Paul 2000

Modeling and Measuring Productivity in the
Agri-Food Sector:
Trends, Causes and Effects
Catherine J. Morrison Paul
Professor, Department of Agricultural and Resource Economics, and

member of the Giannini Foundation, University of California, Davis.
Invited paper
This article overviews recent trends in modeling and measuring productivity patterns, and in distin-
guishing their determinants and implications, for the agri-food sector. Theoretical methodologies as
well as empirical implementation and results are discussed, with a view toward identifying those with
potential for facilitating understanding of productivity measures, and ultimately using them for policy
guidance. Productivity growth evidence for the food systems of the U.S., Canada and the U.K. is sum-
marized, and recent studies distinguishing underlying causes of production structure patterns and link-
ing them with market-structure patterns are reviewed, as a basis for assessing the key messages from
and trends in this literature.
L’auteur fait un survol de l’évolution récente dans les domaines de la modélisation et de la mesure des
courbes de productivité ainsi que de la caractérisation de leurs déterminants et de leurs significations
pour le secteur agroalimentaire. Il passe en revue les méthodes théoriques aussi bien que les applica-
tions empiriques et leurs résultats afin d’en dégager ceux qui pourraient faciliter la compréhension des
mesures de la productivité et qui, éventuellement, pourraient servir de guide aux décideurs. L’auteur
analyse les signes de croissance de la productivité des filières agroalimentaires observés aux Etats-
Unis, au Canada et au Royaume-Uni. Enfin il examine les études récentes sur les causes sous-jacentes
des évolutions des structures de production et sur leurs liens avec l’évolution des structures de marché,
dans le but d’en dégager les messages et les tendances clés.
INTRODUCTION
Productivity and efficiency are crucial aspects of production structure and economic perfor-
mance; they affect the welfare not only of producers and input suppliers, but also of con-
sumers. Characterizing economic performance, as well as its underlying determinants and
resulting implications, is necessary for understanding production patterns and market structure,
and ultimately for guiding policy implementation. Such an understanding is perhaps particu-
larly important for the food system, since it produces one of the most fundamental of con-
sumption commodities, and relies on the farm sector for its primary materials base. Although
numerous issues arise when attempting to model and measure economic performance, a num-
ber of promising trends are apparent in the literature on productivity trends, determinants, and
implications for the agri-food sector.
Canadian Journal of Agricultural Economics 48 (2000) 217–240

217
218 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS
Recent methodological developments in this literature with perhaps the most potential
are those toward incorporating in the analytical framework more structure on the underlying
technological, behavioral and market relationships. This progress has at least partly been
motivated by the proliferation of implementable duality and frontier models of production
and efficiency in the theoretical literature. But it is also consistent with the empirical
emphases of other current bodies of literature, such as the “new endogenous growth” (Romer
and others), “new empirical industrial organization” (Bresnahan and others) and “new trade
theory” (Krugman and others). These topical literatures stress structural modeling, represen-
tation of interactions among economic agents or sectors, careful characterization of factors
underlying supply and demand relationships, and consistency with theoretical optimization
models.
Although these advances suggest increasing analytical complexity, in a conceptual sense
the trend in the literature on productivity/performance and welfare seems to be more “back to
the basics” of costs and benefits. This emphasis on the fundamentals is bolstered, however,
by the more sophisticated and powerful tool kit researchers are equipped with than in even
the recent past, stemming from refinements in theoretical and econometric models and tech-
niques, greater data availability, and expanded number-crunching potential from the high-
tech explosion. These innovations have facilitated a more comprehensive and exhaustive
characterization of supply and demand, or costs and benefits, than was previously feasible.
Improving economic performance fundamentally involves increasing the size of the
overall “pie” through the augmentation of productivity and efficiency. That is, obtaining the
most benefits or output (broadly defined) from a given amount of resources or costs (also
broadly defined) is the optimal outcome for all economic entities in the food system, includ-
ing suppliers, producers and consumers. Such maximization of net benefits implies produc-
ing what people want in the best or most “productive” way. And it embraces a wide variety
of technological or cost and thus market structure issues, which may involve complex inter-
actions that must be modeled and measured for interpretation and use of economic perfor-
mance measures.
Expansion of the pie may be accomplished through various components of overall
productivity. In particular, if producers are effectively cost minimizing, productivity
increases involve a (disembodied or embodied) shift in the technology, and the associated
producer responses as they take advantage of such a technical change.1 This implies a shift
in the production frontier that underlies the technological base of firms in the industry, and
a resulting fall in the (unit) cost of output. The notion of improved efficiency, by contrast,
suggests that firms are within the cost frontier either due to technical inefficiency (they are
not reaching the production function or isoquant boundary) or due to allocative inefficiency
(they are not cost minimizing according to the prices they face). They can thus reach high-
er performance levels by moving toward the frontier. So increased output production for a
given amount of resource use, or reduced costs associated with a given amount of produc-
tion, may occur due to either increased efficiency or some sort of technical change, which
both act to enhance productivity.
A primary building block of this puzzle is costs. Giving short shrift to the cost repre-
sentation seriously limits the construction of interpretable and usable indicators of economic
performance. In particular, a detailed view of the technological characteristics and interac-
tions embodied in the cost structure is an essential foundation for analysis of any notion that
MODELING AND MEASURING PRODUCTIVITY IN THE AGRI-FOOD SECTOR 219
involves costs, including not only productivity/efficiency but also, for example, price-cost
margins from imperfect competition or market power.
So, with a view toward identifying promising trends in cost/productivity analysis for the
agri-food sector, in this article I explore questions involving the definition, measurement, and
cost, market structure, and policy linkages of productivity and efficiency. I first overview var-
ious conceptual issues underlying economic performance analysis, and insights from the lit-
erature on the “stylized facts” about food system productivity in the U.S., Canada and the
U.K. I then summarize studies based on differing methodologies to address a broad array of
issues regarding productivity and efficiency. Finally, I review their overall messages and
implications, regarding what has been learned about, and how one might best approach,
analysis of such issues, with the goal of facilitating policy-relevant analysis of economic per-
formance and technological/market structure for the food system.
MOTIVATION: THE “NEW” COST ECONOMICS (?)

