Adaptive Least Squares Estimation of the Time-Varying Taylor Rule

Clarida, Galí and Gertler (CGG 2000), Orphanides and Williams (2005), Kim and Nelson (2006), and others have found time variation in the Fed’s “Taylor Rule” interest rate policy response function. CGG arbitrarily break their period into two fixedcoefficient 20-year subperiods, however, rather than letting the data tell them when and if any shift in the coefficients occurred. They also proxy their expected inflation and output gap variables using fixed coefficients on several instrumental variables during each subperiod. This effectively models agents as making forecasts with coefficients derived from data that has not yet been observed. The present paper uses the author’s Adaptive Least Squares algorithm (McCulloch 2005a) to estimate this policy response function. First, it is used to simulate expected inflation and the expected unemployment gap using continually time-varying filter estimates that are based only on data that agents could have observed at the time the simulated forecast is made. Then, it is used to estimate the Fed’s policy response function, using continually changing smoother estimates that employ both past and future data. The Likelihood Ratio statistic rejects the hypothesis of constant coefficients in all three equations. Smoother estimates of the Taylor Rule indicate that the coefficient on expected inflation rose from barely 1.0 to 2.0 or higher during 1975-1980. It fell to 1.6 in the 1990’s, but has been nearly 2.0 since 2003. The response to the unemployment gap has been negative throughout, and was strongest near 1980 and since 2002. The equilibrium inflation rate consistent with the Taylor Rule coefficients could be anywhere in the range of 1% to 6% since 2003, depending on the unobserved equilibrium real interest rate.