Matrix Polynomial Conditions for the Existence of Rational Expectations Solutions

Abstract

In this article we derive minimal conditions to determine the existence of rational expectations solutions obtained using a Generalized Bzout Theorem. We demonstrate that as long as the matrix polynomial derived from the model is regular, then a monic polynomial factor always exists and from this result we can derive a backward forward solution. For the existence of the multivariate rational expectations solution, real roots are sufficient, but not necessary as has previously been suggested in the literature. Existence can be established by the presence of a simple rank order condition, this less restrictive approach allows researchers to consider a wider class of models with rational expectations.

Keywords: Generalized Bzout Theorem, Polynomial Divisor, Rank

JEL Classification: C02, C51, C61