Obiettivi formativi
This course is a rigorous introduction to the theory of econometrics.
Prerequisiti
Basic elements of calculus, matrix algebra, probability, and statistics.
Risultati di apprendimento attesi
By the end of the course the students will be able to critically evaluate the credibility of the main empirical strategies adopted in applied work.
Contenuti Del Corso
The course consists of two parts. The first part (Weeks 1-4) will provide a thorough understanding of the workhorses of empirical research in economics, namely the linear regression model and the ordinary least squares estimator, and of the problems that arise when the assumptions of the linear model are violated. The second part (Weeks 5-6) will introduce students to the instrumental variables (IV) method and its extension, the generalized method of moments (GMM).
Under some conditions, these methods offer a solution to the endogeneity problems that arise when the covariates in a regression model cannot be regarded as uncorrelated with the regressors.
Testi Di Riferimento
Hansen B.E. (2022). Econometrics.
Princeton University Press: Princeton (NJ).
The relevant part of this book consists of Chapters 2-13.
Magnus J. R. (2021). Introduction to the Theory of Econometrics (6th printing).
VU University Press: Amsterdam.
Magnus J. R., and Telg S. (2022). Mastering Econometrics: Exercises and Solutions.
VU University Press: Amsterdam.
Metodologie Didattiche
Every week I assign a homework that students are asked to solve and then discuss in class. Spending a significant amount of time each week on the assigned homework is essential to learning the material covered. Homework must be returned on the dates indicated below.
There is no credit for late homework.
Modalità di verifica dell'apprendimento
Grading will depend for 40 percent on the homework, 40 percent on the final exam, and 20 percent on class participation.
Criteri per l’assegnazione dell’elaborato finale
The final exam will cover all the material presented in the course and will last 3 hours. Its date will be finalized at the beginning of the module.
Settimana 1
Regression models and the least squares method. Introduction to the course.
Basic concepts: conditional means and conditional variances, potential outcomes and causal effects, choosing a regression model, best linear predictors, relations between conditional means and best linear predictors. The classical linear model: elements, interpretations, and properties. The ordinary least squares (OLS) problem and its solution, fitted values and residuals, goodness of fit, constrained OLS.
Algebraic properties of OLS: partitioned regression and the Frisch-Waugh-Lovell theorem, adding/dropping variables, adding/dropping observations.
Settimana 2
Exact sampling properties of least squares.
Sampling properties of OLS under ideal conditions. The Gauss-Markov theorem.
Violations of the ideal conditions. Generalized least squares (GLS), Aitken theorem, weighted least squares, feasible GLS. The classical Gaussian linear model: maximum-likelihood estimation, Cramer-Rao bounds, classical confidence sets, Bayesian analysis.
Settimana 3
Asymptotic properties of least squares.
Asymptotic properties of OLS: consistency and asymptotic normality. Applying the asymptotic results: estimates of statistical precision, asymptotically-valid confidence intervals. Resampling methods: the jackknife and the bootstrap. Asymptotic properties of GLS and feasible GLS.
Inconsistency of OLS.
Settimana 4
Hypothesis testing and model selection.
The classical t- and F-tests: exact and asymptotic properties. Likelihood-based tests. Specification tests. Covariate selection: R^2 and adjusted R^2, the C_p criterion, cross-validation, information criteria. Pre-testing vs. honesty.
Settimana 5
The instrumental variables method and GMM. The instrumental variables (IV) method: just- and over-identified models, the Wald estimator, the general class of IV estimators. The generalized method of moments (GMM).Sampling properties of IV estimators: consistency, asymptotic normality, and asymptotic efficiency. Hypothesis testing: Wald tests, tests of overidentifying restrictions, difference tests.
Settimana 6
2SLS and estimation of treatment effects. Two stage least squares (2SLS): GLS and control function interpretations, asymptotic properties. The problems of too many instruments and of weak instruments. Estimating treatment effects:
OLS, local average treatment effects (LATE). Examples of applications from labor and development economics.