The central piece of the New Keynesian Phillips curve is a model of price setting with nominal rigidities that implies that the dynamics of inflation is well explained by the evolution of real marginal costs. The objective of this paper is to analyze whether this model of inflation dynamics has the nature of a structurally invariant relationship. To assess this, we first analyze an unrestricted time series representation of the joint process of inflation and unit labor costs (or labor share), and present evidence that their joint dynamics is well represented by a time series model with drifting coefficients and volatilities. We do this by applying the methodology used in different multivariate contexts by Cogley (2003) and Cogley-Sargent (2002, 2003). Then we apply a two-step minimum distance estimator: taking as given the estimated unrestricted time series representation, we estimate the parameters of the inflation model by minimizing a quadratic function of the restrictions that the inflation model imposes on the unrestricted time-varying representation. If it is possible to fit an inflation model with constant parameters to a drifting time series representation, we argue that the sticky price model has the nature of a true structural Phillips curve.