Issues of productivity and efficiency fundamentally boil down to a comparison of costs and
benefits. In the production context, these concepts can be framed in terms of the resource or
input costs of producing the benefits deriving from commodities, or output. Implementation
of this basic notion is much more complex than it sounds, of course, since production costs
and benefits — or the prices and quantities of inputs and outputs — must be very carefully
measured both to capture the actual economic values of marketed factors or commodities, and
to recognize nonmarketed values. It also requires characterizing various internal and external
aspects of the production structure that affect the relationship of costs and outputs, such as
production rigidities, cost economies (from, say, scale and scope) and spillovers. Although
not easy to model and measure, getting a handle on the impacts of these real-world produc-
tion characteristics is crucial for generating interpretable and useful measures of productivi-
ty and performance.
In standard intermediate microeconomics terms the costs of production and its determi-
nants are typically characterized by a cost function, TC(Y, t, ·), summarizing the minimum
total input costs (TC) of producing a vector of outputs (Y, or aggregate Y), given all other
arguments of the cost function (·) and the technology available at time t. Efficiency involves
getting the most output for a certain level of costs; the objective is to attain the lowest cost-
output or cost-benefit ratio TC/Y (or cost curve in TC – Y space), or the highest Y/TC ratio, as
possible given the existing technological base.2 Productivity growth then involves enhancing
this base.
Thus, progress toward the goal of reducing TC/Y may be supported by various changes
in management practices and the technological environment. The former is represented as
movements toward the production and cost frontiers. The latter implies shifts in the techno-
logical frontier facing firms — the production set underlying production processes. If firms
are effectively using their technology, and optimizing in the sense of cost minimization or
profit maximization, technical and allocative efficiency will be attained and productivity
changes preclude efficiency adaptations and instead imply disembodied (external/exogenous)
or embodied (internal/endogenous) technical change.
Most studies of productivity and efficiency focus in some form on determining what the
cost-benefit ratio TC/Y looks like, how its components might be measured, and how it is
affected by exogenous or endogenous factors. The basic focus is therefore effectively or
appropriately to measure the numerator and denominator of the TC/Y ratio. But this decep-
tively simple idea involves difficult questions about data and methodology.
Perhaps the most fundamental questions involve data. What costs and benefits are
important to include? How do we measure them in a relevant manner? And should input and
output composition changes be recognized? In particular, the multiple-product and -market
nature of the food system raises crucial questions about output demand changes and product
differentiation that can be addressed only in a framework that accommodates output compo-
sition patterns, in turn requiring disaggregated data.
The economic relevance of observed price and quantity measures also raises many ques-
tions. Are market quantities and prices of inputs and outputs appropriate to use for such an
exercise, or do we need to create or impute “effective” measures? Should quality character-
istics of the inputs and outputs be taken into account? Are there nonmarketed inputs or com-
modities (both good, such as food safety, and bad, such as environmental damage) that are
important for more correctly approximating a welfare, rather than a purely market, measure?
Is risk or uncertainty present that should be attributed a risk premium, or imply that informa-
tion value should be incorporated? Do stock/flow problems require us to adjust observed
prices to reflect their flow values? And, drawing on the market structure side of the problem,
should we distinguish between marginal and average prices3 if deviations stem from market
structure characteristics?4
This leads to the related question of the level of analysis: Do we want to evaluate a plant,
a firm, an industry, the entire national food sector, or an even a more global entity? Differing
questions (and answers) as well as data are relevant at each of these levels, as they are for the
layers of the food chain — agriculture, processing, wholesaling and retailing. Varying char-
acteristics and performance may be evident for these levels and layers of the system, with
important spillover effects across them. This also raises aggregation issues, and debate about
whether a top-down or bottom-up approach may be more fruitful for analysis of productivi-
ty, efficiency and welfare in this sector.
These questions not only need to be perused, but also their implications for associated
adaptations to cost and benefit measures need to be established. For example, hedonic analy-
sis might be used to accommodate changes in quality or characteristics. Or valuation of non-
marketed inputs or outputs might be required. Refinements of the observed data might be
accomplished simply by constructing indexes, such as educational attainment indexes for
labor; or perhaps some form of parametric measurement could be used to identify shadow or
virtual prices or quantities.
In turn, once appropriate data are established, distinguishing the determinants of the
TC/Y ratio — or quantifying its dependence on associated production factors — becomes
imperative for interpretation and use of productivity or efficiency measures. In particular, the
productivity literature asks how this ratio changes over time, or with changes in R&D or other
specific technological developments that are assumed to be exogenous. More specifically,
including t (a time trend) or R (R&D) as an argument of the cost function, TC(Y, t, R, ·),
implies that we wish to quantify and evaluate the proportional derivative εTCt = ∂ln TC/ ∂t, or
εTCR = ∂ln TC/ ∂ln R. These cost elasticity measures hold Y constant by definition, thereby
reflecting changes in the TC/Y ratio.
Approximating such productivity changes in index number form involves taking the
percentage change in TC, and subtracting the sum of the (share-weighted) percentage changes
in Y and other arguments of the function (input prices), to see “what’s left” that is not cap-
tured in the recognized cost determinants. This results in the (dual) Solow residual equation
“measure of our ignorance,” that “sources” or identifies direct reasons for changes in the
TC/Y ratio and attributes anything left over to some unidentified form of productivity growth
— possibly due to, say, t or R changes.
That is, the dual Solow residual can be constructed as:
λTCt = dln TC/dt – εTCY dln Y/dt – Σj Sj dln pj /dt (1)
where the logarithmic derivatives are computed as percentage changes; Sj = pjvj/TC is the cost
share of input j, vj, with price pj; and εTCY = ∂ln TC/∂ln Y represents scale economies. This
expression stems from taking the total derivative of the TC(Y, p, t) function (where p is a vec-
tor of the pjs) in percentage terms, using Shephard’s lemma to substitute for vj = ∂TC/ ∂pj,
and solving for the impact of t, ∂ln TC/ ∂t, which becomes the residual.5 λTCt is therefore a
nonparametric approximation to the εTCt elasticity.
Alternatively, such a residual may be computed by subtracting a share-weighted sum of
percentage input changes from the percentage change in output, Y, using the production
instead of cost function as a basis:
λYt = dln Y/dt – Σj Sj dln vj /dt 6 (2)
This primal Solow residual equation is derived by taking the total (logarithmic) deriva-
tive of the production function Y(V, t), and imposing the profit-maximizing conditions VMPj
= pY· ∂Y/ ∂vj = pj, or ∂Y/ ∂vj = pj/pY, where MP denotes the marginal product, VMP the value
of the marginal product, and pY the output price. Solving for ∂ln Y/ ∂t results in Eq. 2, a non-
parametric approximation to the εYt = ∂ln Y/ ∂t elasticity. This is a somewhat more standard
productivity experiment than its dual counterpart, because it is based directly on the output-
input ratio Y/V, rather than being focused on costs.
When Sj is constructed as a cost (rather than revenue) share, λYt has a well-known relation-
ship to λTCt. In particular, when constant returns to scale prevails (so that εTCY = ∂ln TC/ ∂ln Y
= 1), and all the assumptions for Shephard’s lemma or the VMPj = pj equalities to hold are
satisfied (instantaneous adjustment of inputs, observable market values for the true econom-
ic prices and quantities of the inputs, and technical/allocative efficiency), they are exactly
equivalent. If these assumptions do not hold, however, or if other arguments of the cost or
production functions are relevant but do not have readily measured “weights” to place on
their measured percentage changes (like the Sj weights on the pj or vj changes), λTCt and λYt
measures and their components must typically be constructed through parametric estimation.7
Further analysis of productivity patterns requires decomposing such measures to identi-
fy their determinants. This entails refining the input and output (cost and benefit) measures,
making model adaptations for discrepancies from standard assumptions, and specifically
characterizing other aspects of the technological and behavioral structure. This is, explicitly
or implicitly, the goal of much work in the productivity field.
For example, direct (parametric) estimation of εTCt or εTCR elasticities facilitates a move
in this direction by separating the impacts of t or R changes mathematically and statistically
from the effects of other cost determinants. These production factors act as explicit shift vari-
ables for the cost-output relationship, or cost curve. Essentially, these measures establish
weights on t or R changes for an expanded Solow residual measure.
We can similarly identify the contributions of technological characteristics like scale
economies to the cost- output relationship. This is accomplished by estimating the elasticity
εTCY = ∂ln TC/ ∂ln Y (which represents the marginal- to average-cost ratio) allowing for a
detailed set of interactions, rather than making the common assumption that the scale rela-
tionship may be represented by a single parameter (or assumed equal to one). More general-
ly, such a measure provides information on overall cost economies, since the cost-output rela-
tionship also embodies information on, say, scope economies, if Y is a vector of output lev-
els rather than a single aggregated output.
This same idea also provides us a mechanism for valuing some kinds of production char-
acteristics that are not represented directly in the data. For example, if short-run input rigidi-
ties exist, we may want to distinguish the cost effect within these constraints from the poten-
tial long-run costs attainable when adjustment has taken place. In some cases, this may be
accomplished by direct adaptation of the data, such as multiplication of a capital stock vari-
able by a utilization index. But estimation of shadow values or input-output interactions may
also be necessary to characterize relationships not directly distinguishable from the data.8 To
pursue this, fixed factors xk can be included as arguments of the TC(·) function, with the elas-
ticity measures εTCk = ∂ln TC/ ∂ln xk capturing the deviation between the market and shad-
ow prices of the xk.9
More broadly, addressing many problems involved in both measuring the numerator and
denominator of the TC/Y ratio, and establishing its determinants, involves careful considera-
tion of the real economic signals to which economic agents are responding, and their appro-
priate incorporation in the underlying production structure model. Valid representation of
true, effective, shadow or virtual prices — and thus quantities — of inputs and outputs, in
order to weight the contribution of the associated factors to the productive process, is often
the crux of the problem. That is, realistic characterization of the cost-output or cost-benefit
relationship and its determinants requires identifying and quantifying the impacts on cost or
benefits of such production structure components as dynamic adjustment, spillovers/exter-
nalities, uncertainty, market failures, imperfect or missing markets, and quality variations.
Although these impacts are often difficult to conceptualize, much less to measure, much of
the literature on modeling and measuring performance patterns is moving in this potentially
promising direction.
THE LITERATURE: WHAT HAS BEEN DONE — AND FOUND?

