Instructional goals
This course is a rigorous introduction to the theory of econometrics. It consists of two parts. The first part (Lectures 1--9) is meant to 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 (Lectures 10--13) is meant to introduce students to the instrumental variables (IV) method and its extension, the generalized method of moments (GMM). Under a number of conditions, these methods offer a solution to the endogeneity problems that arise when the covariates in a regression model cannot be regarded as exogenous, that is, as uncorrelated with the regressors.
Prerequisites
Basic elements of calculus, matrix algebra, probability and statistics.
Reference Books
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.
Teaching Methods
In person.
Assessment Method
The final grade will be based for 40 percent on the homework, 40 percent on the final exam, and 20 percent on class participation.
Week 1 Contenuto sessioni on line e on campus
Regression models and the least squares method.
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.
Week 2 Contenuto sessioni on line e on campus
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,
and feasible GLS.
The classical Gaussian linear model: maximum-likelihood estimation, Cramer-Rao bounds, classical confidence sets.
Week 3 Contenuto sessioni on line e on campus
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.
Week 4 Contenuto sessioni on line e on campus
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.
Pre-testing.
Post-model-selection and model-averaging estimators.
Week 5 Contenuto sessioni on line e on campus
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 mome (GMM).
Sampling properties of IV estimators: consistency, asymptotic normality, and asymptotic efficiency.
Hypothesis testing: Wald tests, tests of overidentifying restrictions, difference tests.
Week 6 Contenuto sessioni on line e on campus
2SLS and estimation of treatment effects.
Two stage least squares (2SLS): interpretations, asymptotic properties.
The problems of too many instruments and of weak instruments.
Estimating treatment effects:
OLS, local average treatment effects (LATE).