The Phillips curve in the US: A nonlinear quantile regression approach

In this paper we investigate the trade-off between the output gap and inflation using a nonlinear quantile regression approach. This approach combines the classical quantile regression with a nonlinear analysis technique and presents the advantages of discovering the heterogeneous nonlinearity of the Phillips curve across quantiles of the inflation distribution. For the empirical illustration, we compare three types of the Phillips curve models in the quantile regression framework. Empirical results for the United States show that the hybrid Phillips curve model outperforms the other two in terms of goodness of fit and prediction ability. We find that the shape of the Phillips curve for the United States is nonlinear and asymmetric, and varies considerably across quantiles. We also provide a novel look at the inflation changes by estimating the conditional density of inflation given different output gap levels, with the numerical results indicating that an increase of the output gap boosts the level of inflation as well as raises the uncertainty of inflation. Our findings imply that the effectiveness of monetary policy mainly depends on the phase of the economic cycle and the inflation uncertainty.