Structural Stability of the Generalized Taylor Rule

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the existence of a period doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We demonstrate that while the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations, a hybrid rule exhibits the same pattern of period doubling bifurcations as the basic setup.