Time-varying rational expectations models: Solutions, stability, numerical implementation

While rational expectations models with time-varying (random) coefficients have gained some esteem, the understanding of their dynamic properties is still in its infancy. The paper adapts results from the theory of random dynamical systems to solve and analyze the stability of rational expectations models with time-varying (random) coefficients. This theory develops a "linear algebra" in terms of Lyapunov exponents defined as the asymptotic growth rates of trajectories. They replace the eigenvalue analysis used in constant coefficient models and allow the construction of solutions in the spirit of Blanchard and Kahn (1980). The usefulness of these methods and their numerical implementation is illustrated using a canonical New Keynesian model with a time-varying policy rule.