Expected efficiency ranks from parametric stochastic frontier models

In the stochastic frontier model, we extend the multivariate probability statements of Horrace (J Econom, 126:335–354, 2005) to calculate the conditional probability that a firm is any particular efficiency rank in the sample. From this, we construct the conditional expected efficiency rank for each firm. Compared to the traditional ranked efficiency point estimates, firm-level conditional expected ranks are more informative about the degree of uncertainty of the ranking. The conditional expected ranks may be useful for empiricists. A Monte Carlo study and an empirical example are provided.