Recent panel studies of purchasing power parity have reported strong evidence of mean-reversion in real exchange rates. However, these studies fail to control for cross-sectional dependence in the data. This failure has dramatic consequences, raising the significance level of tests with a nominal size of 5 percent to as much as 50 percent. It is shown in this paper that, controlling for cross-sectional dependence, no evidence against the random walk null can be found in panels of up to 64 real exchange rates. This finding cannot be attributed to low power, as there is ample power in panels of this size to reject the unit-root null. (C) 1998 Elsevier Science B.V.