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Inverse Limits and Models with Backward Dynamics

  • 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)

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.

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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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Paper provided by University of Delaware, Department of Economics in its series Working Papers with number 06-12.

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Length: 38 pages
Date of creation: 2006
Date of revision:
Publication status: Forthcoming in Topology and Its Applications.
Handle: RePEc:dlw:wpaper:06-12
Contact details of provider: Postal: Purnell Hall, Newark, Delaware 19716
Phone: (302) 831-2565
Fax: (302) 831-6968
Web page: http://www.lerner.udel.edu/departments/economics/department-economics/

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  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. 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. 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.
  4. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
  5. 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.
  6. Bastiaanssen, W. G. M. & van Dam, J. C. & Droogers, P., 2003. "Introduction," IWMI Books, Reports H043801, International Water Management Institute.
  7. 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.
  8. repec:cup:cbooks:9780521484619 is not listed on IDEAS
  9. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer, vol. 4(3), pages 345-80.
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