Reducing Overlapping Generations Economies to Finite Economies

Abstract

This paper establishes an identification of stationary equilibria of an infinite-horizon economy and equilibria of a naturally related finite economy. More specifically, the connection is established, firstly, between cycles of an overlapping generations economy and the equilibria of a finite economy with a cyclical structure. Such connection is then extended to hold also when extrinsic uncertainty is introduced in the models. In order to obtain the adequate counterpart of the connection once the extrinsic uncertainty is introduced, we are lead to consider in the overlapping generations framework sunspot equilibria of a broad class, called here sunspot cycles. The previous connections between the equilibria of the two frameworks, with and without sunspots, are used to show that: a) overlapping generations economies allowing for heterogeneity across generations typically fluctuate aperiodically for arbitrarily long periods of time, while nevertheless being able to exhibit an approximate cyclical behavior during those periods and b) the presence of asymmetric information on an extrinsic uncertainty may induce continua of equilibria in finite economies.