Traditional Productivity Measures: What Do They Tell Us?
Traditional productivity measurement, motivated within the cost-based or cost-benefit para-
digm represented by TC(Y, p, t), involves characterizing input costs (using measured prices
and quantities of inputs) and usually one aggregate output, and comparing levels of and
changes in these measures, as in Eqs. 1 or 2. The resulting λTCt or λYt measures are based on
representing decreases in the TC/Y ratio (reductions in unit costs for a given output level) or
increases in the Y/V ratio (output expansion for a given input vector). Substitution is taken
into account by recognizing multiple inputs and thus changes in input use and composition
(through the share weights, so the measures reflect multi-factor productivity, MFP), but other
characteristics of the production structure, such as cost economies, are subsumed in the pro-
ductivity residual “measure of our ignorance.” Inputs may be limited to just labor and capi-
tal, but more often include (at least) energy, materials inputs and land for agriculture. Output
measures are typically based on production revenue data, deflated by a price index, usually
constructed by Divisia index number techniques.10
The more detailed and precise (adjusted for quality or other measurable differences) the
data are for the prices and quantities of the inputs and outputs, the more production cost
declines (or output growth) can be decomposed into its various sources. And, if characterized
explicitly in a production theoretic model, the more external and internal technological char-
acteristics are represented — such as technical change (a time trend or, more explicitly, R&D
or other knowledge factors), and cost economies — the more of the productivity residual may
be explained. Productivity determinants are also often suggested either simply by assertion,
or by second-stage regression of productivity growth measures on possible explanatory vari-
ables. Ultimately, an understanding of such driving forces suggests not only how greater effi-
ciency/productivity might be stimulated — say, by regulation — but also how technologi-
cal/economic features like cost economies might be driving market structure characteristics
such as concentration.
A number of agricultural productivity studies of this genre appear in the literature. Those
for the U.S. typically find that productivity growth in agriculture is very strong — in fact,
greater than in virtually any other sector over the past few decades. The estimates vary by
study, depending on the underlying methodology and database, as well as the years repre-
sented. Trueblood and Ruttan (1995), in fact, overview 14 different studies with productivi-
ty growth estimates ranging from 1.15% to 1.94% per year, with most of the studies report-
ing estimates about mid-range.11
Jorgenson and Stiroh (2000) provide measures for the U.S. that are at the low end of the
range identified by Trueblood and Ruttan (1995) — 1.17% per year from 1958–96. However,
Jorgenson and Stiroh have suggested that these measures are likely biased downward from
those based on data constructed at the USDA by Ball et al (1999, 2000a, 2000b) and used for
most current studies. The Jorgenson and Stiroh data may not sufficiently adapt for output
quality or capture the obsolescence of the capital stock embodied in the Ball data. Jorgenson
and Stiroh also document that the agricultural sector is an important contributor to aggregate
U.S. MFP. In fact, they place it third in the country12 after Trade and Electronic/Electric
Equipment.
Similarly, both Thirtle and Bottomley (1992) and McDonald, Rayner and Bates (1992),
report stronger-than- average productivity growth for U.K. agriculture. The former study
finds 1.9% per annum productivity growth from 1967–90, which is somewhat higher than
the McDonald, Rayner and Bates (1992) estimates of 1.84% per year growth from 1954–63,
0.84% for 1967–74, and 1.13% for 1979–84.13 This is similar to rates found for Canada by
Fantino and Veeman (1997), although Echevarria (1999) reports that productivity growth
was roughly the same in agriculture and manufacturing for Canada from 1971–91, with a
relatively low rate of 0.3% per annum, which is more consistent with Hazledine’s (1991)
findings.
Trueblood and Ruttan (1995) find for the U.S. that differences in productivity estimates
are largely due to variations in the years covered rather than the methodology used, which is
consistent with comparisons made by McDonald, Rayner and Bates (1992) for the U.K. And
they emphasize that probably the most useful efforts to refine Solow residual-type estimates
are those that more carefully address data issues, particularly for outputs and inputs likely to
embody significant technical change such as capital (machines, livestock) and materials
(seeds, pesticides).
For the next layer of the agri-food sector, Jorgenson and Stiroh provide an estimate of
U.S. food processing MFP that is about half that of the agricultural sector, but still high com-
pared with most U.S. industries — sixth after those already named, plus Industrial
Machinery/Equipment and Transport/Warehouse. The Jorgenson and Stiroh conclusions are
consistent with those of other studies, such as Weston and Chiu (1996), who focus on growth
strategies and acquisitions in the food system, and find that “surviving food companies have
demonstrated growth rates in revenues and returns to shareholders higher than the market as
a whole.” And the Jorgenson and Stiroh estimates contrast with the higher productivity
growth rates for agriculture and the lower ones for food processing reported by Gopinath, Roe
and Shane (1996, based on the Ball et al data for 1959–91) of 2.31% per year and 0.41% per
year, respectively.
A similar relationship between agricultural and food processing sector productivity is
found for the U.K. by McDonald, Rayner and Bates (1992), who also suggest that food man-
ufacturing has exhibited lower than average productivity growth relative to other manufac-
turing industries.14 Balasubramanyam and Nguyen (1991), however, find that the food pro-
cessing industries have experienced somewhat higher, and the drink industries “considerably
higher” productivity growth than on average for U.K. manufacturing industries.
Hazledine (1991) summarizes MFP measures reported for Canadian food processing,
which range from about zero to 0.5% per annum, and indicates that these rates are close to
those found for Canadian agriculture. Chan-Kang et al (1999) also find significantly lower
productivity growth rates for the Canadian than for the U.S. food processing sector. In par-
ticular, productivity growth was seen to “flatten out” in the mid-1970s and remain negligible
after that in Canada, whereas in the U.S. it dropped in the mid-1970s but then “continued
strongly into the 1990s.”
Gopinath et al (1996, 1999, 2000) highlight the existence and importance of spillover
effects between food system layers in the U.S. that allow agricultural productivity growth to
reduce processors’ costs, ultimately benefiting consumers. This is consistent with the empha-
sis of McDonald, Rayner and Bates (1992) for the U.K., who assert that “efficiency gains in
the provision of food commodities to consumers” overall have exceeded those for manufac-
turing as a whole. They stress that recognizing the interrelationships or interdependencies
between layers of the “modern integrated” food system, and especially the agricultural and
food processing industries, is crucially important for documenting and understanding their
performance patterns.15 They also underscore the importance of efficiency gains in food dis-
tribution networks — as “an indispensable link between producers and consumers” —
although little work has been done in the economics literature on productivity at the retail
level.
In addition to distinctions among layers of the food system, industrial disaggregation or
decomposition helps to explain productivity patterns. For example, Morrison (1985, 1997)
finds quite different productivity patterns across the three- and four-digit SIC divisions with-
in the two-digit SIC food processing sector that are veiled in more aggregate measures. A spa-
tial rather than industrial division also reaps benefits in terms of interpretation; Ball et al
(1999, 2000a, 2000b) estimate U.S. agricultural MFP by state, and find significant variation
across both states and regions. They also establish, however, that “interstate shifts in produc-
tion activity and resource reallocations have had little impact.”
The strong productivity growth found for the food system overall, and especially agri-
culture, has been attributed to many factors — most notably R&D — even if the impact is not
directly measured. For example, Jorgenson and Gollop (1992) assert that the high rate of mea-
sured technical change in agriculture is “consistent with” the story, dating back to early work
by Griliches, of a significant R&D impact on U.S. agricultural productivity. And Gopinath,
Roe and Shane (1996) rely on the importance of R&D to interpret their results, suggesting
that their findings should encourage policy measures supporting R&D, or other policies and
regulations “affecting the competitiveness of agriculture,” such as public infrastructure
investment. A shortfall in Canadian R&D expenditure per unit output relative to that in the
U.S. was also suggested by Chan-Kang et al (1999) as an explanation of a Canada–U.S. pro-
ductivity growth gap found for the food processing sectors.
Heien (1983) instead ascribes trends and cycles in food sector productivity growth large-
ly to adjustment costs — and the energy price changes that may have motivated capital
adjustment in the 1950–77 period. He also notes the potential impact of environmental and
safety regulation impacts on observed MFP patterns. Other input-oriented “drivers” have
been the focus of studies such as Balasubramanyam and Nguyen (1991), which highlights the
roles of size expansion, capital investment and labor “shedding.”
These factors also seem to affect relative performance; Chan-Kang et al (1999) assert
that they have had less impact on Canadian than U.S. productivity. They identify a smaller
cost-saving impact of materials-using technical change in Canada due to higher materials
prices and less exploitation of scale economies, labor-saving, capital accumulation and other
cost-cutting measures. The (related) trend toward mergers evident in the U.S. by the early
1980s was also a target in their investigation of productivity gaps. In particular, they find that
productivity growth in Canadian food processing began to fall behind the U.S. in the early
1980 when U.S. firms “accelerated their capital investment, negotiated extensive mergers and
weeded out middle management.”
In contrast to the supply determinants underscored in most of these studies, Weston and
Chiu (1996) focus on higher layers of the food chain in the U.S. and emphasize demand dri-
vers. They indicate that food sector growth “has been achieved by a high rate of new product
introductions and promotion methods,” to accommodate changing demographic and social
patterns and develop international markets. This is also pointed out by Balasubramanyam and
Nguyen (1991) for the U.K. food and drink manufacturing industries. They note that low
income elasticities of demand for food products result in a “challenging market situation,”
which drives structural changes such as product diversification and differentiation, as well as
growth in size and concentration of firms.
Extensions to the Traditional Analysis: What Do They Add?

