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The Balassa-Samuelson hypothesis is considered the most important structural model of long-run deviations from purchasing power parity (PPP). I present a simple model that builds on the Balassa-Samuelson hypothesis and in which, paradoxically, PPP necessarily holds in the long run. In this model real exchange rates converge because productivity levels converge. The model's predictions are tested empirically for 24 OECD countries in the period 1950-92. Overall, the analysis supports the prediction that productivity convergence is accompanied by real exchange rate convergence