## General information

Course type | AMUPIE |

Module title | Economic modelling and control theory |

Language | English |

Module lecturer | prof. UAM dr hab. Yoichi Uetake |

Lecturer's email | uetake@amu.edu.pl |

Lecturer position | University Professor |

Faculty | Faculty of Mathematics and Computer Science |

Semester | 2024/2025 (winter) |

Duration | 60 |

ECTS | 6 |

USOS code | 06-S2MA03-F11716 |

## Timetable

1.5h lecture (Monday, 10:00-11:30, Room A2-23)

and 1.5h exercise/laboratory classes (Monday, 11:45-13:15, Computer room A1-23) per week

at Faculty of Mathematic and Computer Science Building of AMU

## Module aim (aims)

The main purpose of the course is to present an interaction of modern macroeconomics theory

and mathematical control theory. Basic notions of macroeconomics and control theory will be

explained from scratch. Thanks to this one can learn a rigorous design scheme and analysis

of monetary and fiscal policies. In the exercise/laboratory classes 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)

The required mathematical skills are just a few topics from undergraduate linear algebra and

multivariable calculus, which we will recall in the context of economic and control theory over

the course of the lecture.

## Syllabus

Week 1. IS-LM model – Classical static Keynesian macroeconomic model

Week 2. Description of dynamical macroeconomic models based on the state-space equation

Week 3. State-space realization of input-output systems (e.g. time series models)

Week 4. Stabilization via state feedback, state observer

Week 5. Model following control, Dead beat control 1/2

Week 6. Model following control, Dead beat control 2/2

Week 7. Lucas critique – Rational Expectations hypothesis (RE)

Week 8. The generalized state-space (descriptor) model

Week 9. DSGE model (Dynamic Stochastic General Equilibrium model) 1/2

Week 10. DSGE model (Dynamic Stochastic General Equilibrium model) 2/2

Week 11. Taylor rule for monetary policy

Week 12. Time series analysis (eg. Autoregressive (ARMA) model) of macroeconomic data

Week 13. Kalman filter

Week 14. Design of monetary and fiscal policies based on the state feedback control 1/2

Week 15. Design of monetary and fiscal policies based on the state feedback control 2/2

## 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.