Abstract
Abstract 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.
Highlights
State-space models are useful for many economic applications
After the financial crisis, both approaches lead to very close point estimates of the parameters governing the dynamics of the nonlinear Taylor rule and similar probability distributions of the estimated deviations of the current inflation target from its long-term mean
Our convenient reformulation of the state-space model representation enables the maximum likelihood estimation of the parameters involved in the time evolution of persistent and transitory monetary shocks, including the conditional probability of regime change
Summary
State-space models are useful for many economic applications. As it is well known, under normality, the classical Kalman filter provides the minimum-variance estimate of the current state considering the most recent signal. This article rethinks about the nonoptimality of the Kalman filter by revisiting the signal extraction problem proposed in Andolfatto, Hendry, and Moran (2008) These authors consider a nonlinear Taylor rule where regime shifts reflect the updating of the central bank’s inflation target. Our procedure has two clear advantages over the standard particle filter: (a) the possibility of performing a maximum likelihood estimation of the parameters involved in the monetary policy and, the estimation of conditional time-varying probabilities of regime switching and (b) a remarkable lower computational cost. It could be incorporated into simulation algorithms for DSGE models in a straightforward manner.
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