Graduate Cross Section Econometrics

General Info

This course gives a rigorous introduction to linear and nonlinear econometric methods, in four parts. The first part builds the asymptotic toolkit that the rest of the course relies on, covering the main convergence theorems, the asymptotic linear representation of estimators, the delta method, and how these results extend to dependent data. The second part studies linear regression through the geometry of ordinary least squares, asking what the estimator actually converges to and drawing the distinction between exogeneity, uncorrelatedness, and the linear projection. The third part turns to causal questions and treatment effects, moving from selection on observables and inverse probability weighting to instrumental variables and the local average treatment effect when participation is endogenous. The final part develops the theory of extremum estimation, from M-estimation and the uniform law of large numbers to the generalized method of moments, which provides a unified treatment of estimation and inference for a large class of nonlinear problems.

Discussion Section: Thursday from 5:00 to 6:30 pm, SSB 107. Office hour: Thursday from 6:30 to 7:00 pm, SSB 107.

Material

  1. Basics of asymptotic theory: convergence theorems, asymptotic linear representation and delta method. Exercises on asymptotic of ratio of two estimators and Hodge’s estimator. (Slides)
  2. Geometric properties of OLS: the prediction problem, orthogonal projection of the outcome onto the column space of the regressors, the coefficient of determination, and the Frisch–Waugh–Lovell theorem. (Slides)
  3. Where is the OLS estimator converging to? Exogeneity vs uncorrelatedness vs linear projection. Introduction to bayesian inference and exercise on ridge regression. (Slides)
  4. Practice midterm: a study of asymptotics for dependent data built around the moving-average process MA(1), covering the law of large numbers and central limit theorem under dependence, the unconditional and conditional distributions, and the vector MA(1). (Slides)
  5. Selection on observables: potential outcomes, SUTVA and random assignment, unconfoundedness, inverse-probability weighting and the regression-adjustment estimator, and what the ATE misses. (Slides)
  6. Instrumental variables: the endogeneity problem, the Wald and two-stage least squares estimators, weak and multiple instruments, and the control-function approach. (Slides)
  7. Local Average Treatment Effect: endogenous participation in a job-training setting, the LATE framework under self-selection, and identification through a threshold-crossing model. (Slides)
  8. M-estimation: the general consistency theorem, the uniform law of large numbers, and an application to a Poisson survival model. (Slides)
  9. Mock final exam: 2SLS with multiple instruments, covering method-of-moments estimation, the over-identified case, the GMM weighting matrix and criterion function, identification, and the first-order conditions. (Mock Exam)

Material from the previous edition of the course can be downloaded here.

Evaluation

Instructional Assistant Student Evaluation of Teaching available here.