Master of Science in Economics

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

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.

Updated A.Y. 2021-2022

OVERVIEW AND PREREQUISITIES

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).

OUTLINE

TEXTBOOKS AND MATERIAL

The main references are Wooldridge (2016) and Cunningham (2021). For further study in econometrics I sugest: Hansen (2021), Peracchi (2001) and Train (2009), the latter for limiteded dependent variable models. Angrist and Pischke (2009) for applied issues. Lecture notes, slides and Stata codes will be posted in the material section. Suggestions for further reading and a reading list will be provided in class.

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

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

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

Train, K. E., (2009), Discrete Choice Methods with Simulation, 2nd ed. New York: Cambridge University Press.

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

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

Updated A.Y. 2020-2021

OVERVIEW AND PREREQUISITIES

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. For each topic, course time will be split evenly between theory and practice.

The course consists of eighteen theoretical lectures (1 hour and 45 minutes each) and six practice classes with both theoretical and applied exercises. Students should have completed Mathematics (8011190) and Statistics (8010848). In particular, they need to be able to work with linear algebra and basic asymptotic theory.

OUTLINE

Regression
- Conditional Expectation and Projection
- Algebra of Least Squares
- LS and Gaussian regressions
- Hypothesis testing
- Resampling methods

Instrumental Variables
- Endogenous regressors and instruments
- IV and Two Stages Least Squares estimators 
- Control functions
- Endogeneity and over-identification tests 
- Linear Generalized Method of Moments estimation
- Local Average Treatment Effects

Limited dependent variables  
- Binary choice models
- Multiple choice models
- Truncation and sample selection models (optional)

TEXTBOOK AND MATERIAL

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

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

Hansen B.E., (2020), Econometrics, download the book here.

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

The main references are Wooldridge (2016) and Wooldridge (2010). They can be complemented by some chapters from Hansen (2020) and Peracchi (2001). Lecture slides and R/Stata codes will be posted on the course’s website. Suggestions for further reading will be provided in class.

Updated A.Y. 2019-2020

OVERVIEW AND PREREQUISITIES

In line with the educational objectives of the programme, the aim of this course is to introduce students to the main econometric tools essential for conducting quantitative analyses in the economic field. To this aim, several empirical applications, mostly implemented in Stata, will be discussed. The course consists of eighteen theoretical lectures (1 hour and 45 minutes each) and six practice classes, three of which will be given in the lab. Students should have completed Mathematics (8011190) and Statistics (8010848). In particular, they will need to be able to work with linear algebra and basic asymptotic theory (Law of large numbers and central limit theory for independent and identically distributed observations).

OUTLINE

The structure of economic data

Linear regression model with cross-sectional data:

- Ordinary Least Squares (OLS) estimation
- Mechanics, model specification and interpretation
- OLS Sampling Properties
- Violation of the ideal conditions for OLS
- Hypothesis testing and model selection
- Instrumental Variables (IV) estimation
- Generalized Method of Moments (GMM) estimation
- Control function approach to endogeneity

Linear (static) unobserved-effects regression model with panel data:

- Pooled OLS
- Fixed-effects and first-difference estimation
- Random-effects estimation
- Comparison of estimators

TEXTBOOK AND MATERIAL

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

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

The main references are Wooldridge (2016) and Wooldridge (2010). They will be complemented by some chapters from Peracchi (2001). Lecture slides and Stata files will be posted on the course web site. 

READING LIST

Angrist J., and Krueger A., (2001), "Instrumental variables and the search for identification: From supply and demand to natural experiment", Journal of Economic Perspectives, 15: 69–85.

Wooldridge J.M., (2001), "Applications of generalized method of moments estimation", Journal of Economic Perspectives, 15: 87–100.

Wooldridge J.M., (2015), "Control Function Methods in Applied Econometrics", Journal of Human Resources, 50(2): 420–445.

USEFUL REFERENCES

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

Cameron A.C., and Trivedi P.K., (2005), Microeconometrics. Methods and Applications, Cambridge University Press, New York.

Cook R.D., and Weisberg S., (1982), Residuals and Influence in Regression, Chapman and Hall, New York.

Hall A.H., (2005), Generalized Method of Moments, Oxford University Press, Oxford.

Hansen, B.E., (2019), Econometrics, mimeo (downloadable at https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf).

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

Stock J.H., and Watson M.W., (2015), Introduction to Econometrics (updated 3rd ed.), Pearson, Hoboken (NJ).

White H., (2001), Asymptotic Theory for Econometricians (2nd ed.), Academic Press, San Diego (CA).

Petersen K.B., and Pedersen M.S., (2012), The Matrix Cookbook, mimeo (downloadable at https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf).

Suggestions for further reading will be provided in class.

KNOWLEDGE AND UNDERSTANDING

Based on a systematic and conscious understanding of the discussed techniques, students should be able to elaborate original ideas to answer economic questions of interest.

APPLYING KNOWLEDGE AND UNDERSTANDING

Based on the analytical tools and the knowledge acquired through theoretical and practice sessions, students should be able to apply appropriately the discussed techniques using statistical software such as Stata and/or R. In particular, they will need to be able to correctly specify a linear regression model, choose the most appropriate estimation approach and correctly interpret the empirical results.