A number of refinements may be incorporated more directly into the model underlying stan-
dard productivity analysis. Such extensions add complexity and typically require parametric
estimation to identify relationships not directly evident from observed data, but provide more
specific insights about productivity and efficiency patterns in the food system. This subsec-
tion overviews some recent literature targeting complicating factors potentially underlying
MFP trends such as structural change, dynamic adjustment, multiple markets and externali-
ties. Implications emerge about how augmented productivity and efficiency from spillovers
across food system layers, flexibility, scale and scope economies, maintenance of capacity
utilization levels, internalization of externalities, and attenuation of risk, can be supported by
policy, and may provide motivations for market structure changes such as increased integra-
tion and concentration.
Technical and Structural Change

The most fundamental — but also perhaps the most difficult — issue that arises in the liter-
ature on productivity determinants is how to more explicitly characterize structural and tech-
nical change than is possible using a residual method. Standard productivity growth analysis,
at least indirectly, implies that technical change can be represented by a time trend. Similarly,
structural change might be captured by a discrete shift in technology, perhaps through a dis-
tinction between patterns across time periods (or countries or regions) in a nonparametric
framework, or a dummy variable fixed effect or shift term in a parametric treatment. The role
of more specific technological determinants, such as R&D, is sometimes simply asserted, or
may be incorporated by including these factors as arguments of the production or cost struc-
ture (perhaps with some type of lag structure appended).
The recent literature, however, includes a number of studies that more directly charac-
terize technical or structural change within production theory cost- or profit-based models.
For example, Celikkol and Stefanou (1999) recognize endogenous technical change from
price-induced innovation, in addition to the standard exogenous technical change time trend,
in a profit function model of the U.S. food processing and distribution sector. Their approach
incorporates long-run prices as a factor stimulating firms to seek innovations. They find that
this form of technical progress “has a dominant contribution on input decisions compared
with exogenous technical change,” and provide evidence that expectations are important to
model for appropriate representation of production processes and productivity. Their results
also suggest “wide changes in aggregate technical change patterns” and biases (farm-input-
saving and nonfarm and capital-input-using), and little substitution between farm and non-
farm inputs, but increasing substitution (flexibility) over time.
Goodwin and Brester (1995) model structural change in the food processing industry by
appending multivariate gradual switching regression techniques and Bayesian inferential pro-
cedures to a cost-based translog model of factor demand. They also find that production
processes have become more flexible (greater substitution possibilities, except possibly for
labor), allowing the system to more closely approximate a productive optimum, and that such
changes stem from capital-using and labor-saving biases.
Structural change is modeled in Evenson and Huffman (1997) for U.S. agriculture in
terms of changes in farm size, specialization and part-time farming. Their results suggest that
R&D, extension and government commodity programs have had impacts on both farm struc-
ture and MFP, although input price changes, rather than technology or regulation, seem to
have had the greatest impact on farm size. This finding links structural change to the poten-
tial for scale, size and scope economies.
Morrison and Siegel (1998) focus on external R&D impacts in food processing — or
spillovers within the sector — by incorporating a “knowledge capital” vector comprised of
high-tech, human and research (R&D) capital into a cost-function-based model, and find sig-
nificant impacts for all these knowledge factors. In a similar framework, Morrison (1985,
1997) allows for capital-embodied technical change by incorporating dynamic capital adjust-
ment processes for three separate capital inputs, including high-tech capital, for the U.S. food
processing industry. She finds that cost-savings derived from investment in high-tech inputs
are augmented by long-term increases in capital intensity and by the exacerbating effect of
high-tech investment on disembodied technical change.
Chavas, Aliber and Cox (1997) and Chavas and Cox (1997) address the distinction
between private and public R&D in agriculture.16 Their nonparametric treatment is based on
the weak axiom of profit maximization (rather than a functional representation of technology
and behavior) and a specification of “netput” augmentation (that transforms actual into effec-
tive netputs). They find large rates of return to R&D that are higher for private research in the
short term and public research in the longer term. They also obtain support for induced inno-
vation in “actively traded” inputs, but less so for land and labor inputs.
In studies focusing on rates of return to R&D, measured returns vary dramatically across
studies. This seems largely attributable to the difficulty of establishing the lags for or dynam-
ic patterns of internal R&D investment, and the spillover impacts of external R&D. But most
studies find a significant contribution of R&D to the food system — and especially agricul-
ture. Makki, Tweeten and Thraen (1999), for example, who estimate relatively low rates of
return, still find that they are “high enough to justify continued public investments to raise
productivity,” and suggest “shifting public funds from commodity programs to education and
research would raise U.S. agricultural productivity.”
Rigidities and Dynamics

