Recent advances in testing for the validity of Purchasing Power Parity (PPP) focus on the time series properties of real exchange rates in panel frameworks. One weakness of such tests, however, is that they fail to inform the researcher as to which cross-section units are stationary. As a consequence, a reservation for PPP analyses based on such tests is that a small number of real exchange rates in a given panel may drive the results. In this paper we examine the PPP hypothesis focusing on the stationarity of the real exchange rates in up to 25 OECD countries. We introduce a methodology that when applied to a set of established panel unit-root tests, allows the identification of the real exchange rates that are stationary. Our results reveal evidence of mean-reversion that is significantly stronger as compared to that obtained by the existing literature, strengthening the case for PPP. (This abstract was borrowed from another version of this item.)