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Forward and backward dynamics in implicitly defined overlapping generations models

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  • Gardini, Laura
  • Hommes, Cars
  • Tramontana, Fabio
  • de Vilder, Robin

Abstract

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dynamics 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 (IFSs) 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 71 (2009)
Issue (Month): 2 (August)
Pages: 110-129

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Handle: RePEc:eee:jeborg:v:71:y:2009:i:2:p:110-129

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Web page: http://www.elsevier.com/locate/jebo

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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. 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.
  2. 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.
  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. 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.
  5. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
  6. Luca Gori & Mauro Sodini, 2014. "Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes," Decisions in Economics and Finance, Springer, vol. 37(1), pages 159-179, April.
  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. Zhang, Yan & Chen, Yan, 2009. "Tariff and Equilibrium Indeterminacy - A Global Analysis," MPRA Paper 18296, University Library of Munich, Germany.

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