Forward and backward dynamics in implicitly defined overlapping generations models

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dynamics 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 (IFSs) 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

JEL classification codes: E32; C62; C02