Winding number criterion for existence and uniqueness of equilibrium in linear rational expectations models

Abstract

This paper develops a simple geometric criterion for the existence and uniqueness of equilibrium in linear rational expectations (LRE) models. The class of models considered is very general and includes models with infinitely many lags and/or leads of endogenous variables. I show that the criterion is tightly related to the familiar Blanchard and Kahn (Econometrica 48(5) (1980) 1305), Hansen and Sargent (Rational Expectations and Econometric Practice, 1981), and Whiteman (Linear Rational Expectations Models: A User's Guide, 1983) conditions for the existence and uniqueness of equilibrium in LRE models. The new criterion can be used to extend the policy rule robustness analysis of Onatski and Stock (Macroeconomic Dynamics 6(1) (2002) 85) from purely backward-looking models to forward-looking models.