Estimation of banking technology under credit uncertainty

Credit risk is crucial to understanding banks' production technology and should be explicitly accounted for when modeling the latter. The banking literature has largely accounted for risk by using ex-post realizations of banks' uncertain outputs and the variables intended to capture risk. This is equivalent to estimating an ex-post realization of bank's production technology which, however, may not reflect optimality conditions that banks seek to satisfy under uncertainty. The ex-post estimates of technology are likely to be biased and inconsistent, and one thus may call into question the reliability of the results regarding banks' technological characteristics broadly reported in the literature. However, the extent to which these concerns are relevant for policy analysis is an empirical question. In this paper, we offer an alternative methodology to estimate banks' production technology based on the ex-ante cost function. We model credit uncertainty explicitly by recognizing that bank managers minimize costs subject to given expected outputs and credit risk. We estimate unobservable expected outputs and associated credit risk levels from banks' supply functions via nonparametric kernel methods. We apply this framework to estimate production technology of U.S. commercial banks during the period from 2001 to 2010 and contrast the new estimates with those based on the ex-post models widely employed in the literature.