 1.6 MSE = 24.75
(3.6) (4.1T.TR)
Subtracting the last two variables in Eq. 4.1T.TR and re-estimating:
Model 4.1.T.TRa
(Two Variables Deleted)
CT = 0.52(Y – TT ) + 0.66(TT ) – 0.42(GT& I ) – 8.91PR + 0.41DJ–2

(t =) (7.3) (12.1) (–10.1) (–4.0) (6.2)
+ 0.015POP + 43.21M2AV
(4.0) (3.8)
R2 = 92.2% D.W. = 2.0 MSE = 29.66 (4.1T.TR.a)
Coefficients and significance levels are robust for all the remaining
variables.
We have already seen that dropping the POP16/64 and exchange
rate variables left the remaining parameter estimates nearly unchanged,
so adding it back in would do the same. Adding the real M1money sup-
ply variable to the sample period robust model again leaves coefficient and
significance level estimates stable.
4.2 SPENDING ON IMPORTED CONSUMER GOODS – OLS ESTIMATES 157
Model 4.1.T.TRb
(One Variable Added)
CT = 0.49(Y – TT ) + 0.56(TT ) – 0.36(GT& I ) – 9.74PR
(t =) (11.4) (12.3) (–7.6) (–5.1)
+ .41DJ–2 + 0.017POP + 0.41ICC–1 + 49.30M2AV
(5.8) (4.3) (1.2) (4.9)
+ 0.12 CB2 – 0.15 M1Real R2 = 96.0% D.W. = 1.7 MSE = 22.46
(4.0) (–2.1) (4.1T.TRb)
We conclude that estimates of effects of other variables on consumption
in the original model are robust to specification changes in the model.
Since the full sample period robust model (4.1T.TRb), from a theoret-
ical perspective, is better specified than the truncated alternatives or the
alternative with the added variable, we take the results for 4.1T.TRb as
robust to model specification changes as well as changes in the time period
sampled.
4.2 SPENDING ON IMPORTED CONSUMER

GOODS – OLS ESTIMATES
Imports of consumer goods and services are defined as total imports,
minus imports of capital goods and services as well as industrial supplies
and materials. The initial assumption was that the determinants of domest-
ically produced consumer goods are the same as for imported consumer
goods. A test of that hypothesis using OLS yields the results shown in
Model 4.2 (preliminary) below. The final model, robust to changes in
time period sampled and the number of other variables included in the
model, is presented in Model 4.4.TR further below.
Model 4.2 (Preliminary)

Consumer Imports Model
CM = 0.19(Y – TT ) + 0.25(TT ) – 0.18(GT& I ) – 3.11PR

(t =) (4.6) (6.8) (–3.7) (–1.4)
– 0.01DJ–2 + 1.78XRAV + 98.22POP16 – 0.002POP
(0.1) (1.5) (0.5) (–0.7)
– 0.15ICC–1 + 8.52M2AV + 0.02 CB2

(0.5) (0.8) (0.7) (4.0.2)
R2 = 79.1% D.W. = 1.6 MSE = 21.86
Though several variables are ADF nonstationary, including the dependent
variable, all are cointegrated with CM . Therefore, no adjustments were
made to remove trending were needed.
In first differences, the consumer imports variable was nonstationary
as were 6 of its 11 right-hand side hypothesized determinants: disposable
income, government spending, the wealth variable (stock market average),
ratio of young to old in the population, population, and the average M2
money supply.
An alternative version of this model adds real U.S. exports as an
additional explanatory variable. The theoretical basis was twofold: (1)
to purchase imports, the U.S. must obtain the necessary foreign cur-
rency. Much of this comes from the receipts of export sales, and (2)
much importing is done for goods incorporated in products for export.
(Our export demand model also indicates the same thing; demand for
our exports is in large part a function of U.S. demand for foreign
imports.) Adding this variable significantly strengthens the significance
of the interest rate, wealth, and exchange rate variables and markedly
increases explained variance. Results are presented in Eq. 4.2:
Model 4.2
Consumer Imports Model – Exports Added
CM = 0.09(Y – TT ) + 0.13(TT ) – 0.08(GT& I ) – 2.09PR
(t =) (1.9) (3.3) (–1.8) (–1.3)
+ 0.11DJ–2 + 3.13XRAV + 239.00POP16 – 0.002POP
(1.8) (3.3) (2.1) (–1.2)
(4.2)
– 0.14ICC–1 + 7.16M2AV + 0.12 CB2 + 0.47 X
(–0.6) (1.1) (2.4) (5.7)
R2 = 86.7% D.W. = 2.2 MSE = 17.65
Variance Explained and Robustness Tests for Imported Consumer

Goods Models
Contribution to Explained Variance
The importance of these variables in explaining variation in imported con-
sumer spending can be examined using stepwise regression the model
given in Eq. 4.4 over the 1960–2010 period (Table 4.2.1).
4.2 SPENDING ON IMPORTED CONSUMER GOODS – OLS ESTIMATES 159
Table 4.2.1 Explained variance – consumer imports
Explained variance First-out stepwise method First-in stepwise method (constant added)
(Y-T) 0.84 0.42

T 0.83 0.31
GT& I 0.85 0.04
PR 0.86 0.06
DJ–2 0.86 0.03
XRAV 0.85 0.07
POP16/65 0.86 0.00
POP 0.86 0.03
ICC–1 0.87 0.09
M2AV 0.86 0.05
CBOR 0.82 0.20
XReal 0.79 0.30
The first-out results indicate consumer borrowing and the level of

exports were the most important factors affecting consumer import spend-
ing in the 1960–2010 period. Disposable income and tax cut deficits had
more moderate effects. Other variables effects were marginal at best. The
first-in results suggest disposable income and population growth. For first-
in, the same four variables are important. As noted when discussing total
consumption earlier, stepwise results should be interpreted with caution.
First-out stepwise results tend to understate contributions because the
omitted variable typically shares some ability to explain variable with a
remaining variable. For the same reason, first-in stepwise tends to overstate
contributions. As such, stepwise results can provide some information on
variable importance, but are not considered definitive measurements of a
variable’s contribution to explained variance.
Robustness Over Time
The model is tested in four different, but overlapping time periods to assess
replicability of results. Results are given in Table 4.2.2.
Significant results for at least three of the four sample periods are con-
sidered evidence the initial results were not spurious. However, in models
that initially have large numbers of explanatory variables, some variables
may fail this test simply because of lack of degrees of freedom or multicol-
linearity problems. Hence, in developing our final sample period robust
model, we reenter, one at a time, the variables that were not significant in
at least three of the four tests. If they now (one at a time) can be added to
Table 4.2.2 Robustness over time – consumer imports
Periods sampled
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.09∗ 0.08 0.16∗∗∗ 0.16∗∗∗

T 0.13∗∗∗ 0.14∗∗∗ 0.27∗∗∗ 0.24∗∗∗
GT& I –0.08∗ –0.09∗ –0.19∗∗∗ –0.16∗∗∗
PR –2.09 –2.37 –5.57∗∗∗ –4.93∗∗∗
DJ–2 0.11∗ 0.08 0.21∗∗∗ 0.27∗∗∗
XRAV 3.13∗∗∗ 3.06∗∗∗ 3.21∗∗∗ 3.08∗∗∗
POP16/65 239.00∗∗ 467.71∗∗ 135.53 60.93
POP –0.002 0.000 0.001 –0.002
ICC–1 –0.14 –0.04 0.38∗∗∗ 0.31∗∗
M2AV 7.16 9.48 –8.46 –12.43∗∗
CBOR 0.12∗∗ 0.11∗∗ –0.06 –0.04
X 0.47∗∗∗ 0.44∗∗∗ 0.08 0.14.
Significance levels: ∗∗∗ = 1%; ∗∗ = 5%; ∗ = 10%.
those initially found significant at least three of four samples, they are kept.
A new model is run with all these variables and retested in the four sample
periods. If the variables that initially failed the three out of four tests now
are significant in at least three of four, they, along with the variables that
initially passed the three out of four tests, become our final, sample period
robust model (Eq. 4.3.TR).
One variable originally insignificant (the prime rate) was added to the
five “core” variables originally found significant in three out of four tests
(income, tax and spending deficits, the exchange rate, and the stock mar-
ket index variable). With the new variable in, the stock market variable
was no longer significant in at least three of four time periods sampled
and was dropped from the “final” time period robust model given in
Eq. 4.3.TR.
Model 4.2.TR
Time Period Robust Consumer Imports Model
CM = 0.19(Y – TT ) + 0.25(TT ) – 0.18(GT& I ) + 2.22XRAV
(t =) (7.8) (7.4) (–5.4) (2.6)
– 3.06PR0 R2 = 76.7% D.W. = 1.5 MSE = 21.55
(–1.8) (4.2.TR)
4.3 SPENDING ON IMPORTED CONSUMER GOODS – 2SLS ESTIMATES 161
Robustness to Model Specification Changes (Detrended 2SLS, 1960–2010

Data Set):
Deleting the prime interest rate variable from Eq. 4.2.TR gives
Model 4.2.TR.a
(One Variable Deleted)
CM = 0.19(Y – TT ) + 0.23(TT ) – 0.15(GT&I ) + 2.20XRAV
(t =) (7.5) (6.5) (–5.1) (2.2)
R2 = 75.4% D.W. = 1.4 MSE = 21.89 (4.2.Alt.TR.a)
Remaining coefficients are robust as are significance levels.
Adding the population and consumer confidence variables to the sample
period robust model (4.2.TR) and re-estimating, we obtain
Model 4.2.TR.b
(Two Variables Added)
CM = 0.22(Y – TT ) + 0.26(TT ) – 0.18(GT& I + 2.05XRAV )
(t =) (6.6) (6.7) (–4.4) (2.3)
– 2.35PR0 . – 002POP – 0.25ICC–1 –
(–0.9) (–1.0) (–0.6)
2 (4.2.TR.b)
R = 77.7% D.W. = 1.6 MSE = 21.53
Results are very robust to these model changes, with the exception of the
interest rate variable, whose magnitude is reasonably stable, but which now
becomes insignificant.
We conclude that estimates of effects of other variables on consumption
of imports in the sample period robust model are also robust to specifica-
tion changes, with the exception of the interest rate variable’s significance
level in the model. Hence, Eq. 4.2.TR becomes our final sample period
and model specification robust model of what affect consumer purchases
of imports, and how much.
4.3 SPENDING ON IMPORTED CONSUMER

GOODS – 2SLS ESTIMATES
No variables were found Hausman-endogenous with the dependent
variable, so no 2SLS model was needed.
4.4 CONSUMER SPENDING ON DOMESTICALLY

PRODUCED CONSUMER GOODS (OLS)
Findings for the initial model tested, which included all variables we found
significant in at least one previous study we reviewed, are presented in
Model 4.4.TR further below.
In first differences, the domestically produced consumption goods
variable was nonstationary as were 6 of its 11 right-hand-side hypo-
thesized determinants: disposable income, government spending, the
wealth variable (stock market average), ratio of young to old in
the population, population, and the average M2 money supply.
Five of the six were cointegrated with the dependent variable, so
no detrending was needed. The M2 average money supply was
detrended which restored stationarity. The dependent variable was also
detrended d(CD –68.75–1.8∗ trend) and corrected for nonstationarity
of M2 variable by subtracting the trend d(M2–0.10 – 0.014∗ trend
variable):
Model 4.4
OLS Standard Consumer Spending Model,
with Borrowing Included as a Determinant of Consumer
Spending (No Variable Found Endogenous, So No
2SLS Models)
CD = 0.29(Y – TT ) + 0.31(TT ) – 0.20(GT& I ) – 6.86PR

(t =) (6.0) (5.8) (–3.5) (–2.4)
+ 0.44DJ–2 – 0.33XRAV – 517.17POP16 + 0.020POP
(4.4) (0.2) (–3.5) (5.8) (4.4)
+ 0.53ICC–1 + 38.16M2AV + 0.10CB2
(2.1) (4.3) (3.4)
R2 = 88.7% D.W. = 2.0 MSE = 24.54
The same model is re-estimated using only 1960–2000 data so as to

allow out-of-sample testing of its fit in the 2001–2010 period. See
Chapter 16.
4.4 CONSUMER SPENDING ON DOMESTICALLY PRODUCED CONSUMER GOODS (OLS) 163
Model 4.4 (For Chapter 16)

Included as a Determinant of Consumer Spending (No Variable
Found Endogenous, So No 2SLS Models)
CD = 0.35(Y – TT ) + 0.23(TT ) – 0.13(GT& I ) – 4.33PR

(t =) (5.2) (2.3) (–2.0) (–1.8)
+ 0.32DJ–2 – 1.17XRAV – 508.20POP16 + 0.017POP
(2.0) (–0.8) (–2.8) (4.6)
+ 0.30ICC–1 + 35.93M2AV + 0.16CB2
(1.3) (4.4) (3.1)
2
R = 91.2% D.W. = 1.6 MSE = 21.60 (4.4.16)
Variance Explained and Robustness Tests

Contributions to Explained Variance
The importance of these variables in explaining variation in domestic con-
sumption during the 1960–2010 period can be examined using stepwise
regression to analyze the detrended OLS model given in Eq. 4.4. over the
1960–2010 period (Table 4.4.1).
Results for determinants of domestically produced consumer goods
were the same as for total consumer goods, including imports. The
Table 4.4.1 Explained variance – domestically produced consumer goods
Explained variance: First-out stepwise method First-in stepwise method (with

constant added)
(Y-T) 0.74 0.52

T 0.77 0.28
GT& I 0.84 0.01
PR 0.87 0.03
DJ–2 0.83 0.04
XRAV 0.89 0.05
POP16/65 0.87 0.03
POP 0.73 0.06
ICC–1 0.88 0.13
M2AV 0.83 0.09
CBOR 0.86 0.15
first-out results indicate disposable income and tax cut deficits and popula-
tion growth were the most important factors affecting consumer spending
in the 1960–2010 period. The first-in results suggest disposable income,
tax deficits, consumer confidence, and consumer borrowing. First-out
stepwise results tend to understate contributions because the omitted
variable typically shares some ability to explain variable with a remaining
variable. For the same reason, first-in stepwise tends to overstate contribu-
tions. As such, stepwise results can provide some information on variable
importance, but are not considered definitive measurements of a variable’s
contribution to explained variance.
To test for replicability of the initial results, the model was tested in four
different, but overlapping time periods. Findings are shown in Table 4.4.2.
Results are quite robust for at least three of the four sample periods
sampled for all variables except two: the exchange rate and consumer
confidence. Hence our model robust to period tested will include all
variables except those two. Since multicollinearity or insufficient degrees
of freedom can cause significant variables to appear insignificant in models
with a large number of explanatory variables (like the models above), we
also add back, one at a time, the variables not found significant in at least
three sample periods, and re-estimate. Variables now found significant
are included in the final time period robust model if they now prove
significant in three of four sample periods when tested in this model.
Table 4.4.2 Robustness over time – domestically produced consumer goods
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.29∗∗∗ 0.27∗∗∗ 0.35∗∗∗ 0.33∗∗∗

T 0.31∗∗∗ 0.29∗∗∗ 0.13 0.23∗∗∗
GT& I –0.20∗∗∗ –0.20∗∗∗ –0.07 –0.13∗∗
PR –6.86∗∗ –6.39∗∗ –2.83 –4.32∗
DJ–2 0.44∗∗∗ 0.41∗∗∗ 0.48∗∗ 0.32∗
XRAV –0.33 –0.03 –1.08 –1.18
POP16/65 –517.16∗∗∗ –503.96 –853.34∗∗∗ –507.75∗∗∗
POP 0.020∗∗∗ 0.023∗∗∗ 0.016∗∗∗ 0.017∗∗∗
ICC–1 0.53∗∗ 0.60∗ 0.19 0.31
M2AV 38.16∗∗∗ 37.49∗∗∗ 28.73∗∗∗ 35.93∗∗∗
CBOR 0.10∗∗∗ 0.10∗∗∗ 0.19∗∗∗ 0.16∗∗∗
Significance levels: ∗∗∗ 1%; ∗∗ 5%; ∗ 10%.

4.4 CONSUMER SPENDING ON DOMESTICALLY PRODUCED CONSUMER GOODS (OLS) 165
No additional variables met this criterion. The final sample period robust
model is shown in Eq. 4.4.TR.
Model 4.4.TR
Domestically Produced Consumer Goods – Time Period
Robust Model
CD = 0.29(Y – TT ) + 0.34(TT ) – 0.23(GT& I ) – 5.44PR

(t =) (6.2) (6.5) (–4.5) (–2.1)
+ 0.48DJ–2 – 0.515.07POP16/65 + 0.020POP + 38.00M2AV
(5.1) (3.2) (6.0) (4.9)
+ 0.09CB2 R2 = 87.8% D.W. = 2.2 MSE = 24.88
(3.7) (4.4.TR)
Robustness to Model Specification Changes (Detrended OLS, 1960–2010
Data Set):
Subtracting the last two variables from the sample period robust model
and re-estimating:
Model 4.4.TR.a
Robust Model
CD = 0.39(Y – TT ) + 0.35(TT ) – 0.17(GT& I ) – 2.50PR

(t =) (6.5) (6.1) (–2.8) (–0.8)
+ 0.30DJ–2 – 0.440.52POP16/65 + 0.020POP
(4.2) (1.7) (5.0)
2
R = 72.9% D.W. = 2.0 MSE = 35.10 (4.4T.TR.a)
Coefficients and significance levels of the remaining variables are robust to
these changes in the model, except for the prime interest rate variable.
Adding the M1 money supply and consumer confidence variables to the
sample period robust model 4.1T and re-estimating we get
Model 4.4.TR.b
Robust Model
CD = 0.29(Y – TT ) + 0.31(TT ) – 0.20(GT& I ) – 7.02PR
(t =) (6.1) (5.7) (–3.7) (–2.5)
+ .43DJ–2 – 0.539.17POP16/65 + 0.020POP + 39.58M2AV

(4.3) (3.6) (6.1) (5.4)
+ 0.10CB2 – 0.02M1Real + 0.52ICC–1
(3.9) (–0.5) (1.9)
R2 = 88.7% D.W. = 2.0 MSE = 24.51 (4.4T.TR.b)
Estimates for the variables in the sample period robust model are robust
to the addition of these variables.
We conclude that the parameter estimates for the determinants
of demand for domestically produced consumer goods, as given in
Eq. 4.4T.TR, are robust to both changes in period sampled and changes
to the model itself, with the possible exception of the prime interest rate.
4.5 DETERMINANTS OF CONSUMER

BORROWING – OLS ESTIMATES
Unlike the models above, which examine the determinants of consumer
spending, the next two models examine the determinants of consumer
borrowing. The initial hypothesis tested was that consumers borrow prin-
cipally to finance desired spending. Therefore, some or all of the determ-
inants of spending should be determinants of borrowing. Therefore, the
spending models above are retested, with only three changes:
• The dependent variable is borrowing, not spending.

• The savings component of the real money supply (M2-M1), was
added to reflect the statistically significant positive relationship
between this variable and consumer borrowing. It is interpreted as a
measure of the supply of loanable funds. This form of the money sup-
ply was used because it was more systematically related to borrowing
than either M1 or M2 alone.
• The wealth variable lagged one period (DJ–1 ) was found far more
systematically related to borrowing than the two period lag previously
found related to spending, so it was used. The expected sign, unlike
the spending model, is negative in the borrowing model: a rising
stock market provides an attractive alternative source of funding,
which may reduce borrowing.
Findings for the initial model tested, which included all variables found
significant in at least one previous consumer spending study reviewed,
4.5 DETERMINANTS OF CONSUMER BORROWING – OLS ESTIMATES 167
are presented in Model 4.5 The final model, robust to changes in time
period sampled and the number of other variables included in the model,
is presented in Model 4.6.TR further below.
Model 4.5 (Preliminary)

OLS Standard Consumer Borrowing Model
(XR Variable Found Endogenous; See Also 2SLS Model Below)
CB2 = 0.40(Y – TT ) + 0.75(TT ) – 0.59(GT& I ) – 18.12PR

(t =) (1.6) (3.0) (–2.3) (–2.6)
– 1.71DJ–1 + 19.83XRAV + 384.17POP16 – 0.001POP
(–3.6) (3.1) (0.7) (–0.1)
+ 0.47ICC–1 – 41.22M2AV – 0.16 (M2 – M1)Real
(0.5) (–1.1) (–1.5)
R2 = 59.0% D.W. = 2.1 MSE = 100.32 (4.5.Prelim)
To test the hypothesis that the quantity of savings supplied might con-
strain borrowing, total business and corporate saving was added to the
model, but they were found statistically insignificant. In a separate model,
personal savings only was added to the model, and was significantly neg-
atively related to consumer borrowing, indicating savings is a substitute
for borrowing (prior year personal savings had the same sign, but lacked
statistical significance). OLS results are shown in Eq. 4.5A below. Note
that the savings component of M2 variable loses its statistical significance
when the personal savings variable is added, as would be expected since
part of personal savings is saved in M2 savings instruments. Adding the
savings variable markedly increases the explanatory power of the model,
as shown in Eq. 4.5.
Model 4.5
OLS Standard Consumer Borrowing Model, Savings Variable Added
(XR Variable Found Endogenous; See Also 2SLS Model Below)
CB2 = 0.53(Y – TT ) + 0.42(TT ) – 0.46(GT& I ) – 14.63PR

(t =) (2.3) (1.7) (–2.0) (–2.3)
– 1.56DJ–1 + 17.72XRAV + 520.98POP16 – 0.003POP
(–4.4) (3.1) (1.0) (0.3)
+ 0.75ICC–1 – .58.23M2AV – 0.13(M2 – M1)Real – 0.71(PerSav)Real
(0.91) (–1.0) (–1.0) (1.9)
R2 = 66.8% D.W. = 2.1 MSE = 91.42 (4.5)
In first differences, the consumer borrowing variable was nonstationary

as were 6 of its 11 right-hand side hypothesized determinants: disposable
income, government spending, the wealth variable (stock market average),
ratio of young to old in the population, population, and the average M2
money supply. All six were cointegrated with the dependent variable, so
no detrending was needed.
4.6 DETERMINANTS OF CONSUMER

BORROWING – 2SLS ESTIMATES
Model 4.6
2SLS Model of Eq. 4.5; Exchange Rate Endogenous and Replaced
with Strong Instrument
CB2 = 0.57(Y – TT ) + 0.70(TT ) – 0.52(GT& I ) – 21.89PR

(t =) (4.1) (3.0) (–3.0) (–3.1)
– 1.65DJ–1 + 14.06XRAV + 68.02POP16 – 0.012POP
(–3.7) (4.3) (0.2) (–2.2)
+0.52ICC–1 – 30.60M2AV – 0.14(M2 – M1)Real – 0.07(PerSav)Real
(0.6) (–1.3) (–1.0) (0.2)
– 0.43AR(2) R2 = 59.7% D.W. = 2.5 MSE = 75.42
(–2.0) (4.6)
Variance Explained and Robustness Tests – Consumer

Borrowing Model
The importance of these individual variables in explaining variation in con-
sumer borrowing during the 1960–2010 period can be examined using
stepwise regression on the 2SLS model given in Eq. 4.6 (Table 4.6.1).
Using the first-out technique, by far the largest determinants of con-
sumer borrowing were disposable income, the two deficit variables, the
stock market lagged a year and the exchange rate. Using first-in, the
personal saving, the exchange rate, was the most important.
First-out stepwise results tend to understate contributions because the
omitted variable typically shares some ability to explain variable with a
remaining variable. For the same reason, first-in stepwise tends to overstate
contributions. As such, stepwise results can provide some information on
4.6 DETERMINANTS OF CONSUMER BORROWING – 2SLS ESTIMATES 169
Table 4.6.1 Explained variance – consumer borrowing
Explained variance First-out stepwise method First-in stepwise method (with

constant added)
(Y-T) 0.43 0.19

T 0.51 0.03
GT& I 0.49 0.02
PR 0.54 0.01
DJ–1 0.44 0.05
XRAV 0.49 0.26
POP16/65 0.60 0.01
POP 0.56 0.00
ICC–1 0.59 0.00
(M2AV ) 0.58 0.03
(M2-M1) 0.59 0.06
CSavings(–2) 0.60 0.01
Table 4.6.2 Robustness over time – consumer borrowing, 2SLS Model 4.6
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.58∗∗∗ 0.60∗∗∗∗ 0.64∗∗∗ 0.63∗∗∗

T 0.70∗∗∗ 0.85∗∗∗ 0.91∗∗ 0.78∗∗
GT& I –0.52∗∗∗ –0.56∗∗∗ –0.73∗∗∗ –0.64∗∗∗
PR –21.89∗∗∗ –24.57∗∗∗ –25.14∗∗∗ –22.10∗∗∗
DJ–1 –1.65∗∗∗ –1.80∗∗∗ –1.83∗∗ –1.67∗∗∗
XRAV 14.06∗∗∗ 13.23∗∗∗ 13.74∗∗∗ 13.36∗∗∗
POP16/65 68.01 381.47 148.13 –17.23
POP –0.012∗∗ –0.012 –0.015∗ –0.016∗∗∗
ICC–1 0.52 0.90 0.50 0.33
M2AV –30.60 –27.83 –7.17 –17.39
(M2-M1) –0.14 –0.18 –0.20∗∗ –0.15
CSAVINGS(–2) –0.43∗∗ –0.01 0.21 0.15
variable importance, but are not considered definitive measurements of a

variable’s contribution to explained variance.
Time Period Robustness
The model was tested in four different but overlapping time periods to
determine the replicability of the initial findings. Results are presented in
Table 4.6.2.
Deleting the variables in the initial model that were not significant in
at least three of the four sample periods gives the core components of a
model that is robust to time periods sampled.
Because significant variables can sometimes show as insignificant
because of multicollinearity or inadequate degrees of freedom, we read-
mit the ones deleted, one by one, to the core robust model, and then
re-estimate. Previously deleted variables that are now found significant
are also included in the sample period robust model, provided only that
they now prove to be significant in three of the four sample periods when
retested. No additional variables met this criterion. The final time period
robust model is shown in Eq. 4.6.TR:
Two other adjustments were made. (M2–M1) and the (PerSav) vari-
ables, both of which measure consumer savings, were combined. Doing
so markedly improved the statistical significance. Also, as it left the
population variable insignificant in 3 out of 4 time periods, it was
dropped. Serious multicollinearity of personal savings and population
growth (r = 0.70) seemed the underlying reason for the population vari-
able having the wrong sign and both the personal savings variable and the
savings components of the M2 variable (M2-M1) were found statistically
insignificant.
Model 4.6.TR
2SLS Standard Consumer Borrowing Model – Time Period Robust
CB2 = 0.44(Y – TT ) + 47(TT ) – 0.46(GT& I ) – 14.62PR

(t =) (4.2) (2.0) (–2.2) (–3.2)
–1.37Dj-1 + 19.83XRAV
(–3.0) (3.8) (4.6.TR)
–0.07(PerSev0-9Tot + M2-M10-3Tot)
(–2.7)
R2 = 52.4% D.W. = 2.1 MSE = 76.
Though our sample-period robust findings are strong, they still reliably
explain only 55.3% of all the causes of variation in consumer borrow-
ing. Clearly important factors that affect borrowing are not uncovered
yet. More research is needed.
Robustness to Model Specification Changes (1960–2010 Data Set):
Dropping the last two variables in Eq. 4.6.TR and re-estimating, we have
4.7 MODELING THE MAJOR COMPONENTS OF TOTAL CONSUMPTION 171
Model 4.6.TR.a
CB2 = 0.27(Y – TT ) + 73(TT ) – 0.58(GT& I ) – 14.41PR – 1.23DJ–1

(t =) (2.4) (3.5) (–3.5) (2.7) (–1.7)
R2 = 40.4% D.W. = 1.6 MSE = 112.83 (4.6.TR.a)
Coefficients and statistical significance are robust for all variables left in
except the coefficient on the income variable.
Finally, adding the Population ratio of young to old, and the consumer
confidence variables to the time period robust Model 4.6 gives:
Model 4.6.TR.b
CB2 = 0.49(Y – TT ) + 49(TT ) – 0.44(GT& I ) – 18.12PR – 1.50DJ–1

(t =) (4.0) (2.0) (–2.1) (–3.6) (–3.4)
+ 18.06XRAV – 0.09(PerSav0-9Tot+M2-M10-3Tot)
(3.7) (–2.7)
+1.09ICC-1 + 526.58POP16
(1.2) (1.1)
2
R = 54.7% D.W. = 2.2 MSE = 76.55 (4.6.TR.b)
Coefficient change is minor. The time – period robust model is also robust
to the addition of these variables to the model.
Overall, we conclude the coefficients in the consumer borrowing model
given by Eq. 4.6.TR are robust to significant changes in both sample
period tested and changes in model specification.
4.7 MODELING THE MAJOR COMPONENTS OF TOTAL

CONSUMPTION
The following three sections develop separate models for the three
component parts of total consumption: durables, nondurables, and
services.
4.8 DETERMINANTS OF SPENDING ON CONSUMER

DURABLES (OLS)
The initial model tested which included all variables found significant in
at least one previous consumer spending study reviewed, indicated some
variables were not significant, and some additional variables thought pos-
sibly related to durables spending were added. This model is presented
in Model 4.8 The final model, robust to changes in time period sampled
Model 4.8
OLS Standard Consumer Durables Spending Model, with
Borrowing Included as a Determinant
(Four Variables Found Endogenous, See Also 2SLS Model Below)
CD = 0.13(Y – TT ) + 0.11(TT ) – 0.10(GT& I ) – 3.24PR

(t =) (18.3) (5.5) (–6.0) (–3.8)
+ 0.24 DJAV(–2,–3) + 2.31XRAV + .15IRES – .00050HouseP/Inc
(4.5) (4.3) (3.7) (–13.0)
+ .09M1REAL–1 – 0.14(CND(–1) )
(3.7) (–4.2)
R2 = 91.8% D.W. = 1.9 MSE = 10.08 (4.8)
Variables included in the durables model include those suggested by the-
ory or found significant in other studies. Also included is spending on
consumer nondurables, lagged one period, which had a systematic effect
on purchases of durables a year later and accounts for about 1½% of all
explained variance. It represents a way of representing microeconomic
substitution effects that can have effects in macroeconomic models. The
inclusion was prompted by some initial work by Alvarez presented at the
2014 Eastern Economics Association Conference. The M1 money supply
was significant, which is unusual in our consumption models but dur-
ables are typically “big ticket “items especially dependent on the pool of
loanable funds, which can be related to the money supply.

DURABLES (2SLS)
Hausman endogeneity tests indicated the average exchange rate, taxes,
the lagged average prime interest rate, and the residential investment were
4.9 DETERMINANTS OF SPENDING ON CONSUMER DURABLES (2SLS) 173
endogenously related to the dependent variable, spending on consumer

durable goods. These variables were replaced by Wald-strong instruments
and the model was retested. Results are presented in Eq. 4.9.
Model 4.9
2SLS Consumer Durables Spending Model, with Borrowing
Included as a Determinant
(Four Variables Endogenous; Replaced with Instrument Which Is
Strong for XRAV PR0 and T)
CD = 0.14(Y – TT ) + 0.13(TT ) – 0.08(GT& I ) – 0.24PR

(t =) (5.0) (3.5) (–2.7) (–0.2)
+ 0.19DJAV(–2,–3) + 2.54XRAV + 0.14IRES
(2.5) (4.2) (2.6)
–0.0004HouseP / Inc + 0.015M1REAL–1 – 0.19(CND(–1) ) (4.9)
(–8.4) (0.4) (–2.3)
R2 = 89.0% D.W. = 2.1 MSE = 11.65
Generally results are the same as with the OLS model, except the interest
rate’s coefficient changed considerably, as did the M1 variables’ coefficient
and significance level.
In first differences, the consumer durables variable was stationary. Two
of its nine right-hand-side hypothesized determinants were nonstation-
ary: disposable income, and the wealth variable (stock market average).
Both were cointegrated with the dependent variable, so no detrending
was needed. Standard consumption function variables like POP16, POP,
consumer confidence, M2AV are not included because they were found
nonsignificant in preliminary testing.
Variance Explained and Robustness Tests – Consumer Durables

Model
The importance of these variables in explaining variation in consumer
durables spending during the 1960–2010 period can be examined
using stepwise regression on the 2SLS model given in Eq. 4.9
(Table 4.9.1).
Using the first-out technique, by far the most important determin-
ants of spending on consumer durables were income (positive effect),
and the cost of new housing construction relative to income (negative
effect as prices rise relative to income). Next most important were tax
and spending deficits, and the exchange rate. Using first-in, the largest
determinant was residential investment, followed by house prices relative

to GDP, disposable income and tax cut deficits. First-out stepwise results
tend to understate contributions because the omitted variable typically
shares some ability to explain variable with a remaining variable. For the
same reason, first-in stepwise tends to overstate contributions. As such,
stepwise results can provide some information on variable importance, but
are not considered definitive measurements of a variable’s contribution to
explained variance (Table 4.9.2).
Table 4.9.1 Explained variance – consumer durables
Explained variance First-out stepwise method First-in stepwise method (with

constant added)
(Y-T) 0.78 0.26

T 0.82 0.23
GT& I 0.83 0.00
PR 0.89 –0.01
DJAV–2,–3 0.87 0.00
XRAV 0.84 0.20
INVRES 0.88 0.55
House Pr/GDP 0.81 0.31
M1–1 0.89 0.06
CND(–1) 0.88 0.00
Table 4.9.2 Robustness over time – consumer durables, 2SLS Model (Eq. 4.9)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.14∗∗∗ 0.14∗∗∗ 0.17∗∗∗ 0.16∗∗∗

T 0.13∗∗∗ 0.13∗∗∗ 0.21∗∗∗ 0.22∗∗∗
GT& I –0.08∗∗∗ –0.08∗∗ –0.14∗∗∗ –0.14∗∗∗
PR –0.23 –0.47 –1.53 –1.32
DJAV–2,–3 0.19∗∗ 0.19∗∗ 0.10 0.07
XRAV 2.54∗∗∗ 2.68∗∗∗ 2.67∗∗∗ 2.54∗∗∗
IRES 0.14∗∗ 0.14∗∗ 0.05 0.05
House Pr/GDP- 0.0004∗∗∗ –0.0004∗∗∗ 0.001 0.001
M1–1 0.015 0.023 0.04 0.0824
CND(–1) –0.19∗∗ –0.20∗∗ –0.39∗∗ –0.35∗∗
Significance levels: ∗∗∗ 1%; ∗∗ 5%; * 10%.

4.9 DETERMINANTS OF SPENDING ON CONSUMER DURABLES (2SLS) 175
Five of ten variables were significant in all four periods sampled (dis-
posable income, tax and spending deficits, the exchange rate, and the level
of nondurables purchased). Two others significant in two sample periods
including the 2001–2010 decade, when we had a housing boom which
drove up demand for durables like kitchen appliances. They were the level
of residential investment and the level of house prices relative to income.
The large growth in the stock market during the same decade also con-
tributed to its significance then, but not in the two samples ending in
2000. The prime rate and the M1 money supply were not significant in
any period.
The five significant variables explain 82% of the variance and form the
core of our sample period robust model given in Eq. 4.9.TR. However,
in large models, a variable that truly is significant can appear insignificant
because of multicollinearity or too few degrees of freedom. To ensure we
haven’t rejected truly explanatory variables for this reason, we retest each
rejected variable separately with the core model. The additional variables
found significant this way are then added to the core robust model and
again tested in all four time periods. Only if significant in at least three are
they included in the time period robust model, Eq. 4.9.TR. No additional
variables were found significant in at least three of the four tests. The only
one to come close was the Housing Price/GDP ratio variable, which was
significant in samples including the 2001–2010 decade, as before, but not
in the two samples ending in 2000. We interpret this as meaning it takes
major growth in the ratio to have effect on durables purchases distinct
from that caused by other forces affecting durables demand. The final time
period robust model is given in Eq. 4.9.TR.
Model 4.9.TR
Time Period Robust Standard Consumer Durables Model
CD = 0.18(Y – TT ) + 0.24(TT ) – 0.14(GT& I ) + 2.40XRAV

(t =) (6.4) (5.9) (–5.5) (3.9)
– 0.43(CND(–1) ) R2 = 82.4% D.W. = 2.3 MSE = 12.43
(3.2) (4.9.TR)

Deleting the last variable in Eq. 4.9.TR and re-estimating:
Model 4.9.TR.a
CD = 0.12(Y – TT ) + 0.20(TT ) – 0.13(GT& I ) + 2.91XRAV

(t =) (7.5) (3.9) (–4.7) (4.7)
R2 = 76.0% D.W. = 1.8 MSE = 14.32 (4.9.TR.a)
All the remaining variables remain significant and coefficients on all

retain the same sign are have highly similar coefficients (except disposable
income’s coefficient which dropped 33%, which we view as a moderately
robust response).
Adding the lagged money supply variable to the robust model
Eq. 4.9.TR yields the following.
Model 4.9.TR.b
CD = 0.18(Y – TT ) + 0.24(TT ) – 0.13(GT& I ) + 3.46XRAV

(t =) (7.3) (3.6) (–3.5) (2.6)
– 0.38(CND(–1) ) – 0.01M1–1
(–3.3) (–0.2)
R2 = 76.9% D.W. = 1.9 MSE = 15.65 (4.9.TR.b)
The time period robust model coefficients and significance levels remained
stable (using current year values of M1 did not make a difference). Hence
Model 4.9.TR appears robust to both sample periods tested as well as
(reasonable) changes to the model specified.

NONDURABLES (OLS)
Initially, all the determinants of total consumption were tested to see if
they were significant determinants of nondurables. A number were found
to have no relationship in preliminary testing and were dropped. Two
major alternative variables were added: the mortgage interest rate (on
4.11 DETERMINANTS OF SPENDING ON CONSUMER NONDURABLES (2SLS) 177
the expectation that the more expensive housing was, the less would be
bought, and the more consumers would shift spending to nondurables),
and the level of spending on durable goods (on the expectation that the
more spent on durables, the less available for spending on nondurables).
Use of both the consumer durables and residential investment variable (I),
the same model tended to leave one insignificant, though both were sig-
nificant if used in the model without the other. As we had seen earlier,
the two are related. Hence, both were picking up much the same vari-
ance. The consumer durables variable was dropped. It seemed the weaker
determinant of nondurable goods demand because the investment variable
has higher levels of statistical significance when used alone. This suggests
that while the demand for durables resulting from residential investment
was substantial, other factors were also at work, namely consumer spend-
ing on nondurables dropping as demand shifts to a desire for new housing.
Results are shown in 4.10 below.
The final model, robust to changes in time period sampled and the
number of other variables included in the model, is presented in Model
4.11.TR further below
Model 4.10
Included as a Determinant
(Y-T Variable Found Endogenous, So See 2SLS Model Below)
CND = 0.19(Y – TT ) + 0.11(TT ) – 0.08(GT& I ) + 8.61MORTrREAL

(t =) (14.4) (3.1) (–2.3) (3.7)
– 2.37PR + 0.17DJ–0 – 0.12IRES + 13.01M2AV
(–2.3) (4.0) (–2.6) (2.1)
2
R = 89.4% D.W. = 1.7 MSE = 11.38 (4.10)

NONDURABLES (2SLS)
The tax deficit variable and the consumer durables variable were found
endogenous with CNDUR and replaced with a nonendogenous, Wald-strong
instrument in Eq. 4.11.
Model 4.11
2SLS Estimates of Spending on Consumer Nondurables
(Hausman Tests Indicate TT and CDur were Endogenous)

(t =) (13.2) (3.2) (–2.3) (3.8)
– 2.46PR + 0.17DJ–0 – 0.12IRES + 12.36M2AV
(–2.3) (3.9) (–2.8) (2.1)
R2 = 89.3% D.W. = 1.7 MSE = 11.40 (4.11)
The government spending, M2AV, and stock exchange variables were
found ADF nonstationary, but were cointegrated with the dependent
variable.
Variance Explained and Robustness Tests – Consumer Nondurables

Model
The importance of these variables in explaining variation in con-
sumer borrowing during the 1960–2010 period can be examined
using stepwise regression on the 2SLS model given in Eq. 4.11.1
(Table 4.11.1).
Using the first-out technique, by far the largest determinant of spend-
ing on consumer nondurables was disposable income. The other vari-
ables were marginal. Using the first-in method, disposable income, and
wealth (the stock market variable explained a substantial amount of
variance.
Table 4.11.1 Explained variance – nondurables
Explained variance: First-out stepwise method First-in stepwise method (con-

stant added)
(Y-T) 0.41 0.53

T 0.87 0.20
GT& I 0.88 0.03
MortrREAL 0.86 0.02
PR 0.88 0.08
DJ 0.87 0.42
INVRES 0.88 0.07
M2AV–2,–4 0.86 0.12
4.11 DETERMINANTS OF SPENDING ON CONSUMER NONDURABLES (2SLS) 179
Table 4.11.2 Robustness over time – nondurables, 2SLS Model (Eq. 4.11)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.19∗∗∗ 0.20∗∗∗ 0.20∗∗∗ 0.20∗∗∗

T 0.11∗∗∗ 0.12∗∗∗ 0.13∗∗∗ 0.14∗∗∗
GT& I –0.08∗∗ –0.09∗∗ –0.08∗∗∗ –0.08∗∗∗
MortrReal 8.72∗∗∗ 9.89∗∗∗ 3.99 4.46∗∗
PR –2.46∗∗ –2.91∗∗ –1.56∗∗ –1.63∗∗
DJ 0.17∗∗∗ 0.15∗∗∗ 0.05 0.04
IRES –0.12∗∗∗ –0.13∗∗∗ –0.18∗∗∗ –0.17∗∗∗
M2AV–2–4 12.36∗∗ 14.32∗∗ 0.38 –0.18
determine if initial results could be replicated in different time periods.
Findings are shown in Table 4.11.2 .
Results are quite robust for all variables except residential investment,
the M2 money supply and the stock market index. Both are significant
for samples including 2001–2010, but not for the two samples ending in
2000.
Re-estimating the model using only the six variables found signi-
ficant in three of the four tests, gives the core sample period robust
model. To avoid having discarded variables not meeting this criteria
for statistical, not substantive reasons, e.g., too few degrees of free-
dom for the number of explanatory variables used in the initial large
model, or multicollinearity problems, we add back the discarded vari-
ables one at a time and re-estimate. All that are now found significant
we add to the core model, provided they are significant in three of the
four sample periods. No additional variables met this condition. The
final sample period robust model resulting from this process is given in
Eq. 4.11.TR
Model 4.11.TR
2SLS Estimates of Spending on Consumer Nondurables – Time
Period Robust

(t =) (10.9) (7.2) (–4.7) (2.9)
– 2.44PR – 0.19IRES R2 = 81.8% D.W. = 1.4 MSE = 14.54
(–2.1) (–4.6) (4.11.TR)
Robustness to Model Specification Changes (2SLS, Using Full 1960–2010

Data Set):
Dropping the last two variables from 4.11.TR and re-estimating, we get
Model 4.11.TR.a
Model 4.11.TR.a
Period Robust
CND = 0.23(Y – TT ) + 0.13(TT ) – 0.06(GT& I ) + 9.73MORTRREAL
(t =) (9.7) (5.8) (3.1) (4.1)
R2 = 76.2% D.W. = 1.5 MSE = 16.24 (4.11.TR.a)
Clearly the model is robust to these changes, though fluctuation in the

deficit variables coefficient is greater than desired.
Adding the real M1 variable to 4.11.TR and re-estimating.
Model 4.11.TR.b
Period Robust
CND = 0.24(Y – TT ) + 0.20(TT ) – 0.14GT& I + 8.20MORTRREAL
(t =) (11.7) (5.8) (4.2) (2.0)
– 2.73PR + 0.21IRes + 0.09M1Real
(–2.6) (4.9) (0.8)
R2 = 80.3% D.W. = 1.3 MSE = 15.30 (4.11.TR.b)
All the remaining variables coefficients and significance levels are

reasonably robust to the model changes to the sample robust
model 4.11.TR.
Hence, we conclude Model 4.11.TR is not only robust to time period
changes, but also to model specification changes.

SERVICES (OLS)
The initial model tested is presented as Model 4.12. The final model,
robust to changes in time period sampled and the number of other
variables included in the model, is presented in Model 4.12.TR further
below.
4.13 DETERMINANTS OF SPENDING ON CONSUMER SERVICES (2SLS) 181
Stationarity
The dependent variable was stationary. Three RHS variables in Model 4.12
were nonstationary disposable income, government spending, and the
stock market average but all were cointegrated with the dependent
variable.
Model 4.12
OLS Consumer Services Spending Model
CS = 0.20(Y – TT ) + 0.35(TT–S ) – 0.19(GT& I–S ) – 4.83PR

(t =) (7.6) (11.5) (–5.8) (–2.6)
+ .28DJ–2 + 0.19M1RL–2 + 0.08(M2 – M1)–RL2
(4.3) (2.8) (3.1) (4.12)
–0.001HouseP / Inc + 0.02POP
(–7.9) (11.3)
R2 = 90.5% D.W. = 2.0 MSE = 20.14

SERVICES (2SLS)
In testing the consumer services spending model, no variables were found
Hausman-endogenous, so no 2SLS model was needed. The standard
first-stage regressors used in all testing all consumption functions for
endogeneity, described earlier in the chapter, were used.
Variance Explained and Robustness Tests – Consumer Services Model

The importance of these variables in explaining variation in consumer
services spending during the 1960–2010 period can be examined using
stepwise regression on the 2SLS model given in Eq. 4.12. Results are
shown in Table 4.13.1.
Using the first-out technique, by far the largest determinants of
spending on consumer services were disposable income and tax, pop-
ulation growth and spending deficits. The other variables are of only
marginal significance. Using the first-in method, disposable income,
tax deficits, and stock market variable explained substantial amount of
variance.
Table 4.13.1 Explained variance – consumer services (Eq. 4.12)
Explained variance: First-out stepwise method First-in stepwise method

(constant added)
(Y-T) 0.82 0.39

T 0.72 0.41
GT& I 0.84 0.03
PR 0.89 0.05
DJ–2 0.88 0.27
M1–2 0.89 0.02
(M2-M1)–2 0.89 0.00
HousePr/Inc 0.85 0.02
POP 0.74 0.04
Table 4.13.2 Robustness over time – consumer services, 2SLS model (Eq. 4.12)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Y-T) 0.20∗∗∗ 0.18∗∗∗ 0.24∗∗∗ 0.25∗∗∗

TT–S = TDEF 0.35∗∗∗ 0.35∗∗∗ 0.24∗ 0.23∗∗∗
GT& I–S = GDef –0.19∗∗∗ –0.19∗∗∗ –0.11∗ –0.10
PR –4.83∗∗∗ – –4.67∗∗∗ – –4.33∗∗ –3.84∗∗
DJ–2 0.28∗∗∗ 0.26∗∗∗ 0.17 0.30∗
M1–2 0.19∗∗∗ 0.18∗∗∗ 0.24∗∗∗ 0.22∗∗∗
(M2-M1)–2 0.08∗∗∗ 0.09∗∗∗ 0.13∗∗∗ 10∗∗∗
HousePr/Inc –0.001∗∗∗ –0.001∗∗∗ –0.010 –0.014
POP 0.02∗∗∗ 0.02∗∗∗ 0.02∗∗∗ 0.02∗∗∗ .

determine if the initial results could be replicated. Findings are shown in
Table 4.13.2.
Results are significant in all four periods sampled for six of the nine
explanatory variables, including disposable income, tax deficits, the prime
interest rate, the lagged M1 and M2-M1 money supply, and the level
of population. Two other variables (spending deficits, the stock market
wealth indicator) were significant in three of the four periods sampled.
4.13 DETERMINANTS OF SPENDING ON CONSUMER SERVICES (2SLS) 183
Only one, the ratio of house prices to GDP), was only significant in only
two samples: those including the 2001–2010 decade.
A sample period robust model is presented below. It includes a core
model with the six variables found significant in all four sample periods and
the two found significant in three periods. The final core model is shown
in Eq. 4.12.TR, with results shown for the 1960–2010 period testing.
Model 4.12.TR
OLS Estimates of Spending on Consumer Services – Time Period
Robust Model
CS = 0.26(Y – TT ) + 0.45(TT–S ) – 0.25(GT& I–S ) – 6.99PR

(t =) (5.8) (8.5) (–5.4) (–3.1)
+ 0.19DJ–2 + 0.19M1–2 + 0.06(M2 – M1)–2 + 0.02POP
(2.5) (2.3) (1.6) (5.8)
R2 = 85.4% D.W. = 1.9 MSE = 24.51 (4.12.TR)
Robustness to Model Specification Changes (Using Full 1960–2010 Data

Set):
Dropping the last two variable in 4.12.TR and re-estimating, we get
Model 4.12.TR.a
Robust Model
CS = 0.45(Y – TT ) + 0.44(TT –S ) – 0.21(GT& I–S ) – 7.73PR

(t =) (18.0) (8.6) (–3.9) (–2.2)
+ 0.39DJ–2 + 0.33M1REAL–2
(5.1) (3.8)
R2 = 71.4% D.W. = 1.4 MSE = 33.43 (4.12.TRa)
All remaining variables coefficient and significance level estimates were

robust to this model change.
Finally, let us add the consumer nondurables and mortgage interest
rate variables to model 4.12 and re-estimate. The results are given in
Eq. 4.12.b.
Model 4.12.TR.b
Robust Model
CS = 0.18(Y – TT ) + 0.40(TT–S ) – 0.23(GT& I–S ) – 5.36PR

(t =) (2.9) (7.4) (–4.4) (–2.1)
+ 0.19DJ–2 + 0.15M1REAL–2 + .05(M2 – M1)REAL–2 + 0.02POP
(2.3) (1.7) (1.2) (7)
+ 30CNDur – 6.31IntMort R2 = 86.5% D.W. = 2.1 MSE = 24.48
(1.1)1. (–1.1) (4.12.TR.b)
Adding this variable does not significantly affect parameter estim-

ates or significance levels, except for the consumer savings variable
(M2-M1)Real–2 ,though insignificant in the samples with 2001–2010 data,
remains highly significant in the two 1960–2000 samples. We conclude
that with the exception of this variable,
Model 4.12.TR, our final consumer services model, is robust specifica-
tion changes, and that coefficients are reasonably robust to differences in
time period sampled, but not to statistical significance, because in some
periods, changes in three of the explanatory variable can be modest, rel-
ative to changes in others, but occasionally their changes are substantial,
leaving them significant determinants of consumer services spending.
CHAPTER 5
Models Identifying the Determinants of

Investment Spending and Borrowing
An extensive review of the literature indicated the following variables,

or variants of them, have been identified as determinants of investment
spending (IT ) or borrowing (IB, ) in one or more previous studies. They
are retested here to ensure their status as determinants of investment can
be confirmed. Testing for their precise effects is initially done using OLS.
2SLS is used when endogeneity issues require substituting an endogeneity-
free instrument for an endogenous variable. In this way all identification
issues are fully resolved. Nonstationarity issues are resolved by detrend-
ing or cointegration. All nonstationary variables in the IT , IM , ID, and
IB models were cointegrated with their dependent variables, therefore no
detrending was needed. As usual, all models are run in first differences to
reduce nonstationarity and multicollinearity problems.
IT = total real investment goods and services.

ACC = A Samuelson accelerator variable (Y-Y–1 )
(TT -GT&I ) = real government deficit: total receipts minus total expenditures on gov-
ernment consumption, Investment, transfers, interest, and subsidies. When
tested separately, TT and GT&I are used. The yearly changes in deficits
are shown net of yearly changes in the pool of loanable funds (personal,
corporate and depreciation savings, and foreign borrowing).
(Eckstein (1983), p.128 noted that “. . . the fiscal policy simulations repor-
ted in Chapter 2 show that housing is the final demand that is typically
crowded out by measures of fiscal stimulus . . . ”.

DOI 10.1007/978-3-319-50681-4_5
186 5 MODELS IDENTIFYING THE DETERMINANTS OF INVESTMENT SPENDING . . .
Eckstein’s findings indicate crowd out more than completely offsets stim-
ulus effects of fiscal policy. The greater than 100% crowd out effect
presumably stems from the discrete nature of housing borrowing: when
government borrowing to finance deficits reduce the amount banks have
to lend to consumers by, say, $10,000, the bank has to tell someone who
needs to borrow, say, $100,000 they can only get $90,000. This may cause
a drop in private spending of $100,000, while only providing a government
stimulus of $10,000. Eckstein (p. 37) also noted that “. . . real crowding out
occurs even when the economy is far from the full employment ceiling . . . ”.
This study’s findings are consistent with his, and underscore the importance
of including the deficit variable, a measure of the magnitude of crowd out).
PR = real prime interest rate defined as the nominal rate minus the average of
the past two completed years inflation.
DJ–2 = a measure of wealth (NYSE Composite Index), lagged 2 years (other lags
also used).
XRAV = the real broad U.S. exchange rate average for current and past three years
(foreign currency per dollar).
POP = population size.
M2AV = real M2 money supply; average of second, third, and fourth past years.
M2-M1 = savings components of M2 for the current period.
IB , = business borrowing (annual change in business debt).
Prof–2 = business profits, lagged 2 years (other lags also used).
DEP = depreciation variable.
CAP–1 = % of productive capacity utilized, lagged 1 year.
Table 5.0.1 Determinants of consumption and investment initially assumed

endogenous when applying endogeneity tests
The Deficit variables Unemployment rate

The accelerator Real GDP
Exchange rate average NYSE composite average
Depreciation
When endogeneity is found in investment models, 2SLS is the appro-

priate regression method. The process used for determining endogeneity
was the same as described in earlier for consumption models and in the
methodology section. All the variables used on the right-hand side of the
investment functions were reviewed. The variables shown in Table 5.0.1
were initially assumed “suspect” and tested for endogeneity with the
dependent variable, either some type of investment or business borrowing.
The remaining variables were lagged or initially assumed exogenous
and were used as first-stage Hausman test regressors when testing the
MODELS IDENTIFYING THE DETERMINANTS OF INVESTMENT SPENDING . . . 187
endogeneity of any of the seven suspect variables above used in investment

models. Residuals from each of these seven “first-stage” regressions were
then added to the investment structural equation being tested as an
additional variable, and the model was re-estimated (“second-stage”).
If statistically significant, the variable being tested for endogeneity was
judged Hausman-endogenous, and replaced by a Wald-strong instrument
(itself determined free of endogeneity using the Sargan test) when the
structural model was actually tested.
When instruments were needed, the initial instrument was developed
regressing the endogenous variable on all the variables initially determined
nonendogenous, i.e., all variables used in investment and consumption
equations, plus the exports variable, minus the seven suspected of endo-
geneity. The fitted values from this regression were used as the “initial” or
“standard” instrument. If it proved to be a weak instrument, variables were
added/subtracted to strengthen it. To ensure the same instrument could
be used for all endogenous variables in a model, sometimes additional
variables needed to be added to a strong instrument for one endogenous
variable, to make the same instrument a strong instrument for a second
or third endogenous variable as well. The Wald weak instrument test cri-
teria (F test >10.00 or t-test >3.30) were used to judge weakness. Each
instrument deemed strong met at least one of the Wald criteria and was
Sargan-tested to ensure it was not endogenously related to the dependent
variable it was to be used with. The specific changes made to the initial
instrument are discussed when they are made in the various investment
models.
The variables that were lagged or initially assumed exogenous were used
as the initial instrument components and are shown in Table 5.0.2. They
are the same variables used as Hausman test first-stage regressors in the
earlier consumption tests.
Table 5.0.2 Determinants of consumption and investment initially assumed

exogenous or lagged in their effect when applying endogeneity tests
Dow Jones Composite Index–2 Exports

M2 Average–2 to –4 Business Borrowing–1 (Net)
Real Prime Rate–2 Consumer Confidence Index–1
Population (Young/Old Ratio)
Population0
Capacity Utilization–1
Seven investment models are tested, total investment, fixed,

residential and inventory investment, domestically produced and impor-
ted investment goods, and business borrowing. Of the seven dependent
variables, only the imported investment goods variable was found non-
stationary. A total of 13 variables were hypothesized to be determinants
of one or another of these seven types of investment or business borrow-
ing; six of them were found nonstationary, but all six were cointegrated
with the dependent variable they were used with, so no detrending was
done. Specific variables found nonstationary are described in the write up
of results for each the seven investment models below.
The two separate variable definition of the deficit (TT and GT&I ) is used
throughout to allow the different effects of tax cut and spending deficits
to be clearly seen.
5.1 OLS ESTIMATES OF THE DETERMINANTS OF TOTAL

INVESTMENT SPENDING
Findings for the initial model tested, which included all variables found sig-
nificant in at least one previous study reviewed, are presented in Model 5.1.
The final model, robust to changes in time period sampled and the num-
ber of other variables included in the model, except as subsequently noted,
Model 5.1
OLS Estimates of Determinants of Total Investment Spending
IT = + 0.32(ACC) + 0.33(TT ) – 0.32(GT&I ) + 0.84DEP

(t =) (6.1) (3.2) (–3.9) (2.5)
+ 2.30CAP–1 – 3.20PR–2 – 0.04DJ–0 + 0.13PROF–0
(1.4) (–1.4) (–0.2) (2.1) (5.1)
+ 5.39XRAV + 0.005POP + 0.13(BOR–1 )
(2.2) (1.6) (2.0)
R2 = 93.0% D.W. = 1.9 MSE = 32.99
Business borrowing was positively related to investment, but of only mar-

ginal levels of statistical significance, at best. One variable (stock market
index) was found endogenous with total investment spending. A Sargan
nonendogenous, Wald strong instrument (F = 10) was developed to
replace it, and 2SLS results using the instrument are shown below.
5.2 2SLS ESTIMATES OF THE DETERMINANTS OF TOTAL INVESTMENT 189
Four variables in the model were nonstationary, but were all cointeg-
rated with the dependent variable, which was stationary. The nonstation-
ary variables were government spending, depreciation, the Tobin’s q proxy
and the population size variable.
5.2 2SLS ESTIMATES OF THE DETERMINANTS OF

TOTAL INVESTMENT
Model 5.2
2SLS Estimates of Determinants of Investment Spending
Hausman tests indicate one variable endogenous with investment spend-
ing (DJAV), so Instrumented: (Wald test F = 9.1, but DJ–2 t = 3.5)
and Sargan test NR2 = 6.12 < X2(95,15) = 25.00. Hence, this is a strong
instrument model.
IT = +0.30(ACC) + 0.23(TT ) – 0.26(GT&I ) + 0.68DEP

(t =) (5.8) (1.9) (–2.7) (2.2)
+ 2.28CAP–1 – 6.89PR–2 + 0.53DJ–0 + 0.03PROF–0
(1.1) (–2.5) (2.5) (0.4) (5.2)
+ 5.89XRAV + 0.004POP + 0.06 (BOR–1 )
(2.1) (1.4) (0.7)
R2 = 91.0% D.W. = 2.2 MSE = 37.48
In the 2SLS model, the lagged prime rate and the stock market index were
significant, unlike the OLS model. But the profits and borrowing variables
which were significant in the OLSS model, were not in the 2SLS model.
5.2.1 Variance Explained and Robustness Tests

5.2.1.1 Contributions to Explained Variance
The importance of these variables in explaining variation in unemploy-
ment during the 1960–2010 period can be examined using stepwise
regression the 2SLS model given in Eq. 5.2 over the 1960–2010 period
(Table 5.2.1).
From a first-out perspective, no variable uniquely explains a major
part of the variance, but the accelerator and the two types of deficit
explain moderate amounts. Other variables contributions were marginal
at best. From the first-in perspective, the most important factors were the
Table 5.2.1 Explained variance – total investment

(constant added)
(ACC) 0.82 0.50

(TT ) 0.85 0.22
(GT&I ) 0.82 0.28
(DEP) 0.89 0.02
(CAP–1 ) 0.91 0.00
(PR–2 ) 0.91 0.11
(DJ) 0.93 0.46
(PROF) 0.90 0.25
(XRAV ) 0.90 0.02
(POP) 0.91 0.00
(BOR–1 ) 0.90 0.63
Table 5.2.2 Robustness over time – total investment, 2SLS Model 5.2
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(ACC) 0.30∗∗∗ 0.30∗∗∗ 0.23∗∗∗ 0.23∗∗∗

(TT ) 0.23∗ 0.23 0.39∗∗∗ 0.29∗∗
(GT&I ) –0.26∗∗∗ –0.27∗∗∗ –0.39∗∗∗ –0.30∗∗∗
(PR–2 ) –6.89∗∗ –7.95∗∗ –4.48∗ –4.74∗
(DJ) 0.53∗∗ 64∗ 0.42 0.58∗∗
(PROF) 0.03 0.00 0.03 0.05
(XRAV ) 5.89∗∗ 6.11∗∗ 2.72 2.26∗∗
(POP) 0.004 0.005 0.008 0.004
(BOR–1 ) 0.06 0.02 0.13∗ 0.15∗∗
accelerator and the stock market variable, which serves as our imperfect
proxy for Tobin’s q, and the business borrowing variable. Also important
were the two types of deficit and the level of profits.
5.2.1.2 Robustness Over Time

The model was tested in four separate but overlapping time periods to
determine if initial results could be replicated. Findings are presented in
Table 5.2.2.
5.2 2SLS ESTIMATES OF THE DETERMINANTS OF TOTAL INVESTMENT 191
The six significant determinants of total investment in at least three

sample periods were the accelerator, both spending and tax cut deficits,
the prime rate, stock market index, and the exchange rate.
A core robust model is developed next with the six variables from above
that were significant in at least three of the four samples, plus any addi-
tional variables that, when added one at a time, are also significant. That
new model is tested in all four periods and for any of the formerly insig-
nificant variables to stay, they must now be significant in at least three
periods when this new model is tested. Only depreciation passed this test.
The final sample period robust model is presented below as Eq. 5.2.TR.
Model 5.2.TR
2SLS Estimates of Determinants of Total Investment
Spending – Time Period Robust
IT = + 0.25(ACC) + 0.30(TT ) – 0.32(GT&I ) – 10.53 PR–2

(t =) (8.2) (2.7) (–4.4) (–4.3)
+ 0.87 DJAV + 3.18XRAV + 0.97 DEP
(3.3) (1.5) (4.1)
2 (5.2.TR)
R = 86.6% D.W. = 2.2 MSE = 29.43
5.2.1.3 Robustness to Model Specification Changes (2SLS, 1960–2010
Data Set)
Deleting the last two variables from 5.2.TR above:
Model 5.2.TR.a
IT = + 0.21(ACC) + 0.20(TT ) – 0.12(GT&I ) – 12.63PR–2

(t =) (5.0) (1.6) (–1.0) (4.2)
+ 1.23DJAV R2 = 78.2% D.W. = 2.0 MSE = 54.51
(3.4) (5.2.TR.a)
All variables retained their signs, and somewhat similar magnitudes.
Statistical significance for the deficit variables was not robust.
Adding the interest rate and M1 money supply variables to 5.2.TR and
re-estimating, we get
Model 5.2.TR.b
IT = + 0.32(ACC) + 0.21(TT ) – 0.24(GT&I ) – 8.27PR–2

(t =) (6.2) (1.8) (–2.5) (–3.0)
+ 0.61DJAV + 5.76XRAV + 0.99DEP + 2.65CAP–1
(3.2) (2.1) (6.1) (1.2)
+0.97BOR–1 R2 = 86.6% D.W. = 2.2 MSE = 29.43
(0.3) (5.2.TR.b)
All variables from the robust model have the same signs, remain statistically
significant, and have reasonably robust magnitudes.
We conclude that in general the final time period robust model 5.2.TR
is robust to specification changes, except for the deficit variables signific-
ance levels, as well as differences in period sampled.
5.3 OLS ESTIMATES OF THE DETERMINANTS OF

DOMESTICALLY PRODUCED INVESTMENT GOODS
Spending on domestically produced investment goods (ID ) is defined
as total investment spending (IT ) minus spending on imported capital
goods and imported industrial supplies and materials (IM ). Four of the
explanatory variables tested were found nonstationary, but were found
cointegrated with total investment, the dependent variable. The non-
stationary variables were government spending, depreciation, the stock
market index, and population growth.
Findings for the initial model tested, which included all variables
found significant in at least one previous study reviewed, are presented
in Model 5.3. The final model, robust to changes in time period sampled
Model 5.3
OLS Estimates of Determinants of Spending on Domestically
Produced Investment Goods
2SLS results are also presented further below since the average exchange
rate and depreciation variables were found endogenously related to
spending on domestically produced investment goods.
5.4 2SLS ESTIMATES OF THE DETERMINANTS OF DOMESTICALLY PRODUCED. . . 193
ID = + 0.23(ACC) + 0.34(TT ) – 0.34(GT&I ) + 0.24DEP

(t =) (6.1) (3.0) (–3.9) (0.8)
+ 1.71CAP–1 – 2.41PR–2 – 0.18DJ–0 + 0.11PROF–0
(1.0) (–1.2) (–1.2) (1.3) (5.3)
+ 7.19XRAV + 0.008POP + 0.02(BOR–1 )
(2.8) (3.1) (0.4)
R2 = 89.5% D.W. = 1.8 MSE = 29.75
5.4 2SLS ESTIMATES OF THE DETERMINANTS OF

DOMESTICALLY PRODUCED INVESTMENT GOODS
Replacing the endogenous variables XRAV and GT&I with Wald-strong
instruments gives the following 2SLS results:
Model 5.4
2SLS Estimates of Determinants of Spending on Domestically
Hausman tests indicate two variables endogenous with investment spend-
ing, so instrumented: XRAV (XRAV(–1) t = 8.0), DEP (DEP–1 t = 7.9), so
this is a strong instrument model. Sargan test NR2 = 5.64 < X2(95,16) =
26.30. Hence, the instrument is not endogenous.
ID = + 0.25(ACC) + 0.29(TT ) – 0.31(GT&I ) + 0.08DEP
(t =) (6.7) (2.7) (–3.7) (0.3)
+ 2.60CAP–1 – 3.01PR–2 – 0.19DJ0 + 0.08PROF–0
(1.5) (–1.9) (–0.8) (1.2) (5.4)
+7.08XRAV + 0.011POP + 0.02(BOR–1 )
(2.2) (3.4) (0.3)
R2 = 84.4% D.W. = 2.0 MSE = 28.77
To allow later use in Chapter 16, the same model is re-estimated using only
1960–2000 data. This will allow out-of-sample testing of its fit during the
2001–2010 period. Re-estimation yields the following.
Model 5.4 (For Chapter 16)

(Limited Estimation Period)
ID = + 0.23(ACC) + 0.33(TT ) – 0.34(GT&I ) – 0.18DEP
(t =) (7.3) (3.7) (–4.0) (–0.6)
+ 2.31CAP–1 – 2.89PR–2 + 0.22DJ0 – 0.12PROF–0

(1.9) (–1.7) (1.3) (–.07)
+2.30XRAV + 0.01POP + 0.11(BOR–1 ) (5.4.16)
(0.9) (2.7) (1.5)
R2 = 84.4% D.W. = 2.4 MSE = 24.21

(Table 5.4.1).
From a first-out perspective, the factors which explain the most vari-
ance in total investment are the accelerator (positively) and spending
deficits (negatively). More moderately, tax cut deficits and the exchange
rate were the next two in importance. The rest of the variables had a
negligible impact at best. The other variables only contributed marginally
to explained variance. From the first-in perspective, the accelerator and
spending deficits as well as the prime interest rate and business borrowing
were the most important.