The effects of rigidities (or lack of flexibility/mobility) have often been highlighted in the lit-
erature on technical and structural change. Many studies in the past couple of decades have
directly addressed this issue, along with the resulting importance of utilization changes, sunk
costs, dynamics and expectations. Constraints on rapid adjustment to economic conditions
may affect not only capital, but also labor and land. In fact, many researchers suggest the
rigidities associated with labor may be the most significant factor inhibiting adjustment
processes in agriculture.
For example, Arnade and Gopinath (1998) use output supply and capital investment
functions to model capital adjustment in the U.S. agricultural and food processing sectors.
They find that agricultural capital adjusts very slowly (it is “almost fixed” at 2% adjustment
per year), but that food processing is more flexible (full adjustment takes less than five years).
If these estimates are representative, lack of flexibility imposes serious limitations on pro-
ductivity growth, particularly for agriculture, implying that investment incentives to mitigate
the effects of rigidities should be a primary goal of policy measures to enhance performance.
Morrison targets capital investment in the food processing sector, using a cost-based
model allowing for short- term constraints on capital stock adjustment. The costs of the rigidi-
ties are represented by deviations of shadow values for the capital flow (or utilized capital)
from market investment prices for the capital stock. The resulting measures support the
notion that capital adjusts somewhat slowly in the processing industries, so full equilibrium
is not attained within a year, but suggest that newer high-tech equipment exhibits lower
adjustment costs and greater flexibility.
Stefanou recognizes both adjustment costs and uncertainty in a more complex dynamic
dual (value function- based) model for U.S. agriculture. Luh and Stefanou (1991) expand on
this treatment, and determine that both capital and labor “adjust sluggishly to their long-run
equilibrium levels.” Their results suggest that “asset fixity is important in U.S. agricultural
production,” although they do not find the extreme inflexibility suggested by Arnade and
Gopinath (1998). They emphasize that if such rigidities are not recognized in studies linking
MFP to R&D or other technological determinants the contribution of these determinants is
“misrepresented,” for some inputs are not at their long-run equilibrium levels.17
Luh and Stefanou (1993) pursue this further to bring learning into the picture as a (inter-
nal) knowledge factor, and show that this reduces the “role for technical change and assigns
a substantial role to the . . . contribution of learning-by-doing to the growth of the aggregate
agriculture industry.” They find that evidence of slow capital adjustment seems mitigated
when learning and its dynamic aspects are recognized, with knowledge facilitating the adap-
tation process, although slow adjustment of labor is still an important constraint on produc-
tivity.
Other factors may also be treated as quasi-fixed inputs in a production structure model.
For example, Park (1995) specifies quota licenses as fixed inputs for the Alberta dairy indus-
try in Canada. He finds for 1975–91 that complementarity between livestock (another poten-
tially quasi-fixed input for agriculture) and quota licenses “results in short-run cattle adjust-
ments that are opposite in direction from the long-run adjustments,” and that in fact the “dis-
tortions to cattle investment caused by investing in quota licenses adversely affects produc-
tivity growth.”
Regulation
This raises another likely determinant of — or constraint on — productivity and efficiency:
regulation. If regulatory factors are fixed, they may be considered part of the operating envi-
ronment, although in most cases it is regulatory changes that we wish to investigate. The
treatment of the regulatory constraint typically involves determining the (shadow) costs of the
restriction, which is often how input fixities are dealt with. One such treatment is exemplified
by Fulginiti and Perrin (1993), who incorporate price expectations from taxation changes in
a variable-coefficient cross-country production function for developing countries. They find
for these economies that agricultural productivity would have increased significantly if price
interventions were eliminated.
Another focus in the regulatory effects literature has been on the efficiency impacts of
reducing regulatory distortions through major reforms. In a series of related papers, for exam-
ple, Kalaitzandonakes and Bredahl (1996), Kalaitzandonakes, Gehrke and Bredahl (1994)
and Kalaitzandonakes (1994) identify enhanced technical efficiency from increased liberal-
ization, greater competitiveness, or reduced protectionism in agriculture for various countries.
Lachaal (1994) also finds evidence that reform is positively associated with technical effi-
ciency.
Paul et al (2000), however, using a model that allows for less restricted input and output
substitutability, determine that impacts from regulatory reforms involve changes in input and
especially output composition in response to changing economic (price) inducements. This
finding suggests both that the response to reform should be characterized in terms of alloca-
tive rather than technical efficiency, due to adjustment lags that slow the transition, and that
explicit recognition of substitution and composition adaptations for inputs and outputs is
needed to understand efficiency patterns.
Hu and Antle (1993) explore agricultural policy effects on productivity across countries,
and find the impact is “large and statistically significant only for those countries that tax or
subsidize agriculture moderately.” They interpret this as evidence that farmer incentives in
other countries are “distorted” to such a degree that marginal changes in policy do not mea-
surably affect their behavior.” Their results also suggest that decreased protection is consis-
tent with higher (lower) productivity when agriculture is taxed (subsidized).
Lopez and Pagoulatos (1996) take a different perspective on regulatory impacts and their
political linkages in U.S. food processing. They find, somewhat paradoxically, that “trade
protection tends to be lower in higher concentrated industries,” but “as the number of firms
increases, there is a downward pressure on trade protection, possibly as a result of increased
organizational cost for lobbying.” Both Hu and Antle, and Lopez and Pagoulatos, stress the
costs and distortions associated with high levels of regulation.
Cost Economies — Internal and External

In addition to the effects of input or regulatory rigidities on farm/firm responsiveness and eco-
nomic performance, production characteristics imbedded in the technology may have impor-
tant roles in determining efficiency and productivity patterns. The most commonly recog-
nized factor in this category is scale economies, reflected in the slope of the long-run average
cost curve or a difference between long-run marginal and average costs (in the short run such
a discrepancy can be due to input fixities). Of course, if scale economies prevail, larger-scale
operations will be more efficient in terms of unit costs.
Various other types of cost economies might also exist. Scope economies, for example,
stem from complementarities between outputs such that increasing one output causes the cost
curve for the other to drop. And economies may arise from linkages that cause lower pro-
duction costs for multi-plant firms; examples include spreading across plants of managerial
skill, hiring or information (advertising and connections with suppliers). Other types of link-
ages, spillovers or agglomeration (thick market) effects could also augment the efficiency of
larger or more diversified operations. The existence of such economies and their proliferation
in our age of extensive technological innovation and information may well be a substantive
driving force for productivity growth, and potentially also for integration and concentration.
A number of studies suggest the key role of such cost characteristics in determining
plant, firm, or industry productivity. Kerkvliet et al (1998), for example, allowing for changes
in both technical change and efficiency, suggest that concentration increases in the U.S. brew-
ing industry were due to escalation in advertising expenditures and greater scale economies
(which may be connected and are likely to increase sunk costs).
Lopez (1980) finds for Canadian agriculture, using a cost function approach, that growth
in this sector has been primarily associated with (nonhomothetic or biased) economies of
scale rather than (biased or factor-augmenting) technical change. Such an implication is par-
ticularly important for countries such as Canada and the U.K. where the relatively small size
of the country makes it more difficult to exploit scale economies. Increasing returns to scale
were also found by Andrikopoulous and Brox (1992) for Canadian agriculture.18 This poten-
tial for scale “inefficiency” to have an impact on growth, highlighted as a “traditional
Canadian concern” by Hazledine (1991), is empirically evident also for most studies of scale
economies in the U.S. food sector, such as Morrison (1997).
Stefanou and Madden (1988) focus on size economies in a methodological study that
emphasizes the importance of differential scale effects across inputs, or scale biases, and of
distinguishing short- from long-run scale economies. They also link uncertainty with cost
economies — particularly scope or “multi-product enterprises” and fixities.
MacDonald (1987) discusses the significance of scope economies — output jointness
that implies product diversity is cost-saving and, thus, productivity enhancing.19 He links this
to firm expansion and concentration, and indicates that the presence of such economies can
help us “understand why integrated, diversified corporate structures have developed,” and
“ascertain the costs and benefits, both private and public, of corporate mergers, vertical inte-
gration, diversification and foreign investment.” However, this conceptual study does not
provide estimates of such impacts, whereas Paul finds evidence that scope economies explain
nearly one-third of measured cost economies in beef packing.
The importance of these and other cost structure characteristics for understanding pro-
ductivity patterns is sometimes given lip service in empirical work in the welfare literature,
such as in Bhyuan and Lopez (1995, 1998) who “underscore the importance of cost structure
assumptions” for welfare evaluation. But — as in most of this literature — these studies make
simple one-parameter assumptions about the cost-output relationship, precluding considera-
tion of cost economy components.20
Although economies of scale, size and scope are based on the shapes of cost functions,
or shifts due to (internal) firm decisions such as output supply and plant numbers/sizes,
external cost (shift) factors are also important to recognize. Some of these — in particular,
exogenous technical change and public R&D investment — have already been mentioned and
are often the focus of productivity studies. However, “scale economies” from other external
factors, such as spillovers or externalities due to the public good nature of some types of
investment, might also be substantive.
More specifically, public investment in infrastructure, education or extension could have
vital impacts that should be recognized for a full representation of productivity and its deter-
minants, and for policy guidance. Also playing possible key roles as productivity “drivers”
are agglomeration effects or (horizontal or vertical) spillovers across firms due to thick
markets, high-tech capital proliferation (and enhanced information and communication), and
private R&D investment that generates externalities.
These effects are not straightforward to characterize and measure, but forays into this
area are being made in the literature. For example, Morrison and Siegel (1998) explore shift
impacts on the TC/Y ratio from external or industry-wide R&D, and high-tech and human
capital. They determine that significant scale economies in U.S. food processing industries
can be partially attributed to these knowledge factors and their substitutability with private
capital. The cost-saving value seems greatest for R&D in proportional terms — although the
dramatic observed expansion of high-tech capital causes its total impact to be larger — and
is smaller but still significant (statistically and in magnitude) for human capital. Similarly,
Paul et al (2000) find that public infrastructure has a significant private-cost-saving impact on
U.S. agricultural production.
Non- or Imperfectly Marketed Costs and Benefits

