This course covers empirical strategies aimed at answering economic research questions. The course illustrates several applied econometric models, and develops the skills needed to plan and carry on empirical research projects. Since most applied economic research examines questions with direct policy or managerial implications, this course will clarify the difference between correlation and causal links. Purely predictive methods, grounded in correlation and regression analysis will be presented and compared with alternative estimation techniques (such as instrumental variables) more focused on the analysis of causal effects. The goal of the course is to provide valuable econometric tools for students majoring in several fields, from micro/macro/international/industrial economics to finance, and management.

The course fits into the overall program curriculum pursuing some of the defined general learning goals. In particular, the course contributes to the development of the following capabilities:

• Identify trends, technologies and key methodologies in a specific domain (specialization streams)
• Design solutions applying a scientific and engineering approach (Analysis, Learning, Reasoning, and Modeling capability deriving from a solid and rigorous multidisciplinary background) to face problems and opportunities in a business and industrial environment

With respect to the first learning goal, at the end of the course students will be able to:

• Understand in depth the key aspects of the linear regression model and the relevance of the underlying standard assumptions
• Understand the variants of the linear regression model to be used when the standard assumptions do not hold
• Understand why the linear regression model is not appropriate when the dependent variable is discrete, truncated or censored and which are the appropriate models to be used in those cases

With respect to the second learning goal, at the end of the course students will be able to:

• Select the appropriate econometric model to be applied in practical economic situations.
• Interpret the output of econometric packages implementing econometric models
• Test the validity of the underlying assumptions for each model
• Use econometric models to support economic decisions

Overview

 The agenda includes regression, instrumental variables, differences-in-differences, probit, logit, tobit, survival analysis. One of the goals is to equip students with working knowledge of the tools of probability and statistics, skills in data handling and statistical programming, and an understanding of the models and methods of applied econometrics. To this aim, problem sets with both analytical and computer-exercise components will be a relevant part of the course. The cases will be illustrated and discussed using the open source econometric package Gretl (gretl.sourceforge.net).

Main topics

• 0. Basics refresher: estimation and testing theory, matrix algebra
• 1. The linear multiple regression model under standard assumptions: estimation through Ordinary Least Squares, reading and interpreting the regression output, using the model for prediction.
• 2. Checking assumptions of the regression model: functional form, multicollinearity, heteroskedasticity, autocorrelation, non-normality
• 3. Using the model to investigate causal relationships: omitted variables, endogenous regressors and the method of instrumental variables
• 4. Using the model to analyze the effectiveness of policies and managerial choice: the differences-in-differences method
• 5. Analysis of binary variables (probit and logit models)
• 6. Analysis of categorical variables (multinomial logit models)
• 7. Analysis of ordinal variables (ordered probit models)
• 8. Analysis of count variables (Poisson regression)
• 9. Analysis of truncated and censored variables (Tobit models)
• 10. Analysis of durations (survival model

Students should be familiar with basic concepts in probability, statistics and matrix algebra. To be self contained, the course includes a brief refresher, just in case.

(i) Written exam (80 minutes, weight 60%). The written exam is based on two exercises (the first is on the topics 1 to 4 illustrated above; the second is on the topics 5 to 10). The main purpose of the written exam is to assess the achievement of the second learning goal and the associated learning objectives (ability to select the appropriate model to answer research questions, to read the output of econometric packages, to perfom the appropriate tests, to use the models to support economic decisions)

(ii) Oral exam (15 minutes, weight 40%). The main purpose of the oral exam is to assess the achievement of the first learning goal and the associated learning objectives (understanding of the main theoretical aspects of econometric models). The oral exam has to be taken after the written exam, not necessarily in the same call.

(iii) Non-compulsory team project work  (2 students): a paper about 10/15 pages long, where some of the techniques illustrated in the course is applied to a real problem; the paper has to be illustrated in a 30 minutes presentation, possibly via skype; the project work may increase the final mark by at most 2/30. The project work gives you the opportunity to get an hands-on perspective on the discipline. Highly recommended if you plan to include econometric models in your final thesis, or if you think that a deep understanding of statistics in general and econometrics in particular is a valuable asset for your future.

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