Expected Utility in Models with Chaos
In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X ! X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the backward dynamics xt = f(xt+1). If f represents the forward/backward dynamics, the set of equilibria forms a direct/inverse limit space. We use a natural f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is a natural ¾-invariant measure where ¾ is the shift operator. We utilize this framework in the cash-in-advance model of money where f is the backward map to calculate expected utility when equilibria are chaotic.
|Date of creation:||Oct 2007|
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- Robert E. Lucas Jr. & Nancy L. Stokey, 1984.
"Money and Interest in Cash-In-Advance Economy,"
628, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Handbook of Macroeconomics,
in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 26, pages 1671-1745
- 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.
- David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
- 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.
- A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
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