The authors use a Bayesian Markov chain Monte Carlo algorithm to estimate a model that allows temporary gaps between a true expectational Phillips curve and the monetary authority’s approximating nonexpectational Phillips curve. A dynamic programming problem implies that the monetary authority’s inflation target evolves as its estimated Phillips curve moves. The authors’ estimates attribute the rise and fall of post-World War II inflation in the United States to an intricate interaction between the monetary authority’s beliefs and economic shocks. Shocks in the 1970s altered the monetary authority’s estimates and made it misperceive the tradeoff between inflation and unemployment. That misperception caused a sharp rise in inflation in the 1970s. The authors’ estimates indicate that policy makers updated their beliefs continuously. By the 1980s, policy makers’ beliefs about the Phillips curve had changed enough to account for Fed chairman Paul Volcker’s conquest of U.S. inflation in the early 1980s.