Estimating the FOMC’s interest rate rule with variable selection and partial regime switching

When studying the Federal Open Market Committee’s (FOMC’s) interest rate rule, some authors, such as Gonzalez-Astudillo [(2018) Journal of Monetary, Credit, and Banking 50(1), 115–154.], find evidence for changes in inflation and output gap responses. Others, such as Sims and Zha [(2006) American Economic Review 96(1), 54–81.], only find evidence for a change in the variance of the interest rate rule. 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. 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. When the FOMC responds strongly to the unemployment gap, I find a bimodal density for the inflation response coefficient. Despite the bimodal density, there is a low probability that there have been changes in the FOMC’s response to inflation.