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Inverse Limits and Models with Ill-Defined Forward Dynamics

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Author Info

  • David R. Stockman

    ()
    (Department of Economics,University of Delaware)

  • Judy Kennedy

    ()
    (Department of Mathematical Science, University of Delaware.)

  • James A. Yorke

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

Abstract

Some economic models like the cash-in-advance model of money have the property that the dynamics are ill-defined going forward in time, but well-defined going backward in time. In this paper, we apply the theory of inverse limits to characterize topologically all possible solutions to 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 ill-defined 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 complex dynamics.

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File URL: http://graduate.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2005/UDWP2005-06.pdf
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Bibliographic Info

Paper provided by University of Delaware, Department of Economics in its series Working Papers with number 05-06.

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Length: 45 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:dlw:wpaper:05-06

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Web page: http://www.lerner.udel.edu/departments/economics/department-economics/
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Related research

Keywords: cash-in-advance; chaos; inverse limits; continuum theory.;

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References

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  1. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
  2. Robert E. Lucas, Jr. & Nancy L. Stokey, 1985. "Money and Interest in a Cash-in-Advance Economy," NBER Working Papers 1618, National Bureau of Economic Research, Inc.
  3. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  4. 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.
  5. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer, vol. 4(3), pages 345-80.
  6. 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.
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Cited by:
  1. David Stockman & Judy Kennedy, 2006. "Chaotic Equilibria in Models with Ill-Defined Forward Dynamics," Working Papers 06-03, University of Delaware, Department of Economics.

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