Econometrics (2019/2020)

Learning outcomes

The course provides an overview of the main econometric tools, with particular emphasis on economic applications, developed interactively in the computer laboratory using the professional software Stata™. The program covers standard econometric models (OLS regression and its diagnostics) as well as more advanced models for the analysis of cross-sectional, time series and panel data (IV, probit, tobit, random and fixed effects). Particular attention will be given to the intuition behind each topic, in addition to more formal issues. Towards the end of the course a voluntary assignment will be proposed, with the aim of translating research questions into empirical analyses, applying on real data the tools learnt in class, and stimulating discussion among students. At the end of the course, students should be able to: i) read and critically interpret empirical works developed by other researchers, ii) manage small and large datasets in order to extract useful information, and iii) design and implement on their own empirical analyses based on real data.

1) Introduction
1.1) What is Econometrics?
Definition; cross-section, time series and panel data.
1.2) Stata tutorial
Data management; basic statistics; graphics.

2) Ordinary Least Squares (OLS) Estimator
2.1) Introduction
Univariate and multivariate regression; marginal effects and elasticity; R-squared and adjusted R-squared; outliers.
2.2) Properties
Gauss-Markov assumptions; unbiasedness; efficiency; consistency; asymptotic normality.
2.3) Testing
t-test on one restriction; F test on several restrictions.

3) OLS Diagnostics
3.1) Specification
Collinearity; superfluous and omitted variables; RESET test of specification; Chow test of structural stability.
3.2) Heteroskedasticity
White test and Breusch-Pagan test; White robust standard errors.

4) Instrumental Variable (IV) Estimator
4.1) Estimator
Assumptions; Simple instrumental variable (SIV) and generalized instrumental variable (GIV); properties; two-stage derivation (2SLS).
4.2) Instrument selection
Relevance test; weak instruments; Sargan validity test; Hausman exogeneity test.

5) Limited Dependent Variable (LDV)
5.1) Binary dependent variable
Linear probability model (LPM); probit and logit models; marginal effects; maximum likelihood estimate; goodness of fit; hypothesis testing.
5.2) Truncated and censored data
Truncated regression; tobit-I model; tobit-II and heckman model; marginal effects; goodness of fit.

6) Different Types of Data
6.1) Time series
AR, MA and ARMA processes; Durbin-Watson test and Breusch-Godfrey test; Newey-West robust standard errors; unit root; cointegration.
6.2) Panel data
Pooled effects, fixed effects and random effects; goodness of fit; comparison tests.

Lecture method: frontal teaching

The exam is written; no oral integration is possible.
The final grade is based on one mandatory final exam and one voluntary homework. The final exam includes theoretical, numerical and applied exercises on the topics covered in class; the homework (assigned during the semester) includes applied exercises only. The applied exercise requires the use of the software Stata. During the final exam the use of handheld calculators is allowed, but not the one of textbooks or teaching notes.
The homework adds 1 bonus point to the final grade and accounts for 10% of the final grade. The homework grade and bonus expires after the winter session of exams.

During the summer session the exam is held remotely and takes the form of an oral examination of 20-30 minutes. During the examination, students will be asked to answer exam-style exercises. Nothing about Stata will be asked.