The Forward Solution for Linear Rational Expectations Models

This paper derives a recursive method and the corresponding forward solution for linear Rational Expectations (RE) models in the class of fundamental solutions. Our recursive method is a generalization of the traditional forward method of recursive substitution when predetermined variables are present. This recursive method detects the existence of the real-valued solution to a given model by simply examining whether the model can be solved forward and its solution does not depend on the expectations of the future endogenous variables. The resulting forward solution is unique by construction, whenever it exists. Consequently, as long as one seeks for the stationary forward solution, the issue of multiple stationary solutions is irrelevant. We show that seemingly legitimate model solutions obtained by other methods may not be admissible as valid RE solutions.