Forward and Backward Dynamics in implicitly defined Overl apping Generations Models

Laura Gardini , Cars Hommes , Fabio Tramontana , Robin de Vilder

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dy-namics is well defined. 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 homo-clinic orbit (a "snap-back rep eller"), 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.

Mots clés: E32; C62; C0 2; Forward and backward dynamics; Chaos; Homoclinic orbit; Snap-back repellor; Sunspot equilibria; Overlapping generations models

Domaines: Économie et finance quantitative [q-fin]

Laura Gardini, Cars Hommes, Fabio Tramontana, Robin de Vilder. Forward and Backward Dynamics in implicitly defined Overl apping Generations Models. Journal of Economic Behavior and Organization, 2009, 71 (2), pp.110. ⟨10.1016/j.jebo.2008.09.010⟩. ⟨hal-00693817⟩