ADVANCED ECONOMETRICS

This course is one of the teaching activities of the PhD progam in "Economics". 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 specifially, the course aims to complete students preparation in Econometrics by being able to deal with advanced econometric models and methods. Moreover, it will provide students with the main econometric methods, with special reference to the analytical derivation of the estimators and to inference procedures. The course is well equipped with econometric practice, enhancing practical abilities in the use of programming languages such as MATLAB and R.

Knowledge and competences:
- sound knowledge of the theoretical foundations of econometric methods
- specification and formal derivation of econometric models based on economic models
- investigate, understand and interpret economic and financial phenomena, by means of up-to-data econometric tools

Application of acquired knowledge and skills:
- ability to exploit up-to-date analytical tools and formal derivations to gain insights on relevant economic relationships
- interpretation and management of economic dynamics, through the use of advanced analytical tools
- being able to design empirical strategies to measure and quantify economic phenomena and relationships among economic variables

Judgement and interpretation skills:
- evaluate strengths and weaknesses of the methodologies analysed and of their empirical application
- being able to critically interpret the outcomes of empirical analyses

Mathematical Tools:
Matrix Algebra
Differential Calculus
Integral Calculus

Statistical Tools:
Random Variables and Distribution Theory
Point and Interval Estimation
Hypothesis Testing
Least Squares and Standard Linear Model

1 Bayesian inference
1.1 Decision Theoretical Foundation of Statistics
1.2 Bayesian inference
1.3 Numerical methods for posterior approximation
1.4 Bayesian nonparametric methods
2 Bayesian models
2.1 Linear regression models
2.2 Probit/Logit models, truncation and censoring
2.3 Bayesian SUR and VAR
2.4 Latent Variable Models
2.5 State-space models (Kalman filter, Hamilton filter, particle filter)
3 Network models
3.1 Graph theory
3.2 Models for count data
3.3 Tensor regression models
3.4 Graphical models
4 Latent Variable models
4.1 Latent positioning models
4.2 Stochastic block models
4.3 Topic modelling of health public plans
4.4 Clustering of survey responses
4.5 lLtent trait model for comorbidity

- Notes and slides
- Bayesian inference
Robert, C. P. (2001). The Bayesian Choice - A Decision-Theoretic Motivation (second ed.). Springer Verlag
- Bayesian econometrics
Koop, G., Dale J. P., Tobias, J. L. (2007) Bayesian Econometric Methods, Cambridge University Press
Lancaster, T. (2004) An Introduction to Modern Bayesian Econometrics, Blackwell Publishing
Pole, A., West, M. and Harrison, P. J. (1994) Applied Bayesian Forecasting and Time Series Analysis, Chapman-Hall
- Latent variable models
West, M. and Harrison, P. J. (1997). Bayesian Forecasting and Dynamic Models, Springer-Verlag
Sylvia Frühwirth-Schnatter (2006). Finite Mixture and Markov Switching Models, Springer Verlag

The exam consists in individual and group assignments, and in the preparation and presentation of a final project. The exam is evaluated on a 30-point
basis. The solution of the assignements can yield up to 20 points over 30 and the final project can yield up to 10 points out of 30. The exam is
considered passed with the achievement of 18 total points over 30.
The assignments are intended to verify the progress in the learning activity and the abilities to go deep autonomously to the heart of the topics of the
course. The assignments consist of problems to solve and questions to reply regarding additional reading material properly referenced in the text of
assignments.
The final project develops or extends further the topics of the course and includes an original contribution of the student, 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 oral
presentation of the project aim at verifying the level of knowledge of the topics in the projects and the ability to communicate them in a clear and
rigorous way.

Cycles of seminars and lectures on the various topics

written and oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development