Boston University; Department of Economics

ECONOMICS 708: ADVANCED ECONOMETRICS I

Spring 2020
Instructor: Hiroaki Kaido

The aim of the course is to develop familiarity with a wide range of statistical and econometric
techniques that have proved to be useful in applied contexts. Theoretical results will be developed as
necessary and in order to allow students to apply general principles to their own research problems.
Primary emphasis, however, is placed upon applicability, on the ability to understand the techniques in
use in the literature, and on acquiring a minimal acquaintance with econometric computing. The
material discussed is a reasonable definition of the minimum that a well-trained economics Ph.D.
should know. For those of you who are primarily interested in economic theory, the course should
give you some idea of the way in which economists attempt to confront theory and evidence.

Prerequisites

Economics 707 or equivalent. Familiarity with calculus, linear (matrix) algebra and basic
mathematical statistics is expected. I shall also assume that students are familiar with the general
linear regression model, its algebra, and estimation and inference within that framework. (Students for
whom this last assumption is not true will have a hard time very quickly and should review the
material at once.)

Grading

The course grade will be based on a mid-term (30%) and a final (50%) and 4-5 problem sets (20%).
The final will be a 2 hour exam and will cover all material. Parts of the problem sets can be asked in
the mid-term or final exams.

Academic Conduct

Students should know and understand the GRS Academic Conduct Code, see
http://www.bu.edu/cas/students/graduate/forms-policies-procedures/academic-discipline-procedures/.
Any suspected academic misconduct will be reported to the Dean's Office.

Texts and Notes

Good texts to review the basic notions of probability and statistics useful for this course are:
Casella, G. and R. Berger, Statistical Inference, Duxbury Press, 2nd ed., 2001.
Gallant, A.R. (1997) An Introduction to Econometric Theory, Princeton University Press.

There is no required text, which we will follow closely. The course is based on a set of lecture
notes. However, it is strongly recommended that you complement these notes with one or more of the
following textbooks:
Davidson, R. and J. G. MacKinnon (2004) Econometric Theory and Methods, Oxford University
Press.
Hamilton, J.D. (1994), Time Series Analysis, Princeton University Press.

Hayashi, F. (2000), Econometrics, Princeton University Press.

Wooldridge, J.M. (2010), Econometric Analysis of Cross Section and Panel Data, MIT Press.

You are also encouraged to supplement the material discussed in class with a good introductory level
book that gives an intuitive explanation of the use of the various methods. The one I recommend is:

Stock, J.H. and M.W. Watson (2002), Introduction to Econometrics, Addison-Wesley.

Other useful books are:
Gourieroux, C. and A. Monfort (1995) Statistics and Econometric Models, Cambridge.
Greene, W. (2003) Econometrics Analysis, 5th ed., Prentice Hall.
Judge, G.G., W.E. Griffiths, R.C. Hill and T.C. Lee (1988) The Theory and Practice of Econometrics,
2nd ed., Wiley.
At a more advanced and theoretical level, the following books are very useful:
Amemiya, T. (1986), Advanced Econometrics, Harvard University Press.
Rao, C.R. (1973), Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley.
Silvey, S.D. (1975), Statistical Inference, London: Chapman and Hall.

Cox, D.R. and D.V. Hinkley (1974), Theoretical Statistics, London: Chapman and Hall.
White, H. (1984), Asymptotic Theory for Econometricians, New York: Academic Press.
Griliches, Z. and M.D. Intriligator, eds., Handbook of Econometrics, Volumes 1-3. North-Holland.
Engle, R.F. and D. McFaden (1994), Handbook of Econometrics, Volume 4. North Holland.
Gallant, A.R. and H. White (1988), A Unified Theory of Estimation and Inference for Nonlinear
Dynamic Models, Basil Blackwell.
Godfrey, L.G. (1988), Misspecification Tests in Econometrics, Cambridge University Press.
Phillips, P.C.B. and M.R. Wickens (1978), Exercises in Econometrics, Volume 1 and 2. Phillip Allen.
Politis, D.N., J.P. Romano, and M. Wolf (1999), Subsampling, Springer.
An interesting book with economic applications is:
Berndt, E.R. (1991), The Practice of Econometrics: Classics and Contemporary, Addison-Wesley.
 COURSE OUTLINE

1. A Brief Review of Linear Models & Asymptotics (least squares projection, LLN, CLT, CMT)

2. Instrumental Variables (instruments and estimator, two-stage interpretation, weak

identification, Hausman-Wu test).

3. Generalized Method of Moments (moment restrictions, identification, asymptotic theory, and

specification tests)

4. Linear Panel Data Models (random effects estimator, fixed effects estimator, incidental
parameter problem, and dynamic panel data models)

5. Maximum Likelihood Estimation (the principle of MLE, sufficient statistics, the Cramer-Rao
lower bound, asymptotic distribution of the MLE, an information matrix equality, the MLE in
the standard linear model, consistent estimates of the information matrix).

6. Numerical Optimization (basic results, numerical optimization).

7. Limited Dependent Variable Models (Logit, probit, multinomial choice)

8. Resampling Methods (Bootstrap, subsampling, and others)

9. The Trinity of Test Procedures Revisited (LR, Wald and LM tests, asymptotic distribution,
geometric interpretation, when are LM, LR and Wald tests the same? the LM test in least-
squares problems).

10. Misspecified Models (basic issues of the quasi-MLE, the Kullback-Leibler divergence,
asymptotic distribution of the quasi-MLE, hypothesis testing with potential misspecification, the
information matrix test for misspecification, simplification of the information matrix test).

11. Vector Autoregression (VAR and VMA representations, variance decomposition, impulse
response function)

12. Unit Roots, Cointegration and Spurious Regressions (an example, unit roots, differenced
versus trend stationary models, testing for a unit root, spurious regression, cointegration, error
correction models, testing for cointegration).

