NETWORKS IN ECONOMICS AND SOCIAL SCIENCE

The aim of the course is to provide students with models and tools from network and graph theory for the analysis of a wide variety of social, economic, financial and political interaction effects. The organization of the course can be split into three main parts. The first is an introduction to some background in graph theory with applications to social and economic networks. The second part deals with network models and the third with the practical issues of extracting latent networks and analysing networks in economics and finance. The main focus of the third part will be on financial networks and contagions on financial markets.

Knowledge and understanding skills.
Attendance and active participation in lectures, together with the individual study will allow the student to acquire the following knowledge and understanding skills:
- know and use the main mathematical tools necessary to analyse complex data;
- know the mathematical techniques useful to solve and analyze the proposed models.

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 network data in social science;
- know how to choose the most appropriate technique in order to solve the concrete problem under analysis.

Judgment skills, communication skills, 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 to the approach used in statistical analysis, understanding their relative strengths and weaknesses;
- know how to formulate and communicate an adequate analysis and interpretation of complex data through the use of mathematical models.

Probability and statistics (basic), linear algebra, programming structures (basic).

Contents:

I Introduction to Networks [Jac08, Bol98]
I.1 Networks and Random Graphs
I.2 Basic Graph Theory
I.3 Representing Networks
I.4 Network Characteristics
I.5 Social and Economic Networks

II Network Models [Jac08]
II.1 Random Networks
II.2 Growing Random Networks
II.3 Network Formation
II.4 Diffusion through Networks

III Network inference [Die15]
III.1 Correlation and Granger Networks
III.2 Graphical Models and Network Extraction
III.3 Financial Networks and Financial Contagion
III.4 Financial Volatility Networks
III.5 Financial Tail Networks
III.6 Sparse Graphical Models
III.7 Switching Financial Networks and Contagion Regimes
III.8 Stochastic Blocks and Financial Communities

Main References:
[Bol98] Bollobàs, B. (1998), Mondern Graph Theort, Springer, Ch. 1-7
[Jac08] Jackson, M.O. (2008) Social and Economic Networks, Priceton University Press, Ch.1-8
[Die15] Diebold, F. and Yilmaz, K. (2015), Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring, Oxford University Press.

Further Readings
[Jen96] Jensen, F. (1996), An Introduction to Bayesian Networks, Springer-Verlag
[Lau96] Lauritzen, S. (1996). Graphical Models, Oxford University Press
[Pea98] Pearl, J. (1998). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.
[Whi90] Whittaker, H. (1990). Graphical Models in Applied Multivariate Statistics, John Wiley.

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 and is considered passed with the achievement of 18 total points over 30.

The assignments yield 15 points out of 30 and 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 yields 15 points out of 30 and 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 precise way.

Classes, individual works, and teamworking on specific topics.

English

written and oral

This subject deals with topics related to the macro-area "Circular economy, innovation, work" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development