Notwithstanding persistently-high unemployment following the Great Recession, inflation in the United States has been remarkably stable. We find that a traditional Phillips curve describes the behavior of inflation reasonably well since the 1960s. Using a non-linear Kalman filter that allows for time-varying parameters, we find that three factors have contributed to the observed stability of inflation: inflation expectations have become better anchored and to a lower level; the slope of the Phillips curve has flattened; and the importance of import-price inflation has increased.