This paper presents the first empirical test with German establishment level data of a hypothesis derived by Helpman, Melitz and Yeaple in a model that explains the decision of heterogeneous firms to serve foreign markets either trough exports or foreign direct investment: only the more productive firms choose to serve the foreign markets, and the most productive among this group will further choose to serve these markets via foreign direct investments. Using a non-parametric test for first order stochastic dominance it is shown that, in line with this hypothesis, the productivity distribution of foreign direct investors dominates that of exporters, which in turn dominates that of national market suppliers.