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. Asymptotics under minimal assumptions. Numerical optimization methods: Newton-Raphson and Gauss-Newton. One step estimators.
9. Generalized method of moments. Identification via moment restrictions. GMM estimates. Asymptotic inferences. Tests of overidentifying restrictions.
9. Maximum likelihood. Consistency and asymptotic normality. Asymptotic inference. Examples: binary regression, TOBIT models and count data models.
10. Quantile linear regression. Consistency and asymptotic normality. Asymptotic inference. Causality analysis using quantile regression.
11. Inference on non-parametric models. Kernel estimates of density and regression functions. Local polynomial regression. Discontinuous regression. Asymptotic inference.
12. Semi-parametric models. Varying coefficient models, index models, adaptive estimation.
13. Specification testing. Goodness-of-fit tests for distribution functions. Model checks of regression functions and conditional model restrictions.