Cross-country studies of economic growth have been hampered by the scarcity of reliable data on productivity at the industry level; see Bernard and Jones [American Economic Review, 91 (4) (2001), 1168–1169] and Rogerson [Journal of Political Economy, 116 (2) (2008), 235–259]. We bring together literature on industry prices, human capital, and capital assets to construct industry-level productivity measures that are well grounded in neoclassical production theory. These theory-based measures differ widely from the crude measures commonly used in the literature. We use these to confirm and strengthen the finding of Bernard and Jones [American Economic Review, 86 (5) (1996), 1216–1238] that for advanced OECD countries, patterns of convergence across sectors have differed since 1970: whereas productivity in market services converged, there is no convergence in manufacturing. More detailed analysis confirms that patterns of convergence are highly industry-specific. There is no dominant convergence trend in sectoral productivity growth across advanced countries.