ECONOMETRICS
Syllabus
Obiettivi Formativi
Conoscenza e capacità di comprensione: Al termine del corso, gli studenti saranno in grado di comprendere gli strumenti econometrici di base. Nello specifico, studieremo l'analisi di regressione cross-sezionale in presenza di variabili dipendenti continue o limitate. L'accento sarà posto sull'inferenza statistica robusta e su come affrontare i problemi di endogeneità utilizzando lo stimatore delle variabili strumentali.
Capacità di applicare conoscenza e comprensione: Al completamento con successo del corso, gli studenti saranno in grado di padroneggiare i formati comuni dei dati economici e di condurre un'analisi di regressione utilizzando il software statistico Stata.
Autonomia di giudizio: Al termine del corso, gli studenti saranno in grado di orientarsi tra diverse tecniche e scegliere la migliore per il caso in questione.
Abilità comunicative: Lo studente dovrà saper presentare, anche con l'ausilio degli opportuni strumenti informatici, i risultati delle proprie elaborazioni e analisi.
Learning Objectives
Knowledge and understanding: On successful completion of the course, students will be able to understand standard econometric tools. Specifically, we will study cross-sectional regression analysis in presence of continuous or limited dependent variables. Emphasis will be placed on robust inference and how to address endogeneity issues using instrumental variables estimation.
Applying knowledge and understanding: On successful completion of the course, students will be able to master the common formats of economic data and implement a regression analysis using the Stata statistical software.
Making judgements: On successful completion of the course, students will be able to orient themselves between different techniques and choose the best for the case at hand.
Communication skills: Students will be able to effectively communicate the results of their own elaborations and analyses.
Prerequisiti
Prerequisites
Programma
Modellazione econometrica e struttura dei dati economici
Minimi quadrati ordinari e modello di regressione lineare semplice
- Analisi di regressione multipla:
Stima, interpretazione e aspetti algebrici dei minimi quadrati
Proprietà statistiche dei minimi quadrati (campioni finiti).
Informazioni qualitative
Il modello lineare gaussiano e l'inferenza statistica esatta
Minimi quadrati asintotici e inferenza approssimata
Inferenza robusta
Test di eteroschedasticità e minimi quadrati generalizzati
- Endogeneità e approccio delle variabili strumentali (IV):
Ipotesi principali
Stimatore IV e lo stimatore di Wald
Minimi quadrati a due stadi
Test di endogeneità, rilevanza degli strumenti e sovraidentificazione delle restrizioni
- Modelli per variabili dipendenti limitate:
Variabili dipendenti binarie
Variabili dipendenti multinomiali
Variabili dipendenti di conteggio
Troncamento e selezione del campione
Program
Econometric modeling and the structure of economic data
Ordinary Least-squares and the simple linear regression model
- Multiple Regression Analysis:
Algebraic aspects of least squares
Least squares statistical (finite samples) properties
Qualitative information
The Gaussian linear model and exact statistical inference
Least-squares asymptotic and approximate inference
Robust 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
- Models for limited dependent variables:
Binary outcomes
Multinomial outcomes
Count outcomes
Truncation and sample selection
Testi Adottati
Per alcuni argomenti, Wooldridge (2016) sarà integrato da articoli selezionati che saranno resi disponibili nella sezione materiali del sito web del corso e da alcuni capitoli tratti da:
Greene W.H., Econometric Analysis, 8th ed., Pearson.
Books
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:
Greene W.H., Econometric Analysis, 8th ed., Pearson.
Bibliografia
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).
Bibliography
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Wooldridge J.M., (2010), Econometric Analysis of Cross-Section and Panel Data, 2nd ed., MIT Press, Cambridge (MA).
Modalità di svolgimento
Teaching methods
Regolamento Esame
Gli studenti devono prenotarsi all'esame finale su https://delphi.uniroma2.it. Gli studenti che falliscono o rinunciano all'esame possono sostenerlo nuovamente nello stesso appello.