Model 5.4 was tested in four different, though overlapping, sample
periods. Results are shown in Table 5.4.2.
Table 5.4.1 Explained variance – domestically produced investment goods
Explained variance First-out stepwise method First-in stepwise method

(ACC) 0.71 0.46

(TT ) 0.79 0.02
(GT&I ) 0.73 0.22
(DEP) 0.84 0.00
(CAP–1 ) 0.84 0.00
(PR–2 ) 0.84 0.17
(DJ) 0.84 0.07
(PROF) 0.84 0.14
(XRAV ) 0.79 0.03
(POP) 0.83 0.01
(BOR–1 ) 0.85 0.36
5.4 2SLS ESTIMATES OF THE DETERMINANTS OF DOMESTICALLY PRODUCED. . . 195
Table 5.4.2 Robustness over time: (domestically produced investment goods,

2SLS Model 5.4)
Variable 1960–2010 1970–2010 1970–2000 1960–2000

∗
(ACC) 0.25∗∗∗ 0.26∗∗∗ 0.23∗∗∗ 0.23∗∗∗

(TT ) 0.29∗∗∗ 0.31∗∗ 0.37∗∗∗ 0.33∗∗∗
(GT&I ) –0.31∗∗∗ –0.33∗∗∗ –0.38∗∗∗ –0.34∗∗
(DEP) 0.07 0.12 –0.17 –0.17
(CAP–1 ) 2.60 2.75 1.75 2.31∗
(PR–2 ) –3.01∗ –2.48 –2.89 –2.89∗
(DJ) –0.19 –0.26 0.14 0.22
(PROF) 0.08 0.07 –0.16 –0.12
(XRAV ) 7.09∗∗ 6.96∗∗ 1.96 2.30
(POP) 0.011∗∗∗ 0.012∗∗∗ 0.011 0.011∗∗∗
(BOR–1 ) 0.02 0.02 0.11 0.11
Four variables were found to be statistically significant in all periods

sampled: the accelerator, the tax and spending deficit variables, and popu-
lation growth. Population growth may have been a proxy for GDP growth.
Substituting GDP growth for population growth led to nearly identical
results for all variables in both time periods. Alternatively, one could look
at GDP growth as a response to increases in demand associated with
population growth. The other variables were always, or almost always,
found statistically insignificant, an unexpected finding since all are part
of standard economic theory as to what determines levels of investment.
Insignificance may merely be distinguishing between minor and major
influences during the period sampled.
The four significant variables form the core of a model whose parameter
estimates are time period robust. Because variables can appear insignificant
in models with many explanatory variables due to multicollinearity or lack
of sufficient degrees of freedom, and not for substantive reasons, we again
test each of the insignificant variables from above, one at a time, by adding
them to the core robust model and re-estimating. All the insignificant vari-
ables now found significant are added to the core model and retested in all
four sample periods. Those significant in at least three periods, along with
the four core robust variables, are taken to constitute the final time period
2SLS robust model, shown in Eq. 5.4.TR, estimated using the 1960–2010
data set:
Model 5.4.TR
(Time Period Robust Model)
ID = + 0.26(ACC) + 0.27(TT ) – 0.30(GT&I ) + 0.011POP

(t =) (8.7) (2.9) (–3.8) (5.7)
– 4.72PR–2 + 6.81XRAV + 2.55CAP–1 (5.4.TR)
(–2.7) (2.9) (1.7)
R2 = 83.3% D.W. = 2.0 MSE = 28.25
5.4.1.3 Robustness to Model Specification Changes

Dropping the last two variables from 5.4.TR, we get
Model 5.4.TR.a
(Time Period Robust Model, with Two Variables Deleted)
ID = + 0.23(ACC) + 0.31(TT ) – 0.27(GT&I ) + 0.010POP – 7.39PR–2

(t =) (10.9) (3.3) (–3.4) (3.7) (–3.4)
R2 = 83.3% D.W. = 2.0 MSE = 28.25 (5.4.TR.a)
All variables remain statistically significant and have the same signs. Gen-
erally, magnitude changes are small, except for the interest rate variable,
whose coefficient grows markedly.
Adding the M1 money supply and depreciation variables to the com-
plete time period robust model 4.4.TR gives the following results.
Model 5.4.TR.b
(Time Period Robust Model, with Two Variables Added)
ID = + 0.26(ACC) + 0.27(TT ) – 0.29(GT&I ) + 0.012POP

(t =) (6.6) (2.2) (–3.1) (2.9)
– 5.02PR–2 + 6.95XRAV + 2.53CAP–1 – 0.01DEP
(–2.7) (3.4) (1.7) (–0.0)
– 0.04M1Rea R2 = 83.5% D.W. = 2.0 MSE = 28.86
(–0.3) (5.4.TR.b)
5.5 OLS ESTIMATES OF THE DETERMINANTS OF IMPORTED INVESTMENT GOODS 197
The time robust model variables’ signs, coefficients, and significance are
robust to these additions.
Hence we conclude the model given by Eq. 5.4.TR is robust to both
time period tested and changes in the exact way the model is specified.
(The business borrowing variable is highly collinear with the deficit is
the likely reason for its lack of significance, since it is very highly posit-
ively correlated with government receipts and highly negatively correlated
with government spending (r = .78) when the two are run as one defi-
cit variable. In short, government tax and spending deficits are strongly
related to declines in business borrowing as we might expect due to
crowd out.)
5.5 OLS ESTIMATES OF THE DETERMINANTS

OF IMPORTED INVESTMENT GOODS
The factors driving the demand for imported investment goods were
assumed to be the same as those driving demand for domestically
produced investment goods, at least for purposes of initial testing in
5.5.1 Nonstationarity
For investment imports, five of the explanatory variables were found
nonstationary, but were found cointegrated with total investment, the
dependent variable. The nonstationary variables were government spend-
ing, depreciation, the stock market index, profits, and population
growth.
Model 5.5
OLS Estimates of Determinants of Spending on Imported
Investment Goods
(Several Variables Endogenous; See Section 5.6 for 2SLS Model)
IM = + 0.09(ACC) – 0.01(TT ) + 0.03(GT&I ) + 0.60DEP

(t =) (2.4) (–0.2) (0.6) (2.3)
+ 0.60CAP–1 – 0.78PR–2 + 0.14DJAV + 0.02PROF–0
(0.3) (–0.3) (1.2) (0.4)
–1.80XRAV – 0.002POP + 0.10(BOR–1 )

(–1.3) (–0.9) (2.3) (5.5)
R2 = 72.4% D.W. = 2.6 MSE = 24.15
5.6 2SLS ESTIMATES OF THE DETERMINANTS

OF IMPORTED INVESTMENT GOODS
Three variables in the standard investment model were found endogenous
with spending on imported investment goods. They included the acceler-
ator, profits, and the stock market (Tobin’s q proxy) variable. Finding a
single strong, nonendogenous instrument to replace all these variables has
proven to be a formidable task, not successfully completed. However, a
common strong instrument was found for the profits and accelerator vari-
ables, though of course the coefficients on the variables in the instrument
varied with each variable for which it was an instrument. For the DJAV
variable, the residuals of the first-stage Hausman test (which capture the
portion of DJAV that is endogenous) were deducted from DJAV and the
result (labeled DJAV-Vhat2) was used as the instrument for DJAV. Results
are shown in Eq. 5.6.
Model 5.6
2SLS Estimates of Determinants of Spending on Imported
Investment Goods
Hausman tests indicate three variables endogenous with investment spend-
ing on imports: the accelerator, profits, and DJAV, The instrument used
was a strong instrument for the first two, but not for the third. Sargan test
NR2 = 6.24 < X2(95,15) = 25.0. Hence, the instruments are not endogenous.
IM = + 0.01(ACC) + 0.08(Tax) – 0.04(GT&I ) + 0.08DEP

(t =) (0.2) (2.3) (–1.6) (0.4)
– 0.03CAP–1 – 3.00PR–2 + 0.60(DJAV – Vhat2)
(–0.0) (–1.9) (4.8) (5.6)
+ 0.16PROF + 1.63XR – 0.001POP – 0.06(BOR–1 )
(3.3) (2.0) (0.6) (1.8)
R2 = 79.9% D.W. = 2.3 MSE = 12.59
Results indicate the key factors affect the demand for imported investment
goods positively are the deficit, interest rates, the stock market, profits, the
exchange rate, and access to borrowing.
5.6 2SLS ESTIMATES OF THE DETERMINANTS OF IMPORTED INVESTMENT GOODS 199
5.6.1 Variance Explained and Robustness Tests – Investment

Imports Model
(Table 5.6.1).
From a first-out perspective, the factors which explain the most variance
in total investment are the stock market (positively) and both kinds of
deficits and the prime rate (negatively). From the first-in perspective, three
accounted for much more variance than the others, and tend to move with
the GDP. They were the Tobin’s q proxy (stock market index), profits, and
depreciation.
5.6.1.2 Robustness Over time

The model was tested in four different but overlapping time periods.
Parameter estimates for the four samples tested are given in Table ??.
The only two variables significant in at least three of the four tests were
the stock market index (positively) and the prime interest rate (negatively).
Hence, most initial findings for variables thought to be investment imports
cannot be considered very robust. This may be due to the small amount
of fluctuation in some periods (or overall, since imports are a relatively
Table 5.6.1 Explained variance – imported investment goods

(constant added)
ACC 0.80 0.07

TAX 0.74 0.07
(GT&I ) 0.76 0.12
(DEP) 0.80 0.20
(CAP–1 ) 0.80 0.02
(PR–2 ) 0.74 0.05
DJAV-Vhat2 0.59 0.60
(PROF) 0.76 0.21
XR 0.79 0.02
(POP) 0.80 0.09
(BOR–1 ) 0.77 0.36
Table 5.6.2 Robustness over time: – investment imports, 2SLS
Variable 1960–2010 1970–2010 1970–2000 1960–2000

∗
(ACC) 0.01 0.02 0.00 0.00

(Tax) 0.08∗∗ 0.08∗ 0.02 0.03
(GT&I ) –0.04 –0.05 0.02 0.01
(DEP) 0.08 0.05 0.39∗∗ 0.34∗∗
(CAP–1 ) –0.03 0.40 –0.91 –59
(PR–2 ) –3.00∗ –2.43 –3.59∗∗ –3.43∗∗∗
(DJAV-Vhat2) 0.60∗∗∗ 0.58∗∗∗ 0.66∗∗∗ 0.63∗∗∗
(PROF) 0.16∗∗∗ 0.17∗∗∗ 0.13 0.12
(XR) 1.63∗∗ 1.74∗ 0.74 0.87
(POP) –0.001 –0.000 –0.004∗ –0.002∗∗
(BOR–1 ) –0.06∗ –0.06 –0.03 –0.03.
small amount for much of the period sampled), or because many of the
initial findings were spurious and the model fails to include important
determinants. More research is needed.
The core of our time period robust model will be the prime rate
and stock market variables. When using our usual procedure of adding
variables individually to the robust model, we noted the accelerator was
significant in all periods. We then added the rest individually to this two
variable “core” robust model and found most – individually added as a
third variable – were significant. However, when all those successful in this
way were added together to the model, only two were significant. Elim-
inating the rest left the Eq. 5.6.TR as our final time period robust model,
with each variable being significant in at least three of the four periods
sampled:
Model 5.6.TR
Investment Goods
IM = –3.91(Pr–2 ) + 0.62DJAV – Vhat2 + 0.045TT

(t =) (–4.1) (10.7) (2.0) (5.6.TR)
R2 = 71.5% D.W. = 1.5 MSE = 13.61
5.7 AN ALTERNATIVE METHOD OF CALCULATING COEFFICIENTS. . . 201

Deleting the tax deficit variable, we get
Model 5.6.TR.a
Investment Goods
(Time Period Robust Model, with One Variable Deleted)
IM = –3.84(Pr–2 ) + 0.67DJAV – Vhat2

(t =) (–3.9) (12.1) (5.6.TR.a)
R2 = 68.9% D.W. = 1.3 MSE = 14.05
The remaining variables coefficients and significance levels are robust to

the change.
Finally, we add the M1 money supply variable to the time robust model
5.6.TR and re-estimate.
Model 5.6.TR.b
Investment Goods
(Time Period Robust Model, with One Variable Added)
IM = –3.93(Pr–2 ) + 0.62DJAV – Vhat2 + 0.047TT – 0.005M1Real

(t =) (–3.9) (9.1) (1.6) (–0.1)
R2 = 71.5% D.W. = 1.5 MSE = 13.76 (5.6.TR.b)
Coefficients are very robust as are the significance levels for the prime rate
and stock market variable. The significance level of the tax deficit variable
drops to marginal (11%) significance level (t = 1.6).
We conclude that the time robust model 5.6.TR is also generally robust
with respect to changes in the variables included in the model.
5.7 AN ALTERNATIVE METHOD OF CALCULATING

COEFFICIENTS IN THE INVESTMENT IMPORTS
MODEL
When exactly the same explanatory variables are used on the right-hand
side of both the total investment (IT ) equation, and its two com-
ponent parts, CD and CM , the domestically produced and Imported
Investment goods equation, one can arithmetically determine the

regression coefficients in any one part from knowledge of those regres-
sion coefficients in the other two parts. For example, one can subtract the
regression coefficient on a variable in the domestic goods regression from
the coefficient on the same variable in the total investment model, and get
exactly the same value for that variable’s coefficient in the imports model
as would be obtained from regression, as is done with this model’s IT , ID,
and IM OLS equations below.
With 2SLS models, we can only approximate that result below since the
instruments used for certain variables in the IT and ID models are slightly
different, violating the strict rule that requires they be exactly the same if
the subtraction is to yield exactly the same result for IM variables as the IM
regression itself. Nonetheless, the OLS results do illustrate the underlying
concept.
The total Investment regression from Eq. 5.1 above is
IT = + 0.32(ACC) + 0.33(TT ) – 0.32(GT&I ) + 0.84DEP

(t =) (6.1) (3.2) (–3.9) (2.5)
+ 2.30CAP–1 – 3.20PR–2 – 0.04DJ–0 + 0.13PROF–0
(1.4) (–1.4) (–0.2) (2.1) (5.1)
+ 5.39XRAV + 0.005POP + 0.13(BOR–1 )
(2.2) (1.6) (2.0)
R2 = 93.0% D.W. = 1.9 MSE = 32.99
The domestic investment regression from 5.3 above is
ID = + 0.23(ACC) + 0.34(TT ) – 0.34(GT&I ) + 0.24DEP

(t =) (6.1) (3.0) (–3.9) (0.8)
+ 1.71CAP–1 – 2.41PR–0 – 0.18DJ–0 + 0.11PROF–0
(1.0) (–1.2) (–1.2) (1.3) (5.3)
+7.19XRAV + 0.008POP + 0.02(BOR–1 )
(2.8) (3.1) (0.4)
R2 = 89.5% D.W. = 1.8 MSE = 29.75
And since definitionally, IM = IT–ID, the arithmetically estimated coeffi-

cients of the IM model are (with allowances for rounding) the same as the
actual regression coefficients from Eq. 5.5
IM = + 0.09(ACC) – 0.01(TT ) + 0.03(GT&I ) + 0.60DEP

(t =) (2.4) (–0.2) (0.6) (2.3)
5.8 OLS ESTIMATES OF THE DETERMINANTS OF INVESTMENT BORROWING 203
+ 0.60CAP–1 – 0.78PR–2 + 0.14DJ–0 + 0.02PROF–0

(0.3) (–0.3) (1.2) (0.4)
–1.80XRAV – 0.002POP + 0.10(BOR–1 ) (5.5)
(–1.3) (–0.9) (2.3)
R2 = 72.4% D.W. = 2.6 MSE = 24.15
5.8 OLS ESTIMATES OF THE DETERMINANTS

OF INVESTMENT BORROWING
Unlike the investment spending models above, the next model examines
the determinants of business borrowing. The initial hypothesis for test-
ing was based on the assumption that businesses borrow principally to
finance desired spending. Therefore, some or all of the determinants of
spending should be determinants of borrowing. Therefore, the spending
models above were retested, except the dependent variable used is real
business borrowing. In testing the basic investment model, we found anti-
cipation of next year’s rate of growth of the economy far more significant
in explaining the variance in business borrowing than this year’s, there-
fore we used the accelerator variable with a 1 year forward lead in the final
model. Similarly, we found current year capacity utilization more systemat-
ically related to borrowing than the lagged version found related to actual
investment. We believe this amounts to the same finding: the investment
equations show last year’s borrowing to be key to this year’s investment.
Our find is equivalent to saying we have found last year’s capacity utiliza-
tion to drive last year’s borrowing. Nominal business borrowing is deflated
using the average GDP deflator for the past two years. Initial testing Res-
ults are shown in Model 5.7. The final model, robust to changes in time
period sampled and the number of other variables included in the model,
The GT&I , DEP, and DJ variables used in the model were nonstationary,
but were cointegrated with the dependent variable. Hence, no detrending
was necessary.
Model 5.7
OLS Estimates of Determinants of Business Borrowing
IB = 0.43(ACC+ ) + 0.93(TT ) – 0.77(GT&I ) + 0.09DEP

(t =) (6.0) (7.5) (–7.8) (0.1)
– 9.16CAP–1 – 3.46PR–2 – 0.75DJ–1 + 0.77PROF0

(2.6) (–0.5) (–2.5) (5.8)
(5.7)
+ 8.69XRAV R2 = 80.1% D.W. = 1.7 MSE = 84.07
(1.5)
5.8.1 2SLS Estimates

The government receipts and depreciation variables in this model were
found endogenous with investment borrowing, so a strong, endogeneity-
free instrument was developed and the model re-estimated using 2SLS.
The model is shown in Eq. 5.8.
Model 5.8
2SLS Estimates of Determinants of Business Borrowing
IB = 0.52(ACC+1 ) + 1.62(TT ) – 1.07(GT&I ) + 0.85DEP

(t =) (4.4) (4.4) (–6.1) (1.1)
– 11.26CAP–1 – 6.18PR–2 – 1.61DJ–1 + 0.33PROF0
(5.8)
(2.4) (1.0) (–3.6) (1.5)
2
+ 2.43XRAV R = 71.7% D.W. = 1.8 MSE = 101.71
(0.2)
The results indicate business borrowing is positively affected by the accel-

erator, profit levels, and the exchange rate, and negatively related to the
government deficit stock market growth (a substitute source of funds), and
lagged capacity utilization (current period investment and capacity utiliz-
ation are positively related, as one might expect. The negative relationship
with prior year utilization levels likely reflects the limited need to borrow
the year after you have borrowed a lot to meet investment needs associated
with high capacity utilization.
5.8.1 Variance Explained and Robustness Tests – Business

Borrowing Model 5.8
The importance of these variables in explaining variation in business bor-
rowing during the 1960–2010 period can be examined using stepwise
regression the 2SLS model given in Eq. 5.8 (Table 5.8.1).
From a first-out perspective, the four factors which explain the most
variance in business borrowing are both tax cut and spending induced
5.8 OLS ESTIMATES OF THE DETERMINANTS OF INVESTMENT BORROWING 205
Table 5.8.1 Explained variance – business borrowing

(constant added)
(ACC+1 ) 0.67 0.13

(TT ) 0.65 0.05
(GT&I ) 0.63 0.11
(DEP) 0.74 0.03
(CAP–1 ) 0.71 0.02
(PR–2 ) 0.72 0.05
(DJ–1 ) 0.77 0.07
(PROF) 0.64 0.42
(XRAV0–3 ) 0.70 0.03
deficits, the accelerator, and profits. The other variables only contrib-
uted marginally to explained variance. From the first-in perspective, profit
growth accounted for much more variance than the others; the acceler-
ator and spending deficits were also significantly more important than the
other variables.

determine the extent to which we could replicate the initial results.
Five of the six variables significantly related to borrowing in the first
period sampled were significant in all four periods. Only the exchange rate
average was not; it was only significant in the two samples which included
the 2000–2010 period. The three variables that were insignificant in the
first period sampled were insignificant in most or all of them. The stability
of most findings in different sample periods suggests the Lucas critique
does not well describe the behavior of American businesses (Table 5.8.2).
Four of the variables were significant in all four sample periods and
another in three. These will constitute the core of our time period robust
model. The insignificant variables were added to this core and retested
using the 1960–2010 sample. Those that were now found significant were
as a group, added to the core model, and tested in all four sample periods.
Those significant in at least three were added to the core variables and
constitute the final time period robust model, shown in Eq. 5.8.TR below.
No additional variables were added to the core added to the five core
variables using this procedure.
Table 5.8.2 Robustness over time – business borrowing, 2SLS
Variable 1960–2010 1970–2010 1970–2000 1960–2000

∗
(ACC+1 ) 0.52∗∗∗ 0.52∗∗∗ 0.53∗∗∗ 0.55∗∗∗

(Taxes) 1.62∗∗∗ 1.74∗∗∗ 1.57∗∗∗ 1.61∗∗∗
(GT&I )1 –1.08∗∗∗ –1.15∗∗∗ –1.21∗∗∗ –1.19∗∗∗
(DEP) 0.85 1.04 –0.25 –0.35
(CAP–1 ) –11.26∗∗ –14.63∗∗∗ –10.16∗∗ –7.17
(PR–2 ) –6.17 –8.26 –1.93 0.15
(DJ–1 ) –1.61∗∗∗ –1.79∗∗∗ –1.48∗ –1.46∗∗
(PROF) 0.33 0.22 0.62 0.74∗∗
(XR) 2.43 0.83 10.78∗∗ 11.17∗∗
Model 5.8.TR
2SLS Estimates of Determinants of Business Borrowing – Time
Period Robust Model
IB = 0.59(ACC+1 ) + 1.84(TT ) – 1.12(GT&I ) – 8.67CAP–1 – 1.43DJ–1

(t =) (6.1) (6.1) (–6.3) (–2.1) (–2.6)
2
R = 62.7% D.W. = 1.8 MSE = 111.32 (5.8.TR)

Deleting the last two variables from the model (5.8.TR) and re-estimating
yields the following results:
Model 5.8.TR.a
Period Robust Model
IB = 0.74(ACC+1 ) + 1.41(TT ) – 0.99(GT&I )

(t =) (5.8) (6.9) (–7.5) (5.8.TR.a)
2
R = 60.3% D.W. = 2.0 MSE = 112.33
Here, deletion of these variables resulted in no major changes in both

coefficient values and significance levels.
5.9 DETERMINANTS OF SPENDING ON FIXED PLANT AND EQUIPMENT. . . 207
Finally, let us add the money supply and depreciation variables to the
full model time period robust model given in Eq. 5.8. The new model
results are
Model 5.8.TR.b
Period Robust Model
IB = 0.55(ACC+1 ) + 1.84(TT ) – 1.34(GT&I ) – 10.61CAP–1

(t =) (6.2) (6.8) (–7.7) (–2.2)
– 2.10DJ–1 – 0.425M1Real + 1.46(DEP)
(–4.4) (1.0) (1.8)
R2 = 62.7% D.W. = 1.8 MSE = 111.32 (5.8.TR.b)
Coefficient values on the time period robust variables were reasonably
stable, and all remained statistically significant.
Overall, the evidence suggests borrowing model results are robust to
both time period tested and changes in the model specification.
5.9 DETERMINANTS OF SPENDING ON FIXED PLANT

AND EQUIPMENT INVESTMENT (OLS)
Findings for the initial model tested, which included all variables found sig-
nificant in at least one previous study reviewed, are presented in Model 5.9.
The final model, robust to changes in time period sampled and the num-
ber of other variables included in the model except as noted, is presented
in Model 5.10 TR further below.
5.9.1 OLS Estimates of Determinants of Fixed Investment Spending.
IP& E = + 0.07(ACC) + 0.11(TT ) – 0.13(GT&I ) + 0.94DEP

(t =) (3.9) (2.0) (–2.8) (3.3)
+ 3.48CAP–1 – 0.55PRAV–3–4 + 0.40DJ–0
(2.8) (–0.6) (4.2)
+ 0.08PROFAV–3–6 + 1.79XRAV0–3 – 0.001POP + 0.09(BOR–1 )
(4.3) (1.1) (–0.3) (1.8)
R2 = 91.7% D.W. = 2.1 MSE = 20.35 (5.9)
Five of the explanatory variables were found nonstationary, but were

found cointegrated with fixed investment, the dependent variable. The
nonstationary variables were government spending, deprecation, the stock
market index, profits, and population growth.
5.10 DETERMINANTS OF SPENDING ON FIXED PLANT

AND EQUIPMENT INVESTMENT (2SLS)
In the fixed investment model, the tax, government spending, accelerator,
depreciation, Tobin’s q proxy, and the exchange rate variable were found
endogenously related to fixed investment. All but the Tobin’s q proxy
were replaced by a Wald-strong instrument and re-estimated using 2SLS.
The Tobin’s q was replaced by its own strong instrument. Results are
shown in Eq. 5.10.
Model 5.10
2SLS Model of Investment Spending on Plant and Equipment
IP& E = +0.06(ACC) + 0.12(TT ) – 0.13(GT&I ) + 0.93DEP

(t =) (3.8) (1.4) (–1.9) (3.6)
+ 3.29CAP–1 – 0.67PRAV–3–4 + 0.21DJ–0
(3.1) (–0.8) (1.8)
+ 0.06PROFAV–3–6 + 0.92XRAV (5.10)
(3.0) (0.5)
= – 0.001POP + 0.13(BOR–1 )
(–0.5) (2.0)
R2 = 91.6% D.W. = 2.1 MSE = 20.47
The results indicate business investment in plant and equipment is posit-
ively affected by the accelerator, depreciation allowances, capacity utiliza-
tion levels, stock market levels, past profits and borrowing, and negatively
related to the government deficit.
5.10.1 Variance Explained and Robustness Tests – Plant and

Equipment Investment Model
Table 5.10.1 Explained variance – plant and equipment

investment

(with constant)
(ACC) 0.90 0.11

(TT ) 0.91 0.22
(GT&I ) 0.89 0.27
(DEP) 0.88 0.27
(CAP–1 ) 0.90 0.09
(PRAV–3–4 ) 0.91 0.03
(DJ) 0.90 0.60
(PROFAV–3–6 ) 0.89 0.04
(XRAV ) 0.91 0.00
(POP) 0.92 0.03
(IBOR–1 ) 0.88 0.76
regression the OLS model given in Eq. 5.10.1 over the 1960–2010 period
(Table 5.10.1).
From a first-out perspective, the four factors which uniquely explain
the most variance in plant and equipment investment are spending defi-
cits, depreciation allowances, borrowing and profits, but only 3–4%. The
other variables unique contribution was marginal at best. From the first-
in perspective, the Tobin’s q proxy stock market index and the level of
borrowing were the most important.

The model was separately tested in four time periods to determine if the
initial results were replicable. Results are presented in Table 5.10.2.
Six variables were significant in at least three of the four samples: the
accelerator, spending deficits, depreciation, capacity utilization, the stock
market index and profits, and become the core components of our time
period robust model. Variables which were not significant in at least three
tests were re-estimated, one at a time, with this core model. All those
significant were then collectively added to the core model’s four variables,
and re-estimated in all four periods. Those significant in at least three of
the four samples were added to the core variables to obtain the final time
period robust model, Eq. 5.10.TR, given below:
Table 5.10.2 Robustness over time – plant and equipment, 2SLS Model 5.10
Variable 1960–2010 1970–2010 1970–2000 1960–2000

∗
(ACC) 0.06∗∗∗ 0.06∗∗∗ 0.07∗∗ 0.07∗∗∗

(Tax) 0.12 0.12 0.18∗∗∗ 0.17∗∗∗
(GT&I ) –0.13∗ –0.13∗ –0.19∗∗∗ –0.19∗∗∗
(DEP) 0.93∗∗∗ 0.89∗∗∗ 0.71∗∗∗ 0.77∗∗∗
(CAP–1 ) 3.29∗∗∗ 3.39∗∗ 4.29∗∗ 4.00∗∗∗
(PRAV–2–3 ) –0.67 –0.69 –1.41∗∗∗ –1.47∗∗∗
(DJ0 ) 0.21∗ 0.23∗∗ 0.25∗ 0.29∗
(PROFAV–3–6 ) 0.07∗∗∗ 0.07∗∗∗ 0.12∗∗ 0.11∗∗
(XR) 0.92 1.17 2.22 1.96
(POP) 0.002 –0.001 0.001 0.000
(IBOR ) 0.13∗∗ 0.13∗∗ 0.03 0.03
Model 5.10.TR
Time period Robust 2SLS Model of Investment Spending on
Plant and Equipment
IP& E = + 0.06(ACC) – 0.14(GT&I ) + 0.83DEP + 3.02CAP–1

(t =) (3.8) (–2.0) (7.4) (3.4)
+ 0.18DJ–0 + 0.06PROFAV–3–6 + 0.14(TT ) + 0.14(BOR–1 )
(1.3) (3.0) (1.5) (2.3)
R2 = 91.0% D.W. = 2.1 MSE = 20.30 (5.10.TR)
The tax deficit variable and the borrowing variable are positively correlated
(r = 0.48), indicating the smaller the deficit, the greater private borrow-
ing. This relationship held in all four test periods. Including two highly
correlated variables typically cause the significance level of at least one to
drop, and that is what happened here. Because of the relatively high cor-
relation level, in two of the test periods the deficit variable was significant
and the borrowing variable was not; it the other two tests just the oppos-
ite occurred. We included both in our “final” time period robust model,
convinced that the reason they were sometimes showing as insignificant
was not that their fundamental relationship to the dependent variable was
spurious, but rather because of a multicollinearity problem’s predictable
consequences. (When the other variable was dropped from the model, the
remaining variable was strongly significant in all four periods in the time
period robust model.)

Data Set)
Deleting the last two variables in Eq. 5.10.TR and re-estimating, we get
Model 5.10.TR.a
Time period Robust 2SLS Model of Investment Spending on Plant
and Equipment

(t =) (3.8) (–3.4) (4.8) (3.9)
+ 0.61DJ–0 + 0.03PROFAV–3–6
(5.1) (0.9)
R2 = 81.3% D.W. = 2.2 MSE = 28.66 (5.10.TR.a)
Here, most coefficients are reasonably similar to the full model, and
equally statistically significant, a good indication of robustness to changes
in model specification. However, two the coefficients and significance
levels of two are not: the stock market index and the exchange rate. Hence
we cannot say the time period robust model’s remaining variables are
robust to this change in model specification.
Adding the real M1 money supply variable and prime interest rate
variables to the full time period robust model (5.10.TR) we get
Model 5.10.TR.b
Time Period Robust 2SLS Model of Investment Spending on Plant
and Equipment

(t =) (2.2) (–2.0) (6.5) (2.1)
+ 0.18DJ–0 + 0.06PROFAV–3–6 + 0.14(TT ) + 0.14(BOR–1 )
(1.2) (2.7) (1.5) (2.3)
+ 04(M1Real ) – 0.70PRAV–3–4
(0.3) (–0.7)
R2 = 91.0% D.W. = 2.1 MSE = 20.30 (5.10.TR.b)
Coefficients and significance levels were very robust to the addition of the
money supply and the prime rate to the model.
Overall, we conclude that Model 5.10.TR is robust to both time period
sampled and to some, but not all, model specification changes.
5.11 DETERMINANTS OF SPENDING ON RESIDENTIAL

INVESTMENT (OLS)
Findings for the initial model tested, which included variables found signi-
ficant in at least one previous study reviewed, and some additional variables
thought to influence residential construction are presented in Model 5.11.
The final model, robust to changes in time period sampled and the number
of other variables included in the model, is presented in Model 5.11.TR
further below
Model 5.11
OLS Estimates of Determinants of Residential Construction
Spending
(No 2SLS Model Needed – See Below)
IRes = + 0.10(Y – T) + 0.21(TT ) – 0.22(GT&I ) – 0.21DJAV–1–2

(t =) (4.8) (5.6) (–7.5) (3.7)
– 7.15PRAV(0,–1) + 2.41XRAV(–2–4) + 0.13CB2
(–3.1) (2.2) (4.8)
+ 0.37M1Real – 0.001(HouseP / Inc)Real
(2.9) (–3.6)
R2 = 87.1% D.W. = 2.2 MSE = 20.48 (5.11)
Two of the explanatory variables were found nonstationary, but were
found cointegrated with the dependent variable. The nonstationary vari-
ables were government spending and disposable income. The negative sign
on the stock market index variable (XRAV(–2–4) ) suggests portfolio balan-
cing. As the stock market becomes more attractive, investors shift money
from housing to the stock market.
5.11.1 Variance Explained and Robustness Tests – Residential

Investment Model
5.11.1.1 Contribution to Explained Variance
The importance of these variables in explaining variation in residential
investment during the 1960–2010 period can be examined using step-
wise regression on the OLS model given in Eq. 5.11 over the 1960–2010
period (Table 5.11.1).
From a first-out perspective, the factors which explain the most variance
in residential investment are the tax and spending deficit variables and the
5.11 DETERMINANTS OF SPENDING ON RESIDENTIAL INVESTMENT (OLS) 213
Table 5.11.1 Explained variance – residential investment

(constant added)
(Y-T) 0.79 0.10

(TT ) 0.76 0.15
(GT&I ) 0.68 0.04
(DJAV–1–2 ) 0.82 0.05
(PRAV0,–1 ) 0.84 0.01
(XRAV–2–4 ) 0.85 0.17
(CBOR ) 0.79 0.49
(M1REAL ) 0.84 0.02
(HousePInc–1 ) 0.71 0.00
Table 5.11.2 Robustness over time – residential investment, OLS Model 5.11
Variable 1960–2010 1970–2010 1970–2000 1960–2000

∗
(Y-T) 0.10∗∗∗ 0.11∗∗∗ 0.13∗∗∗ 0.11∗∗∗

(Tax) 0.21∗∗∗ 0.21∗∗∗ 0.27∗∗∗ 0.26∗∗∗
(GT&I ) –0.22∗∗∗ –0.22∗∗∗ –0.24∗∗∗ –0.23∗∗∗
(DJAV–1–2 ) –0.21∗∗∗ –0.22∗∗∗ –0.29∗∗∗ –26∗∗∗
(PRAV0,–1 ) –7.15∗∗∗ –7.10∗∗∗ –6.97∗∗∗ –6.80∗∗∗
(XR) 2.40∗∗ 2.34∗∗ 1.60 1.61∗
(CBOR ) 0.13∗∗∗ 13∗∗∗ 0.11∗∗∗ 0.13∗∗∗
(M1REAL ) 0.37∗∗∗ 0.37∗∗∗ 0.32∗∗ 0.31∗∗
(House P/Inc–1 ) –0.001∗∗∗ –0.001∗∗∗ –0.03∗∗ –0.04∗∗
level of house prices relative to income. Consumer borrowing and dis-

posable income were also important. The other variables only contributed
more marginally to explained variance. From the first-in perspective, con-
sumer borrowing levels were hugely important, and tax cut deficits and
the exchange rate were also important (Table 5.11.2).
Both coefficients and significance levels for all the variables stayed
roughly the same in all four samples as in Eq. 5.11. The one exception
might be the exchange rate which is significant in samples with 2001–2010
in them, and for one, but not both, samples without that decade’s
data. Initial Model 5.11 findings must be considered extremely robust to

differences in time period sampled, hence can be referred to as 5.11.TR.
Model 5.11.TR
Spending

(t =) (4.8) (5.6) (–7.5) (3.7)
– 7.15PRAV(0,–1) + 2.41XRAV(–2–4) + 0.13CB2 + 0.37M1Real
(–3.1) (2.2) (4.8) (2.9)
– 0.001(HouseP / Inc)Real
R2 = 87.1% D.W. = 2.2 MSE = 20.48
(–3.6) (5.11.TR)

Data Set)
Deleting the last two variables in 5.11.TR and re-estimating:
Model 5.11.TR.a
Spending.

(t =) (2.5) (3.0) (–3.9) (1.5)
– 8.28PRAV(0,–1) + 3.93XRAV(–2–4) + 0.15CB2
(–2.5) (2.5) (3.8)
2 (5.11.TR.a)
R = 68.4% D.W. = 2.1 MSE = 32.14
All variables held their sign, and statistical significance, indicating the res-
ults are generally robust. Magnitudes are also generally robust, except for
the stock market index variable, whose coefficient drops by more than
half, and the exchange rate variable whose coefficient grows by more
than half.
Finally, let us add the profits and depreciation variables to the full model
(5.11.TR):
5.13 DETERMINANTS OF SPENDING ON INVENTORY INVESTMENT (OLS) 215
Model 5.11.TR.b
Spending

(t =) (3.8) (5.7) (–6.0) (1.9)
– 6.52PRAV(0,–1) + 2.38XRAV(–2–4) + 0.12CB2 + 0.30M1Real
(–2.8) (2.2) (4.1) (2.3)
– 0.001(HouseP / Inc)Real + 0.07PROF – 0.37DEP
(–3.6) (1.4) (–1.6)
2
R = 88.2% D.W. = 2.0 MSE = 20.10 (5.11.TR.b)
Though there is some volatility in the coefficients when these variables

are added, they are generally very similar. Generally significance levels
were stable, with the exception of the exchange rate which goes from
insignificant to marginally significant.
We conclude the model 5.11.TR is completely robust to time period
sampled and generally robust to model specification.
5.12 DETERMINANTS OF SPENDING ON RESIDENTIAL

INVESTMENT (2SLS)
Hausman endogeneity tests, using the standard first-stage regressors, did
not find endogeneity with the dependent variable, spending on residential
investment. Hence, no 2SLS model was required.
5.13 DETERMINANTS OF SPENDING ON INVENTORY

INVESTMENT (OLS)
Since little past literature on the determinants of inventory investment
was found, the initial model tested was based on some experimentation
with possible determinants. The model present below (5.13) represents
the combination of variables that best explained variance when tested using
the 1960–2010 sample period commonly used for initial tests. The final
model, robust to changes in time period sampled and the number of other
below.
Model 5.13
OLS Estimates of Determinants of Inventory Investment
IINV = + 0.33(ACC) + 0.22GDP–1 – 1.40PRAV–1–2 – 0.32CT

(t =) (11.8) (4.9) (–1.5) (–5.1)
+ 0.10PROFReal – 1.60CAP–0 + 1.40XRAV0–3 – 0.49AR(1)
(5.1) (–2.1) (3.4) (–3.2)
R2 = 88.5% D.W. = 2.3 MSE = 15.34 (5.13)
Two of the explanatory variables were found nonstationary, but were
found cointegrated with fixed investment, the dependent variable. The
nonstationary variables were depreciation and population growth.
Inventory growth was found to be positively related to growth in
accelerator effects in the current year, the level of the GDP, profits,
and the exchange rate. Inventories were negatively related to interest
rates, same period growth in consumption (causing inventory deple-
tion), and increases in capacity utilization. No variables were found
Hausman-endogenous, so no 2SLS tests needed to be performed.
5.13.1 Variance Explained and Robustness Tests – Inventory

Investment Model
5.13.1.1 Variance Explained
The importance of these variables in explaining variation in unemployment
during the 1960–2010 period can be examined using stepwise regression
on the OLS model given in Eq. 5.13.1 (Table 5.13.1).
From a first-out perspective, the factor which explains by far the most
variance in inventory investment is the accelerator. Also significant, but
Table 5.13.1 Explained variance – inventory investment

2
(R = 0.89 to start) (R2 = 0.00 to start)
(ACC) 0.68 +0.71

(GDP–1 ) 0.82 +0.06
(PRAV–1–2 ) 0.88 +0.18
(C) 0.81 +0.01
(PROFReal ) 0.85 +0.31
(CAPUTIL) 0.88 +0.37
(XRAV0–3 ) 0.87 +0.00
at a much smaller level, were lagged GDP and (negatively) the level of
consumer spending. The other variables only contributed marginally at
best to explained variance. From the first-in perspective, the accelerator
was again by far the most important, with profits and % capacity utilized
also explaining significant variance.

The model was tested in four different but overlapping time peri-
ods to determine replicability of initial findings. Results are shown in
Table 5.13.2.
The accelerator, prior year GDP level, consumption, capacity utiliza-
tion, and the exchange rate average had remarkably consistent coefficients
and significance levels regardless of the time period sampled. Interest rates
were a significant factor before 2000, but not after. For profits, it was just
the opposite: not significant before 2000, highly significant after. For the
prime interest rate, significant for period from 1960–2000, but not after.
Those variables significant in three of the four periods will consider the
core of our time period robust model. Separately, the two variables that
were not significant in more than two test periods above are re-entered
and if significant in the 1960–2010 period are retested for all four periods
(with any other variables re-entered and found significant. In doing so,
neither of the deleted variables passed this retest. In addition, with them
out of the model, the capacity utilization and exchange rate variables were
found insignificant in at least two of the four periods retested. Hence, they
were dropped from the final robust model given below (5.13.TR):
Table 5.13.2 Robustness over time – inventory investment 2SLS

Model 5.13
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(ACC) 0.33∗∗∗ 0.33∗∗∗ 0.36∗∗∗ 0.34∗∗∗

(GDP–1 ) 0.22∗∗∗ 0.22∗∗ 0.29∗∗∗ 0.27∗∗∗
(PR–1–2 ) –1.40 –1.30 –3.09∗∗∗ –2.74∗∗∗
(C) –0.32∗∗∗ –0.32∗∗∗ –0.40∗∗∗ –0.37∗∗∗
(PROFReal ) 0.10∗∗∗ 0.10∗∗∗ –0.02 –0.02
(CAPUTIL) –1.60∗∗ –1.55 –2.32∗ –1.62∗
(XRAV0–3 ) 1.40∗∗∗ 1.39∗∗∗ 1.26∗∗∗ 1.17∗∗∗

Model 5.13.TR
IINV = + 0.32(ACC) + 0.16GDP–1 – 0.22CT – 0.41AR(1)

(t =) (7.9) (3.0) (–2.9) (3.7)
2 (5.13.TR)
R = 83.4% D.W. = 2.1 MSE = 17.63

Deleting the last two variables from 5.13.TR and retesting gives
Model 5.13.TR.a
IINV = + 0.19(ACC) – 46AR(1) R2 = 77.8% D.W. = 2.2 MSE = 22.08

(t =) (5.7) (–4.7) (5.13.a)
The remaining variable had the same sign remained statistically significant
as model 5.13.TR. The magnitude of its marginal effect on inventory did
drop from 0.32 to 0.19, we cannot call its magnitude fully robust to this
particular change in specification. We also note that dropping only one of
the last two variables leaves the other insignificant, so our most robust res-
ult is that the Samuelson accelerator effect is by far the main determinant
of inventory change, explaining nearly 80% of the variance.
Finally, if we added back the capacity utilization and exchange rate
variables to the full three variable model 5.13.TR, all three variables stay
significant and coefficients remain reasonably stable. This has is shown in
Model 5.13.b:
Model 5.13.TR.b
IINV = + 0.34(ACC) + 0.20GDP–1 – 0.27CT – 0.78CAP–0

(t =) (7.5) (2.7) (–2.7) (–0.8)
+ 0.48XRAV0–3 – 0.37AR(1)
(0.9) (–3.2)
R2 = 84.5% D.W. = 2.1 MSE = 19.47 (5.13.b)
Coefficients and significance levels of the time period robust model vari-
ables fluctuate somewhat, but are not significantly changed. We conclude
the three variables of the time period robust model are robust to the
addition of other variables to the model, and generally robust to variable
deletions, though with deletions, magnitudes of remaining variables may
fluctuate noticeably.
CHAPTER 6
The Exports Demand Equation
In 2012, 13.5% of the U.S. GDP was produced to meet foreign demand
(EOP, 2013). This is substantial and changes in foreign demand can have
a significant effect on the U.S. economy. The model of export demand
presented below initially theorized that the principal determinants of
demand for U.S. exports were (1) foreign nations’ income and (2) the
exchange rate, i.e., much the same as key determinants driving domestic
demand for the same items. Using Federal Reserve data on the relative
weights of different countries purchases of exports since 1973, and UN
data on our export trading partners GDPs each year during the 1973–
2010 period, we constructed a trade-weighted real average income variable
to represent yearly variation in our trading partners’ real income. The real
exchange rate variable for each year is the average of the current and past
three years exchange rates.
These two variables only explained a small amount of the variance
in spending on exports over the past 40 years, and we had to search
out other factors to explain most of the variance during this period.
Through a process of trial and error, we found two variables exerting a
mild, but systematic relationship with exports: the U.S. real prime interest
rate (positively related, for reasons not clear) and the U.S. inflation rate
(negatively related). Clearly, one would expect inflation to be negat-
ively related, though its marginal levels of statistical significance probably
reflects the fact that we are already controlling for it in the real exchange

DOI 10.1007/978-3-319-50681-4_6
222 6 THE EXPORTS DEMAND EQUATION
rate; but perhaps less than completely. A theory for why the U.S. interest
rate (average for prior 2 years) is empirically positively related to foreign
demand is not so well established; but we hypothesize that since other
evidence in earlier equations indicates domestic U.S. demand drops with
rising rates, that this results in some U.S. production being offered on
the foreign market that normally would be sold domestically. It may also
mean that foreign earnings on U.S. securities may have been high the
past two years because interest rates were high, and that is now translat-
ing into increased foreign demand for U.S. goods. Another reason may
be that the high interest rate implies lower inflation in the U.S. relative
to other countries, stimulating export demand. Finally, it may also be that
foreign interest rates are even higher when U.S. rates are high, limiting the
funds foreigners can afford to borrow, forcing them to search for cheaper
products. Perhaps they find them in the U.S.
Besides the interest rate and inflation rate, a third and by far the most
important other variable found systematically related to foreign demand
for U.S. exports was U.S. demand for imports. This variable explained
more variance in exports over the past 50 years than all the other determ-
inants of export demand combined, even controlling for both U.S. and
foreign income levels.
The economic explanation may be that the single most important
factor affecting foreigners’ ability to purchase American exports is the U.S.
money they received selling their own goods to the U.S. The coefficient
on this variable indicates that almost 0.60 cents of every dollar Americans
spend on imports is returned in the same period to America in the form
of foreign demand for U.S. exports (and this coefficient’s statistical signi-
ficance is very stable regardless of whether U.S. and foreign income are
controlled for).
It is hard to conceive of why foreigners’ MPC U.S. goods out of in-
come from U.S. imports would be as high as 56%. Would, on average, the
rest of the world’s MPC for U.S. goods be 56% out of their total income
from farming or working for other domestic industries? Probably not; the
high MPC out of imports income is more plausibly because to get U.S.
cash with which to buy U.S. goods, foreigners must sell the U.S. their
goods, and that this is the principal reason they are in the export market.
If this is the primary reason foreigners export to the U.S., we would
expect imports to equal or exceed U.S. exports, which is the case.
This relationship may also reflect the tendency of many countries to
import intermediate goods and then export them as finished goods (or to
THE EXPORTS DEMAND EQUATION 223
Table 6.0.1 Import/export relationships among U.S. trading partners
Country Exports Imports Balance Imports/exports
Total, all countries 1,288,882 1,934,006 –645,124 1.50

Europe 289,515 385,359 –95,844 1.33
Euro area 178,076 244,345 –66,269 1.37
France 27,369 38,719 –11,350 1.41
Germany 48,526 82,866 –34,340 1.71
Italy 14,396 28,771 –14,375 2.00
United Kingdom 49,038 50,706 –1,668 1.03
Canada 250,132 281,034 –30,902 1.12
Latin American and other 302,901 365,045 –62,144 1.21
Western Hemisphere
Brazil 35,353 24,203 11,150 0.68
Mexico 163,532 232,726 –69,194 1.42
Venezuela 10,648 32,825 –22,177 3.08
Asia and Pacific 369,060 741,047 –371,987 2.01
China 93,029 366,125 –273,096 3.94
India 19,335 29,682 –10,347 1.54
Japan 61,483 122,925 –61,442 2.00
Korea, Republic of 39,794 49,535 –9,741 1.24
Singapore 29,105 18,454 10,651 0.63
Taiwan 26,763 35,974 –9,211 1.34
Middle East 48,881 76,274 –27,393 1.56
Africa 28,393 85,248 –56,855 3.00
Memorandum: Members of 54,526 151,467 –96,941 2.78
OPEC
Source: Economic Report of the President, 2013, Table B-105
import basic commodities and export as intermediate or final goods).

However, if this were the major reason why the U.S. imports, we would
expect the value of exports to exceed imports, which is not the case
(Table 6.0.1).
Table 6.0.1 indicates that with the relatively minor exceptions of Brazil
and Singapore, all countries sell more to the U.S. than they buy from
U.S. It is perhaps coincidental, but it seems more likely to indicate that
the amount of money received from U.S. imports of their goods sets an
upper limit on the amount of U.S. exports foreign nations can (and do)
buy. Our statistical model shows this as an indication U.S. exports go up
$0.56 for every dollar increase in imports we buy from abroad. If all U.S.
imports went into our exports, one would expect our exports to exceed
our imports, but imports substantially exceed exports, so this cannot be
more than part of the reason why our export levels seem so tied to our
import levels. The larger reason would seem to be that without selling
goods to the U.S., foreigners cannot obtain the U.S. currency needed to
buy goods from the U.S.
Our causality analysis suggests American demand for imports is a
stronger determinant of the demand for U.S. exports than the demand
for U.S. exports is a determinant of the demand by the U.S. for imports.
And from earlier analysis of the demand for U.S. imports, we know U.S.
income is a major determinant of import demand. Taken together, these
two facts suggest the principal reason for the demand by the U.S. for for-
eign imports is to satisfy U.S. consumer and business needs, not to add
value by fabricating and re-exporting. This then implies that the system-
atic relationship of every dollar of imports being related to a 0.56 cent
increase in demand for U.S. exports is probably due to the desire of for-
eigners to meet their demand for U.S. goods through dollars earned from
trading, rather than by borrowing U.S. currency.
As usual in our models, if theory (or past empirical findings) indic-
ates a variable should be included in a model, we include it using the lag
level (or level of linearity) most consistent with theory, i.e., the one that
explains the most variance in the dependent variable. For foreign income,
we found our trading partners income lagged two periods worked best
(controlling for the effects of U.S. imports), the 4-year average exchange
rate, the average interest rate for the past two years, and the average U.S.
inflation rate.
Further, we examined whether perhaps the relationship might work in
reverse: foreign demand for U.S. exports providing needed funds to allow
Americans to buy imports. As shown in Eqs. 6.2 and 6.3, our demand
for our imports is slightly better explained by our export levels than vice
versa. But, if it is the desire to obtain currency to buy U.S. exports that
accounts for the strong sales of foreign goods to the U.S., the coefficient
on exports (1.28) in Eq. 6.3 is irrational. It suggests that for every dol-
lar of imports we buy, we sell more than a dollar’s worth of exports to
foreigners, which we know is not the case. The coefficient in Eq. 6.2
is more reasonable; it suggests that for every dollar of goods the U.S.
imports, $0.65 is returned to the U.S. in the form of purchases of U.S.
exports.
The equation expressing the demand for U.S. exports was found to be
as shown in Eq. 6.1. It was estimated using OLS reflecting the finding of
no endogeneity of the dependent variable with right-hand-side variables.
6.1 OLS MODEL OF EXPORT DEMAND 225
6.1 OLS MODEL OF EXPORT DEMAND

The initial model shown below (Model 6.1) was developed as described
above. The final model, robust to changes in time period sampled and
the number of other variables included in the model, is presented in
Model 6.1
OLS Model of Export Demand
X = 0.16(WGDPRealTP(–2) ) – 9.47(XRAV0 to –3 ) + 0.56(M)
(t =) (2.9) (–4.1) (18.6)
+ 14.74(PRRealAV–1–2 ) – 11.58INFLAV–1 to –2 ) – 0.49AR(6)
(–3.9) (–2.0) (–1.7)
R2 = 87.9; DW = 1.6 MSE = 24.69 (6.1.TR)
Graph 6.1.1
The export demand model in 6.1 explains variation in exports about
equally well in each of the five decades of the sample period.
200
100
–100
80
60 –200
40
20
0
–20
–40
82 84 86 88 90 92 94 96 98 00 02 04 06 08 10
Graph 6.1.1 Equation 6.1 Graphed

Models 6.2 and 6.3

Determining Whether Export Demand Is a Function of Import
Demand, or Vice Versa
X = 0.05(WGDPRealTP(–2) ) + 0.65(M) + 0.70 AR(1)
(t =) (0.7) (12.3) (5.1) (6.2)
R2 = 0.75; DW = 1.6
M = – 0.10(WGDPRealTP(–2) ) + 1.28(X) + 0.70AR(1)

(t =) (–1.1) (12.6) (5.3) (6.3)
R2 = 0.79; DW = 1.3
The results indicate that U.S. demand for imports is at least a margin-
ally better explanation of the foreign demand for U.S. exports than is
the opposite hypothesis, i.e., that our import demand is conditioned by
foreign demand for our exports.
Explained Variance and Robustness Tests
Overwhelmingly, the principal determinant of demand for U.S. exports
is U.S. demand for imports (Table 6.1.1). This may be because of U.S.
demand for intermediate goods, which are then repackaged and sold as
final goods back to foreign markets, or it may reflect a need for foreigners
to obtain U.S. currency in order to buy U.S. goods, and that most of
this has to be obtained from trade, with foreigners unwilling or unable to
borrow sufficient dollars to pay for their desired exports from America.
In first differences only one of its determinants (government spending)
was nonstationary, the variable measuring export goods and services, but
it was cointegrated with the dependent variable, so no detrending was
needed (Table 6.1.2).
Table 6.1.1 Explained variance – exports

(constant added)
Tr. Partners.Av. Income 0.82 0.03

Exchange rate 0.72 0.15
Imports 0.22 0.64
Interest rates 0.79 0.02
Inflation rate 0.86 0.02
6.1 OLS MODEL OF EXPORT DEMAND 227
Table 6.1.2 Robustness over time – exports
1980–2010 1990–2010 1980–2000
Trading Pr. Income–2 0.16∗∗∗ 0.23∗∗ 0.10∗

Exchange RateAV0–3 –9.46∗∗∗ –14.04∗∗∗ –7.91∗∗∗
Imports 0.56∗∗∗ 0.54∗∗∗ 0.58∗∗∗
Prime Int. RateAV–1–2 14.74∗∗∗ 26.76∗∗∗ 13.24∗∗∗
InflationAV–1–2 –11.58∗∗ –48.03∗∗∗ –8.56∗
Significance Levels: ∗∗∗ = 1%; ∗∗ = 5%, ∗ = 10%.
Since the earliest data available was from the late 1970s only three
samples of reasonable size could be taken. Overall, variables statistically
significant in one sample were significant in all. Coefficients were not quite
as stable, especially for the 1980–2000 small sample, but this may have
more to do with small sample size than with robustness over time. Hence,
our time period robust model is the same as our initial Model 6.1.
Model 6.1.TR
Time Period Robust OLS Model of Export Demand
(t =) (2.9) (–4.1) (18.6)
(–3.9) (–2.0) (–1.7)
R2 = 87.9; DW = 1.6 MSE = 24.69 (6.1.TR)
Robustness to Model Specification: To test for robustness with regard to

model specification (i.e., for sensitivity to multicollinearity, random error
effects, etc.) we subtract some variables and retest to see how much
remaining coefficient estimates and significance levels have varied.
Deleting the inflation and interest rate variables from Eq. 6.1.TR and
re-estimating:
Model 6.1.TR.a
X = 0.10(WGDPRealTP(0) ) – 8.26(XRAV0 to –3 ) + 0.58(MT ) – 0.39AR(6)
(t =) (1.8) (–4.2) (16.9) (–1.5)
R2 = 0.73; DW = 1.3 MSE = 31.06 (6.1.TR.a)
Clearly, major changes in specification leave coefficients and significance

levels roughly the same for income and nearly identical for the imports and
exchange rate variables, indicating our results are very robust to changes
in model specification.
Next, we retest by removing the trading partners’ income variable from
the full model ( 6.1.TR). Results are given in Model 6.1.TR.b.
Model 6.1.TR.b
X = – 10.17(XRAV0 to –3 ) + 0.58(MT ) + 14.24(PRRealAV–1–2 )
(t =) (–4.4) (20.0) (–3.4)
– 11.68 INFLAV–1 to –2 ) – 0.10 AR(6)
(–2.0) (–0.5) (6.1.TR.b)
Results are nearly identical to the full model.
Finally, we add the real money supply variable to the full time period
robust Model 6.1.TR and re-estimate:
Model 6.1.TR.c
(t =) (3.0) (–4.3) (21.8)
+ 15.43(PRRealAV–1–2 ) – 11.20INFLAV–1 to –2 ) + 0.09M1Real
(3.2) (–2.0) ()
2
–0.49 AR(6) R = 88.9; DW = 1.6 MSE = 24.12
(11) (6.1.TR.c)
Coefficients and significance levels remain robust with the addition of
this variable.
Hence, we conclude the full model (6.1.TR) is very robust to specific-
ation changes as well as time period changes.
CHAPTER 7
Statistically Estimated Real GDP

Determination Functions (“IS” Curves)
To calculate the GDP, the GDP identity is used as a basis for developing
a model comprised of the system’s exogenous and lagged variables (the
“reduced form,” or “IS” curve model). The general form of such models
is described in Section 2. The reduced form or IS model is derived from
the GDP identity
GDP = C + I + G + (X – M) (7.1)
Or its equivalent form
GDP = CD + ID + GD + X (7.2)
where the variables in the consumption and investment functions, the

determinants of C and I, and their parameter estimates are substituted
for C and I, and the GDP identity in Eq. 7.1 is solved for the value of
the GDP. We have shown in Sections 4 and 5 when developing our con-
sumption and investment models that the data allow for calculation of how
much of total consumption and investment is domestically produced and
how much is imported. Hence we can estimate separately the demand for
imported and domestically produced goods, which permits us to calculate
the Eq. 7.2 version as well. For production represented by government
spending, we have no equivalent ability to separate government purchases

DOI 10.1007/978-3-319-50681-4_7
230 7 STATISTICALLY ESTIMATED REAL GDP DETERMINATION FUNCTIONS. . .
of imported and domestically produced goods, and therefore make an

approximation by assuming it is all domestically produced.
7.1 THE GDP AS A FUNCTION OF THE DETERMINANTS

OF DOMESTICALLY PRODUCED CONSUMER AND
INVESTMENT GOODS AND SERVICES,
GOVERNMENT SPENDING AND EXPORTS
(GDP = CD + ID + G + X)
In Chapter 4 the determinants of domestically produced consumption
goods were found to be
Model 4.4 (Repeated)

2SLS Standard Consumer Spending Model, with Borrowing
Included as a Determinant of Consumer Spending
CD = .29(Y – TT ) + .31(TT ) – .20(GT& I ) – 6.86PR + .44DJ–2

(t =) (6.0) (5.8) (–3.5) (–2.4) (4.4)
– .33XRAV – 517.17POP16 + .020POP + .53ICC–1
(0.2) (–3.5) (5.8) (2.1)
+ 38.16M2AV + .10 CB2 R2 = 88.7% D.W. = 2.0 MSE = 24.54
(4.3) (3.4) (4.4)
And in Chapter 5, the determinants of domestically produced investment

goods were found to be

ID = + .25(ACC) + .29(TT ) – .31(GT& I ) + .08DEP

(t =) (6.7) (2.7) (–3.7) (0.3)
+ 2.60CAP–1 – 3.01PR–2 – .19DJ0 + .08PROF–0
(1.5) (–1.9) (–0.8) (1.2) (5.4)
+ 7.08XRAV + .011POP + .02 (BOR–1 )
(2.2) (3.4) (0.3)
R2 = 84.4% D.W. = 2.0 MSE = 28.77
7.1 THE GDP AS A FUNCTION OF THE DETERMINANTS OF DOMESTICALLY. . . 231
Combining these determinants of consumption and investment, as

well as government spending and exports into a standard “IS” curve
income determination model and estimating its coefficients we have
the following 2SLS strong instrument behavioral model of GDP
determination:
Model 7.1.1
GDP Determination Model: Single Regression Estimates
YT = .26(TT ) – .17(GT& I ) – 7.94PR – .09DJ–0 – .006DJ–2
(t =) (2.4) (–2.0) (–1.9) (–0.5) (0.0)
+ 7.39XRAV + 107.28POP16 + .049POP + 1.32ICC–1
(–1.1) (0.2) (4.4) (2.9)
+ .001M2AV + .62(ACC) + 3.17DEP + 5.76CAP–1
(0.0) (15.0) (2.4) (2.0)
+ .61PR–2 + .05PROF–0 + .03 (CB2 + (IB(–1) ) – .02X
(0.1) (0.4) (0.4) (0.1)
+1.00AR(2) – .34AR(7)
(+5.3) (–2.0)
R2 = 95.8% D.W. = 1.9 MSE = 41.59
(7.1.1)
Clearly the IS curve has many insignificant variables and many variables
whose coefficients seem larger or smaller than we would expect given their
values in the consumption and investment equations. This can result from
four things: Briefly summarized they are:
1. With only 50 years of data, insufficient degrees of freedom to

estimate all variables at meaningful levels of significance.
2. Multicollinearity distorting coefficient values and reducing levels of
significance.
3. Use of autocorrelation controls in some, but not all sub-component
equations added together.
4. Using a method that combines the causal effects of a variable in
one equation with its spurious effects in another. This is discussed in
more detail below.
The same model re-estimated on 1960–2000 data (for later use in

Chapter 16 robustness tests):
Model 7.1.1 (For Chapter 16)

GDP Determination Model: Single Regression Estimates
(Reduced Sample Size)
YT = .49(TT ) – .38(GT& I ) – 5.96PR + .58DJ–0 – .79DJ–2

