The linkages between inflation and the economy's cyclical position are thought to be strongly affected by the credibility of monetary authorities. The author complements existing research by estimating a small forward-looking model of the U.S. economy with endogenous central bank credibility. His work differs from the existing literature in several ways. First, he endogenizes and estimates credibility parameters, allowing inflation expectations to be a mix of backward- and forward-looking agents. Second, his models include both outcome- and action-based credibility. Third, he estimates a non-linear relation between policy credibility and divergences of inflation from target, which is also assumed to change over history. Finally, the author's non-linear time-varying credibility indexes do not rely on a two-regime definition, but on a continuum of credibility regimes. The author finds strong, stable, and statistically significant outcome- and action-credibility effects that generate important inflation inertia. According to his results, the value of the endogenous credibility indexes has risen steadily across the different monetary policy regimes.