Long-Run PPP May Not Hold After All

Recent tests using long data series find evidence in favor of long-run PPP (by rejecting either the null hypothesis of unit roots in real exchange rates or the null of no cointegration between nominal exchange rates and relative prices.) These tests may have reached the wrong conclusion. Monte Carlo experiments using artificial data calibrated to nominal exchange rates and disaggregated data on prices show that tests of long-run PPP have serious size biases. They may fail to detect a sizable and economically significant unit root component. For example, in the baseline case which is calibrated to actual price data, unit roots and cointegration tests with a nominal size of five percent have true sizes that range from .90 to .98 in artificial 100-year long data series, even though the unit root component accounts for 42% of the variance of the real exchange rate in sample. On the other hand, tests of stationarity are shown to have very low power in the same circumstances, so it is quite likely that a researcher would reject a unit root and fail to reject stationarity even when the series embodied a large unit root component.