The profit function system with output- and input-specific technical efficiency

In a recent paper Kumbhakar and Lai (2016) proposed an output-oriented non-radial measure of technical inefficiency derived from the revenue function. They proposed a closed skew-normal distribution for maximum likelihood estimation but they did not apply the model to data and their technique depends on multiple evaluations of multivariate normal integrals for each observation which can be very costly. In this paper we extend their approach to the profit function and we propose both input- and output-oriented non-radial measures of technical inefficiencies. Although the extension to the translog profit function is trivial many observations, in practice, may contain negative profits. For this reason we provide a nontrivial extension to the Symmetric Generalized McFadden (SGM) profit function. We propose and apply (to a large sample of US banks) Bayesian analysis of the SGM model (augmented with latent technical inefficiencies resulting in a highly nonlinear mixed effects model) using the integrated nested Laplace approximation.