Abstract
We develop a framework to incorporate bank risk, as measured from the variance of profits or returns, within a model of frontier efficiency. Our framework follows the premise that risk is endogenously related to efficiency. We estimate our model using panel data for U.S. banks and Bayesian techniques. We show that excluding risk from the efficiency model significantly biases the efficiency estimates and the ranking of banks according to their competitive advantage. We also demonstrate that there is a negative risk-efficiency nexus with causality running both ways, while our estimates of risk are fully consistent with the developments in the banking industry over the period 1976–2014.