Other nonmarketed “goods” and “bads” may also be important to incorporate for appropriate
measurement and interpretation of cost-benefit ratios or productivity, especially with the goal
of representing social rather than private values. For example, quality-of-life factors such as
food safety and environmental protection have a value for consumers, but also impose costs
(with no monetary compensation since they generate nonmarket benefits) on firms. Some
work on establishing the benefits and costs of such factors has been undertaken. However,
missing markets are hard to address in productivity analysis, due to the wide range of poten-
tial “environmental” commodities that might be considered, and the difficulties of valuing
them.
Efforts toward quantifying the benefits and costs of food safety are summarized and dis-
cussed by Antle (1995) and Caswell (1998), who indicate that some work has attempted to
place values on food safety benefits, but little has been done to integrate it with productivity
analyses. Even less attention has been paid to the cost side of the food safety problem, which
could potentially be addressed by incorporating a measure of compliance costs into a cost
structure framework.
Studies have also begun including measures of environmental damage from agricultur-
al production in the representation and measurement of agricultural productivity, which more
directly raises the issue of social costs.21 For example, Ball, Färe, Grosskopf, Hernandez-
Sancho and Nehring (2000) and Ball, Felthoven, Nehring and Paul (2000) find statistically
significant — but not large in magnitude — costs of reducing risk from leaching and runoff.
These costs largely seem to stem from technological change embodied in pesticide inputs,
implying that induced technical change is a central part of the puzzle. This work does not
address the corresponding value of leaching and runoff risk reduction, but provides a base
from which to compare its costs and benefits.
The impacts of uncertainty, risk, and information have also been recognized in the liter-
ature on productivity and efficiency, although few direct insights about their contribution or
measurement seem established. In fact, Pope (1987), who has done important work on uncer-
tainty and risk, indicates that characterizing uncertainty and risk may not be particularly
important for productivity and welfare representation.
Studies addressing uncertainty issues suggest that risk premia might be used to reflect
the effective prices farmers/firms respond to. This would also imply that a value should be
placed on information, perhaps through recognizing advertising expenditures and resulting
demand changes. In addition, risk, information and advertising may be linked to perceived
cost economies. That is, risk may be spread at larger scales of production, and advertising and
information may have scale effects.
For example, Kerkvliet et al (1998) emphasize that concentration may be due to escala-
tion in advertising expenditures, as well as scale economies. Antonovitz and Roe (1987)
determine that information values increase with the amount of risk. Farrell and Tozer (1996)
consider the value of labeling and grading, which is “designed to improve price signals,” sim-
ilarly to Caswell’s (1998) emphasis on the value of labeling to food safety and nutrition. And
Reed and Clark (2000) establish the unpredictable nature of structural change and consumer
behavior, and report that this “poses considerable risk to food producers and can induce
industrial reorganizations that spread this risk across stages of food production.”
The Demand Side

Most of the issues and associated studies on productivity modeling and measurement
reviewed so far focus on the cost or supply side. While this is a central and an often neglect-
ed piece of the puzzle in welfare and market structure evaluation, key cost and benefit drivers
also of course stem from the demand side.
One important point in this context is the value of product differentiation. Issues regard-
ing multiple products and thus output composition changes have not often been targeted in
productivity studies, but may provide crucial clues about productivity and efficiency.
Bringing this explicitly into the analysis involves recognizing new products and characteris-
tics of existing products as well as distinguishing among types of outputs. That is, appropri-
ate measures of “effective” output must be fashioned to reflect quality and composition
changes, in order to generate relevant measures of output quantities as well as to recognize
the demand-side benefits and supply-side costs of differentiation.
This refinement of the cost-output framework is particularly important, since the food
system has been characterized for at least the past couple of decades by dramatic changes in
consumer demand toward convenience foods, as well as diversity in quality and types of food
products. These demand-driven output composition changes, as recognized by Goodwin and
Brester (1995) and Reed and Clark (2000), are factors underlying (induced) structural change
in the food processing industries that may be as important as technological change in deter-
mining the true cost-benefit ratio for food products. Wills and Mueller (1989), in fact, assert
that product differentiation (and its link to advertising), rather than efficiency (cost
economies), may underlie observed price-cost margins or “market power.”
Note that demand adaptations may also stem from changes in markets served — such as
movements into export markets. Lee and Schluter (1993), for example, assess “sources” of
output changes in the food system in terms of domestic final demand, export demand and
interindustry demand, in a descriptive analysis of demand “drivers.” They find that between
1972 and 1982 “export expansion influenced farm output slightly more than domestic
demand did, while domestic demands influenced processed food output more than export
demand did.” Thus, policies affecting export competitiveness seem more likely to enhance
agricultural productivity, while those targeting the health and spending power of domestic
consumers have more effect on performance in the processing sector.
SO WHAT MESSAGES DO WE GET FROM THIS?

