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Chaotic Equilibria in Models with Ill-Defined Forward Dynamics

Author

Listed:
  • David Stockman

    (Department of Economics,University of Delaware)

  • Judy Kennedy

    (Department of Mathematics,University of Delaware)

Abstract

Some economic models like the cash-in-advance model of money or overlapping generations model have the property that the dynamics are ill-defined going forward in time, but well-defined going backward in time. In such instances, what does it mean for an ill-defined dynamical system to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, we provide a definition of chaotic that is in the spirit of Devaney for a dynamical system with ill-defined forward dynamics. We utilize the theory of inverse limits to provide necessary and sufficient conditions for such a dynamical system to be chaotic

Suggested Citation

  • David Stockman & Judy Kennedy, 2006. "Chaotic Equilibria in Models with Ill-Defined Forward Dynamics," Working Papers 06-03, University of Delaware, Department of Economics.
    • Handle: RePEc:dlw:wpaper:06-03
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    File URL: http://graduate.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2006/UDWP2006-03.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. 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.
    3. 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.
    4. 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.
    5. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    6. David R. Stockman & Judy Kennedy & James A. Yorke, 2005. " Inverse Limits and Models with Ill-Defined Forward Dynamics," Working Papers 05-06, University of Delaware, Department of Economics.
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    Cited by:

    1. Mendes, Diana A. & Mendes, Vivaldo M., 2008. "Stability analysis of an implicitly defined labor market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3921-3930.

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    More about this item

    Keywords

    cash-in-advance; overlapping generations; chaos; inverse limits;
    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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