BAYESIAN ECONOMETRICS

This course belongs to the fundamentals teaching activities of the masters: "Models and Methods of Quantitative Economics" and "Sustainable finance, quantitative finance, and risk management". In line with the educational objectives of the course, this activity aims to present the main mathematical and statistical tools necessary for the analysis of economic phenomena; particular attention will be devoted to the use of formal language and methodological rigor. More specifically, the course aims to complete students' preparation in Econometrics by being able to deal with advanced econometric models and methods. Moreover, it will give the student an overview of nonlinear and latent variable modeling for financial data analysis.

Knowledge and understanding skills.
Attendance and active participation in lectures, exercise sessions, and tutoring activities, together with the individual study, will allow the student to acquire the following knowledge and understanding skills:
- know data science and machine learning techniques useful to test the validity of theoretical economic models on data.
- know and use the main mathematical tools necessary to model complex economic phenomena;

Ability to apply knowledge and understanding.
Through the interaction with the instructors, the tutors, and peers and through the individual study, the student acquires the following abilities:
- know how to use quantitative instruments to cope with complex problems related to economic and financial environments;
- know how to choose the most appropriate technique to solve the concrete problem under analysis.

Judgment skills, communication skills, and learning skills.
Regarding the autonomy of judgment, communication skills, and learning abilities, through the personal and group study of the concepts seen in class, the student will be able to:
- formulate rational justifications for the approach used to solve economic and financial problems, understanding their relative strengths and weaknesses;
- know how to formulate and communicate sophisticated quantitative analysis of economic and financial data through mathematical models.

Basic notions of Regression Analysis and Specification of Linear Dynamic Econometric Models

1 Bayesian inference
1.1 Decision Theoretical Foundation of Statistics
1.2 Least square and maximum likelihood inference principles
1.3 Bayesian inference: Prior Distribution, Posterior Distribution, Bayesian Estimator
1.4 Bayesian nonparametric methods
2 Numerical methods for simulation-based inference
2.1 Markov-chain Monte Carlo
2.2 Gibbs Sampling
2.3 Metropolis-Hastings
3 Bayesian Linear Regression.
4 Probit and Logit models. Truncation and censoring. Models for count data.
5 Bayesian SUR and VAR
6 Bayesian Latent Variable Models
7 Nonlinearities in Financial Data
7.1 Conditional Heteroscedasticity: ARCH and GARCH Models, Stochastic Volatility Models
7.2 Switching Regime Models
8 State-space models
8.1 Kalman filter
8.2 Hamilton filter
8.3 Particle filters

Main references:
Notes, slides, and a reading list will be provided for every topic.

Additional references:
Robert, C.P. (2001). The Bayesian Choice: From Decision-Theoretic Motivations to Computational Implementation, Springer-Verlag, New York
Casella, G. and Robert, C.P. (2004). Monte Carlo Statistical Methods, Springer-Verlag, New York.
Chan, J., Koop, G., Poirier, D.J. and Tobias, J.L. (2019). Bayesian Econometric Methods (2nd edition). Cambridge: Cambridge University Press.
Fruehwirth-Schnatter, S. (2006). Finite Mixture and Markov Switching Models, Springer-Verlag.
Lancaster, T. (2004). An Introduction to Modern Bayesian Econometrics, Wiley.

The exam consists of individual and group assignments and the preparation and presentation of a final project. The exam is evaluated on a 30-point basis. The solution of the tasks can yield up to 21 points over 30, and the final project can yield up to 9 points out of 30. The exam is considered passed with 18 total points over 30.

The assignments are intended to verify the progress in the learning activity and the ability to go deep autonomously to the heart of the topics of the course. The assignments consist of problems and questions regarding additional reading material referenced correctly in the text of assignments.

The final project develops or extends further the course's topics and includes the student's original contribution, such as new models, analysis of their properties, or original applications to real data. The project preparation aims at putting into practice the knowledge acquired. The project's oral presentation aims to verify the understanding of the topics in the projects and the ability to communicate them clearly and rigorously.

written and oral

The final grade is based on 2 homework (75%) and a final paper replication, which includes a presentation (25%).

As regards the gradation of the grade (how the grades will be assigned), regardless of the attending or non-attending mode:

A. scores in the 18-22 range will be awarded in the presence of:
- sufficient knowledge and ability to understand and apply in relation to the programme;
- limited ability to interpret the exercise and provide arguments regarding its resolution;

B. scores in the 23-26 range will be awarded in the presence of:
- reasonable knowledge and ability to understand and apply in relation to the programme;
- reasonable ability to interpret the exercise and provide arguments regarding its resolution;

C. scores in the 27-30 range will be awarded in the presence of:
- good or excellent knowledge and ability to understand and apply in relation to the programme;
- good or excellent ability to interpret the exercise and provide arguments regarding its resolution;

D. honours will be awarded due to the remarkable knowledge and understanding of the program, in addition to maximum grades for the written assignments and final project.

Cycles of seminars, lectures on the various topics, group assignements

English

This subject deals with topics related to the macro-area "Climate change and energy" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development