Abstract We use heterogeneity‐robust difference‐in‐differences (DiD) methods to evaluate the impact of membership in the European Union (EU) single market on international trade. On the policy front, we provide evidence that: (i) on average, the EU has been very effective in promoting trade among its member states; (ii) the trade effects of the EU have been long‐lasting, but heterogeneous across EU cohorts; and (iii) while the EU has benefited both ‘old’ and ‘new’ members, the increase in the exports from the ‘old’ members to the ‘new’ joiners has been disproportionately larger. From a methods and practical perspective, the contribution of this paper is to introduce a new, fast and flexible estimation command that combines leading estimation techniques from the gravity literature with recent methods from the heterogeneity‐robust DiD literature.