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History Dependence and Global Dynamics in Models with Multiple Equilibria


  • Christophe Deissenberg, Gustav Feichtinger, Willi Semmler and Franz Wirl


A wealth of literature, reviewed in the first section of this paper, is concerned with the occurence of multiple equilibria in economic optimization models and with the resulting history dependence of optimal solutions. Typically, the existence of multiple equilibria is associated with market imperfections, expectational phenomena, and the like. Less known is that this phenomenon is also possible in efficient, perfect foresight intertemporal optimization models, and that: (1) it can also occur in strictly concave efficient models; (2) the threshold separating the optimal trajectories towards the one or the other long-run optimal outcome does not necessary coincide with an unstable steady-state; (3) unstable steady-states may generically be non-optimal; (4) the policy function at the thresholds is frequently not continuous; and (5) local stability analysis may yield information on the occurence of these properties. In the paper, we demonstrate and discuss these properties in the case of a one-dimensional state space, with an extension to the two-dimensional case. Since in most cases, the first four properties (1)-(4) cannot be addressed analytically, we present three numerical methods for their investigation.

Suggested Citation

  • Christophe Deissenberg, Gustav Feichtinger, Willi Semmler and Franz Wirl, 2001. "History Dependence and Global Dynamics in Models with Multiple Equilibria," Computing in Economics and Finance 2001 257, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:257

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    References listed on IDEAS

    1. repec:cup:etheor:v:13:y:1997:i:3:p:430-61 is not listed on IDEAS
    2. Overbeck, Ludger & Rydén, Tobias, 1997. "Estimation in the Cox-Ingersoll-Ross Model," Econometric Theory, Cambridge University Press, vol. 13(03), pages 430-461, June.
    3. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
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    Cited by:

    1. Andreas Schäfer & Thomas Steger, 2014. "Journey into the Unknown? Economic Consequences of Factor Market Integration under Increasing Returns to Scale," Review of International Economics, Wiley Blackwell, vol. 22(4), pages 783-807, September.
    2. Anne Sophie Crépin, 2003. "Management Challenges for Multiple-Species Boreal Forests," Working Papers 2003.106, Fondazione Eni Enrico Mattei.
    3. Marschall, Paul, 2001. "Lernen und Lebensstilwandel in Transformationsökonomien," Wirtschaftswissenschaftliche Diskussionspapiere 07/2001, University of Greifswald, Faculty of Law and Economics.
    4. Sun, Yixiao X, 2005. "Estimation and Inference in Panel Structure Models," University of California at San Diego, Economics Working Paper Series qt5tf1231k, Department of Economics, UC San Diego.
    5. Löfgren, Åsa, 2003. "Habit Formation in the Environmental Quality: Dynamic Optimal Environmental Taxation," Working Papers in Economics 92, University of Gothenburg, Department of Economics.
    6. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    7. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
    8. Y. Hossein Farzin & Ken-Ichi Akao, 2006. "When is it Optimal to Exhaust a Resource in a Finite Time?," Working Papers 2006.23, Fondazione Eni Enrico Mattei.

    More about this item


    multiple equilibria;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium


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