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Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

Author

Listed:
  • 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.

Suggested Citation

  • Laura Gardini & Cars Hommes & Fabio Tramontana & Robin de Vilder, 2008. "Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models," Working Papers 0806, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  • Handle: RePEc:urb:wpaper:08_06
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.
    3. Zhang, Yan & Chen, Yan, 2012. "Tariff And Equilibrium Indeterminacy: A Global Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 394-410, November.
    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. 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.
    6. 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.
    7. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
    8. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    9. 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.
    10. Tomoo Kikuchi & George Vachadze, 2018. "Minimum investment requirement, financial market imperfection and self-fulfilling belief," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 305-332, April.
    11. 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.
    12. Aloisio Araujo & Wilfredo L. Maldonado & Diogo Pinheiro & Alberto A. Pinto & Mohammad Choubdar Soltanahmadi, 2021. "Refinement of dynamic equilibrium using small random perturbations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(3), pages 258-283, September.
    13. Anna Agliari & Ahmad Naimzada & Nicolò Pecora, 2017. "Nonlinear monetary policy rules in a pure exchange overlapping generations model," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1181-1203, November.

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    More about this item

    Keywords

    forward and backward dynamics; chaos; homoclinic orbit; snap-back repellor; sunspot equilibria; overlapping generations models.;
    All these keywords.

    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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