Course: 2019/2020

Econometrics II

(16861)

Students are expected to have completed

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 parameter 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.

Description of contents: programme

1. Introduction. Narratives. Econometrics. Causality and identification. Data generating processes.
2. Inference on linear reduced form models. 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. Time series processes and causality. Basic concepts: Stationarity and weak dependence. Basic models: Martingale difference and linear processes. Properties. Examples: Distributed lags. Adjustment models. Adaptive expectations. Autoregressions. Trends and seasonality.
7. Asymptotic inference with autocorrelated data. Laws of large numbers and central limit theorems. Regression with time series data. Autocorrelation and Heteroskedasticity-robust inference. Testing for serial correlation. Inference based on GLS and FGLS estimates. IV solutions for autocorrelated errors.
8. 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.
10. Maximum likelihood. Consistency and asymptotic normality. Asymptotic inferences. Examples: binary regression, TOBIT models and count data models.
11. Quantile linear regression. Consistency and asymptotic normality. Asymptotic inferences. Causality analysis using quantile regression.
12. Inference on non-parametric models. Kernel estimates of density and regression functions. Local polinomial regression. Discontinuous regression. Asymptotic inferences.
13. Semi-parametric models. Varying coefficient models, index models, adaptive estimation.
14. Specification testing. Goodness-of-fit tests for distribution functions. Model checks of regression functions and conditional model restrictions.

Learning activities and methodology

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.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Basic Bibliography

- Davidson. Econometric Theory. Blackwell. 2000
- Davidson, R. and Mackinnon, J.G.. Estimation and Inference in Econometrics.. Oxford UP. 1993
- Gorieroux, C. and Monfort, A.. Time Series an Dynamic Models . Cambridge UP. 1997
- Greene, W.H.. Econometric Analysis. Macmillan. 1997
- Hayashi, F.. Econometrics. Princeton UP. 2000
- Stock, J.H. and M. Watson. Introduction to Econometrics. Prentice Hall. 2010
- Stock, J.H. and M. Watson. Introduction to Econometrics. Prentice Hall. 2010
- Stock, J.H. and M. Watson. Introduction to Econometrics. Prentice Hall. 2010
- Wooldridge, J.M.. Introduction to Econometrics. A Modern Approach. South Western. 2000
- Wooldridge, J.M.. Econometric Analysis of Cross Section and Panel Data. MIT Press. 2002
- van der Vaart. Asymptotic Statistics. Cambridge University Press. 1998