Nonlinear models of the Phillips curve

The recent flattening of the Phillips curve has stimulated new empirical research and theoretical discussions regarding the nonlinear nature of the changes in the parameters. The objective of the present paper is twofold: to detect the relevant type of the implied nonlinearity and look for some general model capable of generating a Phillips curve mimicking the empirical one. We find evidence of a convex US price Phillips curve, from 1961 q1 to 2019 q4, assessed both by piecewise and threshold models. The result presents some degree of novelty regarding the role of supply shocks and model-specific convexities; in addition, it supports the use of a regime-switching macro system. The latter accomplishes three tasks. It can generate a Phillips curve resembling its empirical counterparts; it creates a medium-run endogenous cycle where unemployment is not a NAIRU; finally, it opens new perspectives on economic policy issues.