P* revisited: money-based inflation forecasts with a changing equilibrium velocity

This paper implements recursive techniques to estimate the equilibrium level of M2 velocity and to forecast inflation using the P* model. The recursive estimates of equilibrium velocity are obtained by applying regression trees and least squares methods to a standard representation of M2 demand, namely a model in which the velocity of M2 depends on the opportunity cost of holding M2 instruments. Equilibrium velocity is defined as the level of velocity that would be expected to obtain if deposit rates were at their long-run average (equilibrium) value. We simulate the alternative models to obtain real-time forecasts of inflation and evaluate the performance of the forecasts obtained from the alternative models. We find that while a $P^*$ model assuming a constant equilibrium velocity does not provide accurate inflation forecasts in the 1990s, a model based on our time-varying equilibrium velocity estimates does quite well.