Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models

Abstract

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The equilibrium is not necessarily a steady state; for example, demographic and type composition of the population or individuals’ endowments can change over time. However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. In addition, we illustrate our main result using a textbook model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem.