Recent tests using long data series find evidence in favor of long-run PPP, These tests may have reached the wrong conclusion. Using artificial data calibrated to nominal exchange rates and disaggregated data on prices, we show that tests on long-run PPP have serious size biases. In the baseline case, unit root and cointegrarion tests with a nominal size of 5% have true sizes that range from 0.90 to 0.99 in 100-year long data series, even though there is a permanent component that accounts for 42% of the 100-year forecast variance of the real exchange rate, Tests of stationarity are shown to have very low power in the same circumstances. (C) 2000 Elsevier Science B.V. All rights reserved.