The Solution of Linear Difference Models under Rational Expectations

IN HIS SURVEY ON RATIONAL EXPECTATIONS, R. Shiller indicates that the difficulty of obtaining explicit solutions for linear difference models under rational expectations may have hindered their use [14, p. 27]. The present paper attempts to remedy that problem by giving the explicit solution for an important subclass of the model Shiller refers to as the general linear difference model. Section 1 presents the form of the model for which the solution is derived and shows how particular models can be put in this form. Section 2 gives the solution together with the conditions for existence and uniqueness. 1. THE MODEL The model is given by (la), (lb), and (1c) as follows: