Inverse Limits and Models with Ill-Defined Forward Dynamics
AbstractSome 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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Bibliographic InfoPaper provided by University of Delaware, Department of Economics in its series Working Papers with number 05-06.
Length: 45 pages
Date of creation: 2005
Date of revision:
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Web page: http://www.lerner.udel.edu/departments/economics/department-economics/
More information through EDIRC
cash-in-advance; chaos; inverse limits; continuum theory.;
Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
- E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
This paper has been announced in the following NEP Reports:
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- 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.
- David Stockman & Judy Kennedy, 2006. "Chaotic Equilibria in Models with Ill-Defined Forward Dynamics," Working Papers, University of Delaware, Department of Economics 06-03, University of Delaware, Department of Economics.
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