This paper estimates the path of inflation persistence in the United States over the last 50 years and draws implications about the evolution of the Federal Reserve's monetary-policy preferences. Standard models of central bank optimization predict that the central bank's preference for output stability is a determinant of inflation persistence. Hence, time variation of that preference should be reflected in changes in inflation persistence. We estimate an ARMA(1,q) model with a time-varying autore- gressive parameter for monthly U.S. inflation data from 1955 to 2006.The coefficients provide an estimate of the inflation target and the path of inflation persistence. The estimated inflation target over the sample is approximately 2.8 percent and we find that inflation persistence declined substantially during Volcker and Greenspan's tenures to a level significantly less than one and significantly below that of the 1970s and early 1980s.