The purpose of this course is to study linear regressions and to introduce the notion of causality in the social sciences. It shows how and under which conditions causal parameters can be identified and estimated from random samples. The separate issue of prediction will also be addressed. Particular emphasis is placed on the method of least squares, with ordinary least squares and two-stage least squares estimators.
Key Learning Outcomes: Upon completion of the course, the student will be able to:
- Know the basic properties of OLS.
- Make predictions from OLS; select a model that provides a "good" prediction.
- Know the asymptotic properties of the OLS estimator, construct hypothesis tests and confidence intervals from this estimator;
- Understand under which conditions the OLS estimator identifies a causal effect.
- Recognize a situation of endogeneity and use, via the two-stage least squares estimator, an instrumental variable chosen appropriately. Correctly interpret the corresponding causal effect in the case of instrumental and binary "treatment" (LATE).
- Use the difference-in-differences method and the first differences estimator with panel data.
- Conduct a complete econometric analysis with real data in STATA (specification, choice of estimation method, tests, etc.) and interpret the results.
Continuous assessment (including the mid-term exam) (1/3), final exam (2/3).
1. The fundamentals of linear regressions: definition of OLS, finite distance properties, quality of regressions, convergence of OLS, interpretation of theoretical regressions.
2. Precision in linear regressions: asymptotic properties of OLS, precision of OLS and predictions, choice of regressors, tests and confidence intervals.
3. Relationship between linear regressions and causality: Rubin's causal model, selection bias, causal models and linear regressions.
4. Instrumental variables: motivation in randomized experiments, generalization to linear models, two-stage least squares estimator, inference.
5. Repeated cross-section and panel data: differences of differences, first differences estimator in panel data.
Angrist, J. D., et Pischke, J. S. (2008). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton university press.
Wooldridge, J. M. Introductory Econometrics. Thomson South-Western (2003).
Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT press.