Selected Readings.

1. The Basic Linear Model; Asymptotic Results: Wooldridge, ch. 4.1-4.2;

Thurman, W.N. (1989), “Unconditional asymptotic results for simple linear regression,” The American
Statistician, 43: 148-152.
White, H. (1984), Asymptotic Theory for Econometricians, New York: Academic Press.

2. Instrumental Variables: Wooldridge, ch. 5;

Angrist, J.D. and A.B. Krueger (2001), “Instrumental variables and the search for identification: from
supply and demand to natural experiments”, Journal of Economic Perspectives 15 (4), 69-85.

Hausman, J.A. (1978), “Specification tests in econometrics,” Econometrica 46, 1251-1272.

Stock, J.H., M. Yogo and J. Wright (2002), “A survey of weak instruments and weak identification in
generalized method of moments,” Journal of Business and Economic Statistics 20, 518-529.

3. Generalized Method of Moments: Hayashi, ch. 3;

Hansen, L.P. (1982), “Large sample properties of generalized method of moments estimators,”
Econometrica 50, 1029-1054.

Hansen, L.P. and K.J. Singleton (1892), “Generalized instrumental variable estimation of nonlinear
rational expectations models,” Econometrica 50, 1269-1296.

4. Linear Panel Data: Wooldridge, ch. 10;

Arellano, M. and S. Bond (1991), “Some tests of specification for panel data: Monte Carlo evidence
and an application to employment equations.” Review of Economic Studies 58, 277-297.

Mundlak, Y. (1978), “On the Pooling of Time Series of Cross Section Data,” Econometrica 46, 69-85.

5. Maximum Likelihood Estimation: Wooldridge, ch. 12.1-3, 13;

Bollerslev, Tim. (1986), “Generalized autoregressive conditional heteroskedasticity,” Journal of

Econometrics 31, 307-327.

Newey, W.K. and McFadden, D.L. (1994), “Large sample estimation and hypothesis testing,” in
Handbook of Econometrics, vol.4, ch.36, Elsevier.

6. Numerical Optimization: Hayashi, ch.7.5;

Amemiya, T. (1984), “Nonlinear regression models,” in Handbook of Econometrics, vol. 1, ch. 6.

Quandt, R.E. (1983), “Computational problems and methods,” in Handbook of Econometrics, vol. 1,
699-764.

7. Limited Dependent Variable Models: Wooldridge, ch. 15, 16.1-2.

McFadden, D.L. (1983), “Econometric analysis of qualitative response models,” in Handbook of
Econometrics, Vol. II, Ch.24, Elsevier.

Keane, M.P. (1992), “A note on identification in the multinomial probit model,” Journal of Business
and Economic Statistics, 10, p.193-200.

8. Resampling Methods: Wooldridge, ch.12.8.

Horowitz, J.L. (2001), “The Bootstrap,” in Handbook of Econometrics, vol. 5, Ch. 52, Elsevier.

Politis, D.N., J.P. Romano, and M. Wolf (1999), Subsampling, Springer.

9. The Trinity of Test Procedures revisited: DM, ch. 4.1-4.5, 10.6;

Buse, A. (1982), “The likelihood ratio, Wald and Lagrange multiplier tests: An expository note,” The
American Statistician, 153-157.

Engle, R.F. (1984), “Wald, likelihood ratio and Lagrange multiplier tests in econometrics,” Handbook
of Econometrics, Vol. III, Ch. 13.

Breusch, T.S. (1979), “Conflict among criteria for testing hypotheses: extensions and comments,”
Econometrica 47, 203-207.

Holly, A. (1982), “A remark on Hausman’s specification test,” Econometrica 50, 749-760.

10. Misspecified Models

White, H. (1980), “A heteroskadasticity-consistent cavariace matrix estimator and a direct test for
hetroskedasticity,” Econometrica 48, 817-838.

White, H. (1982), “Maximum likelihood estimation of misspecified models,” Econometrica 50, 1-26.

White, H. (1994), Estimation, Inference and Specification Analysis, Econometric Society Monographs,
Cambridge University Press.

11. Vector Autoregression Models: Hayashi, ch. 6.4-6.6, Hamilton, ch. 11

Granger, C.W.J. (1969), “Investigating Causal Relations by Econometric Models and Cross-Spectral
Methods,” Econometrica 37, 424-438.

Sims, A.S. (1980), “Macroeconomics and Reality,” Econometrica 48, 1-48.

12. Unit Roots and Spurious Regressions: Hayashi, ch. 9, Hamilton, ch. 17

Granger, C.W. and P. Newbold (1974), “Spurious regressions in econometrics,” Journal of

Econometrics 2, 111-120.
Campbell, J.Y. and P. Perron (1991), “Pitfalls and opportunities: What macroeconmists should know
about unit roots,” NBER Macroeconomics Annual Vol. 6, O.J. Blanchard and S. Fisher (eds), 141-201.

Stock, J.H. and M.W. Watson (1988), “Variable trends in economic time series,” Journal of Economic
Perspective 2, 147-174.

Perron, P. (1989), “The great crash, the oil price shock and the unit root hypothesis,” Econometrica
57, 1361-1402.

Hendry, D.F. (1986), “Econometric modelling with cointegrated variables: An overview,” Oxford
Bulletin of Economics and Statistics 48, 201-212.

Dickey, D.A. and W.A. Fuller (1979), “Distribution of the estimators for autoregressive time series
with a unit root,” Journal of the American Statistical Association 74, 427-431.

Engle, R.F. and C.W. Granger (1987), “Co-integration and error correction: Representation, estimation
and testing,” Econometrica 55, 251-276.