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We examine differences in wage rates across countries for workers in the same industry, distinguishing between low- medium- and high-skill groups. These differences are large and persistent. We ask whether there is evidence of unconditional or conditional convergence, as is done in studies of convergence in per-capita income across countries. We expect convergence to reflect, at least in part, the degree of integration of an industry into the world economy and examine particularly the role of exposure to trade in goods and services. Our results show strong evidence of convergence in a diverse sample of 40 countries, which includes most large economies whether rich or poor. When we control for variation in the rate of growth of domestic production as well as for direct effects of trade exposure the estimated conditional rate of convergence is lower than the unconditional estimates, and the output growth rate impacts significantly on the growth of wages relative to the convergence prediction.