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Chaotic equilibria in models with backward dynamics

  • Kennedy, Judy A.
  • Stockman, David R.

Some economic models like the cash-in-advance model of money or overlapping generations model have the property that the dynamical system characterizing equilibria in the model are multi-valued going forward in time, but single-valued going backward in time, i.e., the model or dynamical system has backward dynamics. In such instances, what does it mean for a dynamical system (set-valued) to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, we provide a definition of chaos that is in the spirit of Devaney for a dynamical system with backward 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.sciencedirect.com/science/article/B6V85-4NMC861-5/1/b5fc420e3f4fdfb4ed329744370dc5c0
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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 3 (March)
Pages: 939-955

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:939-955
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Working Paper Series, Macroeconomic Issues WP-96-16, Federal Reserve Bank of Chicago.
  2. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  3. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
  4. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
  5. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  6. 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.
  7. 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.
  8. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
  9. 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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