Time–varying rational expectations models

Abstract

This paper develops a comprehensive theory for rational expectations models with time–varying (random) coefficients. Based on the Multiplicative Ergodic Theorem it develops a “linear algebra” in terms of Lyapunov exponents, defined as the asymptotic growth rates of trajectories. Together with their associated Lyapunov spaces they provide a perfect substitute for the eigenvalue/eigenspace analysis used in constant coefficient models. In particular, they allow the construction of explicit solution formulas similar to the standard case. These methods and their numerical implementation is illustrated using a canonical New Keynesian model with a time–varying policy rule and lagged endogenous variables.