The foundation of the New Keynesian Phillips curve is a model of price setting with nominal rigidities which implies that the dynamics of inflation are well explained by the evolution of real marginal costs. The objective of this paper is to analyze whether this is a structurally-invariant relationship. To assess this, we first estimate an unrestricted time-series model for inflation, unit labor costs, and other variables, and present evidence that their joint dynamics are well represented by a vector autoregression with drifting coefficients and volatilities, as in Cogley and Sargent (2004). Then, following Sbordone (2002, 2003), we apply a two-step minimum distance estimator to estimate deep parameters. Taking as given estimates of the unrestricted VAR, we estimate parameters of the NKPC by minimizing a quadratic function of the restrictions that the theoretical model imposes on the reduced form. Our results suggest that it is possible to reconcile a constant-parameter NKPC with the drifting-parameter VAR, and therefore we argue that the price-setting model is structurally invariant.