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Using data for Italy from 1994 to 2015, we appraise the nexus between Basel II and III accords and both the cost and the profit inefficiency of profit‐oriented and mutual cooperative banks. Our analysis further deals with the effects of the regulation in different market structures. To assess the efficiency of the two types of banks under scrutiny, a stochastic frontier approach has been proposed. The evidence reported in this paper indicates that the regulatory framework of the Basel accords had heterogeneous effects on the efficiency of Italian banking institutions. Specifically, Basel II is associated with a contraction in the profit inefficiency and an increase in the cost inefficiency for mutual cooperative banks. On the other hand, Basel III worsened the profit inefficiency, though it is found to reduce the profit inefficiency of mutual cooperative banks, with no significant impact on cost inefficiency. Furthermore, once we control for the degree of market competition, the effects of the regulation are shown to be statistically insignificant. The advent of the 2008 recession and the application of the revenue inefficiency do not alter the main findings. There is also some evidence of spatial effects of the Basel II regulation at the LMA level. [ABSTRACT FROM AUTHOR]