Economic modelling and control theory

Timetable

1.5h lectures and 1.5h exercise/laboratory classes per week

Module aim (aims)

The main purpose of the course is to present an interaction of modern macroeconomics theory and mathematical control theory.
The course starts from classical IS-LM model analysis to help the student understand basic ideas of macroeconomics.
Basic notions of control theory will be explained from scratch. The course topics will also cover the so-called Lucas critique in rational expectations hypothesis and its relation with control theory.
The highlight of the lecture is the introduction of the New Keynesian DSGE (Dynamic Stochastic General Equilibrium) model combined with some notions from control theory.
Thanks to this combination one can construct a comprehensive framework for a rigorous model for analysis and design of monetary and fiscal policies.

In the exercise course we will focus on practical implementation of the theory using real economic data.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

We will use elementary undergraduate matrix theory. We will explain it in the context of economic and control theory over the course of the lecture for students with no knowledge of matrix theory from scratch.

Syllabus

Week 1. IS-LM model - Hicks' static Keynesian macroeconomic model
Weak 2. Phillips curve, various notions of unemployment
Weak 3. The role of expectations in economic theory
Weak 4. Policy interest rate, bond yield, their infuence on the financial market
Weak 5. Difference equations, stability, Samuelson's model
Week 6. Description of dynamic macroeconomic models based on the state-space equation
Week 7. Controllability, stability
Week 8. Stabilization via state feedback
Weak 9. Observability, Luenberger observer
Week 10. Model following control, the internal model principle, servomechanism
Weak 11. Lucas critique
Weak 12. Rational vs adaptive expectations hypothesis
Week 13. DSGE (Dynamic Stochastic General Equilibrium) model
Week 14. Design of monetary policy based on the state feedback, Taylor rule
Week 15. The generalized stae-space (descriptor) model, time series analysis

Reading list

1. B. J. Heijdra, Foundations of Modern Macroeconomics (3rd Edition), Oxford University Press, 2017.
2. N. G. Mankiw, Principles of Macroeconomics (6th Edition), South-Western College Pub, 2011.                              3. P. A. Samuelson and W. D. Nordhaus, Economics (19th Edition), McGraw-Hill, 2010.                                            4. Y. Uetake, Economic Modelling and Control Theory, Lecture Notes, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 2025 (delivered during the course).