Time-consistent decisions and rational expectation equilibrium existence in DSGE models

TL;DR

This paper investigates the conditions under which rational expectation equilibrium (REE) exists in DSGE models, highlighting the importance of initial conditions and proposing a limit-based approach to address non-existence issues.

Contribution

It introduces a limit-based method to ensure REE existence in DSGE models affected by initial conditions, emphasizing the need for careful analysis of equilibrium existence.

Findings

Initial conditions can prevent REE existence in DSGE models.

Using limits of economies can overcome REE non-existence.

Careful consideration of initial conditions is crucial for equilibrium analysis.

Abstract

Under some initial conditions, it is shown that time consistency requirements prevent rational expectation equilibrium (REE) existence for dynamic stochastic general equilibrium models induced by consumer heterogeneity, in contrast to static models. However, one can consider REE-prohibiting initial conditions as limits of other initial conditions. The REE existence issue then is overcome by using a limit of economies. This shows that significant care must be taken of when dealing with rational expectation equilibria.