Despite a large literature documenting that the efficacy of monetary policy depends on how inflation expectations are anchored, many monetary policy models assume: (1) the inflation target of monetary policy is constant; and, (2) the inflation target is known by all economic agents. This paper proposes an empirical specification with two policy shocks: permanent changes to the inflation target and transitory perturbations of the short-term real rate. The public sector cannot correctly distinguish between these two shocks and, under incomplete learning, private perceptions of the inflation target will not equal the true target. The paper shows how imperfect policy credibility can affect economic responses to structural shocks, including transition to a new inflation target—a question that cannot be addressed by many commonly used empirical and theoretical models. In contrast to models where all monetary policy actions are transient, the proposed specification implies that sizable movements in historical bond yields and inflation are attributable to perceptions of permanent shocks in target inflation.