Policy implications are derived for an inflation-targeting central bank, whose credibility is endogenous and depends on its past ability to achieve its  targets. This is done in a New Keynesian framework with heterogeneous and  boundedly rational expectations. We find that the region of allowed policy  parameters is strictly larger than under rational expectations. However,  when the zero lower bound on the nominal interest rate is accounted for, self-fulfilling deflationary spirals can occur, depending on the credibility of the central bank. Deflationary spirals can be prevented with a high inflation  target and aggressive monetary easing.