The relationship between general equilibrium models with infinite-lived agents and overlapping generations models, and some applications

TL;DR

This paper establishes a formal link between infinite-lived agent models and overlapping generations models, showing their equivalence under certain conditions, and explores implications for asset bubbles and indeterminacy.

Contribution

It proves the equivalence of equilibrium concepts between GEILA and OLG models with multiple assets, broadening understanding of their relationship and applications.

Findings

Equilibrium in GEILA models can be characterized as two-cycle equilibria.

Under certain conditions, OLG equilibria are part of GEILA equilibria.

Asset price bubbles and indeterminacy occur in both models.

Abstract

We prove that a two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) constitutes an equilibrium in an overlapping generations (OLG) model. Conversely, an equilibrium in an OLG model that satisfies additional conditions is part of an equilibrium in a GEILA model. Our framework, which includes three assets (physical capital, a Lucas tree, and fiat money), encompasses both exchange and production economies. As an application, we demonstrate that equilibrium indeterminacy and rational asset price bubbles can arise not only in OLG models but also in GEILA models.