Endogenous price stickiness, trend inflation, and the New Keynesian Phillips curve

For standard calibration, this paper shows that the optimal price, in a model with Calvo form of price stickiness and strategic complementarities, is only defined for annualised trend inflation rates of under 5.5%. This critical inflation rate is below the average inflation rate over recent decades. Furthermore, over the range for which the optimal price is defined, the slope of the New Keynesian Phillips curve generated by this model is decreasing in trend inflation. That contradicts the stylised fact that Phillips curves are flatter in low-inflation environments. Substituting endogenous price stickiness for the Calvo form of time-dependent pricing can help avoid these implications.