Uniformly Self-Justified Equilibria

TL;DR

This paper introduces uniformly self-justified equilibria (USJE) for dynamic stochastic economies, proving their existence, providing a computational algorithm, and illustrating their application with numerical examples in an overlapping generations model.

Contribution

The paper defines USJE, proves their existence, and develops a simple algorithm for their computation, enhancing tractability over traditional rational expectations equilibria.

Findings

USJE always exist in the considered models.

A computational algorithm for USJE is developed.

Numerical examples demonstrate USJE application in an overlapping generations economy.

Abstract

We consider dynamic stochastic economies with heterogeneous agents and introduce the concept of uniformly self-justified equilibria (USJE) -- temporary equilibria for which forecasts are best uniform approximations to a selection of the equilibrium correspondence. In a USJE, individuals' forecasting functions for the next period's endogenous variables are assumed to lie in a compact, finite-dimensional set of functions, and the forecasts constitute the best approximation within this set. We show that USJE always exist and develop a simple algorithm to compute them. Therefore, they are more tractable than rational expectations equilibria that do not always exist. As an application, we discuss a stochastic overlapping generations exchange economy and provide numerical examples to illustrate the concept of USJE and the computational method.