A panel frontier system model with good and bad outputs and endogenous treatment decision

Abstract In this paper we consider a simultaneous panel stochastic frontier system for the production of good and bad outputs when inefficiency is present in both. In addition, we consider treatment of bad output when the treatment decision is endogenous. Inclusion of a treatment decision is important because treatment affects production of bad output which, in turn, affects production of good output. Because of simultaneity, inefficiency from the production of good (bad) output is transmitted to the production of bad (good) output. We derive the likelihood function and formulas for predicting inefficiency (efficiency) for both good and bad outputs as well as overall inefficiency.