(t =) (4.7) (–3.3) (1.2) (2.1)
+ 1.68 XRAV + 679.08POP16 + .026POP + 1.18ICC–1
(–1.7) (0.4) (1.5) (3.3) (3.2)
+ .92M2AV + .52(ACC) + 1.89DEP + 3.93CAP–1 + 3.93PR–2
(3.2) (10.5) (2.5) (1.0) (1.0)
+.33PROF–0 + .21(CB2 + (IB(–1) ) + .52 X + .62 AR(1)
(2.4) (2.2) (1.6) (3.7)
–.26AR(2)
(–1.3) R2 = 97.2% D.W. = 1.8 MSE = 32.77 (7.1.1.16)
The dependent variable was stationary in first differences. Of the
explanatory variables in this model, nine variables were found nonstation-
ary in first differences, but all were cointegrated with the dependent
variable (YT ), so no detrending was necessary.
Our results in 7.1.1 are impeccable from an econometric point of view.
But Eq. 7.1.1 takes variables from two separate models whose determin-
ants’ parameters, statistically estimated, make good economic sense when
the models are estimated separately. But, by combining them into one
regression model, create nonsensical results. Combining them was anti-
cipated to give us, upon estimation of the combined model, coefficients
for each variable which were a sum of their values in the two component
equations (except for G and X, which were separately added). But that is
not what happened.
For example, the interest rate variable’s coefficient (–3.01) in the
investment equation was found negatively related to investment, con-
sistent with economic theory. But even though the only way this lagged
value of this variable is theorized to affect GDP is thorough its effect on
investment, its effect in the IS function is found to be positive (+0.61)! As
noted earlier, There are four reasons why may occur, three of which apply
to coefficient values:
1. Use of different autocorrelation controls in the GDP function and

the component functions.
2. Multicollinearity levels among variables have changed, which affects
coefficient values.
3. In the GDP determination equation, the estimate of the lagged

interest rate variable’s effect obtained by regression is an additive
combination of the empirical relationships of that interest rate to the
investment, consumption, government spending and exports com-
ponents of the GDP. This occurs even though lagged interest rates
were not found to have a causal effect on consumption (only current
interest rates were). However, lagged interest rates are correlatively
related in a negative way to consumption and positively correlated
with current government spending and net exports. Yet our models
of government spending’s determinants and consumption’s determ-
inants, though discerning this correlation with lagged interest rates,
did not find them statistically significant so lagged interest rates’
observed effects on consumption and government spending is bet-
ter thought of as merely spurious: i.e., (noncausally) correlational.
Therefore, the variables’ coefficients in such equations are better not
added to the coefficient in the investment equation when estimating
the GDP if we are to accurately assess the effect of lagged interest
rates on GDP. Our model of exports does assume lagged interest
rates are a determinant of export demand. Normally, we would add
it to the investment effect to get a net effect on the GDP, but
our Chapter 7 model is simplified and includes the exports vari-
able as a given. Hence, its effect is not added to the investment
effect.
This is shown in Table 7.1.1, where we have taken our IS equation

determinants from Eq. 7.1.1 above, modified slightly to
• Remove the net exports and autoregression correction terms from

the right side. This was done because autoregression terms can dis-
tort the coefficients of subcomponent functions so they are not
addable.
• The exports variable was excluded from the right-hand side because
we want to use it as part of the dependent variable, and it can’t be on
both sides of the equation.
• We also replaced d(real gdp) with d(real C+I+G+X–M). The reason
for this is that when using chain linked deflators, adding individually
deflated components does not usually add precisely to the deflated
whole (Bernanke).
Table 7.1.1 Comparison of PR –2 effects in GDP, C, I, G, and (X–M) functions

(i.e., all components of GDP)
Model estimated GDP C I G (X–M)
PR –2 coefficient in the model +2.91 = –4.01 –2.44 +6.88 +2.48

Or
Model estimated GDP CD ID GD (X)
PR –2 coefficient in the model +2.91 = –1.52 –0.85 +6.88 –1.60
Clearly we do not have any generally accepted theory that tells us that while rising interest rates have
negative effects on consumption and investment, rising interest rates have a positive effect on government
spending. The government effect is a spurious correlation at best; an example of the “correlation does not
imply causation.” Further, consumption function studies (Eq. 4.4 only found current interest rates, not
lagged rates, statistically significant. Hence, the lagged effect is presumed spurious This leads good studies
to only test variables that have a sound theoretical foundation. Running a regression of GDP on all the
determinants of GDP simple gives an estimate of the marginal effect of the interest rate variable that is
the sum of its measured effects in all the individual component models of GDP, whether these effects are
causal or merely spuriously correlative).
Section 2.2.4.4 presented an even simpler example of the same problem and how it affects VAR models.
Then we re-estimated the lagged prime interest rate coefficients (PR–2 ) in

the individual equations making up GDP, using consumption, investment,
government spending or net exports as the dependent variable. The right-
hand side variables in the subcomponent models were exactly the same as
for the full GDP model similar to Eq. 7.1.1., which we just described.
The result is the coefficient on the lagged interest rate variable (PR–2 )
in the GDP regression model was the same as the sum of the coefficients
on the lagged interest rate variable when each of the four subcompon-
ent models were regressed on the full list of variables regressed in the
GDP model. The GDP model’s coefficient for the lagged interest rate
variable was the same as the sum of the coefficients on the lagged interest
rate variable, if all four were added together. The fact that two of the
four coefficients were just (spuriously) correlational (the G and C equa-
tion coefficients – see analysis in Table 7.1.1), and not causal, did not
mean they were excluded in the GDP model’s calculation of the coeffi-
cient on the lagged interest rate variable. Hence, this result is not the same
as adding the coefficients in only the investment and net exports equa-
tions – where the variable is included it is thought to be causally related.
For that reason, the latter is the preferred method, and we will use this
preferred method further below.
As can be seen in the table above, the sum of the regression coefficients
for the parts equals the regression coefficient for the whole and considerably
misstates the effects of the lagged interest rate considered causal. There-
fore, we conclude that only adding values for coefficients of variables
actually included in the consumption, investment, etc., function models
is more correct than the method employed in 7.3 above: regressing GDP
on all variables found significant in any equation in the system.
The failure to do so is a is a particularly serious potential flaw in VAR –
methodologies, which typically regress each dependent variable on exactly
the same right hand side variables. If one of the VAR model’s depend-
ent variables (e.g., GDP) is the sum of several subcomponents (e.g., C,
I., etc.), each in reality determined by different variables, estimates of the
effect on GDP of any one variable will invariably be biased by the VAR
standard method of inclusion of the same determining variables in each
VAR equation. In this way, spurious components in one equation can be
added to causal components in another to get the total effect of (say) C
and I determinants on GDP. VAR only avoids this problem if all depend-
ent variables in its model are causally determined by exactly the same
right-hand side variables (and lags of them). See Section 2.2.4.4 for an
example.
We will show further below that estimating the GDP not by regres-
sion, but by adding only coefficients in subcomponent regressions where
the variable is actually considered a determinant leads to estimates whose
average error of estimate over time is only 40% of the average error
obtained using the single statistically estimated GDP function, such as
7.1.1 above. A smaller average error is exactly what we would expect if
estimates in the single equation GDP determination model, econometric-
ally estimated, distort the actual causal effects of the GDP’s determinants
on the GDP.
Hence, adding the specific parameter estimate for each variable
obtained in our consumption, investment and export regressions, where
only variables thought causally related are included, rather than estimating
a GDP regression, will be the process used to estimate GDP in Section 8.
(This would not be a problem if the scientific techniques we rely on in
economics were experimental rather than correlational, but they are not.)
Generally, this is a problem which makes statistical estimation of a func-
tion that is the sum of two or more separate sub-functions that have
separate determinants inappropriate. It results in biased coefficients. We
have shown this for the GDP function here.
A few other examples from the same equations used to illustrate interest
rate effects in Table 7.1.1 above are provided below:
Equation providing Variable estimated Spending deficit Wealth –2 Population

Estimate source: Tax deficit
GDP +0.33 –0.07 +0.53 +0.038

CD +0.28 –0.12 +0.65 +0.026
ID +0.19 –0.17 +0.10 +0.012
GD +0.01 –0.16 +0.04 +0.002
X –0.15 –0.06 –0.26 –0.002
By the same line of reasoning, is there any theory that says spending defi-
cits increase exports or that wealth and population growth cut them? Yet
this enters into the IS curve-type regression calculation of a change in
these variables on the economy. Here again, the only way to avoid this
problem is to regress each component of the GDP, (C, I, G, and X–M),
on its own determinants, and only add those estimated effect together to
get the total effect on GDP.
7.2 THE GDP AS A FUNCTION OF THE

DETERMINANTS OF TOTAL CONSUMER
AND INVESTMENT GOODS AND SERVICES,
GOVERNMENT SPENDING, AND
EXPORTS MINUS IMPORTS
(GDP = CT + IT + G + X – M)
The determinants in this model are the same as in the Section 7.1 “IS”
curve model, except that we use net exports instead of just exports as
a determinant because imported goods (CM ) are included in the “CT ”
and “IT ” used in the most common version of the GDP identity (such
that, e.g., C D & CM = CT ). For this reason, coefficients on variables
will differ from their Eq. 7.1 values. Combining and investment determ-
inants, as well as government spending and net export variables into
a standard “IS” curve income determination model and retesting we
have the following 2SLS strong instrument behavioral model of GDP
determination;
7.2 THE GDP AS A FUNCTION OF THE DETERMINANTS OF TOTAL CONSUMER. . . 237
Model 7.2.1
GDP Determination from One Regression Equation (X–M Model)
YT = 0.25(TT ) – 0.17(GT& I ) + 6.60PR – 0.10DJ–0 + 0.05 DJ–2

(t =) (2.5) (–1.9) (1.5) (–06) (0.2)
+ 5.37 XRAV + 107.90POP16 + 0.050POP + 1.48ICC–1
(0.8) (0.3) (5.2) (2.8)
+ 0.01M2AV + 0.62(ACC) + 3.02DEP + 6.31CAP–1
(0.1) (15.0) (2.7) (1.8)
+0.29PR –2 + 0.06PROF–0 + 0.01(CB2 + (IB(–1) )
(0.5) (0.4) (0.1)
–0.26(X – M) + 0.97AR(1) – 0.36AR(2)
(–0.8) (4.5) (–1.7)
R2 = 95.9% D.W. = 1.8 MSE = 41.09
(7.2.1)
This model, of course, is subject to the same four limitations as Eq. 7.1.1.
The same model is re-estimated below using only 1960–2000 data (for
use in robustness tests in Chapter 16).
Model 7.2.1 (For Chapter 16)

GDP Determination from One Regression Equation (X–M Model)
(Limited Sample Size)
YT = 0.36(TT ) – 0.30(GT& I ) – 4.21PR + 0.59DJ–0

(t =) (3.0) (–2.7) (1.1) (2.3)
– 0.82 DJ–2 – 2.01 XRAV + 545.31POP16 + .027POP
(–1.7) (–0.4) (1.5) (3.7)
+1.43ICC–1 + 0.96M2AV + 0.55(ACC) + 2.11DEP
(4.8) (4.6) (14.2) (3.0)
+11.36CAP–1 + 4.30PR–2 + 0.53PROF–0 + 0.11(CB2 + (IB(–1) )
(3.1) (0.8) (4.2) (1.0)
–0.70(X – M) + 0.62AR(1) – 0.37AR(7)
(–2.0) (3.5) (–1.6)
2 (7.2.1.16)
R = 97.1% D.W. = 1.7 MSE = 33.20
The dependent variable was stationary in first differences. Of the right-

hand side variables in this model, in first differences eight variables were
found nonstationary, but all were cointegrated with the dependent variable
(YT ) so no detrending was necessary.
As you can see, the same problem with combining causal and correlat-
ive effects is present, so a better way of estimating the separate effects of,
e.g., current period versus lagged interest rate effects needs to be con-
structed. For this reason, Eqs. 7.1.1 and 7.2.1 are included here only
for reference and as a way of illustrating the problems resulting from
this method of statistical GDP determination. The actual behavioral IS
model of GDP determination used as part of this large scale model of the
American economy is given in Chapter 8.
CHAPTER 8
Real GDP Determination Function

(“IS” Curve) Coefficients Aggregated from
Parameter Estimates Obtained by Statistically
Estimating the Subcomponent Functions
Comprising the GDP
8.1 USING THE GDP DETERMINATION MODEL

GDP = CD + ID + GD + X
8.1.1 The Initial Model Results
The initial model results are presented in Model 8.1 below; the robust
model results are presented in Model 8.1.TR further below.
For initial results, we aggregate the coefficient values for determinants
of domestically produced consumer goods (4.4T) and investment goods
(5.4), government spending, and exports into the GDP function given in
Eq. 7.2 (using 1.00 as the coefficients for G and X)
GDP = CD + ID + GD + X (7.0.2)
i.e., domestically produced consumption.

2S LS Standard Consumer Spending Model, with Borrowing
Included as a Determinant of Consumer Spending
CD = 0.29(Y – TT ) + 0.31(TDef ) – 0.20(GDef ) – 6.86PR
(t =) (6.0) (5.8) (–3.5) (–2.4)
+ 0.44DJ–2 – 0.33XRAV – 517.17POP16 + 0.020POP
(4.4) (0.2) (–3.5) (5.8)
DOI 10.1007/978-3-319-50681-4_8
240 8 REAL GDP DETERMINATION FUNCTION (“IS” CURVE)
+ 0.53ICC–1 + 38.16M2AV + 0.10 CB2

(2.1) (4.3) (3.4) (4.4)
R2 = 88.7% D.W. = 2.0 MSE = 24.54
Plus domestically produced investment goods.
Model 5.4
ID = + 0.25(ACC) + .29(TDef ) – 0.31(GDef ) + 0.08DEP

(t =) (6.7) (2.7) (–3.7) (0.3)
+ 2.60CAP–1 – 3.01PR–2 – 0.19DJ0 + .08PROF–0
(1.5) (–1.9) (–0.8) (1.2) (5.4)
+ 7.08XRAV + .011POP + 0 .02(BOR–1 )
(2.2) (3.4) (0.3)
R2 = 84.4% D.W. = 2.0 MSE = 28.77
Plus government spending plus exports.
+0.49 GT& I + 1.00X
Note: The 1.00 coefficient on GT reflects traditional assumption that

every dollar of government spending results in an additional dollar of
goods and services produced. But GT here represents spending on trans-
fers as well as goods and services. Increased spending on transfers, e.g.
a new unemployment insurance program, may just replace spending in
prior periods by the unemployed out of savings or asset sales. If so,
the coefficient on GT would be considerably less than 1.00. Tests by
author suggest 0.49 is a better estimate (see explanation in Section 8.1.1.1
below).
Consolidating Y terms to obtain the multiplier, adding coefficients on
like variables together, and multiplying all coefficients by the multiplier
(1/(1-0.30)) gives the following results:
8.1 USING THE GDP DETERMINATION MODEL GDP = CD + ID + GD + X 241
Model 8.1.1.1
GDP Determination by Adding Together Subcomponent Model
Parameter Estimates
YT = – 0.41 (TT ) + 0.69 (GT& I ) + 0.85(TDef ) – 0.72 (GDef )
– 9.67PR – 4.24PR–2 – 0.27DJ–0 + 0.62 DJ–2
+ 9.52 XRAV – 729.21POP16 + 0.044POP
+ 0.75ICC–1 + 53.81M2AV + 0.14 CB2
+ 0.35(ACC) + 0.11DEP + 3.67CAP–1
+ 0.11PROF–0 + 0.03(IB(–1) ) + 1.41 X
(8.1.1.1)
8.1.1.1 IS Curve Effects Inferred from C and I Model Test Results

In calculating the “IS” curves it is typically assumed every dollar of gov-
ernment spending initially adds a dollar to the GDP (before multiplier
effects). Hence the coefficient on it in the IS curve equation is 1.00
before adding multiplier effects. Typically, when this assumption is made,
the type of government spending being modeled is government spending
on goods and services, the portion included in the GDP. This represents
roughly 60% of all government spending. The use of the 1.00 coefficient
probably not a bad assumption when discussing only the effects of gov-
ernment spending on goods and services, but clearly would overstate the
effect on GDP of an increase in government spending on transfers. For
example, an increase in government spending to provide a new unem-
ployment insurance benefits to those already unemployed might simply
replace drawdowns of savings or sales of family assets used in prior periods
to purchase the same level of necessities.
In this study, we use total government spending including transfer pay-
ments in measuring the effects of deficits (crowd out) on consumer and
business spending. Similarly, In this study we use total government rev-
enues, not total revenue minus transfer payments to balance the use of
total government expenditures. Hence, some coefficient on government
spending less than 1.00 might be more appropriate. Our job is to obtain
sound, robust empirical estimates what it might be, estimates found to be
reliable when tested in four different time periods and in models including
different combinations of variables.
To test the appropriateness of the assumed 1.00 coefficient on the
government spending variable in IS curve, we used exactly the same con-
sumption and investment equations developed earlier in this book, each of
which already measures crowd out effects, We now simply add a separate
government spending variable to measure the stimulus effect as well. The
net stimulus effect is the difference between the estimated tax or spending
stimulus effect and its crowd out effect. Our empirical estimate of stimu-
lus effects – the coefficient on the government spending variable – will be
compared to the 1.00 coefficient commonly assumed when constructing IS
curves. To check the validity of our estimates, we will then run the same
model, this time deleting the spending deficit crowd out variable – only
the total government spending level variable will be retained. It should
measure the net stimulus effect, after accounting for crowd out, e.g.,
GNet = GStimulus – GCrowd out . It does so, exactly. This provides addi-
tional confidence our estimate of the coefficient on the spending vari-
able is correct. Results for the modified consumption equation are as
follows:
CT = 0.29(Y – TT ) + 0.31(TDef ) + 0.02GT+I – 0.21(GDef )

(t =) (5.7) (5.6) (0.2) (–2.7)
– 6.89PR + 0.44DJ–2 – 0.30XRAV – 501.83POP16
(–2.3) (4.3) (–0.2) (–3.2)
+ 0.019POP + 0.52ICC–1 + 37.22M2AV + 0.10CB2
(4.4) (2.1) (4.0) (3.2) (4.4.Rev1)
R2 = 88.8% D.W. = 2.0 MSE = 24.82
And the equation showing only the net of consumption stimulus and
crowd out effects for government spending is Eq. 4.4.Rev2 below. The
Revision 2 model is exactly the same as the Revision 1 model, except the
stimulus and crowd out effects have been combined, i.e., 0.02GT+I –
0.21(GDef )=02GT+I – 0.21(GT+I – LF) = –0.19(GT+I ) +0.21LF)
where LF is the loanable funds variable. Regression coefficients obtained
are exactly the same as would have been obtained arithmetically from Revi-
sion 1, increasing our confidence in the correctness of our results. Coef-
ficients on all other variables in Revision 2 stay exactly the same as they
were in Revision 1. t-statistics are the same or only marginally different.
CT = 0.29(Y–TT ) + 0.31(TDefT ) – 0.19GNet + 0.21LF

(t =) (5.7) (5.6) (–2.5) (2.7)
– 6.89PR + 0.44DJ–2 – .30XRAV – 501.83POP16
(–2.3) (4.3) (–0.2) (–3.2)
+ 0.019POP + 0.52ICC–1 + 37.22M2AV + 0.10CB2
(4.4) (2.1) (4.0) (3.2)
R2 = 88.8% D.W. = 2.0 MSE = 24.82
(4.4.Rev2)
And the modified investment equations are shown below. Revision 1 to

our earlier Eq. 5.4 adds the government spending variable (GT+I ) as a
separate variable to allow separate measurement of stimulus effects. Revi-
sion 2 re-estimates the equation deleting the (GDEF ) variable to allow
(GT+I ) to be estimated capturing just the net of stimulus and crowd
out effects of a change in government spending. The results adding the
separate spending variable to capture stimulus effects are
ID = + 0.19(ACC) + 0.30(TDef ) + 0.46(GT+I ) – 0.42(GDef )

(t =) (4.8) (2.8) (5.9) (–4.2)
– 0.97CAP–1 – 5.89PR–2 – 0.10DJ–0 + 0.11PROF–0
(–0.5) (–3.0) (–0.4) (1.3)
+ 7.02XRAV + 0.05(BOR–1 )
(2.3) (0.7)
R2 = 80.2% D.W. = 1.6 MSE = 32.04
(5.4.Rev1)
The depreciation and population variables from the original Model 5.2
were dropped because of severe multicollinearity effects on the estim-
ates of (GT+I ), causing its sign to be negative. That result implies that
along with the negative effects of crowd out, there are other reasons why
investment drops as government spending increases. While this is possible,
e.g., the business community may take increases in government spend-
ing as a sign the economy is declining, and cut investment. However,
there is no widely accepted theory that makes that argument. Therefore,
we rejected it as implausible on theoretical grounds, and searched for a
statistical problem, like multicollinearity, that may have distorted results.
Commonly a way to test for distortive multicollinearity effects is to add
or subtract variables from the suspect model (5.4.Rev1) to see the effect
on the suspect coefficient. Eliminating the depreciation and population
variables and re-estimating the model produced a coefficient on the stim-
ulus variable was positive, and therefore consistent with normal Keynesian
stimulus theory. No other variable, when removed, changed the negative
sign. Hence we concluded multicollinearity was the problem, and removed
the depreciation and population variables, yielding the estimates above in
Eq. 5.4.Rev1 of the stimulus effects of government spending deficits on
investment of +0.46 per dollar of deficit, and crowd out effects of –0.42
per dollar of deficit.
And the effects of deleting the (GDEF ) variable so that (GT+I ) only
captures the net of the stimulus and crowd out effects of government
spending deficits on investment is given in Revision 2 below:
IT = + 0.19(ACC) + 0.30(TDef ) + 0.04(GT+I ) + 42(LF)

(t =) (4.8) (2.8) (0.4) (4.2)
– 0.97CAP–1 – 5.89PR–2 – 0.10DJ–0 + 0.11PROF–0
(–0.5) (–3.0) (–0.4) (1.3)
+7.02XRAV + 0.05(BOR–1 )
(2.3) (0.7)
R2 = 80.2% D.W. = 1.6 MSE = 32.04
(5.4.Rev2)
The statistically estimated net effect (+0.04) is exactly what could be
deduced from netting the stimulus and crowd out effects in Eq. 5.2.Rev1,
increasing our confidence we correctly estimated these effects originally.
Hence, the sum of the consumption (+0.024) and investment (+0.463)
stimulus effects (= $0.49) seems a better estimate to use when estimating
the initial stimulus effects of a dollar change in government spending
than the $1.00 traditionally assumed when using the IS curve method
to estimate the determinants of the GDP. The full S curve is presented
in Eq. 8.1.1.1. The same stimulus effect is also used in its robust version,
Eq. 8.1.1.1.TR further below.
In concluding, it should be noted that using the 1.00 coefficient with
the traditional definition of government spending (goods and services
only), and using the modified 0.49 estimate above with the total govern-
ment spending definition used in the 10-year out-of-sample goodness of
fit projections, leads to nearly identical estimates. of how well the Cowles
model fits the out-of-sample data for GDP. Therefore, it leaves our con-
clusions in Chapter 2 that the Cowles model fits the data far better than
the DSGE or VAR models also unchanged. Where it makes a difference is
in estimating the stimulus effect of government spending. Using the 0.49
estimate, which we consider the much better estimate, leaves the estimated
stimulus effect much lower, and changes the estimates of the net effect
of government deficit spending on the GDP from positive (based on an
assumed coefficient 1.00) to negative (based on an empirically derived
coefficient 0.49). We have left the other estimates in the IS equation
the same as those deduced from the initial consumption and investment
equations (4.4 and 5.4). That IS model included the depreciation and
population variables in the investment equation when calculating IS equa-
tion coefficients, which makes it more satisfactory on theoretical grounds
for estimating the other variable effects on GDP, and therefore provides
better empirical estimates.
Robustness Tests of the CD , ID Models

The stimulus and crowd out effects for both the CD and ID mod-
els were tested in four different time periods (1960–2010, 1960–2000,
1970–2000, and 1970–2010). Initial findings of magnitude and statist-
ical significance for the government spending stimulus effect were found
robust for all four periods, with only marginal changes from period
to period. In addition, model specification robustness tests were also
undertaken, deleting two variables from the initial findings model and re-
estimating, and then adding two variables to the initial findings model
and re-estimating. For consumption, the variables subtracted were the
exchange rate and POP16 variables; the variables added were the exports
and profits variables. For investment, the variables subtracted from the ini-
tial findings model were the stock market index (DJAV) and the profits
variable. The variables added were the consumer confidence index and the
exports variable. Initial model findings were found robust to all changes
in model specification.
Again, most coefficients in the robust model are very similar to the coef-
ficients in the initial model; the worst fit is the coefficient on the current
period prime rate which varies about 20% between the initial and robust
equations, and the two period lagged prime rate which varies about 50%.
This method avoids the perverse effects of mixing causal and spuri-
ously correlative effects unintentionally when combining subcomponent
functions into something more aggregated, like the GDP.
8.1.2 Using the Robust Model Results

Repeating the time period and specification robust models of domestically
produced consumption and investment goods (Eq. 4.4.TR and 5.4.TR):
Model 4.4.TR (Repeated)

Robust Domestically Produced Consumption Model
CD = 0.29(Y–TT ) + 0.34(TDef ) – 0.23(GDef ) – 5.44PR + 0.48DJ–2
(t =) (6.2) (6.5) (–4.5) (–2.1) (5.1)
– .515.07POP16/65 + 0.020POP + 38.00 M2AV + 0.09 CB2
(3.2) (6.0) (4.9) (3.7)
R2 = 87.8% D.W. = 2.2 MSE = 24.88
(4.4.TR)
Model 5.4.TR (Repeated)

Robust Domestically Produced Investment Goods Model
ID = +0.26(ACC) + 0.27(TDefT ) – 0.30(GDef ) + 0.011POP

(t =) (8.7) (2.9) (–3.8) (5.7)
– 4.72PR–2 + 6.81XRAV + 2.55CAP–1

(–2.7) (2.9) (1.7) (5.4.TR)
↔
R2 = 83.3% D.W. = 2.0 MSE = 28.25
Estimating the coefficients on variables in the robust IS curve model

of GDP determination by adding these tow curves together and adding
government spending (G) and adding exports (X) gives
Model 8.1.2.1TR
GDP Determination by Adding Together Subcomponent
Model Parameter Estimates
(Robust Model)
Y = – 0.41TTot + 0.69(GTot) + 0.86(TDef ) – 0.75(GDef )

– 7.67PR + 0.68DJ–2 – 0.726.24POP16/65 + 0.044POP
+ 53.58M2AV + 0.13 CB2 + 0.37ACC – 6.66PR–2
+9.60XRAV + 3.60CAP–1 + 1.41X
(8.1.2.1TR)
8.2 USING THEGDP DETERMINATION MODEL

GDP = CT + IT + GT + (X – M)
8.2.1 The Initial Model Results
The initial model results are presented in Model 8.2 below; the robust
model results are presented in Model 8.2.TR further below, except as
noted in comments following that model . . .
8.2 USING THE GDP DETERMINATION MODEL GDP = CT + IT + GT + (X – M) 247
Model 4.1.T
Total Consumption Model (Repeated)
CT = 0.48(Y–TT ) + 0.56(TDefT ) – 0.39(GDef ) – 9.98PR

(t =) (10.6) (10.2) (–8.7) (–4.9)
+ 0.43DJ–2 + 1.44XRAV – 418.25POP16 + 0.018POP
(5.1) (0.9) (–1.6) (4.7)
+ 0.37ICC–1 + 46.31M2AV + 0.12CB2
(1.2) (4.3) (3.0)
2
R = 95.3% D.W. = 1.6 MSE = 24.12
(4.1T)
Model 5.2
Total Investment Model (Repeated)
IT = + 0.30(ACC) + 0.23(TDef ) – 0.26(GDef ) + 0.68DEP

(t =) (5.8) (1.9) (–2.7) (2.2)
+ 2.28CAP–1 – 6.89PR–2 + 0.53DJ–0 + 0.03PROF–0
(1.1) (–2.5) (2.5) (0.4) (5.2)
+ 5.89XRAV + 0.004POP + 0.06 (BOR–1 )
(2.1) (1.4) (0.7)
R2 = 91.0% D.W. = 2.2 MSE = 37.48
Following the same procedure used in Section 8.1, but with the model
GDP = CT + IT + GT + (X – M) (7.0.1)
where CT or IT = total imported and domestically produced consumer

or investment goods. Summing the coefficient values for variables in
the consumer goods (4.1T) and investment goods (5.2) models, and
adding government spending, and exports gives the GDP function given
in Eq. 7.0.1 above.
Model 8.2.1.1
GDP Determination by Addition of Component
functions of the GDP
YT = – 0.92(TT ) + 1.04(GT& I ) + 1.51 (TDef ) – 1.25(GDef )
– 19.16PR – 13.23PR–2 + 1.02DJ–0 + 0.83 DJ–2
+ 14.07 XRAV – 803.04POP16 + 0.04POP + 0.71ICC
+ 88.92M2AV + 0.23CB2 + 0.58 ACC + 1.31DEP
+ 4.38CAP–1 + 0.06PROF–0 + 0.12(IB(–1) ) + 1.92 (X – M)
(8.2.1.1)
8.2.1.1 IS Curve Effects Inferred from C and I Model Test Results

As noted earlier, in calculating the “IS” curves it is typically assumed every
dollar of government spending adds a dollar to the GDP (before multiplier
effects). Hence the coefficient on It before adding multiplier effects is typ-
ically set at 1.00. As also noted earlier, the use of the 1.00 coefficient
probably not a bad assumption when discussing only the effects of gov-
ernment spending on goods and services, but clearly would overstate the
effect on GDP of an increase in government spending on transfers. For
example, an increase in government spending to provide a new unem-
ployment insurance benefits to those already unemployed might simply
replace drawdowns of savings or sales of family assets used in prior periods
to purchase the same level of necessities.
In this study, we use total government spending including transfer pay-
ments in measuring the effects of deficits (crowd out) on consumer and
business spending. Hence, some coefficient on government spending less
than 1.00 might be more appropriate. Our job is to obtain sound, robust
empirical estimates what it might be.
To test the appropriateness of the assumed 1.00 coefficient on the gov-
ernment spending variable in the IS curve Equation, we used the same
consumption and investment equations developed earlier to construct the
IS curve, each of which already contains variables measuring the effects
of crowd out. We now add a separate government spending variable to
measure the stimulus effect as well. The net stimulus effect is the differ-
ence between the estimated tax or spending stimulus effect and its crowd
out effect. Our empirical estimate of stimulus effects – the coefficient on
the government spending variable, will be compared to the 1.00 coef-
ficient commonly assumed To check the validity of our estimates, we will
then run the same model without the government spending deficit (crowd
out) variable – only the separate spending level variable will be retained.
It should measure the net stimulus effect, after accounting for crowd
out, e.g., GNet = GStimulus – GCrowd out . It does, exactly. This provides
additional confidence our estimate of the coefficient on the spending vari-
able is correct. Results for the modified consumption equation used in IS
Model 8.2.1.1 below are as follows:
CT = 0.50(Y – TT ) + 0.59(TDef ) + 0.18GT+I – 0.45(GDef )

(t =) (11.6) (11.1) (2.1) (–9.5)
– 10.13PR + 0.45DJ–2 + 1.62XRAV – 308.34POP16
(–5.2) (5.3) (0.9) (–1.3)
+ 0.013POP + 0.30ICC–1 + 39.93M2AV + 0.12CB2
(3.1) (1.0) (4.1) (3.3)
2
R = 95.6% D.W. = 1.6 MSE = 23.74
(4.1T.Rev1)
And the equation showing only the net of consumption stimulus and
crowd out effects for government spending is Eq. 4.1T.Rev2. The Revi-
sion 2 model is exactly the same as the Revision 1 model, except the
stimulus and crowd out effects have been combined, i.e., 0.18GT+I –
0.45(GDef ) = 18GT+I – 0.45(GT+I – LF) = –0.27(GT+I ) + 0.45LF).
Regression coefficients obtained are exactly the same as would have been
obtained arithmetically from Revision 1, increasing our confidence in the
correctness of our results. Coefficients on all other variables in Revision 2
stay exactly the same as they were in Revision 1. In general, t-statistics are
only marginally different.
CT = 0.50(Y – TT ) + 0.59(TDefT ) – 0.27GNet + 0.45LF

(t =) (12.4) (11.9) (–3.0) (7.5)
– 10.13PR + 0.45DJ–2 + 1.62XRAV – 308.34POP16
(–4.2) (4.9) (1.0) (–1.4)
+0.013POP + 0.30ICC–1 + 39.93M2AV + 0.12CB2
(3.6) (1.0) (4.2) (3.7)
R2 = 95.6% D.W. = 1.6 MSE = 23.74
(4.1T.Rev2)
And the modified investment equations are shown below. Revision 1 to
our earlier Eq. 5.2 adds the government spending variable (GT+I ) as a sep-
arate variable to allow separate measurement of stimulus effects. Revision 2
just re-estimates the equation deleting the (GDEF ) variable to allow (GT+I )
to be estimated capturing just the net of stimulus and crowd out effects
of a change in government spending. The results adding the separate
spending variable to capture stimulus effects are:
IT = + 0.20(ACC) + 0.18(TDef ) + 36(GT+I ) – 0.31(GDef )

(t =) (3.5) (1.1) (3.5) (–1.9)
– 0.29CAP–1 – 10.38PR–2 + 1.03DJ–0 – 0.05PROF–0
(–0.1) (–2.4) (2.2) (–0.3)
+ 6.26XRAV + 0.07(BOR–1 )
(2.0) (0.6)
2
R = 82.9% D.W. = 2.1 MSE = 51.12
(5.2.Rev1)
The depreciation and population variables from the original Model 5.2
were dropped because of severe multicollinearity effects on the estim-
ates of (GT+I ), causing its sign to be negative. That result implies that
along with the negative effects of crowd out, there are other reasons why
investment drops as government spending increases. While this is possible,
e.g., maybe the business community takes increases in government spend-
ing as a sign the economy is declining, and cuts investment, there is no
established widely accepted theory that makes that argument. Therefore
we rejected it as implausible on theoretical grounds, and searched for a
statistical problem, such as multicollinearity, that may have distorted res-
ults. Commonly a way to test for distortive multicollinearity effects is to
add or subtract variables from the suspect model (5.2.Rev1) to see the
effect on the suspect coefficient. Eliminating the depreciation and popu-
lation variables and re-estimating the model produced a coefficient on the
stimulus variable was positive, and therefore consistent with normal stim-
ulus theory. No other variable in the model, when removed, changed the
negative sign. Hence we concluded multicollinearity was the problem and
removed the depreciation and population variables, yielding the estimates
above in Revision 1 of the stimulus effects of government spending defi-
cits on investment of +0.36 per dollar of deficit, and crowd out effects of
–0.31 per dollar of deficit.
And the effects of deleting the (GDEF ) variable so that (GT+I ) only
captures the net of the stimulus and crowd out effects of government
spending deficits on investment is given in Revision 2 below:
IT = + 0.20(ACC) + 0.18(TDef ) + 0.05(GT+I ) + 0.31(LF)

(t =) (3.5) (1.1) (0.4) (1.9)
–0.29CAP–1 – 10.38PR–2 + 1.03DJ–0 – 0.05PROF–0
(–0.1) (–2.4) (2.2) (–0.3)
+ 6.26XRAV + 0.07(BOR–1 )
(2.0) (0.6)
R2 = 82.9% D.W. = 2.1 MSE = 51.12
(5.2Rev2)
The statistically estimated net effect (+0.05) is exactly what could be
deduced from netting the stimulus and crowd out effects in Eq. 5.2.Rev1,
increasing our confidence we correctly estimated these effects originally.
Hence, the sum of the consumption (+0.18) and investment (+0.36)
stimulus effects (= $0.54) seems a better estimate to use when estimat-
ing the initial stimulus effects on GDP of a dollar change in government
spending than the $1.00 traditionally assumed when using the IS curve
method to estimate the determinants of the GDP. The full IS curve is
presented in Eqs. 8.2.1.1 (shown above) and 8.2.2.1TR. below. Both use
the 0.54 (times the multiplier) estimate.
We conclude noting that using the 0.54 estimate, which we consider
the much better estimate, leaves the estimated stimulus effect much lower
and changes the estimates of the net effect of government deficit spending
on the GDP from positive to negative. We have left the other estimates in
the IS equation the same as those deduced from the initial consumption
and investment equations (4.1T and 5.2). That IS model included the
depreciation and population variables when calculating revised equation
results above, which makes it more satisfactory on theoretical grounds for
estimating the other variable effects on GDP.
See Section 8.1.1.1 above for an explanation of how the GT&I coef-
ficient was developed. Most coefficients on variables in the robust model
are very similar to those in the initial model, except for total population,
the exchange rate and the business borrowing variable. Coefficients for all
three varied by 50–75% between the initial and robust models.
8.2.2 Using the Robust Model Results

Recall the time period and specification robust total consumption and total
investment models given by Eq. 4.1T.TR and 5.2.TR
Model 4.1.T.TR
Robust Total Consumption Model (Repeated)
CT = 0.49(Y–TT ) + 0.57(TDef ) – 0.38(GDef ) – 9.31PR + 0.44 DJ–2
(t =) (10.8) (11.0) (–7.9) (–4.6) (5.4)
+ 0.017POP + 0.41ICC–1 + 44.78M2AV + 0.13 CB2
(4.3) (1.2) (4.3) (3.6)
R2 = 94.8% D.W. = 1.6 MSE = 24.75
(4.1T.TR)
Repeating the final robust total investment model from Eq. 5.2.TR above
Model 5.2.TR
Robust Total Investment Model (Repeated)
IT = + 0.25(ACC) + 0.30(TDef ) – 0.32(GDef ) – 10.53 PR–2
(t =) (8.2) (2.7) (–4.4) (–4.3)
+ 0.87 DJAV + 3.18XRAV + 0.97 DEP
(3.3) (1.5) (4.1) (5.2.TR)
R2 = 86.6% D.W. = 2.2 MSE = 29.43
Combining the parameter estimates in the CT and IT equations with

GT& I and (X–M), we get our IS curve GDP determination model, given
below as Eq. 18.2.TR.
Model 8.2.2.1TR
GDP Determination by Addition of Component
Functions of the GDP
Y = – 0.96(TT ) + 1.06 (GT& I ) + 1.71(TDEF ) – 1.37(GDEF )
– 18.25PR – 20.64 PR–2 + 1.71 DJ0 + 0.86 DJ–2 + 0.033POP
+ 0.80ICC–1 + 87.77M2AV + 0.25 CBOR + 0.49ACC
+ 6.23XRAV + 1.90 (DEP) + 1.96 (X – M)
(8.2.2.1TR)
Most of the coefficients are close in value to the initial model, despite the
elimination of several variables as spuriously significant in the first test.
CHAPTER 9
Determinants of the Prime Interest Rate:

Taylor Rule Method
Heim (2008) examined a wide range of interest rates, including the federal
funds rate, the prime interest rate the Aaa and Baa rates, and the mortgage
rate to determine which had the largest and most systematic impact on
the economy. A typical simple Keynesian IS model in which consumption
was driven mainly by income and investment was driven mainly by interest
rates and the accelerator was used to evaluate the results. That study indic-
ated the rate most systematically related to variation in GDP was the prime
interest rate, which is derived from the federal funds rate. This is consist-
ent with data indicating bank lending historically was a greater source of
business credit than the bond market.
Traditionally, the prime interest rate has been set by the business com-
munity rigidly at 3 percentage points above the federal funds rate (though
that spread was reduced for a while during the 2008 fiscal crisis), not by
the interaction of supply and demand. Since the federal funds rate is set
by the Board of Governors of the Federal Reserve, we can consider the
federal funds rate and therefore the prime rate, as exogenously determ-
ined by an outside body. However, to the extent the behavior of the Fed
is determined by economic conditions, the rate can be considered endo-
genously determined by the variables that affect Fed behavior. Modern
practice has been to consider it determined endogenously, with the Fed-
eral Reserve’s “exogenous” behavior determined some by variant of the
Taylor rule and/or other variables. We have been able to explain about

DOI 10.1007/978-3-319-50681-4_9
254 9 DETERMINANTS OF THE PRIME INTEREST RATE: TAYLOR RULE METHOD
80% of the variation in the prime rate endogenously over the past 50 years
using the following Taylor rule model:
9.1 OLS ESTIMATES

The initial model tested (9.1) was developed as described above. The final
below.
Model 9.1 OLS Model of the Determinants of the

Prime Interest Rate
PRREAL = 0.43INFL – 1.19UNEM – 0.007M1REAL
(t =) (2.8) (–4.3) (–3.3)
– 0.012M1REAL(–1) – 0.002TAX – 0.002SPEND
(9.1)
(2.9) (–0.9) (–0.9)
+ 0.36AR(1)
(2.7) R2 = 0.80; DW 1.8
where, PRREAL = real prime rate, INFL = inflation rate, UNEM =

unemployment rate, M1REAL = the real M1 money supply, Tax = total
government receipts – total loanable funds, SPEND = total government
spending – total loanable funds and AR(1) is an autocorrelation control.
OLS is applied to U.S. data, 1962–2010.
Preliminary results indicated 69% of all interest rate variation in the
sample period is endogenously determined by changes in inflation, unem-
ployment and the current year M1 money supply’s liquidity effect.
However, this rises to 80% when the 1 year lagged value of real M1 is
added to pick up variance associated with its inflation effect, which estim-
ates indicate follows the liquidity effect (that quickly!). The results clearly
show what theory leads us to expect: initially, the liquidity effect of increas-
ing the money supply dominates, and interest rates decline. Eventually, the
delayed inflation effect dominates, and interest rates rise as a result of the
increased money supply. Our estimates of the effects on the prime interest
rate of an increase in the M1 money supply are that the increase causes the
Prime rate to drop in the first year, but then rise in the second.
No relationship of the prime interest rate to the government deficit was
found, where the deficit was represented by the government spending and
9.2 2SLS ESTIMATES 255
taxing variables. This is an important finding. Traditionally the argument

has been made that the channel though which government deficits affect
the economy is the interest rate channel. The argument is that government
borrowing to finance deficits can cause crowd out of private borrowing
(and private spending out of it), by bidding up interest rates as government
competes with private borrowers for funds (Friedman, 1978). It is often
argued that all crowd out effects operate though this supply and demand
effect. This totally ignores evidence that the rate is not determined by
free-market supply and demand, but exogenously (institutionally) by the
Fed. The evidence suggests government deficits do not cause crowd out
by making borrowing more expensive for prime rate borrowers, but by
reducing the total pool of money available to them to borrow by some
other form of rationing. Put another way, just because more people want
to borrow loanable funds does not mean the Fed raises federal funds rates,
raising prime rates. The rate stays the same as long as the Fed wishes it to,
and some potential borrowers just go without.
9.2 2SLS ESTIMATES

A number of variables in the Taylor rule interest rate determination model
were tested for endogeneity, including inflation, unemployment, M1, gov-
ernment receipts and government spending variables. Only the inflation
variable was found Hausman – endogenous with the real prime interest
rate. It was replaced by a Wald-strong and Sargan-valid instrument which
was used in a 2SLS model producing the results in Eq. 9.2:
Model 9.2 2SLS Model of the Determinants of the

Prime Interest Rate
PRREAL = 0.42INFL – 1.29UNEM – 0.0075 M1REAL
(t =) (2.6) (–4.8) (–3.4)
+ 0.012M1REAL(–1) – 0.002TAX – 0.001SPEND
(9.2)
(2.8) (–1.1) (–0.5)
+ 0.44AR(1)
(2.4) R2 = 0.81; DW 2.0
The OLS and 2SLS models produce nearly identical estimates.

In first differences, government spending was the only nonstation-
ary variable on either side of the Taylor rule mode of interest rate
determination, and it was cointegrated with the dependent variable.

Therefore, no detrending was needed.

Variance Explained: Stepwise Regression Tests of the 2SLS Model:
Table 9.2.1 shows the separate contributions to explained variance of the
determinants of the prime interest rate.
Table 9.2.1 Explained variance – Taylor rule model, using 2SLS

(R2 = 0.81 to start) (R2 = 0 to start)
INFL 0.70 0.40

UNEM 0.71 0.56
M1Real 0.80 0.10
M1Real(–1) 0.72 0.08
Taxes 0.80 0.04
Govt.Spending 0.80 0.35
Using the first-out method, the three variables uniquely accounting for
the most variation in the prime rate were the inflation rate, the unemploy-
ment rate and the inflation effect of an increase in the money supply. Using
the first-in method, the three variables accounting for both unique vari-
ance and variance that could be assigned to other variables are inflation,
unemployment and government spending.
Table 9.2.2 shows the results of testing the prime interest rate in four dif-
ferent but overlapping time periods as a means of testing the replicability
of the initial results in other time periods. The ability to replicate initial
findings is a key requirement of good science, a key goal of this study.
Results indicate that the effects of the Taylor rule variables (inflation
and unemployment) are extremely robust to time period sampled, as are
the results for the deficit variables (consistently insignificant).
The effects of changes in the money supply on the prime rate are not
robust: only with the 2001–2010 decade in the sample do money supply
changes appear significant. With that decade in the sample, they seem to
9.2 2SLS ESTIMATES 257
Table 9.2.2 Robustness over time – Taylor rule model: 2SLS model 9.2
Variable 1960–2010 1970–2010 1970–2000 1960–2000
INFL 0.42∗∗∗ 0.43∗∗∗ 0.56∗∗ 0.56∗∗

UNEM –1.29∗∗∗ –1.29∗∗∗ –1.55∗∗∗ –1.55∗∗∗
M1Real –0.007∗∗∗ –0.007∗∗∗ –0.001 –0.001
M1Real(–1) 0.012∗∗∗ 0.012∗∗∗ 0.004 0.004
Taxes –0.002 –0.002 –0.001 –0.003
Govt.Spend. –0.001 0.001 –0.001 –0.001
Significance levels: ∗∗∗ = 1%; ∗∗ = 5%.
have a strong effect in a way consistent with theory. This may be because
variation in the yearly change in the money supply was much greater in the
later part of the 2001–2010 decade, allowing a tighter confidence interval
around its estimated average yearly effect.
In the 1960–2000 and 1970–2000 samples, changes in the money sup-
ply did not seem to affect the prime rate. One theory why (untested here)
is that the Fed makes changes in the federal funds rate when the consensus
in the credit markets is that changes are needed. Hence, just announcing
changes to the federal funds rate just sends a signal to the banking com-
munity that now is the time to make changes to the prime rate, changes
they already thought it was time to do. In this way, by changing the
prime, the banks are simply, concurring with the timeliness of the Fed’s
own change to the federal funds rate. Of course, by this theory, the Fed’s
change only occurred because the Fed sensed the credit markets thought
it was time for a change.
Our time period robust model becomes the two variables found sig-
nificant in all four tests above, plus any found insignificant above which
are now found significant in three of four tests of this time-period robust
model (none were). It is given as Eq. 9.2.TR. This becomes our final time
period robust model:
Model 9.2.TR Time Period Robust 2SLS Model of the

Determinants of the Prime Interest Rate
PRREAL = 0.42INFL – 1.30UNEM + 0.20AR(1)
(t =) (2.8) (–6.6) (1.4) (9.2.TR)
2
R = 0.67; DW 1.9
Robustness with Respect to Model Specification:

Removing either of the variables and re-estimating yields Eq. 9.2a
and 9.2b:
Model 9.2.TR.a&b Time Period Robust 2SLS Model of the

Determinants of the Prime Interest Rate (One Variable Deleted)
PRREAL = 0.78INFL R2 = 0.40; DW 1.9
(9.2a)
(t =) (6.0)
PRREAL = –1.60UNEM R2 = 0.56; DW 1.8

(9.2b)
(t =) (–5.0)
The model is robust in that the signs on variables remain the same,
and they remain statistically significant. However, the magnitude of the
remaining variable’s coefficient rises, which is to be expected as long as
any correlation between the two exists and both are major explanatory
variables. Hence, we judge the model robust to this change as regards its
sign and statistical significance, but not with respect to coefficient mag-
nitude, particularly for the inflation variable whose coefficient fluctuates
more (0.42 vs. 0.78) than our rough limit for defining consistency (1/3).
Adding the GDP variable to the time period robust model:
Model 9.2.TR.c Time Period Robust 2SLS Model of the

Determinants of the Prime Interest Rate (One Variable Added)
PRREAL = 0.48 INFL – 1.23UNEM + 0.0001 GDP + 0.16AR(1)
(t =) (2.7) (–3.7) (–0.2) (1.1)
2
R = 0.68; DW 1.3
(9.2.TR.c)
Clearly, adding the income variables does not change estimates of the
effects of either the inflation or unemployment variables. The model
9.2.TR appears to be generally both time period robust and specification
change robust, excepting the coefficient on the inflation variable.
CHAPTER 10
Determinants of the Prime Interest

Rate – LM Curve Method
The Keynesian demand for money can be expressed as
(M/P)D = αY – βr
where, (M/P)D represents the demand for real money balances, Y repres-
ents aggregate income, and r represents the interest rate
Implying that when (M/P)S = (M/P)D
r = (α/β)Y – (1/β)(M/P)S
with the first determinant (Y) representing the transactions and precau-
tionary need for money, and the second the speculative.
10.1 OLS MODELS OF THE LM CURVE

The initial model tested (10.1) was based on Keynesian LM theory. Test-
ing this model using the prime interest rate, GDP as our income variable,
and real M1. The final model, robust to changes in time period sampled

DOI 10.1007/978-3-319-50681-4_10
260 10 DETERMINANTS OF THE PRIME INTEREST RATE – LM CURVE METHOD
Model 10.1 OLS LM Curve Model of Prime Interest Rate

Determination
PR = 0.002Y – 0.015M1Real + 0.018M1Real AV(–1–2)
(t =) (2.1) (–5.2) (4.3) (10.1)
R2 = 0.31; DW = 1.6
Overall, the standard Keynesian model of money demand and interest rate
determination explains less than half the variance explained by the Taylor
rule model. A third of the variance explained by the Keynesian model is
only due to adding a lagged money supply variable (average of M1–1 and
M1–2 ) variable to test the inflationary effects as well as the liquidity effects
of expansion of the money supply. This would not have been done in the
early Keynesian models and gives a more modern interpretation to the
classic Keynesian function. Further, as was the case with the Taylor rule
model, the subsequent inflationary effects of increasing the money supply
more than offset the current year liquidity (stimulus) effects, consistent
with the more classical notion that inflation is the only long run effect of
changing the money supply.
10.2 2SLS MODELS OF THE LM CURVE

The M1 real money supply was found Hausman-endogenous with the
real prime interest rate. Therefore it was replaced with Wald-strong
instrument, Sargan-valid, instrument. Results are shown in Eq. 10.2.
Model 10.2 2SLS LM Curve Model of Prime Interest Rate

Determination
(t =) (1.9) (–4.3) (4.0) (10.2)
2
R = 0.22; DW = 1.6
Results are similar to the OLS results, but with the money supply variable
having stronger liquidity and inflation effects, this time with the liquidity
effect slightly stronger than the inflation effect. Clearly though the initial
Keynesian LM model of interest rate determination leaves most of the
behavior of the prime interest rate unexplained. The initial Taylor rule
model discussed earlier, by comparison, explained 80% of the variance over
10.2 2SLS MODELS OF THE LM CURVE 261
the same period and therefore provides a much more compelling theory
of what drives interest rates. In Keynes’ defense, his interest rates were
market determined by the supply and demand for money; the prime rate
is not; it is an administered rate, determined in small part by fluctuation
in the M1 money supply, but principally by inflation and unemployment,
which explains most of the variation in the prime rate (and therefore the
federal funds rate) over time.
In first differences, neither the dependent variable nor any one of its
three determinants were found ADF nonstationary, so no cointegration
tests or detrending was needed.

Stepwise regression is used to examine the contributions to explained
variance made by each of the explanatory variables (Table 10.2.1).
Results as to which variable explains the most variance are ambigu-
ous. Using the first-out method indicates less variance in the prime rate
is explained by the changes in the money supply (speculative demand)
than by income (transactions and precautionary demand). The first-in
method indicates both the inflation effect and the transactions effect have
the greatest effect. The first-out method indicates the inflation effect has
the greatest effect, followed by the income effect.
He model was tested in four different, but overlapping time periods to see
if initial results could be replicated in other time periods (Table 10.2.2).
All three variables remain statistically significant and coefficients are
quite stable. Hence, Eq. 10.2 also becomes our final time period robust
Table 10.2.1 Explained variance LM curve interest rate model

GDP 0.18 0.08

M1Real 0.15 0.05
M1Real(–1) 0.15 0.11
262 10 DETERMINANTS OF THE PRIME INTEREST RATE – LM CURVE METHOD
Table 10.2.2 Robustness over time: LM curve interest, 2SLS model
Sample period 1960–2010 1970–2010 1970–2000 1960–2000
GDP 0.002∗ 0.002∗ 0.002∗ 0.002∗

M1Real(0) –0.027∗∗∗ –0.025∗∗∗ –0.017∗∗∗ –0.022∗∗∗
M1Real AV(–1–2) 0.022∗∗∗ 0.021∗∗∗ 0.020∗∗∗ 0.022∗∗∗
Significance level: ∗ 1%; ∗∗ 5%; ∗∗∗ 10%.
model 10.2.TR. Overall, the results seem relatively robust to time period
sampled. The variable representing the transactions demand effect is only
marginally statistically significant regardless of time period tested. If dis-
posable income is used instead of gross income, results are the same. This is
significant because virtually all theories of money demand historically have
considered transactions demand as the principal cause of the demand for
money. This seems not to be the case, since it was only of marginal signi-
ficance here, and of no significance when added to the Taylor rule interest
rate function earlier. As Baumol (1952) and Tobin (1956) suggested over
half a century ago, even transactions demand for money may be interest
rate driven.
Essentially the same model with inflation and unemployment variables
added to it is the Taylor rule model. When these two are added, the
money variables become insignificant for the first 40 (1960–2000) of the
50 years (1960–2010) tested. This suggests the prime (and federal funds)
rate relationship to how much money the Fed is creating is more likely
correlational than causal. Though the Fed reduces target interest rates in
recessions, the money supply may not have to increase much to do so,
causing the data to show the unemployment rate is a more important
influence than the money supply. A similar argument can be made sug-
gesting that in periods of inflation, a Fed attempt to increase the target
rate may not take much of a reduction in the money supply. If the Fed
announces an increase in the target Fed funds rate, banks are more than
happy (usually the same day) to increase the prime rate before the Fed
has even had a chance to engage in open market operations to achieve its
goal.
Robustness to Changes in Model Specification (2SLS Model)

Our final time period robust Keynesian LM curve model of interest rate
determination is Model 10.2 from above:
10.2 2SLS MODELS OF THE LM CURVE 263
Model 10.2.TR Time Period Robust 2SLS LM Curve Model of

Prime Interest Rate Determination
(t =) (1.9) (–4.3) (4.0) (10.2.TR)
R2 = 0.22; DW = 1.6
Deleting the income variable:
Model 10.2.TR.a Time Period Robust 2SLS LM Curve Model of

Prime Interest Rate Determination (One Variable Deleted)
PR –0.025M1Real + 0.025M1Real AV(–1–2)
(t =) (–4.7) (4.0) (10.2a)
R2 = 0.18; DW = 1.7
Deleting the inflation effect variable:
Model 10.2.TR.b Time Period Robust 2SLS LM Curve Model of

Prime Interest Rate Determination (One Variable Added)
PR = 0.002Y – 0.018M1Real
(t =) (2.5) (–3.5) (10.2b)
R2 = 0.15; DW = 1.5
Overall, results indicate results are quite robust to specification changes as

well as changes in the time period tested.
CHAPTER 11
Determinants of Inflation – The Phillips

Curve Model
Modern macroeconomic theory suggests economies move from the

Keynesian short run, with its possibilities of unemployment due to sticky
wages and prices, to the neoclassical long run by the tendency of wages
and prices to be flexible in the long run under the pressure of con-
tinuing unemployment or inflation. Hence, long-run downward pressure
on wages and prices addresses the problem of short-run unemployment.
Given the real wages and profits in workers’ and business owners’ pockets
from yesterday’s work (which equals the value of yesterday’s production),
if workers and businesses cut wages and prices in half today, the real income
in peoples’ pockets from yesterday’s work doubles, allowing demand for
goods and services to markedly increase today, creating a need for addi-
tional hiring to provide the additional supply needed. Ultimately we expect
full employment to result from this (unemployment-induced) decline in
the wage and price level. The 25% decline in the U.S. price level between
1929 and 1933, and the subsequent drop in unemployment from 25% to
17% in the 1933–1936 period are considered by some economists to as
evidence of this long-term effect. Of course at full employment, if prices
and wages are cut in half, the doubling of real income and demand by this
strategy would only result in raising prices back up. The Phillips curve has
historically been used to capture this relationship between unemployment
and inflation. Our OLS model is given in Eq. 11.1: the final model, robust

DOI 10.1007/978-3-319-50681-4_11
266 11 DETERMINANTS OF INFLATION – THE PHILLIPS CURVE MODEL
to changes in time period sampled and the number of other variables

included in the model, is presented in Model 11.1.TR further below.
Model 11.1 OLS Phillips Curve Model

(infl) = – 2.20(UnemAv(0 and –1) ) + 0.009(M1Real(–2) )
(t =) (–10.0) (4.7)
– 135.67 ( (M-X)/Y)Real AV(0,–1) + 13.12(ForBor–1 /Inv–1 )Real
(–2.8) (5.7)
–46.46(Gross Sav–1 /Y–1 )Real + 2.73(OPEC73&78 Shock)
(–5.1) (11.0)
2
+ 0.52Ar(2) R = 0.78; DW = 1.7
(3.5)
(11.1)
where,
UnemAV(0 and –1) = average unemployment rate for the current and past
year
M1 = change in the M1 Money supply, lagged two years
((M-X)/Y)RealAV(0–1) = net exports as a percent of GDP (average of cur-
rent and past year). Results show trade deficits are deflationary, since
deficits (M-X) have a positive sign.
ForBor–1 /Y–1 = real foreign borrowing by the U.S. as a percentage of
real investment
GrossSav(–1) /Y(–1) = prior year net U.S. savings + prior year depreciation
allowances, divided by prior year GDP
OPEC 73, 78 Shocks = OPEC 1973 & 78 Oil Price Increases (dummy
variable: 1 for 74, 75, 79, 80). Shocks were also entered in first
differences.
As a possible alternative, shock was also run in levels with a constant

added, not differences, as suggested by Wooldridge (2003, p. 448+).
The constant was later deleted as statistically insignificant; other variables
coefficients and t statistics were virtually unchanged or only very minor
changes caused by the deletion. Nonetheless, the first difference formula-
tion was used because it gave much stronger levels of statistical significance
to all variables in the model, and increased the R2 from 0.70 to 0.78.
Clearly, the model has substantial explanatory power, explaining 78% of
inflation variation over the 50-year period studied.
DETERMINANTS OF INFLATION – THE PHILLIPS CURVE MODEL 267
In first differences, neither the dependent variable nor any one of its five
determinants were found ADF nonstationary, so no cointegration tests or
detrending was needed. No current period variables were found Hausman-
endogenous, so no 2SLS was needed. Further tests below are in OLS.
11.0.2 Explained Variance and Robustness Tests

Stepwise regression is used to examine the individual contributions to each
explanatory variable to total explained variance. Results are presented in
Table 11.1.
Table 11.1 Explained variance – Phillips curve

UnemAV 0.51 0.27

(M1–2 ) 0.68 0.08
(M-X)/Y 0.72 0.00
ForBor–1 /Y–1 0.68 0.01
Gross Sav–1 /Y–1 0.72 0.08
OPEC Price Shocks 0.56 0.35
Using the first-out process, the most important determinant of infla-

tion was the unemployment rate, which had a negative effect on inflation.
The most important variables found positively related to inflation were
the OPEC price shocks of the 1970s, the rate of change in the money sup-
ply two years earlier, and foreign borrowing. Using the first-in approach,
the OPEC shocks and unemployment were again the most important
by far.

