The objective of this study is to provide estimates of the Phillips curve in the US during the period 1951-2001 using some time-varying parameters and the Kalman filter. Time-varying estimates for the sensitivity of inflation to the unemployment rate are provided in addition to time-varying estimates for the NAIRU (the non-accelerating inflation rate of unemployment). Our results for the NAIRU do not significantly differ from that of others with time-varying estimates of it, with it peaking around 1980 (1979 in our case). Inflation is found to have become increasingly sensitive to unemployment in the late 1950s through the early 1970s, and peaked in the late 1970s – early 1980s. After that, the sensitivity decreased only slightly.