Bayesian Artificial Neural Networks for frontier efficiency analysis

Artificial neural networks have offered their share of econometric insights, given their power to model complex relationships. One area where they have not been readily deployed is the estimation of frontiers. The literature on frontier estimation has seen its share of research comparing and contrasting data envelopment analysis (DEA) and stochastic frontier analysis (SFA), the two workhorse estimators. These studies rely on both Monte Carlo experiments and actual data sets to examine a range of performance issues which can be used to elucidate insights on the benefits or weaknesses of one method over the other. As can be imagined, neither method is universally better than the other. The present paper proposes an alternative approach that is quite flexible in terms of functional form and distributional assumptions and it amalgamates the benefits of both DEA and SFA. Specifically, we bridge these two popular approaches via Bayesian artificial neural networks while accounting for possible endogeneity of inputs. We examine the performance of this new machine learning approach using Monte Carlo experiments which is found to be very good, comparable to, or often better than, the current standards in the literature. To illustrate the new techniques, we provide an application of this approach to a data set of large US banks.