The model was tested in four different but overlapping time periods to test
for the replicability of initial results. Results are presented in Table 11.2.
All variables stayed significant in all time periods tested, with coefficients
and significance levels varying little. Hence, we conclude Model 11.1 is
very robust to time period sampled and is our final time period robust
model, 11.1.TR.
Table 11.2 Robustness over time: Phillips curve
Sample period 1960–2010 1970–2010 1970–2000 1960–2000
Unem –2.19∗∗∗ –2.31∗∗∗ –2.26∗∗∗ –2.10∗∗∗

M1–2 0.009∗∗∗ 0.009∗∗∗ 0.01∗∗ 0.009∗∗
(X-M)/YAV –135.66∗∗∗ –154.75∗∗∗ –162.21∗∗∗ –147.08∗∗
ForBor 13.12∗∗∗ 14.34∗∗∗ 14.13∗∗∗ 11.30∗∗
GrSav –46.46∗∗∗ –47.82∗∗∗ –44.55∗∗∗ –42.09∗∗∗
OPEC7378 2.72∗∗∗ 2.65∗∗∗ 2.60∗∗∗ 2.70∗∗∗
Significance levels: ∗∗∗ = 1%; ∗∗ = 5%; ∗ = 10%.
Model 11.1.TR Time Period Robust OLS Phillips Curve Model

(t =) (–10.0) (4.7)
– 135.67 ( (M-X)/Y)Real AV(0,–1) + 13.12 (ForBor–1 /Inv–1 )Real
(–2.8) (5.7)
(–5.1) (11.0)
+ 0.52Ar(2) R2 = 0.78; DW = 1.7
(3.5)
(11.1.TR)
Robustness to Model Specification
To test for robustness with regard to model specification (i.e., for sens-
itivity to multicollinearity, random error effects, etc.) we subtract some
variables and retest to see how much remaining coefficient estimates &
significance levels have varied.
Removing the last three variables from the model leaves the coefficients
and t statistics relatively stable:
Model 11.1.TR.a Time Period Robust OLS Phillips Curve

Model (Three Variables Deleted)

(t =) (–5.1) (–3.2)
– 155.19 (Real((X-M)/Y)Av(0 and –1) + 0.05AR(2) (11.1a)
(–2.4) (0.3)
R2 = 0.49; DW = 1.6
11.1 RECONCILING THE MONEY SUPPLY VARIABLE IN THE TAYLOR. . . 269
Removing the M1–2 variable, we get
Model 11.1.TR.b Time Period Robust OLS Phillips Curve Model

(infl) = – 1.82(UnemAv(0 and –1) ) – 62.89(Real((X-M)/Y)Av(0 and –1)

(t =) (–5.5) (–1.0)
+ 12.18(ForBor–1 /Inv–1 )Real – 49.63(Gross Sav–1 /Y–1 )Real
(3.07) (–3.8)
+ 3.33(OPEC 73& 78 Shock) R2 = 0.68; DW = 1.7
(8.0)
(11.1b)
Coefficients and t statistics for the remaining variables are very similar to
the full model results.
Hence we conclude model 11.1.TR is not only time period robust, but
also specification-change robust.
11.1 RECONCILING THE MONEY SUPPLY VARIABLE

IN THE TAYLOR RULE AND LM EQUATION
INTEREST RATE MODELS WITH THE MONEY
SUPPLY VARIABLE IN THE INFLATION
(PHILLIPS CURVE) EQUATION
The Taylor rule interest rate model showed that the prime interest rate is
positively related to the current inflation rate and the prior year’s money
supply growth. In the LM model section, we showed prime interest rate
growth is related to the average of the past two years’ money supply
growth. In the Phillips curve analysis, we show that a key determinant of
inflation is the change in the money supply growth rate from two periods
ago. Are these findings consistent?
Our finding is that they are all saying the same thing; in the LM model,
when we find that this year’s growth in the prime rate is a function of
not only last year money growth rate, but the year before that as well,
we are simply saying the change in the prime rate is a function of the
inflation rate and (only) last year’s growth in the money supply. This
is because the inflation determination model (Phillips Curve) shows the
change in the money supply two periods ago to be a key determinant of
current year inflation, as a simplified comparison of the three models below

shows:
Models 11.1.1–11.1.3 Models of Money’s Effect on the Prime

interest rate and the Inflation Rate
Taylor Rule Function : PR = f (M1, M1–1 )R2 = 0.78 (11.1.1)

LM Function : PR = f (M1, M1AV(–1,–2 )
R2 = 0.22 = f (Infl, M1–1 , )
where Infl = f (M1–2 ) (11.1.2)
Phillips Curve Function : Infl = f ( M1–2 ) R = 0.78
2
where M1–2 = (M1–2 – M1–3 ) (11.1.3)
Hence, though not identical, the functions are closely related: M1–1 and
M1–2 play a key role in all of them.
This can be shown statistically as well. If we add M1–2 in the Taylor
rule model (11.1.1) by averaging it with the lagged M1 variable already in
it, M1–1 , we reduce the coefficient and significance level of the inflation
variable in the Taylor rule equation, suggesting something in the M1–2
variable is now picking up variation formerly picked up by the inflation
variable, as shown in 11.1.4 below
Model 11.1.4 Taylor Rule Model with Money Supply Variable

Averaged Over the Past Two Years
PRREAL = 0.31 INFL – 1.53 UNEM – 0.010 M1REAL

(t =) (1.8) (–4.5) (–3.5)
+ 0.016M1REALAV(–1–2) – 0.00TAX + 0.00SPEND
(2.6) (0.9) (0.5)
+ 0.46AR(1) R2 = 0.77; DW = 1.8
(3.4)
(11.1.4)
We can also show that entering M1–2 as a separate variable (in addition
to M1–1 ) in the Taylor rule equation leaves it statistically insignificant,
whereas if we rerun the same model except without the inflation variable it
becomes highly statistically significant, indicating is just serving as a proxy
11.1 RECONCILING THE MONEY SUPPLY VARIABLE IN THE TAYLOR. . . 271
for the inflation variable (and vice versa), as shown in 11.1.5 and 11.1.6
below:
Models 11.1.5 and 11.1.6 The 2-Lag M1 Variable (M1–2 ) as a Proxy

for the Inflation (INFL) Variable
PRREAL = 0.39 INFL – 1.40 UNEM – 0.009 M1REAL
(t =) (2.2) (–4.6) (–3.4)
+ 0.012M1REAL(–1) + 0.002M1REAL(–2) – 0.00TAX
(2.6) (0.7) (–0.4)
+ 0.00SPEND + 0.46AR(1)
(0.3) (3.2)
R2 = 0.79; DW = 1.9
(11.1.5)
PRREAL = – 1.40UNEM – 0.011 M1REAL + 0.011M1REAL(–1)

(t =) (–4.5) (–3.8) (3.1)
+ 0.008M1REAL(–2) – 0.00TAX + 0.00SPEND + 0.47AR(1)
(2.5) (–0.9) (0.3) (3.1)
R2 = 0.71; DW = 1.8
(11.1.6)
Hence, we conclude that both the Taylor rule model and the LM mode,
are showing much the same thing regarding the relationship of lags of M1
changes to subsequent PR changes. What is illuminating about comparing
the two is that it implies that a change upward in inflation this year (which
may have occurred because of Fed increases in the money supply the previ-
ous two years) will cause the Fed to increase interest rates by now cutting
the money supply, that is, by rescinding its increase of two years earlier.
CHAPTER 12
Determinants of Unemployment
In the long run, factors like technological progress, levels of capital, and
changes in the size of the labor force play a role in determining the level
of output. In the short run, since technology and capital are fixed, gen-
erally, to produce more output, more labor from the existing labor force
is required, though varying levels of efficiency over the business cycle can
affect how much. Therefore, we would expect growth in demand for GDP
to be a driving force in levels of demand for labor at the macroeconomic
level.
Four OLS models of unemployment variation are presented below
which explain 70–80% of the amount of variance in unemployment over
the 1960–2010 sample period.
12.1 A SIMPLE OLS MODEL BASED ON OKUN’S LAW

The most complete initial model is Model 12.2, presented below. The final
robust model is given in Model 12.4.TR further below.
Okun’s (1962) law tying unemployment to the GDP is commonly
given as
% GDP = 3% – 2(%Unemployed) (Mankiw 2010)

DOI 10.1007/978-3-319-50681-4_12
274 12 DETERMINANTS OF UNEMPLOYMENT
Or, in the equivalent form we will use, which more clearly shows the
demand-driven nature of the relationship:
%Unemployed = 1.5 – 0.5%(% GDP)
Each percentage point increase in GDP’s growth rate reduces unemploy-

ment by ½ percent. Estimation of this model using 1960–2010 data yields
the following results:
Model 12.1.1
Okun Unemployment Model (OLS)
%Unemployed = 1.31 – 0.4%(% GDP)

(9.9) (–10.5) (12.1.1)
R2 = 0.72; DW = 1.9; MSE = 0.55
which is a close approximation of reality today to a hypothesis coined a

half century ago, and based on the behavior of the economy at that time.
However, by adding a variable showing the lagged effects from changes
in last year’s GDP, we can slightly improve the model as shown in Model
12.1.2 below:
Model 12.1.2
Okun Unemployment Model (OLS Modified)
%Unemployed = 1.45 – 0.37% (% GDP)

(9.7) (–9.4)
– 0.08% (% GDP–1 ) (12.1.2)
(–2.3)
R2 = 0.73; DW = 1.7; MSE = 0.54
But Okun’s explanation of unemployment may be incomplete. The mod-

ern Phillips curve theory suggests inflation and shocks may also be related
to unemployment. Adding inflation, the 1973 and 1978 oil shocks, the
2005 Hurricane Katrina shock, and the 2008 banking crisis shock to
Eq. 12.1.2 model gives the following results:
12.1 A SIMPLE OLS MODEL BASED ON OKUN’S LAW 275
Model 12.1.3
Okun OLS Unemployment Model Augmented to
Include the Effects of Inflation and Shocks
%Unemployed = 1.19 – 0.30% (% GDP) – 0.07% (% GDP–1 )

(7.9) (–7.2) (–2.7)
– 0.11 (Infl) + 0.83 (Shock73) + 0.34 (Shock78)
(–3.5) (3.2) (2.0)
– 0.53 (shock05) + 1.09 (shock08)
(–5.0) (56)
2
R = 0.83; DW = 1.7; MSE = 0.44
(12.1.3)
In first differences, the dependent variable was stationary, as were all of the
RHS variables. The Woodridge (2003) method of using dummy variables
in levels with a constant term was used; it explained significantly more
variance than the same model running the dummies in first difference form
without a constant.
The current year inflation rate was found significant. The best res-
ults for the 1973 OPEC oil price shock were found using a dummy
variable with negative shock effects indicated for only 1974 and 1975;
and for the 1978 shock, best estimates were for shock effects for 1979
and 1980. The best dummy for Katrina counted 2005 and 2006 as
impact years, and the dummy for 2008 hypothesized 2009 as the impact
year (small effects for 2008 and 2010 were also seen, but were not
statistically significant). Overall, this augmented Okun model captures
the effect of the GDP on unemployment quite nicely, as shown in
Graph 12.2.1. Interestingly, not all shocks have a negative effect on
the unemployment rate: the 1973, 1978, and 2008 shocks did, but the
2005 natural disaster shock did not presumably because of the imme-
diate and large scale rebuilding effort that followed that shock required
large amounts of labor. Interestingly, the shocks that did increase the
unemployment rate were financial; the shock that decreased it was real
(Katrina).
The basic Okun model explains unemployment trends the past 50 years
quite well, including the sharp rise in unemployment in 2008 and 2009 as
the banks crisis impacted the economy.
0
1.2
0.8 –2
0.4
–4
0.0
–0.4
–0.8
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 12.2.1 The augmented Okun model (Eq. 12.4) model for explaining
variation in unemployment 1960–2010
12.2 THE 2SLS OKUN MODEL

Equation 12.4 provides the strong instrument (Wald test) and valid
instrument (Sargan test) version of this model, required because the
GDP growth rate variable was found Hausman endogenous with
unemployment.
Model 12.2.1
Okun 2SLS Unemployment Model Augmented to Include the
Effects of Inflation and Shocks
%Unemployed = 1.37 – 0.38% (% GDP) – 0.04% (% GDP–1 )
(10.9) (–12.2) (–1.5)
– 0.09 (Infl) + 0.54 (Shock73) + 0.14 (shock 78)
(–2.6) (1.8) (0.8)
– 0.56 (shock05) + 0.75 (shock08)
(–4.9) (3.5)
R2 = 0.84; DW = 1.7; MSE = 0.44
(12.2.1)
Equation 12.4 model is shown in Graph 12.2.1.
12.2 THE 2SLS OKUN MODEL 277
Table 12.2.1 Explained variance – Okun unemployment model

% GDP 0.59 0.72

% GDP–1 0.78 0.21
Infl 0.82 0.16
Shock73 0.82 0.05
Shock78 0.84 0.13
Shock05 0.83 0.01
Shock08 0.82 0.25
The OLS and 2SLS results are similar, differing most notably for the
OPEC shocks, where the estimated effects and statistical significance of
both decline, though the 1973 shock stays significant.
The importance of these variables in explaining variation in unemployment
during the 1960–2010 period can be examined using stepwise regres-
sion the 2SLS model given in Eq. 12.4 over the 1960–2010 period
(Table 12.2.1)
Clearly, changes in the GDP are the most important factor driving
changes in unemployment.
allow examination of robustness of the initial results in different time
periods. Results are given in Table 12.2.2.
Table 12.2.2 Robustness over time: (Okun unemployment 2SLS model)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
%GDP –0.38∗∗∗ t –0.38∗∗∗ –0.37∗∗∗ –0.36∗∗∗

%GDP–1 –0.04 –0.07∗∗∗ –0.07 –0.04
Infl –0.11∗∗∗ –0.10∗∗∗ –0.10∗ –0.10∗
Shock73 0.54∗ 0.59∗∗ 0.63∗ 0.60
Shock78 0.14 0.25∗ 0.26 0.17
Shock05 –0.56∗∗∗ –0.48∗∗∗ (NA) (NA)
Shock08 0.75∗∗∗ 0.70∗∗∗ (NA) (NA)

Estimates of current year GDP, inflation, the 1973 oil shock, the Kat-
rina and financial crisis shocks were all robust to the time period sampled.
Estimates of the effects of the 1978 oil shock and prior year GDP effects
were not.
We define the core time period robust model as a model containing
the variables above that were found significant in at least three of four
time periods sampled. To this model we add either of the two nonsignific-
ant variables which, when added to this reduced size core robust model,
now are found significant in three of four periods sampled, but not when
both are included in the same model. Hence, they are left out of the
time period robust model. This final time period robust model is given
in Eq. 12.2.1.TR.
Model 12.2.1.TR
(Time Period Robust)
%Unemployed = 1.27 – 0.41%(%GDP) – 0.14(Infl)

(10.5) (–12.8) (–4.0)
+ 0.57(Shock73) – 0.51(shock05) + 0.75(shock08)
(1.9) (–4.7) (3.5)
R2 = 0.84; DW = 1.7; MSE = 0.44
(12.2.1.TR)
Robustness to Model Specification Changes (2SLS, 1960–2010 Data Set):
Dropping the shocks from Eq. 12.2.1.TR and re-estimating gives
Eq. 12.2.1.TR.a below:
Model 12.2.1.TR.a
(Time Period Robust Model, with Three Variables Deleted)
%Unemployed = 1.43 – 0.44 (%GDP) – 0.11(Infl)

(10.5) (–11.9) (–4.2)
R2 = 0.78; DW = 1.6; MSE = 0.49
(12.2.1.TR.a)
The modification leaves all of the remaining estimated effects about the
same; the explained variance drops from 84% to78%.
12.3 THE OLS TECHNOLOGICAL CHANGE MODEL 279
Adding the lagged GDP and Shock78 variables back gives us

Eq. 12.2.1. Estimates and significance levels are very similar to those in
the time period robust model 12.2.1.TR.
We conclude the time period robust model 12.2.1.TR also appears
robust to specification changes.
12.3 THE OLS TECHNOLOGICAL CHANGE MODEL

An additional model, more long run in nature, is shown in Model 12.3.1
below. It allows for the effects of technological progress to result in pro-
gressively less reductions in unemployment for a given increase in GDP
over time. In this model, the change in the unemployment rate is tied to
actual changes in the level of the real GDP, not percentage changes. Here,
the hypothesis that we test is that a desired change in the unemployment
rate require successively larger increases in the GDP as GDP grows, due
to technological growth in labor productivity over time. The initial model
is presented as Model 12.3.1 below. The final model, robust to changes
in time period sampled and the number of other variables included in the
model, is presented in Model 12.7.TR further below.
Model 12.3.1 (Preliminary)

OLS Technological Change Model
%Unemployed = 1.66 – 51.50 (GDP0.17 ) – 16.96 (GDP–1 0.17 )

(13.8) (–11.3) (–4.0)
R2 = 0.82; DW = 1.9; MSE = 0.43
(12.3.1.Prelim)
Adding inflation, the 1973 and 1978 oil price shocks, the 2005 Hurricane
Katrina shock, and the 2008 banking crisis shock to this model yield the
following OLS results:
Model 12.3.1
OLS Technological Change Model Augmented by Shocks

(10.4) (–9.6) (–3.2)
– 0.09 (Infl) + 0.69 (Shock73) + 0.26 Shock78
(–2.9) (2.7) (1.7)
– 0.38 (shock05) + 0.79(shock08)

(–3.9) (4.4) (12.3.1)
R2 = 0.86; DW = 1.9; MSE = 0.41
12.4 THE 2SLS TECHNOLOGICAL CHANGE MODEL

A 2SLS model was needed because of endogeneity between the unem-
ployment and current GDP variable. The strong instrument (Wald test),
valid instrument (Sargan test) 2SLS model is presented in Eq. 12.4.1
below:
Model 12.4.1
2SLS Technological Change Model Augmented by Shocks

(12.2) (–11.9) (–2.5)
– 0.08 (Infl) + 0.43 (Shock73) + 0.06 (Shock78)
(–2.1) (1.4) (0.4)
– 0.41 (shock05) + 0.47 (shock08)
(–3.8) (1.9)
R2 = 0.86; DW = 1.9; MSE = 0.41
(12.4.1)
The same variables are significant as were in the OLS model, except for the
OPEC oil shocks. Estimated marginal effects, again, are very similar to the
OLS model findings, especially for the statistically significant variables. The
73 and 78 shock values changed significantly, with both declining to lack of
statistical significance. The estimate marginal effect of the 2008 crisis also
declined almost half, and its strong significance reduced to marginal signi-
ficance. Just as GDP growth in the Okun model was the most significant
determinant of unemployment, GDP growth dampened by technological
progress is the most important here.
The extent to which this model accurately models the movement of
unemployment over the 1960–2010 period is shown in Graph 12.4.1.
regression the 2SLS model given in Eq. 15.5A over the 1960–2010 period
(Table 12.4.1).
12.4 THE 2SLS TECHNOLOGICAL CHANGE MODEL 281
0
0.8
–2
0.4
–4
0.0
–0.4
–0.8
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 12.4.1 Technological change model of determinants of unemployment

(Eq. 12.4.1)
Table 12.4.1 Explained variance – technological progress unemployment model

GDP.17 0.59 0.77

% GDP–1 .17 0.85 0.21
Infl 0.85 0.16
Shock73 0.85 0.13
Shock78 0.86 0.01
Shock05 0.86 0.01
Shock08 0.85 0.25
In the first out tests, only current GDP had more than a marginal
effect on employment levels. The first in tests also indicated current
GDP was the most important factor, but also indicated all the other vari-
ables were of more than marginal importance, except the 1978 and 2005
shocks.

Table 12.4.2 presents results of testing this model in four different but
overlapping time periods.
Current year GDP and the 2005 shock were significant in all periods
tested. Lagged GDP and inflation were significant only when 2001–2010
data was included in the data set. This becomes our final time period
robust model, given below in Eq. 12.4.1.TR:
Model 12.4.1.TR
%Unemployed = 1.55 – 63.53 (GDP0.17 ) – 0.48 Shock05
(12.4) (–12.9) (–5.7) (12.4.1.TR)
R2 = 0.78; DW = 2.2; MSE = 0.49
Robustness to Model Specification Changes (2SLS, 1960–2010 Data Set):

Retesting 12.4.1.TR without the 2005 (Katrina) shock gives the following
results:
Model 12.4.1.TR.a
(Time Period Robust Model with One Variable Deleted)
%Unemployed = 1.53 – 63.64 (GDP0.17 )
(12.4) (–13.0)
R2 = 83; DW = 1.8; MSE = 0.43
(12.4.1.TR.a)
Table 12.4.2 Robustness over time: (tech. progress unemployment, 2SLS model)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
GDP.17 –53.44∗∗∗ –54.65∗∗∗ –51.74∗∗∗ –49.99∗∗∗

GDP–1 .17 –8.89∗∗ –10.04∗∗ –8.85 –8.20
Infl –0.08∗∗ –0.08∗∗ –0.09 –0.09∗
Shock73 0.43∗ 0.44 0.55 0.54
Shock78 0.06 0.11 0.18 0.14
Shock05 –0.41∗∗∗ –0.36∗∗∗ NA NA
Shock08 0.47∗ 0.41 NA NA
Significance levels: ∗ 10%;** 5%;∗∗∗ 1%.

12.4 THE 2SLS TECHNOLOGICAL CHANGE MODEL 283
Retesting 12.4.1.TR by adding back the variables deleted from Eq. 12.4.1
indicates the signs and significance levels of the two variables in the time
period robust model stay the same, and the variation in coefficient is
moderate.
We conclude the time period robust model 12.4.1.TR is also largely
robust to specification changes as well.
CHAPTER 13
The Savings Functions
The flow of funds accounts divides total U.S. savings into personal savings,
corporate savings, and depreciation. All three components constitute gross
U.S. savings and are taken from Table B.32 (“Gross Savings and Invest-
ment”) of the 2005 (for 1959–1963 data) and the 2013 (for 1964–2010
data) Economic Report of the President. Net savings are gross savings minus
depreciation, and equal net private saving (undistributed corporate profits
and personal saving) and net government saving. Gross saving and foreign
borrowing equal total investment (+ statistical discrepancy) in the flow of
funds accounts and in Table B.32.
13.1 THE CORPORATE SAVINGS FUNCTION

Corporate savings were initially postulated to be a function of all the
determinants of investment spending discussed in an earlier section of
this chapter. To some extent, investment spending was expected to be
a trade off with corporate savings since savings finances some of it. Hence,
some or all of the variables that affect one may also affect the other.
Equation 13.1.1 shows the results of testing that hypothesis. The final
variables included in the model, is presented in Model 13.1.2.TR further
below.

DOI 10.1007/978-3-319-50681-4_13
286 13 THE SAVINGS FUNCTIONS
13.1.1 The OLS Corporate Savings Function
Model 13.1.1
OLS Estimates of Determinants of Corporate Saving
(2SLS results presented further below since the average exchange rate and
government spending were found endogenously related to spending on
domestically produced investment goods.)
SC = 0.02(ACC) + 0.82(TT ) – 0.91(GT& I ) – 59DEP
(t =) (0.4) (8.4) (–12.3) (–1.4)
= 0.06CAP–1 + 3.42PR–2 – 0.30DJ–0 + 0.70PROF–0
(0.0) (1.0) (–1.8) (7.9) (13.1.1)
+ 7.65XRAV + 0.007POP – 0.10(BOR–1 )
(3.6) (1.6) (1.3)
2
R = 94.0% D.W. = 1.9 MSE = 36.39
Key variables affecting the level of corporate saving include the gov-
ernment deficit, which affects corporate savings negatively regardless of
whether the deficit is the result of tax cuts or spending increases, profits
and the exchange rate. Marginally significant was the negative relationship
between stock market values and corporate savings. The model explains
virtually all the variance in corporate savings the past 50 years and does so
as well in one decade as another.
The completeness with which the model explains yearly changes
in corporate savings is shown in the graph below of Eq. 13.1.1
(Graph 13.1.1).
13.1.2 The 2SLS Corporate Savings Function

The accelerator, government tax, government spending, and depreciation.
NYSE index, real profits, and the exchange rate variables were Hausman-
tested for endogeneity with the corporate savings variable. Only the stock
market index and profits variables were found endogenous, and they were
replaced by a Wald- strong instrument which was also a Sargan-valid
instrument. Results are presented in Eq. 13.1.2.
13.1 THE CORPORATE SAVINGS FUNCTION 287
400
200
120 –200
80 –400
40 –600
–40
–80
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 13.1.1 Fifty years annual variation in corporate saving (calculated from
Eq. 13.1.1, then compared to actual)
Model 13.1.2
2SLS Estimates of Determinants of Corporate Saving
SC = –0.03(ACC) + 0.85(TT ) – 0.93(GT& I ) – 96DEP

(t =) (–0.2) (9.5) (–14.6) (–1.8)
– 0.39CAP–1 + 2.72PR–2 – 0.25DJ–0 + 0.73 PROF–0
(–0.1) (0.6) (–0.6) (2.2)
+ 7.92XRAV + 0.011POP – 0.10 (BOR–1 )
(3.9) (2.6) (–0.7)
R2 = 94.0% D.W. = 2.2 MSE = 37.03
(13.1.2)
The same variables in the 2SLS model were found significant or insig-
nificant as in the OLS model, with three exceptions. In the 2SLS model
the DJ variable (Tobin’s q proxy) was not significant, and the depreciation
and population variables were, contrary to the OLS findings. Coefficients
on the variables significant in both models did not vary substantially

(though due to ever present effect of multicollinearity on any change in
model specification, “not substantially” is used by this author to mean less
than 35% or so). Hence, we conclude there is little difference between
the OLS and 2SLS versions of this model, except for the two variables
cited.
In first differences, the dependent variable (corporate savings) was sta-
tionary. Four right-hand side variables in model were nonstationary in
first differences: government spending, depreciation, the stock market
average, and population, but all were cointegrated with the dependent
variable except d(Pop), which was detrended and became stationary when
detrended.
Stepwise least squares was used to examine the contributions of individual
variables to explained variance (Table 13.1.1).
The first-out method indicates that either type of government deficit
has a devastating negative effect on corporate savings, and next most
important is profit growth, positively. The first-in method indicate the
most important factors positively affecting corporate savings are the accel-
erator, profits and the NYSE Index (our proxy for Tobin’s q), government
spending deficits, and business borrowing. All had negative effects except
profits.
Table 13.1.1 Explained variance – corporate savings (as % of GDP)
Explained variance: First-out stepwise method First-in stepwise method (constant added)
Accelerator 0.95 0.25

Govt.Receipts 0.37 0.09
Govt.Spending 0.00 0.49
Depreciation 0.93 0.00
% Capacity Utilization–1 0.95 0.01
Prime Int. Rate–2 0.94 0.10
NYSE Index 0.94 0.33
Real Profits 0.82 0.41
Exchange RateAV(0-3) 0.92 0.00
Population Size 0.92 0.01
Business Borrowing–1 0.93 0.33
13.1 THE CORPORATE SAVINGS FUNCTION 289

Model 13.1.2 was tested in four different but overlapping time periods to
see if the original time period results were replicable in other time periods.
Results are shown in Table 13.1.2.
The only factors affecting savings as a percent of GDP, whose results
are significant in all periods sampled, were the government spending and
tax deficit variables. The only other variables showing significance were
depreciation, real profits, and the exchange rate, which were not significant
in 1960–2000 or 1970–2000 samples, but were in samples that included
the 2001–2010 decade.
We will refer to the two variables significant in all periods as the “core”
robust model. However, this may not be a complete representation of the
robustness all variables in the model. For any given number of observa-
tions in a data set, the larger the number of variables in the regression,
the lower the t-statistics on those variables will be, ceteris paribus. In addi-
tion, in large models, multicollinearity, which also reduces t-statistics may
be a factor. So few hypothesized determinants were found statistically sig-
nificant in all four sample periods, we suspected it may have to do with
our carrying so many variables in the model which clearly did not signific-
antly relate to corporate savings in any period, let alone all periods. Hence
we re-estimated a new model containing the original robust variables and
any others which when separately added to the model proved significant.
All variables found significant this way were then tested with the original
Table 13.1.2 Robustness over time – corporate savings, Eq. 13.1.2 2SLS Model
Variable 1960–2010 1970–2010 1970–2000 1970–2010
(Accelerator) –0.03 –0.00 0.15 0.04

(Taxes) 0.85∗∗∗ 0.89∗∗∗ 0.77∗∗ 0.68∗∗∗
(Govt. Spending) –0.93∗∗∗ –0.96∗∗∗ –0.93∗∗∗ –0.81∗∗∗
(Depreciation) –0.96∗ –0.93∗ –0.40 –0.42
(Capacity Utilized–1 ) –0.39 0.69 1.54 –0.75
(Prime Int. Rate–2 ) 2.72 3.73 –1.65 –0.88
(NYSE Index) –0.25 –0.36 –0.40 –0.08
(Real Profits) 0.73∗∗ 0.73∗∗ –0.27 0.54
(Exchange RateAV(0-3) 7.92∗∗∗ 8.11∗∗∗ 2.02 2.59
(Population Size) 0.011∗∗ 0.012∗∗ 0.014 0.01
(Business Borrowing–1) –.10 –0.11 –0.01 0.06.

robust variables. If was found significant in at least three of the four sample
periods, they became the “final” time period robust model. The results are
shown in Eq. 13.1.2.TR.
Model 13.1.2.TR
Time Period Robust 2SLS Estimates
of Determinants of Corporate Saving
SC = + 0.66(TT ) – 0.77(GT& I ) – 0.17 ACC

(t =) (4.2) (–8.9) (3.8) (13.1.2.TR)
R2 = 78.2% D.W. = 2.1 MSE = 64.38
With this improvement in model specification, not only the govern-

ment deficit variables, but the accelerator proved to be highly significant
determinants of corporate saving as a percent of GDP in all time periods.
Robustness to Model Specification:
itivity to multicollinearity, random error effects, etc.) we subtract or add
a variable to our time period robust model 13.1.2.TR and retest to see
how much remaining coefficient estimates and significance levels have
varied.
Eliminating the last variable from the time period robust model and
re-estimating, we get
Model 13.1.2.TR.a
Time Period Robust 2SLS Estimates of Determinants
of Corporate Saving
SC = + 0.76(TT ) – 0.83(GT& I )

(t =) (6.3) (–10.1) (13.1.2.TR.a)
R2 = 73.7% D.W. = 1.6 MSE = 69.92
Coefficients and significance levels on the remaining variables are a little

higher, but stay at roughly the same level of magnitude. Hence, the
model’s remaining variables are robust to this change
Adding the capacity utilization and profits variables to the time period
robust model:
13.2 THE DEPRECIATION ALLOWANCES SAVINGS FUNCTION 291
Model 13.1.2.TR.b
Time Period Robust 2SLS Estimates of Determinants of
Corporate Saving
SC = + 0.65(TT ) – 0.77(GT& I ) + 17ACC – 4.37CAP–1

(t =) (4.4) (–8.8) (–3.4) (–0.9)
+ 0.57 PROF–0 R2 = 90.0% D.W. = 1.6 MSE = 48.70
(2.5)
(13.1.2.TR.b)
The profits and accelerator variables are correlated (r = 0.51). Hence using
them together can lead to variance formerly assigned to one to become
assigned to the other. In prior tests the accelerator was found significant
in three of four tests, the profit variable only two. So it was not included
in the time period robust model, but the accelerator was. Here, both were
significant in only two of the four time periods sampled, hence this result
did not indicate the accelerator variable was a robust determinant of cor-
porate savings as a percent of GDP. Nonetheless, there is some ambiguity
here in our finding regarding the importance of the accelerator.
13.2 THE DEPRECIATION ALLOWANCES SAVINGS

FUNCTION
The largest component of U.S. savings is corporate depreciation allow-
ances. Allowable depreciation from business income is largely determined
by standards for depreciation set by the accounting profession, and tend
to be a set percentage of current and prior year investments, and is so
expressed in model 13.2.1 below, which explains over 90% of the variation
in business depreciation the 50-year sample period.
13.2.1 OLS Estimates of Determinants of Depreciation Saving

Since depreciation allowances corporations are permitted to take is derived
by formula from investments made previously, investment as a single
explanatory variable accounts nearly completely for all the variation in
depreciation savings the past 50 years. Other variables tested, but found
insignificant included the accelerator. Using the GDP instead of average
investment over the lagged period (–6 to –17), though significant, did not
explain as much variance as the average investment variables for the same
periods. Investment averages older than 17 years did were not statistically
significant.
Initial findings are presented in Model 13.2.1. The final model, robust
to changes in time period sampled, is presented in Model 13.2.1.TR fur-
ther below. Because of multicollinearity issues discussed after that model
is presented, we cannot say the model is robust to the addition or deletion
of variables to the model.
Model 13.2.1
OLS Model of Depreciation Savings
SD = 0.06 (INV0 ) + 0.10(INV–1 ) + 0.10(INV–2 ) + 0.07(INV–3 )

(t =) (7.8) (9.4) (7.0) (5.2)
+ 0.03INV–4 ) + 0.04(INV–5 ) + 0.03(INVAV–(6–10) )+
(2.4) (3.4) (8.7)
+ 04(INVAV–(11–17) ) + 0.13 AR(8) R2 = 0.966 DW = 2.1
(9.2) (1.0)
(13.2.1)
The same model explains depreciation well in any decade from 1980
to 2010, which was the longest we could test for with the data avail-
able. In first differences, the dependent variable (depreciation savings)
was nonstationary (Graph 13.2.1). Two of the eight right-hand-side
variables in model were nonstationary in first differences: average invest-
ment lagged 6–10 years, and average investment lagged 11–17 years, but
both were cointegrated with the dependent variable, hence detrending
was not required. The investment variable was tested, but no vari-
ables were found endogenous with depreciation, so no 2SLS model was
developed.
We can examine contributions to explained variance over the past 50 years
using the stepwise regression models in Table 13.2.1.
Using the first-out method, clearly the highest contributors to
explained variance in depreciation savings is investment taken from 6 to
17 years year earlier, which were significantly affecting total depreciation
allowances taken in the current year. In addition are investment in the cur-
rent and past year were important using the first-out method. The first-in
80
60
40
12 20
8 0
4 –20
–4
–8
86 88 90 92 94 96 98 00 02 04 06 08 10
Graph 13.2.1 Explained and actual depreciation allowance savings the past 50
years
Table 13.2.1 Explained variance depreciation allowance savings

(INV0 ) 0.86 –2.02

(INV–1 ) 0.81 –1.43
(INV–2 ) 0.89 –1.05
(INV–3 ) 0.91 –1.47
(INV–4 ) 0.96 –1.97
(INV–5 ) 0.94 –2.24
(INVAV-(6-10) ) 0.85 –0.74
(INVAV-(11-17) ) 0.70 –1.38
method provided no useful information, essentially indicating any 1 year’s

effect on investment is so small compared to the total year to year variance
in depreciation due to variation in all 17 years of past investment, any one
individual year’s contribution gets lost in the statistical noise.
Table 13.2.2 Robustness over time – depreciation allowance savings
Variable 1985–2010 1995–2010 1985–2000
(INV–0 ) 0.06∗∗∗ 0.06∗∗∗ 0.02

(INV–1 ) 0.10∗∗∗ 0.09∗∗∗ 0.11∗∗∗
(INV–2 ) 0.10∗∗∗ 0.11∗∗∗ 0.08∗∗∗
(INV–3 ) 0.07∗∗∗ 0.08∗∗∗ 0.09∗∗∗
(INV–4 ) 0.03∗∗ 0.02 0.04∗∗
(INV–5 ) 0.04∗∗∗ 0.03∗∗ 0.07∗∗∗
(INVAV-(6-10) ) 0.03∗∗∗ 0.03∗∗∗ 0.04∗∗∗
(INVAV-(11-17) ) 0.04∗∗∗ 0.04∗∗∗ 0.03∗∗
With so many lagged values in the model, and the need for eight additional lags for the AR(8) process, the
model could only be tested on the 1985–2010 data set, or subdivisions of it. Three samples were tested.
Significance Level: * 10%; ∗∗ 5%; ∗∗∗ 1%.

The model was tested in four different but overlapping time periods.
The model explained 97–98% of the variance in each time period, and
all variables were significant in all samples, except current year investment
in one. Hence we conclude the model is strongly robust to period sampled.
Model 13.2.1 becomes or final time period robust model, 12.2.1.TR
Model 13.2.1.TR
OLS Model of Depreciation Savings
SD = 0.06(INV0 ) + 0.10 (INV–1 ) + 0.10 (INV–2 ) + 0.07(INV–3 )

(t =) (7.8) (9.4) (7.0) (5.2)
+ 0.03INV–4 ) + 0.04(INV–5 ) + 0.03(INVAV–(6–10) )
(2.4) (3.4) (8.7)
+ 04(INVAV–(11–17) ) + 0.13 AR(8) R2 = 0.966 DW = 2.1
(9.2) (1.0)
(13.2.1.TR)
Robustness to Model Specification:
itivity to multicollinearity, random error effects, etc.) we subtract some
variables from our original Model 13.2.1.TR and retest to see how much
remaining coefficient estimates and significance levels have varied.
The same model with only lags 0–5 represented yields
Model 13.2.1.TR.a
Time Period Robust OLS Model of Depreciation Savings
(Lags 6–17 Deleted)
SD = 0.08 (INV0 ) + 0.11 (INV–1 ) + 0.14(INV–2 ) + 0.12(INV–3 )

(t =) (3.8) (4.6) (4.4) (3.9)
+ 0.12INV–4 ) + 0.09(INV–5 ) + 0.13 AR(8)
(4.2) (2.9) (1.0)
2
R = 0.517, DW = 0.7
(13.2.1.TR.a)
The variables representing lags 6–17 explains nearly half the total explained
variance. Since there is some collinearity between 1 year’s investment levels
and another, it is not surprising that we note the coefficients on the
variables remaining in the equation get larger. We conclude the original
model is robust as regards the continued statistical significance of variables
remaining in the equation, but not as to their coefficient values.
The original model without the current period and lagged one period
investment variable.
Model 13.2.1.TR.b
Time Period Robust OLS Model of Depreciation Savings
(Lags 0, 1 Deleted)
SD = + 0.19(INV–2 ) + 0.00(INV–3 ) + 0.05INV–4 ) + 0.04(INV–5 )

(t =) (5.2) (0.1) (1.0) (1.1)
+ 0.04(INVAV–(6–10) ) + 02(INVAV–(11–17) ) + 27AR(8)
(3.1) (1.8) (1.2)
2
R = 0.555, DW = 1.5
(13.2.1.TR.b)
Both coefficients and significance levels of investment lags 2–5 are substan-
tially changed by omitting lags 0 and 1, though not for the coefficients and
significance of the lag 6–10 variable or the lag 11–17 variable.
Again there is nearly a 50% drop in explained variance, suggesting that
most firms take accelerated depreciation, since these two lags account for
nearly as much depreciation variance as lags 6–17 combined.
We conclude that though time period robust, Model 13.2.1.TR is
not fully specification robust. Data on current and lagged values is
too multicollinear. Removing variables that explain a lot of variance
almost invariably will distort coefficients on variables with which they are
collinear. This is perhaps the single most important unresolved issue in
econometrics today.
13.3 PERSONAL SAVINGS

Personal savings is much smaller than either corporate savings or depre-
ciation allowance savings. In 2010, personal savings was $567 billion,
corporate savings $728 billion and depreciation $1,873 billion. Govern-
ment dissaving (the government deficit) was $1,398 billion, greater than
the total of business and personal net savings.
Our initial model of the demand for personal savings hypothesized
that the same factors that drive consumer spending drive consumer sav-
ing, though possibly with the opposite sign. Most of these variables, in
one form or another, proved statistically significant and explained about
half the variance in personal saving over the 50-year period. Experiments
adding other variables to this basic model did not add much, with two
exceptions. The two exceptions were adding a variable to capture the (neg-
ative) effects of inflation on saving, and adding variables to represent a
1993, 1999, and 2005 shocks to saving described below.
Population growth was one of the initial variables hypothesized as
a determinant of the total personal savings over the 50 years, but it
proved highly statistically insignificant and was dropped. Though popu-
lation growth is an important determinant of growth, it works through its
effects in increasing demand, and this is already captured in our disposable
income variable. If we drop disposable income from the model, the pop-
ulation variable becomes statistically significant, confirming our belief that
the two variables account for the same variance.
The deficit variables and the exchange rate variables had signs that
were consistent with theory and other related equations in this model.
For example, the deficit variable signs suggest that as deficits grow,
personal savings increases, which is consistent with our earlier consump-
tion function findings that, holding income constant, increasing deficits
reduced consumption (because of crowd out); reduced consumption
implies increases saving, ceteris paribus. Similarly, our exchange rate find-
ings from the consumption function indicated an increase in the exchange
rate, controlling for income, making imports cheaper, increased consump-
tion, which, ceteris paribus, implies a reduction in saving, which is what this
model shows. However, both the deficit and exchange rate variables were
13.3 PERSONAL SAVINGS 297
statistically insignificant. Unlike population growth, this does not seem to

be because some other variable in the model is proxying for them. Rather
it is likely their effects are just too small to be measured accurately in a
model with only 50 observations of data to use in assessing the individual
impacts of the 14 variables in this equation. Therefore, since the rejec-
tion of statistical significance seemed less a refutation of the theory that
they affect consumption (and therefore saving), and more an indication
of the limitations of the scientific method used, they were left in, follow-
ing the standard admonition in statistical practice that if the parameter
estimate derived from a sample proves insignificant, the best estimate of
the population mean is not zero, but the sample mean (Triola 2011).
This of course assumes there is reason to assume a non-zero relationship
to start with, e.g., that the average height of men in the population is
greater than zero. In such a case, a sample estimate of average height,
even if statistically insignificant, would be a better estimate than zero. The
initial model is presented as Equation 13.3.1. The time period/model spe-
cification robust version is presented as Model 13.3.1.TR further below,
excluding its consumer confidence variable.
Model 13.3.1
OLS Estimates of Determinants of Personal Saving.
(No 2SLS results presented since no variables were found endogenously
related to personal saving.)
SP = – 9.05 + 0.31 (Y – TT ) – 0.11(TDef ) – 0.05(GDef ) + 0.11PR3

(t =) (–1.5) (8.4) (–2.3) (–0.7) (3.5)
– 2.29∗E-25(DJ9 + DJ9–2 ) + 1.80XRAV + 440.60 POP16
(–6.8) (1.1) (1.5)
– 713.64ICC0.10 – 30.86M2 AV – 0.18 C B2 – 0.02 Infl
3
(–2.7) (–3.8) (–5.6) (–2.2)

– 32.39 Shock93 – 195.10 Shock99 – 160.05 Shock05
(–2.8) (–12.7) (–11.8)
R2 = 84.4% D.W. = 2.6 MSE = 32.70
(13.3.1)
Equation 13.3.1 indicates the major economic determinants related pos-
itively to personal savings are disposable income, interest rates and the
percentage of young people in the population. Negatively related to
personal savings are stock market growth, consumer confidence, the build
up of savings in prior years, and the amount of consumer borrowing. In

addition to these variables, three shocks explained considerable additional
variance. As suggested by Woodridge, 2003, 448+), though the model is
in first differences, the shocks are run in levels with a constant added to
the equation.
Without the 1993, 1999, and 2005 shock variables included in the sav-
ings model, the model explains only 54% of the variance. The 1993 shock
refers to the large upper income tax increase of that year, later partially
retracted with the Bush tax cut of 2001. Using dummy variable with a
value of one from 1993 to 2010 explains additional variance, and explains
even more (5%) if the dummy variable’s ones are returned to zeros after
2003. The 1999 shock is technical, and reflects the BEA’s elimination of
mutual fund capital gains from its calculation of personal income in 1998,
which reduced income but left consumption data unchanged, leading to
reduced personal savings calculations for 1999. In late 1999, other BEA
changes had the effect of restoring much of the loss. To reflect this, our
dummy variable for 1999 contains a one for that year, zeroes for all other
years, and adds an additional 13% to explained variance. The 2005 dummy
is an attempt to account for the effects of Hurricane Katrina on savings in
the southern U.S., beyond that controlled by the loss in income. Here,
we hypothesize that even for millions employment and income were not
reduced because of Katrina, expenses to repair damaged property resulted
in a one-time need to spend more that was typical out of their income,
markedly reducing personal savings for 1 year (only). This dummy has a
one for 2005, zeros otherwise.
In defining these as the “cause” of major savings declines in 1993,
1999, and 2005, we also examined inflation, unemployment, and interest
rates for unusually large changes in those years, which would not be picked
up by regression coefficients on these variables. Coefficients show only
the average way over the whole sample period changes in these vari-
ables relate to changes in savings, and not an extraordinary impact of
an unusually large change. None of these changes seemed particularly
great during 1993 and 1999, and only increases in interest rates did
in 2005–2007. But replacing our 1 year dummy with a 3-year interest
rate dummy did not explain any of the variance that the Katrina-defined
dummy did. So we concluded Katrina provided the better explanation.
This dummy adds an additional 10% to explained variance over that
explained by the 1993 and 1999 dummies, raising total explained variance
400
300
200
100
0
–100
100 –200
75
50
25
0
–25
–50
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph 13.3.1 The explanatory power of the Eq. 13.3.1 model
to 82% Graph 13.3.1 shows how well adding these three shock variables
explains the large previously unexplained drops in savings in the three
shock years.
In first differences, the dependent variable (personal savings) was
stationary. Seven of the 13 right-hand-side variables in model were non-
stationary in first differences: government spending, the current year stock
market average, the twice lagged stock market index, young to old age
ratio in the population, population, and the lagged money supply average
and population, but all were cointegrated with the dependent variable so
no detrending was required.
Explained Variance
Using the first-out process, the most important determinants of positive
personal saving are disposable income, wealth, and to lesser extent, rising
interest rates. Negatively affecting personal saving were the growth of (the
non-M1 components) of the M2 money supply, the 99 shock caused by
changing the savings definition, the Katrina 05 shock, and the 1993 tax
increase (Table 13.3.1).
Table 13.3.1 Explained variance – personal savings model
Explained variance: First-in stepwise method

First-out stepwise method (constant added)
Disp. Inc. 0.72 0.01

TDef 0.83 0.07
GDef 0.84 0.00
Prime Int. Rate3 0.83 0.00
DJAV Wealth0 9 + (–2)9 0.78 0.16
Exchange RateAV 0.84 0.02
% Young in Pop. 0.83 0.01
Consumer Conf.0.1 0.81 0.15
M2AV 0.82 0.01
Cons. Borrowing 0.77 0.24
Infl3 0.84 0.00
Shock93 0.83 0.02
Shock99 0.72 0.12
Shock05 0.74 0.15
Using the first-in approach, increases in current year wealth have the
most positive effect on personal savings. The most important negative
effects on personal saving result from increases in consumer borrowing,
the Katrina Hurricane 05 shock, the 99 shock, and tax increases.

Findings on how robust initial sample period results were to testing in
other time periods are given in Table 13.3.2.
Seven variables were significant in all four periods tested: disposable
income, tax deficits, the prime interest rate, consumer confidence, infla-
tion, shock99 and shock05. These seven variables become the “core”
time period robust model. Five additional variables were significant in two
samples including wealth, the exchange rate, M2 money supply average,
consumer borrowing, and the 93 shock.
The variables found nonsignificant were retested individually with the
core robust model. Those now found significant were added as a group
to the core robust model and retested to see if they were significant in
at least three of four samples, if so they along with the core were taken
to be the final time period robust model. The final model is given in
Eq. 13.3.1.TR:
Table 13.3.2 Robustness over time – Personal savings model
Variable 1960–2010 1970–2010 1970–2000 1960–2000
Disp. Inc. 0.31∗∗∗ 0.36∗∗∗ 0.33∗∗∗ 0.22∗∗

TDef –0.11∗∗ –0.11∗∗ –0.26∗∗ –0.29∗∗∗
GDef –0.05 –0.08 0.03 0.10
PR0 3 0.11∗∗∗ 0.09∗∗∗ 0.10∗ 0.13∗∗
Wealth0+(–2) 7 –2.29E-25∗∗∗ –2.08E-25∗∗∗ 4.24E-24 5.92E-25
Exch.Rate 1.80 +2.28∗ 2.00 1.24
POP%Young 440.60 –97.68 –419.15 446.95
ConsConf0.1 –713.64∗∗∗ –952.05∗∗∗ –990.39∗∗∗ –677.78∗∗
M2AV(–2–4) –30.86∗∗∗ –32.32∗∗∗ –32.36 –10.33
Borrowing –0.18∗∗∗ –0.16∗∗∗ –0.06 –0.08
Infl. Rate3 –0.02∗∗ –0.02∗∗ –0.01∗ –0.02∗
Shock93 –32.38∗∗∗ –34.20∗∗∗ –25.91 –3.40
Shock99 –195.10∗∗∗ –192.08∗∗∗ –215.15∗∗∗ –199.33∗∗∗
Shock05 –160.50∗∗∗ –155.11∗∗∗ NA NA
Model 13.3.1.TR
Time Period Robust OLS Estimates of Determinants of
Personal Saving
SP = – 17.89 + 0.22(Y – TT ) – 0.14(TDef ) + 0.14PR3 – 725.37ICC0.10
(t =) (–1.6) (4.8) (–1.9) (3.6) (3.9)
– 0.03Infl3 – 195.94 Shock99 – 716.30 Shock05
(–3.1) (12.9) (–18.3)
–2.27E-25 (DJ9 + DJ9–2 ) – 0.16CB2
(–5.8) (–4.4)
R2 = 78.7% D.W. = 2.1 MSE = 35.82
(13.3.1.TR)
Robustness to Model Specification: To test for robustness with regard to

model specification (i.e., for sensitivity to multicollinearity, random error
effects, etc.) we subtract or add some variables from the time period
robust model 13.3.1.TR and retest to see how much remaining coefficient
estimates and significance levels have varied.
Subtracting the last two variables from Eq. 13.3.1.TR and re-estimating
gives the following results:
Model 13.3.1.TR.a
Personal Saving
SP = – 21.11 + 0.25 (Y – TT ) – 0.18(TDef ) + 0.14PR3
(t =) (–1.0) (1.9) (–2.4) (3.2)
– 1179.80ICC0.10 – 0.02 Infl 3
– 202.03 Shock99
(2.8) (–5.5) (5.6)
– 172.58 Shock05 R2 = 78.7% D.W. = 2.1 MSE = 35.82
(–16.7)
(13.3.1.TR.a)
Clearly, the signs, magnitudes and statistical significance of the remaining
variables are robust to the model change, with very little variation generally
occurring, except possibly for the magnitude of the consumer confidence
variable.
Adding the money supply and the 1993 shock to the full time period
robust model
Model 13.3.1.TR.b
Personal Saving
SP = –16.87 + 0.25(Y – TT ) – 0.13(TDef ) + 0.10PR3
(t =) (–1.7) (4.7) (–2.29) (2.3)
0 – 0.03Infl – 187.99 Shock99
3
– 766.79ICC0.1
(3.7) (–3.1) (9.6)
– 191.23 Shock05 – 2.63E-25 (DJ9 + DJ9–2 ) – 0.16CB2
(–14.0) (–5.4) (–3.9)
– 0.19 M1Real – 18.99DJ
(–1.4) (–1.3)
R2 = 80.1% D.W. = 2.3 MSE = 35.51
(13.3.1.TR.b)
Here again, coefficients, signs, and statistical significance of the model are
robust to these added variables.
We conclude the personal savings model results given in model
13.3.1.TR are robust to variation over time, and reasonable variation in
model specification.
CHAPTER 14
Determinants of Government Receipts
Government tax receipts are determined in part by economic conditions,

and in part by tax policy established by Congress. Therefore, government
receipts are partially endogenous and partially exogenous. Model 14.1
estimates the part that is endogenously determined.
A dummy variable was added to represent the 1986 indexing of taxes
shock (1987–2010 = 1 for tax indexing effects)). Results indicate the 1986
indexing shock had a negative impact on tax revenue growth. The indexing
appears to have been effective. When run on the period before indexing,
inflation is a highly significant factor affecting government revenues. But
for samples after indexing is introduced, the model indicates the inflation
variable, though its coefficient indicates a positive effect on government
revenues, the effect is no longer statistically significant.
The 1993 tax increase shock was found to increase government revenue
an average of $31 billion a year, though this change was not significantly
different from zero statistically. The estimate of the effect of the 1993 tax
increase is sensitive to the assumption its effects were repealed with the
2001 tax cut. If we assume the increase was not repealed, the dummy con-
tinues to take a 1 value for years 2001–2010, and the estimated effect
of the tax increase on total tax collections is negative, i.e., a backward
bending labor supply curve effect. Our best evidence was that the former
assumption was more accurate, but further research is warranted. Though
this is a first difference model, the shocks are modeled in levels with a

DOI 10.1007/978-3-319-50681-4_14
304 14 DETERMINANTS OF GOVERNMENT RECEIPTS
constant term added to the model, following a procedure suggested by

Woodridge (2003, p. 448+)
This initial model is Model 14.1. The time period/model specification
robust version is given as Model 14.1.TR further below.
Model 14.1
OLS Government Receipts Model
(TT ) = – 4.38 + 0.30(GDP) + 12.28INFLAV(–1–2) – 48.59(UNEM)

(t =) (–0.2) (3.2) (2.3) (–3.2)
– 27.02 Shock86 + 31.12 shock93 + 0.42AR(1)
(–0.8) (1.0) (3.6)
R2 = 0.73; DW = 1.8; MSE = 62.24
(14.1)
14.1 CONTRIBUTIONS TO EXPLAINED VARIANCE

Stepwise regression was used to examine the contributions of individual
variables to total explained variance (Table 14.1).
For both the first-out and first-in stepwise methods, the two vari-
ables which explained the most variation in government receipts over the
50-year sample period were the real GDP and unemployment.
14.2 ROBUSTNESS OVER TIME

The Government receipts model’s initial results were retested in three
additional different, but overlapping, time periods to determine their
replicability over time. Results are given in Table 14.2.
Table 14.1 Explained variance – government receipts

(including constant)
GDP 0.68 0.53

InflAV 0.71 0.05
Unem 0.67 0.58
Shock86 0.72 0.00
Shock93 0.72 0.11
14.2 ROBUSTNESS OVER TIME 305
Table 14.2 Robustness over time – government receipts (assumes 1993 tax
increase repealed by 2001 tax cut)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
GDP 0.30∗∗∗ 0.28∗∗ 0.19∗∗∗ 0.21∗∗∗

InflAV 13.17∗∗ 14.07∗∗ 10.11∗∗∗ 8.91∗∗
Unem –48.75∗∗∗ –54.25∗∗∗ –50.17∗∗∗ –43.22∗∗∗
Shock86 –31.11 –29.53 17.75∗∗ 18.87∗∗
Shock93 42.50 41.87 7.42 4.51
Statistical significance: ∗∗∗ = 1%; ∗∗ = 5%; ∗ = 10%.
The GDP, inflation and unemployment variable, and the 93 shock res-
ults are robust to changes in period sampled. The results for the 1986
tax cut are ambiguous: the sign is positive for samples including only
1960–2000 data, indicating the tax cut increased tax revenue. But when
2001–2010 data is added to the sample the effect of the tax cut on gov-
ernment revenue is not significantly different from zero. One (untested)
hypothesis is that this may reflect the difference in the two key aspects
of the 1986 cut: a ∼25% cut in rates, and indexing and when they made
a noticeable difference. The rate cut would be felt quickly; the indexing
effect would manifest itself more slowly, taking until 2001 to offset the
insignificant effect of the rate cut on government revenue. (The observed
non-significant effect of the rate cut on total revenue is consistent with
the notion of a backward bending supply curve, i.e., that tax cuts finance
themselves.)
The 1993 tax rate increase also appears to have had a positive, but
not statistically significant effect on revenue 1994–2000. There was some
uncertainty as to whether to model the 1993 tax increase as effect-
ive only through 2000, or continue it until 2010; the model above
shows the results of modeling its effects only through 2000, on the
assumption the Bush tax cut of 2001 restored the pre-1993 rates.
Below we repeat the same time period robustness tests, using exactly
the same models except for an alternate 1993 shock variable which
contains the assumption the 1993 tax increase on high-income earners
continued in effect through 2010. Doing so gives results consistent with
the notion the tax increase had a negative effect on total government
revenues.
Model 14.1.Alt
Determinants of Government Receipts Assuming 1993
Tax Increase Continued Through 2010

(t =) (–0.3) (3.4) (2.3) (–2.8)
+ 12.74 Shock86 – 50.05 shock93 + 0.42AR(1)
(1.1) (–1.8) (2.8)
R2 = 0.73; DW = 1.8; MSE = 62.10
(14.1Alt)
Here, the statistical evidence for the 1986 tax cut is consistent with the
back bending supply curve notion that tax cuts increase total tax collec-
tions, ceteris paribus, though not significantly when the 2001–2010 decade
is added in, possibly due to the growing cumulative effect of indexing. Still,
the effect of the tax cut on revenue is not found to be negative. Assuming the
1993 tax increase was in effect up through 2010 the estimated effect of the
tax increase on revenue shifts from positive (without 2001–2010) to negative
when the 2001–2010 decade is added to the sample. This again would sug-
gest a backward bending supply curve. The lack of significance of the 1993
tax cut in the samples ending in 2000 may simply indicate the tax had
been in effect too short a part of the period to register its effect with any
significance. Adding the Bush tax cut of 2001 as effective from 2003 on
leaves the Bush tax cut indicating a positive effect on total tax collections.
However, when added, the positive effect is not statistically significant
(Table 14.3).
The time period robust model then becomes Eq. 14.1 minus the 1993
and 1986 tax shocks, because they were not a significant effect on tax
collections in at least three of the four models.
Table 14.3 Alt robustness over time (assumes 1993 tax increase continues
through 2010)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
Y 0.33∗∗∗ 0.32∗∗∗ 0.19∗∗∗ 0.21∗∗∗

InflAV 12.85∗∗ 13.78∗∗ 10.11∗∗∗ 8.91∗∗
Unem –46.96∗∗∗ –52.06∗∗∗ –50.17∗∗∗ –43.22∗∗∗
Shock86 12.74 14.00 17.75∗∗ 18.87∗∗
Shock93 (Alt) –50.05∗ –50.05∗ 7.42 4.51
Statistical significance: ∗∗∗ = 1%; ∗∗ = 5%; ∗ = 10%.

14.3 ROBUSTNESS TO MODEL SPECIFICATION CHANGES (1960–2010 DATA SET) 307
Model 14.1.TR
OLS Government Receipts Model
(TT ) = – 11.17 + 0.30(Y) – 50.87 (UNEM) + 13.64INFLAV(–1–2)

(t =) (–0.5) (3.4) (–3.3) (2.5)
+ 0.43AR(1) R2 = 0.72; DW = 1.8; MSE = 61.96
(3.5)
(14.1.TR)
14.3 ROBUSTNESS TO MODEL SPECIFICATION

CHANGES (1960–2010 DATA SET)
Eliminating the last variable from 14.1.TR, and re-estimating:
Model 14.1.TR.a
OLS Government Receipts Model (One Variable Deleted)
(TT ) = – 12.77 + 0.30(Y) – 42.01 (UNEM) + 0.45AR(1)

(t =) (–0.6) (3.7) (–3.1) (4.1) (14.1.TR.a)
R2 = 0.70; DW = 1.7; MSE = 62.99
The results for the remaining variables are clearly robust.

Adding the 1986 and 1993 tax shocks to the time period robust model
returns us to Model 14.1 above.
Model 14.1.TR.b
OLS Government Receipts Model (Two Variables Added)

(t =) (–0.2) (3.2) (2.3) (–3.2)
– 27.02 Shock86 + 31.12 shock93 + 0.42AR(1)
(–0.8) (1.0) (3.6)
R2 = 0.73; DW = 1.8; MSE = 62.24
(14.1.TR.b)
Clearly the time period robust model is robust to these additions.
We conclude that the time period robust model 14.1.TR is also robust
to reasonable specification changes. (We say “reasonable”: Unemploy-
ment is the variable most strongly correlated with government receipts,
while as the same time strongly correlated with inflation, which has a
much weaker correlation with the dependent variable. As noted earlier,

pulling a variable like unemployment, with both a strong correlation to
the dependent variable and other explanatory variables is likely to lead
to significant changes in some or all of the remaining variables. It does:
inflation becomes insignificant.)
CHAPTER 15
Endogeneity of Government
Spending Levels
15.1 THE MODEL FOR TOTAL GOVERNMENT

SPENDING FOR ALL PURPOSES: GOODS,
SERVICES, AND TRANSFERS
Total real federal, state, and local government spending for all purposes
(including transfers as well as goods and services) was found positively
related to the unemployment rate, and population growth in the dec-
ade 21–31 years earlier, presumably because growth in population then
meant new household formation and school-age children now for those
in their twenties. If the GDP is substituted for the unemployment rate, it
is significant, but explains 10% less total variance; it is insignificant if the
unemployment rate is left in the model. Unemployment drives heavy trans-
fers spending. A dummy variable was added to explain the very large excess
of government spending over model estimates in the 1965–1968 period
(Vietnam build up), and another dummy variable for the combined effects
of the Reagan military build up 1983–1987, and Iraq/Afghanistan war
spending 2002–2004, and again later in 2008–2010. A third dummy was
added to reflect the heavy government spending associated with the finan-
cial crisis bailouts of 2009. Results indicate these factors explain 65.7% of
the variance in government spending over the 50-year period. Other exo-
genous, politically based, factors not included in the model led to roughly

DOI 10.1007/978-3-319-50681-4_15
310 15 ENDOGENEITY OF GOVERNMENT SPENDING LEVELS
1/3 of all the variation in government spending during the period. Initial
OLS model results are shown in Eq. 15.1.1. The more limited, but time
period and model change robust model is presented as Model 15.1.1.TR
further below.
Model 15.1.1
OLS Total Government Spending Model
GT& I = 61.69 + 0.03 (GDP–0 ) + 23.85(UNEM)
(t =) (4.6) (0.5) (3.2)
+ 0.028 (Pop. Size–31–21 ) + 64.66(Viet. Build Up)
(4.5) (4.9)
+ 34.85(Reagan, Iraq Build Up) + 74.56 (Fin. Crisis Shock’09)
(2.1) (4.5)
R2 = 0.66; DW = 1.8; MSE = 30.62
(15.1.1)
Attempts to insert Okun’s law for the unemployment variable gave the
expected statistically significant signs for the GDP growth rate, but
explained some, but not as much variance as using the unemployment
rate itself as an explanatory variable. It is also worth noting that GDP
tested with 1–4 lags also was not significant (even if unemployment vari-
able was removed from the model). The sign on the GDP variable is
positive for all lags tested except the first year lag which was negat-
ive, presumably indicating major increases in government spending on
transfer payments via unemployment insurance in the year after a decline
in GDP.
The unemployment rate and GDP variables were tested, but not found
endogenous with government spending, so no 2SLS model was needed.
In first differences, the dependent variable (government spending) was
nonstationary. One of the right-hand side variables in model was non-
stationary in first differences: population changes between 21 and 31 years
earlier periods but it was cointegrated with the dependent variable, so
detrending was not required.
15.1.1 Contributions to Explained Variance

Stepwise regression was used to examine the contributions to total
explained variance made by individual variables (Table 15.1.1).
15.1 THE MODEL FOR TOTAL GOVERNMENT SPENDING FOR ALL. . . 311
Table 15.1.1 Explained variance – total government spending

(R2 = 0.66 to start) (R2 = 0.00 to Start)
GDP–0 0.66 0.10

Unem 0.57 0.21
Pop–(31–21) 0.52 0.16
Vietnam 0.55 0.01
Iraq 0.58 0.22
Shock 09 0.62 0.26
From the first-out perspective, the variables which accounted for the
largest amount of variance which they alone could account for were the
population growth and Vietnam build up variables, with Iraq and unem-
ployment next. From the first-in perspective, unemployment, Iraq, and the
shock in 2009 were the most important.
15.1.2 Robustness Over Time

The model was tested in four different but overlapping time periods so
the time robustness of results could be examined. Findings are presented
in Table 15.1.2.
Clearly the statistical significance of the findings is robust with respect
to sample period selected, as are the magnitudes of estimated effects.
Hence, Eq. 15.1 also becomes Eq. 15.1.1.TR, the time period robust
model.
Table 15.1.2 Robustness over time – total government spending
Variable 1960–2010 1970–2010 1970–2000 1960–2000
GDP–0 0.03 0.03 0.014 0.001

Unem 23.85∗∗∗ 24.92∗∗∗ 29.29∗∗ 25.87∗∗∗
Pop–(31–21) 0.028∗∗∗ 0.027∗∗∗ 0.036∗∗∗ 0.029∗∗∗
Vietnam 64.66∗∗∗ NA NA 65.97∗∗∗
Reagan, Iraq 34.85∗∗ 35.48∗∗ 41.41∗∗ 40.95∗∗
Shock 09 74.56∗∗∗ 75.47∗∗∗ NA
Significance levels: ∗∗∗ = 1%, ∗∗ = 5%; ∗ = 10%.

