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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)

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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://www.lerner.udel.edu/economics/WorkingPapers/2006/UDWP2006-03.pdf
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Publisher 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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Postal: Purnell Hall, Newark, Delaware 19716
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Web page: http://www.lerner.udel.edu/departments/economics/
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Related research
Keywords: cash-in-advance; overlapping generations; chaos; inverse limits;

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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  1. David R. Stockman & Judy Kennedy & James A. Yorke, 2005. " Inverse Limits and Models with Ill-Defined Forward Dynamics," Working Papers 05-06, University of Delaware, Department of Economics. [Downloadable!]
  2. 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)
  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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