Insegnamento a.a. 2020-2021

• Introduction to econometrics. (What is Econometrics?; Steps in empirical economic analysis; The structure of economic data; Causality and the notion of ceteris paribus in econometric analysis).  
• Simple regression model. (Definition; Multiple ways of deriving the Ordinary Least Squares (OLS) estimates; Properties of OLS in any sample of data).
• Multiple regression analysis: Estimation. (Motivation for multiple regression; Mechanics and interpretation of OLS; Expected value and variance of OLS estimator; Gauss-Markov Theorem and Efficiency of OLS estimator).
• Multiple regression analysis: Inference. (Distribution of OLS estimator in finite samples.
• Confidence intervals; Tests of simple and multiple hypotheses about population parameters).
• Multiple regression analysis: OLS asymptotics. (Properties of OLS estimator in infinite samples).
• Multiple regression analysis with qualitative information: Dummy variables. (Use of dummy explanatory variables and their interactions to the aims of incorporating qualitative or ordinal information in regression analysis and of performing tests of hypothesis and policy analysis involving comparisons of groups. Dummy dependent variables and the linear probability model).
• Heteroskedasticity of known and unknown forms. (Heteroskedasticity-robust standard errors; Weighted Least Squares (WLS) estimation; Feasible Generalized Least Squares (FGLS) estimation.
• Pooling cross sections across time: Simple panel data methods. (Differences-in-Differences; First Differencing).
• Instrumental variables (IV) estimation and Two stages least squares (2SLS).
• Limited dependent variable (LDV) models with binary dependent variables. (Logit and Probit; Maximum Likelihood Estimation).

• Define key concepts in econometrics, for instance “econometric model”; “random sample;” “ceteris paribus;” “counterfactual;” “causal effect;” “exogeneity/endogeneity;” “homoskedasticity/heteroskedasticity;” “restricted/unrestricted model;” “finite-sample/asymptotic bias;” “omitted variables bias;” “dummy variable trap.”
• Explain key differences and links between distinct but related econometric concepts, for instance “econometric model and estimation method;” “population and sample;” “population parameter, estimator, and estimate;” “correlation and causal effect;” “error term and residual;” “point estimate and confidence interval;” “significance level and critical value;” “proxy variable and instrumental variable.”
• Recognize different types of econometric data among: cross sections, time series, pooled cross sections, and panel/longitudinal data. Explain their differences and similarities.
• State the assumptions of the classical linear regression model and explain their roles within the Gauss-Markov Theorem. Name and discuss the main consequence(s) of the failure of each assumption, illustrating with specific microeconomic examples or applications.
• Describe different ways of deriving and interpreting the OLS estimators (estimates) for the parameters of a linear regression model, among: Minimizing the sum of the squared residuals; Method of moments & Sample analog principle; Maximizing the likelihood function.   
• Discuss the advantages and disadvantages of different econometric strategies used to identify and estimate causal effects, including: Differences-in-Differences; First differences; Instrumental Variables.

• Apply simple and multiple regression analysis to quantify relationships among economic variables of interest and to test simple and joint hypotheses about such relationships.
• Assess the statistical and economic significance of estimated relationships among economic variables.
• Perform simple analysis of bias to assess whether estimated relationships among economic variables may be interpreted as ceteris paribus (causal) effects and, if not, to assess the likely direction of the bias. 
• Interpret and critically assess empirical findings presented by others based on regression analysis of economic data.
• Incorporate dummy variables and their interactions into regression analysis to test stability of regression parameters across different groups or time periods.
• Choose and apply the appropriate econometric strategy among those covered in class (e.g., Differences-in-Differences, First Differences, Instrumental Variables) to quantify causal effects among economic variables, taking in to account the characteristic features of the application and of the available data.
• Evaluate the causal effects of policy interventions/programs using simple econometric tools such as Differences-in-Differences or Instrumental Variables methods.
• Interact in a constructive way and think critically.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)

The learning experience of the course includes:

• Face-to-face lectures, introducing and illustrating the main topics of the course.
• NOTE: Due to the COVID emergency, students will rotate between in-person and virtual (synchronous) attendance. That is, each week half of the students will attend in person and the other half will attend remotely. For students attending virtually, classes will be shown in streaming. 
• Interactive in-class discussions around stylized microeconomic applications, particularly on specific aspects of their implementation and interpretation.
• The solution in class of homework exercises assigned to students throughout the course.
• The latter gives students the opportunity to practice on their own by applying the methodological and analytical tools covered in the course to a variety of microeconomic and policy-relevant applications.
• Moreover, systematic and interactive in-class discussions of stylized applications, where students are encouraged to bring their own contributions and share their insights, create a setting where students can further learn from the instructor and from one another while monitoring their own progress and receive immediate feedback.

To the end of measuring the acquisition of the above-mentioned learning outcomes, the students’ assessment is based on a written exam.

• The exam consists of a mix of open questions, multiple choice questions, and applied exercises. The first tests students’ understanding of, and ability to explain in their own words and yet rigorously, key econometric concepts and their relationships. The second further tests student’s familiarity with the language of econometrics as well as with concepts and tools commonly used to carry out and/or interpret empirical economic analysis. The third assesses students’ ability to carry out and interpret results from empirical econometric work.
• Students can take a partial written exam (first partial) and complete the written exam at the end of the course (second partial). In this case the weights are: 50% for the first partial and 50% for the second partial. Alternatively, students can take a final written exam (general) that accounts for 100% of the final grade.

The main course material for both attending and non-attending students is:

• J.M. WOOLDRIDGE, Introductory Econometrics: A Modern Approach, CENGAGE Learning, 2016, 6th Edition.
• The slides of the course, problem sets, and additional support material are uploaded to the BBoard platform of the course.