Model 15.1.1.TR
GT& I = 61.69 + 0.03(GDP–0 ) + 23.85 (UNEM)

(t =) (4.6) (0.5) (3.2)
+ 0.028(Pop. Size–31–21 ) + 64.66(Viet.Build Up)
(4.5) (4.9)
+ 34.85 (Reagan, Iraq Build Up) + 74.56 (Fin. Crisis Shock’09)
(2.1) (4.5)
R2 = 0.66; DW = 1.8; MSE = 30.62
(15.1.1.TR)
Robustness to Model Specification Changes (1960–2010 Data Set)
Eliminating the Vietnam build up shock variable from 15.1.1.TR, and
re-estimating:
Model 15.1.1.TR.a
(One Variable Eliminated)
GT& I = 73.24 + 16.59 (UNEM) + 0.022 (Pop. Size–31–21 )

(t =) (4.8) (1.9) (2.8)
+ 32.35 (IraqBuild Up) + 80.18 Shock09
(2.1) (4.8)
2
R = 0.55; DW = 1.5; MSE = 34.85
(15.1.1.TR a)
Unemployment and population size variables magnitude and significance
levels drops moderately when Vietnam is removed from the model, but
the Reagan, Iraq, and Shock 09 variables remain relatively stable. Overall,
the remaining variables from 15.1.TR are relatively robust to this model
change.
Adding the M1 variables variable to the full time period robust model
15.1.TR and re-estimating:
Model 15.1.1.TR.b
OLS Total Government Spending Model (One Variable Added)
GT& I = 59.02 + 0.04 (GDP–0 ) + 23.76 (UNEM)

(t =) (4.4) (0.8) (3.5)
+ 0.027 (Pop. Size–31–21 ) + 62.08(Viet. Build Up)
(4.1) (4.8)
15.2 THE MODEL FOR GOVERNMENT SPENDING ON GOODS AND SERVICES ONLY 313
+ 25.21(Reagan,Iraq Build Up)

(1.3)
+ 82.18 (Fin. Crisis Shock’09) + 0.13M1Real (15.1.1.TR.b)
(4.4) (1.5)
R2 = 0.66; DW = 1.8; MSE = 30.62
All variables remain relatively stable except the significance of the Iraq
military spending shock variable, which becomes insignificant. Notice the
M1 variable is not statistically significant. We expect that when a variable
which is significant when included alone in a regression are included with
a highly correlated second variable, significance levels on both drop. This
multicollinearity problem appears to be the culprit here. Initially, adding
it to a model with a (significant) Iraq variable results in two insignific-
ant variables. Remove either one form the model, and the remaining one
becomes significant. Hence, the lack of robustness is a sign of a technical,
not a substantive problem.
We conclude the time period robust model is also generally model spe-
cification robust, though one variable is vulnerable to the multi collinearity
problem if the M1 money supply is added to the model.
15.2 THE MODEL FOR GOVERNMENT SPENDING ON

GOODS AND SERVICES ONLY
The analysis of government spending’s determinants in 15.1.1.TR above
are given using total government spending, defined as spending on goods
and services (the “G” used in the GDP) and spending on transfer pay-
ments, which are not in the GDP definition. In Eq. 15.2.1, we reevaluate
these determinants to see their effect on government goods and ser-
vices purchases alone. The more limited number of variables robust to
time period and model specification changes is given in Model 15.2.1.TR
further below.
Model 15.2.1
OLS Model of Government Spending on Goods and Services Only
GG& S = 7.47 + 0.09 (GDP–2 ) + 1.76 (UNEM)

(t =) (1.0) (3.8) (0.6)
+ 0.011 (Pop. Size–31–21 ) + 34.70 (Viet. Build Up)
(1.5) (3.5)
+ 29.48(Reagan,Iraq Build Up) – 21.69 Shock09 + 0.51 AR(1)

(6.3) (–2.7) (4.5) (15.2.1)
R2 = 0.71; DW = 1.9; MSE = 19.38
Here, without transfer payments affecting the government spending

aggregate, we see lagged GDP exercising a sizeable influence on the level
of government spending, and unemployment not exercising much influ-
ence, contrary to our finding of its strong impact on total government
spending in 15.1 above. In addition, the 2009 shock, involving government
spending on things not directly entering the GDP (securities) has a negat-
ive sign here, suggesting that cutbacks in government purchases of goods and
services was part of how the bailout was financed.
15.2.1 Explained Variance

The relative importance of the determinants in explaining the variation in
government spending on goods and services (only) government spend-
ing over the 50-year period is examined in Table 15.2.1 using stepwise
regression.
From the first-out perspective, clearly, the Vietnam and Iraq wars,
and the Reagan military build up explain large portions of the variation
in government spending on goods and services over the 1960–2010
period. Also significant was GDP growth, presumably reflecting a need
for more infrastructure, including educational facilities and staff to oper-
ate the larger economy (per capita). From the first-in perspective, the
Reagan/Iraq build ups and increased demand for government goods and
Table 15.2.1 Explained variance – government spending model (goods and

services only)

GDP–2 0.61 0.30

Unem 0.70 0.00
Pop–(31–21) 0.68 0.09
Vietnam 0.67 0.07
Iraq 0.63 0.21
Shock 09 0.70 0.00
15.2 THE MODEL FOR GOVERNMENT SPENDING ON GOODS AND SERVICES ONLY 315
Table 15.2.2 Robustness over time – government spending (goods and services
only)
Variable 1960–2010 1970–2010 1970–2000 1960–2000
GDP–2 0.09∗∗∗ 0.09∗∗∗ 0.07∗∗ 0.06∗∗

Unem 1.76 1.85 1.09 1.17
Pop–(31–21) 0.01 0.007 0.007 0.011
Vietnam 34.70∗∗∗ (NA) (NA) 35.37∗∗∗
Reagan, Iraq 29.48∗∗∗ 31.29∗∗∗ 30.58∗∗∗ 30.26∗∗∗
Shock 09 –21.69∗∗∗ –21.70∗∗ (NA) (NA)
Significance levels: ∗∗∗ = 1%, ∗∗ = 5%; ∗ = 10%.
services were the main factors associated with variation in government

spending.
15.2.2 Robustness Over Time

The model was tested in four different but overlapping time period to test
its robustness to changes in time period sampled. Results are presented in
Table 15.2.2.
Results appear robust over time. In all samples, the same variables
appear significant or insignificant, and the magnitude of the significant
variables does not vary much.
From these findings for different sample periods, we can settle on a
time period robust model. As usual, we take the core variables of this
model to be those significant in at least three of the four samples above,
and retest individually each of the nonsignificant. Those formerly not sig-
nificant which now are collectively added to the core model and retested.
If now significant in three of the four sample periods, they are included in
the final time period robust model given in 15.2.1.TR below:
Model 15.2.1.TR.
OLS Government Goods and Services Spending Model
GG& S = 2.76 + 0.10 (GDP–2 ) + 30.88(Viet. Build Up)
(t =) (0.5) (5.8) (3.1)
+ 32.32 (Iraq Build Up) – 17.43 Shock09 + 0.48 AR(1)
(6.3) (–7.0) (4.0)
R2 = 0.68; DW = 1.8; MSE = 19.60
(15.2.1.TR)
15.2.3 Robustness to Model Specification Changes

Eliminating the Vietnam build up shock variable from 15.2.1.TR, and
re-estimating:
Model 15.2.1.TR.a
OLS Government Goods and Services Spending Model (One
Variable Eliminated)
GG& S = 5.56 + 0.10 (GDP–2 ) + 29.69 (Iraq Build Up) – 17.12 Shock09
(t =) (0.7) (6.2) (6.2) (–7.6)
+ 0.58 AR(1) R2 = 0.65; DW = 1.6; MSE = 20.24
(7.5)
(15.2.1.TR.a)
The remaining variables’ coefficients and significance levels are nearly
identical to the full model, therefore the model is very robust to this
particular change.
Adding the population variable back to the core robust model
15.2.1.TR and re-estimating:
Model 15.2.1.TR.b
OLS Government Goods and Services Spending Model (One
Variable Eliminated)
GG& S = 6.17 + 0.09 (GDP–2 ) + 34.59(Viet. Build Up)

(t =) (0.9) (4.6) (3.5)
+ 29.81(Iraq Build Up) – 17.04 Shock09
(6.1) (–5.8) (15.2.1.TR.b)
+0.010 (Pop. Size–31–21 ) + 0.49 AR(1)
(1.3) (4.3)
2
R = 0.70; DW = 1.9; MSE = 19.20
The GDP variable is very robust to this change; the population size, Viet-
nam build up, and 2009 shock coefficients change 25–33%, though their
significance levels remain fairly stable.
Overall, the model 15.2.1.TR seems reasonably robust to changes in
model specification as well as robust to changes in time period sampled.
CHAPTER 16
Capacity of the Model to Explain Behavior

of the Macroeconomy Beyond the Period
Used to Estimate the Model
We already know the model of the real economy presented in this book is
quite robust in explaining variations in investment and consumer behavior
within the sample period: R2 s are generally 0.90% or higher; coefficients
are generally stable over different sample periods and model specifications.
However, here is nothing scientific about our work unless the models
found to be good at explaining within-sample period variance are as good
at explaining behavior 5–10 years beyond the sample period. We must
show that our results have identified the true underlying, (reasonably) time
invariant, structure of the economy, not just (nonrepeating) peculiarities
of the particular set of data we examined. We now wish to examine how
well the structural models employed in this study explained the economy’s
behavior in years long after the end of the period used to estimate the
model. Since our data covered the period 1960–2010, not a lot of time
has passed that we can use to test the hypothesis that the model is robust
for extended periods of time outside the period sampled – up to 10 years.
To do this we re-estimated our successful models using only data from
1960 up to the year 2000. The theory was that if our “successful” models
really were successful at uncovering the true structure of the economy, the
model would yield similar parameter estimates m the 40-year sample data.
Since the same (true) structure would underlie the economy in the out
of sample period, the 1960–2000 parameter estimates should explain the
out-of-sample data as well.

DOI 10.1007/978-3-319-50681-4_16
318 16 CAPACITY OF THE MODEL TO EXPLAIN BEHAVIOR. . .
Obtaining parameter estimates this way for all the explanatory variables
in the model, we then use these parameters and the actual values of the
explanatory variables that occur during the period 2001–2010 to calculate
the model’s estimates for the values of the GDP, C, and I during these
10 years after the end of the period covered by the sample. These estim-
ates will then be compared to the actual data. The basic model used to
determine the GDP is
GDP = CD + ID + G + X
where we substitute the determinants of CD, ID, X, and their parameter

estimates into a typical Keynesian “IS” equation to obtain estimated values
of the GDP based on the model. If the model isn’t just a fluke of the data
period used to construct it, and does powerfully describe the underlying
structure that drives the economy, it should explain the behavior of the
economy outside the sample period as well as within for extended periods
of time. This is not too much to ask of a model purporting to be good
science.
16.1 MODEL #1 TREATING ALL DETERMINANTS

OF C, I, AND X AS EXOGENOUS
In Section 4, Eq. 4.4 showed the parameter estimates for the full model
of domestically produced consumer goods for the full 1960–2010 data
sample. Results are repeated here:
CD = 0.29(Y – TT ) + 0.31(TT ) – 0.20(GT& I )

(t =) (6.0) (5.8) (–3.5)
– 6.86PR + 0.44DJ–2 – 0.33XRAV – 517.17POP16
(–2.4) (4.4) (0.2) (–3.5) (4.4)
+ 0.020POP + 0.53ICC–1 + 38.16 M2AV + 0.10CB2
(5.8) (2.1) (4.3) (3.4)
R2 = 88.7% D.W. = 2.0 MSE = 24.54
The same model is re-estimated using only 1960–2000 data so as to allow

out-of-sample testing of its fit in the 2001–2010 period.
16.1 MODEL #1 TREATING ALL DETERMINANTS OF C, I, AND X AS EXOGENOUS 319
CD = 0.35(Y – TT ) + 0.23(TT ) – 0.13(GT& I ) – 4.33PR

(t =) (5.2) (2.3) (–2.0) (–1.8)
+ 0.32DJ–2 – 1.17XRAV – 508.20POP16 + 0.017POP
(2.0) (–0.8) (–2.8) (4.6)
+ 0.30ICC–1 + 35.93M2AV + 0.16CB2
(1.3) (4.4) (3.1)
R2 = 91.2% D.W. = 1.6 MSE = 21.60
(4.4.16)
Though there are some differences, generally coefficients on significant
variables remain reasonably close to their estimated values in the full data
set model given in Eq. 4.4., which we would expect since the graph of
this equation shows it explains consumer behavior equally well in each of
the five decades included in the sample. Dropping one decade should not
change the coefficients much.
In Section 4, Eq. 5.4 calculated the parameter estimates for the full
model of domestically produced investment goods for the full 1960–2010
data sample. Results are repeated here:
ID = + 0.25(ACC) + 0.29(TT ) – 0.31(GT& I ) + 0.08DEP

(t =) (6.7) (2.7) (–3.7) (0.3)
+ 2.60CAP–1 – 3.01PR–2 – 0.19DJ0 + ..08PROF–0
(1.5) (–1.9) (–0.8) (1.2) (5.4)
+7.08XRAV + 0.011POP + 0.02 (BOR–1 )
(2.2) (3.4) (0.3)
R2 = 84.4% D.W. = 2.0 MSE = 28.77
The same model, re-estimated using only 1960–2000 data, so as to allow

out of sample testing of its fit during the 2001–2010 period yields the
following:
ID = + 0.22(ACC) + 0.33(TT ) – 0.34(GT& I ) – 0.18DEP

(t =) (7.3) (3.7) (–4.0) (–0.6)
+ 2.31CAP–1 – 2.89PR–2 + 0.22DJ0 – 0.12PROF–0
(1.9) (–1.7) (1.3) (–.07)
+ 2.30XRAV + 0.01POP + 0.11(BOR–1 )
(0.9) (2.7) (1.5)
R2 = 84.4% D.W. = 2.4 MSE = 24.21
(5.4.16)
Here again the estimates from the 1960–2000 sample are quite similar
to the full 50-year period model (and for the same reason – the model
explains investment behavior about equally well in any decade).
In Section 6, Eq. 6.1 showed the parameter estimates for the model
of domestically produced goods for export for the full 1960–2010 data
sample. Results are repeated here:
X = 0.16(WGDPRealTP(0) ) – 9.47 (XRAV0 to –3 ) + 0.56(M0 )

(t =) (2.9) (–4.1) (18.6)
+ 14.74 (PRRealAV–1–2 ) – 11.58 INFLAV–1 to –2 ) – 0.49 AR(6)
(3.9) (–2.0) (–1.7)
R2 = 87.9; DW = 1.6 MSE = 24.69
(6.1)
Recalculating the model using only 1960–2000 data gives the model
results shown in Eq. 6.1.16 below:
X = 0.10(WGDPRealTP(0) ) – 7.91(XRAV0 to –3 ) + 0.58(M0 )

(t =) (1.8) (–4.7) (9.3)
+ 13.24 (PRRealAV–1–2 ) – 8.56 INFLAV–1 to –2 ) – 0.38AR(6)
(3.9) (–1.9) (–1.5)
R2 = 78.6; DW = 2.0 MSE = 18.19
(6.1.16)
Table 16.1.1 compares the actual values of real CD , ID , and GDP for
the years 2001–2010 with the values fitted from the parameter estimates
developed using only 1960–2000 data when applied to actual data for the
determinants from 2001–2010.
During the 2001–2010 period, the actual average yearly growth of
GDP was 2.2%, the actual average growth of consumption was 1.9%, the
average growth of investment was 5.2%, and the average growth in exports
was 6.8%.
The error in prediction does grow: For the first five years after the estim-
ation period, the average error of prediction for GDP was only 3/10 of
1%; in the second five years, 6/10 of 1%. For consumption it was also
slightly higher in the second 5-year period (5.8/10 of 1%) than the first
(5.1/10). For investment, it was 2.9% in the first five years after the estim-
ation period, 3.5% for the second five years. For exports, it was 1.1% in the
first five years, 2.4% in the second five years.
Table 16.1.1 Model 1 How well the model fits the data for the 10 periods following the 1960–2000 period used to
estimate the modela (billions of 2005 dollars)
Yearly change Absolute values of % changes

(as a % of (GDPACTUAL – GDPPRED ) (CACTUAL – CPRED ) (IACTUAL – IPRED ) (XACTUAL – XPRED )
GDP) GDPACTUAL ConACTUAL Inv.ACTUAL XACTUAL
2001 0.0090 0.0052 0.0474 0.0106

2002 0.0022 0.0139 0.0814 0.0194
2003 0.0009 0.0040 0.0194 0.0007
2004 0.0028 0.0026 0.0072 0.0002
2005 0.0019 0.0058 0.0007 0.0182
2006 0.0039 0.0006 0.0235 0.0002
2007 0.0018 0.0049 0.0548 0.0322
2008 0.0061 0.0026 0.0182 0.0446
2009 0.0124 0.0001 0.0742 0.0037
2010 0.0049 0.0078 0.0142 0.0199
Average error 51/100 of 1% 48/100 of 1% 3.4% 1.5%
Of fit of GDP 1 of Con. of Inv. of X
a GDP predictions used coefficients estimated from consumption, investment and export function determinants, applied to actual data for those determinants
for the year specified in the model, plus actual data for government spending. Method of estimating error taken from that used in the DRI Econometric
Model (Eckstein 1983, p.25).
16.2 MODEL #1 TREATING ALL DETERMINANTS OF C, I, AND X AS EXOGENOUS
321
16.2 MODEL 2: TREATING C, I, AND X MODEL

DETERMINANTS FOR WHICH WE HAVE
EXPLANATORY FUNCTIONS AS ENDOGENOUS
In Model 1 above, we expressed the GDP as a function of the determinants
of domestically produced consumption, investment and export goods and
services (taken from our domestic consumption, investment and export
models- Eq. 4.4, 5.4, and 6.1 respectively), to which we added the actual
values of government goods and services spending. The actual value of
each of those determinants of C, I, and X was taken as an exogenous value
for us to enter into Model 1 above. Though we have a function which ties
part of the variation in provision of government services to fluctuations
in economic variables like unemployment, a sizeable proportion of the
spending is exogenous-determined by government policy decisions. Our
only way of measuring this is to subtract our estimates of the endogenous
part from total government spending. To incorporate this into our GDP
model, we would have to add the two parts together, which is what we
already have using the government data available.
As noted, in our first model, the actual value of each of the determin-
ants of C, I, and X was taken as an exogenous value, and used in Model
1 above. However, the 45-equation GDP determination model contains
nine equations describing the determinants of many of the variables. For
each of the variables (determinants of C, I, or X) used in Model 1 for
which we have an equation describing the variable’s own determinants,
we now replace its actual value (used in Model 1) with the calculated val-
ues from the function that describes its determinants and their parameters.
This will be Model 2. Variables from Model 1 which will be replaced by
functions in Model 2 below include
Y = real GDP
(Y-TT ) = disposable Income
TT = total government receipts
PR0 =prime interest rate (calculated from Taylor rule theory of rate
determination)
PR–1 = “ ”
PRAV–1–2 = “ “
PR–2 = “ “
DEP = depreciation allowances retained by business
X = exports
Infl = inflation
16.2 MODEL 2: TREATING C, I, AND X MODEL DETERMINANTS FOR WHICH WE HAVE. . . 323
CB2 = consumer borrowing

BOR–1 = business borrowing (lagged one period)
The models used were presented earlier in the text and are repeated
here for reference. Results are shown in Model 2 below:
(1) GDP
YT = .26(TT ) – 0.17(GT& I ) – 7.94PR – 0.09DJ–0 – 0.006DJ–2

(t =) (2.4) (–2.0) (–1.9) (–0.5) (0.0)
+ 7.39XRAV + 107.28POP16 + 0.049POP + 1.32ICC–1
(–1.1) (0.2) (4.4) (2.9)
+ 0.001M2AV + 0.62(ACC) + 3.17DEP + 5.76CAP–1
(0.0) (15.0) (2.4) (2.0)
+ 0.61PR–2 + 0.05PROF–0 + 0.03 CB2 + (IB(–1) ) – 0.02X
(0.1) (0.4) (0.4) (0.1)
+ 1.00 AR(2) – 0.34 AR(7)
(+5.3) (–2.0)
R2 = 95.8% D.W. = 1.9 MSE = 41.59 (7.1.1)
And the coefficients for the 1960–2000 sample:
YT = .49(TT ) – 0.38(GT& I ) – 5.96PR + 0.58DJ–0

(t =) (4.7) (–3.3) (1.2) (2.1)
– 0.79DJ–2 + 1.68XRAV + 679.08POP16 + 0.026POP
(–1.7) (0.4) (1.5) (3.3)
+ 1.18ICC–1 + 0.92M2AV + 0.52(ACC) + 1.89DEP
(3.2) (3.2) (10.5) (2.5)
+ 3.93CAP–1 + 3.93PR–2 + 0.33PROF–0
(1.0) (1.0) (2.4)
+0.21(CB2 + (IB(–1) ) + 0.52X + 0.62 AR(1) – 0.26AR(2)
(2.2) (1.6) (3.7) (–1.3)
R2 = 97.2% D.W. = 1.8 MSE = 32.77 (7.1.1.16)
(2) Government receipts
(TT ) = . – 4.38 + 0.30(GDP) + 12.28INFLAV(–1–2) – 48.59(UNEM)

(t =) (–0.2) (3.2) (2.3) (–3.2)
– 27.02 Shock86 + 31.12 shock93 + 0.42AR(1)
(–0.8) (1.0) (3.6)
R2 = 0.73; DW = 1.8; MSE = 62.24 (14.1)
And the coefficients for the 1960–2000 sample
(TT ) = .18.14 + 0.19(GDP) + 8.68INFLAV(–1–2) – 44.37(UNEM)

(t =) (1.3) (3.0) (2.4) (–3.7)
+16.68 Shock86 + 12.90 shock93 + 0.11AR(1)
(2.0) (1.1) (0.9)
R2 = 0.80; DW = 2.0; MSE = 34.29
(14.1.16)
(3) Disposable income
(Estimated as calculated GDP minus calculated government receipts)
(4) Prime interest rate (Taylor rule function)

(t =) (2.6) (–4.8) (–3.4)
+0.012M1REAL(–1) – 0.002TAX – 0.001SPEND
(9.2)
(2.8) (–1.1) (–0.5)
+ 0.44AR(1) R2 = 0.81; DW 2.0
(2.4)

(t =) (2.4) (–6.5) (–0.3)
+ 0.004M1REAL(–1) – 0.003TAX – 0.001SPD
(9.2.16)
(1.0) (–0.8) (–0.2)
+ 0.58AR(1) R2 = 0.85; DW 1.8
(4.1)
(5) Exports
X = 0.16(WGDPREALTP(0) ) – 9.47(XRAV0 to –3 ) + 0.56(MT )

(t =) (2.9) (–4.1) (18.6)
+14.74(PRRealAV–1–2 ) – 11.58INFLAV–1 to –2 ) – 0.49AR(6) (6.1)
(–3.9) (–2.0) (–1.7)
R2 = 87.9; DW = 1.6 MSE = 24.69
X = 0.10(WGDPREALTP(0) ) – 7.91(XRAV0 to –3 ) + 0.58(MT )

(t =) (1.8) (–4.7) (9.3)
(–3.9) (–1.9) (–1.5)
R2 = 78.6; DW = 2.0 MSE = 18.19
(6.1.16)
(6) Depreciation
SD = 0.06(INV0 ) + 0.10(INV–1 ) + 0.10(INV–2 ) + 0.07(INV–3 )

(t =) (7.8) (9.4) (7.0) (5.2)
+ 0.03INV–4 ) + 0.04(INV–5 ) + 0.03(INVAV–(6–10) )
(2.4) (3.4) (8.7)
+ 04(INVAV–(11–17) ) + 0.13AR(8)
(9.2) (1.0)
R2 = 0.966 DW = 2.1, MSE = 4.77
(13.b.1)
And the coefficients for the 1960–2000 sample:
SD = 0.02(INV0 ) + 0.11(INV–1 ) + 0.08(INV–2 ) + 0.09(INV–3 )

(t =) (1.2) (5.6) (4.3) (5.7)
+ 0.04INV–4 ) + 0.07(INV–5 ) + 0.04(INVAV–(6–10) )
(2.5) (4.3) (4.3)
+ 03(INVAV–(11–17) ) + 0.20AR(8)
(2.2) (1.2)
R2 = 0.977 DW = 1.9, MSE = 4.14
(13.b.1.16)
(7) Consumer borrowing
CB2 = 0.57(Y – TT ) + 0.70(TT ) – 0.52(GT& I ) – 21.89PR

(t =) (4.1) (3.0) (–3.0) (–3.1)
– 1.65DJ–1 + 14.06XRAV + 68.02POP16 – 0.012POP
(–3.7) (4.3) (0.2) (–2.2)
+ 0.52ICC–1 – 30.60M2Av – 0.14(M2 – M1)Real (4.6)
(0.6) (–1.3) (–1.0)
– 0.07(PerSav)Real – 0.43AR(2)
(0.2) (–2.0)
R2 = 59.7% D.W. = 2.5 MSE = 75.42

CB2 = 0.63(Y – TT ) + 0.78(TT ) – 0.64(GT& I ) – 22.10PR
(t =) (4.4) (2.4) (–3.7) (–3.9)
– 1.67DJ–1 + 13.36XRAV – 17.23POP16 – 0.016POP
(–2.8) (5.1) (–0.0) (–3.0)
+ 0.33ICC–1 – 17.39M2Av – 0.15(M2 – M1)Real
(0.4) (–0.6) (–1.3)
+ 0.15(PerSav)Real – 0.14AR(1)
(0.3) (–0.9)
R2 = 59.2% D.W. = 2.5 MSE = 67.68
(4.6.16)
(8) Business borrowing
IB = 0.52(ACC+1 ) + 1.62(TT ) – 1.07(GT& I ) + 0.85DEP
(t =) (4.4) (4.4) (–6.1) (1.1)
+11.26CAP–1 – 6.18PR–2 – 1.61DJ–1 + 0.33PROF0
(5.8)
(2.4) (1.0) (–3.6) (1.5)
+ 2.43XRAV R2 = 71.7% D.W. = 1.8 MSE = 101.71
(0.2)
IB = 0.55(ACC+1 ) + 1.61(TT ) – 1.19(GT& I ) – 0.35DEP

(t =) (3.6) (4.5) (–3.8) (–0.4)
– 7.17CAP–1 + 0.15PR–2 – 1.46DJ–1 + 0.74PROF0
(–1.5) (0.0) (–2.0) (2.1)
+ 11.17XRAV R2 = 55.9% D.W. = 2.1 MSE = 85.68
(2.6)
(5.8.16)
(9) Inflation model (Phillips curve)

(t =) (–10.0) (4.7)
– 135.67((M – X)/Y)Real + 13.12(ForBor–1 / ln v–1 )Real
(–2.8) (5.7)
–46.46(Gross Sav–1 /Y–1 )Real (11.1)
(–5.1)
+ 2.73 (OPEC73&78 Shock) + 0.52Ar(2)
(11.0) (3.5)
R2 = 0.78; DW = 1.7

(t =) (–7.8) (2.2)
– 147.08((M – X)/Y)Real + 11.30(ForBor–1 / ln v–1 )Real
(–2.3) (2.5)
(–3.8) (10.8)
+ 0.46Ar(2) R2 = 0.75; DW = 1.6
(2.3)
(11.1.16)
Table 16.2.1 compares the actual values of GDP for the years 2001–
2010 with the values predicted from Model 1 (taken from Table 16.A.1)
and Model 2. Both involve fitting a model whose parameters were
developed using only 1960–2000 data to the data for the 2001–2010
period to determine how well the parameters estimated from the 1960–
2000 data work, when coupled with data on the determinants for the
2001–2010 period, to predict the GDP during those 10 post-sample years.
(Table 16.2.1).
As noted earlier, during the 2001–2010 period, the actual average
yearly growth of GDP was 2.2%.
Table 16.2.1 How well models 1 and 2 fit the data for the 10 periods following
the 1960–2000 estimation period (billions of 2005 dollars)
Yearly change Model 1 Model 2

(as a % of GDP) (GDPACTUAL – GDPPRED ) (GDPACTUAL – GDPPRED )
GDPACTUAL GDPACTUAL
2001 0.0090 0.0253

2002 0.0022 0.0230
2003 0.0009 0.0020
2004 0.0028 0.0101
2005 0.0019 0.0001
2006 0.0039 0.0107
2007 0.0018 0.0075
2008 0.0061 0.0272
2009 0.0124 0.0323
2010 0.0049 0.0267
Average error 0.51 of 1% 1.6%
Of fit: of GDP of GDP
The extended model appears to fit the data for a decade beyond the
estimation period less well than the simpler model, but still reasonably
well relative to GDP size, since we can say our average estimate of GDP
for the 10 years after the model’s parameters were estimated is only 1.7%
off the actual GDP. This we take as a sign of internal consistency within the
different regression results we obtained for the 45 component equations
of this large scale econometric model. That said, the average yearly error
of estimate is about ¾ of the actual size of the change in GDP, which is
not so good. The better estimator is Model 1. Since each of the Model 1
determinants was replaced in Model 2 inexactly by its own determinants,
this result should not surprise us.
It was noted earlier that in general, adding the coefficients of variables
from the previously tested subcomponents C, I, and X of the GDP gave
more rational estimates of parameter estimates of their relationship to the
subcomponent (and therefore to the GDP when added together) than
just running a regression on the same variables, using CD + ID + G + X
as the dependent variable. We noted parameter estimates in the aggregate
regression can vary considerably, even their sign, compared to what was
obtained in desegregated function (See Section 7.1). The same problem
also affects how well the two approaches (Models 1 and 2) estimate the
GDP in the decade after estimation. Below we compare actual GDP to
calculated figures for 2001–2010 based on the parameters obtained from
regression of GDP on its determinants (16.3.16, repeated below),
YT = ..49(TT ) – 0.38(GT& I ) – 5.96PR + 0.58DJ–0

(t =) (4.7) (–3.3) (1.2) (2.1)
– 0.79DJ–2 + 1.68XRAV + 679.08POP16 + 0.026POP
(–1.7) (0.4) (1.5) (3.3)
+ 1.18ICC–1 + 0.92M2AV + 0.52(ACC) + 1.89DEP
(3.2) (3.2) (10.5) (2.5)
+3.93CAP–1 + 3.93PR–2 + 0.33PROF–0
(1.0) (1.0) (2.4)
+ 0.21(CB2 + (IB(–1) ) + 0.52X + 0.62AR(1) – 0.26AR(2)
(2.2) (1.6) (3.7) (–1.3)
R2 = 97.2% D.W. = 1.8 MSE = 32.77
(7.1.1.16)
and combining parameter estimates from C, and I regressions (recall
Eq. 8.1.1.1, repeated below)
Table 16.2.2 How well models 1 and 2 fit the data for the 10 periods follow-
ing the 1960–2000 estimation period (nine additional equations substituted for
variables treated as exogenous in Model 1)
Yearly Single GDP regression model Sum of C & I Eq. coefficients, plus G+X model
change
(GDPACTUAL – GDPPRED ) (GDPACTUAL – GDPPRED )
(as a %
of GDP) GDPACTUAL GDPACTUAL
2001 0.0305 0.0090

2002 0.0296 0.0023
2003 0.0070 0.0010
2004 0.0095 0.0028
2005 0.0085 0.0019
2006 0.0018 0.0039
2007 0.0095 0.0018
2008 0.0395 0.0061
2009 0.0485 0.0124
2010 0.0282 0.0050
Average 2.1% 0.51 of 1%
error
Of fit of GDP of GDP
YT = – 0.41(TT ) + 0.69(GT& I ) + 0.85(TDef ) – 0.72(GDef )

– 9.67PR – 4.24PR–2 – 0.27DJ–0 + 0.62DJ–2
+ 9.52XRAV – 729.21POP16 + 0.044POP + 0.75ICC–1
+ 53.81M2AV + 0.14CB2 + 0.35(ACC) + 0.11DEP
+ 3.67CAP–1 + 0.11PROF–0 + 0.03(IB(–1) ) + 1.41X
(8.1.1.1)
But 8.1.1.1 was calculated from Eqs. 4.4 and 5.4 estimated using the
whole 1960–2010 data set. Re-estimating those equations (Eqs. 4.4.16
and 5.4.16 presented earlier) using only the 1960–2000 data set is actu-
ally what we did earlier in Model 1, where the average error for the decade
after the estimation period was found to be 0.46 of 1%.
The average error of the GDP was calculated as (Actual GDP-calculated
GDP)/Actual GDP). For the model (7.1.1.16) above which just did one
regression on all the C and I equation determinants, plus G and X, for the
10 years 2001–2010, the average error of fit was 2.1% as shown in the first
column of Table 16.2.2. This was 4.6 times more than the 46/100 of 1%
error for the GDP estimates obtained for our first model which added
C&I model parameter estimates for each variable, plus G and X (all
adjusted by the multiplier).
The reason for discrepancy is that the single regression of GDP on a
variable captures correlational as well as causal relationships the variable
may have with the C and I subcomponents of the GDP. The observed
coefficient is the sum of the causal effect measure in one subcomponent
of GDP and the merely correlational (spurious) effect found in another.
The approach of adding up only measured effects of a variable only from
subcomponent equations in the GDP in which the variable was statistic-
ally significant, or at least left in the equation because it was considered
theoretically important, avoids this. The calculated errors are presented in
Table 16.2.2.
CHAPTER 17
Converting the Older Keynesian IS-LM

Model to the More Modern AS-AD
Interpretation of the Keynesian Model
17.1 SHORT- AND LONG-RUN AGGREGATE

SUPPLY CURVES
In conventional aggregate supply and aggregate demand curve (AS/AD)
mechanics, there are two aggregate supply curves: a long-run (LRAS) and
a short-run (SRAS) curve.
The short-run supply curve is often presented as a horizontal line on a
graph with the price level given on the vertical axis and the real GDP on
the horizontal, indicating ability, because of fixed or sticky costs to offer
varying quantities of output on the market for the same price per unit
(Mankiw, 2010).
A more classical formulation shows an up-sloping SRAS curve, repres-
enting the effects of diminishing returns on producers’ need to be able
to recoup a larger price per unit on large quantities of production than on
small to maintain constant profit levels per unit. In such short-run models,
capital is assumed to be constant.
An alternative explanation for the up-sloping AS curve (Krugman and
Wells, 2013) reflects the fact that a rising price level allows producers to
charge more and increase profits per unit when faced with sticky or fixed
costs of production. Thus, higher prices create a profit-maximizing incent-
ive to produce to more as prices increase to make more profits. (Notice

DOI 10.1007/978-3-319-50681-4_17
332 17 CONVERTING THE OLDER KEYNESIAN IS-LM MODEL. . .
the two theories of what causes the SRAS curve to be up-sloping have
exactly the opposite directions of causation: diminishing returns suggests
decisions to increase production forces the increase in prices just to main-
tain profits, while the increased profits view suggests increased prices leads
to increased production.)
Either the flat or the up-sloping SRAS curves are consistent with Keyne-
sian mechanics; both allow for shifts in aggregate demand to effect the
GDP, the result predicted by traditional Keynesian IS/LM mechanics.
Only a vertical curve is inconsistent with this possibility.
The long-run supply curve is portrayed as a vertical line drawn at the
point on the horizontal axis representing the economy’s maximum level
of (long-term sustainable) output at a particular point in time. It also rep-
resents the more neoclassical point of view that shifts in demand result in
instantaneous adjustment of prices and wages, and therefore have no effect
on real GDP (or employment).
Temporary deviations along the SRAS above this level are allowed for
when for cultural or other reasons, e.g., the Christmas shopping rush,
wartime patriotism), additional supplies of labor make themselves tempor-
arily available, but only for the holiday season or national crisis. Similarly,
machinery (capital) may be used temporarily above its long-term sustain-
able level by temporarily ignoring the need for down time to perform
preventive maintenance such as lubrication, cleaning, etc. This also allows
for temporary increases in output above LRAS levels, but increases that
are not sustainable over time.
17.2 THE AGGREGATE DEMAND CURVE AND THE

ROLE OF VELOCITY IN AGGREGATE DEMAND
Classical mechanics, at least in the form of Fisher’s equation of exchange,
MV = PY, allows for the existence of a down sloping AD curve when
the money supply (M) and the income velocity of money (V) are held
constant. With MV constant, the AD curve becomes:
(MV)
=Y (17.2.1)
P
where MV is taken as the money measure of aggregate demand in the

economy. It is obvious from 17.2.1 how monetary policy, by increasing
the money supply, can be used to shift the AD curve rightward, to increase
17.2 THE AGGREGATE DEMAND CURVE AND THE ROLE OF VELOCITY. . . 333
aggregate demand to achieve public policy objectives related to the GDP

and unemployment. (Provided of course, the method of increasing the
money supply puts it in the hands of those who will spend it on GDP
components, not things like existing securities which, though they push
the price of securities up, don’t enter the GDP, except perhaps, through
the wealth effect on consumption, or the Tobin’s q effect on investment.)
Fisher’s equation of exchange was written a decade before the Fed
adopted open market operations as the principal means of changing the
money supply. Prior to that, the “real bills” theory dominated Federal
Reserve thinking and resulted in increases in money only to replen-
ish bank loanable funds depleted by loans for real investment spending
(Mishkin, 2009). But open market operations rely on buying securities
from whoever is selling them. This is usually securities dealers/investors
who see an opportunity to improve their portfolios by selling government
bonds to obtain cash to buy a different security which typically will be sold
to them by another dealer who wishes to sell one security to buy another,
etc. In a world in which 99% of securities outstanding in any period are
already existing, not new issues (Mishkin, 2009), this means the increase
in money may go principally to inflating security values, not increasing the
GDP. It is questionable whether Fisher would have formulated the equa-
tion of exchange had he written in an era in which open market ops were
the means of increasing the money supply.
To be useful in translating IS-LM mechanics into a truly Keynesian
AD curve, Fisher’s equation has to be able to show the effects of fiscal
as well as monetary stimulus. It is not so obvious how Fisher’s model
can be used to show the effects of fiscal policy on the real GDP, i.e., by
increasing government spending, or cutting taxes in ways that create or
increase government deficits. For this, we have to look behind the “V” in
Fisher’s equation, because, holding M constant, fiscal policy can only work
by changing V, i.e., change the number of times the same money is spent
in a particular period, thereby shifting the AD curve rightward.
Doing this, Fisher’s theory does offer an explanation of the stimulus
effects of monetary policy consistent with traditional IS/LM mechanics.
To see if Keynesian fiscal policy does shift the AD curve, we must
determine what causes velocity to change, and which of these determ-
inants can themselves be changed when changes in GDP are desired. We
must also show how fiscal policy can bring about the desired change in
velocity. Equation 17.2.2a shows how fiscal policy must work if it is to
lead to shifts in the AD function consistent with Keynesian mechanics.
(PY) P P
i.e., V = = (Y) = fy (. . .) (17.2.2a)
M M M
Equation 17.2.2a indicates that holding the price level and the money supply
constant, velocity can be increased by some action that increases the demand
for real GDP, e.g., increased government demand for goods (or tax cuts)
financed by borrowing unused funds – idle reserves – from banks. This will
provide the increase in velocity desired. Put another way, any change in the
GDP not caused by an increase in the real money supply must be the result of
some action that increases velocity, and the same effect occurs regardless of
whether we measure in nominal or real values if the price level is constant.
As we will show below, increasing government spending or cutting taxes
does increase velocity, provided they induce or increase the government
deficit.
Financing either tax cuts or government spending by means of a deficit
means financing them out of money borrowed from a bank or other finan-
cial institution where people are storing their savings until needed. Using
these savings to finance spending now (that would otherwise not occur
now if the money were left unused in banks), increases aggregate money
demand, and in Keynesian mechanics this elicits an increase in the GDP.
If M2 stays constant, it increases V. (If we are only using M1 money in
Fisher’s equation, M1 might increase if the loan to the government is fin-
anced out of non-M1 components of M2 (like savings deposits) available
as excess reserves, leaving V constant).
Bank lending to the government out of savings which the bank expects
will remain unused and in the bank until a future period, clearly increases
the current GDP by increasing the number of times the same money is
used to purchase goods in the current period, i.e., by increasing the rate
at which the same money is turned over in successive sales (velocity). This
holds for loans financed out of excess reserves. This is basic Keynesian
stimulus theory as it affects the economy in the short run.
Long-run effects may be different. In later periods, government repay-
ment of debts to banks allows the bank to repay its debt to the original
saver when the original savers wish to withdraw their money. This repay-
ment may reduce the government deficit, as it requires revenues in excess
of those earmarked for spending, thereby reducing the GDP (and velo-
city) in that future period. This would leave the net long-run effect of the
stimulus program zero. Alternatively, the government can just roll over
the debt in perpetuity, allowing repayment of the old debt out of issuance
of new debt, a scenario uncomfortably like current government practice

in many countries. But doing the rollover borrowing itself (perhaps from
the same banks) reduces funds otherwise available at that future time for
private borrowing by a comparable amount. Hence, the deficit’s initial
effect in increasing velocity (and GDP) will eventually be matched by a
reduction of comparable amount in some later period.
It may be however, that money lent to the government in the current
period will create crowd out, i.e., cut back on funds available for private
borrowing that would have been borrowed by consumers or businesses to
finance purchases that also would have increased the GDP by, the same
amount as the fiscal stimulus. If so, we have the “crowd out” problem:
government spending (or tax cuts) that leads to GDP-increasing spend-
ing are offset in the same period, in whole or part, by decreases in private
spending that would otherwise have occurred. This offsets any increase
in GDP (or velocity) that would have occurred though government bor-
rowing of this money. Its stimulus effects have now been crowded out.
(Similarly, the eventual payback by the government would not have a net
negative effect: it would be offset by private borrowing out of the newly
available money in the bank resulting from the repayment.) So, if crowd
out is a problem, Keynesian stimulus may not work in either the short or
the long run.
An alternative theory is the notion that any money borrowed from
banks by the government, then spent to increase the GDP, is replaced
in banks (in the same period) by multiplier effects on saving. Hence, if the
MPC is = 0.90, government borrowing of $100 from banks leads to an
increase in income of $1000, 10% of which, or $100 is saved, replacing
the $100 lost to private borrowers by government borrowing. However,
later in the current period, or in some future period, when government
repays the loan, thereby reducing the deficit, the GDP and velocity will
again decrease, offsetting the stimulus effects. Also, this explanation fails
to include the fact that the initial $100 “crowd out” ultimately causes
a $1000 decline in income and a corresponding $100 decline in saving,
offsetting the stimulus effect.
Finally, if the Federal Reserve pursues accommodating monetary policy
by increasing bank loanable reserves, it will replace the reduction in funds
available for private borrowing, perhaps by buying the very government
bonds sold to the bank earlier, which caused the reduction in private credit
availability. Here, we would say the Keynesian stimulus would work. This,
of course, assumes the money created by the Fed is placed in the hands of
those who will spend it in its entirety on goods and services, not just on
purchases of other existing securities, whose main effect will be to increase
existing security prices, not raise the GDP.
Since the effect of deficits can have different theoretical outcomes when
considering the current period alone (depending on repayment schedules
and crowd out effects), the effect of deficits on velocity for the current
period becomes an empirical question, answered in the sections below.
In the following sections, OLS and 2SLS tests are performed on selected
variables having a theoretical basis for consideration as determinants of
velocity. The theory is an extension of Eq. 17.2.2a above
V = (Y)(P/M) = [fy (T, G, Wealth, PR, ICC, Etc.) + G + (X – M)] (P/M)

(17.2.2b)
Coefficients of the tax and (TT ) government spending (GT&I ) vari-
ables should show statistically significant Keynesian stimulus effects unless
changes in TT and GT&I also create crowd out effects. In this case, the
coefficients will show the stimulus effect net of crowd out effects. This
is the model of velocity’s determinants we will test in Section 17.3. it is
tested in first differences to reduce multicollinearity and nonstationarity
problems, i.e.,
V =Y∗ (P/M) = Y∗t (P/M)t – Y∗t–1 (P/M)t–1

=fy [(T – G)(P/M), Wealth(P/M), PR(P/M), ICC(P/M), Etc.)
+ G(P/M) + (X – M)] (P/M) (17.2.2c)
The initial OLS model tested estimates the net effects of changes in taxes
and government spending on M1 velocity. Normally, without crowd out,
we would expect a positive sign on the coefficient for government spend-
ing and a negative sign on the tax variable (as we found with our GDP
tests of crowd out earlier in the chapter). This would in fact be the case
if only state and local taxes were collected. For the day a taxpayer reduces
his checking count M1 by paying his taxes, the state or local government
deposits it in its own checking (or possibly savings) account at the com-
mercial bank it uses to pay state bills. However, in either case, paying
taxes generally will not affect the M1 money supply, and certainly not
M2. However, when a taxpayer pays federal taxes, reducing commercial
bank balances of M1, the check is deposited in the U.S. Treasury depart-
ment’s checking account (TGA account) at the Federal Reserve. Though
identical in function to the demand deposit accounts at commercial banks

which are part of the M1 money supply, the contents of the government’s
demand deposit account is not part of M1 (U.S. Treasury, 2014). Hence,
payment of federal taxes reduces the M1 (and M2) money supply by an
equal amount, whereas payment of state and local taxes leaves the money
supply unchanged. Fortunately, with the hypothesis to be tested formu-
lated as it is in Eq. 17.2.2c), this problem does not present itself in a way
that distorts results, since each variable’s coefficient is a partial derivative;
it is obtained assuming the other variables stay constant.
17.2.1 An Alternate Way of Explaining How Government Deficits

Increases Velocity: An Apple Economy
17.2.1.1 The Keynesian Stimulus Effect
Suppose, to make money, a farmer grows an apple on January 1 (private
production of goods and services), sells it to a dealer for $1 (the only
money in circulation), and plans on buying it back to consume on July
1. S/he stores the $1 in a bank until needed July 1. Later on January
1, the government borrows the dollar and uses it to hire an unemployed
worker to produce another apple (fiscal stimulus). The worker produces it
(government production of goods and services), the government pays the
worker the $1 it borrowed in exchange for the apple the worker produced.
Later, getting hungry, the worker buys back the apple from the govern-
ment (taxes), providing the government with the funds needed to repay
its debt to the bank by July 1. On July 1, the original farmer withdraws
his $1 from the bank and buys his apple back from the dealer. Net result:
$1 was used to finance purchases of two apples for final consumption: one
on late January 1 by the worker, and one on July 1 by the farmer. The
same dollar was used twice: velocity was two because of government fiscal
stimulus financed by the deficit, instead of the one it would have been.
This is an example of traditional Keynesian fiscal stimulus.
17.2.1.2 The Crowd Out Effect

Suppose a business man was planning to borrow (the first farmer’s) dollar
deposited in the bank to hire a second farmer to privately produce an
apple in January, paying him with the borrowed dollar in exchange for the
apple (additional private production). Later the second farmer would buy
the apple back from him (additional revenue), providing the business with
enough money to repay the bank. However, before the business could
borrow, suppose the government got there and borrowed the dollar.
The government then hired the second farmer to provide a government

service (grow the apple) and paid him $1 in exchange for the apple.
Later, to feed himself, the second farmer bought the apple back from the
government, which provided the government with the funds needed to
pay back the bank loan so that the first farmer could use the money to
buy his apple on July 1.
Notice that in this case, the production of apples and velocity of money
would have been two even if the government didn’t borrow farmer #1’s
dollar from the bank (i.e., did not institute a fiscal stimulus program).
By borrowing the same dollar the private sector was going to borrow, it
prevented the private sector from producing an apple, thereby offsetting
the increase in output stemming from its own use of the borrowed money
to produce a second apple. With the government (instead of the business)
borrowing the dollar the velocity of money and production of apples stays
at two.
Hence, fiscal stimulus programs must necessarily increase velocity in
order to increase money demand for goods and services (and therefore
production). Theoretically, deficit types of fiscal stimulus work in classical
mechanics by increasing the money demand for goods and services by
increasing the velocity of money.
Note: At full employment, there is no second farmer available to hire,
so production can’t increase and the idle dollar can’t buy two apples: only
one, thereby keeping velocity at one.
17.3 OLS TESTS OF M1 VELOCITY’ S DETERMINANTS

The formulation of classical mechanics given in Eq. 17.2.2a asserts that
deficit financed fiscal stimulus affects the real GDP through its effect on
velocity. To empirically determine if this assertion is correct, Eq. 17.3.1
tests whether increases in government spending or tax cut stimulus are
positively related to increases in M1 velocity. For ease of exposition all
explanatory variables shown below are understood to be multiplied by
(Price Level/Nominal M1), as in Eq. 17.2.2b, though this is not shown
explicitly.
Initially, all variables in the C and I models, plus G, plus net exports
(X–M) were hypothesized to be determinants of M1 money supply’s
income velocity (V1). A huge number of variables were involved and as
a result, in initial testing, because of this degrees of freedom problem
and multicollinearity, many proved statistically insignificant. Because of
17.3 OLS TESTS OF M1 VELOCITY’S DETERMINANTS 339
the possibility that the insignificance could be for substantive reasons as

well as technical reasons, the insignificant variables were removed one
by one, and the revised model was retested. The variable with the low-
est t-statistic was removed from the initial model first, then the revised
model was retested. The variable with the lowest t-statistic in the revised
model was then removed from the revised model, and the second revision
was retested. The process was repeated until only statistically significant
variables (5% level) remained in the model.
This stepwise procedure is not a perfect way of deciding which vari-
ables that determine GDP are systematically affected by changes in velocity
(“determined” leaves no room for theory arguing certain deleted vari-
ables should be left in on theoretical grounds). Also, order of removal
can affect the final list of variables remaining. However, though not per-
fect, it is an objective way which removes the results from suspicions the
variables were removed in a way to influence the results. Again, recall
that each explanatory variable tested was the variable shown below times
(PLevel /M1Nominal = “m1” = inverse of the real M1 money supply), where
the GDP deflator (divided by 100) is used as the measure of the price level.
The results of the initial large-scale OLS test of V1’s determinants are
shown in Eq. 17.3.1. This test includes a variable which controls for effects
on private borrowing on velocity. In some other formulations, this variable
will not be used. The version of this model which is robust time period
tested is given in Model 17.4.1.TR, though the model is not fully robust
to changes in variables included in the model, i.e., the distortive effects of
multicollinearity.
Model 17.3.1
OLS M1 Velocity Model
Note: (All right-hand-side variables multiplied by P/M1 (e.g., “TT ” in
17.3.1 is actually “TT *(P/M)”)
V1 = + 0.48(TT ) + 0.43(GT&I ) + 5.00PR – 0.01DJ–0

(t =) (2.2) (1.8) (0.5) (0.0)
+ 0.91DJ–2 – 10.90XRAV – 393.20POP16 + 0.016POP
(1.7) (–1.9) (–0.5) (2.4)
– 0.01ICC–1 + 75.60M2AV – 0.003(ACC) + 1.52DEP
(–0.0) (2.2) (–0.1) (1.2)
– 12.04CAP–1 + 0.61PR–2 + 0.03PROF–0 + 0.41(CB2 + IB(–1) )
(–2.1) (0.1) (0.1) (3.3)
– 0.35(X – M) R2 = 97.5%, D.W. = 1.8, MSE = 0.07
(–0.5) (17.3.1)
This model shows the stimulus effects of fiscal policy to cut total taxes
or increase total government spending in the form of the coefficients
on those variables (TT , GT&I ) in Eq. 17.3.1. However, these coeffi-
cients are “net” of some (described below) but not all crowd out effects.
Even with only some crowd out accounted for, we see that the effect
of a deficit financed tax cut on velocity (and therefore GDP) is negat-
ive. For government spending, the net effect shown still leaves the effect
of increased spending on velocity positive (V1, and therefore real GDP,
increase 0.43 for each dollar of additional government spending), but not
to the extent expected theoretically in Keynesian mechanics, i.e., 1/(1–
MPC) (GT&I ) where the multiplier is generally assumed to be greater
than one.
But this only partially shows the extent to which crowd out offsets
traditional Keynesian stimulus effects, as indicated in the note below:
(Note: Total crowd out effects include the reduction in private spending equal
to the amount of reduced private borrowing, plus additional negative effects
on spending that may occur because borrowing is typically done for “big ticket”
items, partially financed by consumers and businesses out of income, partially
out of borrowing. When borrowing declines, total spending may decline some
multiple of that. This multiple effect is the only part of crowd out’s effects
that show up in the coefficients on taxes and government spending when bor-
rowing levels are explicitly controlled for in the model, as in 17.3.1 using the
(CB2 + (IB(–1) ) variable. Results can be positive for both the tax and spend-
ing variables if crowd out effects dominate stimulus effects for tax cuts, but
don’t for government spending. In an attempt to disentangle, we have added
a variable (the government deficit) to explicitly pick up crowd out effects and
re-estimated the model in Eq. 17.3.2.
Another way of showing the crowd out effect of deficits’ net negative
effect on V1 is to add the deficit size as a variable explicitly to the model,
retaining variables showing the general effects of taxes and government
spending deficits. This is done in Model 17.3.2 below, which is just Model
17.3.1 with the deficit (TT –GT&I ), net of changes in the size of the pool
of loanable funds, added as the first variable in the model.
Model 17.3.2
OLS V1 Velocity Model (Deficit Variable Added)
Note: All right-hand-side variables multiplied by P/M1. Model includes
explicit deficit variable and private borrowing control variable
V1 = 0.47(TT – GT&I ) – 0.36(TT(–1) ) + 1.04(GT&I ) + 4.53PR

(t =) (2.5) (–2.2) (3.5) (0.5)
+ 0.19DJ–0 + 1.07DJ–2 – 13.31XRAV – 369.51POP16
(0.9) (1.9) (–2.6) (–0.6)
+ 0.015POP + 0.52ICC–1 + 63.53M2AV – 0.000(ACC)
(2.5) (0.4) (1.9) (–0.0)
+ 2.05DEP – 8.59CAP–1 + 1.24PR–2 – 0.08PROF–0
(1.8) (–1.8) (0.2) (–0.3)
+ 0.44(CB2 + (IB(–1) ) – 0.33(X – M)
(3.2) (–0.5)
R2 = 97.6%, D.W. = 1.9, MSE = 0.07 (17.3.2)
Doing this separates all deficit crowd out effects from stimulus effects. It
shows both taxes and government spending variables having the appropri-
ate signs to show Keynesian stimulus effects. Both the negative crowd
out effects shown by the deficit variable, and the Keynesian stimulus
effects shown by the tax and government spending variables are statistic-
ally significant, as is the positive effect on velocity of consumer or business
borrowing, which we also expect.
This equation provides what may be a major step forward in resolv-
ing the age – old argument: “Do stimulus programs work, or not?” This
equation says, yes, they do, but that other simultaneously occurring effects
(crowd out) offset some or all of the stimulus.
To avoid perfect collinearity between the deficit variable and the sep-
arate G and T variables representing total taxes and total government
spending, we had to approximate the TT variable with its prior year value,
TT(–1) . Otherwise the matrix of explanatory variables was singular and
would not invert to allow calculation of regression coefficients.
Model 17.3.3 eliminates the variable controlling for the effects of
private borrowing on velocity, allowing the deficit variable to pick up
declines in private borrowing due to crowd out effects not picked up in
Eq. 17.3.2 because we hold the effects on private borrowing constant.
Model 17.3.3
OLS V1 Velocity Model (Deficit Variable Added, Borrowing
Variable Deleted)
V1 = 0.65(TT – GT&I ) – 0.21(TT(–1) ) + 0.89(GT&I ) + 14.19PR
(t =) (3.1) (–1.5) (2.4) (1.1)
+ 0.39DJ–0 + 0.38DJ–2 – 10.63XRAV – 755.85POP16
(1.6) (0.8) (–1.5) (–1.0)
+ 0.015POP + 0.61ICC–1 + 78.65M2AV – 0.01(ACC)

(1.9) (0.4) (1.6) (–0.2)
+ 2.13DEP – 7.12CAP–1 – 5.54PR–2 – 0.15PROF–0
(17.3.3)
(1.6) (–1.6) (–0.6) (–0.4)
2
– 1.39(X – M) R = 96.8%, D.W. = 1.9, MSE = 0.08
(–2.0)
Note: all right-hand-side variables multiplied by P/M1.

As expected, when effects of private borrowing were not controlled
for, the impact of an increase in the deficit on grew from 0.49–0.65; the
coefficient of the tax variable has the expected Keynesian negative sign and
shows the expected decrease in absolute value from 0.36–0.21 when the
control for effects on private borrowing are eliminated, and the expected
decrease in the spending variable’s coefficient from 1.04–0.89 occurs for
the same reason.
Overall, we conclude tests 17.3.1–17.3.3 show the expected Keynesian
stimulus effects on the velocity of M1 money, and, separately, the expected
crowd out effects predicted by other theoreticians as well.
17.4 2SLS TESTS OF M1 VELOCITY’ S DETERMINANTS

Hausman endogeneity tests indicated the government spending and
depreciation variables were endogenous with the dependent variable, V1.
They were replaced with a Wald-strong instrument and parameters in
the initial OLS Model 17.3.3 were re-estimated using 2SLS. A Sar-
gan test indicated the instruments themselves were free of endogeneity.
Equation 17.4.1 presents the 2SLS estimates:
Model 17.4.1
2SLS V1 Velocity Model (Deficit Variable Added, Borrowing
Variable Deleted))
Note: All right-hand-side variables multiplied by P/M1. Includes explicit
deficit variable; does not control for private borrowing effects. GT&I and
DEP replaced by strong, nonendogenous instrument
V1 = 0.72(TT – GT&I ) – 0.53(TT(–1) ) + 0.81(GT&I ) + 4.90PR

(t =) (1.9) (–1.7) (0.6) (0.4)
17.4 2SLS TESTS OF M1 VELOCITY’S DETERMINANTS 343
+ 0.39DJ–0 – 0.31DJ–2 – 0.10XRAV + 140.63POP16

(1.0) (–0.4) (–0.0) (0.1)
– 0.004POP + 1.96ICC–1 + 21.49M2AV + 09(ACC)
(–0.2) (1.2) (0.3) (0.8) (17.4.1)
+ 6.34DEP – 3.64CAP–1 – 9.87PR–2 – 0.18PROF–0
(1.8) (–0.5) (–0.9) (–0.5)
– 0.36(X – M) R2 = 95.7%, D.W. = 1.6, MSE = 0.10
(–0.3)
17.4.1 Explained Variance and Robustness Tests

The importance of individual variables in explaining M1 velocity can be
assessed using stepwise regression. See Table 17.4.1 for results.
The first-out results indicate there were so many explanatory variables,
it was difficult to find one whose variance could not be picked up by
other variables remaining in the model. First-in suggested most of the
Table 17.4.1 Explained variance – V1 velocity

(R2 = 0.96 to Start) (R2 = 0.00 to Start)
(Deficit) 0.94 0.25

(Taxes) 0.96 0.61
(Govt. Spending) 0.95 0.70
(Prime Rate0 ) 0.95 0.13
(DJAV0 ) 0.96 0.49
(DJAV–2 ) 0.96 0.11
(Exchange RateAV(0–3) 0.96 0.29
(POP16/65 ) 0.96 0.23
(POP0 ) 0.96 0.67
(ICC–1 ) 0.96 0.15
(M2av–2–4 ) 0.95 0.75
(ACC) 0.96 0.28
(DEP) 0.96 0.84
(Capacity Utilized–1 ) 0.95 0.26
(Prime Int. Rate–2 ) 0.96 –0.05
(Real Profits) 0.96 0.29
(X-M) 0.95 0.23
Table 17.4.2 Robustness over time – M1 velocity, 2SLS Eq. 17.4.1
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Deficit) 0.72∗∗ 0.86 1.20 0.90∗∗∗

(Taxes) 0.53∗∗ –0.31 –0.17 –0.52
(Govt. Spending) 0.81 1.22 3.15∗∗ 1.99∗∗∗∗
(Prime Rate0 ) 4.91 7.47 –2.93 0.98
(DJAV0 ) 0.39 0.34 1.47 1.43
(DJAV–2 ) –0.30 –0.16 –1.10 –0.05
(Exchange RateAV(0–3) –0.10 –1.81 –3.21 1.37
(POP16/65 ) 140.64 558.20 4875.57 761.45
(POP0 ) –0.004 –0.003 –0.04 –0.01
(ICC–1 ) 1.97 1.39 1.79 0.46
(M2av–2–4 ) 21.49 32.00 –5.48 4.13
(ACC) 0.09 0.05 0.14 0.09
(DEP) 6.34∗∗ 4.83 4.98∗∗∗ 2.81
(Capacity Utilized–1 ) –3.64 –9.82 –7.62 –12.40
(Prime Int. Rate –2 ) –9.87 –14.24 –20.48 –6.29
(Real Profits) –0.18 –0.23 0.88∗ 0.92∗∗∗∗
(X-M) –0.36∗ –0.47 0.14 –0.67
Significance level: ∗ 15%; ∗∗ 10%; ∗∗∗ 5%; ∗∗∗∗ 1%.
variation in V1 was highly correlated with depreciation, the M2 average,

government spending and taxes and population growth.
The model was tested in four separate but overlapping time periods.
Nothing tested was significant in more than two tests. Suspecting that it
was multicollinearity more than substantive reasons for this, we tentatively
defined anything significant in two tests as the core time period robust
model, and then retested each of the insignificant variables individually
with the core model to see if the variable was now significant. All which
were added to the core model and the whole model was retested in all
four time periods. Those that proved significant in at least three of the
four periods were taken to constitute the final time period robust model,
given in Eq. 17.4.1.TR:
V1 = 1.18(TT – GT&I ) – 0.54(TT(–1) ) + 1.85(GT&I ) + 4.62DEP

(t =) (5.7) (–3.3) (3.8) (4.5)
–005POP – 15.80PR–2 – 0.65(X – M)
(1.8) (–2.5) (–1.8)
R2 = 95.4%, D.W. = 1.8, MSE = 0.09 (17.4.1.TR)
17.4 2SLS TESTS OF M1 VELOCITY’S DETERMINANTS 345
Graph 17.4.1
Specification Robustness
Deleting the last two variables from the model and re-estimating gives
Model 17.4.1.TR.a
Variable Deleted)
V1 =1.40(TT – GT&I ) – 0.64(TT(–1) ) + 1.80(GT&I ) + 5.29DEP
(t =)(6.3) (–3.4) (3.7) (5.1)
2
– 007POP R = 94.0%, D.W. = 1.8, MSE = 0.10
(–2.2) (17.4.1.TR.a)
The remaining model parameter estimates and significance levels appears

robust to the model change.
Adding the stock market and exchange rate variables to the full time
period robust model (17.4.1.TR) and re-estimating
1.0
0.5
0.0
–0.5
0.2 –1.0
0.1 –1.5
0.0
–0.1
–0.2
–0.3
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 17.4.1 Actual and fitted V1 values 1960–2010 (taken from

Eq. 17.4.1.TR)
Model 17.4.1.TR.b
Variable Deleted)
V1 = 1.15(TT – GT&I ) – 0.51(TT(–1) ) + 1.85(GT&I ) + 4.29DEP

(t =) (4.6) (–2.6) (3.1) (2.1)
– 003POP – 15.35PR–2 – 0.80(X – M) + 0.08DJ–2
(0.4) (–2.3) (–1.2) (0.1)
– 2.65XRAV R2 = 95.6%, D.W. = 1.8, MSE = 0.09
(–0.3) (17.4.1.TR.B)
Coefficients are reasonably robust, but both the population and net
exports variables fall from marginally significant to insignificant.
We conclude that though robust to period sampled, Eq. 17.4.1.TR is
not fully robust to model changes.
17.5 OLS TESTS OF M2 VELOCITY’ S DETERMINANTS

We now wish to repeat the tests of the determinants of velocity implied in
the classical model (Fisher’s Equation of Exchange). Unlike the previous sec-
tion, here, we use the M2 money supply and V2 as our velocity definition, i.e.,
repeating Eq. 17.2.1a from earlier:
Model 17.2.1.a (Repeated)

V2 Velocity Conceptual Model
V2 = (Y)(P/M2) = [fy (T, G, Wealth, PR, ICC, . . . Etc . . . .)+G+(X–M)] (P/M2)

(17.2.1a)
Here again we see that Fisher’s equation implies that there has to be a
direct correspondence between changes in velocity and changes in real
GDP if we hold the price level and the M2 money supply constant.
To test whether government fiscal stimulus positively affects the GDP
by increasing velocity, Eq. 17.5.1 below tests whether changes in stimulus
levels are positively related to changes in M2 velocity (where all explanat-
ory variables noted below in tests are understood to be multiplied by the
ratio of the price level to nominal M2).
Initially, all determinants of GDP, including all determinants of con-
sumption and investment, plus government spending and net exports were
hypothesized to be determinants of V2. However, in initial testing, many
proved statistically insignificant. Because of the possibility that this could

be for technical reasons (multicollinearity and limited degrees of freedom
with so many explanatory variables), and not substantive ones, the insigni-
ficant variables were removed one by one, those with the lowest t-statistics
first, retesting after each subtraction, and reevaluating each set of new res-
ults before determining which variable was now lowest and next to be
removed. Using the Y = C + I + G + (X – M) model of the economy, the
original model estimated was 17.5.1 below.
Again, recall that each explanatory variable tested was the vari-
able shown below times (“m2” = PLevel /M2Nominal = GDP Deflator/
M2Nominal):
Note: Total crowd out effects are equal to the reduction in spend-
ing equal to the amount of reduced private borrowing, plus additional
negative effects on spending that may occur because borrowing is typ-
ically done for “big ticket” items, partially financed by consumers and
businesses out of income, partially out of borrowing. When borrowing
declines, total spending may decline some multiple of that. This multiple
effect shows up in the coefficient on the deficit variable. Total taxes and
government spending and borrowing levels are explicitly controlled for
in Model 17.5.1 below). In an attempt to disentangle, we have added a
variable (the government deficit) to explicitly pick up crowd out effects
in Eq. 17.5.1 below. The final model, with results robust to differences
in time period tested, and to changes in model specification, is given as
Model 17.5. 2.TR further below.
Model 17.5.1
OLS V2 Velocity Model (With Borrowing Variable)
V2 = 0.35(TT – GT&I ) + 0.19(TT(–1) ) + 0.66(GT&I ) – 3.60PR
(t =) (2.2) (1.2) (24) (–0.5)
+ 0.06DJ–0 + 0.29DJ–2 – 10.80XRAV – 443.41POP16
(0.2) (0.6) (–2.3) (–1.1)
+ 0.008POP – 0.45ICC–1 + 2.88 M2AV + 0.31(ACC)
(1.8) (–0.6) (0.1) (5.1)
+ 1.84DEP + 3.18CAP–1 + 4.66PR–2 + 0.081PROF–0
(3.0) (0.7) (0.6) (0.3)
+ 0.32(CB2 + (IB(–1) ) – 0.30(X – M)
(3.3) (–0.7)
R2 = 95.1%, D.W. = 1.6, MSE = 0.015
(17.5.1)
Though the clutter of variables relative to degrees of freedom and col-

linearity issues leaves some known determinants of GDP insignificant
here, the results do clearly show the expected Keynesian stimulus effect
of government spending increases on velocity (0.66GT&I ), the expec-
ted negative effect of deficits 0.35 (TT –GT&I ), and the positive effect of
private borrowing +0.32(CB2 + (IB(–1) ). For reasons that are not clear,
the tax variable’s coefficient (0.19) does not have the expected negative
sign.
To avoid perfect collinearity between the deficit variable and the
separate G and T variables representing total taxes and total govern-
ment spending, we had to approximate the TT variable with its prior
year value, TT(–1) . Otherwise the matrix of explanatory variables was
singular and would not invert to allow calculation of regression coef-
ficients. This unfortunately leads to an “errors in variables” downward
bias in the estimated effect given by the tax regression coefficient, but is
unavoidable.
This model calculates the stimulus effects of tax cuts and spending
increases holding the level of private borrowing by consumers and businesses
constant, i.e., not allowing for crowd out effects of government borrowing on
private borrowing to be included in the estimation of the net effect of tax cuts
and spending increases on velocity. In Model 17.5.2 below, we correct for this
deficiency by re-estimating Model 17.5.1 excluding the controls on business
and consumer borrowing
Finally, we wish to test the full model with the deficit variable left in,
but the borrowing variable out. Results are given in 17.5.2 below.
Model 17.5.2
OLS V2 Velocity Model (Without Borrowing Variable)
V2 = 0.45(TT – GT&I ) + 0.43(TT(–1) ) + 0.52(GT&I ) + 4.66PR

