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Using panel estimates and Stochastic Frontier Analysis this paper aims to contribute to the analysis of bank efficiency of the European banks in the aftermath of the international financial crisis and the sovereign crisis that seriously affected many EU countries. It also considers hypothetical scenarios of exit from the EU of some of the particularly relevant member-states, including the Brexit scenario. The results obtained very clearly demonstrate the existence of statistically significant technical inefficiencies in all considered scenarios. Nevertheless, the results reveal that the exclusion of the Italian banks and of the UK banks from our estimates would be more beneficial to the decrease of the banks’ cost inefficiencies than the exclusion of the French and the German banks. Moreover, the worst scenario in terms of the decrease of the EU banks’ cost inefficiencies would be the exclusion of the banks from the five EU countries that were deeply affected by the international financial and sovereign crises and were obliged to restructure their bank systems, that is, Cyprus, Greece, Ireland, Portugal and Spain.
