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7 - Subsystems and sensitivity analysis of the KMG model

Published online by Cambridge University Press:  22 September 2009

Carl Chiarella
Affiliation:
University of Technology, Sydney
Peter Flaschel
Affiliation:
Universität Bielefeld, Germany
Reiner Franke
Affiliation:
Technische Universität Wien, Austria
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Summary

Introduction

The main result of chapter 4 was the mathematical proposition that the steady state of the six-dimensional KMG model is locally asymptotically stable if certain reaction parameters are sufficiently small. The statement may suggest that these coefficients are destabilizing, in the sense that higher values cause the system to lose its stability. It is almost hopeless, however, to extend the mathematical analysis such that it can verify or falsify this conjecture. Therefore, if we want to gain deeper insights into the stabilizing or destabilizing role of the parameters, we have to turn to a different approach. Generally, we may choose between the following two options: either the mathematical treatment is restricted to a suitable low-dimensional submodel of the full system, or the KMG model is maintained as it stands and a numerical investigation is conducted.

Sections 7.2 to 7.4 are mainly, though not exclusively, devoted to the first alternative. Three two- or three-dimensional subdynamics are considered in turn. In short, these are the inventory dynamics (section 7.2), the real wage dynamics (section 7.3) and the monetary dynamics (section 7.4). These models, or at least the feedback mechanisms portrayed by them, are rather well known in the literature on Keynesian macrodynamics. The submodels will thus make more precise how the whole KMG model is rooted in the Keynesian tradition.

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Chapter
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Foundations for a Disequilibrium Theory of the Business Cycle
Qualitative Analysis and Quantitative Assessment
, pp. 287 - 368
Publisher: Cambridge University Press
Print publication year: 2005

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