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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,)

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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://www.lerner.udel.edu/economics/WorkingPapers/2005/UDWP2005-06.pdf
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Publisher 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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Postal: Purnell Hall, Newark, Delaware 19716
Fax: (302) 831-6968
Web page: http://www.lerner.udel.edu/economics/
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Related research
Keywords: cash-in-advance chaos inverse limits continuum theory.

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September. [Downloadable!] (restricted)
  3. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer, vol. 4(3), pages 345-80.
  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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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. [Downloadable!]
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