This paper examines how central banks influence inflation expectations via public signals on inflation, and particularly how their forecast accuracy impacts this effect. We find, using an incentivized experiment, that forecast performance matters. Our main, and novel, finding is the presence of recency bias when subjects evaluate forecast accuracy. This bias, which applies to both short-term and medium-term forecasts, is especially strong after poor forecasting performance. In a New Keynesian model, such biases lead to endogenous forecast credibility which can increase the persistence of inflation. Importantly, narrative communication can partly mitigate the detrimental effect of recent poor forecasting.