Reverse Kalman Filtering US Inflation with Sticky Professional Forecasts

Abstract

We provide a new way to filter US inflation into trend and cycle components, based on extracting long-run forecasts from the Survey of Professional Forecasters. We operate the Kalman filter in reverse, beginning with observed forecasts, then estimating parameters, and then extracting the stochastic trend in inflation. The trend-cycle model with unobserved components is consistent with numerous studies of US inflation history and is of interest partly because the trend may be viewed as the Fed’s evolving inflation target or long-horizon expected inflation. The sluggish reporting attributed to forecasters is consistent with evidence on mean forecast errors. We find considerable evidence of inflation-gap persistence and some evidence of implicit sticky information. But statistical tests show we cannot reconcile these two widely used perspectives on US inflation forecasts, the unobserved-components model and the sticky-information model.