Econometrics I: Applied Econometrics

Stern School of Business

Professor W. Greene
Department of Economics
Office:;MEC 7-90, Ph. 998-0876
e-mail: wgreene@stern.nyu.edu
WWW: http://people.stern.nyu.edu/wgreene

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Abstract: This is an intermediate level, Ph.D. course in Applied Econometrics. Topics to be studied include specification, estimation, and inference in the context of models that include then extend beyond the standard linear multiple regression framework. After a review of the linear model, we will develop the asymptotic distribution theory necessary for analysis of generalized linear and nonlinear models. We will then turn to instrumental variables, maximum likelihood, generalized method of moments (GMM), and two step estimation methods. Inference techniques used in the linear regression framework such as t and F tests will be extended to include Wald, Lagrange multiplier and likelihood ratio and tests for nonnested hypotheses such as the Hausman specification test. Specific modelling frameworks will include the linear regression model and extensions to models for panel data, multiple equation models, time series models and models for discrete choice.

Prerequisites: Multivariate calculus, matrix algebra, probability and distribution theory, statistical inference, and an introduction to the multiple linear regression model. Appendices A and B in Greene (2011) are assumed. We will survey the parts of Appendix C and Chapter 2 that would have appeared in prerequisite courses. A significant part of this course will focus on the advanced parts of Appendices C and D and Chapters 4 through 7. We will also make use of a few of the results in Appendix E.

Course Requirements: Grades for the course will be based on:

  • Midterm examination (30%), The midterm examination will be given in class.
  • Take home final exam (40%)
  • Several problem sets and small projects (total 30%).

 

Course Materials:

Text: The required text for the course is Greene, W., Econometric Analysis, 7th Edition, Prentice Hall, 2011. (You may use the 6th edition if you prefer.) Other texts that might be useful are: Davidson, R., and MacKinnon, J., Econometric Theory and Methods, Oxford University Press, 2004, which is more advanced than Greene; Johnston, J. and DiNardo, J., Econometric Methods, 4th Edition, McGraw-Hill, 1997, which is comparable to Greene; and Kennedy, P., A Guide to Econometrics, 4th Edition, MIT Press, 1998, Woolridge, J., Introductory Econometrics: A Modern Approach, 3rd Edition (or later), Southwestern, 2006 (or later) or Gujarati, D., Basic Econometrics, 4rd Edition, McGraw-Hill, 2004, all of which are less advanced. Note: A useful list of errata and comments submitted by readers of the text are listed at the website for the text, http://people.stern.nyu.edu/wgreene/Text/econometricanalysis.htm where there is a button for the errata/discussion list.

Software: Some of the outside work for this course will involve using a computer. Students may use any computer software that they are familiar with for this purpose.  I will provide a copy of NLOGIT to anyone who wishes to use it.  Data sets needed for the exercises will be distributed to the class via the course website.  The data sets used for the examples in the text are all available at the text website.

Readings: A few relevant articles from the literature will be suggested (not required). The papers listed are useful pedagogical literature, and students intending to do empirical research for their dissertations will probably find them worthwhile reading. The others are a selection from a huge literature that should be both interesting and accessible to students in this course.

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Course Outline: Reading assignments given in red in brackets refer to sections in Greene (2012).