Exam Rules
Obiettivi Formativi
CONOSCENZA E CAPACITÀ DI COMPRENSIONE: Sulla base di una comprensione sistematica e consapevole delle tecniche econometriche trattate, lo studente dovrà saper elaborare idee originali per rispondere a domande di interesse nell'ambito della letteratura economica.
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE: Sulla base degli strumenti analitici e delle conoscenze acquisiti attraverso lezioni teoriche ed esercitazioni guidate, lo studente apprenderà le nozioni necessarie per condurre analisi empiriche attraverso il software statistico Stata.
AUTONOMIA DI GIUDIZIO: Lo studente dovrà avere la capacità di integrare autonomamente le conoscenze acquisite per gestire analisi empiriche anche complesse, definendone gli obiettivi, formulando ipotesi, ricercando autonomamente le informazioni ed i dati necessari per lo svolgimento dell'analisi, motivando la scelta della metodologia più appropriata e interpretando i risultati ottenuti al fine di ricavarne indicazioni e implicazioni utili per il problema analizzato. Inoltre, lo studente dovrà saper leggere e commentare criticamente articoli in campo economico/statistico.
ABILITÀ COMUNICATIVE: Lo studente dovrà saper presentare, anche con l'ausilio degli opportuni strumenti informatici, i risultati delle proprie elaborazioni e analisi sia ad un pubblico di interlocutori esperti che non esperti.
CAPACITÀ DI APPRENDIMENTO: Lo studente dovrà saper studiare autonomamente, sviluppando le capacità di apprendimento necessarie per affrontare corsi di econometria più avanzati o per intraprendere le analisi quantitative richieste in altri corsi o per la tesi di laurea.
Learning Objectives
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.
Prerequisiti
Prerequisites
Programma
Econometria, dati e concetto di causalita'
Aspettative condizionata, varianza e modello di regressione lineare
I minimi quadrati ordinari e il modello di regressione lineare semplice
Analisi di regressione multipla:
Stima e interpretazione
Proprietà statistiche dei minimi quadrati (campioni finiti).
Informazioni qualitative
Il modello lineare gaussiano e l'inferenza statistica esatta
Proprieta' asintotiche dei minimi quadrati e inferenza approssimata
Test di eteroschedasticita' e minimi quadrati generalizzati
Endogeneita' e approccio delle variabili strumentali:
Assunzioni principali
Stimatore IV e lo stimatore di Wald
Minimi quadrati a due stadi
Outcomes potenziali:
Modelli ad effetti di trattamento omogenei ed eterogenei
Effetti medi locali di trattamento (LATE)
Endogeneità e approccio control function
Verifica di ipotesi:
Rilevanza degli strumenti
Test di endogeneità
Test delle restrizioni di sovraidentificazione
Program
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)
Testi Adottati
Per alcuni argomenti, Wooldridge (2016) sarà integrato da articoli selezionati che saranno resi disponibili nella sezione materiali del sito web del corso e da alcuni capitoli tratti da:
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.
Books
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.
Bibliografia
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Hansen B.E., (2021), Econometrics. Mimeo
Bibliography
Peracchi F. (2001), Econometrics, Wiley, Chichester (UK).
Hansen B.E., (2021), Econometrics. Mimeo
Modalità di svolgimento
Teaching methods
Regolamento Esame
Exam Rules
Updated A.Y. 2021-2022
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
- Conditional expectation and projection
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.
For a focus on applied issues see:
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
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
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
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
- The OLS Method
- Mechanics and Interpretation of OLS
- Sampling Properties
- Hypothesis Testing
- Issues: Omitted Variables and Measurement error
- Instrumental Variables (IV) Estimation
- The IV Method
- Multiple Instruments and Over-identified Models
- Asymptotics
- Pitfalls of IV: Weak Instruments
- Testing: Endogeneity and Over-identifying Restrictions
- 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:
- Pooled OLS
- Fixed-Effects Estimation
- First-Differencing Estimation
- Random-Effects Estimation
- 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
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.