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Forward and Backward Dynamics in implicitly defined Overlapping Generations Models

Author

Listed:
  • Gardini, L.

    (University of Urbino)

  • Hommes, C.H.

    () (University of Amsterdam)

  • Tramontana, F.

    (University of Ancona)

  • de Vilder, R.

    (University of Amsterdam)

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 (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.

Suggested Citation

  • Gardini, L. & Hommes, C.H. & Tramontana, F. & de Vilder, R., 2009. "Forward and Backward Dynamics in implicitly defined Overlapping Generations Models," CeNDEF Working Papers 09-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:09-02
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tramontana, Fabio & Westerhoff, Frank & Gardini, Laura, 2010. "On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders," Journal of Economic Behavior & Organization, Elsevier, vol. 74(3), pages 187-205, June.
    2. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
    3. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
    4. 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.
    5. 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;Associazione per la Matematica, vol. 37(1), pages 159-179, April.
    6. repec:spr:joevec:v:28:y:2018:i:2:d:10.1007_s00191-017-0510-z is not listed on IDEAS
    7. repec:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0522-8 is not listed on IDEAS
    8. Zhang, Yan & Chen, Yan, 2012. "Tariff And Equilibrium Indeterminacy: A Global Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 394-410, November.
    9. 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.
    10. Davide La Torre & Simone, Marsiglio & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-Similar Measures in Multi-Sector Endogenous Growth Models," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201509, University of Turin.
    11. 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.

    More about this item

    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
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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