The forward method as a solution refinement in rational expectations models

Abstract

This paper generalizes the standard forward method of recursive substitution to a general class of linear rational expectations models with potentially multiple fundamental solutions. It is shown that the existence and uniqueness of the well-known forward solution are preserved in a general context. We also propose a key property embedded in the forward solution - the no-bubble condition - as an economically sensible solution refinement in the class of fundamental solutions. In the literature, the no-bubble condition has been assumed to rule out non-fundamental bubble solutions. We show that the forward solution is the only rational expectations equilibrium satisfying the no-bubble condition and consequently, it is the most relevant fundamental solution within the class of fundamental equilibria. Several economic examples are provided where the fundamental solutions obtained by other solution methods and refined by other solution selection criteria violate the no-bubble condition.