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 (2012) 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 (45%)
  • Several problem sets and small projects (total 25%).

 

Course Materials:

Text: The required text for the course is Greene, W., Econometric Analysis, 7th Edition, Prentice Hall, 2012. (You may use the 6th edition if you prefer.) Other texts that might be useful are: Wooldridge, J., Econometric Analysis of Cross Section and Panel Data, 2nd Ed., MIT Press, 2010, which is more advanced than Greene; Woolridge, J., Introductory Econometrics: A Modern Approach, 5th Edition (or later), Southwestern, 2012 (or later) or Gujarati, D., Basic Econometrics, 4rd Edition, McGraw-Hill, 2004, both of which are less advanced. Note: A useful list of errata and comments submitted by readers of Greene (2012) 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 in portable format 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)
      • 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]
      • 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]
    • 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. Endogeneity, Instrumental Variables and Treatment Effects [8.1 - 8.3]
    • A. Instrumental variables estimation and measurement error [8.1 - 8.3, 8.5]
    • 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]
      • 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]
    • 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]
      • 3. GARCH models [20.10]
      • 4. Likelihood ratio, Lagrange multiplier tests [14.6,]
      • 5. Two step estimation [14.7] (Heckman, Murphy/Topel, Terza et al.)
      • 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] (Newey/West)
      • Dynamic panel data models [13.6.5]
    • C. Estimation by simulation; models with unobserved heterogeneity [Chapter 15]
    • 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)

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.

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.

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.

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.

Terza, J., A. Basu and P. Rathouz, "Two Stage Residual Inclusion Estimation: Addressing Endogeneity in Health Econometric Modeling, " Journal of Health Economics, 27, 2008, pp. 531–543.

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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