Econometrics (2011/2012)

Learning outcomes

The course provides an overview of the main econometric tools, with particular emphasis on economic applications, developed interactively in class using the professional software Stata™.
The program is divided in four parts. The first part shows the standard econometric method (ordinary least squares regression, OLS), its properties, and statistical tests. The second part discusses the main limitations of OLS: wrong specification of the functional form, heteroskedasticity and autocorrelation. The third part introduces the problem of endogeneity and the instrumental variables (IV) estimators. The final part presents models suited for limited dependent variables (LDV): probit models, poisson models.

1) Introduction
Econometrics; cross-section data and time series

2) Ordinary Least Squares (OLS) estimator
2.1) Introduction
Univariate and multivariate regression; marginal effects and elasticity
2.2) Goodness of fit
R2, adjusted R2, AIC and BIC criteria; forecast; outliers
2.3) Properties
Gauss-Markov assumptions; unbiasedness; efficiency; consistency; asymptotic normality
2.4) Hypothesis testing
t-test on one restriction; F test on several restrictions

3) OLS failures
3.1) Specification and functional form
Collinearity; superfluous and omitted variables; RESET test of specification; Chow test of structural stability
3.2) Heteroskedasticity of the errors
White test and Breusch-Pagan test; possible remedies: specification change, White robust standard errors, weighted least squares (WLS)
3.3) Autocorrelation of the errors
Durbin-Watson test and Breusch-Godfrey test; possible remedies: specification change, Newey-West robust standard errors, generalized least squares (GLS)

4) Instrumental variables (IV) estimator
4.1) Endogeneity
Autocorrelation and lagged dependent variable; measurement error; omitted variables; simultaneity
4.2) Simple instrumental variables (SIV) and generalized instrumental variables (GIV)
Assumptions; properties of the IV estimator; two-stage derivation (2SLS)
4.3) Instrument properties
Relevance test; weak instruments; Sargan validity test; Hausman exogeneity test

5) Models for limited dependent variable (LDV)
5.1) Models for binary dependent variable
Linear probability model (LPM), probit and logit models; marginal effects; goodness of fit; maximum likelihood estimate; hypothesis testing; ordered probit
5.2) Models for count data
Poisson regression; over-dispersion tests; negative binomial regression; marginal effects

The exam is written, and it includes both theoretical, numerical and applied exercises on the topics covered in class.
During the course it is possible to submit up to two voluntary homeworks on specific parts of the program. These homeworks will contribute to the final grade.