Much research studies US inflation history with a trend-cycle model with unobserved components. A key feature of this model is that the trend may be viewed as the Fed’s evolving inflation target or long-horizon expected inflation. We provide a new way to measure the slowly evolving trend and the cycle (or inflation gap), based on forecasts from the Survey of Professional Forecasters. These forecasts may be treated either as rational expectations or as adjusting to those with sticky information. 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 and professional forecasts, the unobserved-components model and the sticky-information model.