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Inverse Limits and Models with Backward Dynamics

Author

Listed:
  • David Stockman

    (Department of Economics,University of Delaware)

  • Judy Kennedy

    (Department of Mathematics,University of Delaware)

  • James Yorke

    (Institute for Physical Science and Technology, University of Maryland)

Abstract

Some economic models like the cash-in-advance model of money have the property that the dynamical system characterizing equilibria is multi-valued going forward in time, but single-valued going backward in time, i.e., the model has backward dynamics. In this paper, we apply the theory of inverse limits to characterize topologically the set of equilibria in a dynamic economic model with this property. We show that such techniques are particularly well-suited for analyzing the dynamics going forward in time even though the dynamics are multi-valued in this direction. In particular, we analyze the inverse limit of the cash-in-advance model of money and illustrate how information about the inverse limit is useful for detecting or ruling out complicated dynamics.

Suggested Citation

  • David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
    • Handle: RePEc:dlw:wpaper:06-12
    as

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    File URL: http://graduate.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2006/UDWP2006-12.pdf
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    References listed on IDEAS

    as
    1. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    2. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    3. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 345-380.
    4. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
    5. Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
    6. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
    2. David R. Stockman & Judy Kennedy & Brian Raines, 2007. "Expected Utility in Models with Chaos," Working Papers 07-16, University of Delaware, Department of Economics.

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    More about this item

    Keywords

    backward dynamics; chaos; inverse limits; continuum theory; cash-in advance;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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