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This paper investigates the development of efficiency and the progress of banking integration in the European Union by checking for convergence among banks of European and Eurozone countries as well as contrasting the results with those of United States banks.

Initially, we employ the two-stage semi-parametric double bootstrap DEA method, which absorbs the effects of possible integration barriers in the measurement of efficiency. Afterwards, we apply a panel data model, in order to investigate the process of banking integration by testing for convergence and for convergent clusters in banking efficiency.

Our main findings show that the bank efficiency of the US is considerably higher than that of the Eurozone and the European Union. Although there is no evidence of convergence across the banking groups, our results indicate the presence of club convergence. We also conclude that the US banking system is closer to convergence than the Eurozone and the European Union banks. Nevertheless, this outcome is subject to change in the future due to the fact that Eurozone and European Union banks' speed of convergence is higher than that of US banks.

Our survey is unique in trying to check for convergence while controlling for country-specific and bank-specific factors that affect the efficiency of European and Eurozone banks. Moreover, recent literature does not compare the convergence of efficiency of Eurozone, European and US banking. Finally, in our paper special consideration was given to the comparison of commercial, cooperative and savings banks, as subsets of our banking groups.