A non-recursive solution for the linear rational expectations model

Abstract

This paper summarizes two new results on the solution of linear rational expectations models arising from optimizing behavior. The first result concerns the development of conditions under which the general solution of the Euler equation associated with the Linear Rational Expectations (LRE) model can be obtained by finding the eigenvalues and the eigenvectors of its characteristic matrix polynomial. 1 The second result concerns the development of conditions under which the general solution of the Euler equation associated with the LRE model becomes the globally asymptotically stable particular solution of that equation. The conditions of these two results take the form of restrictions on the eigenvalues and the eigenvectors of the characteristic matrix, polynomial associated with the Euler equation of the LRE model. The usefulness of these results stems primarily from two facts. First, these results may be combined with the generaiized Wiener-Kolmogorov prediction formulae to obtain a non-recursive 'as dosed as possible to a closed form' solution to the LRE model. 2'3 Second, this solution is established under less restrictive conditions than the recursive solution of Hansen and. Sargent