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The inverse limits approach to chaos

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  • Kennedy, Judy
  • Stockman, David R.
  • Yorke, James A.

Abstract

When analyzing a dynamic economic model, one fundamental question is are the dynamics simple or chaotic? Inverse limits, as an area of topology, has its origins in the 1920s and since the 1950s has been very useful as a means of constructing "pathological" continua. However, since the 1980s, there is a growing literature linking dynamical systems with inverse limits. In this paper, we review some results from this literature and apply them to the cash-in-advance model of money. 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

  • Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:5-6:p:423-444
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    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. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
    2. David R. Stockman, 2008. "Uniform Measures On Inverse Limit Spaces," Working Papers 08-25, University of Delaware, Department of Economics.
    3. 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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