Nonlinearities in the Phillips curve for the United States : evidence using metropolitan data

With the unemployment rate in the United States currently below estimates of its natural rate we examine if the relationship between inflation and unemployment is nonlinear. Using aggregate data we are unable to reject a linear relationship. However, using metropolitan-level data we find the slope of the Phillips curve is roughly twice as large when unemployment is low compared to when it is high. Nevertheless the simple nonlinear Phillips curves used here suggest a core CPI inflation rate that is only slightly different than the linear version over the next couple of years