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Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

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Author Info
Laura Gardini () (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))
Cars Hommes () (CeNDEF, Department of Quantitative Economics, University of Amsterdam)
Fabio Tramontana () (Università Politecnica delle Marche & Dipartimento di Economia e Metodi Quantitativi, Università di Urbino)
Robin de Vilder () (Department of Mathematics, University of Amsterdam)

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Abstract

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely de fined, while the backward dynamics is well de fined. We derive properties of the global forward equilibrium paths based on properties of the backward dynamics. We propose the framework of iterated function systems (IFS) to describe the set of forward equilibria, and apply the IFS framework to a one- and a two-dimensional version of the overlapping generations (OLG)-model. We show that, if the backward dynamics is chaotic and has a homoclinic orbit (a "snap-back repeller") the set of forward equilibrium paths converges to a fractal attractor. Forward equilibria may be interpreted as sunspot equilibria, where a random sunspot sequence determines equilibrium selection at each date.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_06.pdf
File Format: application/pdf
File Function: First version, 2008
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Publisher Info
Paper provided by University of Urbino Carlo Bo, Department of Economics in its series Working Papers with number 0806.

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Length: 37 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:urb:wpaper:08_06

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Web page: http://www.econ.uniurb.it/
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Related research
Keywords: forward and backward dynamics; chaos; homoclinic orbit; snap-back repellor; sunspot equilibria; overlapping generations models.;

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Find related papers by JEL classification:
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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This page was last updated on 2009-11-17.

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