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A Geometric Approach to Local Indeterminacy & Local Bifurcations in Three-Dimensional Dynamical Systems

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Author Info

  • Barinci, J.-P.
  • Drugeon, J.-P.

Abstract

In discrete three-dimensional dynamical systems frequently encountered in dynamic general equilibrium models, local indeterminacy -sunspot equilibria - and local bifurcations -endogenous deterministic fluctuations - issues are quite difficult to handle. Pitfalls derive from the fact that in generic models a standard analysis of the spectrum of the 3 x 3 Jacobian matrix, though achievable, usually turns out to be of no use. It is the purpose of this contribution to develop geometrical tools which avoid cumbersome computations or numerical investigations. Rather tractable necessary and sufficient conditions are provided, that ensure the occurence of generic local bifurcations and also a useful "toolkit" for assessing the local determinacy / indeterminacy of intertemporal equilibria. The usefulness of this method is finally illustrated in a productive model of overlapping generations with elastic labour supply.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Papiers d'Economie Mathématique et Applications with number 1999.40.

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Length: 33 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:fth:pariem:1999.40

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Keywords: BUSINESS CYCLES ; MATHEMATICAL ANALYSIS ; ECONOMIC GROWTH;

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