Decomposition of inflation and its volatility: A stochastic approach

This paper presents a decomposition of inflation and its volatility. According to the traditional quantity theory of money, the rate of inflation is decomposed into three components: the rate of change in the money supply, plus the rate of change in the velocity of circulation, minus the rate of change in real output. We derive a generalization of this decomposition by postulating that the rate of change of money supply, velocity, and output follow diffusion equations. Using stochastic calculus techniques, two expressions are obtained decomposing inflation and its volatility as a sum of several economically important terms. We also use two sets of U.S. data to illustrate these decompositions with actual numbers.