This paper adopts the Impulse-Response methodology to understand inflation persistence. It has often been argued that existing models of pricing fail to explain the persistence that we observe. We adopt a common general framework which allows for an explicit modelling of the distribution of contract lengths and for different types of price setting. We also evaluate how far the theories are consistent with recent evidence on price and wage rigidity. We find that allowing for a distribution of durations can take us a long way to solving the puzzle of inflation persistence, but not all the way yet.