Optimal combinations of stochastic frontier and data envelopment analysis models

Recent research has shown that combination approaches, such as taking the maximum or the mean over different methods of estimating efficiency scores, have practical merits and offer a useful alternative to adopting only one technique. This recent research shows that taking the maximum minimizes the risk of underestimation, and improves the precision of efficiency estimation. In this paper, we propose and implement a formal criterion of weighting based on maximizing proper criteria of model fit (viz. log predictive scoring) and show how it can be applied in Stochastic Frontier as well as in Data Envelopment Analysis models, where the problem is more difficult. Monte Carlo simulations show that the new techniques perform very well and a substantive application to large U.S. banks shows some important differences with traditional models. The Monte Carlo simulations are also substantive as it is for the first time that proper and coherent optimal model pools are subjected to extensive testing in finite samples.