Control Theory Methods in Economics

By: Jati Sengupta, Phillip Fanchon

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Hardcover | 1 April 2002

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272 Pages

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Control theory methods in economics have historically developed over three phases. The first involved basically the feedback control rules in a deterministic framework which were applied in macrodynamic models for analyzing stabilization policies. The second phase raised the issues of various types of inconsistencies in deterministic optimal control models due to changing information and other aspects of stochasticity. Rational expectations models have been extensively used in this plan to resolve some of the inconsistency problems. The third phase has recently focused on the various aspects of adaptive control. where stochasticity and information adaptivity are introduced in diverse ways e.g .â¢ risk adjustment and risk sensitivity of optimal control, recursive updating rules via Kalman filtering and weighted recursive least squares and variable structure control methods in nonlinear framework. Problems of efficient econometric estimation of optimal control models have now acquired significant importance. This monograph provides an integrated view of control theory methods, synthesizing the three phases from feedback control to stochastic control and from stochastic control to adaptive control. Aspects of econometric estimation are strongly emphasized here, since these are very important in empirical applications in economics.

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Published: 10th October 2012

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Preface	p. ix
Introduction to Control Theory
Transition from the calculus of variations to optimal control	p. 1
Transition from theory to practice	p. 3
References
Continuous Time Models
Overview of control problems	p. 9
Observability and controllability	p. 10
Stability analysis	p. 15
The maximum principle	p. 32
Constraints	p. 39
Example 1; A limit pricing model	p. 41
Example 2; reaching a steady state cycle	p. 54
References
Discrete Time Models
Introduction	p. 63
General deterministic and discrete control problems	p. 63
The linear quadratic problem	p. 68
Analytic solution of the Riccati equation	p. 80
Equivalent dynamic equations	p. 83
Discrete control of nonlinear systems	p. 87
Observability and observers	p. 89
Economic examples	p. 89
References
Stochastic Control Theory
Introduction	p. 97
Stochastic processes under control	p. 97
Economic applications	p. 102
Kalman filtering methods	p. 117
Concluding remarks	p. 143
References
Economic Implications of Stochastic Control
Introduction	p. 147
Time inconsistency problems	p. 147
Short-run vs. long-run optimality	p. 152
Model of adjustment costs with rational expectations	p. 158
An application to new growth theory: dynamic adjustments with learning by doing	p. 160
Concluding remarks	p. 175
References
Variable Structure Systems
Introduction	p. 181
The variable structure control formulation	p. 181
A VSC approximation of an optimal control law	p. 191
Example; The expectations-augmented Phillips relation	p. 193
Concluding remarks	p. 207
References
Risk Sensitivity, Adjustment of Control and Estimation
Introduction	p. 211
Learning process in differential games	p. 211
Adjustment costs in portfolio models	p. 213
Econometric estimation of controlled systems	p. 232
Estimating transversality conditions	p. 239
Concluding remarks	p. 247
References
Appendix	p. 249
Index	p. 253
Table of Contents provided by Syndetics. All Rights Reserved.

Control Theory Methods in Economics

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