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Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

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Author Info

  • Laura Gardini

    ()
    (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

  • Cars Hommes

    ()
    (CeNDEF, Department of Quantitative Economics, University of Amsterdam)

  • Fabio Tramontana

    ()
    (Università Politecnica delle Marche & Dipartimento di Economia e Metodi Quantitativi, Università di Urbino)

  • Robin de Vilder

    ()
    (Department of Mathematics, University of Amsterdam)

Abstract

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely de fined, while the backward dynamics is well de fined. 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 homoclinic orbit (a "snap-back repeller") 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.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_06.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 0806.

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Length: 37 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:urb:wpaper:08_06

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Web page: http://www.econ.uniurb.it/
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Related research

Keywords: forward and backward dynamics; chaos; homoclinic orbit; snap-back repellor; sunspot equilibria; overlapping generations models.;

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References

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Citations

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Cited by:
  1. Gori, Luca & Sodini, Mauro, 2012. "Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes," MPRA Paper 35942, University Library of Munich, Germany.
  2. Zhang, Yan & Chen, Yan, 2012. "Tariff And Equilibrium Indeterminacy: A Global Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 394-410, November.
  3. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
  4. Fabio Tramontana & Frank Westerhoff & Laura Gardini, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Working Papers 1005, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2010.
  5. Stockman, David R., 2011. "Chaos and capacity utilization under increasing returns to scale," Journal of Economic Behavior & Organization, Elsevier, vol. 77(2), pages 147-162, February.
  6. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
  7. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers 157, Institute of Public Policy and Public Choice - POLIS.
  8. Raines, Brian E. & Stockman, David R., 2010. "Chaotic sets and Euler equation branching," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1173-1193, November.

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