  • I. The Paradigm of Econometrics: [Chapter 1 (pp. 1-7)]
    • A. Modeling in economics
    • B. Econometrics: statistics, economics, mathematics
    • C. Econometric modeling: understanding, prediction, control
    • D. Modeling frameworks:
      • 1. Bayesian and Classical (frequentist) approaches [16.1, 16.2]
      • 2. Estimation and inference: Nonparametric, semiparametric, parametric [Chapter 12]
    • E. Estimation and inference in econometrics, methodological issues
  • II. The Classical Linear Regression Model. Part 1. Specification and Computation
    • A. The conditional mean function [B.1-B.3, B.7-B.8] ; regression (Waugh)
    • B. The classical linear regression model and its functional form
      • 1. The linear regression model [2.1-2.3]
      • 2. Linear models and intrinsic linearity [2.3, 6.3]
      • 3. Logs and levels, estimating elasticities [2.3]
      • 4. Functional form and linearity. Transformations and dummy variables [6.1-6.3]
      • 5. Linearized regression and Taylor series, linearity in economic modelling [2.3, 7.2]
    • C. Least squares regression [Chapter 3] ; (Frisch and Waugh, Longley)
      • 1. Least squares regression [3.1-3.2]
      • 2. Partitioned regression and the Frisch-Waugh theorem [3.3, 3.4]
      • 3. Applications of partitioned regression: a fixed effects model [11.4]
    • D. Evaluating the fit of the regression [3.5] , ANOVA, Adjusted R2 [3.5]
    • E. Least squares with restrictions [5.5.1], principal components [4.7.3]
  • III. The Classical Linear Regression Model. Part 2. Statistical Inference in Finite Samples
    • A. Statistical properties of the least squares estimator in finite samples [4.2-4.3]
      • 1. Why least squares? [4.1]
      • 2. Sampling distributions [Example 4.1]
      • 3. Expectation [4.3] ;
      • 4. The effects of omitted and superfluous variables - The Omitted Variable Formula (A VIR) [4.3.2]
      • 5. Variance of the least squares estimator [4.3.4]
      • 6. The Gauss-Markov theorem [4.3.5]
    • B. Estimating the Variance of the least squares estimator
      • 1. Conventional estimation [4.3.7]
      • 2. The effect of multicollinearity [4.7.1]
      • 3. Introduction to bootstrapping; least absolute deviations [12.3.3, 15.4]
    • C. The sampling distribution of the least squares coefficient vector [Chapter 4]
      • 1. Generalities about sampling distributions [C.2-C.4]
      • 2. Sampling distributions and properties of estimators [C.5, 4.3 - 4.5]
      • 3. Linear estimation and normality [4.3.8]
      • 4. Efficient estimation, precision, mean squared error [4.3.4, 4.7.2]
      • 5. Describing the sampling distribution of the estimator - kernel density estimator [4.3.8, C.4]
    • D. Statistical Inference in the linear model [Appendix C, Chapter 5] (Greene and Seaks)
      • 1. Standard results for testing [5.1 - 5.5]
      • 2. Structural change [6.4], Model selection [6.4], [5.8]
    • E. Prediction using the linear model [4.6], the Oaxaca decomposition [4.5.3]
  • IV. Asymptotic Theory
    • A. Large sample distributions, asymptotic and limiting distributions [Appendix D]
    • B. Basic large sample results for the classical model [4.4] (McCallum)
    • C. Large sample results for a function of a statistic - the delta method [4.4.4], Krinsky and Robb method [15.3]
    • D. Test procedures for large samples; t, F, chi-squared, Wald statistic [5.3, 5.4]
  • V. Instrumental Variables [8.1 - 8.3]
    • A. Instrumental variables estimation and measurement error [8.1 - 8.3, 8.5] (Ashenfelter)
    • B. Two stage least squares [8.3.4]
    • C. The Hausman and Wu specification tests [8.4]
    • D. Weak Instruments [8.7]
    • E. Natural Experiments and Causal Effects [8.8]
  • MIDTERM
  • VI. The Generalized Regression Model
    • A. Nonspherical disturbances [9.1]
      • 1. General formulation [9.1-9.3]
      • 2. Heteroscedasticity [9.4-9.7] (Harvey)
    • B. Implications for least squares [9.4, 9.5]
      • 1. Robust covariance matrix estimation [9.3-9.4, 9.5] (White, Newey/West)
      • 2. Bootstrapping [15.4] ;
    • C. Testing for nonspherical disturbances [9.5]
    • D. Generalized least squares and weighted least squares [9.3,9.6]
    • E. Two step feasible GLS estimation, familiar applications [9.7]
    • F. Applications of two step, feasible GLS estimation
      • 1. Seemingly Unrelated Regressions [10.1 – 10.3, 10.5]
      • 2. Autocorrelation [20.1 – 20.9]
      • 3. Demand System [10.5] (Christensen/Greene)
      • 4. Vector Autoregression [21.3]
  • VII. Techniques for Analyzing Panel Data
    • A. Traditional Models: Fixed and Random Effects [11.1-11.6]
    • B. Random Parameters and Latent Class Models [11.11, 15.7-15.8] (Greene (two papers)
    • C. Treatment Effects and Difference in Differences [6.2.5]
    • D. Parameter Heterogeneity [11.11]
    • E. Endogeneity [11.8]
  • VIII. Nonlinear Regression Models [7.1 - 7.2]
    • A. Nonlinear regression and nonlinear least squares [7.1-7.2] (McCullough and Vinod)
    • B. Partial Effects [7.2]
    • C. Nonlinear Least Squares [7.2.6]
  • IX. Methods of Estimation
    • A. Maximum likelihood estimation [Chapter 14] (Harvey)
      • 1. Computation [E.2, E.3]
      • 2. Covariance matrix estimation [14.4.6] (BHHH)
      • 3. GARCH models [20.10]
      • 4. Likelihood ratio, Lagrange multiplier tests [14.6,]
      • 5. Two step estimation [14.7] (Heckman, Murphy/Topel, Newey)
      • 6. Binary Choice, Loglinear Models [17.2, 17.3]
      • 7. GARCH Model [20.10]
      • 8. Sample selection [19.5]
    • B. Generalized method of moments (GMM) estimation [13.1 – 13.5] (Hansen, Newey/West)
      • Dynamic panel data models [13.6.5] (Hausman and Taylor, Arellano and Bover)
    • C. Estimation by simulation; models with unobserved heterogeneity [Chapter 15]   (Revelt and Train)
    • D. Bayesian Estimation [Chapter 16]
  • X. Non- and Semiparametrics
    • A. Kernel density estimation [12.4.1, 12.3.4]
    • B. Nonparametric regression [12.3, 12.4]
    • C. LAD and Quantile regression [12.3]
  • XI. Time Series Modeling [20.1, 20.2, 20.5, Chapter 21] (not likely we will have time for much of this)

