Pairwise Tests of Purchasing Power Parity

Given nominal exchange rates and price data on N+1 countries indexed by i=0,1,2,, N, the standard procedure for testing purchasing power parity (PPP) is to apply unit root or stationarity tests to N real exchange rates all measured relative to a base country, 0, often taken to be the U.S. Such a procedure is sensitive to the choice of base country, ignores the information in all the other cross-rates and is subject to a high degree of cross-section dependence which has adverse effects on estimation and inference. In this article, we conduct a variety of unit root tests on all possible N(N+1)/2 real rates between pairs of the N+1 countries and estimate the proportion of the pairs that are stationary. This proportion can be consistently estimated even in the presence of cross-section dependence. We estimate this proportion using quarterly data on the real exchange rate for 50 countries over the period 1957-2001. The main substantive conclusion is that to reject the null of no adjustment to PPP requires sufficiently large disequilibria to move the real rate out of the band of inaction set by trade costs. In such cases, one can reject the null of no adjustment to PPP up to 90% of the time as compared to around 40% in the whole sample using a linear alternative and almost 60% using a nonlinear alternative.