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## Syllabus

### Updated A.Y. 2022-2023

OVERVIEW AND PREREQUISITES

This course provides an introduction to multiple regression techniques focusing on economic applications. The course consists of eighteen theoretical lectures (1 hour and 30 minutes each) and six practice classes with both theoretical and applied exercises. It is intended for students who have taken and passed Mathematics (8011190) and Statistics (8010848).

LEARNING OUTCOMES

At the end of the course, students should be able to:

1. specify a linear regression model, even using flexible functional forms, and in the presence of qualitative information;
2. master the least squares (OLS) and the instrumental variables (IV) estimation methods;
3. understand and apply conventional statistical and diagnostic tests;
4. exploit the Stata statistical software to estimate the parameters of the specified regression model using cross-sectional data and to run hypothesis and diagnostic tests;
5. understand and interpret the empirical results.

ASSESSMENT

The final grade will be given by a weighted average of the grades in two take-home problem sets (10% + 10%), a précis summarizing an assigned academic reading (10%), and a final written closed book exam (70%).

CLASS SCHEDULE

Lectures on Monday, Tuesday, and Wednesday (11:00 am - 1:00 pm). Practices on Thursday (11:00 am - 1:00 pm).

OUTLINE

- Intro
Econometrics, data structures, and the concept of causality
Conditional expectations, variances, and the linear regression model
Ordinary Least-squares and the simple linear regression model

- Multiple Regression Analysis
Estimation and interpretation
Least-squares statistical (finite samples) properties
Qualitative information
The Gaussian linear model and exact statistical inference
Least-squares asymptotics and approximate inference
Testing for heteroskedasticity and Generalized Least Squares

- Endogeneity and the Instrumental Variables (IV) approach:
Main assumptions
Simple IV and the Wald estimator
Two Stage Least Squares
Testing for endogeneity, instruments' relevance, and overidentifying restrictions
Control Function approaches to endogeneity

- Potential outcomes framework:
Homogeneous vs Heterogenous treatment effects model
Local Average Treatment Effects (LATE)

TEXTBOOKS AND MATERIAL

The main reference is Wooldridge J.M., (2016), Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning.

For some topics, Wooldridge J.M., (2016) will be complemented by selected articles which will be made available on the material section of this website and by some chapters from:

1. Cunningham S., (2021) Causal Inference: The Mixtape. Yale University Press;
2. Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).

Lecture slides, and Stata codes will be posted on the material section. Suggestions for further reading will be provided in class.

For further study in econometrics, I suggest Hansen (2021), and Peracchi (2001). Angrist and Pischke (2009) for an "applied" perspective.

Hansen B.E., (2020), Econometrics. Mimeo

Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).

Angrist J.D., and Pischke J.-S., (2009), Mostly Harmless Econometrics: An Empiricists’ Companion, Princeton University Press, Princeton.