This paper tests some of the predictions of recent advances in trade theory that have focused on different trade patterns of firms within the same sector. Helpman, Melitz and Yeaple (2005) develop a model in which innate productivity differences between firms determine the degree of international engagement of firms: The least productive firms produce for the domestic market, better performers engage in export activities, and the top firms establish foreign subsidiaries. Using German firm-level data from 1996 to 2002, we test this prediction using non-parametric methods, by examining the distribution functions of the three subsets of firms for stochastic dominance. Rather than just comparing first moments, this technique allows us to compare productivity over the entire distribution. Our results show robust support for the prediction from theory.