Output distance functions from a complexity perspective: The Neural Network approach

The output distance function is a key concept in economics. However, its empirical estimation is less than satisfactory because it often violates properties dictated by economic theory. In this paper we introduce the neural distance function (NDF) which constitutes a global approximation to any arbitrary production technology with multiple outputs given by a neural network (NN) specification and imposes all theoretical properties implied by production theory such as monotonicity, curvature, homogeneity for all economically admissible values of outputs and inputs. The model possesses all of the properties thought as desirable in production theory in a way not matched by its competing specification. Fitted to data sets originating in US data for all commercial banks between 1989-2000, the NDF is capable of explaining a very high proportion of the variance of output while keeping the number of parameters to a minimum and satisfying all the theoretical properties dictated by production theory.