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Forward and Backward Dynamics in implicitly defined Overl apping Generations Models

Author

Listed:
  • Laura Gardini

    ()

  • Cars Hommes
  • Fabio Tramontana
  • Robin de Vilder

Abstract

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dy-namics is well defined. We derive properties of the global forward equilibrium paths based on properties of the backward dynamics. We propose the framework of iterated function systems (IFS) to describe the set of forward equilibria and apply the IFS framework to a one-and a two-dimensional version of the overlapping generations (OLG)-model. We show that if the backward dynamics is chaotic and has a homo-clinic orbit (a "snap-back rep eller"), the set of forward equilibrium paths converges to a fractal attractor. Forward equilibria may be interpreted as sunspot equilibria, where a random sunspot sequence determines equilibrium selection at each date.

Suggested Citation

  • Laura Gardini & Cars Hommes & Fabio Tramontana & Robin de Vilder, 2009. "Forward and Backward Dynamics in implicitly defined Overl apping Generations Models," Post-Print hal-00693817, HAL.
  • Handle: RePEc:hal:journl:hal-00693817
    DOI: 10.1016/j.jebo.2008.09.010
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00693817
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    File URL: https://hal.archives-ouvertes.fr/hal-00693817/document
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    Cited by:

    1. Arifovic, Jasmina & Hommes, Cars & Salle, Isabelle, 2019. "Learning to believe in simple equilibria in a complex OLG economy - evidence from the lab," Journal of Economic Theory, Elsevier, vol. 183(C), pages 106-182.

    More about this item

    Keywords

    E32; C62; C0 2; Forward and backward dynamics; Chaos; Homoclinic orbit; Snap-back repellor; Sunspot equilibria; Overlapping generations models;

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C0 - Mathematical and Quantitative Methods - - General

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