This paper provides an explanation for the run-up of U. S. inflation in the 1960s and 1970s and the sharp disinflation in the early 1980s, which standard macroeconomic models have difficulties in addressing. I present a model in which rational policy-makers learn about the behavior of the economy in real time and set stabilization policy optimally, conditional on their current beliefs. The steady state associated with the self-confirming equilibrium of the model is characterized by low inflation. However, prolonged episodes of high inflation ending with rapid disinflations can occur when policy-makers underestimate both the natural rate of unemployment and the persistence of inflation in the Phillips curve. I estimate the model using likelihood methods. The estimation results show that the model accounts remarkably well for the evolution of policy-makers' beliefs, stabilization policy, and the postwar behavior of inflation and unemployment in the United States.