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One of the most striking features of economic growth is the process of structural change whereby the share of agriculture in GDP decreases as countries develop. The cross-country growth literature typically estimates an aggregate homogeneous production function or convergence regression model that abstracts from the process of structural change. In this paper, we investigate the extent to which assumptions about aggregation and homogeneity matter for inferences regarding the nature of technology differences across countries. Using a unique World Bank dataset, we estimate production functions for agriculture and manufacturing in a panel of 40 developing and developed countries for the period from 1963 to 1992. We empirically model dimensions of heterogeneity across countries, allowing for different choices of technology within both sectors. We argue that heterogeneity is important within sectors across countries implying that an analysis of aggregate data will not produce useful measures of the nature of the technology or productivity. We show that many of the puzzling elements in aggregate cross-country empirics can be explained by inappropriate aggregation across heterogeneous sectors. Copyright 2013, Oxford University Press.