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Investigates the doctrine of Relative Purchasing Power Parity. Mixed evidence is found supporting the concept when using a method analogous to that used by Lucas in testing the quantity theory of money. Relative Purchasing Power Parity is not consistently rejected in the long run between Canada and the United States and between Japan and the United States using quarterly data covering two separate periods: 1957 QI‐1973 QII, and 1973 QIII‐1989 QIV. Given the inconclusive results associated with relying on the methodology of Lucas, considers two alternatives: first, where the requisite smoothed time series are obtained via appropriate autoregressive integrated moving average filters and, second, where cointegration techniques are employed. In these instances, the results are unequivocal. Relative Purchasing Power Parity does not hold.