Relying on the backward-looking Phillips curve, we estimate the level of inflation that erodes price rigidity and investigate its time constancy. To this end, we employ smooth transition regression models with rolling regressions to account for varying threshold inflation levels. Studying six advanced countries over the 1970-2012 period, our results show that both the slope of the Phillips curve and the threshold trend inflation that erodes price rigidity are time varying. These characteristics could not be captured by a static linear or nonlinear model, illustrating the rich flexibility embedded in our proposed model.