(t =) (3.1) (2.6) (1.7) (0.6)
– 0.05DJ–0 – 0.26DJ–2 – 7.96XRAV – 748.876POP16
(0.2) (–0.7) (–1.3) (–1.6)
+ 0.006POP – 0.62ICC–1 + ..13 M2AV + 0.36(ACC)
(1.1) (–0.8) (–0.0) (5.8)
+ 1.96DEP + 4.90CAP–1 + 1.43PR–2 + 0.20PROF–0
(2.9) (1.4) (0.2) (0.6)
– 1.01(X – M) R2 = 93.8%, D.W. = 1.6, MSE = 0.016
(–2.3)
As expected, the estimated marginal effect of crowd out on V2 increased

from 0.35 in Eq. 17.5.1 to 0.45 here.
Hausman endogeneity tests indicated that none of the right-hand side
variables were endogenous with the dependent variable V2 in Eq. 17.5.2.
Hence, no 2SLS was needed.
Explained Variance and Robustness Tests
Contributions To Explained Variance
The importance of individual variables in explaining M1 velocity can be
assessed using stepwise regression. See Table 17.5.1 for results.
The first-out results indicate there were so many explanatory variables,
it was difficult to find one, virtually all of whose variance could not be
picked up by other variables remaining in the model. The two exceptions
were the accelerator and depreciation. First-in suggested most of the vari-
ation in V2 was highly correlated with depreciation and the M2 average.
Robustness to Time Period Tested
In Table 17.5.2 we present the results of testing the model given in 17.5.2
in four different, though overlapping time periods.
Table 17.5.1 Explained variance – V2 velocity

(Deficit) 0.93 0.31

(Taxes) 0.93 0.08
(Govt. Spending) 0.93 0.31
(Prime Rate0 ) 0.94 0.36
(DJAV0 ) 0.94 0.18
(DJAV–2 ) 0.94 0.00
(Exchange RateAV(0–3) 0.93 0.08
(POP16/65 ) 0.93 0.09
(POP0 ) 0.94 0.30
(ICC–1 ) 0.94 0.16
(M2av–2–4 ) 0.94 0.75
(ACC) 0.90 0.34
(DEP) 0.92 0.50
(Capacity Utilized–1 ) 0.94 0.21
(Prime Int. Rate –2 ) 0.94 0.05
(Real Profits) 0.94 0.29
(X-M) 0.93 0.04
Table 17.5.2 Robustness over time – M2 velocity, 2SLS Eq. 17.5.1.2
Variable 1960–2010 1970–2010 1970–2000 1960–2000
(Deficit) 0.45∗∗∗∗ 0.442∗∗∗ 0.77∗∗∗ 0.26

(Taxes) 0.43∗∗∗a 0.58∗∗ 0.92∗∗∗ 0.46∗∗∗∗
(Govt. Spending) 0.52∗∗ 0.63 1.48∗∗∗ 0.58
(Prime Rate0 ) 4.65 12.48∗∗∗ 11.73∗ 4.73
(DJAV0 ) –0.05 0.003 –0.59 0.14
(DJAV–2 ) –0.26 –0.18 0.28 –0.51
(Exchange RateAV(0–3) –7.96 –6.76 –2.36 –6.14
(POP16/65 ) –748.87∗ 610.29 771.45 –461.67
(POP0 ) 0.006 0.008 –0.006 0.003
(ICC–1 ) –0.62 –0.82 –1.25 –0.92
(M2av–2–4 ) 0.13 –2.15 –21.66 –3.18
(ACC) 0.36∗∗∗∗ 0.33∗∗∗∗ 0.33∗∗∗∗ 0.34∗∗∗∗
(DEP) 1.96∗∗∗∗ 1.46∗∗ 4.98∗∗∗ 2.14∗∗∗∗
(Capacity Utilized–1 ) 4.90 –2.98 0.89 6.63∗∗
(Prime Int. Rate–2 ) 1.43 –3.76 –3.33 5.80
(Real Profits) 0.20 0.18 0.85∗∗∗∗ 0.98∗∗∗∗
(X-M) –1.01∗∗∗ –0.86∗ –0.67 –1.55∗∗∗
Significance level: ∗ 15%; ∗∗ 10%; ∗∗∗ 5%; ∗∗∗∗ 1%.

a Estimated with a one period lag to reduce multicollinearity effects.
The “core time period” robust model is defined as those variables that
were statistically significant in at least three of the four periods sampled.
In addition, we individually add to the core any variable found significant
only two or less times in the original tests of the four-period samples. All
variables now found significant are collectively added to the core model
variables and retested in all four periods. Those found significant in at
least three of the four sample periods, along with the core, become the
final time period robust model, shown below as Eq. 17.5.2.TR:
Model 17.5.2.TR
Time Period Robust OLS V2 Velocity Model
(Without Borrowing Variable)
V2 = 0.64(TT – GT&I ) + 0.48(TT(–1) ) + 0.59(GT&I ) + 0.43 ACC
(t =) (4.9) (3.1) (2.9) (8.3)
+ 1.96DEP + 0.48 AR(1) R2 = 93.1%, D.W. = 1.6, MSE = 0.015
(2.6) (3.1)
(17.5.2.TR)

Eliminating the last variable in Eq. 17.5.2.TR and re-estimating, we get
Model 17.5.2.TR.a
(One Additional Variable Deleted)
V2 = 0.77(TT – GT&I ) + 0.62(TT(–1) ) + 1.00(GT&I ) + 0.44 ACC
(t =) (6.3) (4.6) (6.1) (11.3)
+ 0.48 AR(1) R2 = 91.8%, D.W. = 1.6, MSE = 0.016
(3.1) (17.5.4.TR.a)
Significance levels of the remaining variables remain high; coefficients for
the deficit and total government revenues and the accelerator remain fairly
constant. However, the coefficients on the marginal effect of government
spending grow by two-thirds.
Adding the profits variable to the final time period robust model
17.5.2.TR and re-estimating, we get:
Model 17.5.2.TR.b
(One Additional Variable Added)
V2 = 0.60(TT – GT&I ) + 0.49(TT(–1) ) + 0.57(GT&I ) + 0.41 ACC
(t =) (4.5) (2.9) (2.7) (7.0)
+ 1.94DEP + 0.30PROF–0 + 0.43 AR(1)
(2.7) (1.9) (2.5)
R2 = 93.5%, D.W. = 1.7, MSE = 0.015 (17.5.4.TR.b)
The model estimates are highly robust to the addition of the profits
variable.
Overall we conclude that the model is robust to time period sampled
and largely robust to additions and subtractions of variables from the
model, with the exception of the coefficient on the government spend-
ing variable. The time period/specification robust model is graphed in
Graph 17.5.1.
0.15
0.10
0.05
0.00
–0.05
0.04
–0.10
0.02 –0.15
0.00
–0.02
–0.04
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 17.5.1 Actual and fitted V2 values 1960–2010 (taken from

Eq. 17.5.2.TR)
17.6 WHICH DETERMINANTS OF GDP ARE ALSO

DETERMINANTS OF VELOCITY
As noted in Eq. 17.3.1–4 and 17.4.1–5, after stepwise elimination of non-
significant variables in the original velocity models, only the following
remained as significant determinants of velocity:
V1 determinants (Eq. 17.4.4.TR; R2 = 0.96) V2 determinants (Eq. 17.5.2.TR (R2 = 0.93)
The Deficit (TT -GT&I ) The Deficit (TT -GT&I )

Taxes (TT–1 ) Taxes (TT–1 )
Government Spending (GT&I ) Government Spending (GT&I )
Depreciation (DEP) Accelerator (ACC)
Real Prime Interest Rate–2 Depreciation (DEP)
Net Exports (X-M)
Recall that in the initial models of velocity, all variables found signific-
ant determinants of GDP in consumption and investment models, plus
net exports, were included, a total of 17 variables (see 17.3.1, 17.4.1).
17.6 WHICH DETERMINANTS OF GDP ARE ALSO DETERMINANTS OF VELOCITY 353
Though all were significant determinants of GDP, only some were found
to be significant determinants of either M1 or M2 velocity. This may have
been for technical reasons related to multicollinearity or degrees of free-
dom relative to the large number of variables used (as was the case when
we directly statistically estimated the GDP function using these 17 vari-
ables as the explanatory variables. However, it may also have been because
not everything that raises GDP necessarily raises velocity, even when the
money supply is held constant.
Why Certain Variables Affect Velocity
Possible reasons for the findings of significant impact on velocity (or lack
thereof) are noted below, explained in terms of their impact on velocity in
the equation
Velocity = [GDPReal × (Price level/Money Supply)]

= [GDPReal /Money SupplyReal ] (17.2.1 or 17.2.1.a)
Which is the same thing as saying that anything that raises the real GDP,
real money supply constant, raises velocity, yet some factors were not
found statistically significantly related to velocity.
Five factors were found to affect both M1 and M2 money supply
velocity:
Tax or spending deficits: Borrowing to finance the deficits is usually done
out of unused M1 funds held by the investment community or by banks
(in the bank’s own corporate checking account). When open market pur-
chases of government bonds are made, the government bonds are paid
for by check, and deposited in Treasury’s bank account at the Fed. This
deposit reduces the money supply, but when this deposit is re-spent by
the government to finance the spending deficit, it is generally deposited
by the recipient of the transfer payment or seller of the goods and services
in their checking account, or kept as cash. This raises the nominal M1
money supply back to its former level. The nominal M1 money supply in
Eq. 17.2.1 or 17.2.1.a is unchanged. If the price level remains constant,
the real money supply must also remain unchanged, and this must mean
M1 velocity increases.
Alternatively, the bond purchase may be made by the investment com-
munity by converting unused (non-M1) M2 money, e.g., savings account
deposits, to M1 money, raising the M1 money supply, but not changing
M2. It is then spent in open market purchases of government bonds issued
to finance the deficit. Here again, the government deposits this in Treas-
ury’s account at the Fed (reducing M1and M2), and then subsequently
re-spends it on goods, services or transfer payments. The recipient sub-
sequently deposits it in their M1 account (restoring the earlier M1 and M2
balance. Or they may deposit it in their (non-M1) M2 account, restoring
the original M2 balance. If the price level remains constant, the GDP rises,
though M2 (and perhaps M1) remains unchanged. Hence M2 velocity
must increase, since it is but the calculation of (P/M2)*Y. (The increased
M1 money supply would mean M1 velocity would remain constant. Our
statistical results confirm that a change in GDPReal *(P/M1 or 2 ) is posit-
ively correlated with V1 or V2. If the (P/M1 or 2 ) portion is constant, this
must mean V1 or V2 rises with a rise in real GDP.
The financial community uses its M1 to buy government bonds in
open market operations. This M1, when received by the government, is
taken out of circulation and deposited in the Treasury’s checking account,
reducing M1.
However, the tax cuts financed by deficits leave extra money in people’s
M1 or non-M1 M2 accounts, or available for use financing goods and
services purchases. The money used for purchases would be deposited by
sellers in M1 or M2 accounts), If the tax cut just stays in M1, M1 stays
constant despite the deficit. If the tax cut stays in other parts of M2 as
savings, M2 stays constant. In either case, since not used to raise the GDP,
velocity stays constant. If the taxpayer’s unexpected M1 windfall money is
used to purchase goods and services, the GDP rises. If the M1 used to buy
the goods is deposited by the sellers in their M1 accounts, the M1 money
supply again remains constant, but since the GDP rises, so V1 must rise.
Taxes (controlling for deficits and effects on private borrowing) were
found negatively related to velocity, suggesting a cut in taxes raised velocity
(holding money supply constant). Keynesian fiscal stimulus theory sug-
gests tax cuts should positively affect the GDP (controlling for effects on
private borrowing). Fisher’s equation suggests that velocity and GDP are
positively related (holding the real money supply constant). Hence our
finding of a negative relationship between taxes and velocity is consist-
ent with both Fisher and Keynes. Similarly, a rise government spending
controlling for the deficit means an equal rise in taxes, causing a positive
effect on GDP for the same reason. For both tax cuts (+0.48) and spend-
ing increases (+0.59), this is what our empirical results show: for each
$1 of stimulus, split equally between tax cuts and spending increases, a
slight stimulus effect of 1.06 occurs, slightly larger per dollar of spending
increase than the stimulus itself.
Exchange rate: If the price of foreign goods drops because the cost
of foreign currency drops (which would show as a rise in the variable
(XRAV0 to –3 ), the price level indicator used in this study (GDP deflator)
may change somewhat since the price of American produced goods
includes the cost of foreign components. But since imported compon-
ents constitute only a portion of the price, the reflection of changes in the
price of foreign goods in the price of American goods should be less than
complete, though some downward change may occur, freeing up money
for expenditure on additional foreign or U.S. goods. Put another way, real
income rises.
This would be in addition to normal income and substitution effects
resulting from foreign goods of all types being cheaper, which would
occur when the price of foreign goods drop. Some of the existing M1
or M2 money supply, no longer needed to purchase foreign goods,
may shift toward purchase of domestic goods (if income effect domin-
ates substitution effect), raising the real GDP. The real money supply
(M1Nom /GDPDeflator) may rise as much (if nominal money is deflated
using a deflator that includes the prices of foreign goods). If it does, no
change in velocity, since (V = YReal /MReal ). If it doesn’t, the resulting rise
in GDP will cause velocity to increase (which is not what we observe,
since the exchange rate variable’s sign is negative, suggesting the substitu-
tion effect is more dominant). If the substitution effect is stronger than the
income effect, the drop in foreign currency prices will result in a net switch
in demand from U.S. to foreign goods, reducing real U.S. GDP. This will
cause a decline in velocity, which is what our empirical results show. (Some
increase in the real money supply may also occur if the money deflator
includes the prices of foreign goods, which would also decrease V since
(V = YReal /MReal ). This study uses the GDP deflator, so the real money
supply does not change, except perhaps because of the effect of cheaper
foreign components in U.S. products noted in the previous paragraph.)
Population Growth: If the population grows, demand for goods and
services increases. If produced, GDP will rise. If P and M remains constant,
velocity must increase. This is what our empirical results show.
Depreciation: Increases in depreciation allowances were also associated
with an increase in V1 and V2 velocity.
The increased allowances tend to occur in periods when investment,
and therefore GDP, is increasing.
Therefore, growth in depreciation should be associated with an increase
in velocity (controlling for the real money supply), which is what this study
finds.
In addition, there were three additional variables whose increases

affected M1 but not M2 velocity:
Average Growth in M2 2–4 Years Ago: This provides a wealth effect.
Eventually part of it, e.g., the M1 growth part, may be used to purchase
goods and services, raising the GDP and V1 velocity without altering the
real M1 money supply (if P is constant). In essence, M1 that would other-
wise sit idle, is used to make additional transactions. Transactions demand
money balances are reduced. However, if the past growth of M2 is in the
non-M1 part, and it stays there, leaving GDP unaffected by the M2 wealth
increase, it will have no statistically significant effect on V2 (as long as we
control for private borrowing, which we do). Growth in the non-M1 com-
ponents of M2 is consistent with our empirical findings of no relationship
of V2 and growth in M2.
Another alternative is that if the past period growth in the savings part
of M2, is converted to M1 and spent it raises real M1 and GDP, which
should leave V1 constant. Since our models held real M1 constant, we
could not test for this. If the vendor whose sales increased the GDP depos-
its the proceeds in a (non-M1) M2 account, M1 returns to old level, but
since GDP is up, V1 increases. This is also consistent with our findings,
but not something we tested for explicitly by including a variable to show
the change in M1 and non-M1 components of M2 in each period.
Capacity utilization: The findings of a negative relationship of last
year’s capacity utilization growth to this year’s V1, but a positive but not
significant relationship to V2 may be explained as follows.
Last year’s capacity utilization grew, causing GDP growth last year,
either as inventories, or as final sales. Sales this year out of inventories,
rather than new production, reduce GDP. Controlling for real M1 this
year, which this study does in this model, we should observe this year’s V1
decline, creating the observed negative relationship with last year level of
capacity utilization.
Financial wealth (lagged 2 years): Increases in stock market (finan-
cial wealth) create a wealth effect. This should increase spending relative
to observed current income, i.e., the (apparent) MPC should increase,
and this should increase current GDP, increasing V1 (if M1 and P stay
constant, as they do in our V1 models).
If the increase in stock market wealth is liquidated and converted to
savings or money market accounts, M2 increases, but since the money is
not spent, however, V2 should decrease since (V2 = YReal /M2Real ). This
negative relationship is what our V2 models indicate happens, though not
at statistically significant levels. The lack of significance may indicate the

amounts of stock market wealth transferred to M2 accounts is too small to
create enough variance in V2 behavior to be considered significant.
In addition, there was one variable, the accelerator, whose increases
increased V2 velocity, but not V1.
The accelerator: Growth in current year GDP, holding real M2 con-
stant, requires increased V2. For the same reason, increases in the current
year GDP growth rate over the prior year’s was found statistically associ-
ated with an increase in V2 velocity, but not V1. Presumably this occurs
because of more frequent borrowing from all components of M2 as the
economy grows, e.g., DD accounts, savings accounts, CD’s and money
market fund deposits. When borrowed from non-M1 components of M2,
they become M1 and as spent, they raise the real M1 money supply and the
real GDP (implying V1 stays constant), but leave M2 unchanged (implying
V2 increases).
A number of other variables were dropped from the initial model
because they were not found related to either V1 or V2. These included
Financial wealth (current year value): as noted above, wealth lagged
two periods is related to velocity. Hence, we conclude the current value
of financial wealth does affect velocity, just not for two more years, pre-
sumably because it takes a while to adjust sending habits to changes in
wealth levels. Alternatively, the origin of the current year financial wealth
variable is its use as a proxy for the Tobin’s q effect on investment. In the
investment models it was not found statistically significant, i.e., did not
affect investment or therefore, GDP. As such, our non-significant finding
here is consistent with those results.
Prime interest rate (current or 2-lag): Lower interest rates should stimu-
late the GDP which should increase velocity, P and M constant. However,
previous studies (Heim 2007) show that the interest rate most influen-
cing the GDP is the Prime rate, which moves in lock step with the federal
funds rate, which is determined by the Federal Reserve. The mechanism by
which the Fed lowers interest rates is by increasing M. Hence the increase
in M1 and M2 may proportionately offset the increase in GDP, causing
measured velocity to stay constant when interest rates drop (and vice versa
when interest rates rise). An alternative, more S and D-driven explana-
tion, is that as the economy slumps demand for loans declines and interest
rates fall. Net M1 and M2 drop, since repayment of old loans continues,
reducing the money supply, but is not offset fully by issuance of new loans
due to economic conditions.
Profits: Profits may rise because, if due to borrowing, an increase in the

real money supply occurs, spending it raises GDP the same amount. Our
Fisher equation model indicates these two changes occurring in the same
period if proportionately equal should leave velocity unchanged. This is
what our empirical evidence shows.
Profits may also rise because the firm is reducing expenses. If so, the
increase in profits may not represent more spending on GDP out of cur-
rent M levels (which would raise velocity), but just a shift in spending from
costs of production such as labor costs, to spending on things profits are
used for, e.g., purchasing more investment goods. If so, no change in velo-
city should be associated with the profit increase, which was the situation
we observed.
Young–to-old population ratio. As the percentage of young people in
the population (24 and under) relative to those 65 or older grows, the
empirical evidence indicates a decline in total consumer spending. (ceteris
paribus) and hence GDP, but no similar change in money velocity. This
may be because the money supply declines with the GDP decline. Younger
people have smaller incomes, and hence smaller transactions demand for
money (and smaller savings accounts, CD’s and money market funds).
Hence both M1 and M2 may drop as GDP drops due to an increase of
young relative to old in the economy. This would cause velocity to remain
constant.
The Index of Consumer Confidence, lagged 1 year, was found system-
atically related to consumer spending, and therefore the GDP in some
types of consumption. When confidence goes up, habit persistence may
cause a lagged effect: we may see consumer spending (therefore the GDP)
go up the following year. If financed by borrowing, the increase in bor-
rowing could create an increase in M1 money proportionately equal to
the increased spending. If the source of the funds lent was loanable funds
obtained by the bank from other than customer deposits (e.g., issuance
of commercial paper), then the increase in money offsets the increase in
GDP, keeping velocity constant.
In other cases, we simply did not find consumer confidence to be a
significant determinant of consumption. Therefore, its rise would not be
associated with a rise in GDP, and our velocity model indicates that there-
fore, we should find velocity unchanged, which is what our empirical
evidence indicates.
Conclusions regarding determinants of velocity: Changes in velocity are
the result of behavioral responses to economic change, and different
17.8 ALTERNATIVE METHOD: CALCULATING IMPACT OF DETERMINANTS OF GDP. . . 359
responses are sometimes equally theoretically plausible a priori. For

example, a change in current spending may occur because of an increase
2 years ago in wealth. If the increased spending is financed out of exit-
ing M1 balances, chances are great it will just result in a transfer of M1
from spender to vender’s account, leaving an increase in V1. However, if
financed by converting a saving, CD, etc., deposit to an M1 account, M1
increases by the amount of increased spending (GDP) and no V2 increase
may occur. Hence, the effect on V1 of an increase in wealth is indetermin-
ate theoretically; we must look to people’s actual practice, and statistically
report the results, which we have done above, “reverse engineering” the
process to find the theoretically plausible alternative that best describes
the data.
17.7 STATIONARITY ISSUES

The augmented Dickey-Fuller (ADF) test was used to determine station-
arity. Results for the variables used in the stepwise regression V1 and V2
models (see Eqs. 17.3.1 and 17.4.1) are given below. The models tested
the velocity effects of all variables found to have been determinants of GDP
in our earlier consumption and investment models and also included net
exports. To be judged ADF stationarity, the test statistic must be smaller
than the test criterion. Since all variables used except V1 and V2 are used
in a form multiplied by either M1 (=P/M1Nominal ) or M2 (=P/M2Nominal),
which are the inverses of the real money supply, they are tested for station-
arity in this same multiplied form. Stationarity statistics in some cases were
found to be different for M1 and M2 (Table 17.7.1).
Hence no revisions to our earlier OLS V1 and V2 models, either in
original or stepwise form, is require to ensure variables are stationary or at
least cointegrated with their dependent variables.
17.8 ALTERNATIVE METHOD: CALCULATING IMPACT

OF DETERMINANTS OF GDP ON VELOCITY USING
REGRESSION COEFFICIENTS OBTAINED
ESTIMATING CONSUMPTION, INVESTMENT, AND
EXPORT FUNCTIONS
In Chapter 8, we employed an alternative to directly estimating statistic-
ally the GDP function from its determinants. Instead, we arithmetically
calculated parameters for GDP determinants by using (i.e., aggregating)
Table 17.7.1 Variables significant in stepwise models
5% level M1 M2
Variable (tests of first differences) Test criterion Test statistic Test statistic
V1 –1.95 –4.70
V2 –1.95 –6.47
Taxes (TT ) –1.95 –4.82 –5.03
Government Spending (GT&I ) –1.95 –7.03 –4.37
Exchange Rate (XRAV ) –1.95 –4.05 –2.26
Population Size (POP) –1.95 –4.72 –2.43
Consumer and Business Borrowing –1.95 –7.25 –6.54
Depreciation –1.95 –3.97 –4.98
M2 Levels, Past Years Av. (M2AV ) –1.95 –5.28 –
Capacity. Utilization % (CAP–1 ) –1.95 –5.54 –
Accelerator –1.95 – –9.61
Wealth Measure (DJ–2 ) –1.95 –1.47∗ –
Variables deleted in stepwise procedure:
Accelerator (ACC) 1.95 –8.93 –
Prime Rate–2 (DJ–2 ) 1.95 –8.78 –9.87
Prime Rate–0 (DJ–0 ) 1.95 –8.65 –9.99
Net Exports (X-M) 1.95 –3.72 –4.46
Wealth Measure (DJ–0 ) 1.95 – –2.14
Cons. Confidence (ICC–1 ) 1.95 –5.78 –6.70
Young/Old Age Ratio (POP16 ) 1.95 –3.70 –2.24
% Cap. Utilized (CAP–1 ) 1.95 – –3.09
Wealth Measure (DJ–2 ) 1.95 – –2.07
Wealth Measure (DJ–0 ) 1.95 –1.03∗ ∗ –2.14
∗ –1.79 when detrended, using DJAV *P/M1
–2 Nom –0.007@trend. However, failure to meet the ADF
criterion is not a problem since the wealth measure (without trend) is also cointegrated with d(V1), as its
M2Nom form cointegrated with d(V2).
∗∗ (–1.98 when detrended using DJAV *P/M1–0.01@trend. Also, DJAV without trend is cointegrated
–0 0
w/V1, hence, no detrending is needed.)
parameter estimates for these variables that were obtained regressing con-
sumption and investment on their determinants, and adding government
spending and exports. We can incorporate the calculated GDP function
(Eq. 8.1) into our velocity model to see the estimated effects of fiscal
policy variables on velocity as well as others that are determinants of the
GDP. The model, using 8.1, would be as follows:
(PY) P P
i.e., V= = (Y) = fy (determinants of Y) (Repeating Eq. 17.2.2a)
M M M
P P
i.e., V = (Y) = (C + I + G + NX)
M M
17.8 ALTERNATIVE METHOD: CALCULATING IMPACT OF DETERMINANTS OF GDP. . . 361
V = (Y)(P/M) = [fy (T, G, Wealth, PR, ICC, Etc.) + G + (X – M)] (P/M)

(17.2.2a)
Coefficients of the tax and (TT ) government spending (GT&I ) vari-
ables should show statistically significant Keynesian stimulus effects unless
changes in TT and GT&I also create crowd out effects. In this case, the
coefficients will show the stimulus effect net of crowd out effects. This is
the model of velocity’s determinants we test, except that it is tested in first
differences to reduce multicollinearity and nonstationarity problems, i.e.,
V = Y∗ (P/M) = Y∗t (P/M)t – Y∗t–1 (P/M)t–1

= fy [(T – G)(P/M), Wealth(P/M), PR(P/M), ICC(P/M), Etc.)
+ G(P/M) + (X – M)(P/M)]
(17.2.2b)
Repeating the final robust total consumption model from Eq. 4.1T.TR
above
CT = 0.49(Y – TT ) + 0.57(TT ) – 0.38(GT&I ) – 9.31PR

(t =) (10.8) (11.0) (–7.9) (–4.6)
+ 0.44DJ–2 + 0.017POP + 0.41ICC–1 + 44.78M2AV
(5.4) (4.3) (1.2) (4.3)
+ 0.13 CB2 R2 = 94.8% D.W. = 1.6 MSE = 24.75
(3.6)
(4.1T.TR)
Repeating the final robust total investment model from Eq. 5.2.TR above
IT = + 0.25(ACC) + 0.30(TT ) – 0.32(GT&I ) – 10.53PR–2

(t =) (8.2) (2.7) (–4.4) (–4.3)
+ 0.87DJAV + 3.18XRAV + 0.97DEP
(3.3) (1.5) (4.1)
R2 = 86.6% D.W. = 2.2 MSE = 29.43
Combining the parameter estimates in the CT and IT equations with GT&I

and (X–M), we get our IS curve GDP determination model, given below
as Eq. 17.8.0.TR:
Y = – 0.06(TT ) + 1.06(GT&I ) + 1.71(TDEF ) – 1.37(GDEF ) – 18.25PR

– 20.64PR–2 + 1.71DJ0 + 0.86DJ–2 + 0.033POP + 0.80ICC–1
+ 87.77M2AV + 0.25CBOR + 0.49ACC + 6.23XRAV

(17.8.0.TR)
+ 1.90(DEP) + 1.96(X – M)
Therefore, V1 and V2 can be calculated as
V1 = (Eq.18.1) ∗ (P/M1) (17.8.1)

V2 = (Eq.18.1) ∗ (P/M2) (17.8.2)
In the alternate GDP function obtained by parameter estimates from

domestic consumption determinant Eq. 4.4TR and domestic investment
determinant Eq. 5.4TR, consolidating Y terms to obtain the multiplier,
adding coefficients on like variables together, and multiplying all coeffi-
cients by the multiplier (1/(1–.30)) gives the following results, previously
calculated in Chapter 8:
Y = – 0.41TTot + 0.69(GTot) + 0.86(TDef ) – 0.75(GDef ) – 7.67PR

+ 0.68DJ–2 – 0.726.24 POP16/65 + 0.044POP + 53.58 M2AV
+ 0.13CB2 + 0.37ACC – 6.66PR–2 + 9.60XRAV + 3.60CAP–1
+ 1.41X (8.1.TR)
Therefore, V1 and V2 can be calculated as
V1 = (Eq.8.1.TR) ∗ (P/M1) (17.8.3)

V2 = (Eq.8.1.TR) ∗ (P/M2) (17.8.4)
Clearly the results indicate that the marginal stimulus effect of a cut in
government revenue (–0.41TTot net of crowd out effects +0.86TTot) is
that velocity declines. The effect of an increase in government spending
on velocity, net of crowd out, is positive (+1.41–0.86), though whether
statistically significant is uncertain. This approach does not suffer from the
problem of estimating the GDP directly, i.e., the combination of effects of
a determinant that are correlational as well as causal.
CHAPTER 18
Dynamics
18.1 INTRODUCTION
You can think of the results obtained in Chapters 4–17 as the basic sci-
ence describing how the macroeconomy operates. Parameter estimates
indicate how a change in one explanatory variable can affect that equa-
tion’s dependent variable, holding the other variables in the model constant.
This ceteris paribus methodology allows us to avoid attributing to one
explanatory variable the influence of another.
But it does not deal with the very real fact that changes in the dependent
variable often subsequently cause “feedback” changes in some or all of the
explanatory variables. That is, there are feedback loops that cause a shock
to the system to have a direct effect on (say) GDP. This change in GDP
can then cause a subsequent change to the variable that caused the shock,
or other explanatory variables. These changes cause further changes in
GDP, which causes even further changes in the explanatory variables, etc.
Determining the path of these changes, until a new equilibrium is reached,
is the business of economic dynamics. Shocks we wish to evaluate are typ-
ically fiscal or monetary policy shocks, though shocks in other variables in
the system can also be of interest.
Unlike models with a limited number of explanatory variables, the
Cowles model described in this volume does not need Chomsky decom-
positions or other alternative ways of isolating the effects of changes in

DOI 10.1007/978-3-319-50681-4_18
364 18 DYNAMICS
fiscal or monetary policy variables (or any other variables) to simulate their
effects on the GDP. At least in theory, Cowles models, such as the one
presented in Chapters 4–17, explicitly contain all the variables that affect
the economy, and parameter estimates indicating how each of them affects
other variables. Hence, there is no need to observe changes in the error
term in a model before and after a known shock, and try to disentangle
the policy change’s effect on the error from other factors.
For example, the Cowles model developed in this volume provides
regression estimates of the current period effects of tax, government
spending, interest rate or monetary changes on other variables in the sys-
tem. They measure the marginal effects on a model’s dependent variable
of a change in some explanatory variable of interest.
However, the models do not show the feedback loop effects over time
of such initial changes. Estimating such dynamic effects is not a science
problem; the science has been already done (as in Chapters 4–17). It is
a mathematics problem to be solved using these coefficients provided by
the science. This can be a complex problem in a model with a large num-
ber of variables and relations. It becomes all the more complicated in a
model where some of the determinants of a variable (say, the GDP) are
determined in the same period as the dependent variable. For example,
in the model developed in this book, the “IS” model for GDP determ-
ination contains 8 explanatory variables as determinants of current period
GDP that themselves are determined in the current period. Often, in part,
they are determined by what GDP is determined to be in the current
period, as well as by other variables in the system, some of which are also
determined in part by what GDP becomes during this period. Hence, it
appears as though the dependent and eight explanatory variables have to
be “simultaneously” determined. How should we do this?
The clue to how to solve this puzzle lies in the definition of “period”
used. Make each period large enough, say 20 years, and it would seem that
almost every variable is determined in the same period. However, make it
small enough, say a month, and, in simulations, every small change in
the system from the initial shock onward can be examined recursively. For
example, an increase in government spending resulting in more firemen
being hired in this (mini) period may increase the GDP in this (mini)
period. In the next (mini) period, the changed GDP may cause changes
in the inflation and unemployment rates. In the subsequent (mini) period,
the change in inflation and unemployment may change interest rates and
the loanable funds pool, etc. Hence, if we can discover the order in which
18.1 INTRODUCTION 365
these mini steps takes place we can show how feedback loops cause changes
in all variables in the system over time.
How do we know the order in which an initial shock to the system
translates into changes in individual variables? This is a hugely import-
ant question. Romer (2016) has insightfully pointed out that the order in
which these steps are assumed to occur can affect your ultimate conclu-
sions about how big a change in a variable of interest will be in response
to a shock.
We feel the model developed in this volume avoids this problem. As
we have noted in earlier chapters, it is remarkably successful in explaining
the variation in the economy over the past 50 years, and does so about
as well in one decade as another. It is also very successful when used to
explain out-of-sample period behavior of the economy using the parameter
estimates developed with the help of data from earlier periods. Hence, we
feel the model represents good science.
When we apply this science to solving the IS equation (Eq. 8.1.2.1TR),
substituting into it our other models for its endogenously determined
explanatory variables, we find that there is only one ordering of the (mini)
period effects that allows the system to be solved at all! And solving the sys-
tem is needed if a dynamic path is to be plotted out over time showing the
impact, period by period, of the initial shock. We found no other ordering
of effects would work.
Hence we feel we have no major “identification” problem of the type
that involves uncertainty in determining whether in response to a shock,
variable X is determined before variable Y, or vice versa. In our Cowles
model, there is no ambiguity, since the model only solves one way, and
the model, from a scientific point of view, appears to be a good one. One
issue that did remain unresolved, in the period a deficit-induced stimulus
was introduced, was whether to have its stimulus effects or its crowd out
effects occur first. We found the choice only made a marginal difference.
We chose to model the crowd out effects as occurring first.
Our model for GDP determination (Eq. 8.1.2.1TR) tells us that the
effect of a change in government spending on GDP is +.69 times the
change in government spending, or –.41 ( Taxes). The recursive pro-
cess we found had to be used to measure the dynamic path of this shock
on the GDP and its determinants was as follows:
1 Determine the shock’s initial impact on GDP.

2 Use (1) to solve for the shock’s initial impact on unemployment.
366 18 DYNAMICS
3 Use (2) to determine the shock’s initial effect on inflation.

4 Use values determined for (2) and (3) to determine the Prime
interest rate and Loanable funds effects. They can’t be solved
without knowing the shock’s effect on unemployment and inflation.
Nor can the prime rate be solved before the loanable funds level is
solved, or vice versa. Solving (2) and (3) solves both simultaneously.
Total Government receipts and spending also are resolved simultan-
eously with the prime rate and loanable funds variables, since they
also are function of only the unemployment and inflation rates (and
the initial GDP change).
5 Once total government spending and receipts and loanable funds are
determined, changes to the government deficit (which measures the
crowd out problem) can be determined.
6 Use deficit values and other variables determined in (1–5) to determ-
ine values for imports, and consumer borrowing. (You can’t solve for
either until you know deficit effects.) Both imports and consumer
borrowing solve simultaneously once deficits are known. Neither can
be solved before the other.
7 Once you know imports, you can solve for exports.
8 Use the additional change to GDP resulting from the changes in (2–
8) to determine the change in GDP that starts the second iteration
of the process over again.
9 Continue these iterations until the system reaches an equilibrium.
In this way we determine the initial effects of a shock on GDP and other
variables in the system, and also the feedback effects that subsequently
occur until the new equilibrium is established.
We conclude that if all the standard statistical tests are telling you the
structural model is a good model, i. e., provides good estimates of how the
economy operates, then it is probably also telling you the order in which
things have to be resolved in order to get these good estimates.
At the time this book went to press, we were still working on the math
required to accurately articulate the whole IS curve variable set’s dynamic
path. We do have results for a slightly simpler model, given in Table 18.1
below. Unlike our earlier chapters, the results here should be considered
illustrative, not definitive. We have employed some simplifying assump-
tions about how quickly (in “mini” periods) the lagged variables become
effective, and start influencing the GDP. In our simplified model, there
is only one iteration of the model per period. In reality many iterations
18.1 INTRODUCTION 367
occur, and lags do not kick in until after the “many” have occurred. For
example, many iterations of the consumption multiplier effect occur in
the same year as an initial change in income. Lagged effects of changes
in other variables would not start until the following year or later, after
several iterations (“mini” periods) have occurred. A few other simplifica-
tions are employed. A 500 line Excel program was developed to run the
simulations. The dynamic path of GDP is presented in Table 18.1 below
for various monetary and fiscal stimulus policy options. Table 18.2 details
the effects on other key economic variables of these stimulus programs.
The dynamic paths of deficit financed $400 billion tax cuts, and $400
billion increased government spending programs are estimated, as is a
$400 billion change in the money supply. $800 billion combinations of
tax cuts and spending increases, with (and without) an $800 increases in
money supply are also simulated. The numbers were picked to represent
magnitudes associated with the 2009 U.S. stimulus program, The Amer-
ican Recovery and Reinvestment Act. Money supply growth 2007–11 was
also about $800 billion. Other initial condition variables were selected
to roughly represent 2010 values, or 2000–10 averages, as seemed most
appropriate.
Variable definitions follow the usage in earlier chapters, with a few
exceptions:
Total Savings = SPCD = Personal, corporate and depreciation savings
Loanable Funds(LF) = Total savings and Foreign borrowing (FB)
X = exports
M= Imports
PR = Prime Interest rate
Cons.Bor. = Consumer borrowing
The dynamic effects simulations are all based on the empirical model
estimated in Chapters 4–17. Clearly, the 33 period simulations suggest
that the structure of the American economy is such that both fiscal and
monetary stimulus programs are unlikely to be successful, and more likely
than not will have net negative effects. This, of course would change
if “accommodating” monetary policy did its job. But if accommodating
monetary policy worked, we would not have found the strong, statistically
significant crowd out effects so commonly found in Chapters 4–17 mod-
els. It is not clear why accommodating monetary policy does not seem to
work. More work remains to be done on this topic.
368
Table 18.1 Dynamic Effects of Stimulus Programs on the GDP

18 DYNAMICS
Time Per. $400 Increase in Gov’t. $400B decrease in Taxes $400B increase in M1 $800B Increase, 1/2 $800B Increase, 1/2
Spending Gov’t.Sp., 1 /2 in Taxes Gov’t.Sp., 1 /2 Taxes and
$800B increase in M1
1 Period Perm. 1Period Perm. 1Period Perm. 1 Period Perm. 1 Period 1 Permanent
Initial Conditions: GDP Without-Stimulus (Billions)
0) $18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000
GDP With Stimulus
1) 18,000 18,000 18,000 18,164 18,000 18,000 18,000 18,000 18,000 18,000
2) 18,091 18,091 17,902 17,902 18,055 18,055 17,991 17,991 18,099 18,099
3) 17,881 18,052 17,821 17,770 18,014 18,098 17,702 17,382 17,738 18,017
4) 17,691 17,987 17,801 17,716 17,938 18,082 17,492 16,950 17,396 17,867
5) 17,639 17,959 17,824 17,736 17,920 18,073 17,463 16,895 17,429 17,846
10) 17,721 17,996 17,843 17,776 17,954 18,078 17,546 17,122 17,540 17,933
20) 17,700 18,017 17,848 17,818 17,957 18,080 17,549 17,184 17,559 18,002
30) 17,675 18,025 17,844 17,834 17,964 18,092 17,520 18,186 18,546 18,051
33) 17,669 18,027 17,844 17,838 17,966 18,095 17,513 17,187 17,543 18,063
Table 18.2 Dynamic Effects of Stimulus Programs on the GDP (Detailed effects on other key economic variables after 33
periods)
Variables GDP T Total G Total UNEM% INFL% PR% Tot.Saving TDEF GDEF M X Cons. Personal Investment M1
PCD = LF-FB Bor Saving
Initial Conditions 18,000 3,600 3,600 5.00 2.00 3.00 2,568 0 0 3,600 3,100 500 275 2,790 1,000
Pre-Stimulus
(Period 0)
Stimulus Results After 33 Periods:
programs:
$400 Govt. 17,669 3,639 3,596 4.91 5.95 4.78 2,581 18 (19) 3,584 3,073 456 260 2,771 1,000
Spending Incr. (1
Yr. Only)
$400 Govt. 18,027 3,725 4,006 4.88 4.19 4.08 2,393 305 587 3,616 3,100 426 286 2,474 1,000
Spending Incr.
(Permanent)
$400 Tax Cut 17,838 3,230 3,596 4.83 3.56 3.88 2,236 (32) 335 3,598 3,094 413 380 2,408 1,000
(Permanent)
$400 M1 Incr 18,095 3,608 3,609 5.16 (0.93) 1.56 2,636 (62) (61) 3,636 3,132 447 326 2,840 1,400
(Non-Accom,)
(continued)
18.1 INTRODUCTION
369
370
18 DYNAMICS
periods)
$400B Tax Cuts, 18,063 3,372 4,020 5.00 (0.09) 2.09 2,174 174 822 3,691 3,161 239 486 2,193 1,800
$400B Govt. Spend-
ing Inc., $800B
Increase in M1 (All
Permanent)
$400B Tax Cuts, 17,507 3,269 3,592 4.73 7.54 5.67 2,248 (12) 317 3,583 3,067 368 385 2,389 1,000
$400B Govt.
Spending Inc., No
Accomodating M1
(T Permanent, not
spending which is 1
year only)
periods)
$400B Tax Cuts, 17,705 3,287 3,611 5.05 1.69 2.81 2,361 (111) 218 3,660 3,134 270 459 2,491 1,800
$400B Govt. Spending
Inc., $800 (non-
Account) Incr. in M1
(All Permanent, except
G Spending which is 1
year only)
18.1 INTRODUCTION
371
CHAPTER 19
Summary and Conclusions (Production Side

of the NIPA Accounts)
Table 19.1 provides a summary of the variables found significant enough

for use in the 38 behavioral equations in the model. Findings for key
variables in each model were found robust to time period sampled and
usually to choice of regression tool: OLS or strong-instrument 2SLS. Key
results were also robust to changes in model specification (other vari-
ables included in equation), provided variables removed were not the key
determinants themselves. (Key variables tend to be somewhat correlated
among themselves, so eliminating one of them tends to create a “left out”
variables problem, causing coefficients on remaining variables to jump
around. This is typically most pronounced for left-out variables that have
the strongest impact on the dependent variable.)
When looking at the different components of consumption (dur-
ables, nondurables, and services), additional variables were found to
be determinants of one or more of them: the level of investment in
housing, the price of housing, mortgage interest rates, demand for
durables (negative determinant of demand for nondurables and ser-
vices), and demand for nondurables (negatively related to demand for
durables).
There are eight separate consumption and nine investment models; not
all variables listed above were found to be determinants in every one,
though all were tested in each model. The lists above do not detail the
specific lag level found significant. See the summary of model statistical
results (Section 1.4) for this level of detail.

DOI 10.1007/978-3-319-50681-4_19
374 19 SUMMARY AND CONCLUSIONS (PRODUCTION SIDE OF THE NIPA ACCOUNTS)
Table 19.1 Determinants of consumption, investment, government spending,

interest rates, and exports
Consumption Investment
Disposable income (Y-TT ) Samuelson’s accelerator (ACC)

Deficit variables (TT , GT& I ) Deficit variables (TT , GT& I )
Wealth (DJAV) Tobin’s q (DJAV)
Interest rates (PR or r) Interest Rates (PR or r)
Exchange rates (XRAV ) Exchange rates (XRAV )
Population size (POP) Population size (POP)
Consumer confidence (ICC–1 ) Profits (PROF)
Pop. young/old ratio (POP16 ) Depreciation allowances (DEP)
Consumer borrowing (CB or B2 ) Business borrowing (IB(–1) )
Money supply (M2, M2AV ) Capacity utilization (CAP–1 )
Personal savings (SP )
Government spending Export demand Prime interest rate (Taylor

rule model)
GDP–2
Unemployment rate GDP(Trad. Ptnrs-2) Inflation rate
Pop growth Exchange RateAV Unemployment rate
Vietnam U.S. imports M1 Money Supply0
Reagan Mil. Build up Prime Interest RateAV-1-2 M1 Money Supply–1
Iraq Mil. Build Up U.S. Inflation RateAV-1-2 Gov’t. deficit (crowd out test)
Personal savings only was found to be a determinant of consumer

borrowing, not consumer spending.
Conspicuously absent from all 17 consumption and investment equa-
tions except the consumption services residential housing demand equa-
tions are current values of the M1 or M2 money variable. The only
other money variable we found affecting either consumption or investment
models directly was the average value of M2 for lagged years 2–4. Hence,
only that variable appears in consumption equations. Even here, only the
savings (non-M1) components of this lagged variable made a difference,
indicating growth in liquid asset wealth in prior periods. Indirectly, M1
made some difference since both consumption and investment were signi-
ficantly affected by either current or (twice) lagged interest rates, and M1
money was one of the prime interest rate’s determinants in our interest
rate models. But the statistical evidence indicates the effect of interest
rates is a minor one in terms of its contribution to explained variance:
SUMMARY AND CONCLUSIONS (PRODUCTION SIDE OF THE NIPA ACCOUNTS) 375
Fernandez-Villaverde (2010) also found little impact for the money vari-
able in his research, noting “I must admit that I am myself less than totally
convinced of the importance of money outside the case of large infla-
tions” (Fernandez-Villaverde 2010). Our own Taylor rule model indicated
the current year liquidity effect of increasing the money supply was to
lower the prime interest rate, but that the inflation effect 1 year later fully
restored the prime rate to its previous level.
For the equations representing the individual components of invest-
ment, three additional determinants were found to affect the demand for
residential housing: consumer borrowing, the M1 level and (negatively)
the price of housing. Inventory investment was affected by two addi-
tional variables: (negatively) related to same period growth in consumer
spending, and positively related to prior year growth in GDP.
In the prime interest rate model, current period growth in M1 was
negatively related to the prime rate, as expected, but the same growth in
M1 lagged one period had a slightly larger positive effect, thus accounting
for both the liquidity and inflation effects expected with changes in the
money supply. The government-deficit variables were included as a test of
the oft-stated hypothesis that the way crowd out affects the economy is
through its effect on interest rates, We found no such crowd out effect on
the prime rate, which is the interest rate found most systematically affected
the GDP, consumption, and investment. This is perhaps not surprising
since the prime rate is not a market determined rate in the U.S., it is an
administered rate changed by the banking community to reflect changes
in the federal funds rate (also an administered rate).
For total government spending (including transfers), the variable best
explaining the endogenous part was found to be the unemployment rate.
By comparison, government spending for only goods and services was
more dependent on lagged GDP than on unemployment. More exogen-
ous effects included population growth, the Vietnam and Iraq military
build ups, and the 2008 financial crisis.
The exports demand model (unexpectedly) showed U.S. demand for
imports to be overwhelmingly the most important variable determining
the level of foreign demand for U.S. exports the same year. One explan-
ation for this is that foreigners must obtain U.S. currency to buy U.S.
exports, which, in the main, they get from sales of their goods to the
U.S. Another possible reason (probably a component part of the first
explanation) is that trade is so internationalized that much of what any
country exports is assembled from parts or other resources imported from
376 19 SUMMARY AND CONCLUSIONS (PRODUCTION SIDE OF THE NIPA ACCOUNTS)
abroad. As expected, high exchange rates (expensive U.S. currency) were

negatively related to export demand, as was the U.S. inflation rate. Also
unexpectedly, the U.S. prime rate was found positively related to export
demand. It is not clear why the relationship is positive, though possibly it
is because increased export demand increases GDP, reducing unemploy-
ment and increasing inflationary pressures, both of which are “Taylor rule”
reasons for the Fed to increase interest rates. Hence, there may be a cause
and effect issue here that requires further work on what to include on the
causal side of this model.
For a list of determinants of the other 11 equations in the model, see the
specific section describing their testing, or Section 1.4, which summarizes
the statistical results, including variables found to be determinants, for
each equation in the larger model.
19.1 OTHER MAJOR FINDINGS
1. In out-of-sample tests, Cowles structural models outperformed both

DSGE and VAR models.
2. Theory suggests that positive changes in the money supply should
stimulate the economy, and that when fiscal policy is used, if mon-
etary policy is accommodating, it should compensate for any crowd
out effects engendered by the fiscal policy.
3. This study did not find that changes in the money supply had a major
effect on the economy. One hypothesis as to why (untested) has to
do with where the open market mechanism for expanding the money
supply places the new money it generates. It may be that when the
Fed buys government bonds in the open market to increase money
in circulation, most of the new money is bought by credit market
dealers/investors. These dealer/investors wish to convert govern-
ment bonds they are holding to cash, so they can buy some other
security which currently now seems to offer a greater return.
4. The (second) dealer/investor this first dealer/investor buys from
generally is only selling the security because (s)he wants to
buy another security, one with a higher expected yield. A third
dealer/investor, from whom the second will buy securities, is gener-
ally selling for the same reason, etc.
5. The net effect is that most “new money” stays in the securities world,
chasing around securities, causing their prices to go up, causing the
19.1 OTHER MAJOR FINDINGS 377
markets to rise. This new money is not used to raise the GDP, i.e.,
buy real goods and services.
6. Securities sold by banks to the Fed for increased reserves is an excep-
tion. The increased reserves are generally used to give loans that
will be used to buy real goods and services. This fits with our find-
ings that changes in the money supply were significantly related to
spending on residential housing.
7. A new way of achieving the neoclassical synthesis is introduced using
Fisher’s income equation of exchange (MV = PY), instead of the
Phillips curve to meld together Keynesian short-run and neoclassical
long-run mechanics. The method shows that Keynesian fiscal policy
shifts the aggregate demand curve through its effects on velocity, a
key variable in Fisher’s equation.
PART II
Income Side of the NIPA Accounts

CHAPTER 20
Determinants of Factor Shares
20.1 INTRODUCTION, THEORY OF FACTOR SHARES,

AND SUMMARY OF FINDINGS
This chapter identifies variables related to variation over time in labor,
profit, rental, and interest income in the U.S. Both the percentage share of
national income received by factors and the levels of income are examined.
This is an area in which surprising little empirical work has been done,
except on labor’s share. This chapter is different from Piketty’s (2014)
work, which focuses on wealth and on the inequality in income received
by specific deciles of the income distribution, whatever their source of
income. There is some overlap since upper-income deciles receive more of
their income from profit, interest, and rental income than do lower deciles.
The idea for this chapter was provided by Nobel Laureate Robert
Solow. In agreeing to review an earlier draft of the 45-equation model
of the product side of NIPA developed presented in previous chapters,
Solow indicated he was currently working on the factor shares problem.
This led to the realization that product side-only models, characteristic
of econometric models of the macroeconomy, are incomplete. There was
a need to undertake an income-side project like this to help address that
incompleteness. After all, NIPA is a two-sided balance sheet.
For each of the four types of factor income studied, two models are
developed. One presents findings on the determinants of levels of real

DOI 10.1007/978-3-319-50681-4_20
382 20 DETERMINANTS OF FACTOR SHARES
income for the factor, the other presents findings on variables related
to variation in the factor’s share of national income over time. These
four factors’ incomes, combined with proprietor’s income, total national
income. Proprietor income is taken as a given because of the difficulty
separating its profit and labor income components.
The focus of this chapter is on the distribution of income, not the pro-
duction of income. Total income is determined by how much product
is produced. In the best year-to-year explanatory models, production of
goods and services is largely a function of the demand for them. In the
long run, technological progress is the key. This chapter contains 11 addi-
tional equations to describe how the distributional of income generated
producing the GDP is determined, given the level of production. Eight
are behavioral and three are identities.
The eight behavioral equations are developed in Section 20.4.
Section 20.4.1 identifies the determinants of labor’s level and share of
national income, Section 20.4.2 does the same for profit’s share and level.
Sections 20.4.3 and 20.4.4 deal with rental and interest income in the
same way. In each part, results obtained are tested exhaustively for robust-
ness over time of results and in different models, to ensure as best as
possible that results for any particular variable thought to be a determ-
inant of factor shares are not merely idiosyncratic to the particular time
period or model tested.
Besides the eight behavioral equations, we include three standard eco-
nomic identities connecting the income and product sides of the GDP to
each other, and to national income:
GDP = consumption + investment + government purchases + net exports

GDP = depreciation + indirect taxes + labor income, profit income + rental
income + interest income + proprietor’s income
National Income = labor income + profit income + rental income + interest
income + proprietor’s income
Section 4 is preceded by this introductory section, a literature review

(Section 2) and a discussion of methodology (Section 3).
Summary of Findings
This study finds at least 48%, and perhaps all, the long-term decline in
labor’s share of national income since 1970 was due to the growth of
U.S. profit income from foreign operations. The growth of profit’s per-
centage share reduced labor’s percentage share of national income, but
20.1 INTRODUCTION, THEORY OF FACTOR SHARES, AND SUMMARY OF FINDINGS 383
not the level of labor income. It was the result of increased investment by
U.S. companies in productive capacity overseas. The rest of the long-run
decline was due to a long-term slowdown of productivity growth. Sub-
stantial short-run changes in labor’s share around these long-term trends
are found to be common, driven mostly by Keynesian changes in demand.
Capital is relatively fixed in the short run, and labor is not. Therefore,
increases in demand are initially met by short-run increases in the labor
force. With capital constant, this increases labor’s share.
The decline in labor’s share due to growing foreign investment was pre-
dictable. When a new factory is built (or bought) in a foreign land with
a domestic country’s investment, the profits flowing back home and are
included in the domestic country’s national income, increasing capital’s
share. Labor income is counted in the foreign country’s national income,
since that’s where it is generated. Hence, other things equal, increased for-
eign investment over time by U.S. firms should lead to a larger share of income
for capital, and a lesser share for labor in the U.S.
The major determinants of profits’ growing share were rising profits
from foreign operations, a cheaper dollar making U.S. goods more
competitive, and increases in labor productivity, which appears mainly
to benefit profits. Rental income’s major determinant was house prices.
Growth in housing prices was found to decrease rent’s share, presumably
indicating a shift in housing preferences toward home ownership. Interest
income was driven by prime and bond interest rate levels and the level of
employment relative to GDP (growing employment stimulates borrowing
among those who can now afford to).
20.1.1 Trends in Levels and Shares of National Income

Table 20.1.1.1 shows indexes of growth in the level of real labor and
profit income relative to national income for the 1929–2010 period
(1960 = 100).
During the great depression decade of the 1930s, the percentage drop
in labor income was significantly smaller than for profit income, and it
rebounded more quickly. By 1940 labor income was 18% higher than in
1929, profit income was up only 3%. However, during the next decade,
which included the World War II years and afterward, profits rebounded
strongly due to the war stimulus, growing over 100% between 1940 and
1950; labor income grew only 50% during the same period.
From 1960 to 2000, growth in profit income lagged behind growth in
labor income. However, during 2001–2010, profit growth far exceeded
Table 20.1.1.1 Index of real profit and labor income growth 1929–2010
(1960 = 1.00)
Labor income Profit income National income
1929 0.33 0.37 0.37

1930 0.31 0.25 0.31
1940 0.39 0.38 0.38
1950 0.63 0.82 0.62
1960 1.00 1.00 1.00
1970 1.58 1.10 1.49
1980 2.15 1.59 1.98
1990 2.87 1.98 2.72
2000 4.07 3.06 3.92
2010 4.49 5.77 4.51
Sources: EOP (1963), Table C11; (1974), B3; (2010 and 2012), B28, B3
growth in labor income. The profit index grew from 3.09 to 5.77; the
labor index only grew from 4.07 to 4.49. Most to the profit growth
was in 2003–2005, when the index grew from 3.40 to 5.77. However,
profit growth was not because labor income declined; it just grew slower.
The labor income index grew from 4.07 to 4.49 for the whole decade
and achieved most of its growth during 2005–2007, growing from 4.23
to 4.40.
The overall picture shown by Table 20.1.1.1 is one in which the level
of labor’s income grew more rapidly than profits coming out of the
depression, and in the more normal times which characterized the over-
all 1960–2000 period. By comparison, in boom periods characterized by
the World War II decade and the 2001–2010 decade, particularly the
super boom years of 2006–2007, profit income grew more rapidly than
labor income. But profit income did not grow by redistributing labor
income. Labor income also increased during both boom periods, just not
as fast.
Table 20.1.1.2 shows labor and profits’ share of national income, rather
than their level. It indicates that both labor’s and profits share of national
income grew during the recession decade 1930s, because the shares of
other types of income fell more precipitously. Labor and profit income
shares grew again during the boom decade 1940 and 1950. Labor’s share
increased 1950 until 1980, increasing from 64% to 68%, but since then has
declined to 62%. Profits share declined 1950–2000 but increased during
the boom decade 2001–2010.
Table 20.1.1.2 Nominal income levels and shares for labor, profit, rent, and
interest 1930–2010
Labor Labor Profit Profit National Rental Interest

income share of income share of income share of share of
Natl. Inc. Natl. Inc. Natl. Inc. Natl. Inc.
1930 46.8 0.62 6.6 0.09 75.7 0.063 0.079

1940 52.1 0.64 9.1 0.11 81.6 0.036 0.055
1950 154.2 0.64 35.7 0.15 241.9 0.037 0.023
1960 296.4 0.63 53.1 0.11 473.9 0.034 0.022
1970 617.2 0.66 82.5 0.09 929.5 0.023 0.042
1980 1647.6 0.68 201.4 0.08 2433 0.012 0.075
1990 3326.3 0.66 434.4 0.09 5059.5 0.010 0.088
2000 5788.8 0.65 819.2 0.09 8938.9 0.024 0.060
2010 7971.4 0.62 1800.1 0.14 12,840.1 0.027 0.044
Source: EOP (2012, 2010) Table B28; EOP(1963), Table C-11
Hence changes in shares and levels of income from decade to decade

are not in one-to-one correspondence: In all decades, levels of income for
both labor and profits increased, shares changed as follows:
• In the 1930s–1940s shares increased for both labor and profits

• In the 1950s–1970s shares increased for labor, decreased for profits
• In the 1980s shares decreased for labor, increased for profits
• In the 1990s shares decreased for labor, constant for profits
• In the 2000s shares decreased for labor, increased for profits
In general, the percentage increases in the level of income for profits was
greater in boom periods. The percentage increases in the level of income
for labor was greater normal times and rebounding from the depression.
It is much harder to find a pattern for their factor shares. This suggests the
factors driving changes in levels from decade to decade are, at least in part,
different than the factors driving changes in shares.
Rental and interest shares of national income have also varied consid-
erably over the decades, but the variation is not so consistently related to
just the general condition of the economy.
20.1.2 Should Capital’s and Labor’s Shares Be Constant Over Time?

