Are all firms inefficient?

In the usual stochastic frontier model, all firms are inefficient, because inefficiency is non-negative and the probability that inefficiency is exactly zero equals zero. We modify this model by adding a parameter p which equals the probability that a firm is fully efficient. We can estimate this model by MLE and obtain estimates of the fraction of firms that are fully efficient and of the distribution of inefficiency for the inefficient firms. This model has also been considered by Kumbhakar et al. (J Econ 172:66–76, 2013 ). We extend their paper in several ways. We discuss some identification issues that arise if all firms are inefficient or no firms are inefficient. We show that results like those of Waldman (J Econ 18:275–279, 1982 ) hold for this model, that is, that the likelihood has a stationary point at parameters that indicate no inefficiency and that this point is a local maximum if the OLS residuals are positively skewed. Finally, we consider problems involved in testing the hypothesis that p = 0. We also provide some simulations and an empirical example. Copyright Springer Science+Business Media New York 2015