Econometrics I, Mathematics

This is a graduate course on Econometrics. The first part of the course discusses inferences on linear models under standard conditions, paying attention to identification issues in structural simultaneous equation systems and testing linear restrictions. The second part of the course discusess econometric modeling under serial dependence and unobserved heterogeneity, which includes time series modeling and causality analysis in dynamic models. The third part of the course covers asymptotic inferences in non-linear in parameters models, paying particular attention to generalized method of moments and maximum likelihood. The last part of the course discuses inference tools in quantile regression, non-parametric models, semi-parametric models, and specification testing.

1. Inference on linear reduced form models. Causality and identification. Least Squares Estimates. Asymptotic inference. Restricted estimation. Measurement error. Control variables. Hypothesis Testing. 2. Inference on structural linear equations. Two Stage Least Squares Estimates. Specification Tests: Endogeneity, Overidentifying restrictions, Functional form, Heteroskedasticity. 3. Inference on systems of reduced form equations. Inference on a multivariate linear system based on OLS; GLS and FGLS; Seemingly unrelated systems of equations; the linear panel data model. The generalized method of moments: 2SLS, 3SLS. Testing overidentifying restrictions. Optimal instruments. 4. Inference on linear structural equations systems. Identification in a linear system. Estimation after identification. Identification with cross-equation and covariance restrictions. Models nonlinear in the endogenous variables. 5. Inference in the presence of unobserved heterogeneity. Random Effects Methods. Fixed Effects Methods. First Differencing Methods. Comparison of Estimators. 6. Inference with autocorrelated data. Basic concepts: Stationarity and weak dependence. Basic models: Martingale difference, linear processes, autogregressions. Laws of large numbers and central limit theorems. Autocorrelation and Heteroskedasticity-robust inference. Testing for serial correlation. GLS and IV estimates. 7. Inference on parameters in non-linear models. Examples: Non-linear regression, maximum likelihood, quantile regression, minimum distance. M and Z estimators. Asymptotic properties under classical assumptions. Numerical optimization methods: Newton-Raphson and Gauss-Newton. GMM estimates. Examples: binary regression.

Training activities Lectures Practical classes Problem Sets Individual student work Tutorials Teaching methodology Exhibitions in class with teacher support and audiovisual media, in which the main concepts of matter are developed and the literature is provided to supplement student learning. Practical classes with resolution of exercises and problems that illustrate the theory and allow to study particular cases and small extensions. Problem sets to solve at home individually, helping to systematize the study of the subject and to revise fundamental concepts.