Singular Invariant Markov Equilibrium in Stochastic Overlapping Generations Models

This paper examines the invariant Markov distribution associated with the rational expectations

equilibrium in multi-period stochastic overlapping generations models under

pure exchange. We prove that a simple linear iterated function system can generate the

invariant distribution in these models under small discrete aggregate shocks. We provide

sufficient conditions for the linear iterated function system to generate a singular invariant

measure. We also characterize the set of economies which satisfy the sufficient conditions.

The attractors of the singular invariant measure in our models exhibit fractal patterns.

The existence of the linear iterated function system implies that an algorithm based on its

structure can allow computing equilibria in long-period stochastic overlapping generations

models with heterogeneity.