Rational Random Walks

Abstract

The paper examines, within the framework of a multi-dimensional one-step forward-looking model, a special category of rational expectations equilibria. Their support is infinite with two accumulation points (steady states); the stochastic motion of the system is of random-walk type. A general strategy for an existence proof—associated with the study of a dynamical system—stresses necessary conditions. In a simple overlapping-generations model, the proof is made complete—no backwards bending labour supply is required in the pure sunspot case. By continuity, heteroclinic random walk equilibria are also shown to exist when shocks are real.