PMMMR Mathematical models of regulation

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: graded credit.
Teacher(s)
prof. Ing. Osvald Vašíček, CSc. (lecturer)
Guaranteed by
prof. Ing. Osvald Vašíček, CSc.
Department of Economics – Faculty of Economics and Administration
Contact Person: Lydie Pravdová
Timetable
Thu 9:20–11:00 VT206
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main objective of the course is to familiarize students with approaches of the theory of dynamic systems to modeling and optimal control of economic systems.
At the end of this course, students should be able to:
- understand and practically handle internal system description in state space
- identify such dynamic system on time series of real economy
- analyze economic system represented by an identified state space model, which is a subject of optimal control
- understand the derivation of a two-point border problem of optimal control, i.e. Hamiltonian, necessary conditions of optimality, Riccati equations, which lead to a design of an algorithm of feedback optimal control
- practically control or stabilize fiscal policy, monetary policy or mixed policy on a controlled macroeconomic model of US economy
Syllabus
  • 1. Introduction to dynamic systems problems and its application to control real economy
  • 2. Internal and external description of a dynamic system
  • 3. State-space representation of a real economic framework as an econometric system of 1st order equations and description of the same framework by a system of state-space equations.
  • 4. Practical application on a US real economy model
  • 5. Simultaneous estimation of parameters and stochastic components of a state-space model with PEM (prediction error method) including an estimate of whitening filter of a process noise
  • 6. Analysis of economic behavior with estimated impulse responses to model inputs
  • 7. Practical estimate of eigenvalues impulse responses in unit circle
  • 8. Observability, controllability and minimal realization of a dynamic system
  • 9. Derivation of a solution to a linear-quadratic control task (Hamiltonian, quadratic functional and necessary conditions of optimality)
  • 10. Derivation of a feedback as a tool to control economic system represented by an identified dynamic model (feedback represented by a Riccati equation and direct component of control)
  • 11.Explanation of optimal control algorithm and its use to control or stabilize real macroeconomic system represented by a model
  • 12. Solution of practical optimal control/stabilization tasks of US economy (fiscal policy, monetary policy, mixed fiscal and monetary policy)
  • 13. Assignment of a task to control/stabilize US economy in its characteristic periods of post-war macroeconomic control or stabilization of US economy as an individual assignment for seminar papers for students.
Literature
  • PINDYCK, Robert S. and Daniel L. RUBINFELD. Econometric models and economic forecasts. 4th ed. Boston: Irwin, 1997, xx, 634. ISBN 0070502080. info
  • D. Kendrick: Stochastic control for economic models, New York: McGraw-Hill, 1981, pp. i–xiii, 1–242
Assessment methods
semestral project and its defense as a part of exam, oral exam
Language of instruction
Czech
Further Comments
The course is taught annually.
  • Enrolment Statistics (recent)
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