The Solution of Linear Difference Models under Rational Expectations

TLDR

Shiller’s survey highlights that the difficulty of deriving explicit solutions for linear difference models under rational expectations has limited their practical use. This paper provides an explicit solution for a key subclass of Shiller’s general linear difference model to address that gap. The authors derive the solution in Section 2, after specifying the model form in Section 1 and demonstrating how specific models fit this framework, and they establish conditions for existence and uniqueness. 1.

Abstract

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: