This paper estimates a New Keynesian model to draw inferences about the behavior of the Federal Reserve's unobserved inflation target. The results indicate that the target rose from 1-1/4 percent in 1959 to over 8 percent in the mid-to-late 1970s before falling back below 2-1/2 percent in 2004. The results also provide some support for the hypothesis that over the entire postwar period, Federal Reserve policy has systematically translated short-run price pressures set off by supply-side shocks into more persistent movements in inflation itself, although considerable uncertainty remains about the true source of shifts in the inflation target.