Integrating national markets is a major policy target in the European energy market. Yet, wholesale prices for electricity still differ significantly. Whether these price differences are caused only by limited interconnector capacities or also by lack of cross-border competition is an open question. To address this question, we develop a new approach to determine to which extent price differences stem from limited participation in cross-border trade. We derive a theoretical integration benchmark, using Grossman's (1976) notion of a rational expectations equilibrium. We compare the benchmark to data from European electricity markets. The data reject the integration hypothesis and indicate that well informed traders do not engage in cross-border trade.