Singular Invariant Markov Equilibrium in Stochastic Overlapping Generations Models

<div>This paper examines the invariant Markov distribution associated with the rational expectations</div><div>equilibrium in multi-period stochastic overlapping generations models under</div><div>pure exchange. We prove that a simple linear iterated function system can generate the</div><div>invariant distribution in these models under small discrete aggregate shocks. We provide</div><div>sufficient conditions for the linear iterated function system to generate a singular invariant</div><div>measure. We also characterize the set of economies which satisfy the sufficient conditions.</div><div>The attractors of the singular invariant measure in our models exhibit fractal patterns.</div><div>The existence of the linear iterated function system implies that an algorithm based on its</div><div>structure can allow computing equilibria in long-period stochastic overlapping generations</div><div>models with heterogeneity.</div>