MAKING JUDGEMENTS 

Students should be able to autonomously integrate the acquired knowledge in order to manage complex empirical analyses, by appropriately defining the objectives, by formulating hypotheses, by autonomously searching for the information and data necessary for carrying out the analysis, by motivating the choice of the most appropriate methodology and by extracting useful strategic indications and/or policy implications based on the empirical results.

COMMUNICATION SKILLS 

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

Updated A.Y. 2018-2019

Overview

The main aim of this course is to provide students with the necessary analytical tools to apply microeconometric methods to the analysis of economic data. The course is organized in three modules. The first module (Single-equation linear models) will familiarize students with the workhorse in empirical economics, namely the estimation of the linear regression model by Ordinary Least Squares (OLS) and Instrumental Variables (IV) estimators. The second module (Systems of linear equations) will introduce students to the estimation of linear system of equations, emphasizing the modern approach to system instrumental variables estimation based on the Generalized Method of Moments (GMM). Finally, the third module (Linear Unobserved-Effects Panel Data Models) will cover the econometric analysis of static linear panel data models. At the end of the course students should be able to specify the appropriate econometric model for investigating the problem under study and draw proper conclusions based on the results.

This course is taught at a level assuming comfort with the course content in Mathematics (8011190) and Statistics (8010848).

Outline

Intro: The Structure of Economic Data

Single-Equation Linear Models:

• Ordinary Least Squares (OLS) Estimation

1. The OLS Method
2. Mechanics and Interpretation of OLS
3. Sampling Properties
4. Hypothesis Testing
5. Issues: Omitted Variables and Measurement error

• Instrumental Variables (IV) Estimation

1. ​The IV Method
2. Multiple Instruments and Over-identified Models
3. Asymptotics
4. Pitfalls of IV: Weak Instruments
5. Testing: Endogeneity and Over-identifying Restrictions
6. Control Function Approach to Endogeneity

• Estimation and Inference by Generalized Method of Moments

Systems of Linear Equations (optional):

• Estimation and Inference by OLS

• Estimation and Inference by Generalized Least Squares

• The System IV estimator

Linear Unobserved-Effects Panel Data Models:

• Assumptions: Covariates vs Unobserved-Effects and Idiosyncratic Errors

• Estimation and Inference:

1. Pooled OLS
2. Fixed-Effects Estimation
3. First-Differencing Estimation
4. Random-Effects Estimation
5. Comparison of estimators

References and material

• Wooldridge J.M. (2010), Econometric Analysis of Cross-Section and Panel Data,  2nd ed., MIT Press, Cambridge (MA).
• Wooldridge J.M. (2016), Introductory Econometrics: A Modern Approach, 6th ed., Cengage Learning.
• Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).

The main references are Wooldridge (2016) and Wooldridge (2010). They will be complemented by some chapters from Peracchi (2001). Lecture slides will be posted on the course web site. Suggestions for further reading will be provided in class.

Updated A.Y. 2017-2018

Overview

The course is organized in two modules of equal length. The first module (Static Regression) will familiarize students with the workhorses of empirical work in economics, namely the linear regression model and the ordinary least squares (OLS) estimator, and with the problems that arise when the model assumptions are violated, in particular when the regressors cannot be regarded as exogenous, that is, uncorrelated with the regression errors. The second module (IV & GMM) will pay special attention to the method of instrumental variables as a way of solving the endogeneity problem and the specific issues that arise with the use of this method.

Outline

Static Regression:

• Conditional expectations and best linear predictors

• The classical linear model and the OLS estimator

• Sampling properties of OLS

• Generalized least squares (GLS) and feasible GLS

• Diagnostic procedures

• Hypothesis testing and model selection

IV & GMM:

• Estimation of causal effects

• The instrumental variables (IV) method

• Properties of conventional IV estimators under weak instruments

• Robust inference under weak instruments

• The generalized method of moments (GMM)

References and material

• Angrist J.D., and Pischke J.-S. (2010), Mostly Harmless Econometrics: An Empiricist’s Companion, Princeton University Press, Princeton.
• Angrist J., and Krueger A. (2001) “Instrumental variables and the search for identification: From supply and demand to natural experiment”, Journal of Economic Perspectives, 15: 69-85.
• Bowden R.J., and Turkington D.A. (1984) Instrumental Variables, Cambridge University Press, Cambridge (UK).
• Cameron A.C. and Trivedi P.K. (2005), Microeconometrics, Cambridge University Press, New York.
• Cook R.D., and Weisberg S. (1982), Residuals and Influence in Regression, Chapman and Hall, New York.
• Hansen B.E. (2017), Econometrics, mimeo.
• Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
• Stachurski J. (2016), A Primer in Econometric Theory. MIT Press, Cambridge, MA.
• Stock J.H., and Watson M.W. (2015) Introduction to Econometrics (updated 3rd ed.), Pearson, Hoboken (NJ).
• White H. (2001), Asymptotic Theory for Econometricians (2nd ed.), Academic Press, San Diego (CA).
• Wooldridge J.M. (2010), Econometric Analysis of Cross-Section and Panel Data,  2nd ed., MIT Press, Cambridge (MA).
• Wooldridge J.M. (2001) “Applications of generalized method of moments estimation”, Journal of Economic Perspectives, 15: 87-100.

The material, including lecture notes, will be posted on the course web site. Suggestions for further reading will be provided in class.