IMPLICIT EQUILIBRIUM DYNAMICS
Alfredo Medio () and
Macroeconomic Dynamics, 2012, vol. 16, issue 04, 518-555
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.
References: Add references at CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
https://journals.cambridge.org/abstract_S1365100510000738 link to article abstract page (text/html)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:cup:macdyn:v:16:y:2012:i:04:p:518-555_00
Access Statistics for this article
More articles in Macroeconomic Dynamics from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Keith Waters ().