Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The theory of economic policy and the linear model
- 3 Optimal-policy design
- 4 Uncertainty and risk
- 5 Risk aversion, priorities and achievements
- 6 Non-linear optimal control
- 7 The linear rational-expectations model
- 8 Policy design for rational-expectations models
- 9 Non-cooperative, full-information dynamic games
- 10 Incomplete information, bargaining and social optima
- Notes
- References
- Index
6 - Non-linear optimal control
Published online by Cambridge University Press: 17 September 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The theory of economic policy and the linear model
- 3 Optimal-policy design
- 4 Uncertainty and risk
- 5 Risk aversion, priorities and achievements
- 6 Non-linear optimal control
- 7 The linear rational-expectations model
- 8 Policy design for rational-expectations models
- 9 Non-cooperative, full-information dynamic games
- 10 Incomplete information, bargaining and social optima
- Notes
- References
- Index
Summary
INTRODUCTION
So far we have been concerned with the economic-policy aspects of linear models. But the majority of econometric models which are used for forecasting, policy simulation and optimisation in the economic-policy process are actually non-linear. In principle this can create a number of difficulties because the analytical results of linear systems are no longer available.
Solutions to the problem of designing economic policy when the model is non-linear have taken two basic forms:
(i) A linearisation approach by which the apparatus of linear theory is then applied to the linear approximation.
(ii) A direct approach by which the problem of finding the minimum of an objective function subject to the non-linear model is treated as non-linear constrained optimisation, or non-linear programming problem.
For the first approach the main problems are how to generate the linearisation and how good an approximation the linearisation is. For the second approach the main difficulties are concerned with the type of algorithm which is used to find the minimum of the objective function and what kind of derivative information is needed.
The examination of non-linear models does not throw any fresh light upon the problems of economic policy. But since most of the models in practical use are non-linear it is worth considering how they can be handled and how the results which are obtained can be related to the results obtained for linear systems.
- Type
- Chapter
- Information
- Optimal Control, Expectations and Uncertainty , pp. 105 - 116Publisher: Cambridge University PressPrint publication year: 1989