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Backward dynamics, inverse limits and global sunspots


  • Alfredo Medio


In economic theory, there exist many important problems whose mathematical formulation is a function relating the current value of a certain state variable to its (accurately forecast) future value. The most widely studied class of such problems is the Overlapping generations (OLG) models in their innumerable variations are probably the best known example of such problems. A difficulty arises when, for certain specifications of ``fundamentals"", the map relating future to present values of the state variable is many—to—one and therefore the dynamics defined by the iterates of the map is backward in time. Since in real life agents are concerned about the future not the past, one would like to use the investigation of backward-moving dynamical models to understand the general properties of the forward dynamics associated with them. The purpose of this paper is to provide a complete characterization of this problem by means of certain concepts and methods known in the mathematical literature as ``inverse limits"". After a concise introduction to these ideas relatively little known in economics, the paper provides a systematic application to a basic OLG model. In this context, we also provide an analysis of global sunspots (i.e., sunspots that are not necessarily located near a stationary state or a periodic orbit), arising in OLG models characterized by backward dynamics.

Suggested Citation

  • Alfredo Medio, 2004. "Backward dynamics, inverse limits and global sunspots," Computing in Economics and Finance 2004 90, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:90

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    References listed on IDEAS

    1. Finn E. Kydland & Edward C. Prescott, 1996. "The Computational Experiment: An Econometric Tool," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 69-85, Winter.
    2. Johann Peter Murmann & Thomas Brenner, 2003. "The Use of Simulations in Developing Robust Knowledge about Causal Processes: Methodological Considerations and an Application to Industrial Evolution," Computing in Economics and Finance 2003 66, Society for Computational Economics.
    3. Machlup, Fritz, 1978. "Methodology of Economics and Other Social Sciences," Elsevier Monographs, Elsevier, edition 1, number 9780124645509 edited by Shell, Karl.
    4. Franco Malerba & Luigi Orsenigo, 2002. "Innovation and market structure in the dynamics of the pharmaceutical industry and biotechnology: towards a history-friendly model," Industrial and Corporate Change, Oxford University Press, vol. 11(4), pages 667-703, August.
    5. Schwerin, Joachim & Werker, Claudia, 2003. "Learning innovation policy based on historical experience," Structural Change and Economic Dynamics, Elsevier, vol. 14(4), pages 385-404, December.
    6. Dominique Foray & Robin Cowan, 2002. "Evolutionary economics and the counterfactual threat: on the nature and role of counterfactual history as an empirical tool in economics," Journal of Evolutionary Economics, Springer, vol. 12(5), pages 539-562.
    7. Malerba, Franco, et al, 1999. "'History-Friendly' Models of Industry Evolution: The Computer Industry," Industrial and Corporate Change, Oxford University Press, vol. 8(1), pages 3-40, March.
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    More about this item


    backward dynamics; inverse limits; sunspots;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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