Real-Time Estimation of Trend Output and the Illusion of Interest Rate Smoothing

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Abstract
Empirical estimates of the Federal Reserve's policy rule typically find that the regression coefficient on the lagged federal funds rate is around 0.8 and strongly significant. One economic interpretation of this result is that the Fed intentionally "smoothes" interest rates, i.e., policymakers move gradually over time to bring the current level of the funds rate in line with a desired level that is determined by consideration of recent economic data. This paper develops a small forward-looking macroeconomic model where the Federal Reserve estimates the level of trend (or potential) output in real time by running a regression on past output data. Using the model as a data-generating mechanism, I show that efforts to identify the Fed's policy rule using final data (as opposed to real-time data) can create the illusion of interest rate smoothing behavior when in fact none exists. In particular, I show that the lagged federal funds rate can enter spuriously in final-data policy rule regressions because it helps pick up the Fed's serially correlated real-time measurement errors which are not taken into account by the standard estimation procedure. In model simulations, I find that this misspecification problem can explain as much as one-half of the apparent degree of "inertia" or "partial adjustment" in the U.S. federal funds rate.

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