Exchange rates, prices and their speed of adjustment

This paper addresses the problem of measuring the speed of adjustment of exchange rates and relative prices to purchasing power parity (PPP), in the multivariate context of Vector Autoregressive Processes (VAR). We consider the speed of adjustment of one variable y in response to another variable x, where x, y belong to the VAR. We propose a multivariate measure defined as the forecasting horizon for which the cumulated interim multiplier of x on y surpasses a given fraction p of the corresponding total multiplier. This measure of speed for p = 1/2 coincides with the usual concept of half-life when restricted to univariate processes. We emphasize the importance to separate the concepts of long run e¤ect size and its speed of adjustment, where the latter is unambiguosly defined only when the long run e¤ect is non-zero. We discuss likelihood-based point estimators and confidence sets for this notion of half-life, and reconsider evidence on adjustment to PPP in monthly post-Bretton Woods data for five major industrialized countries against the U.S. dollar. Results show that nominal exchange rates bu¤er the entire adjustment to PPP disequilibrium, wheras relative prices do not adjust either in the short or the long run to PPP deviations. Concluding in such a situation that prices adjust faster than exchange rates is a matter of how one interprets the absence of short run and long run effects.