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Business–Cycle Models and the Dangers of Linearizing

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Abstract

This paper studies the consequences of linearizing nonlinear business–cycle models near their interior steady state. It is shown that dynamic objects, created for example in a Bogdanov-Takens bifurcation, may be lost in the linearization procedure. Sufficient conditions are provided ensuring the absence of various dynamic features in the nonlinear version of the model.

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Authors and Affiliations

  1. Department of Mathematics, Warwick University, Warwick, UK

    O. Kozlovski (Professor) & S. van Strien (Professor)

  2. GREQAM and Department of Economics, Université de la Mediterranée Aix-Marseille II, Marseille, France

    P. Pintus (Professor)

  3. DELTA-CNRS-EHESS-ENS, Paris, France

    R. de Vilder (Professor Researcher)

  4. Department of Mathematics, University of Amsterdam, Amsterdam, Netherlands

    R. de Vilder (Professor Researcher)

Authors
  1. O. Kozlovski
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  2. P. Pintus
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  3. S. van Strien
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  4. R. de Vilder
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Additional information

The authors thank Andy Atkeson and Hal Cole for useful comments and suggestions. They also thank three anonymous referees who have helped to greatly improve the exposition of this paper.

Part of this research was done while the author was affiliated with the University of Cergy Pontoise (THEMA) and during visits at DELTA.

Part of this research has been done while the author was working as a Marie Curie Fellow at INSEE/CREST and during visits at the University of Warwick.

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Kozlovski, O., Pintus, P., Strien, S.v. et al. Business–Cycle Models and the Dangers of Linearizing. J Optim Theory Appl 128, 333–353 (2006). https://doi.org/10.1007/s10957-006-9019-6

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  • DOI: https://doi.org/10.1007/s10957-006-9019-6

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