Escape Dynamics : A Continuous Time Approximation

We use a continuous-time approximation approach to analyze dynamics of a model where government adaptively learns the Phillips curve while running monetary policy (Phellps problem). This approach is based on approximating the discrete-time dynamics with learning by a limiting continuous-time diffusion and subsequent characterization of the escape dynamics (recurrent excursions from the neighborhood of equilibrium) for this limit process. We characterize escape dynamics by analytically deriving dominant escape path and expected escape time. We discuss the average behavior of the learning process (the mean dynamics) and its relationship to the escape dynamics. Finally, we discuss the appropriateness of our approximation for the parameterizations of the learning which are commonly used in the literature.