This paper proposes a dynamic stochastic general equilibrium model that endogenously generates inflation persistence. We assume that although firms change prices periodically, they face convex costs that preclude optimal adjustment. In essence, the model assumes that price stickiness arises from both the frequency and size of price adjustments. The model is estimated using Bayesian techniques and the results strongly support both sources of price stickiness in the U.S. data. In contrast with traditional sticky price models, the framework yields inflation inertia, delayed effect of monetary policy shocks on inflation, and the observed "reverse dynamic" correlation between inflation and economic activity.