A characterization of Markov equilibrium in stochastic overlapping generations models

Abstract

This paper characterizes the Markov equilibrium in stochastic overlapping generations models with both pure exchange and production using the theory of linear iterated function systems. We provide conditions for the linearized Markov equilibrium to have an absolutely continuous invariant measure or a singular invariant measure. We also examine relationships between the linear equilibrium system and the model parameters. This analysis identifies the set of economies for each type of invariant measure. We show that the attractor of the singular invariant measure exhibits fractal patterns, which supports the proposition that self-affinity patterns in financial data can be explained via rational expectations equilibrium as an economic mechanism.