Real exchange rates between the United States and its major trading partners were calculated for the Bretton Woods and flexible exchange rate periods. Unit root tests indicate that Purchasing Power Parity performed poorly in both periods. Tests for cointegration reveal limited instances in which it is possible to estimate the deviations from PPP as an error correcting model. The estimated error correcting models indicate that foreign, but not U.S., prices responded to deviations from PPP. Frenkel's (1981b) finding that Purchasing Power Parity (PPP) worked better during the 1920s than the 1970s caused considerable controversy. For example, Davutyan and Pippenger (1985) contend that the socalled collapse of PPP is a result of an increase in the relative importance of real versus monetary shocks. They argue that the 1970s, as opposed to the 1920s, was characterized by real supply shocks and the international coordination of monetary policies. The argument is that PPP did not fail; rather, there was an increase in the volatility of those factors giving rise to deviations from PPP. Hakkio (1984) reestimated PPP over the 1920s and 1970s; using cross-country tests (i.e., SURE estimates) to improve the efficiency of his estimates, he was able to support the hypothesis that PPP worked better in the 1970s than in the 1920s. On the other hand, papers by Adler and Lehman (1983), Dornbusch (1980), Frenkel (1981a), Junge (1985), and Krugman (1978) report findings contrary to the PPP hypothesis. Moreover, Kenen and Rodrik (1986) find that the volatility of real exchange rates has increased throughout the flexible rate period. This paper tries to shed some light on the importance and persistence of the observed deviations from Purchasing Power Parity under alternative exchange rate systems. While it is interesting to compare PPP in the 1920s versus the 1970s, it is equally useful to compare the 1960s versus the 1970s and 1980s. If real supply shocks and lack of monetary coordination are characteristic of the latter period, PPP should perform better in the 1960s. To illustrate the issues involved, consider the following econometric model of (Relative) Purchasing Power