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IMPLICIT EQUILIBRIUM DYNAMICS

Published online by Cambridge University Press:  03 November 2011

Alfredo Medio  and
Brian Raines
Alfredo Medio*
Affiliation:
University of Udine
Brian Raines
Affiliation:
Baylor University
*
Address correspondence to: Alfredo Medio, 54 Route de la Pauvetta, 06140 Tourrettes Sur Loup, France; e-mail: alfredomedio@gmail.com
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Abstract

We discuss the problem known in economics as backward dynamics occurring in models of perfect foresight, intertemporal equilibrium described mathematically by implicit difference equations. In a previously published paper [Journal of Economic Dynamics and Control 31 (2007), 1633–1671], we showed that by means of certain mathematical methods and results known as inverse limits theory it is possible to establish a correspondence between the backward dynamics of a noninvertible map and the forward dynamics of a related invertible map acting on an appropriately defined space of sequences, each of whose elements corresponds to an intertemporal equilibrium. We also proved the existence of different types of topological attractors for one-dimensional models of overlapping generations. In this paper, we provide an extension of those results, constructing a Lebesgue-like probability measure on spaces of infinite sequences that allows us to distinguish typical from exceptional dynamical behaviors in a measure–theoretical sense, thus proving that all the topological attractors considered in MR07 are also metric attractors. We incidentally also prove that the existence of chaos (in the Devaney–Touhey sense) backward in time implies (and is implied by) chaos forward in time.

Keywords

Backward DynamicsOverlapping GenerationsInverse LimitsAttractorsLebesgue-Like Measure

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Type
Articles
Information
Macroeconomic Dynamics , Volume 16 , Issue 4 , September 2012 , pp. 518 - 555
Copyright
Copyright © Cambridge University Press 2011

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