 

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Reading List (annotated)

Arellano, M. and O. Bover  "Another Look at the Instrumental Variable Estimation of Error-Components Models," Journal of Econometrics, 68, 1995, pp. 29-51.

Ashenfelter, O., and Krueger, A., "Estimates of the Economic Returns to Schooling from a New Sample of Twins," American Economic Review, 84, 5, 1994, pp. 1157-1173. An intriguing study of measurement error and instrumental variables estimation. Intriguing study of data on twins gathered at a convention of twins in Twinsburg, Ohio.

Breusch, T., and Pagan, A., "The LM Test and Its Applications to Model Specification in Econometrics," Review of Economic Studies, 47, 1980, pp. 239-254. Began a methodological shift in econometrics toward a reinterpretation of existing tests and development of many new ones. Short lived paradigm shift, as the tests are strongly parametric, and conflict with the current trend toward less stringently parameterized models. An excellent book with similar material, developed at length is Godfrey, L., Misspecification Tests in Econometrics, Cambridge University Press, 1988. (Important contribution to methodology.)

Breusch, T., and Pagan, A., "A Simple Test for Heteroscedasticity and Random Coefficients Variation," Econometrica, 47, 1979, pp. 1287-1294. Application of the LM methodology developed in fuller detail in the 1980 paper (they were done simultaneously) to a common problem. Has become essentially the standard test for heteroscedasticity - soon to be supplanted by the conditional moment test. (See Pagan and Vella.)

