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Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models

  • 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)

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 Function: First version, 2008
Download Restriction: no

Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini 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
Contact details of provider: Web page: http://www.econ.uniurb.it/

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