Disentangling Permanent and Transitory Monetary Shocks with a Nonlinear Taylor Rule

This article provides an estimation method to decompose monetary policy innovations into persistent and transitory components using the nonlinear Taylor rule proposed in Andolfatto, Hendry, and Moran (2008) [Are inflation expectations rational? Journal of Monetary Economics, 55, 406–422]. To use the Kalman filter as the optimal signal extraction technique, we use a convenient reformulation for the state equation by allowing expectations to play a significant role in explaining the future time evolution of monetary shocks. This alternative formulation allows us to perform the maximum likelihood estimation for all the parameters involved in the monetary policy as well as to recover conditional probabilities of regime change. Empirical evidence on the US monetary policy making is provided for the period covering 1986-Q1 to 2021-Q2. We compare our empirical estimates with those obtained based on the particle filter. While both procedures lead to similar quantitative and qualitative findings, our approach has much less computational cost.