## ECONOMETRICS

## Syllabus

EN
IT

### Learning Objectives

LEARNING OUTCOMES: This course contributes to the program outcomes of the M.Sc. in Economics by providing students with the main econometric tools essential for conducting applied economic analyses.

KNOWLEDGE AND UNDERSTANDING: Based on a systematic and conscious understanding of the discussed techniques, students should be able to conduct meaningful and creative empirical work.

APPLYING KNOWLEDGE AND UNDERSTANDING: Based on the analytical tools and the knowledge acquired through theoretical and applied sessions, students will learn the basics of the Stata statistical software and how to use it for implementing empirical analyses.

MAKING JUDGEMENTS: Students should be able to autonomously integrate the acquired knowledge in order to manage complex empirical analyses, by appropriately defining the objectives, formulating hypotheses, autonomously searching for the information and data necessary for carrying out the analysis, motivating the choice of the most appropriate methodology and extracting useful strategic indications and/or policy implications based on the empirical results. Students will also become familiar with reading and critiquing empirical work from others.

COMMUNICATION SKILLS: Students should be able to present the results of their own elaborations and analyses both to an expert and non-experts audience.

LEARNING SKILLS: Student should be able to study independently, developing the learning skills needed to tackle more advanced econometrics courses or to undertake the quantitative analyses required in other courses or for the final dissertation.

KNOWLEDGE AND UNDERSTANDING: Based on a systematic and conscious understanding of the discussed techniques, students should be able to conduct meaningful and creative empirical work.

APPLYING KNOWLEDGE AND UNDERSTANDING: Based on the analytical tools and the knowledge acquired through theoretical and applied sessions, students will learn the basics of the Stata statistical software and how to use it for implementing empirical analyses.

MAKING JUDGEMENTS: Students should be able to autonomously integrate the acquired knowledge in order to manage complex empirical analyses, by appropriately defining the objectives, formulating hypotheses, autonomously searching for the information and data necessary for carrying out the analysis, motivating the choice of the most appropriate methodology and extracting useful strategic indications and/or policy implications based on the empirical results. Students will also become familiar with reading and critiquing empirical work from others.

COMMUNICATION SKILLS: Students should be able to present the results of their own elaborations and analyses both to an expert and non-experts audience.

LEARNING SKILLS: Student should be able to study independently, developing the learning skills needed to tackle more advanced econometrics courses or to undertake the quantitative analyses required in other courses or for the final dissertation.

### Prerequisites

Students should have completed Mathematics (8011190) and Statistics (8010848). A basic knowledge of the Stata statistical software is required.

### Program

- 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

Control Function approaches to endogeneity

Testing for endogeneity, instruments' relevance, and overidentifying restrictions

- Potential outcomes framework:

Homogeneous vs Heterogeneous treatment effects model

Local Average Treatment Effects (LATE)

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

Control Function approaches to endogeneity

Testing for endogeneity, instruments' relevance, and overidentifying restrictions

- Potential outcomes framework:

Homogeneous vs Heterogeneous treatment effects model

Local Average Treatment Effects (LATE)

### Books

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

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

Cunningham S., (2021) Causal Inference: The Mixtape. Yale University Press;

Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).

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

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

Cunningham S., (2021) Causal Inference: The Mixtape. Yale University Press;

Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).

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

### Bibliography

For further study in econometrics, I suggest Peracchi (2001), Hansen (2021) and references therein:

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

Hansen B.E., (2021), Econometrics. Mimeo

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

Hansen B.E., (2021), Econometrics. Mimeo

### Teaching methods

Unless otherwise stated, according to the evolution of the COVID19 emergency, lectures will be held in class.

### Exam Rules

The evaluation of the student includes three intermediate tests and a final written exam. The final grade will be given by a weighted average of the grades in three take-home problem sets (10% + 10% + 10%), and a final written closed book exam (70%). Each of the take-home problem sets and the final exam will contain two exercises; the first will be more theoretical (derive/prove a specific result/property), and the second more practical (interpret empirical results or make some calculations). With this evaluation, the student will be asked to demonstrate that she: i) can specify a linear regression model, even using flexible functional forms, and in the presence of qualitative information; ii) masters the least squares (OLS) and the instrumental variables (IV) estimation methods; iii) understands and can apply conventional statistical and diagnostic tests; iv) can interpret a Stata estimation/testing output.