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Chaotic Equilibria in Models with Ill-Defined Forward Dynamics

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Author Info

  • 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

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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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Bibliographic Info

Paper provided by University of Delaware, Department of Economics in its series Working Papers with number 06-03.

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Length: 18 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:dlw:wpaper:06-03

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Web page: http://www.lerner.udel.edu/departments/economics/department-economics/
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Keywords: cash-in-advance; overlapping generations; chaos; inverse limits;

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References

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  1. 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.
  2. David R. Stockman & Judy Kennedy & James A. Yorke, 2005. " Inverse Limits and Models with Ill-Defined Forward Dynamics," Working Papers, University of Delaware, Department of Economics 05-06, University of Delaware, Department of Economics.
  3. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 31(5), pages 1633-1671, May.
  4. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, 9.
  5. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 22(7), pages 1117-1137, May.
  6. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  7. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
  8. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer, Springer, vol. 4(3), pages 345-80.
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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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