The data above indicate factor shares are not constant over time. They
may vary for unpredictable, noneconomic reasons, like wars. Business cycle
factors may also cause variation in factor shares. As demand increases,

increases in production result mainly from increased labor usage, since
capital is relatively fixed in the short run. In the long run, a return to
factor usage that represented profit maximization levels before the demand
increase may occur. Hence, factor shares may return to some constant ratio
in the long run, as long as relative marginal productivities of factors stay
the same as before demand increased.
In the long run living standards grow only because of technological
innovation, Solow’s “g” (1956), which increases capital or labor pro-
ductivity. Suppose that prior to a technological innovation, factor and
product markets were in equilibrium. Let the unit real cost of capital
(=MPK) and the unit real cost of labor (=MPL) be the same. Suppose
a mechanical technological innovation then occurs that doubles the out-
put of machines, without requiring any change in the amount or quality
of labor used per machine. We would show that by an upward shift of
the marginal productivity of capital curve (MPK), as in Graph 1A below,
where K1 was the initial pre-innovation equilibrium level of capital. Profit
maximizing businesses would then have incentive to increase the level of
capital used to K2 . But this increase in machine productivity also means
each worker’s output doubles per unit of time worked, doubling labor
productivity.
Hence, the marginal product of labor curve also shifts upward,
providing an incentive to businesses to increase labor, as shown in
Graph 20.1.2.1. Labor usage will increase until the old marginal pro-
ductivity of labor (= old marginal productivity of capital) is restored. The
old ratio of marginal productivities was given by the ratio of units of cap-
ital to units of labor used. Though the technological innovation initially
affected only the productivity of machines, profit maximization requires
adjusting the quantities of both factors to keep the marginal productivit-
ies of the two factors the same, and equal to marginal costs. This requires
the same proportional increase in use of both factors after the innovation
is adopted, though one factor (machines) may be increased before the
other (labor), increasing payments to the owners of capital, without redu-
cing payments to labor. Hence, capital’s share or national income may
increase in the short term, but will decline to old levels as additional labor
is brought on. Factor shares remain unchanged in the long run, though
they may vary in the short (Graph 20.1.2.1).
Suppose the technological innovation raised one of the factor marginal
productivity curves without changing its slope, but raised the other one
Graph 1A Graph 1B
MPK2 MPL2
Real cost Real

of K = r wage = w
MPK1 MPL1
K1 K2 L1 L2
Graph. 20.1.2.1 MPK and MPL curves – constant slopes

20.1 INTRODUCTION, THEORY OF FACTOR SHARES, AND SUMMARY OF FINDINGS
387
and changed its slope. In this case, the marginal productivity-equating

increases in factors usage would be different. For example, if the MPK
curve shifted upward but retained the same slope, while the MPL curve
shifted upward and equivalent amount, but became steeper (shift from
MPL2 to MPL3 in Graph 20.1.2.2). Growth in labor used would be less
than proportional to growth in capital because its marginal productivity is
falling faster, cutting labor’s share as long, as r and w remain competitively
set at their MPK and MPL, as shown in Graph 20.1.2.2. Such a situ-
ation might occur when new, more productive machinery is introduced for
which less labor is required so labor’s marginal productivity now declines
faster than with the old machine.
Alternatively, suppose the adaption of machine technological change
left the marginal product of labor curve unchanged, but led to demand
for increased wages because the companies adopting the change were now
doing better. If so, changes in relative factor prices will also change the
ratio with which labor is used with capital, most likely changing factor
shares. This study in Sections 1.1 and 1.2 find that increases in labor’s
real wages, ceteris paribus, lower labor’s share of national income and raise
profits share. A similar result was found by Karabarbounis and Neiman
(2013). One way this may occur is shown in Graphs 3A and 3B, where
the gain in productivity of labor is accompanied by an increase in the real
wage. Hence the long-run effects of technological change may not be
neutral if either the marginal productivity curve or the factor payment
ratios are disturbed by adoption of the innovation (Graph 20.1.2.3).
Over the long run, Solow (1956) has shown that national income can
only grow due to technological progress. However, there is evidence that
as growth occurs, it may affect factor shares in different ways. Exactly how
depends on the relative response of different factor prices and the stability
of relative marginal productivity relationships. Hence, where factor shares
are likely settle in the long run, after a technological progress shock, may
not be a question theory can answer definitively; since there are multiple
possibilities. It may be strictly an empirical question. The empirical work
on the Cobb-Douglas production function has indicated a fairly stable
share of national income for labor at about 67% over the long run, with
year to year deviations ultimately returning to this long run equilibrium.
In this sense, the picture we painted in Graphs 1A and 1B may best reflect
the dominant way in which microeconomic factors, particularly profit max-
imizing, determines the levels of capital and labor usage and factor shares
that we observe in the real world.
Graph 2A Graph 2B
MPK2 MPL2
MPL3
Real cost Real
of K = r wage = w
MPK1 MPL1
K1 K2 L1 L3 L2
Graph. 20.1.2.2 MPK and MPL curves – varying slopes

20.1 INTRODUCTION, THEORY OF FACTOR SHARES, AND SUMMARY OF FINDINGS
389
390
Graph 3A Graph 3B
Real
wage = w2
MPK2 MPL2
Real cost Real
of K = r wage = w1
20 DETERMINANTS OF FACTOR SHARES
MPK1 MPL1
K1 K2 L1 L3 L2
Graph. 20.1.2.3 MPK and MPL curves – non – market wages

That said, for the U.S. at least, a long-term change may be occur-
ring which lowers labor’s share of national income, though not its level
of national income. Fifty years ago the U.S. made little foreign invest-
ment; little of the profit component of national income was derived from
foreign operations. In a simple world of two factors, labor and capital, if
investment is only in domestic industries, generally any investment that
increases the level of returns to capital also increases the level of returns to
labor. This is because it takes both capital and labor to make a new factory
produce anything. The increases in both are included in national income.
Even investment that initially only raises capital income eventually raises
labor income (Graphs 1A and 1B).
With foreign investment, the new factory is built (or bought) in a for-
eign land; the profits flow back home and are included in the domestic
country’s national income, increasing capital’s share. Labor income is
counted in the foreign country’s national income, since that’s where it
is generated. Hence, other things equal, increased foreign investment over
time by U.S. firms should lead to a larger share of income for U.S. capital,
and a lesser share for U.S. labor.
For a long time this may reduce labor’s share in the U.S (and other
countries with large foreign investment programs). Our calculations in
Section 3.1 indicate about half of all the decline in Labor’s share since
1980 has been due to growth in profits due to foreign investment, without
the simultaneous growth in labor income that would have occurred if the
investment had been domestic. The decline in labor’s share was not caused
by a decline in labor income in the U.S. (it has grown). It is due in large
part to the much faster growth in profits, due to the rapid growth of profits
on foreign operations.
The opposite is true in the country receiving U.S. foreign investment.
Its national income will only be increased by labor’s income from the new
factory, not by the income earned by the factory’s U.S. owners. Hence,
ceteris paribus, we should see increases in labor’s share of national income
in countries whose growth is financed by foreign investment.
Even so, in the long, long run, the countries now receiving U.S. for-
eign investment will become more and more developed, with large pools
of their own investment capital, and turn, use part of it to make foreign
investments. When the U.S. receives some of this investment, e.g., when
Korea builds a factory in the U.S., labor’s share in U.S. national income
should grow, without growth in the profits portion. This may ultimately
restore the old Cobb-Douglas equilibrium of factor shares.
A Note on Outsourcing
With foreign investment, the discussion above contemplates a new factory
being built (or bought) in a foreign country. This decreases labor’s share,
but not its level of national income. No domestic workers lose their jobs.
At the macro level, this is what seems to have been going on in the U.S.
since 1980. Outsourcing is something different. If a firm closes a domest-
ically located factory and builds or buys a comparable factory in a foreign
country, then labor’s share and level of income will decline since less labor
will be needed domestically.
20.1.2.1 Relevance to Piketty Concerns

Piketty (2014) anticipates growing inequality in the twenty-first century
as long as real return to new capital (r) exceeds the rate of growth of the
economy as a whole (g). Since incomes of capital and labor are taken to
equal total income, and total income equals GDP, r > g is taken to imply
capital’s income is growing faster than labor’s. As Mankiw (2015)] has
pointed out, Piketty’s conclusions are not consistent with what is argu-
ably our best way of understanding of how the economic growth process
occurs: Solow’s growth model. We elaborate on Mankiw’s basic points in
this regard by noting
1. In the simplest of Solow’s (1956) models, with the potential for

capital growth, but no population growth or technological progress,
Solow shows us that because output (income) is subject to dimin-
ishing returns, savings is just a fraction of income, and depreciation
is not subject to diminishing returns, capital increases at a declin-
ing rate as it grows, but depreciation does not. Hence, no matter
how much the capital stock grows, eventually its growth only equals
depreciation in the same period, and no further growth takes place.
At that point, the system enters a steady state, and whatever capital
and labor’s shares are at that point, they grow no further.
Here is where the disagreement with Piketty comes in. Though
g = 0, there is no reason to think the return on capital (r) is also
zero. If a unit that depreciated to uselessness this year was being
used, it is only because its marginal productivity was greater than
zero. Since it has a positive marginal product, it will be replaced
until the marginal cost of capital equals its nonzero marginal pro-
ductivity. Capital’s share is r per unit of capital used, but since capital
has reached steady state, no further growth in capital’s share can take
place, even though it remains greater 0, contrary to Piketty’s spec-

ulation. Piketty (2015) later acknowledged r is likely to be greater
than g in steady state in most economic models.
If we add technological progress (g) to Solow’s model, the eco-
nomic growth rate, g, becomes positive. The impact of technological
progress is to initially raise the marginal productivity of capital (or
labor, depending on the particular type of innovation involved),
affecting income distribution for both labor and capital as shown
earlier in Graphs 20.1.2.1–20.1.2.3, i.e., not by considerations of
whether r is greater than g. Suppose technological progress is 2% a
year. If pre-innovation marginal productivity of capital was 5%, when
it is replaced, the productivity of new machines will be 7%. By Graph
1A, profit maximization should lead to capital growth until the mar-
ginal product falls back to 5%. The growth in capital stock means
more total income for capital than before the innovation. For reas-
ons shown in Graphs 1 and 2 above, this also means labor’s income
will increase proportionally, unless the innovation not only raises
marginal productivity curves, but also changes their relative elasti-
cities. Hence, absent elasticity issues, income distribution, i.e., factor
shares, will not change. Noncompetitive changes in factor prices can
cause the same problem.
2. Further, Cobb and Douglas’s empirical work have shown us that the
long-term behavior of the U.S. economy is characterized by constant
factor shares, something on the order of 1/3 for capital and 2/3
for labor. Even significant changes in the ratio of the units of labor
to the number of units of capital does not change this distribution.
Changing the ratio of factors used in one direction changes marginal
productivities in the opposite way, just enough to leave total factor
shares unchanged.
Hence the decade-by-decade variation in factor shares we see in
the data probably are, in large part, just reflections of adjustment
to technological change or, as we will show when analyzing labor’s
share, in the short run, more Keynesian factors affecting aggregate
demand. For example, we show below that short-term increases in
aggregate demand typically bring about an increase in the employ-
ment/GDP ratio, reflecting the fact that in the short run capital
is relatively fixed. This means short-run output increases must come
mainly from hiring more labor, increasing in labor’s share of national
income. For the same reason, we expect labor’s share to fall back to
old levels if the increase demand for GDP persists into the long run,
warranting capital expansion.
The time it takes to adjust to technological innovations can
cause similar cyclical swings. Implementation first boosts one factor’s
share, then increases the other factor’s usage enough to restoring the
old factor share ratio equilibrium.
Permanent, long-term changes in factor shares depend on
changes in the relative elasticity of marginal product curves over
very long periods of time. How long? Even for the 50-year period
studied in this chapter, 1960–2010, we did not have to factor this
in to account for most variation in factor shares. About 85% of
the variation in labor’s share and 93% of the variation in profits
share is shown to occur from cyclical economic factors driven by
changes in the level of aggregate demand, or the growing presence
of profits from foreign operations in profit’s share of national income
(occurring without an offsetting decline in labor income). Labor
productivity was also a factor, positively affecting both labor and
profit’s shares.
20.2 LITERATURE ON FACTOR SHARES

There are a large number of studies of the determinants of factor shares,
mostly focused on labor. Some more widely read studies are reviewed
below.
Bentolila and Saint-Paul (2003)

Notes that the U.S. has undergone sizable short-run fluctuations in labor’s
share, around a mild downward trend (which this chapter also finds). It also
finds that correlation between changes in wages and changes in labor’s share
“is not tight” across countries, though wage levels are sometimes used as
a proxy for labor’s share. Using a panel regression of 12 OECD countries
data for 1972–1993, findings indicated reductions in capital stock could
have a positive effect on labor’s share if labor and capital were substitutes,
but a negative effect if they were compliments in a particular industry. The
sum of industry results determines the effect. Findings also indicated growth
in total factor productivity had a negative impact on labor share, as did
employment growth. By comparison, this study finds positive effects for the
employment factor, and positive, but not generally significant effects for a
labor productivity variable. Bentolila and Saint-Paul finds union bargaining
power positively and significantly effects labor share. This chapter also
20.2 LITERATURE ON FACTOR SHARES 395
finds a positive relationship, but often insignificant, or marginally significant

at best.
Gollin (2002)
Finds wide ranges of labor shares among counties, but mostly due to inac-
curate methods of calculation. When calculated correctly, most counties
labor share falls within a 65% – 80%. The low end of this range is roughly
consistent with this chapter’s finding for the U.S.
Guscina (2006)
Examines causes of declining labor share in 18 OECD industrialized coun-
tries, 1960–2000, using a panel regression. Post-1985 regression results
indicate causes of declining labor share included factor biased technological
progress e.g., information technology development after 1985, and negat-
ive effects of globalization, by reducing labor bargaining power. Regression
results for pre-1985 data indicated positive effects on labor share of (lagged)
productivity growth and employment protection measures and negative
effects of globalization (defined as total trade/GDP). Robustness testing
was extensive: variables were tested in various models and all tests were in
levels and first differences for comparison.
(This study has somewhat similar results for globalization, general pro-
ductivity growth and %unionized. % unionized is similar to Guscina’s
“employment protection” variable.)
Hein (2009)
This is a theoretical, Post-Kaleckian model, not an empirical study. It con-
cludes the most likely outcome of financialization is increasing shareholder
power causing economic contraction. “Financialization” is defined as the
relationship of financial to nonfinancial sectors. The model suggests object-
ives and constraints of firms may be affected by growing financialization:
rising shareholder power may subordinate management’s and workers’ pref-
erence for (long run) growth of the firm, to shareholders’ preference for
(short term) profitability. Greater shareholder power may mean increasing
dividend payments, share buybacks etc., which restricts the availability of
finance for firms’ real investment projects. Distribution of income may be
affected due to changes in power relations between shareholders, managers
and workers, which will then feedback on investment and consumption.
This may lead to a contractive regime, in which higher interest and dividend
payments to rentiers have a restrictive effect on the rates of capacity utiliz-
ation, profit and capital accumulation. These distribution of income results
seem at odds with Piketty [11] who finds growth in maldistribution mainly
caused by growth of labor income at the very top. This model does suggest
slower capital accumulation will occur as a result of financialization. This
is consistent with this study’s finding that labor’s declining share may be
related to declining labor productivity growth.
Jaumotte and Tytell (2007)

Globalization has had some negative impact on labor’s share, but techno-
logical progress, especially in the information and communications sectors
has been a bigger negative factor, particularly on the labor share of unskilled
labor in 18 advanced countries, 1982–2002. This study’s finding on global-
ization are the same, but did not test the I&C sector relationship. Figure 1,
presented earlier, suggests this may be a short-run adjustment problem.
ILO (2011)
The ILO paper finds labor’s share is declining because financialization has
reduced the bargaining power of labor. It finds globalization has increased
the possibilities for investment in (physical or financial) capital geographic-
ally, resulting in the erosion of labor and management influence in favor
of shareholder interests, often in the form of higher dividends reducing
funds for investment and expansion. Panel data of 16 advanced economies
1981–2003 are examined. Key regression results are that both global finan-
cialization and increasing international trade have negative effects on labors
share, but that government consumption and trade unions have a positive
effect. This study’s results for foreign profits, by which we measure globaliz-
ation, and to some extent financialization, since it represents earlier foreign
investment, says the same thing, as do our unionization results, though not
always at levels of statistical significance.
Imf (2007)
This panel regression of 18 advanced OECD countries using 1982–2002
data, is one of the more widely read studies of labor’s share. Findings indicate
labor’s share significantly related to exports (-), Imports (+), Labor/capital
ratio (+) Offshoring (-), immigration (-) and Information & communica-
tions technology capital (- short term, + long term). (The labor/capital ratio
is similar to this study’s employment/GDP ratio, whose positive finding
may be explained by capital being relatively fixed in the short run, resulting
in most short-term GDP increases occurring from increased employment.
The findings for exports and imports are also consistent with this chapter’s
findings for a related variable, the positive effect of the real exchange rate
on labor’s share: a strong exchange rate will reduce exports and increase
imports.
Stockhammer (2012)
Shows wages in OECD countries, and some developing countries, have
fallen the past 25 years. Statistical tests indicated the decline was attributed
to strong negative effects of globalization, financialization (growth of the
finance industry), and welfare state retrenchment. Technological change is
20.3 METHODOLOGY 397
found to positively affect labor’s share in developing countries, but negat-

ively in advanced economies. (Similar to this study’s findings for all variables
except financialization, which this chapter finds positively related to labor’s
share.) Method: panel regression, with robustness tests of levels vs. first
differences; 2SLS vs. GMM.
Piketty (2014, 2015)

The previous studies reviewed focus on the declining labor share of national
income and its causes. This is not Piketty’s main interest, which is wealth, We
examine his work here because, more than any other recent work, his has
drawn attention to the issue of labor’s share of income simply by addressing
the related issue of the share of wealth owned by the top few. His focus
is on wealth distribution, not income distribution. He argues that r>g has
meaning for inequality of wealth distribution, which is the subject of his
book. Piketty notes that in a representative agent framework, a family need
reinvest only the fraction g/r of its capital income to ensure its capital stock
will grow at the same rate as the economy, but the long-run magnitude of
wealth inequality will tend to grow rapidly if r>g.
Piketty notes that rising income inequality in the U.S. 1980–2010 is
mostly due to rising inequality of labor earnings within labor’s share of
national income, in part due to “exploding top managerial compensation”
having little to do with r>g, Piketty (2015). He does not see it as stem-
ming from the faster growth of capital-generated income compared to labor
income.
In the eight studies by others reviewed (excluding Piketty, since it dealt

with a different topic), six found globalization to adversely affect labors
share, three found technological progress or labor productivity growth
negatively related, and two found unions positively related. No other
factors discussed above were found significant in more than one study.
Only two studies directly cited factors increasing profit’s share of
national income: one cited financialization, the other globalization. Often,
factors cited above as affecting labor’s share will have the opposite
effect on profit’s share, but we can’t infer this with certainty, since it
is possible interest and/or rent’s share may have received the offsetting
effects.
20.3 METHODOLOGY
OLS or 2SLS, as appropriate, was used to test for variables related to both
the level and share of income received by four factors of production: labor,
profits, interest and rental income. Proprietor’s income was not tested.
Initial results were obtained using a 1965–2010 sample of U.S. data.

Three additional samples were then used verify results. Most explanatory
variables tested were those discussed in the literature as possible determ-
inants of a factor’s level or share of income, i.e., variables considered
theoretically plausible determinants of factor share or level. This was done
because our tool of analysis, regression, is correlational, not experimental.
Correlational relationships can be notoriously spurious. To help ensure
correlations cited as likely to be causal really are, we subject to testing only
hypotheses that are considered theoretically plausible by at least some eco-
nomists. This issue was extensively discussed in Section 2.2.4.4 presented
earlier in this study.
Stationarity Issues
All variables described above were tested for nonstationarity using the
ADF test. Nonstationary explanatory variables were then tested for coin-
tegration with the dependent variable. If not found cointegrated, they
were detrended.
Endogeneity Issues
Explanatory variables in the models used were tested for endogenously
with their dependent variable using the Hausman endogeneity test. The
test involves regressing a variable suspected of endogeneity on all the mul-
tifactor model’s exogenous and lagged variables. The residuals from this
regression are then added to labor share model as an additional variable.
If the residual variable’s t-statistic is significant at the 5% level the variable
is replaced with an endogeneity-free, Wald strong instrument in a 2SLS
estimator. See Griffiths et al. (2008, 2011).
The Sargan test was applied to ensure the instrument itself was not
endogenous with the dependent variable.
Multicollinearity and Serial Correlation Issues

All models were estimated in first differences of the data, significantly redu-
cing both the multicollinearity and serial correlation problems. Related
work by the author had indicated use of first differences on U.S. time series
data reduced the average simple correlation among explanatory variables
from about 0.80 to 0.40, and increased almost all Durban Watson serial
correlation statistics to 1.6 or greater.
20.3 METHODOLOGY 399
Heteroskedasticity
Newey-West standard errors were used to address heteroskedasticity
issues.
Robustness Testing
The chapter’s foremost methodological goal is to ensure its findings rep-
resent good science. It is not “just another study” offering a set of
unverified initial findings.
Serious efforts are made to verify the results presented in this chapter are
not idiosyncratic to the time period or particular model tested. Robustness
testing of initial findings is exhaustive. Only one study in the literat-
ure reviewed met this standard (Guscina 2006), who studied labor’s
share.
This robustness testing enhances the credibility of the model consid-
erably, moving it, we believe, from the oft seen (but never intellectually
satisfying) category of “one more study of . . . .” to something more akin
to true, reliable science. Economics long ago developed methodologically
to the point where this kind of robustness testing of findings could be
done with minimal time and effort, and should be a minimal requirement
for publication, if economics is to be considered a twenty-first-century
science. This extensive use of robustness testing is how we meet the
requirement for good science noted by physicist L. M. Krauss [17], i.e.,
of “trying exhaustively, but failing, to disprove” our own initial findings
before submitting them for publication.
Here, more pages are devoted to robustness testing than to developing
the initial findings. Initial results are retested in three additional, though
overlapping, time periods. Only initial results replicated in at least two of
three additional time periods tested are deemed valid, and only then if the
results remain robust when adding or subtracting additional variables to
the model. The “2 of 3” rule was used because some explanatory vari-
ables show little or no movement in some sample periods and can appear
statistically insignificant when in fact they are not. Spuriously high mul-
ticollinearity levels in one period can negatively affect significance levels,
causing the same problem.
Finally, where both OLS and 2SLS are used, we present both results,
though we only rely on the 2SLS results in our analysis. This is done to
allow comparison of results of older studies which used only OLS, a com-
mon problem with older studies. It provides one way of testing whether
differences with findings in older studies were simply a result of them using
older testing methods, or whether they are substantive. It is a third form

of robustness testing.
20.4 DETERMINANTS OF LABOR, PROFITS, RENT, AND

INTEREST FACTOR SHARES AND INCOME LEVELS
20.4.1 Labor’s Share of National Income – OLS and 2SLS Models
There has been much discussion regarding Labor’s declining share of
national income in the U.S. After five decades of growth, 1930–1980
when it grew from 62% to 68%, it has declined during the three dec-
ades 1980–2010 from 68% to 62%. Economists have noted the decline;
our literature review indicates there is no consensus on causes. We exam-
ine variation in the share of national income going to labor in the 45-year
period 1965–2010. Our findings from this sample were that 10 variables
explained 90% of the variation, at least in some samples. One additional
variable (the % of U.S firms with 1–4 employees), raised the explanatory
power slightly to 91% of variance, but data were only available for the
1978–2010 period for this variable. Actual model test results and tests for
robustness of these findings are presented further below. Robustness test-
ing reduced the number of reliably related factors driving labor’s share to
seven, discussed below, and factors driving labor income levels to two (the
size of the GDP and labor force participation rates), also discussed below.
Stationarity Issues
ADF test. Variables found nonstationary included the following:
Ratio of Employment to National Income (Empl/Y)

Ratio of #Firms Employing 1–4 to # of all firms (Firms 1–4)
Both nonstationary explanatory variables were then tested for cointeg-

ration with the dependent variable. All were found cointegrated, so no
detrending was needed.
Endogeneity Issues
Explanatory variables in the models above were tested for being endogen-
ously related to the dependent variable, using the Hausman endogeneity
test. The test involves regressing a variable suspected of endogeneity with
the dependent variable on all the multifactor model’s exogenous and
20.4 DETERMINANTS OF LABOR, PROFITS, RENT, AND INTEREST FACTOR SHARES. . . 401
lagged variables. The residuals from this regression are then added to labor
share model as an additional variable. If the residual variable’s t-statistic is
significant at the 5% level the variable is replaced with an endogeneity-free,
Wald strong instrument in a 2SLS estimator. See Griffiths et al. [16].
None were found endogenous except the government deficit (T-G),
which was replaced by a Wald strong instrument. The Sargan test was
applied to ensure the instrument itself was not endogenous with the
dependent variable.
Choice of Dependent Variable
The dependent variable was the average of labor’s share of real national
income in the current and prior year (LSAV ). The average was used to
eliminate “white noise” occurring in individual year data on the depend-
ent variable which considerably lowered the amount of variance explained.
The explanatory variables found to most systematically explain year-to-year
variation in labor’s share of national income as shown below (acronyms
given in parentheses).
Equation 20.4.1.1 shows parameter estimate and significance level find-
ings for all the hypothesized determinants of labor’s share except the ratio
of the number of firms employing less than five to the total number of
private firms in the U.S. Data for all these variable was available for 1965–
2010. Model 20.4.1.1 presents the initial results. The final model, robust
to changes in time period sampled and the number of other variables
included in the model, is presented in Model 20.4.1.2.TR further below.
Model 20.4.1.1
OLS Model of Labor’s Share of National Income
LSAV0,–1 = 0.000020 YAV0–1 + 0.03 (Empl / NI) – 1.15 (Wage / NI)
(t =) (2.1) (6.6) (–1.2)
+ 0.001 %Union – 0.64 PROFROW /NI
(1.2) (–1.5)
+0.011 (FinProf / TProf) + 0.72 LProd(av–1–2) /NI
(1.9) (1.9).
+0.14 INFL – 0.0069 UNEMAV–1–2
(1.1) (–4.9)
+0.006 LParRate–3 – 0.00004 (T – G)
(1.8) (–3.1)
R2 = 0.84; DW = 1.5
(20.4.1.1)
where the variables are defined as
(YAV0,–1 ) = variation in average of current and previous year real

GDP
(Empl/NI) = changes in the ratio of employment to national
income
(Wage/NI) = changes in the real wage/national income ratio
(%Union) = changes in the % unionized
(PROFROW) = changes in real U.S. profits (derived from
operations outside the U.S.), as a percent of real
national income
(FinProf/TProf) = financial industry profits as a % of total profits
(LPRODav–1–2 )/N) = average of past two years labor
productivity/national income
(Firm<5) = % of firms with 1–4 employees
(UNEMAV–1,–2 ) = unemployment rate: average of past two years
(LParRate–3 ) = labor force participation rate
Tests indicated the deficit variable was endogenous with the model’s
dependent variable. It was replaced by a strong instrument (Wald test)
which was not itself endogenous with the dependent variable (Sargan
test). Results Of retesting using 2SLS are shown in Model 20.4.1.2
below.
Model 20.4.1.2
2SLS Model of Labor’s Share of National Income
LSAV0,–1 = 0.000019 YAV0–1 + 0.03 (Empl / NI) – 1.10 (Wage / NI)
(t =) (1.7) (5.3) (–1.0)
(0.5) (–1.4)
+0.008 (FinProf / TProf) + 0.64 LProd(av–1–2) /NI
(1.2) (1.7).
+0.16 INFL – 0.0071 UNEMAV–1–2
(0.9) (–4.3)
+ 0.005 LParRate – 0.000046 (T – G)
(1.6) (–2.6)
R2 = 0.83; DW = 1.5
(20.4.1.2)
Results are very similar for the two models; nearly identical for some
variables. Only two variables significant in the OLS model became
insignificant in the 2SLS model (PROFROW /NI; FinProf/TProf). Aver-
age income, the employment /national income ratio, labor productivity,
the unemployment rate, the labor force participation rate and the govern-
ment deficit were found significant (with the sign on the deficit estimate
indicating deficits have a positive impact on labor’s share).
Since all factor shares must add to unity, a gain in one factor’s share
has to come at the expense of some other factor’s share. Many of the
same variables are in both the profit and labor share models, but with the
opposite sign. This may not occur for economic reasons (of the zero sum
game type), but simply for arithmetic ones. A variable which has, for sound
economic reasons, raised one factor’s share, must (for simple arithmetic
reasons), show a relationship with the opposite sign with another.
Adding the “Firms 1–4” Variable
We next added the variable “% of firms with 1–4 employees as percent of
the total number of firms” to the model and re-estimating it using the
shorter 1978–2010 period for which data was available. Results indicated
the larger the number of firms with 1–4 employees relative to the total
number of firms, the smaller would be labor’s share of national income,
possibly indicating small firms more typically pay less. See Eq. 20.4.1.3.
Model 20.4.1.3
2SLS Model of Labor’s Share of National Income
(Including Firms 1–4 Variable)
LSAV = 0.000028 YAV0–1 + 0.024 (Empl / NI) + 1.46 (Wage / NI)
(t =) (3.2) (4.4) (2.5)
(1.1) (–1.4)
+ 0.009 (FinProf / TProf) + 4.65 LProd(–1) /NI – 0.15 INFL
(1.4) (1.0) (–0.9)
– 0.006 UNEMAV–1–2 + 0.009 LParRate–3 – 0.000027 (T – G)
(–2.8) (3.6) (–1.8)
– 0.55 Firms1 – 4 R2 = 0.93; DW = 2.2
(–3.8)
(20.4.1.3)
The 2SLS results for the more limited 1978–2010 data set found all the
same variables significant (plus firms 1–4) that were found significant in
the full 1965–2010 initial model, except two: labor productivity, found
insignificant here, and the ratio of average wages to national income, found
significant here.
Robustness of Parameter Estimates Over Time
Physicist Lawrence Krauss (2012) notes that good science requires
researchers to spend as much time trying to disprove a hypothesis as they
spend trying to prove it. Having obtained a significant result in one test,
only if you fail to disprove it in others can you be reasonably sure your
initial results are valid, not spurious. This study uses two methods to try
and disprove its initial results. First, it attempts to verify or disprove results
found statistically significant in one time period sampled by retesting the
same models in three other sample periods. If results cannot be repeated in
other time periods, initial results are judged likely to be spurious and dis-
carded. Second, we also attempt to verify or disprove results for variables
obtained testing one model by retesting them in other plausible mod-
els purporting to explain the same relationship. We do this by adding or
subtracting variables from the original model and retesting. This type of
robustness testing is critical in economic time series models, where signific-
ant multicollinearity is common and can easily change parameter estimates
obtained when even small model changes occur.
Explained Variance and Robustness
Stepwise regression can be used to estimate the contribution of individual
variables to total explained variance. Variables in the initial 2SLS labor
Share Model 20.4.1.2 are tested and their contributions (using both first-
in and first-out methods) are shown in Table 20.4.1.1.
Using the first-out method, the most important contributors to
explained variance were the ratio of employment income to national
income, the unemployment rate and the government deficit. All three were
positively related to labor’s share. Using the first in method, the same three
variables were most important.
Robustness of Initial Results Over Time
All variables were tested in four different, but overlapping, time peri-
ods to determine the replicability of results. Findings are presented in
Table 20.4.1.2.
In Table 20.4.1.2 we attempt to disprove our initial results by testing
the hypothesis that our initial results were spurious. We test this hypothesis
Table 20.4.1.1 Stepwise estimate of individual variable’s contributions to total

explained variance

(YAV0,–1 ) 0.81 –0.00

EMPL/NI 0.70 0.31
W/NI 0.81 0.02
%Union 0.83 –0.00
Prof ROW /NI 0.82 0.08
FinProf/TProf 0.82 0.08
(LProd /NI)av–1–2 0.82 0.02
INFL 0.83 0.04
UNEMAV–1,–2 0.74 0.35
LPARRATE 0.81 0.02
(T–G) 0.76 0.16
Table 20.4.1.2 Coefficient stability in Eq. 20.4.1.2: 2SLS labor share model
Variable Sample period

1965–2010 1975–2010 1965–2000 1975–2000
(YAV0,–1 ) 0.000019∗∗∗ 0.000032∗ 0.000036∗∗ 0.000044∗

EMPL/Y 0.030∗ 0.031∗ 0.023∗∗ 0.036∗∗∗
W/NI– 1.10 0.83 0.09 0.68
%Union 0.001 0.001∗∗∗ 0.001 –0.001
Prof ROW /NI –0.74 –0.72 –1.74∗∗ –0.81
FinProf/TProf 0.008 0.01 0.05 0.003
(LProd /NI)av–1–2 0.74∗∗∗ 0.77 0.70∗∗ 5.92
INFL 0.16 –0.11 0.64∗∗∗ –0.02
UNEMAV–1,–2 –0.007∗ –0.007∗∗ –0.003∗∗∗∗ –0.007∗∗
LPARRATE 0.005∗∗∗ 0.009∗ 0.004 0.007
(T–G) –0.00005∗∗ –0.00003∗∗∗ –0.00008∗∗∗∗ –0.000037
Significance level: ∗∗∗∗ 15%; ∗∗∗ 10%; ∗∗ 5%; ∗ 1% level.
by retesting the same model in three additional, different time periods.

We reject this null hypothesis that our initial results were spurious if sub-
sequent results replicate our earlier results. Ideally, the time periods tested
would be totally separate, but since our data set is limited to 45 yearly
observations, we have overlapped samples to keep at least 30 observations
to ensure sample sizes are more than adequate for small sample statistical
properties to hold.
Several of the results from our initial 1965–2010 sample period test
seem to have been based on spurious correlations. Only three variables
significant in the initial sample were also found significant in all three other
time periods sampled. They were 2-year average GDP size, the ratio of
employment to national income, and the unemployment rate. The deficit
variable was significant in three of the four samples. We draw attention to
those found significant in at least three of the four tests because a variable
can be found insignificant in an isolated sample simply because of lack of
adequate variation during the period, or because of multicollinearity, as
well as for substantive reasons. Taking this into consideration, we adopt
three of the four sample periods as our standard of verification of results.
Hence, there are four variables we judge sufficiently robust to changes
in time period sampled to be considered reliable determinants of labor’s
share of national income, likely to again be found significant in any future
tests.by other researchers. The relationship of the other variables tested is
problematic at best.
Reducing the original 11 variable model to the four variables found
significant in at least three of the four samples, and re-estimating using
2SLS, we have:
Model 20.4.1.2.TR (Preliminary)

Time Period Robust 2SLS Model of Labor’s Share of National
Income
LSAV = 0.000026 YAV0–1 + 0.03 (Empl/NI) – 0.005 UNEMAV–1–2
(t =) (3.1) (11.5) (–4.4)
– 3.29 (T – G) + 0.58 AR(2) R2 = 0.85; DW = 2.1
(–3.9)
(20.4.1.2.TR.Preliminary)
When initial tests include a large number of explanatory variables, as was
the case above, a variable which is truly statistically significant may appear
statistically insignificant because multicollinearity tends to bias signific-
ance levels downwards; see Fox (1968). In addition, in small samples
when a large number of explanatory variables are tested, simply a lack of
an adequate number of degrees of freedom can drive significance levels
down. Either problem can cause us to reject a variable inappropriate,
noneconomic reason.
To protect against this, we retested all variables rejected for not meet-
ing the “3 out of 4” test. Retesting was done using a 1965–2010 sample
0.04
0.02
0.00
0.012
0.008 –0.02
0.004
–0.04
0.000
–0.004
–0.008
–0.012
1965 1970 1978 1985 1990 1995 2000 2005 2010
Graph. 20.4.1.1 Model of only variables robust in at least three of four sample
periods (Eq. 20.4.1.2.TR)
model containing only the four time period robust variables discussed
above, and one of the variables previously found insignificant in at least
3 of 4 sample period tests and rejected. Three were now found significant
and were added back to the model (labor force participation rate, ratio
of average wage to national income and labor force participation rate).
This new seven variable model was retested again in the other three time
periods. All variables were significant in all four sample periods tested,
except foreign profits which was significant in three. These seven variables
became the “semi-final” model, a model robust to time period sampled,
and is presented below. It is marked time-period robust “final,” but is
really “semi”-final, because we still must test for robustness of parameter
estimates to model changes.
The time-period robust, seven variable semi-final, model of the determ-
inants of labor’s share of national income is given below and shown in
Graph 20.4.1.1, tested using the longest sample period, 1965–2010.
Model 20.4.1.2.TR (Final)

Time Period Robust 2SLS Model of Labor’s Share
of National Income
LSAV0,–1 = 0.000027 YAV0–1 + 0.033 (Empl / NI)
(t =) (3.3) (10.2)
– 0.006 UNEMAV–1–2 – 0.000033 (T – G) + 0.006 LParRate

(–5.0) (–3.4) (2.8)
– 0.11 W / NI – 0.45 ProfROW /NI + 0.54 AR(2)
(2.5) (–1.6) (5.0)
R2 = 0.88; DW = 2.0
(20.4.1.2.TR)
The graph’s top two curves represent the actual yearly changes in labor’s
share, and the model’s fitted estimate of what they should be. Values of
both are measured on the right hand vertical axis. Clearly the model does
an excellent job of simulating actual results. The bottom curve shows the
differences (residuals) between actual and fitted. The small differences are
measured on the left vertical scale.
Mistaking Lack of Movement in Explanatory Variables for Lack

of Significance
Generally, testing the robustness of initial results by retesting in other
time periods works to “shake out” spuriously significant relationships
obtained in the initial sample. However, it can fail when some of the
other periods tested are periods in which there was little or no variation
in a specific explanatory variable. A statistics test cannot find a relation-
ship if there is no movement in one variable. Even if the variable is
truly a significant determinant of the dependent variable, it will show as
statistically insignificant in sample periods where there is little or no vari-
ation. To avoid this problem, the variables found significant in our initial
sample, but insignificant in at least two of the other three samples were
reexamined to see if they lacked noticeable variation in sample periods
in which the variable was found insignificant. If there was lack of vari-
ation in a sample, we excluded the sample when determining if enough
samples were significant to consider the results as indicating a funda-
mental, rather than spurious, relationship with the dependent variable.
However, no explanatory variables were found that appeared to have this
problem.

The coefficients and significance levels of the seven explanatory vari-
ables in the time period robust model above are also very robust to
changes in model specification, as we can see from comparing the initial
11 variable version to the seven-variable final version (Eq. 20.4.1.2.TR).
In one further test of specification robustness, we remove two differ-

ent variables (W/NI and ProfROW /TProf ratios) from the seven-variable
robust model, and retest. Coefficients again were very similar to those
found in the full seven explanatory variable model, and all variables
remained statistically significant. Our findings were robust to this model
change.
Finally, we note that even adding two variables (financial industry/total
industry profits and percent unionized) to the final seven-variable model
leaves coefficients in all but one variable largely unchanged, and all
eight are still statistically significant. Coefficients for the income variable
changed noticeably, but this variable is highly correlated with the deficit
variable, which is now picking up some of income’s variation. Nonetheless,
it remains statistically significant and its sign is unchanged.
We conclude that coefficient values and significance levels in the “semi-
final” seven-variable model, which was robust to time period sampled,
given in Eq. 20.4.1.2.TR above, are also robust to changes in model
specification. Hence, this becomes our final labor share model.
Our hope is that the exhaustiveness of robustness testing allows this
work to meet the criteria of being good science, not just “another study.”
The results are likely to be as accurate a set of representations of economic
reality as can be obtained using economic methods, and are almost cer-
tain to be replicated by other researchers in the future looking at the same
variables in reasonable models, assuming adequate controls for multicol-
linearity, the left-out-variables problem, and other econometric problems.
These seven variables appear to be stable, key determinants of changes in
labor’s share of national income. It is unlikely any other structural model,
controlling for similar variables, will show otherwise, and be as robust to
different types of testing. However, our seven variables, though system-
atic and predictable in their effects, only explain 88% of the variance. The
fact that future studies are likely to also find these same variables signific-
ant does not mean the work is done and we should turn to other issues.
Clearly we would expect future researchers to find at least one or two
additional variables which affect labor’s share of national income, since
a significant part of total variation (12%) remains unexplained. We hope
that the final model developed here (Eq. 20.4.1.2.TR) can serve as a
jumping off point for future efforts in search of these yet undiscovered
additional variables affecting how large a share of national income labor
receives.
Policy Recommendations for Increasing Labor’s Share of

National Income
Based on the findings of the robust Model (20.4.1.2.TR) above, there
are seven recommendations for those who would like to increase Labor’s
share:
1. encourage GDP growth

2. encourage employment growth relative to GDP growth
3. reduce foreign-earned profits as a share of total profits
4. encourage programs to reduce unemployment
5. encourage programs to increase participation in the labor force
6. enact deficit–generating fiscal stimulus programs
7. recognize that when wages grow faster than national income, it leads
to a reduction in labor’s share, as factor utilization shifts toward less
expensive factors. This suggests increases in labor share due to higher
wages (relative to national income) are more than offset by declines
in job opportunities.
We note in recommendation 6 above that government deficits spending

improves labor’s share. Though the detail is not shown, the effects of tax
and spending deficits are different. Tax cut deficits were found significant
in raising labor’s share, but spending deficits were not. These separate
deficit results held in three of the four periods sampled; in the fourth,
neither type deficit had any effect.
Over the 45 years studied, 1/2 of the loss of labor’s share has been
due to growth of profits earned by U.S. firms on foreign operations, yet
this does not seem to be by reducing labor’s total income. No relation-
ship between the level of U.S. labor income and foreign-earned profits/
national income ratio was found. But it was found negatively related to
labor’s share, suggesting the effect on labor’s share is arithmetic, not sub-
stantive. That is, not the result of shifting labor income to profits, but
arithmetic in the sense that if one factor’s share goes up, at least one other’s
has to come down.
The increase in profit’s share due to growth in foreign earnings share,
though small in any 1 year, has increased steadily over the 45 years, leading
a large long-term drift upward of profit’s share, and may also have been
caused by the decline in the U.S. labor productivity rate growth rate since
1960, since labor’s share was previously found to grow and decline as labor
productivity growth increased or declined.
Table 20.4.1.3 Comparisons of GDP and labor productivity

growth rates
U.S. GDP growth rate Labor productivity growth

(decade average) rate (decade average)
1960s 4.3% 2.4%

1970s 3.1 2.5
1980s 2.8 2.2
1990s 3.1 1.9
2000–2009 2.1 1.8
Source: EOP [3] 2011, Table B2, B49
Short term, the labor share models clearly indicate year-to-yearly ups
and downs in labor’s share is overwhelmingly due to more Keynesian
factors, like variation in income, employment, unemployment, labor force
participation rates that cause fluctuation in labor’s share. They have ten-
ded to decline more in downturns than increase in upturns, leading to
some long-term downward net drift in labor’s share (even after account-
ing for the 1/2 of the decline attributable to foreign profit growth).
This net drop we suspect is caused by the decline in productivity growth
(Table 20.4.1.3).
Using the Models to Simulate the Effects of Counterfactuals on

Labor’s Share
Labor’s share of national income in the U.S. peaked in 1980 and has been
declining since. There are seven variables in our final model of labor share’s
determinants that explain 88% of this variation. We now estimate how
much labor’s share would have changed if just one of these variables had
not changed at all, while all the others changed as indicated by the his-
torical data. In other words, we examine the change in each explanatory
variable, ceteris paribus.
The test below compares average changes during the 1980s (the decade
the decline began) with average changes in the most recent decade in our
model, 2000–2009, using “final’ Model 20.4.1.2.TR, repeated here:
LSAV0,–1 = 0.000027 YAV0–1 + 0.033 (Empl / NI)

(t =) (3.3) (10.2)
– 0.006 UNEMAV–1–2 – 0.000033 (T – G)
(–5.0) (–3.4)
+ 0.006 LParRate – 0.11 W/NI – 0.45 ProfROW /TProf

(2.8) (2.5) (–1.6)
+ 0.54 AR(2)
(5.0) R2 = 0.88; DW = 2.0
(20.4.1.2.TR)
Results of the simulation are presented in Table 20.4.1.4.
The simulation indicates that the most important variable was the
decline in the level of employment relative to national income. Since
employment itself grew during this period, this probably reflects a faster
growth in national income due to a faster growth in its profits component
(largely foreign profits growth). Had this decline not occurred, we would
have seen an increase in labor’s share of 16.1%, instead of a decline of 1.6%.
In other words, labor’s share lost not because labor income dropped, but
because profit income grew faster, taking a larger share.
The second most important effect was the growth in GDP. Had the
GDP not grown it is estimated labor’s share would have fallen 16.7%,
Table 20.4.1.4 Effects of counterfactuals on labor’s share
Actual labor’s share of NI = –0.016(–1.6%) (Decade av.

2000–2009 – av.
1980–1989)
Predicted labor’s share (from Model 20.4.1.2.TR) = –0.015(–1.5%) Calculated using

actual for all
explanatory
variables
Explanatory variables Reg. coef. Actual data Pred. L Share after

used in simulation simulation (using actual
(2000s average – data except “0” for
1980s average) simulated variable)
GDP Growth RateAV0,–1 +0.000027 (+5599) –0.167 (vs. –0.016

Using Actual
Data For All)
Empl./NI +0.033 (–5.34) +0.161 (vs. –0.016 “ “)
UnemAV–1,–2 –0.006 (–0.034) –0.015 (vs. –0.016 “ “ )

L.F. Par. Rate–3 +0.006 (+2.71) –0.031 (vs. –0.016 “ “ )
Wages/NI –0.11 (+0.016) –0.013 (vs. –0.016 “ “)
(Government Deficit) –0.000033 (–212.13) –0.022 (vs. –0.016 “ “)
(ProfROW/ TProf)av–1–2–3) –0.45 (+0.026) –0.003 (vs. –0.016 “ “)
instead of the much smaller decline of only 1.6% that actually occurred. As
we calculated real wages, they were essentially stagnant, suggesting labor
costs relative to other factor costs declined, and that the wage decline kept
the decline in labor’s share much smaller than it would otherwise have
been. Further, if the GDP growth rate had been merely 1/3 higher than
its 2.5% average level during the 1980–2010 period, i.e., 3.33%, labor’s
share would have increased 3.5% instead of declining 1.6%. Hence, the
Study concludes that in addition to foreign profits growth, the other major
source of decline in labor’s share was the decline in GDP growth rates
during this period.
Three other factors would also have made sizable changes: if the labor
force participation rate had not increased, the decline in labor’s share
would have been 3.1%, not 1.6%. Had foreign profits not grown relative to
national income, Labor’s share would have remained virtually unchanged,
dropping only 3/10 of 1%. Had the government deficit not grown, labor’s
share would have dropped 2.2%, not just 1.6%.
The remaining two factors had much smaller, or marginal effects. Had
the growth in the ratio of average wages to national income not occurred,
the loss in labor’s share would have only been 1.3% instead of 1.6%.
The unemployment rate drop, though substantial (3.4%) had virtually
no effect on predicted labor’s share, presumably because the effects of
the social safety net offset much of any change in labor income due to
changing unemployment. The coefficient on the unemployment variable
is (–0.006). Multiplied by the change in unemployment rate, we have
(–0.006)(–0.034) = +0.0002, i.e., a mere 2/100 of 1% change.
20.4.2 OLS and 2SLS Models of Fluctuations in the Level of Total

Labor Income
We wish the investigation into the determinants of factor shares to be
more than just a game of “whack-a-mole”, where strictly for arithmetic,
not economic reasons, if 1% share goes up, another must come down.
To avoid judging changes in labor’s share as economic that are just arith-
metic, we will also examine whether the variables found to affect labor’s
share also affect its level of aggregate income. To do so, we rerun the
same model used for shares, except the dependent variable changes from
labor’s share of national income to just the level of labor income. We have
also added one explanatory variable, the real exchange rate average for the
past three years, which explains significant variance in the level of labor
income, though was found to have no significant effect on labor’s share

and therefore was excluded from the model above. Results are shown in
Eq. 20.4.2.1.
No endogeneity was found between the dependent variable and the
government deficit, so no 2SLS was needed.
Results for the initial model tested are presented in Model 20.4.2.1.
The final model, robust to changes in time period sampled and the
number of other variables included in the model, is presented in Model
20.4.2.1.TR further below.
Model 20.4.2.1
OLS Model of Determinants of the Level of Labor Income
LSLEVELS = 0.55 YAV0–1 + 13.52 (Empl / NI)

(t =) (11.4) (0.9)
– 197.61 (Wage / NI) + 4.62 %Union
(–0.6) (1.1)
– 783.18 PROFROW /NI + 63.38 (FinProf / TProf)
(–0.3) (2.7)
+ 406.03 LProd(av–1–2) /NI + 153.38 INFL
(0.3) (0.4)
– 23.79 UNEMAV–1–2 + 42.79 LParRate
(–2.5) (2.6)
+ 0.02 (T – G) + 3.50XRateAV–1–3 + 0.45AR(1)
(0.3) (1.7) (3.5)
R2 = 0.94; DW = 1.7
(20.4.2.1)
Three variables that were robustly significant in determining labor’s share
of national income were also significant for the level of labor’s aggregate
income: average income, unemployment rate and labor force participation
rate. The first and third had a positive effect, the second a negative effect.
Two additional variables were found significant in determining real labor
income levels. The first is exchange rate (Foreign currency/$), positively
related real labor income. Cheaper foreign currency may indicate reduced
prices of imports raise labor’ real income, but direction of causation
is unclear: rising labor income also leads to increased imports, pressur-
ing exchange rates downward. By comparison, Section 20.4.2 shows the
exchange rate to have the opposite effect on the level of profit income.
The second new variable found significant was the ratio of finance industry
profits to total profits. This ratio was found positively related to the level
of aggregate income for labor. This was somewhat surprising, since finan-
cialization variables in other factor share studies are more typically found
negatively related.
In robustness tests, however, only the GDP and labor force participa-
tion rates were significant in at least three of the four time periods sampled.
Subsequent modeling of labor income levels as a function of these two
variables alone left only the level of GDP significant. This becomes our
robust model, shown in Eq. 6R. In short, in the levels model, labor income
is driven by Keynesian variables that determine the GDP. The robust
model results with autocorrelation controls are given in Eq. 20.4.2.1.TR.
LILEVELS = 0.55 YAV0–1 + 0.88 AR(1) – 0.41 AR(2)

(t =) (16.3) (4.7) (–1.8) (20.4.2.1.TR)
R2 = 0.90; DW = 1.8
Our findings with levels in the models above provide some support our
findings with shares. Five of the seven variables found to be significant
determinants of share are the same as (or driven by) changes in GDP and
the labor force participation rate found to be key determinants of the level
of labor income. They include
1. GDP
2. Employment/national income ratio
3. Unemployment
4. Labor force participation rate
5. The deficit (reduced by growing GDP)
Hence, variation in labor’s share does not seem to chiefly be simply

an automatic arithmetic response to substantive changes in other factor
income levels. The main factor that changes labor’s income level also tends
to change its share in the same direction.
20.4.3 Profit’s Share of National Income

What causes variation in profit’s income as a percentage share of national
income? Since shares must sum to unity, our initial hypothesis was that
anything that affected labor’s share may affect profits share in the opposite
way. Therefore, labor share’s determinants were included in our tests to
determine what causes variation in profit’s share. Of the variables taken

from the labor model, only the ratio of employment to national income
was found related to profit’s share in this initial model. It was found
negatively related, not surprisingly, since previously it had been found
positively related to labor’s share. Other variables that had been found
to be determinants of labor’s share were found insignificant though, as
expected many had signs opposite those in the labor model. Unlike the
Labor share model, averaging current and past year profit shares did not
improve explanatory power, so only current year profit share is used as the
dependent variable in profit share models.
Several other variables were found to be significant determinants of
profit’s share. The new variables include a Samuelson accelerator and the
lagged prime interest rate variable (lagged an average of their values 3 and
4 year ago). When these additional variables were added, several of these
original variables from the labor share model again became statistically
significant.
Stationarity Issues
ADF test. Dickey-Fuller t-statistics less than -1.95 allow us to reject the
null hypothesis of nonstationarity the 95% confidence level.
Endogeneity Issues
Explanatory variables described below were tested for endogeneity with
the profit’s share dependent variable using the Hausman endogeneity test.
First-stage Hausman test regressors used were lagged variables used or
variables used in the labor share and profit share models not thought to
be endogenous with the profit’s share variable.
The second stage Hausman model was the model shown below in
Eq. 20.4.3.1, with an additional variable representing the residuals from
the first-stage model. If the residuals variable’s t-statistic is significant at the
5% level the variable is considered endogenously related to the dependent
variable, and must be re-estimated using 2SLS and an endogeneity-free
Wald-strong instrument (Griffiths et al. 2008, 2011). Results indicated no
endogeneity in the profit’s share model tested, so no retesting using 2SLS
was needed. The model was tested using 1965–2010 data.
20.4.3.1 OLS Models of Profit’s Share of National Income

Model 6 includes results for all the hypothesized determinants of profit’s
share found significant (or marginally significant at the t = 1.5 = 15% level
in preliminary testing. Its graph is also shown. The final model, robust to
changes in time period sampled and the number of other variables included
in the model, is presented in Model 20.4.3.1.TR further below.
Model 20.4.3.1
OLS Model of Profit’s Share of National Income
PS = – 0.000006 (Y) – 0.000008 (Y – Y–1 ) – 0.011 (Empl / NI)

(t =) (–1.9) (–2.6) (–3.3)
+ 0.77 (Wage / NI) – 0.002 %Union – 0.01 INFL
(1.4) (–1.9) (–0.2)
+ 7.08 (LPROD(–1) /NI–1 ) + 4.32 PROFROW /NI
(1.9) (4.5)
– 0.43 (ProfROW /TProf) – 0.001 PRav–3–4
(–7.1) (–1.6).
+ 0.000013 (CDebt) – 0.00058 (XRAV–0,–1,–2,–2 )
(3.7) (–3.2)
R2 = 0.93; DW = 1.6
(20.4.3.1)
where
(Y) = GDP
(Y–Y–1) = the Samuelson accelerator
(Empl/NI) = ratio of employment to real national income
(Wage/NI) = The real wage/real NI ratio
(%Union) = % unionized
(INFL2 ) = the inflation rate (squared):
(LPROD(–1) /NI(–1) )
= ratio of labor productivity growth to real national
income growth, lagged 1 year
(PROFROW/NI) = real U.S. profits derived from operations in the rest
of the world (ROW) as a portion of real national
income
(PROFROW/TProf) = profits on foreign operations as % of total profits
(PRAV–3–4 ) = average of real prime interest rate lagged 3 and 4
years
(CDebt) = consumer debt
(XRAv.0,–1,–2 ) = the real exchange rate average for current and past
two years
Other variables used in preliminary tests, but not found significantly

related to profit’s share included: the government deficit, depreciation
allowances, capacity utilization levels, and the NYSE Composite Index.
Since all factor shares must add to 1.00, a gain in one factor’s share has
to come at the expense of at least one other factor’s share. Hence, we will
find many of the same variables in both profit’s and labor’s share models,
but with the opposite sign, not for economic reasons, but simply because
a variable which for sound economic reasons, raises one factor’s share,
must, show a statistical relationship having the opposite sign with another
(for arithmetic, not economic reasons). As expected, 6 of the 12 variables
found at least marginally significant are the same as in the labor’s share
model, but with the opposite sign. They include GDP, employees/NI
ratio, average wage/NI ratio, % union, inflation, and foreign profits/NI
ratio. The Labor productivity/NI ratio enters both with a positive sign.
The graph’s top two curves represent the actual yearly changes in
profit’s share, and the model’s fitted estimate of what they should be. Val-
ues of both are measured on the right hand vertical axis. Clearly the model
does an excellent job of simulating actual results. The bottom curve shows
the differences (residuals) between actual and fitted. The small differences
are measured on the left vertical scale (Graph 20.4.3.1).
0.04
0.02
0.00
0.010
–0.02
0.005
–0.04
0.000
–0.005
–0.010
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Graph. 20.4.3.1 Graph of the initial profit’s share model (Eq. 20.4.3.1)

Contributions to Total Explained Variance
Stepwise regression is used in Table 20.4.3.1 to estimate the contribution
to total explained variance attributable to any one variable. Findings are
presented in Table 20.4.3.1.
First-out results indicate the two main contributors to explained vari-
ance were profits on foreign operations as a percent of total profits,
and profits on foreign operations as a percent of national income. First-
in results indicate the most important variables were profits on foreign
operations as a percent of total profits, the accelerator and consumer
borrowing.

All variables in the model (Eq. 20.6) were tested in for different, but
overlapping time periods to determine the replicability of initial results.
Findings are presented in Table 20.4.3.2.
Only three variables are statistically significant in all four samples:
foreign profits as a percent of National income (positively related), for-
eign profits as a percent of total profits (negatively related to profit’s
share because a small denominator reflects a weak U.S. economy, and
therefore weak profits) and the 3year average exchange rate (negatively

explained variance in profit’s share

Variable
(Y) 0.92 0.04
(ACC) 0.92 0.22
EMPL/NI 0.90 0.12
W/NI 0.92 0.00
%UnionAV 0.92 0.00
LProd(–1 /NI–1 0.92 0.11
Prof ROW /NI 0.80 0.02
ProfROW /TProf 0.70 0.50
PRAV–3–4 0.91 0.01
INFL 0.93 0.00
Cons.Borrowing 0.91 0.18
XRAV0,–1,–2,–2 0.91 0.07
Table 20.4.3.2 Determinants of profit’s share of national income coefficient

stability over time
Variable 1965–2010 1975–2010 1965–2000 1975–2000
(Y) –0.000008∗∗∗ –0.000008 –0.000001 –0.000006

(ACC) –0.000008∗∗ –0.000010∗∗ –0.000004 –0.000005
EMPL/NI –0.011∗ –0.012∗∗∗∗ –0.006∗∗∗ 0.004
W/NI 0.77 0.24 0.83∗∗∗ 0.37
% UnionAV –0.002∗∗∗ –0.002 –0.002∗∗ –0.001
LProd(–1 /NI–1 7.08∗∗∗ 7.24∗∗∗∗ 3.65∗∗∗∗ 1.29
Prof ROW /NI 4.32∗ 4.34∗ 6.08∗ 6.55∗
FProf/TProf –0.43∗ –0.43∗ –0.53∗ –0.60∗
PRAV–3–4 –0.0010∗∗∗∗ –0.0010 –0.0003 0.0003
INFL –0.009 0.005 –0.012 –0.06
Cons.Borrowing 0.000013∗ 0.000013∗ –0.0000007 0.000003
XRAV0,–1,–2,–2 –0.0006∗ –0.0005∗∗ –0.0002∗ –0.0002∗∗∗
Significance level: ∗∗∗∗ 15%; ∗∗∗ 10%; ∗∗ 5%; ∗ 1%.
related). Collectively they can explain 88% of the variation in profit’s

share over the 1960–2010 period (of the 93% we can explain with all
variables).
Two additional variables were significant in three of the four samples,
the employment/national income ratio (negatively related to profit’s
share) and labor productivity/national income ratios (positively related).
When added to those significant in all four tests, the five together explain
89% (Eq. 20.4.3.1.TR). Hence we conclude the growth in profit’s share of
national income is largely due to the growth of foreign-earned profits as a
component of profit during the 1965–2010, and changes in the exchange
rate. In real terms, foreign profits grew from 6% of total profits in 1960 to
22% in 2010, representing 6/10 of 1% of national income in 1960, and
3.1% in 2010.
The variables not found significantly related to profit’s share of national
income in three or more of the four tests include the GDP, the accelerator,
the ratio of wages to national income, the % unionized, the lagged prime
interest rate, inflation, and consumer borrowing. Notice the signs on the
effects of the GDP, accelerator, wage/NI ratio, and % unionized variables
are the opposite of what they were in the labor share model, indicating
a general tendency (if not a statistically reliable one) for any increases in
these variable’s effects on labor’s share to be reflected in changes in profit’s
share in the opposite direction.
Since factor shares must sum to unity, the growth of foreign profits in
the denominator of the labor share definition, (= Labor income/national
income) without affecting the numerator does explain half the total decline
in labor’s share over the 1960–2010 period, as we noted earlier.
Re-estimating the model using only the explanatory variables found
significant in at least three of the four sample periods, we have our time
period robust model, robust to sample period tested, but not yet tested
for robustness to changes in the model itself:
Model 20.4.3.1.TR
Time Period Robust OLS Model of Profit’s Share of
National Income
PS = – 0.003 (Empl / NI) + 1.92 (LPROD(–1) /NI–1 )

(t =) (–1.7) (1.1)
+ 4.76 PROFROW /NI – 0.50 (FProf / TProf)
(20.4.3.1.TR)
(5.6) (–14.2)
– 0.0003 (XRAV–0,–1,–2,–2 ) R2 = 0.89; DW = 1.6
(–2.0)
Though the labor productivity variable coefficient declines and it now

becomes statistically insignificant, we retain it in the “semi-final” time
period robust model because it was so strongly significant in three of the
time periods tested using the initial model. We suspect the lack of signific-
ance is a multicollinearity problem, not a substantive indicator the variable
does not affect profit’s share.
When testing large numbers of variables which might be potential
determinants of the dependent variable, as we did in our initial model,
multicollinearity (or lack of degrees of freedom in small samples) can cause
variables to look nonsignificant when they really are significant. To test for
this, we ran additional regressions on the full 1965–2010 sample, each
containing the variables in the “final” model above, plus one of the vari-
ables originally found nonsignificant in at least two of the four time periods
originally tested. In only one case was one of the originally nonsignificant
variable found significant (consumer borrowing, t = 2.3), but when tested
for robustness with the other three samples, failed to reach significance in
two. Hence, we have not added it to the model above of variables most
robust to changes in the periods sampled.
Lack of Variation in Explanatory Variables vs. Lack of Significance

When analyzing the determinants of labor’s share, we found the ratio of
wages to national income was a significant negative determinant of labor’s
share, but only when 1965–1974 decade data was added to the data set.
This was because for much of the time thereafter there was little or no vari-
ation in this variable. Without variation, we cannot estimate if its changes
are related to changes in the dependent variable.
We have the same problem in evaluating the ratio of average wages
to national income’s effect on profit’s share. It has a significant effect
on profits share in the initial 12 variable model tested for the same two
sample periods as for labor (but with the opposite sign), but not the other
two. When we retested it with our “final” model above. The relationship
was positive (as expected, since its sign was negative in the labor share
model) though it was not found significant in any of the four time periods
sampled, so it was not added to this “final” model.
Robustness to Model Specification Changes: Adding to and Deleting

Variables to the Model
To check the robustness of the parameter estimates and significance levels
in our five variable time period robust profits model, we first subtracted
two variables from it (employment/Y and labor productivity/NI) and
checked the remaining variables for estimate robustness. Coefficients and
significance levels remain nearly the same for the two profits variables, and
fairly similar for the exchange rate variable.
Then two variables were added (inflation and the prime interest rate) to
the five variable time period robust model and again checked for robust-
ness of the estimates on the five variables used in the final model. With the
exception of labor productivity, whose coefficient and significance level
grew markedly, all other variables coefficients and significance levels are
close to identical with those obtained in the final model.
The labor productivity variable, which was insignificant in the final
model because of its collinearity with others, shows the tendency of
multicollinearity-sensitive variables’ coefficients and significance levels to
jump around when variables are added to or subtracted from the model,
particularly when correlation levels are high among explanatory variables,
but low between the explanatory variable of interest and the dependent
variable, which is the case here. (r = 0.08). The correlation is low because
year-to-year changes in labor productivity are small, thought the long-term
cumulative effect is huge, and each change is not likely to affect profits
with exactly the same time lag as the last.
We conclude that findings for variables in the time-robust profit’s

share model are generally robust to model changes. Hence, it becomes
our “final” model, robust to both model specification and time period
sampled. Because of the robustness of results, we feel this meets the cri-
teria for being good science, not just “another study” presenting some
initial findings, but not testing their robustness. The results are as likely
to be as accurate a set of representations of economic reality as can be
obtained using economic methods, and are almost certain to be replicated
by other researchers looking at the same variables in reasonable models
going forward. These five variables appear to be stable, key determinants
of changes in profit’s share of national income. It is unlikely any other
structural model, controlling for similar variables, will show otherwise,
and be as robust to different types of testing. However, the five variables,
though systematic and predictable in their effects, only explain 89% of the
variance. The fact that future studies are likely to also find these same vari-
ables significant does not mean the work is done and we should turn to
other issues. Clearly we would expect future researchers to find at least one
or two additional variables which affect labor’s share of national income,
since a significant part of total variation (11%) remains unexplained, which
seems too large to just be random error. We hope that the profit share
model developed here (Eq. 20.4.3.1.TR) can serve as a jumping off point
for future efforts in search of these yet undiscovered additional variables.
These results represent our findings as to which variables are important
determinants of profit’s share. Profit’s share will grow if the ratio of labor
productivity to national income grows, if foreign profits grow as a percent
of national income, if the ratio of employment to GDP declines, if the
ratio of foreign profits to total profits declines (indicating an improving
economy), and if the U.S. exchange rate declines, making exports cheaper
for foreigners to buy (and imports more expensive for Americans to buy).
Using the Models to Simulate the Effects of Counterfactuals on

Profit’s Share
Labor’s share peaked at the end of the 1970s and has been declining since.
Profit’s share has been growing since the start of Labor’s decline. There
are five variables in our final model of profit’s share’s determinants that
explain 89% of the variation in profit’s share during this period. We now
estimate how much profit’s share would have changed if one of these vari-
ables had not changed at all, while all the others changed to the extent
indicated by the historical data. In other words, we examine a change in
one explanatory variable, ceteris paribus.
The test below compares average changes during the 1970s (the decade
before the labor decline began) with average changes in the most recent
decade in our model, 2000–2009, using the robust five-variable profit’s
share model (Eq. 20.4.3.1.TR, repeated below).
PS = – 0.003 (Empl / NI) + 1.92 (LPROD(–1) /NI–1 )

(t =) (–1.7) (1.1)
+ 4.76 PROFROW /NI – 0.50 (FProf / TProf)
(20.4.3.1.TR)
(5.6) (–14.2)
– 0.0003 (XRAV–0,–1,–2,–2 ) R2 = 0.89; DW = 1.6
(–2.0)
The simulation indicates that the variable affecting profit’s share of

national income the most was the growth in the ratio of foreign profits/
total profits. This ratio grew during the period, indicating the growth in
foreign profits far exceeded growth in total profits. Had total domestically
earned profits grown proportionally, profits share would have risen by a
predicted 5.9%, not just the 3.5% predicted using the amount this ratio
actually grew.
The second most important variable was the growth in foreign profits
relative to the growth in national income. This variable grew; had this vari-
able not grown at all profit’s share would have declined a predicted 1.4%
instead of growing the 3.5% predicted by the model when this variable’s
actual growth is included.
Third most important was the growth in labor productivity. On average,
it was lower relative to national income in the 2000–2009 period than
during the 1980s. Had it not declined, profit’s predicted share would have
grown 3.9%, not just the 3.5% predicted by the model when the decline in
the labor productivity ratio is included in the projection.
Fourth most important was the decline in the exchange rate during this
period. This had a positive effect on profit’s share, but a small one. Had
the exchange rate not fallen, profit’s share would have grown a predicted
3.4%, slightly less than the 3.5% the model predicted including the growth
in the exchange rate.
Finally, the drop in the employment/national income ratio was in part
due to rising foreign profits effect of raising national income faster than
employment. Had this not occurred, instead of growing a predicted 3.5%,
profits share would have only grown 3.4% (Table 20.4.3.3).
Table 20.4.3.3 Simulation of effects on profit’s share of counterfactuals
Actual profit’s share of NI (av. for 2000–2009 minus av. for 1980–1999 = 0.0347 (3.5%)
Predicted profit’s share (from Model 3.2.1.1A) = 0.0348 (calculated using actual for
all explanatory variables)
Explanatory variables Reg. coef. (Actual data Pred. profit share after simulation
used in simul. (using actual data except “0” for
2010– 1980) simulated variable)
Empl/NI –0.003 (–0.5.34) +2.1% (vs. +3.5% Using

Actual Data for All)
(Labor Prod./NI)–1 +1.92 (–0.002) +3.9 (vs. +3.5 “ “ )
ForPr/NI +4.76 (+0.010) –1.4 (vs. +3.5 “ “ )
ForPr/TPr –0.508 (+0.048) +5.9 (vs. +3.5 “ “ )
XRAV0,–1,–2,–2 –0.00027 (–2.48) +3.4 (vs. +3.5 “ “ )
20.4.4 OLS Models of the Level of Profit Income

To determine if this investigation into the determinants of factor shares
is more than a game of “whack-a-mole”, we will also examine how the
factors found to influence profit’s share also affect the level of aggreg-
ate profit income. To do so, we rerun the same model except with the
level of total profit income as the dependent variable. Results are shown in
Model 20.4.4.1. The final time period/model specification robust model
is presented as Model 20.4.4.1.TR .
Model 20.4.4.1
OLS Model of the Determinants of Level of Profit Income
PLevel = + 0.008(Y) – 0.08(Y – Y–1 ) – 0.35.60(EmpI / NI)
(t =) (1.7) (–1.2) (–1.0)
+ 674.58(Wage / NI) – 7.72%Union
(0.2) (–0.5)
+ 56430.86(LPROD(–1) /NI–1 ) + 41221.13PROFROW /NI
(1.1) (3.7)
– 4273.90(FProf / TProf) – 7.44PRav–3–4
(–7.5) (–0.9).
+ 232.06INFL + 0.18(CDebt)
(0.3) (2.9)
– 4.28(XRAV–0,–1,–2,–2 ) R2 = 0.88; DW = 1.8
(–1.4)
(20.4.4.1)
This “levels” model was also tested in three other sample periods to
determine the robustness of findings to time period sampled. Only three
variables were found significant in at least three of the four samples of
profit levels tested: GDP, foreign profits/national income ratio, and for-
eign profits/total profits ratio. These three variables explain 83 of the 88%
of variance explained by the larger levels model above. The robust model
is shown in Eq. 8R.
Model 20.4.4.1.TR
Time Period Robust OLS Model of the Determinants
of Level of Profit Income
PLevel = + 0.10(Y) + 47766.69PROFROW /NI – 5077.98(FProf/TProf)
(t =) (3.6) (7.9) (–13.2)
R2 = 0.83; DW = 1.9
(20.4.4.1.TR)
Previously, we found the same two foreign profits variables are the key
variables determining profit’s share. The levels model leads us to conclude
that the main variables explaining growth in profits since 1965, both in
levels and as a share of national income, is the increase in GDP and the
contribution made by foreign profits to total U.S profits. As was the case
with labor income, the principal driver of profit income in the long run is
GDP growth. This is not totally surprising, since in general income can’t
grow unless output is growing. However, with profits, growth in U.S.-
owned foreign production has led to U.S. profit growth, too. Notice the
exchange rate variable has the opposite sign it had in the labor income
levels model. Here, its negative sign means a strong U.S. dollar reduces
exports and increases imports, both of which hurt company profits.
The growth in profit income levels was not found matched by any
decline in labor’s total income. Hence profit’s gain did not occur because
of a “beggar thy neighbor” effect in which profit’s gain came at the
expense of labor’s loss. However, one could argue that labor’s share might
not have declined at all relative to profit’s if the foreign investment that
led to profit growth had been invested domestically, creating labor jobs in
the states rather than in foreign countries. But this would probably be a
“beggar thy neighbor” approach, since presumably, the reason U.S. busi-
nesses invested abroad was because profits were expected to be better than
what was available from investing the same money domestically.
As the test below shows, the growth in profits on foreign (ROW)
operations as a percent of national income is associated with declining
unemployment in the U.S. This suggests a net benefit to labor of for-

eign investment, since declining unemployment is also associated with
rising labor share. However, the benefit is moderate at best. Without
the autocorrelation control variables, the growth in foreign profits for
the current and past year only accounts for 6% of the variation in the
unemployment rate.
Model 20.4.4.2
Relationship of Unemployment Rate to Foreign Profits/NI Ratio
UNEM% = 6.32 – 0.006(ProfROW /NI)–0&–1 + 1.24AR(1) – 0.47AR(2)

(t =) (12.0) (–3.7) (7.8) (–3.8)
R2 = 0.78, D.W. = 1.9
(20.4.4.2)
The same result can be shown by adding the foreign profits/national
income ratio variable to a sophisticated version of Okun’s simple model
of unemployment’s determinants during the 1960–2010 period:
Model 20.4.4.3
Okun Unemployment Model After Adding Profits Variable
UNEM% = 1.41 – 0.38GDP – 0.05GDP–1 – 0.06INFL

(t =) (8.4) (–9.4) (–1.7) (–1.7)
+ 0.38Shock73 + 0.13Shock78 – 0.54Shock05
(1.2) (0.7) (–4.0) (20.4.4.3)
+ 0.41Shock08 – 75.58(ProfROW /NI)–0&–1
(2.2) (–2.3)
2
R = 0.85; D.W. = 1.7
where
UNEM% = U.S. unemployment Shock73 = OPEC oil price increase

rate Shock78 = OOPEC oil price increase
GDP = U.S. real GDP Shock05 = Hurricane Katrina
INFl = inflation (cpi) Shock08 = 2008 financial crisis
Thus, the revised Okun model confirms our earlier finding that the growth
in foreign-earned profits as a fraction of national income did not come at
the expense of employment in the U.S. in fact appears to have stimulated
it. This may mean that some foreign profits are reinvested in the U.S.,
representing investment that would otherwise have not occurred in the
U.S., increasing employment opportunities.
Summary of Findings – Profit Models
See Table 20.4.4.1.
Table 20.4.4.1 Summary of factors affecting profit’s % share and level of real
national income
Profit’s % share of NI (Eq. 20.4.3.1.TR) Profit’s level of NI (Eq. 20.4.4.1.TR)
Positive effects Positive effects

Increased labor productivity/NI GDP growth
Increased foreign profits/NI Foreign profits/NI ratio growth
Negative effects Negative effects
Increased employment/NI Ratio Foreign/total profits ratio growth
Increased foreign/total profit ratio
Increasing exchange rate
20.4.5 OLS Models of Rent’s Share of National Income

Surprisingly little empirical work has been done to determine the under-
lying causes of fluctuation in rental income share of national income. In
this section we hypothesize and test a number of variables to determine if
they are related to variation in rent’s percentage share and level of national
income.
Stationarity Issues
ADF test. Only one possible explanatory variable was found nonstationary:
the variable measuring profit income’s share of national income. This vari-
able was tested for cointegration with the rental share of national income
variable. It was found cointegrated, so no detrending was needed.
Endogeneity Issues
Explanatory variables in the models were tested for endogeneity with the
dependent variable using the Hausman endogeneity test. Results indicated
no endogeneity in either the rental share or rental levels models tested, so
no retesting using 2SLS was needed. The model tested was the full model
given in Eq. 9 below tested using 1965–2010 data.
20.4.5.1 OLS Rental Share (RS) of National Income Model

A preliminary model was tested on the full 1969–2010 data set and
included the variables in Eq. 20.4.5.1 plus the population size variable,
lagged residential investment levels and the variables representing labor
and profits shares of national income. However, these last four variables
were found insignificant in early testing and were dropped. Variables are in
2005 dollars. The final, robust model is presented in Model 20.4.5.1.TR.
Model 20.4.5.1
OLS Estimates of Determinants of Rent’s Share of National Income
RS = – 0.0000094(HPrice /NI) + 26.82(Prop.Inc/NI) + 0.025Mort.Int–1
(t =) (–117.8) (2.6) (2.3)
–19.41(Av.Wage–1 /GDP–1 ) R2 = 0.77; DW = 2.0
(–2.1)
(20.4.5.1)
where here or in the levels equation further below:
(HPrice /NI): = the ratio of real house prices to real

GDP
(Prop/NI, L/NI and Prof/NI) = proprietor’s, labor’s and profit’s share
of real national income
(InvR ) = investment in residential housing
(Mort) = real mortgage interest rates
(Av.Wage–1 /GDP–1 ) = the ratio of average real wage rates to
GDP, lagged 1 year
The housing price variable was overwhelmingly the most important

determinant of rent’s share of national income, accounting for 70 of the
77% explained variance. The negative sign suggests that a rise in hous-
ing prices relative to income is the result of a shift in housing preferences
toward home ownership, and is pushing prices up. This results in lower
rental income as people’s housing demand shifts away from rentals and
toward house ownership. The increased demand for housing increases
profits and labor income, increasing their share of national income while
lowering that of rentals. Growth in average wages relative to GDP also
seems to have the same effect, the higher wages indicating housing was
becoming more affordable. Rising mortgage interest rates had a posit-
ive effect on rental share, reflecting a shift away from home ownership
toward rental housing. Finally, we note growth in proprietor income was
also positively related to rental share of national income in this sample.