An important message from this literature is that a detailed production/cost structure repre-
sentation is an essential foundation of production and market structure analyses, and that such
a representation fundamentally involves the appropriate measurement of “effective” input
and output prices and quantities. Adaptations must be made whenever measured values do not
reflect the true economic concepts we wish to represent.
Deviations of measured prices from their true economic benefits or costs have, in vari-
ous contexts in the literature reviewed, been recognized as key factors for appropriate mea-
surement and interpretation of performance indicators. For example, Celikkol and Stefanou
(1999) emphasize that price measures should reflect long-run expectations and that the role
of these prices in inducing technical change should be incorporated. A primary concern of
Chavas and Cox (1997) is the transformation of actual into effective netput quantities, with
an induced innovation motivation. The measurement of shadow values to represent the true
flow values of quasi-fixed inputs is (explicitly or implicitly) the purpose of the treatments of
capital by Morrison (1985, 1997), and of capital and labor by Luh and Stefanou (1991). In
Luh and Stefanou (1993), learning is recognized to be a stock resource associated with the
quality of labor that should be taken into account for appropriate valuation of labor. And
Morrision and Siegel (1998) emphasize the characterization of true marginal, as distinguished
from average, costs of output — which may be a driving force for market structure — as the
point of cost economy measurement and analysis.
These adaptations to observed prices and quantities accommodate internal changes in
effective input or output values. Values may similarly be attributed to externalities from, say,
environmental impacts, or distortions from, say, regulations. For example, Ball, Felthoven,
Nehring and Paul (2000) focus on computing shadow values for the reduction of nonmarket-
ed bad outputs (risk from leaching and runoff), as well as constructing hedonic measures for
effective pesticide prices and quantities.22
Overall, many — if not most — of the issues raised in previous sections and in the lit-
erature can be embraced within this conceptual perspective. Adapting for deviations between
market and effective values of factors and commodities, and establishing the determinants of
these discrepancies, may involve characterizing a broad range of shadow values or virtual
prices for mismeasured, public good, or otherwise imperfectly marketed inputs and outputs,
as well as accommodating changes in input and output composition or differentiation. Such
mechanisms also have potential for bringing “quality of life” factors into the picture. And
they can provide vehicles for valuing information (perhaps through advertising costs and
demand impacts), or uncertainty and risk (for example, by adapting prices for expectations or
by a risk premium).
The appropriate methods for data or model adaptation depend on the question being
addressed and the reasons for the deviations of (average) market — if marketed — and true
economic values (or levels) of productive factors and commodities. The representation of vir-
tual, shadow, or effective prices and quantities can be pursued through careful measurement
techniques. Changes in output or input characteristics or composition may be recognized
through disaggregation. Variations in quality characteristics have alternatively been account-
ed for by creating quality indexes (such as for educational attainment), or using hedonic tech-
niques. Or parametric estimation of shadow values can be carried out, for example, to accom-
modate rigidities from input fixities or regulation, to incorporate knowledge factors like
learning, or to establish values for nonmarketed goods (or bads).
Another central issue is distinguishing among layers and levels of the system, and their
individual and linked roles in overall performance. In particular, although the layers of the
food sector are useful to evaluate individually, identifying spillovers across them is essential
for appraising overall sectoral performance and understanding driving forces toward integra-
tion, as emphasized by Gopinath, Roe and Shane (1996) for the United States and
MacDonald, Rayner and Bates (1992) for the United Kingdom.23
Similarly, both diversity and linkages across products and plants/firms/industries are key
factors underlying observed economic performance and its role in stimulating mergers and
acquisitions. Especially crucial for understanding trends in the food sector is the exploration
of technological and demand forces motivating increased product differentiation, comple-
mentarities among products, new product development, and expanding demand for a diverse
range of food items.
Analysis at various levels of industry aggregation may also illuminate aspects of pro-
duction structure and productivity. And, as highlighted by Traill (1997) and increasingly
emphasized in the literature on trade and competitiveness, even broader globalization issues
have “important implications for productivity and growth, and market integration,” at least
partly due to convergence in consumer demand, and to the “exploitation of economies of

scale in finely differentiated markets.”
Another point to underscore is that knowledge not only of cost-benefit or productivity
levels but also of their determinants and implications is crucial for interpreting food system
performance measures. An understanding of what underlies observed performance trends,
such as rigidities, cost economies or spillovers, is key to interpreting and using performance
measures — in particular for policy guidance to augment growth and welfare. And because
of fundamental links between productivity and efficiency, and between cost and market
structure, cost structure measures can provide essential insights about the driving forces of
market structure patterns such as mergers and concentration that have caused concern for
policy makers.
That is, a major focus of efficiency measurement in agricultural economics has been on
establishing the extent of “welfare losses” from market power, based on deviations between
measured output prices and marginal costs, or price-cost margins. The issues raised here
about the production/cost side of this problem, however, suggest that various production
characteristics could underlie such deviations. So attributing “welfare loss” to price-cost mar-
gins raises the question: Is this deviation truly an indication of inefficiency? Or is it an indi-
cation of offsetting efficiency factors that could be welfare enhancing?
As has been recognized at least since Demsetz (1973), scale or more generally cost
economies are a potential offsetting factor or driver from the cost side. For example,
Kerkvliet et al (1998) establish that scale “inefficiencies” in the brewing industry imply a
deviation between price and marginal cost, but that lack of excessive profitability suggests
“market power exercised is very small.” And Azzam and Schroeter (1995) find for the U.S.
beef packing industry that the “cost savings necessary to neutralize the anticompetitive effects
of consolidation . . .” are lower than those arising from estimated scale economies. Such indi-
cators of efficiency motivators for measured “market power” are also consistent with studies
that reveal a positive relationship of mergers and acquisitions to productivity and wage
growth, employment and survival, such as by McGuckin, Nguyen and Reznek (1995).
For the U.K. food processing sector, Balasubramanyam and Nguyen (1991) emphasize
that diversification as well as increasing size of firms and concentration of firms is motivat-
ed by the potential to take advantage of “proven managerial and marketing skills” through
economies of scale in marketing, typically involving increased capital costs. Along the same
lines, Gopinath and Vasavada (1999) state that “deadweight losses from imperfect competi-
tion may be offset by greater product variety and quality of food products for consumers,”
and determine that R&D is more prevalent in firms exhibiting noncompetitive behavior, pro-
viding support for Demsetz-like efficiency/innovation arguments. And Gopinath, Pick and
Worth (2000) find offsets from “dynamic welfare gains such as reduced price variability.”24
Various aspects of the production or cost and demand structure of firms in the food sys-
tem may thus be indicators of stimuli for both concentration and enhanced productivity. In
particular, cost economies (that imply both lower costs and a greater proportion of sunk costs
at higher or more diversified scales of operation), short-run rigidities (that affect flexibility
and the importance of utilization levels), innovation (or knowledge factors that may involve
spillovers) and product differentiation, not only may have important impacts on productivity
growth trends, but also be more fundamental determinants of concentration than is a desire to
exploit market power.
CONCLUDING REMARKS: WHAT DO WE KNOW?

