Nonlinear Phillips curve, sacrifice ratio, and the natural rate of unemployment

This paper estimates the unemployment cost of lowering inflation and the natural rate of unemployment for the U.K. and the U.S. on a nonlinear Phillips curve. The nonlinearity is accommodated through a logistic smooth transition autoregression specification, which is flexible to allow various nonlinear shapes. Empirically, the models are shown to capture the nonlinear features present in the data well. The unemployment costs for lowering inflation vary, depending critically on the state of the economy, the size of intended inflation change, and whether policy makers seek to disinflate or prevent inflation from rising. As a further application, the natural rate of unemployment is produced using a nonlinear analog of the historical decomposition. The estimates are well consistent with the economic episodes.