Estimating the FOMC’s Interest Rate Rule with Variable Selection and Partial Regime Switching

In many recent empirical studies of the Federal Open Market Committee's (FOMC's) interest rate rule, the parameters of the rule are allowed to change over time. However, within this literature, there is no consensus about the nature of the parameter change. Some authors, such as Sims and Zha (2006) only find evidence for a change in the variance of the interest rate rule, while others such as Gonzalez-Astudillo (2018) find evidence for changes in inflation and output gap responses. In this paper, I develop a new two-regime Markov-switching model that probabilistically performs variable selection and identification of parameter change for each variable in the model. After performing Bayesian estimation of this model and allowing for stochastic volatility, I find substantial evidence that there have been changes in the FOMC's response to the unemployment gap and in the volatility of the rule, but a low probability that there have been changes in the response to the inflation gap or any of the other parameters