AND WHERE DO WE GO FROM HERE?
This article overviews conceptual, methodological and empirical issues and findings that
seem crucial for considering “what we know” about food system productivity and efficiency
and where it might be “productive” to move from here to expand our understanding of per-
formance determinants and implications.
The empirical literature shows that the food sectors of the U.S. and U.K., and perhaps to
a lesser extent Canada, have exhibited stronger productivity growth than most other sectors.
The productivity gains are especially marked for agriculture, with slower growth rates as we
move “up the food chain.” Emphasis has been placed on the importance of spillovers across
layers of the system, the diversity of industry sectors, regions, and plants/firms, and changes
in the composition and quality of both inputs and outputs. And numerous determinants of
observed productivity gains and gaps have been highlighted, including R&D, flexibility and
dynamics, and various induced, internal and external knowledge-based factors underlying
cost economies.
More specifically, the literature establishes the importance of production flexibility, both
to reach optimal cost-output levels rapidly in response to changes in the economic and tech-
nological climate, and to adapt to diverse and changing product demands. The role of tech-
nology embodied in new capital investment, and the knowledge or education of laborers, in
motivating flexibility and mobility has been documented. Innovation stemming from R&D
that may be induced by observed input prices has been identified as more important than gen-
eral technical change trends, although the returns to both public and private R&D still defy
clear quantification. The limiting effects of rigidities from excessive regulation have been
recognized. Crucial cost structure aspects that affect (internal and external) cost economies
and thus productivity, such as utilization changes, scale and size effects, and scope
economies, have been emphasized. And the role of input — and potentially output — biases
from all of these impacts (and from adaptations in consumer demand patterns), in the context
of compositional changes, has been stressed.
It thus seems evident that policy to facilitate flexibility — by increasing knowledge as
well as encouraging innovation and investment — has the potential to reap gains by enhanc-
ing adjustment and spillovers. Stimulating technical change is also important, although which
are the most important technical change “drivers” is not yet well understood. And the impacts
of various types of cost economies should be recognized, so that regulations are not imposed
that limit their potential cost-saving contributions.
Although it is difficult to construct a single, sufficiently broad model to embrace all of
these productivity determinants in a consistent and implementable fashion, inroads have been
made toward measuring many of them individually, and sometimes enough characteristics
have been imbedded in models to also determine their relative impacts. More information
quantifying the absolute and relative contributions of these and other types of productivity
factors will be important to establish in subsequent research to provide guidance for policy
development.
In terms of methodology, increased attention to the appropriate measurement of inputs
and outputs embodied in the cost-output ratio underlying productivity/efficiency — which
can be pursued through careful data construction, disaggregation, hedonic analysis, or para-
metric estimation of virtual or shadow prices — appears key to gaining further insights. And
the fundamental role of a full consistent representation of the cost structure and its character-
istics as a basis for evaluation of performance in the food system is apparent. Recognizing
these pieces of the puzzle is essential for justifiable representation of economic performance,
and the interpretation and use of resulting measures.
Some of these points are consistent with those emphasized in recent literatures. The New
Empirical Industrial Organization (NEIO) literature highlights structural modeling and theo-
retical underpinnings, although the cost structure is often neglected given the primary atten-
tion on the demand side. The New Trade Theory recognizes the importance of imperfect com-
petition, which is not necessarily characterized as “bad,” but as supported by product differ-
entiation and scale economies. And the New (endogenous) Growth Theory stresses the key
role of knowledge factors through their impact on “scale” economies and spillovers.
Much of the recent literature on performance in the food sector seems in step with these
trends and goals. It focuses on identifying and quantifying rigidities that limit — or knowl-
edge factors that enhance — flexibility and technology and netput characteristics that affect
input and output measurement. Such developments provide an important thrust in the right
direction, although much more needs to be accomplished to enhance our understanding of
productivity patterns, and causes and effects, in the agri-food sector.
NOTES
1Paul (1999) develops and elaborates these concepts in great detail.
2For a more traditional cost-benefit analysis, this becomes more complex, at least in part due to dis-
tinctions between private and social costs, and due to ambiguities about the role of prices. For example,
expressing Y in dollars may seem more relevant in this context. But this brings in output pricing issues
that raise other issues of market structure or profitability that are often better addressed separately.
Enhanced performance in a social sense implies more output from a given amount of inputs, or costs
(resource use) rather than more “value” of output, so Y should be measured in constant dollars. Note
also, that if both Y and TC are measured in dollars, the ratio becomes the inverse of the returns/costs
ratio (pYY/pVV, where pY is output price and pV input price). So not only productivity growth (in the pri-
mal sense of a comparison of Y to V, as discussed further below), but also the “terms of trade” for the
sector, are reflected in the measure.
3For example, compare prices or average revenue to marginal revenues (AR to MR) for outputs, or
prices or average factor costs to marginal factor costs (AFC to MFC) for inputs.
4In this case, we ultimately also need to determine whether this deviation between measured and actu-
al economic determinants of behavior are a problem, or if they simply arise from, say, product differ-
entiation that might have its own value.
5This very brief description of the standard (dual and primal) productivity residual equations is elabo-
rated in many places in the literature. A comprehensive discussion of both the nonparametric and para-
metric methodologies, the classic and current literature in this area, and the methodological adaptations
necessary if inefficiency exists, is offered in Paul (1999).
6Note that this expression is implicitly based on a Divisia or Tornqvist input index, since the input con-
tribution is represented by a share-weighted sum of the input changes. Such a chained (as opposed to
fixed-weight) index recognizes input changes or substitutability through the share measures, and is con-
sistent with flexible functional forms such as the translog. Although this article finesses the index num-
ber issue, the use of such flexible indexes has been an important step in the analysis of productivity
growth in nonparametric (index number) frameworks.
7Although space constraints preclude a digression on index number as contrasted to econometric mea-
surement, it should be noted that econometric analysis is designed to measure the true or effective shares
of the inputs, as well as the weights on the other factors included in the cost (or other, such as produc-
tion ) function used as a basis for analysis, rather than making assumptions about optimization in order
to impute marginal products (say, from measured prices). These two routes to productivity and perfor-
mance measurement both, however, have important contributions to make to the literature. The index
number (nonparametric) approach may be implemented with only observed data, whereas the econo-
metric (parametric) approach allows more structure to be put on the technological and optimization
problem, and thus more factors affecting observed productivity/cost trends to be identified and quanti-
fied. This difference in perspective has sometimes been referred to theory- intensive (relying on theo-
retical assumptions to use observed data to impute true economic concepts) rather than data-intensive
(requiring extensive data manipulation) approaches to the problem.
8Careful modeling of the stochastic structure, such as allowing for errors in variables in the economet-
ric analysis to reflect the deviation of market from true or effective prices, could also prove fruitful for
this purpose.
9See Morrison (1985) for further discussion of these procedures and their implementation.
10In Canada, price and quantity indexes were in the past often measured with Laspeyres indexes,
although this has been superseded by the use of Tornqvist or Divisia procedures (as discussed by
Fantino and Veeman 1997). These chained or variable- weight indexes are much preferable to the fixed-
weight Laspeyres indexes, particularly given the proliferation of new goods and dramatic changes in
input and output composition evident for the food system.
11Although these differences may not seem that substantial, over time they could cause a significant
variation in productivity levels.

12This is computed by multiplying the productivity growth rate by a Domar weight, which essentially
reflects this sector’s share of GDP.

13Thirtle and Bottomley (1992) also find higher growth after the U.K. joined the European Community.
14Note, however, that it is the low productivity growth rate numbers for the early 1980s that pull the
averages down.
15One component of this, raised in McDonald, Rayner and Bates (1992), is the increasing proportion of
processed products in the composition of final demand for this sector, as documented by Paul and
MacDonald (2000).
16This is just one example in the wide-ranging, but not yet definitive, literature on R&D impacts in the
agricultural sector that is comprehensively overviewed by Alston et al (1995).

17They also find that technical change dominates the growth of total factor productivity, with scale,
quality and disequilibrium factors explaining only 3.44% of the growth.

18However, the strongly negative (parametrically) estimated productivity growth rate, which is driven
by a drop in materials productivity, seems suspect in this study.

19Value associated with product diversity or differentiation may also derive from spreading risk due to
uncertain consumer choices, or simply from consumers’ desires and thus demand for a broad choice of
commodities.
20Or, in many cases, the even stricter assumption of constant returns to scale is imposed.
21This work has been carried out using data on “bad output” risk due to leaching and runoff from agri-
cultural chemicals use developed by Ball, Nehring, Kellogg and others at the USDA/ERS.
22Note that although I have focused on the measurement of effective shadow values for inputs and mar-
ginal costs for outputs, due to the cost orientation I have pursued here, such issues can also be addressed
in a primal framework. For example, distance function “shadow value” measures were constructed to
represent the production consequences of negative outputs in Ball, Färe, Grosskopf, Hernandez-Sancho
and Nehring (2000). This treatment also allows for the existence of inefficiency.
23This is particularly crucial since, as French (1987) notes, the “food system beyond the farm gate” is
growing, but productivity growth at higher levels of the chain is less than at primary levels.
24This conclusion stems from their finding that “the rate of inflation and product heterogeneity increase
intra-industry price variability in food industries, but industrial concentration lowers the sensitivity of
relative prices to changes in the rate of inflation.”
ACKNOWLEDGMENT
Thanks are due to the Economic Research Service/USDA and the Giannini Foundation for support
toward my research on food system performance, and to an anonymous Journal referee and a Journal
editor for insightful comments.
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Modeling and Measuring Productivity in the

Professor, Department of Agricultural and Resource Economics, and

Canadian Journal of Agricultural Economics 48 (2000) 217–240

MOTIVATION: THE “NEW” COST ECONOMICS (?)

λTCt = dln TC/dt – εTCY dln Y/dt – Σj Sj dln pj /dt (1)

λYt = dln Y/dt – Σj Sj dln vj /dt 6 (2)

THE LITERATURE: WHAT HAS BEEN DONE — AND FOUND?

Extensions to the Traditional Analysis: What Do They Add?

Technical and Structural Change

Rigidities and Dynamics

Cost Economies — Internal and External

Non- or Imperfectly Marketed Costs and Benefits

The Demand Side

SO WHAT MESSAGES DO WE GET FROM THIS?

partly due to convergence in consumer demand, and to the “exploitation of economies of

CONCLUDING REMARKS: WHAT DO WE KNOW?

variation in productivity levels.

reflects this sector’s share of GDP.

agricultural sector that is comprehensively overviewed by Alston et al (1995).

quality and disequilibrium factors explaining only 3.44% of the growth.

by a drop in materials productivity, seems suspect in this study.

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