APPLIED STATISTICS AND ECONOMETRICS

APPLIED STATISTICS AND ECONOMETRICS

Andrea Pozzi, Alessandro Casini

Instructional goals

The course aims at providing the students with a basic toolkit to understand and perform empirical analysis in economics. The focus will be on the linear model (with some extensions to nonlinear models). The students will learn the theory and the practice of estimating a linear model via Ordinary Least Squares and will learn to judge the suitability of different specifications to answer empirical questions in economics.

Intended learning outcomes

Knowledge and understanding: The course will offer the theoretical tools to understand the working of the Ordinary Least Squares estimation technique, which represents the workhorse of empirical research in economics. The students will be able to understand the assumptions behind the validity of the OLS estimator and to detect potential threats to it Applying knowledge and understanding: The student will be able to specify, estimate and interpret simple econometric models to answer questions of policy interest in economics and finance. They will be able to discuss and defend the assumption behind the models they develop and to be aware of their potential weaknesses. Making judgments: Students will be able to read and understand policy reports and academic literature as well as interpreting their findings and flagging potential flaws with the analysis. The course will offer several example of academic papers putting to use the methodologies illustrated in class to help students grasping both their potential and limitations. Communications skills: The toolkit acquired in the course will enable students to produce empirical analysis to answer questions of relevance for public policy or business practices. This will allow them, for example to pursue empirical projects for their BA dissertation Learning skills: Understanding the basic of econometrics analysis will allow students to better understand and judge any type of empirical evidence brought before their eyes by experts, co-workers or media sources. They will then be empowered as decision makers having a better sense of the validity of quantitative arguments weighted for and against a certain policy or business decision. Similarly, they will learn how to formulate theories in way that are empirically testable in order to support empirically their claims and ideas or simply find answers to questions that are relevant to them.

Course Contents

The aim of Applied Statistics and Econometrics is to provide an introduction to the practice of econometrics. While both theoretical and practical aspects are covered, emphasis will be on intuitive understanding and concepts will be illustrated with real-world applications. The course will cover the linear regression model, both univariate and multivariate. We will learn how to use the OLS estimator to estimate parameters of interest and use them to make inference. We will then extend the analysis to a class of nonlinear models. We will explore potential threat to the validity of the OLS estimator and introduce the Instrumental Variable estimator as a possible solution. Finally, we will introduce technique to take advantage of the availability of panel data.

Reference Books

Stock, J. H., & Watson, M. W. (2020). Introduction to econometrics (Fourth, global ed.). Pearson. Link

Teaching Methods

Lectures and exercise sessions. The exercise sessions are designed to cover the material covered in class from a more applied point of view. In particular, practical problems and question from past exams will be solved to help students transfer their understanding of the theoretical material to actual problems of estimation and inference. We will make use of econometric software (Stata) to introduce students to a tool to perform estimation and to develop their ability to read and interpret output from statistical analysis. During lectures, quizzes, polls and open questions to the class will be employed to make the teaching more interactive and increase students’ participation.

Assessment Method

The student will be evaluated on the basis of the individual score in a written exam touching upon the topics of the entire course through which to assess the knowledge and understanding of the material and the level of autonomy in interpreting empirical research The points collected through submission of the weekly problem sets which help solidify understanding of the concepts along the way and encourage the transition between theoretical knowledge of the subject and ability to put it to work. The final exam will be a mix of theoretical and application based questions. In the latter, students will be presented an econometric model and the results from its estimation and will be asked to answer question using them as input. Some questions will be in the multiple choice format, others will require students to impute short statements (ex. null hypothesis) or numbers. The exam will be designed in such a way to elicit the understanding of the basic concepts and to test students in their ability to apply them. There will be 9 weekly problem sets students will be required to solve and submit through LEARN. Students who submit by the stated deadline between 6 and 8 problem sets will receive 1 bonus point to be added to the grade obtained in the final. Students submitting by the stated deadline all 9 problem sets will receive 2 bonus points to be added to the grade obtained in the final. The bonus points can only be awarded to students who take the final exam in the first available date (December 2024). At then end of the first half of the course, students will be given a take-home midterm exam. The midterm will not be graded and it will not count towards the course grade but it will help students familiarize with the exam format and will serve as a checkpoint to evaluate their learning. Students failing to achieve a score of at least 18/30 (before the application of possible bonus points) in the final written exam will not pass the exam.

Thesis assignment criteria

Individual interview with the instructor.

Week 1

Session 1 Introduction to the types of data and their representation; review of bivariate analysis. (Reference to textbook: SW 1.1-1.3, 2.3) Session 2 Review of statistics: moments of a distribution, estimators of the moments of a distribution. (SW 2.1-2.6) TA Session 1 Exercise review on basic statistics and data representation

Week 2

Session 3 Review of statistics: testing and confidence intervals. Introduction to the bivariate linear model and its estimation. (SW 3.1-3.5) Session 4 The bivariate linear model: measures of fit, the least squares assumptions and the sampling distribution of the OLS estimators. (SW 4.1-4.5) TA Session 2 Exercise session on estimation of bivariate OLS models

Week 3

Session 5 The bivariate linear model: Hypothesis testing and confidence intervals. Bias. (SW 5.1-5.2) Session 6 The bivariate linear model: Dummy variables, heteroskedasticity, Gauss-Markov theorem. Omitted variable bias. (SW 5.3-5.5, 6.1) TA Session 3 Exercise session on estimation and inference in the bivariate linear model. Interpretation of dummy variables.

Week 4

Session 7 Multivariate regression model: measures of fit, sampling distribution of the estimator (SW 6.2-6.6). Session 8 Multivariate regression model: hypothesis testing and confidence interval (SW 7.1). TA Session 4 Exercise session on estimation and inference in the multivariate linear model.

Week 5

Session 9 Categorical variables, testing of joint hypotheses (SW 7.2). Session 10 Control variables and causal variables (SW 7.5) TA Session 5 Exercise session on categorical variables and joint hypotheses testing.

Week 6

Session 11 Assessment of regression models (SW 7.5) Session 12 Review session on topics of the first part of the course TA Session 6 Exercise session on topics of the first half of the class

Week 7

Session 13 Introduction to nonlinear models. Quadratic models: estimation, interpretation and inference. (SW 8.1-8.2) Session 14 Logarithmic models: estimation, interpretation and inference. (SW 8.2) TA Session 7 Exercise session on Quadratic and logarithmic models.

Week 8

Session 15 Interaction models: interactions of dummies, interactions of dummy and continuous variables. (SW 8.3) Session 16 Interactions of continuous variables. Graphical representation of interaction models. (SW 8.3-8.4) TA Session 8 Exercise session on quadratic and logarithmic models.

Week 9

Session 17 Internal and external validity of econometric models. Failures of internal validity. (SW 9.1-9.2) Session 18 Introduction to instrumental variables. IV in the univariate model. (SW 12.1) TA Session 9 Exercise session on models with interactions.

Week 10

Session 19 Generalized IV model. (SW 12.2) Session 20 Validity of the instruments. Examples of good instrumental variables strategies.(SW 12.3, 12.5) TA Session 10 Exercise session on instrumental variables.

Week 11

Session 21 Introduction to panel data. Panel data with two time periods (SW 10.1-10.2) Session 22 Panel data with multiple time periods: fixed effects vs. demeaning estimators. (SW 10.3) TA Session 11 Exercise session on fixed effects models.

Week 12

Session 23 Time fixed effects. Standard errors in fixed effects models. (SW 10.4-10.5) Session 24 General review of all the topics covered in the course. TA Session 12 Exercise session on the entire program to prepare for the exam.