In modeling bank failure, estimating inefficiency separately from the hazards model results in inefficient, biased, and inconsistent estimators. We develop a method to simultaneously estimate a stochastic frontier model and a hazards model using Bayesian techniques. This method overcomes issues related to two-stage estimation methods, allows for computing the marginal effects of the inefficiency over the probability of failure, and facilitates statistical inference of the functions of the parameters such as elasticities, returns to scale, and individual inefficiencies. Simulation exercises show that our proposed method performs better than two-stage maximum likelihood, especially in small samples. In addition, we find that inefficiency plays a statistically and economically significant role in determining the time to failure of U.S. commercial banks during 2001 to 2010.
