Returns to scale, productivity and efficiency in US banking (1989-2000): the neural distance function revisited

Productivity and efficiency analyses have been indispensable tools for evaluating firms’ performance in the banking sector. In this context, the use of Artificial Neural Networks (ANNs) has been recently proposed in order to obtain a globally flexible functional form which is capable of approximating any existing output distance function while enabling the a priori imposition of the theoretical properties dictated by production theory, globally. Previous work has proposed and estimated the so-called Neural Distance Function (NDF) which has numerous advantages when compared to widely adopted specifications. In this paper, we carefully refine some of the most critical characteristics of the NDF. First, we relax the simplistic assumption that each equation has the same number of nodes because it is not expected to approximate reality with any reasonable accuracy and different numbers of nodes are allowed for each equation of the system. Second, we use an activation function which is known to achieve faster convergence compared to the conventional NDF model. Third, we use a relevant approach for technical efficiency estimation based on the widely adopted literature. Fitting the model to a large panel data we illustrate our proposed approach and estimate the Returns to Scale, the Total Factor Productivity and the Technical Efficiency in US commercial banking (1989-2000). Our approach provides very satisfactory results compared to the conventional model, a fact which implies that the refined NDF model successfully expands and improves the conventional NDF approach.