Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

Laura Gardini (), Cars Hommes, Fabio Tramontana and Robin de Vilder ()
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Robin de Vilder: Department of Mathematics, University of Amsterdam

No 806, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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.

Keywords: forward and backward dynamics; chaos; homoclinic orbit; snap-back repellor; sunspot equilibria; overlapping generations models. (search for similar items in EconPapers)
JEL-codes: C02 C62 E32 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2008, Revised 2008
New Economics Papers: this item is included in nep-dge and nep-mac
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http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_06.pdf First version, 2008 (application/pdf)

Related works:
Journal Article: Forward and backward dynamics in implicitly defined overlapping generations models (2009)
Working Paper: Forward and Backward Dynamics in implicitly defined Overlapping Generations Models (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:urb:wpaper:08_06

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