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This paper studies the effect of structural change on the historical path of aggregate labor productivity growth for a large sample of European countries, and it builds a quantitative multi-sector growth model to analyze the potential impact that structural change may have on future productivity growth. We document that the observed reallocation of economic activity since the 1970s towards the service sector has exerted a strongly negative effect on aggregate productivity growth in most European countries. Moreover, we perform a quantitative analysis to show that the expected path of structural change might continue to have a sizeable dent on future productivity growth in Europe. By contrast, the impact in the U.S. is expected to rapidly diminish. We show that this differential result can be explained by the large expansion, in Europe, of certain service sub-sectors characterized by stagnant productivity.