86530 - Econometrics

Learning outcomes

In this course the student learns the basic econometric tools useful for a proper empirical analysis of economic phenomena. At the end of the course the student is able to: - Critically evaluate the application and empirical economic literature; - Apply the basic econometric methods to conduct empirical analysis (forecasts and estimates) in the economic field with the use of an appropriate econometric software.

Course contents

Requirements

The course assumes familiarity with introductory calculus, linear algebra, probability, and statistics. Basic knowledge of microeconomics is recommended. All empirical applications are implemented using the statistical software R.

MAIN TOPICS

Part 1: Introduction to econometrics

This part introduces the objectives of econometric analysis and the role of econometric models in economics. We discuss the distinction between descriptive, predictive, and causal analyses, review the basic concepts of probability and statistical inference, and introduce the workflow of empirical research.

Part 2: Linear regression models

Simple linear regression

We introduce the simple linear regression model, the Ordinary Least Squares (OLS) estimator, and its statistical properties. We discuss estimation, interpretation of regression coefficients, goodness of fit, and statistical inference through confidence intervals and hypothesis testing.

Multiple linear regression

We extend the regression framework to multiple explanatory variables. Topics include estimation and inference, model specification, interpretation of coefficients, categorical regressors, interaction terms, and the assumptions underlying OLS estimation.

Part 3: Regression models in empirical research

Model specification and evaluation

This part discusses how regression models are used in empirical economic research. We study functional form, nonlinear transformations, model diagnostics, and the interpretation of empirical results. Particular attention is devoted to assessing the credibility of regression-based studies and understanding the distinction between predictive performance and causal interpretation.

Part 4: Econometric methods for causal inference

Panel data models

We introduce regression models for longitudinal data and discuss how repeated observations on the same units can be exploited to control for unobserved heterogeneity and estimate causal effects.

Regression models for binary outcomes

We study econometric models for binary dependent variables, focusing on their interpretation, estimation, and applications in economics.

Instrumental variables

We introduce instrumental variables estimation as a solution to endogeneity problems arising from omitted variables, reverse causality, and measurement error. Applications illustrate how instrumental variables can be used to identify causal effects when standard regression methods fail.

Readings/Bibliography

J. H. Stock, M. W. Watson, "Introduction to Econometrics" (4th global edition), Pearson 2020.

The slides used during classes, sketches of training sessions, exercises solutions and mock exams will be made available for download from Virtuale.

Teaching methods

Teaching combines the introduction of the theoretical foundations of econometric methods with empirical applications implemented in R. During the course, students will apply the techniques discussed in class to real datasets, learning how to estimate econometric models, interpret the results, and assess their validity. Attendance is not compulsory but is strongly recommended, as classroom discussions and practical exercises are designed to reinforce students' understanding of the material.

Assessment methods

The final examination is designed to assess whether students have achieved the following learning outcomes:

• knowledge of the main econometric methods and techniques introduced during the course, including their theoretical foundations, appropriate applications, assumptions, and expected outputs;
• understanding of the fundamental distinction between econometric models used for prediction and those used for causal inference;
• ability to apply econometric methods to empirical problems involving both prediction and the estimation of causal effects.

Assessment consists of a written examination followed by an oral examination. The written examination is held in the computer laboratory, while the oral examination takes place shortly afterwards. The questions in both parts are randomly selected from a predefined pool; consequently, the specific content of the examination differs across students.

The written examination consists of multiple-choice questions and exercises requiring numerical answers to be computed using the R statistical software. The written examination is automatically graded. Students are admitted to the oral examination only if they achieve a passing grade on the written examination.

The oral examination consists of open-ended questions aimed at assessing students' understanding of the theoretical foundations of the methods covered in the course, their ability to interpret econometric results, and their capacity to discuss the assumptions and limitations of the techniques employed.

During both the written and oral examinations, students may not use calculators, mobile phones, smartwatches, or any other electronic devices, nor may they communicate with other candidates or consult notes, books, or any other written material. The use of artificial intelligence tools in any form is strictly prohibited. Any violation of these rules will result in exclusion from the examination.

The written examination lasts 60 minutes.

As an alternative to the final examination, students may take two midterm examinations. In this case, the final grade is the arithmetic average of the grades obtained in the two midterms. The dates of both the midterm and final examinations are fixed and cannot be rescheduled. Requests for additional examination dates will not be considered.

Students with specific learning disorders (SLD) and/or temporary or permanent disabilities are invited to contact the University office responsible for disability and inclusion services (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as early as possible. Requests for examination accommodations must be submitted to the instructor at least 15 days before the examination date. Accommodations will be granted in accordance with University regulations and the learning objectives of the course.

The maximum grade for both the written examination and each midterm examination is 30/30. The final grade is awarded after completion of both the written and oral examinations. The distinction 30 cum laude may be awarded only if the student's performance in the oral examination is outstanding.

Grades are interpreted as follows:

• <18: Fail
• 18–23: Satisfactory
• 24–27: Good
• 28–30: Very good
• 30 cum laude: Excellent

Students may reject the final grade only once. To do so, they must notify the instructor by email no later than the deadline for grade registration. The instructor will acknowledge receipt of the request.

Grade rejection always applies to the examination as a whole. For students taking the midterm option, this refers to the overall grade obtained by averaging the two midterm examinations. If the final grade is rejected, the student must retake the complete examination, including both the written and oral components.

The only exception concerns the first midterm examination. Students may decide not to retain the grade obtained in the first midterm without submitting a formal rejection. In this case, they may either take the second midterm or sit the complete final examination, thereby forfeiting the first midterm grade.

Students who pass the first midterm may take the second midterm either during the first examination session immediately following the end of the course or during the subsequent examination session. The second midterm may be taken only once. If a student fails the second midterm or rejects the overall grade obtained through the midterm option, the student must take the complete final examination and forfeits the grade obtained in the first midterm.

Teaching tools

Students will also be requested to constantly test their understanding of the basic concepts discussed in class by means of quizzes that will be published on the on-line e-learning platform (Virtuale) at the end of each week. Quizzes are not compulsory, can be retaken as many times as students wish, and will not be corrected. The tutor of the course will be available one hour per week to answer questions on the quizzes.

Office hours

See the website of Sergio Pastorello