Tests for robustness in other time periods indicate this was probably a
spurious correlation.
Stepwise regression is used in to estimate the contribution to total
explained variance attributable to any one variable. Findings are presented
in Table 20.4.5.1.
Using either first-in or first-out methods, overwhelmingly, the ratio of
house prices to national income is the variable most systematically related
to rent’s share of national income.
Robustness of Parameter Estimates Over Time
Table 20.4.5.2 tests rental share model 20.10 to determine the stability of
coefficients from sample to sample.
When the 2001–2010 decade is included in samples, all four variables
are found significant. But, in samples excluding this last decade, only
the housing price/GDP ratio and average wage/GDP ratio were found

explained variance in interest share model 20.4.5.1

(HPrice /NI) 0.07 0.70

(Prop.Inc/NI) 0.70 0.03
Mort.Int.Rate–1 0.74 –0.03
Av.Wage–1 /GDP–1 0.75 –0.03
Table 20.4.5.2 Determinants of rent’s share of national income coefficient stabil-

ity over time in Eq. 20.4.5.1
Variable 1965–2010 1975–2010 1965–2000 1975–2000
(HPrice /NI) –0.000009∗ –0.000009∗ –0.00017∗∗∗ –0.00084∗

(Prop.Inc/NI) 26.83∗ 37.75∗ 9.36 3.74
Mort.Int.Rate–1 0.025∗∗ 0.045∗ 0.005 0.007
Av.Wage–1 /GDP–1 –19.41∗∗ –32.18∗∗ –7.03∗∗∗∗ –27.98∗
Significance level: ∗∗∗∗ 15%; ∗∗∗ 10%; ∗∗ 5%; *1%.

significantly related. Both were negatively related to the level of rental

income, indicating a preference for home ownership over renting as aver-
age incomes rise, and reflecting a tendency for rental income to decline
when housing demand was strong pushing up house prices, also sug-
gesting a shift in housing preference from rentals to home ownership.
Mortgage interest rates, though having the same sign, were statistically
insignificant determinants of rental share without the 2001–2010 data in
the samples, but this may reflect the decline in owned housing in the later
part of the decade, even with low mortgage rates.
Re-estimating our original rent’s share model (Eq. 20.4.5.1) without
the proprietor’s income and mortgage interest variables yields the follow-
ing preliminary robust model results:
Model 20.4.5.1 TR (Prelim.)

Preliminary Robust Model of Rent’s Share of National Income
RS = – 0.0000095(HPrice /NI) – 2.40(Av.Wage–1 /GDP–1 )

(t =) (–371.3) (–0.7)
R2 = 0.70; DW = 2.1
(20.4.5.1TR Prelim)
Robustness to Model Change: Adding and Deleting Variables to the
Final Model
Though the housing price variable’s parameter estimates are stable after
deleting the proprietor’s income and mortgage interest rate variables, this
is not true for the wage/GDP ratio variable. Hence this variable is dropped
for lack of robustness with regard to model specification. The revised
model (10R) is shown below.
Model 20.4.5.1 TR (Final)

Final Robust Model of Rent’s Share of National Income
RS = – 0.0000095(HPrice /NI) R2 = 0.70; DW = 2.1
(t =) (–382.4)
(20.4.5.1TR)
To test robustness of the parameter estimates in this time period robust
model to specification changes involving adding variables to the model, we
added two variables to the model: a variable representing 2-year average
residential investment levels, and the unemployment rate. No significant
change in the housing variable’s coefficient or significance was noted.
Hence, we conclude that our final model, found robust to both changes
in time period sampled and model changes, is the one explanatory vari-
able model (Housing Price /GDP ratio) given in Eq. 20.4.5.1TR, which
explains 70% of the variance in rental income over the 1961–2010 period
tested. With the variables we examined, we were not able to find other sig-
nificant determinants, though with 30% of the variance in rent’s share of
national income still unaccounted for, suggests other factors are at work.
We expect research work in the future will uncover some of them, but
because of the robustness of our own tests, do not expect these future
studies to overturn the results found here, which indicate absolutely noth-
ing is more important in determining rent’s share of national income than
how strong demand for home ownership is, i.e., how high housing prices
are relative to GDP.
20.4.6 Models of the Level of Rental Income

OLS Tests of Rental Income (in Levels)
Initial tests, using the available 1969–2010 data yielded the following res-
ults. We were unable to find a combination of variables that were time
period robust.
Model 20.4.6.1
OLS Model of Determinants of the Level of Rental Income
RILevel = + 0.00027(HPrice /NI) + 2.60Mort.Int–1
(t =) (6.6) (2.9)
– 3769.09(Av.Wage–1 /GDP–1 ) – 0.108Res.Inv.–1,–2
(–1.4) (–4.0)
– 488.51(LaborInc / NI) + 0.72AR(1)
(–2.0) (6.9)
R2 = 0.78; DW = 1.9
(20.4.6.1)
Here, higher house prices are positively related to the level of rental
income, seem to indicate a shift away from home ownership to renting
(earlier, when analyzing shares, it symbolized a reduction in rent’s share
(not necessarily its level) due to growth in labor and profit income when
housing booms occur, but not necessarily a reduction in rental income
levels). Mortgage interest rates effect on rental income is again positive.
Rising wages relative to GDP again is found negatively related, as is growth
in labor’s share of national income. Both factors increase worker income,

and may cause renters to leave rental housing for home ownership. The
negative relationship of residential investment to rental income also prob-
ably is measuring the effects of an exodus from rental properties toward
home ownership.
Next, we tested the robustness of these initial findings in the remaining
three sample periods.
Robustness tests for 1969–2010, 1979–2010, and 1989–2010 showed
the same variables significant. However, no variables were found signific-
ant if the 2001–2010 decade data were not included in the test. Hence,
by the standard we have used throughout this study, we cannot say that
any variables in the model are robust to time period tested. Clearly, more
research is needed on the determinants of the level of rental income for
the 1960–2000 period.
Summary of Findings: Rental Income’s Level and Share of NI
Table 20.4.6.1 summarizes our findings regarding the determinants of
rental income and share.
Table 20.4.6.1 Summary of factors affecting profit’s % share and level of real
national income
Determinants of share (Eq. 20.4.5.1.TR) Determinants of level (Eq. 20.4.6.1∗ )
Positive Positive
HPrice /GDP growth HPrice /GDP growth
Real mortgage interest rate growth(–1)
Level of residential investmentAV–1,–2
Growth in labor’s share of NI
∗ Findings not robust for samples without 2001–2010 data
20.4.7 OLS and 2SLS Models of Interest’s Share of National Income

In developing a model of the determinants of interest’s share of national
income, initial tests included all the following variables:
(DebtB& C ) = total business and consumer real debt levels

(PRAv0,–1,–2 ) = average real prime interest rates
(Aaa/NI) = real Aaa bond interest rate/national income ratio
(Baa/NI) = real Baa bond interest rate/national income ratio
(Mort/NI) = real mortgage interest rate/national income ratio

(Empl/NI) = employment/NI ratio
(DJAV) = NYSE Composite Index
(Prof/NI) = profit income/NI ratio
(Labor/NI) = labor income/NI ratio
(Rent/NI) = rental income/NI
(Prop.Inc/NI) = proprietor income/NI
Stationarity Issues
All variables listed above were tested for nonstationarity using the ADF
test. Only one variable was found nonstationary: the stock market index
variable. This variable was tested for cointegration with the interest share
of national income variable, which is the dependent variable in the model
in which the stock market index is used as an explanatory variable. It was
found cointegrated using the Dickey-Fuller test, so no detrending was
needed.
Endogeneity Issues
Explanatory variables in the models above were tested for endogen-
eity with the dependent variable using the Hausman endogeneity test,
described in detail earlier. Results indicated no endogeneity except
between consumer and business debt, and the interest share variable. A
nonendogenous, Wald strong instrument was developed to replace it.
In preliminary tests, all the variables mentioned at the beginning of this
section were tested, but only the variables in the model shown below were
found significant. The others were dropped from the model during this
preliminary testing process. The final, time period and model specification
robust model is given in Model 20.4.7.2 further below.
Model 20.4.7.1
OLS Model of Interest Income’s Share of National Income
IntS = – 0.42Debt0.3
C& I + 27.20PRAV–1,–2,–3 /NI + 0.021Empl / NI
(t =) (–4.1) (9.0) (14.2)
– 0.0005(T – G) + 7.34Baa / NI + –0.27AR(1)
(–13.2) (2.5) (–1.8)
2
R = 0.95; DW = 2.0
(20.4.7.1)
Model 20.4.7.2
2SLS Model of Interest Income’s Share of National Income
C& I + 27.17PRAV–1,–2,–3 /NI + 0.021Empl / NI
(t =) (–3.9) (8.6) (14.2)
– 0.0005(T – G) + 7.24Baa / NI + –0.28AR(1)
(–12.7) (2.3) (–1.6)
R2 = 0.95; DW = 2.1
(20.4.7.2)
Stepwise regression was used to estimate the contribution to total
explained variance attributable to any one variable. Findings are presented
in Table 20.4.7.1.
With both methods, the variable that explains the most variance is the
ratio of employment to national income; the ratio of the average prime
rate to national income was the second most important.
Table 20.4.7.2 shows tests of interest share model 12 to determine the
stability of coefficients from sample to sample.
All the variables except the government deficit remained significant in
all samples, hence, for them, results are robust to time period sampled,
and our confidence in our model of the determinants of interest’s share
of the NI enhanced. For the government deficit, its effect on interest’s
share here is dominated by the large deficits in the 2001–2010 decade,
which significantly increased interest’s earnings, and positively affected
interest’s share of national income. For the two periods 1968–2000 and

explained variance in interest share model 20.4.7.2

PRAV–1,–2,–3 /NI 0.88 0.66

Baa/NI 0.94 0.03
(Debt.3 C& I ) 0.94 0.02
(T-G)/GDP 0.89 0.11
EMPL/NI– 0.81 0.69
Table 20.4.7.2 Determinants of interest’s share of national income coefficient

stability over time in Eq. 20.4.7.2
Variable 1968–2010 1978–2010 1968–2000 1978–2000
PRAV–1,–2,–3 /NI 27.17∗ 30.73∗ 26.07∗ 40.02∗

Baa/NI 7.24∗∗ 12.94∗ 6.45∗∗∗∗ 13.99∗
(Debt.3 C& I ) –0.39∗ –0.39∗ –0.40∗ –0.27∗∗
(T-G)/GDP –0.0005∗ –0.0005∗ 0.0006 0.10∗∗
EMPL/NI– 0.02∗ 0.02∗ 0.02∗∗ 0.01∗∗∗∗
Significance level: ∗∗∗∗ 15%; ∗∗∗ 10%; ∗∗ 5%; ∗ 1%.
1978–2000, the sign changes to positive, and the variable is significant

in only one of the two periods. This may be due to the relatively small
amount of variation of the deficit/GDP ratio through most of the period
up to 2000. Hence, our results which initially indicated deficits improved
interest’s share, did not prove robust to different time periods sampled.
All others did.
Because of this, our model of the variables determining interest’s share
of national income that is robust to period sampled omits the deficit
variable. Results are given in Eq. 20.4.7.2.TR (Preliminary) below.
Model 20.4.7.2.TR (Preliminary)

Time Period Robust Model of Determinants of Interest’s Share
of National Income
C& I + 36.47PRAV–1,–2,–3 /NI + 0.014Empl / NI
(t =) (–0.2) (3.7) (3.0)
+ 12.52Baa / NI + –0.31AR(1)
(2.3) (–3.7)
2
R = 0.89; DW = 2.0
(20.4.7.2.TR.Prelim)
Robustness to Model Change: Adding and Deleting Variables to the Time

Period Robust Model
After deleting the deficit variable, consumer and business debt as a sig-
nificant determinant of interest’s share does not prove robust to model
change. Deleting it here and re-estimating indicates the rest of the model
parameters are robust to this change, as shown in Eq. 20.4.7.2.TR (Final)
below.
Model 20.4.7.2.TR
Determinants of Interest’s Share of National Income
(Final Time Period and Specification Robust Model)
IntS = 36.68PRAV–1,–2,–3 /NI + 0.014Empl / NI + 12.57Baa / NI

(t =) (4.0) (3.7) (2.4)
+ – 0.30AR(1) R2 = 0.89; DW = 2.0
(–3.2)
(20.4.7.2.TR)
Changing the model further by deleting the Baa interest rate variable also
leaves the remaining parameter estimates generally stable. Adding the cur-
rent period GDP to the model also leaves the parameter estimates for the
variables already in the model very stable. Adding an additional variable
(2-year average residential investment) to this model still leaves the key
parameters estimates essentially unchanged, attesting to their parameter
robustness.
Hence, we conclude the estimates in our final three-explanatory variable
model (Eq. 20.4.7.2.TR) are robust to both choice of sample period tested
and reasonable changes in model specification. This enhances the credib-
ility of the model considerably, moving it, we believe, from the oft seen
(but never intellectually satisfying) category of “one more study of . . . .”
to something more akin to true, reliable science.
20.4.8 OLS and 2SLS Models of the Level of Interest Income

The following variables were initially found significantly related to the
level of interest income: the final robust model (20.4.8.2.TR) is presented
further below.
Model 20.4.8.1
OLS Model of the Determinants of the Level of Interest Income
IntLevel = + 41.14Debt0.3
C& I + 27.63PRAV–1,–2,–3
(t =) (1.8) (5.1)
– 21.16UNEM + 0.034(T – G) + 3.40Baa
(–3.4) (4.1) (1.3) (20.4.8.1)
+5112.72INFLAV0,–1,–2 + 0.30DJAVAV0,–1
(4.0) (2.2)
R2 = 0.73; DW = 2.0
The variables have the same meaning as in the shares model except the
two interest rate variables stand alone; they no longer represent interest
rate/national income ratios. In addition, “UNEM” stands for the unem-
ployment rate and “INFL” the inflation rate. Together, these only explain
73% of the variation in the level of interest income over the 50 years
sampled, 1965–2010. Additional determinants most likely exist, but were
not found.
In testing for levels of interest income, in addition to the variables
shown above, all the other variables described at the beginning of this
section were tested, as well as the exchange rate and the trade deficit,
which were also found insignificant. Also tested were the mortgage and
Aaa bond rates. These were found insignificant when the Baa rate was also
included in the model, but were at least marginally significant if not. This is
essentially the behavior we would expect if they were serving as imperfect
proxies for the Baa rate. Since market interest rates tend to move together
(rrealBaa,Aaa = 0.93), we interpret our Baa finding as capturing the effect
of all such highly correlated market-driven rates on the level of interest
income. The prime interest rate by comparison, also significant, is not a
market-determined rate. It is rigidly linked to the level of the federal funds
rate, which is an administered one established by the Federal Reserve. To
a large extent, it moves independently of market rates. For this reason we
find both the prime rate and the Baa rate significant in the model.
The debt, inflation, and Baa interest rate variables were tested for endo-
geneity with the level of interest income. Only the Baa interest rate variable
was found endogenous and was replaced with a Wald-strong instrument
containing the same variables used as an instrument in the interest’s
share model, but with two lagged values of the Baa variable added to
strengthen it. The model was then re-estimated, yielding the following
results:
Model 20.4.8.2
2SLS Model of the Determinants of the Level of Interest Income
C& I + 30.40PRAV–1,–2,–3 – 21.30UNEM
(t =) (1.9) (5.2) (–3.1)
+ 0.032(T – G) + 5.19Baa + 5669.50INFLAV0,–1,–2
(3.7) (1.6) (4.1)
+ 0.28DJAVAV0,–1 R2 = 0.74; DW = 2.1
(1.9)
(20.4.8.2)

From the first-out stepwise perspective, the variables that explain the most
variation in the level of interest income are the prime rate/NI average
and the average inflation rate, which are positively related to the level of
interest income, and the government deficit as a % of GDP (the smaller
the percentage, the greater the level of interest income (Table 20.4.8.1).
From the first-in perspective, the stock market index (positively), the
unemployment rate (negatively) and the deficit/GDP ratio (negatively)
are the most important contributors to explained variance.
Time Period Robustness
To test the robustness of these results over time, we also retested the model
in three additional sample periods. Results for all four sample periods are
compared in Table 20.4.8.2.

explained variance in interest level model 20.4.8.2

(Debt.3 C& I ) 0.71 0.03

PRAV–1,–2,–3 /NI 0.55 0.12
UNEM 0.65 0.07
(T-G)/GDP 0.62 0.08
Baa/NI 0.73 –0.03
INFLAV0,–1,–2 0.63 –0.01
DJAVAV0,–1 0.71 0.38
Table 20.4.8.2 Determinants of interest’s share of national income coefficient

stability over time in Eq. 20.4.8.2
Variable 1968–2010 1978–2010 1968–2000 1978–2000
(Debt.3 C& I ) 40.91∗ 66.79∗ 68.95∗∗∗ 129.48∗∗∗

PRAV–1,–2,–3 /NI 30.40∗∗∗ 31.25∗∗∗ 25.65∗∗∗ 23.67∗∗∗
UNEM –21.30∗∗∗ –30.31∗∗∗ –8.43 –16.78∗
(T-G)/GDP 0.03∗∗∗ 0.04∗∗∗ –0.08 3.45
Baa/NI 5.19 1.06 4.59∗ –2.47
INFLAV0,–1,–2 5569.50∗∗∗ 5560.31∗∗∗ 3749.96∗∗∗ 4406.76∗∗
DJAVAV0,–1 0.28∗ 0.14 –0.04 –0.29

Four of the variables were found significant in all four sample peri-
ods: consumer debt (+), the prime interest rate/national income ratio
(+), inflation (+) and unemployment (–). None of the other three vari-
ables in the initial test was found significant in more than two of the four
sample periods, nor were any of them found significant when individually
retested with the four-variable core robust model. Though two were found
individually significant, when both were added to the core model and
retested, none passed the “3 of 4” test. Hence, the results for these three
variables were not considered time period robust. The four-variable core
model becomes the time period robust model, shown as Eq. 20.4.8.2.TR
below.
C& I + 30.97PRAV–1,–2,–3 – 29.33UNEM
(t =) (2.1) (5.7) (–4.4)
+ 5518.62INFLAV0,–1,–2 R2 = 0.74; DW = 2.1
(3.4)
(20.4.8.2.TR)
Robustness Tests: Model Specification

Coefficients and significance levels for the four robust variables are very
similar to those in the initial model which had three additional variables.
Deleting the debt and inflation variables from the robust model left the
coefficients and significance levels of the two remaining variables very sim-
ilar to those in the robust model. Hence, we conclude Eq. 20.4.8.2.TR
above is robust to model specification as well as sample period tested.
20.4.9 Summary of Interest Rate Model Results

See Table 20.4.9.1.
Table 20.4.9.1 Summary of factors affecting interest’s % share and level of real
national income
Determinants of share (Eq. 20.4.7.1TR) Determinants of level (Eq. 20.4.8.2.TR)
Positive Positive
Real Prime Int. RateAV–1–2–3 /NI Prime Int. RateAV–0–5
Real Baa Int. Rate/NI Unemployment Rate
Employment/NI Ratio Consumer and Business Debt
Inflation
20.5 SUMMARY AND CONCLUSIONS (INCOME SIDE OF THE NIPA ACCOUNTS) 441
20.5 SUMMARY AND CONCLUSIONS (INCOME SIDE

OF THE NIPA ACCOUNTS )
We often forget that there are two sides to the balance sheet referred to
at the NIPA Accounts. The most attention in both theory and empirical
work has been on the product side, describing the determinants of the
different types of economic product produced. Less attention is given to
the other half of the NIPA accounts: how what is produced each year
is distributed among those who helped produce it. That is, what factors
determine how the money value of production gets distributed among the
factors of production? Does change in these determinants over time cause
factor returns to vary from one decade to the next? This chapter deals with
income, but a related topic (why is wealth concentrated among so few?),
has gained much attention recently (Piketty 2014, 2015; Mankiw 2015;
etc.).
Chapter 20 is designed to address the need to identify the determinants
of how the GDP is distributed among the factors that produce it, and how
change in these determinants can change how factor shares and levels of
income are distributed over time to different factors of production.
We summarize our findings in two ways: (1) what variables determine
what percentage share of the total income that goes to each factor of pro-
duction, and (2) what factors determine the actual level of income received
by each factor. Results are summarized in the sections below.
20.5.1 What Determines the Percent of National Income

Going to Different Factors?
Labor’s Share
Overall, two factors determine most of the fluctuation in labor’s percent-
age share from a high of 68% in 1980 to a low of 62% in 2010, each
accounting for about half the variation:
1. The enormous increase in profit’s percentage share attributable to

the rapid growth in profits from overseas operations of U.S.-owned
firms. This has caused labor’s percentage share to decline, even
though the level of labor’s total income has actually grown (see
Table 20.1.1.2). If the problem had been more one of outsourcing
(moving existing production overseas), we would have expected to
see a decline in the level of labor income as well. Instead, the main
thing seems to be increased creation of new productive capacity

overseas, raising U.S. profits without lowering total incomes of
workers in existing U.S. production facilities.
2. Keynesian demand-driven fluctuations in spending on goods and ser-
vices. Because capital is relatively fixed in the short run, and labor
supply is more variable, labor’s percentage share of national income
tends to grow as demand for goods and services grows; declines as
demand for goods and services declines. In particular this study finds
labor’s share grows as any of the following changes occur:
(a) GDP growth
(b) employment growth relative to GDP growth
(c) declining unemployment
(d) growth in labor force participation rates
(e) growth in government deficits (labor tends to be the main
beneficiary)
(f) declining average wage levels relative to national income
(The negative sign on the wage/national income ratio variable in
regressions suggests that the increased income received by labor
due to increased labor demand resulting from wage decline, is
greater than the income lost due to the fall in wages. This finding
is consistent with neoclassical synthesis theory, which suggests that
long-term declines in real prices and wages restores full employment
equilibrium.)
Profit’s Share
Four factors were found related to profit’s share of nation income. They
were
Positive Effects
Growth in the labor productivity/national income ratio
Growth in the ratio of U.S. profits from foreign operations relative to
national income (this was the most important factor since 1980)
Negative Effects
Growth in employment/national income ratio
Increased U.S. exchange rates (units of foreign currency/$), which
decreases export attractiveness and increases import attractiveness
Rental Income’s Share
The one factor found systematically related to rent income’s share was
the ratio of house prices to GDP. It was significant in every one of the
20.5 SUMMARY AND CONCLUSIONS (INCOME SIDE OF THE NIPA ACCOUNTS) 443
four time periods sampled, but not as a substitution effect, i.e., not with a
positive sign. The house price/NI ratio consistently had a positive sign,
suggesting the finding is indicating shifting housing preferences from
rental to home ownership, which would be expected to push up house
prices, is the more fundamental factor causing the decline in rent’s share
of national income.
Interest Income’s Share

Interest income’s share of national income increased with growth in the
prime interest rate, growth in the Baa bond rate (proxying for itself and
other private bond rates). The prime interest rate was far more important
than bond interest rates, reflecting bank lending’s historically larger role in
the economy compared to bonds. Growth in the ratio of employment to
national income was also important. The last variable is taken to indicate
that the demand for loans increases as the number of people employed
increases.
20.5.2 What Determines the Total Amount of Income (Its Level)

Going to Different Factors?
Determinants of Labor’s Income Level
The only variable found related to the level of labor income in at least
three of the four time periods sample was the GDP, significant in all four.
This makes some sense, since over the long run, labor income can only
grow if productivity is growing, causing real GDP to grow. The ups and
downs of the business cycle, important in explaining short-term variation,
largely cancel each other out over the long run. In some preliminary test-
ing, without the GDP variable included, the labor force participation rate
and unemployment rate both showed a relationship to the level of labor
income, but when the GDP was added as a third explanatory variable,
they became insignificant, suggesting their variation’s effect on total labor
income is more a proxy for GDP variation.
Determinants of Profits’ Income Level

Here again, the major factor affecting the level of total income was the
level of GDP. But the rate of growth in GDP understates the rate of
growth in profit income. Profits grew at a faster rate because of the
extraordinary growth of profits derived from foreign operations, which
causes profit income to grow much faster.
Determinants of Rent’s Income Level

Initial testing in 50-year models indicated the higher mortgage interest
rates, the higher rental income, reflecting the fact that mortgage rates
reflect the cost of home ownership, and high costs cause consumers to
shift housing preferences to rental property. In addition, the same prelim-
inary testing indicated that both total labor income growth (and growth
in average wages), relative to national income, were negatively related to
rental income. This indicates a preference for home ownership over rent-
ing as incomes rise. These three variables were found to be significant
determinants in at least three of the four sample periods tested.
Unfortunately, none of these three variables remained significant when
only they alone were rerun in a new regression as determinants of rental
income levels. So, by this study’s usual standard for robustness, we cannot
assure the reader our findings for rental income levels are robust.
Determinants of the Level of Interest Income
The level of consumer and business debt, the level of the prime interest
rate, and the level of inflation were all found positively related to the total
level of income earned by all interest income recipients. A fourth variable
was also found significant: the unemployment rate was found negatively
related to total interest income.
Proprietor’s Income
In concluding this summary, we note no attempt to analyze the determin-
ants of proprietor income was made. Part of proprietor’s income is labor,
and part is profit, and we would have liked to include the appropriate
share of proprietor income in the analysis of both those categories, but
could not. This was unfortunate, but necessary, because of the difficulty
of sorting out labor from profit income components when analyzing this
type of income.
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Wilcox, D. (2015). Correspondence with J. Heim dated 7/17/2015.
Woodridge, J. (2003). Introductory Economics: A Modern Approach, 2nd ed.
Mason, OH: Thomson South Western.
Woodridge, J. (2012). Economic Report of the President. Washington, DC: Gov-
ernment Printing Office (also reports for 1963, 2010).
Woodridge, J. (2012). Economic Report of the President. Washington, DC: Gov-
ernment Printing Office (also reports for 1963, 2011).
I NDEX
A Brayton, F., 72, 74, 140

Accelerator, 1, 5, 67, 104, 105, Business borrowing, 67, 186, 188,
109, 144, 189–191, 194, 195, 190, 194, 197, 203, 204, 207,
198, 200, 203–205, 208, 209, 251, 288, 338, 341
216–218, 253, 286, 288, 290,
291, 349, 351, 357, 412, 415, C
416 Calibration, 83–84
Adaptive expectations, 56, 57, 70, 87 Capacity Utilization Rate, 9, 95, 149
AD curve, 2, 332, 333 Christoffel, K., 55
Aggregate Demand(AD), 2, 331–362, Chung, H., 72
389, 390 Clothing, 126, 127
Aggregate Supply(AS), 2, 116, Coenen, G.
331–362 Colander, D.
Appliances, 127, 174 Consumer borrowing, 14, 57, 62, 65,
AR(1), 254, 314, 316 67, 113, 150, 159, 164, 166, 167,
ARIMA, 90, 91, 126 168, 170, 171, 178, 213, 298,
AS curve, 331 300, 348, 370, 371, 415, 416,
Astronomers, 8 417
Autoregressive coefficients, 90, Consumer confidence index, 65, 244
102 Consumer durables, 16, 82, 109, 110,
Autos, 117, 118, 119, 128, 143 118, 133, 134, 143, 171–177
Average error of fit, 101, 329 Consumer Goods, 1, 2, 48, 80, 119,
127, 128, 140, 149–166, 239,
B 247, 318
Behavioral equations, 2, 4, 9, 14, 16, Consumer nondurables, 75, 133, 134,
108, 122, 123, 369, 378 172, 176, 177, 178, 179, 180,
Bentolila, S., 390 183
Bond interest rate, 135, 379 Consumer services, 14, 132, 134,
Brayton, F, 74, 75 180–184

DOI 10.1007/978-3-319-50681-4
452 INDEX
Consumption, 6, 7, 9, 12–14, 40, D

41, 44–45, 47, 50, 52–54, DeLeeuw, F., 72
56–63, 65, 66, 68, 72–78, 80, Del Negro, M., 54
82–84, 86, 87, 93, 94, 104–106,
Dependent variable, 10, 11, 16, 30,
109–118, 131, 132, 136–138,
42, 43, 45, 51, 57, 58, 77, 78, 90,
140–143, 145, 147–184, 186,
91, 96, 102, 103, 104, 106, 107,
187, 217, 229, 231, 233, 234,
111, 116, 127, 139, 140, 147,
235, 241–244, 248, 250, 253,
148, 149, 150, 151, 152, 154,
296–298, 320, 322, 333, 337,
158, 162, 166, 168, 172, 173,
346, 352, 358–362, 369–371,
178, 181, 185, 187, 188, 189,
391, 392
192, 197, 203, 208, 210, 212,
Cooley, T. F., 84 215, 216, 224, 226, 232, 233,
Corporate profits, 285 234, 235, 256, 261, 267, 275,
Correlation, 13, 16, 44, 45, 89, 90, 288, 292, 299, 308, 310, 328,
91, 98, 102, 104, 105, 106, 124, 342, 349, 359, 369, 394, 396,
139, 210, 233, 234, 258, 308, 397, 398, 404, 409, 410, 412,
390, 394, 418, 426 417, 418, 421, 424, 430
Cost push inflation, 1 Depreciation, 44–45, 77, 104–106,
Cowles, 3, 4, 39, 40, 49, 51, 52, 76, 122, 134, 136, 140, 144, 145,
80, 84, 86, 96, 108–110, 114 189, 191, 192, 196, 197, 199,
204, 207–209, 216, 243, 244,
Cowles Commission, 1, 3, 9, 39, 48,
249–251, 285–289, 291–296,
100, 108, 115, 125
342, 349, 355, 388, 414
Cowles Commission Models, 1, 48, Depreciation allowance, 44, 82, 208,
144 209, 291–296, 355, 414
Cowles Foundation, 108 Disposable income, 47, 56, 58, 60, 62,
Cowles model, 1, 3, 4, 10, 39, 40, 63, 65, 148, 151, 154, 158, 159,
49–56, 66, 71–73, 76, 78, 80–82, 162, 164, 168, 173, 174, 178,
86, 88, 90–92, 95–97, 101, 181, 262, 296, 299, 300
107–114, 115, 139, 142, 145, Domestically Produced Consumer
244 Goods, 149, 157, 162–166, 239,
Cowles–type model, 3, 7, 86, 131 318
Cowls methodology, 4, 39, 40, 73, Domestically produced investment
114 goods, 94, 192, 193, 197, 286,
Crowd out, 1, 2, 66, 109, 112, 319
197, 241–244, 247–250, 255, DRI Model, 9, 39, 55, 90, 125, 126,
296, 335, 336, 337, 340–342, 131
347–349, 361–362, 371, 372 DSGE methodology, 72, 73, 83
Current income, 5, 41, 50, 56, 57, 59, DSGE modeling, 8, 50, 52, 84, 86,
60, 61, 77, 82, 87, 104, 128, 131, 110, 131
141, 356 Durbin Watson test, 16
INDEX 453
Dynamic Stochastic General Equilib- Exchange rate, 13, 41, 57, 62, 65,
rium (DSGE), 3–6, 8, 9, 11, 12, 67, 86, 123, 156, 158, 160, 164,
13, 39, 40, 48–56, 58, 59, 61, 63, 168, 172, 174, 191, 192, 194,
66, 68, 69, 70–73, 77, 78, 81–88, 198, 204, 205, 208, 211, 213,
103, 108, 109–111, 113, 114, 214, 215, 216, 217, 218, 221,
115, 131, 140, 142, 145, 244, 224, 228, 244, 251, 286, 289,
372 296, 300, 345, 355, 372, 392,
409, 410, 415, 416, 418, 419,
E 420, 422, 434, 438
Eckstein, Otto, 1, 4, 7, 9, 13, 39, 41, Exogenous, 42, 68, 123, 148,
49, 55, 67, 87, 90–92, 110, 111, 149, 186, 187, 229, 253, 255,
115, 125–131, 145, 155 303, 309, 318–320, 371, 394,
Econometric model, 1, 7, 8, 9–14, 39, 396
49, 57, 108, 114, 115, 144, 148, Explained variance, 43, 45, 60, 63, 65,
328, 377 69, 98, 111, 141, 150, 153, 154,
Economic philosophy, 5–9 155, 158, 159, 163, 164, 168,
Economic Report of the President, 40, 169, 172, 173, 174, 178, 181,
47, 61, 77, 285 189, 194, 199, 204, 205, 208,
Economic science, 5–9, 124 212, 213, 215, 217, 226, 256,
Edge, R., 53, 111 261, 267, 277, 278, 280, 288,
Endogeneity, 13, 39, 41, 42, 45, 292, 295, 298, 299, 304, 310,
47, 57, 78, 96, 116, 126, 314, 343, 349, 370, 400, 415,
147, 148, 149, 150, 172, 181, 425, 426, 431, 435
185, 186, 187, 215, 224, 255, Explanatory model, 139, 378
280, 286, 309, 342, 349, 394, Explanatory variable, 7, 8, 11, 14,
396, 397, 410, 412, 424, 45, 46, 49, 52, 57, 63, 90,
430, 434 98, 101, 104, 105, 106, 107,
Endogenous, 10, 41, 42, 57, 108, 116, 113, 116, 131, 140, 148, 150,
147–149, 151, 172, 177, 181, 158, 159, 164, 175, 179, 182,
185, 187–189, 192, 193, 198, 184, 192, 195, 197, 201, 208,
204, 208, 254–255, 276, 286, 212, 216, 232, 258, 261, 267,
292, 303, 310, 322–330, 342, 291, 308, 310, 318, 338, 339,
349, 371, 394, 396, 397, 398, 341, 343, 346, 347, 348, 349,
412, 434 353, 394, 395, 396, 397, 402,
Engineering, 4, 7, 11, 24, 50, 81, 88 404, 405, 407, 409, 412, 417,
Engineering Manual, 4, 11, 24, 418, 419, 424, 428, 430, 433,
50, 81 439
Engineering manual, 4, 11, 24, Export demand, 117, 221, 222,
50, 81 225–228, 233, 372
Equation of Exchange, 2, 332, 333, Exports, 1, 10, 44–45, 82, 93–95,
373 109, 110, 115, 117, 123, 131,
Euler condition, 61 138, 139, 144, 149, 158, 159,
454 INDEX
187, 221–228, 230, 231, 233– G

236, 239, 244–247, 320, 322, Gale, W., 91
324, 338, 346, 352, 359, 360, GDP Identity, 15, 94, 229, 236
371–372, 392, 419, 422, 438
GDP, income side, 437
GDP, product side, 378, 437
F
Gollin, D, 391
Factories, 130 Government deficit, 1, 5, 57, 62, 112,
Factor Shares, 116, 377–440 204, 208, 244, 250, 254, 255,
Factors of production, 393, 437 286, 288, 290, 296, 333, 334,
Fair, Ray, 1, 4, 9, 10, 49, 54, 68, 73, 337, 347, 371, 397, 399, 400,
81–84, 86, 91, 108, 111, 115, 406, 409, 410, 414, 431, 435,
131–140, 144, 145 438
Federal Funds interest rate, 68, 100, Government receipts, 1, 197, 204,
253, 255, 257, 261, 262, 357, 254, 255, 303–308, 323
371, 434 Government spending deficits, 243,
Federal Reserve Board, 100, 111 250, 288, 340
Fernandez–Villaverde, J., 83, 371 Government spending, goods and
1st In Stepwise, 155, 159, 164, 168, services, 123, 226, 230, 236,
174, 304 240–241, 244, 247, 309, 313,
1st Order Autocorrelation, 138 314, 371
1st Out Stepwise, 78, 154, 155, 159, Government spending, total, 80, 241,
164, 168, 174, 435 244, 248, 254, 309–313, 322,
Fiscal policy, 2, 66, 67, 111, 112, 155, 340, 341, 348, 371
333, 340, 360, 372, 373 Government spending, transfers, 93,
Fisher, Irving, 2, 332, 333, 334, 346, 241, 247, 248, 309, 310, 313,
354, 358, 373 314
Fixed Plant and equipment investment, Gramlich, E., 72
207, 208 Granger, C., 89, 90
Flow of Funds, 40, 285 Griffiths,W, 42, 394, 397, 412
Food Products, 123 Gross Domestic Product (GDP), 2,
Forecasting model, 10, 75, 100, 116 12, 13, 44, 45, 47, 69–71, 77,
90–94, 103, 106, 107, 110–113,
Foreign borrowing, 267, 285
116, 122, 126, 132, 139, 148,
Foreign Profits, 392, 403, 408, 409,
174, 175, 195, 199, 203, 216,
414, 415, 416, 417, 419, 420,
217, 221, 229–253, 259, 273,
422, 423, 424 275, 278–282, 289, 290, 291,
FRB/NY, 12, 56, 68 305, 309, 310, 313, 314, 318,
FRB/US, 12, 72, 73–78, 80, 115, 320, 322, 328–330, 331–336,
140, 142, 145 338–340, 346, 348, 352–362,
Friedman, M., 59, 87, 140, 255 371–373, 378, 379, 388–390,
Furniture, 127 396, 402, 408, 409, 411, 414,
INDEX 455
416, 419, 422, 425–428, 433, Instruments, 8, 13, 41, 42, 116, 147,
435, 439 149, 167, 172, 187, 193, 198,
Gurnayak, R., 53, 111 202, 342
Guscina, A, 391, 395 Interest income, 16, 377, 378, 379,
430, 431, 433, 434, 435, 439,
H 440
Hausman, 42, 47, 57, 148, 149, 161, Interest income, level, 433–435, 440
172, 181, 186–187, 189, 193,
Interest income, share, 430, 431, 439
198, 215, 216, 255, 260, 267,
276, 286, 342, 349, 394, 396, interest rate, 5, 6, 11, 15, 52, 62,
412, 424, 430 63, 65–67, 69, 70, 86, 91,
Heim, J., 47, 56, 57, 61, 87, 112, 141, 96–98, 100, 104, 109, 113–115,
147, 253, 357 117–120, 131–134, 142–145,
Heteroskedasticity, 39, 44, 395 158, 161, 165, 166, 172, 173,
Hill, R., 91, 107 176, 182, 183, 191, 194, 198,
Housing, 41, 82, 113, 117, 120, 122, 199, 211, 216, 217, 221, 222,
128, 129, 134, 135, 138, 143, 224, 227, 232–235, 253–263,
174, 175, 176, 177, 212, 369, 269–271, 297–300, 357, 365,
370, 371, 373, 379, 425, 426, 369–372, 379, 412, 416, 418,
427, 428, 429, 439, 440 425, 427, 428, 433, 434, 436,
439, 440
I Inventory investment, 13, 121, 136,
Identification, 4, 5, 7, 8, 13, 41, 51, 188, 215, 216, 218, 371
96, 147, 185 Investment, 1, 9, 10, 13, 40, 44–
Identities, 2, 9, 14, 126, 378 45, 52, 67, 72–76, 82, 93,
ILO, 392 94, 104–107, 109, 110–117,
IMF, 392 119–122, 126, 129–132, 134–
Imported Consumer goods, 140, 150, 140, 143–145, 148, 149, 172,
151–157, 161 174, 176, 177, 178, 185–219,
Imported investment goods, 188, 197, 229–245, 247–251, 253, 285,
198, 200, 201 291–295, 317, 320, 322, 333,
Imports, 14, 82, 83, 93, 109, 117, 346, 352, 353, 355, 357–362,
123, 124, 137, 138, 140, 144, 369–371, 379, 387, 388, 391,
149, 150, 157, 158, 159, 160, 392, 422–424, 427, 429
161, 163, 197, 198, 199, 200, IS curve, 1, 44, 94, 138, 139, 229,
201, 202, 222, 223, 224, 226, 231, 236, 239, 240, 241, 244,
228, 296, 371, 392, 410, 419, 246, 247, 248, 250, 252, 361
422 IS curve, 1, 94, 138, 139, 229–252
Income distribution, 377, 389, 393
Instruments, 8, 13, 41, 42, 116, 147,
149, 167, 172, 187, 193, 198, J
202, 342 Jaumotte, F., 392
456 INDEX
K LM curve, 2, 109, 259–263

Katrina, 274, 275, 278, 279, 282, 298, Loanable funds, 166, 172, 254, 255,
299, 300 333, 340, 358
Keynesian, 1–3, 5, 6, 10, 12, 48, 49, Lucas Critique, 4, 11, 56, 66–68, 72,
52, 56–59, 61, 72, 75, 78, 80, 86, 76, 86, 110, 155, 205
87, 108, 109, 111, 112, 115–116, Lucas, R., 50, 67, 86
125, 140, 142, 243, 253, 259,
260, 265, 318, 331–362, 379, M
389, 407, 411, 438 M1, 156, 165, 166, 172, 174, 182,
Keynesian Mechanics, 3, 332, 333, 254, 255, 259, 260, 261, 313,
334, 340 336–346, 349, 353–359, 370,
Keynes, J. M., 1, 5–6, 50, 261, 354 371
Klein, Lawrence, 1, 7, 49, 111, M1 Velocity, 336, 338–346, 349, 353,
115–125, 145 354
Krauss, L., 395, 400 M2, 58, 62, 67, 152, 162, 166–168,
178, 299, 300, 334, 336–337,
L 343, 346–358, 370
Labor income, 140, 378, 379, 380, M2 Velocity, 346–354, 356
387, 391, 393, 396, 406, 408, Macroeconomics, 5, 6, 7, 12, 49, 73,
409–411, 417, 422, 425, 437, 84, 85, 88, 104, 112, 141
439, 440 Macroeconomy, 4, 7, 39, 48, 49, 73,
Labor income, level, 379, 409, 410, 88, 108, 125, 131, 317–330, 377
411, 437, 439 Macro Foundations, 13, 110, 127
Labor income, share, 378, 379, 380, Mankiw, N.G., 87, 331, 388, 437
387, 390, 391, 393, 396, 406, Manufactured goods, 124
408, 409, 410, 411, 417, 422, Manufacturing, 117, 119, 121, 122,
425, 437 124
Labor productivity, 279, 379, 382, Marginal product of Capital, 382, 389
390, 392, 393, 399, 400, 406, Marginal Product of Labor, 382, 384
414, 416, 417, 418, 419, 420, Mean square error, 44, 54
438 Methodology, 4, 5, 9, 39–114, 115,
Lagged variables, 42, 98, 99, 148, 149, 130, 139, 149, 186, 378, 393
229, 394, 397, 412 Microeconomics, 110
Large scale econometric model, 7, Micro-foundations, 4, 12, 13, 50, 110,
9–14, 108, 114, 115, 328 111
“left out” variables, 46, 369 Model specification, 7, 11, 43, 103,
Leontief, V., 7, 110 157, 161, 171, 207, 211, 244,
Lifetime income, 50, 52, 56, 59, 83, 245, 288, 290, 297, 313, 317,
87, 110, 114, 141, 143 347, 369, 404, 405, 418, 419,
Lim, G. 421, 427, 430, 433, 436
Livio, M., 5 Model specification robust, 16, 161,
LM curve, 2, 109, 259–263 244, 304, 313, 421, 430
INDEX 457
Modigliani, F., 50, 59, 87, 140 291, 292, 294, 295, 297, 301,
Monetary policy, 2, 67, 112, 113, 115, 302, 304, 307, 310, 312, 313,
332, 333, 335, 367, 372 315, 316, 336, 338, 339, 340,
Monetary policy, 2, 67, 112–113, 115, 341, 342, 346, 347, 348, 350,
332, 333, 335, 372 351, 359, 369, 393, 395, 396,
Mortgage interest rate, 13, 133, 134, 397, 399, 409, 410, 412, 413,
176, 369, 425, 427, 428, 440 417, 421, 422, 424, 425, 428,
Mountford, A., 91, 92, 93, 107 429, 430, 433
OPEC, 125, 267, 275, 277, 280
N Orszag, P., 91
National income, 6, 14, 16, 47,
377–382, 384, 387–390, 393, P
396–400, 402, 403, 405–413, Paccagnini, A., 54
415–420, 422–432, 434, Participation Rate, 396, 399, 403,
436–440 407, 409, 410, 411, 438, 439
National Income and Product % Unionized, 391, 416
Accounts, 14 Phillips Curve, 1, 265–271, 274, 326,
Neoclassical Mechanics, 3 373
Neoclassical models, 3 Piketty, T., 377, 388, 389, 391, 393,
New Keynesian models, 56 437
NIPA, 377, 437 Population, 58, 62, 65, 67, 132, 133,
Nonstationarity, 7, 131, 162, 185, 134, 152, 154, 158, 159, 161,
197, 336, 361, 394, 396, 412, 162, 164, 168, 181, 182, 189,
424, 430 192, 195, 197, 208, 216, 236,
NYSE Composite Index, 414 243, 244, 249, 250, 251, 288,
296, 297, 299, 309, 310, 311,
O 312, 316, 343, 346, 355, 358,
Okun, 273–280, 310, 423 371, 388, 425
Okun’s Law, 273–276, 310 Population Age Distribution, 149
“Old” Keynesian models, 1, 12, Prime Interest Rate, 62, 67, 98, 100,
56–59, 87, 108, 112 113, 132, 166, 172, 182, 194,
OLS, 4, 8, 11, 30, 41, 43, 45, 47, 57, 199, 211, 217, 221, 234, 253–
78, 108, 111, 132, 147, 150, 151, 263, 269, 300, 357, 370–371,
152, 157, 162, 163, 165, 166, 412, 416, 418, 434, 436, 439,
167, 171, 172, 173, 176, 177, 440
180, 181, 183, 184, 185, 188, Profit income, 378, 379, 380, 408,
189, 192, 193, 196, 197, 202, 410, 421, 422, 424, 428, 439,
203, 207, 209, 212, 214, 215, 440
216, 218, 224, 225, 227, 228, Profit income, level, 378–380, 408,
254, 255, 259, 260, 265, 266, 410, 421–424, 428, 439
267, 268, 269, 273, 274, 275, Profit income, share, 378–380, 408,
277, 279, 280, 286, 287, 288, 410, 421, 422, 424, 428
458 INDEX
Profits, 48, 82, 109, 138, 189, 190, 231, 237, 244, 256, 258,
197, 198, 199, 205, 208, 209, 261, 262, 267, 268, 277, 278,
214, 216, 217, 244, 265, 285, 282, 289, 290, 294, 300, 301,
286, 288, 289, 290, 331, 332, 304, 305, 307, 311–313, 315,
351, 358, 379, 380, 381, 384, 343–345, 349, 351, 378, 393,
387, 390, 392, 394, 396, 403, 403, 404, 411, 415, 417–419,
405, 406, 408, 409, 411, 414, 422, 426–429, 431–433, 435,
415, 416, 417, 418, 419, 420, 436, 440
422, 423, 425, 437, 438, 439 Robustness testing, 8, 11, 46, 146,
391, 393–396, 400, 405
R Rule of thumb, 56, 75, 76, 77, 78, 80
R2 , 16, 44, 48, 63, 65, 154, 317
Rational Expectations, 5, 12, 50, 52, S
56, 63, 68, 70, 72, 73, 75, 78, 80, Saint-Paul, G., 390
81, 83, 84, 87, 114, 125, 131, Sample period, 4, 7, 8, 11, 12, 14, 45,
140 53, 71, 78, 91, 98, 99, 103, 106,
Real Wage, 265, 384, 409 150, 154, 155, 156, 157, 159,
Regression Coefficients, 16, 44, 45, 160, 161, 164, 166, 170, 171,
52, 77, 90, 102, 103, 113, 139, 174, 175, 176, 179, 183, 191,
145, 150, 202, 235, 242, 248, 195, 205, 215, 254, 273, 289,
298, 341, 348, 359–362 290, 291, 298, 300, 304, 311,
Reiss, A, 5 315, 317, 318, 350, 395, 400,
Rental income, 16, 377, 378, 379, 402, 403, 404, 417, 418, 422,
394, 424, 425, 427–429, 430, 429, 433, 435, 436, 440
440 Samuelson accelerator, 1, 218, 412
Rental income, level, 16, 377, 378– Sargan, 42, 187–189, 193, 198, 255,
379, 394, 424, 425, 427, 428, 260, 286, 342, 394, 397
429, 438, 440 Savings, corporate, 10, 167, 285–291,
Rental income, share, 377–379, 424, 296
425, 427, 428, 429, 430, 438 Savings, depreciation, 291, 292, 294,
Residential construction, 13, 74, 143, 295
212, 214, 215 Savings, personal, 167, 168, 285,
Residential investment, 134, 172, 174, 296–302, 370
176–178, 212, 215, 425, 427, Sbordone, A., 68, 70, 71, 81
429, 433 Scientific, 4–7, 9, 13, 46, 51, 83, 89,
RHS, 181, 275 96, 104, 110, 111, 112, 125, 235,
Robustness, 4, 30, 36, 42–44, 145, 297, 317
152, 153, 156, 158, 159, 161, Self Evident Truths, 5, 9, 83, 110, 111
163–165, 168–170, 173, 175, Semi-manufactured goods, 123, 124
178, 179, 181–183, 189–191, Serial correlation, 13, 16, 44, 91, 124,
194, 196, 199, 201, 204–206, 139, 394
208–214, 216–218, 226, 227, Shoc08, 275, 276, 278, 280, 423
INDEX 459
Shock05, 275, 276, 278, 280, 282, T

300, 301, 302 Tax deficits, 164, 181, 182, 300
Shock09, 312, 314, 315, 316 Taxes, 11, 47, 62, 66, 67, 83, 86, 112,
Shock73, 275, 276, 278, 280, 423 133, 135, 153, 154, 159, 164,
Shock78, 275, 279, 423 172, 174, 177, 181, 182, 188,
Shock86, 304, 306, 307, 323, 324 191, 194, 195, 197, 204, 208,
210, 212, 213, 241, 247, 248,
Shock93, 297, 304, 306, 323, 324
254, 286, 289, 298–300, 303,
Shoes, 126, 127 305, 306, 333–338, 343, 347,
Significance levels, 16, 45, 98, 102, 348, 354, 406
108, 151, 156, 161, 165, 176, Taylor Rule, 1, 6, 96, 97, 100, 101,
180, 184, 192, 201, 206, 211, 109, 137, 253–258, 260, 262,
213, 215, 217, 219, 227, 228, 269–271, 371, 372
267, 268, 279, 290, 294, 295, Technology Shocks, 12, 56, 61
301, 312, 313, 316, 345, 351, Time period robust, 45, 46, 150, 151,
395, 402, 404, 405, 418, 436 156, 157, 160, 161, 164, 165,
Sims, C., 12, 50, 51, 55, 83, 89, 90, 169, 170, 171, 175, 176, 179,
91, 92, 96, 102, 103, 104, 107 180, 183, 184, 191, 192, 195,
Smets, F., 53, 55, 72, 82, 83, 86, 111 196, 200, 201, 205, 206, 207,
Smith, N., 55 209, 210, 211, 217, 219, 227,
Solow, R., 40, 85, 373, 382, 384, 388, 228, 257, 258, 261, 262, 263,
389 267, 268, 269, 278, 279, 282,
Stationarity, 7, 10, 13, 39, 42, 57, 58, 283, 290, 291, 294, 295, 300,
77, 131, 150, 152, 181, 359, 394, 301, 302, 305, 306, 307, 311,
396, 412, 424, 430 312, 313, 315, 344, 345, 350,
351, 402, 403, 404, 417, 418,
Stepwise regression, 4, 14, 45, 78,
422, 427, 428, 432, 435, 436
150, 153, 158, 163, 168, 173,
Tinbergen, Jan, 7, 41, 49, 115
178, 181, 189, 194, 199, 204,
Tinsley, P., 72–74, 140
212, 216, 261, 267, 277, 280,
292, 304, 310, 314, 343, 349, Tobin’s q, 119, 189, 198, 199, 208,
359, 400, 415, 426, 431 209, 287, 288, 333, 357
Total Consumer Spending, 80, 95, 151
Stockhammer, E., 392
Total investment, 67, 188–192, 194,
Stock, J and Watson, M, 96, 97, 100 197, 199, 201–202, 251, 285
Strong instruments, 147, 149 Total investment spending, 188–189,
Structural Models, 1, 6, 8, 10, 49, 51, 191, 192
72, 86, 89, 92, 96, 101, 104, 106, Tovar, C, 55
107, 108, 111, 125, 126, 127, Treasury bill interest rate, 137
131, 142, 143, 155, 317, 372 Triola, M., 41, 102, 297
Structural vector autoregressive model Two Stage Least Squares (2SLS), 4, 8,
(SVAR), 96–101 11, 30, 41, 43, 45, 57, 66, 78, 96,
SVAR methodology, 96, 100, 101 108, 111, 116, 126, 139, 147,
460 INDEX
149, 150, 151, 152, 155, 161, 221, 222, 224, 226, 254,
162, 163, 167, 168, 169–174, 256, 260, 261, 267, 273, 275,
177–182, 185, 186, 188–195, 277, 278, 280, 286, 288, 291,
197–202, 204, 206, 207, 208, 292, 294–296, 298, 299, 304,
210, 211, 212, 214, 215, 216, 309–311, 314, 317, 343, 349,
217, 230, 231, 236, 240, 255, 357, 370, 396, 397, 400, 405,
256, 257, 258, 260, 262, 263, 409, 415, 419, 422, 425, 426,
267, 276, 277, 278, 280, 282, 428, 431, 435
286, 287–292, 297, 310, 336, VAR methodology, 115
342, 344, 345, 346, 349, 350, Vector autoregressive model (VAR), 3,
369, 393, 394, 395, 396–403, 8, 9, 12, 13, 39, 40, 45, 48–52,
409, 410, 412, 424, 429, 431, 54, 55, 71–73, 75, 84, 87–94,
433, 434 96–100, 101, 103–107, 109, 111,
Tytell, I. 113–114, 115–116, 126, 130,
139, 141, 235, 244, 372
U Velocity, 2, 15, 332–362
Uhlig, H., 91, 92, 93, 107
Unemployment inflation, 116 W
V Wald, 13, 42, 149, 172, 177, 187,
188, 193, 208, 255, 260, 286,
Variance, 8, 10, 14, 43–46, 52, 53,
342, 394, 397, 412, 430, 434
57–63, 65, 69, 71, 74, 77, 78, 80,
81, 87, 98, 106, 108, 109, 111, Warne, A.
112, 114, 115, 131, 132, 137, Wharton Econometric Model, 116
139–141, 145, 150, 153–155, Wickens, M., 55
158, 159, 168, 172–176, 178, Wilcox, D., 72
181, 189, 194, 199, 203–205, Wouters, R., 53, 55, 72, 82, 83, 86,
208, 209, 212, 213, 215–218, 111

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An Econometric Model of the US Economy

ISBN 978-3-319-50680-7 ISBN 978-3-319-50681-4 (eBook)

Library of Congress Control Number: 2017940494

© The Editor(s) (if applicable) and The Author(s) 2017

Cover illustration: Lyroky / Alamy Stock Photo

Printed on acid-free paper

This Palgrave Macmillan imprint is published by Springer Nature

engineering courses, where every equation describes what actually works,

SUNY, Albany John J. Heim

Most of all, I am indebted to Nobel Laureate Robert Solow for providing

Part I Production of the GDP

3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4 The Consumption Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5 Models Identifying the Determinants of Investment

5.8 OLS Estimates of the Determinants of Investment

6 The Exports Demand Equation . . . . . . . . . . . . . . . . . . . . . . 221

7 Statistically Estimated Real GDP Determination

8 Real GDP Determination Function (“IS” Curve)

9 Determinants of the Prime Interest Rate: Taylor

10 Determinants of the Prime Interest Rate – LM

11 Determinants of Inflation – The Phillips Curve Model . . . . 265

12 Determinants of Unemployment . . . . . . . . . . . . . . . . . . . . . . 273

13 The Savings Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

14 Determinants of Government Receipts . . . . . . . . . . . . . . . . . 303

16 Capacity of the Model to Explain Behavior

16.2 Model 2: Treating C, I, and X Model Determinants

17 Converting the Older Keynesian IS-LM Model to

19 Summary and Conclusions (Production Side of the

Part II Income Side of the NIPA Accounts

20 Determinants of Factor Shares . . . . . . . . . . . . . . . . . . . . . . . 381

Fig. 4.1.1 Actual consumption compared to levels

Graph. 20.4.1.1 Model of only variables robust in at least

Table. 1.4.1 Determinants of consumption . . . . . . . . . . . . 18

Table. 1.4.14 Determinants of interest total income

Table. 4.0.2 Determinants of consumption

exogenous or lagged in their effect

Table. 7.1.1 Comparison of PR –2 effects in GDP,

Table. 14.2 Robustness over time – government

Table. 18.2 Dynamic Effects of Stimulus Programs

Table. 20.4.6.1 Summary of factors affecting profit’s %

THE PRODUCTION SIDE MODEL

a Keynesian model. However, when a variable to measure “crowd out” is

and why it is used here. Chapter 2 is literally a paper within a paper. It

. . . Your arguments in favor of Cowles-type models as against VAR and

After Keynes himself, Solow is arguably the greatest economist of the

THE INCOME SHARES MODEL

interest income. An additional four equations describe the variables found

The econometric model of the U.S. economy developed in this

© The Author(s) 2017 1

Gross Domestic Product (GDP). Other behavioral equations describe the

Total consumption Consumer savings

Domestically produced consumer goods and services Durable consumption goods

The nine investment goods equations express the determinants of demand

Total investment Corporate savings

Domestically produced investment goods Depreciation savings

There are 75 variables (or different lags of variables) in the 45 equations.

Cooley (1997) Calibration too informal compared to econometric methods . . .

Earlier criticisms of Cowles models, particularly the Lucas critique, have

1.1 MODERN MACROECONOMICS: MOVING FROM