COMPUTATIONAL METHODS WITH SOCIO-ECONOMICS APPLICATIONS

The PhD in Economics offers advanced courses in economics and finance and aims to give selected students the skills to conduct innovative research, opening up career prospects at university or in economic and financial institutions and bodies. This course aims to give you quantitative and computational skills by exploring fundamental modeling and computer programming ideas, mostly related to dynamical environments (or dynamical systems) and their computational applications.

For some years, I tried hard to write the syllabus in terms of knowledge, skills and abilities. I'm sorry, but this was increasingly unsatisfactory and bombastic. Hence, I now prefer to describe the course through "the what", "the how" and "the why", as suggested by Paul Halmos, "What is teaching?", Annual Meeting of The Mathematical Association of America, Cincinnati, 14 January 1994.

Students must know the contents of the first year courses of the PhD program, including calculus and basic linear algebra. Knowledge of a programming language is useful but not needed, don't despair if you have no programming experience!

What: the course explores mathematical ways to model dynamic environments (theory and applications) and provides computer programming foundations to write code and solve related problems, mainly through the use of R, see https://cran.r-project.org/ . In particular, we will deal with
- linear difference equations, in which one future state variable is a linear function of lagged values of the same variable(s). If time permits, ordinary differential equations will be treated (as they are essentially "the same");
- discrete nonlinear dynamical systems in one variable and chaos. We will produce the code needed to reproduce the famous bifurcation diagram of the logistic map and its Lyapunov exponents;
- Markov chains.

How: definitions and the main results are discussed, exemplified and proved. In all cases, about half of the time is devoted to learn how to write programs to solve difference equations, investigate the dynamics, analyze the outputs and simulate the systems/chains.

Why: systems "in motion" are important and several ideas should be used to model their behaviour (linear vs nonlinear, stochastic vs deterministic or chaotic, transient phase vs equilibrium). Analytical results, as well as numerical solutions or simulations, should be used to explore outcomes and provide context to interpret the systems' evolution and give policy suggestions. Theory and programming skills must go together to foster understanding.

Linear difference equations: Simon Carl and Blume Lawrence, "Mathematics for Economists", 1994, Norton and Company (or any other edition). Chapters 23, 24 and 25.
Nonlinear dynamical systems: Strogatz Stevem, "Nonlinear Dynamics and Chaos", 1994, Perseus Books (or any other edition). Chapter 10.
Markow chains: Resnick Sydney, "Adventures in stochastic processes", 2005, Birkhauser. Chapter 2 (essentially).
Handouts will be provided.

A combination of active participation, homework, presentations in PechaKucha style (20x20 slides, see https://www.pechakucha.com/ ), and one written exam o saggio. Orientativamente, su base 100, la partecipazione attiva vale 10%; homework 20%, presentazione 30% e saggio 40%.

scritto e orale

Il/la docente ha il dovere di vigilare affinché siano rispettate le regole di autenticità e originalità delle prove d'esame. Di conseguenza, nei casi in cui vi sia il sospetto di un comportamento irregolare, l'esame può prevedere un ulteriore approfondimento, contestuale alla prova d'esame, che potrà essere realizzato anche in modalità differente rispetto alle modalità sopra riportate.

Work must be original and accurate. The final paper should contain some novelty or provide fresh insights on the topic under treatment. Details will be given in due time, with an eye to the specific cohort and on how the assessment worked in the previous academic year. Very original and very accurate work, jointly with very insightful papers, will receive an A.

Lectures, presentations by students, programming sessions.

If you need something, say something (paolop@unive.it). More explicitly, if you are, say, color-blind, hearing impaired, diabetic T1, disabled or differently equal in any dimension, please let me know and we will find ways to improve feasibility, interaction and fun.