We investigate long-run Purchasing Power Parity with data from the current floating exchange rate period by using tests where stationarity and cointegration are the null, rather than the alternative, hypotheses. In most cases, we cannot reject either the null hypothesis of stationarity of the real exchange rate or the null of cointegration between the nominal exchange rate and the domestic and foreign price levels. This constitutes evidence of long-run Purchasing Power Parity because, using the same tests, we can reject the null of stationarity for the nominal exchange rate. Confirmation of the results is provided by a Monte Carlo study. © 1999 Elsevier Science Ltd.