This paper studies long‐run inflation targets and stability in an imperfect information environment. When central banks set an inflation target that is not fully communicated, agents draw inferences about inflation from recent data and remain alert to structural change by forming expectations from a forecasting model that is estimated via discounted least squares. Inflation targets can lead agents' beliefs to depart from rational expectations through two channels. First, implementing a higher inflation target can lead to overshooting. Second, there can be nearly self‐fulfilling inflation, disinflation, or deflation that arises as an endogenous response to shocks. Policy implications for implementing a higher target without deanchoring expectations are discussed.