Statistics, Econometrics and Applications
A.Y. 2026/2027
Learning objectives
The course provides students with a working knowledge of probability and statistics, skills in data handling and statistical programming, and an understanding of the models and methods of applied econometrics. It equips students with the essential tools for statistical analysis, also introducing a Bayesian perspective for inference and decision-making. Building on these foundations, the course presents the linear regression model, starting with a single regressor and extending to multiple regressors, and examines the properties of the OLS estimator. It then addresses key econometric challenges such as heteroskedasticity, autocorrelation, and endogeneity through techniques including generalized least squares and instrumental variables. The analysis is further extended to panel data and discrete choice models. Practical applications in economics are central to the course, with students consolidating their knowledge through applied problem sets carried out with statistical software.
Expected learning outcomes
After completing the course, students will be able to specify linear regression models, estimate coefficients, and perform hypothesis testing; understand the properties of estimators (unbiasedness, efficiency, consistency, and asymptotic normality) in order to assess the appropriateness and limitations of different econometric approaches; identify and address key issues such as nonlinearity, heteroskedasticity, autocorrelation, and endogeneity; develop and apply Bayesian models; understand and apply econometric methods for panel data and discrete choice models; use statistical software to produce and interpret empirical results for policy and real-world economic issues; and critically evaluate econometric analyses, including policy reports and academic research. These outcomes will also enable students to engage with empirical analyses presented in other courses and provide them with quantitative tools for their final thesis.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
The course equips students with a working knowledge of the tools of probability and statistics, with skills in data handling and statistical programming, and with an understanding of the models and methods of applied econometrics. To this end, problem sets with both analytical and computer-exercise components will form a substantial part of the course.
Main topics:
0. Basics refresher: parametric families and joint probability distributions of random variables; sampling distributions, frequentist parameter estimation and hypothesis testing.
1. Bayesian inference: the likelihood function, prior distributions and Bayes' rule; posterior and predictive computation; Bayesian models, credible intervals and tests.
2. The linear regression model: estimation through ordinary least squares, reading and interpreting regression output, and using the model for prediction; extension to multiple regressors.
3. Checking the assumptions of the linear regression model: functional form, multicollinearity, heteroskedasticity, autocorrelation, non-normality.
4. Causal inference with the regression model: omitted variables, endogenous regressors, and the method of instrumental variables.
5. Panel data analysis: fixed effects estimator, random effects estimator, specification tests, Hausman-Taylor estimator.
6. Models for binary dependent variables: probit and logit models.
Main topics:
0. Basics refresher: parametric families and joint probability distributions of random variables; sampling distributions, frequentist parameter estimation and hypothesis testing.
1. Bayesian inference: the likelihood function, prior distributions and Bayes' rule; posterior and predictive computation; Bayesian models, credible intervals and tests.
2. The linear regression model: estimation through ordinary least squares, reading and interpreting regression output, and using the model for prediction; extension to multiple regressors.
3. Checking the assumptions of the linear regression model: functional form, multicollinearity, heteroskedasticity, autocorrelation, non-normality.
4. Causal inference with the regression model: omitted variables, endogenous regressors, and the method of instrumental variables.
5. Panel data analysis: fixed effects estimator, random effects estimator, specification tests, Hausman-Taylor estimator.
6. Models for binary dependent variables: probit and logit models.
Prerequisites for admission
Students are expected to be familiar with the basic concepts of matrix algebra and to have completed an introductory course in probability and statistics. They should also possess basic computer skills and be able to use at least one of the following operating systems: Windows, macOS, or Linux.
Teaching methods
- Theoretical lectures delivered in person.
- Practical sessions using RStudio and Stata, during which students will be required to solve problem sets on their laptops.
Attendance is strongly recommended.
NB: Up to 10% of Part 1 is delivered online, covering specific R packages and structured case studies.
- Practical sessions using RStudio and Stata, during which students will be required to solve problem sets on their laptops.
Attendance is strongly recommended.
NB: Up to 10% of Part 1 is delivered online, covering specific R packages and structured case studies.
Teaching Resources
- Hill, Griffiths & Lim, Principles of Econometrics, 5th ed., Wiley, 2018. ISBN: 978-1-119-32094-4.
- Greene, Econometric Analysis, 8th ed., Pearson. ISBN: 978-0-13-446136-6.
- Stock & Watson, Introduction to Econometrics, 4th ed., Pearson. ISBN: 978-0-13-446199-1.
- Online resources on Bayesian methods (course website on myAriel).
- Greene, Econometric Analysis, 8th ed., Pearson. ISBN: 978-0-13-446136-6.
- Stock & Watson, Introduction to Econometrics, 4th ed., Pearson. ISBN: 978-0-13-446199-1.
- Online resources on Bayesian methods (course website on myAriel).
Assessment methods and Criteria
The exam assesses whether students have achieved the course learning objectives, such as selecting appropriate models for research questions, interpreting econometric software output, performing relevant tests, and applying statistical models to support economic decision-making.
The exam consists of three parts:
- Part 1. Statistics (mandatory): A written test comprising up to four open-ended and four closed-ended questions. Questions may be theoretical and/or involve the interpretation of R output. Maximum score: 14 points. Passing score: 7 points.
- Part 2. Econometrics (mandatory): A written test with two exercises, each including multiple open-ended questions. The exercises may be theoretical or based on applied analysis (e.g., interpretation of Stata output). Maximum score: 14 points. Passing score: 7 points.
- Part 3. Project work (optional): A group project (teams of two or three students), requiring the submission of a written report on a case study. Maximum score: 3 points.
Students must pass both Part 1 and Part 2 to complete the exam successfully. Part 3 is optional. The final grade is a single score calculated as the sum of the scores from all three parts. To pass Part 1 and Part 2, students must obtain at least 7 points in each, and the sum of the two scores must be at least 18. The final grade is measured on a 30-point scale. A total score of 31 corresponds to 30 cum laude.
NB: Students are required to bring only a pen. The use of a pocket calculator is permitted, provided it is not capable of remote communication. Mobile phones, tablets, laptops, smart glasses, earphones, smartwatches, and any other connected devices are strictly prohibited.
The exam consists of three parts:
- Part 1. Statistics (mandatory): A written test comprising up to four open-ended and four closed-ended questions. Questions may be theoretical and/or involve the interpretation of R output. Maximum score: 14 points. Passing score: 7 points.
- Part 2. Econometrics (mandatory): A written test with two exercises, each including multiple open-ended questions. The exercises may be theoretical or based on applied analysis (e.g., interpretation of Stata output). Maximum score: 14 points. Passing score: 7 points.
- Part 3. Project work (optional): A group project (teams of two or three students), requiring the submission of a written report on a case study. Maximum score: 3 points.
Students must pass both Part 1 and Part 2 to complete the exam successfully. Part 3 is optional. The final grade is a single score calculated as the sum of the scores from all three parts. To pass Part 1 and Part 2, students must obtain at least 7 points in each, and the sum of the two scores must be at least 18. The final grade is measured on a 30-point scale. A total score of 31 corresponds to 30 cum laude.
NB: Students are required to bring only a pen. The use of a pocket calculator is permitted, provided it is not capable of remote communication. Mobile phones, tablets, laptops, smart glasses, earphones, smartwatches, and any other connected devices are strictly prohibited.
ECON-05/A - Econometrics - University credits: 9
Exercises: 16 hours
Lessons: 64 hours
Lessons: 64 hours
Professors:
Gobbi Alessandro Pietro, Stefanini Federico Mattia
Professor(s)
Reception:
by appointment on Tuesday and Wednesday (email)
Via Celoria 10