Christensen, L., and Greene, W., "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, 84, 1976, pp. 655-676. Application of specification testing in a model, showing how theoretical propositions produce testable restrictions on the empirical model. Fairly straightforward application of the seemingly unrelated regressions model, maximum likelihood estimation, and use of likelihood ratio tests.

Frisch, R., and Waugh, F., "Partial Time Regressions as Compared with Individual Trends," Econometrica, 1, 1933, pp. 387-401. Purely empirical discovery of one of the fundamental pillars of econometrics, the Frisch-Waugh theorem for partitioning a linear projection. Another high water mark in the literature.

Greene, W., and Seaks, T., "The Restricted Least Squares Estimator: A Pedagogical Note," Review of Economics and Statistics, 73, 1991, pp. 563-567. Some interesting matrix algebra for the linear regression model and restricted least squares. Surprise discovery of an apparently theretofore overlooked (by econometricians, though not statisticians) aspect of linear regression.

Harvey, A., "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, 44, 1976, pp. 461-465. Very general model for heteroscedasticity. A good companion to Breusch and Pagan. Also illustrates an interesting application of Newton's method and the method of scoring for maximum likelihood estimation.

Hansen, L., "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, 50, 1982, pp. 1029-1054. Soon to be classic, if not already, study of the method of moments. Pioneering paper that has produced a major shift in the direction of econometric methodology. One of the most influential methodological pieces since 1980, in close competition with Dickey-Fuller on unit roots. Shows how estimators of model parameters can be developed without need to make strong distributional assumptions. Innovation in the literature - extremely influential.

Hausman, J., "Specification Tests in Econometrics," Econometrica, 46, 1978, pp. 1251-1271. Develops the "Hausman Test," a now widely used specification test that gets around the need for nested models imposed by the conventional likelihood, Neyman-Pearson based tests.

Hausman, J., and Taylor, W., "Panel Data and Unobservable Individual Effects," Econometrica, 49, 1981, pp. 1377-1398. Extends the familiar fixed and random effects models to some more involved cases. For example, how to deal with fixed effects in models in which group effects are fixed over time.

Heckman, J., "Sample Selection Bias as a Specification Error," Econometrica, 47, 1979, pp. 153-161. First in a literature on two step estimation of models. A clever application of two step estimation in a model of nonrandom sampling. (His work began on it as a Ph.D. student in 1970-1972) Began a debate on sample selection models that continues. Interesting application for the form that methodological progress takes place.

Murphy, K., and Topel, R., "Estimation and Inference in Two Step Econometric Models," Journal of Business and Economic Statistics, 3, 1985, pp. 370-379. Lays out the computations needed for handling two step maximum likelihood or least squares estimation. A now standard result. Applications becoming increasingly common. Worth reading.

Newey, W., and West, K., "A Simple, Positive Semi-definite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, 55, 1987, pp. 703-708. The canonical presentation of one of the most important tools in the applied econometricians toolkit. Generalizes White's estimator, and makes feasible, many GMM estimators in time series settings.

Revelt, D. and K. Train, "Mixed Logit with Repeated Choices: Households' Choices of Appliance Efficiency Level," Review of Economics and Statistics, 1998, 80, , pp. 1-11.

Waugh, F., "The Place of Least Squares in Econometrics," Econometrica, 29, 1961, pp. 386-396. Historical piece. Argues that OLS, which at that time, was becoming "old fashioned" and ordinary was underappreciated in economics and produced important results. Sounds like he was about 40 years before his time.

White, H., "A Heteroscedasticity-Consistent Covariance Matrix Estimator and Direct Test for Heteroscedasticity," Econometrica, 48, 1980, 817-838. The White estimator for unknown heteroscedasticity. Remarkably simple yet powerful estimator. A major step toward robust estimation in econometrics. Very important paper.  (Unfortunately) not simple reading.
 

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