Substitution effects in multi-output production. Evidence from Italian universities

In this paper we provide a unifying approach to introduce external environmental variables in nonparametric models of production frontiers. Completing the work done in DS we introduce a conditional Data Envelopment Analysis (DEA) estimator, i.e., a DEA estimator of production frontiers conditioned to some external-environmental variables that are neither inputs nor outputs under the control of the producer. In order to control for the influence of extremes or outliers we introduce also a robust version of our conditional DEA estimator, based on the concept of order¡m frontiers. We aim at enriching the toolbox of applied researchers in productivity analysis offering a complete range of conditional measures of efficiency, i.e., measures of perfor- mance which take into account the operating environment (or other external factors) in which firms operate in, without imposing their positive or negative impact, but letting the data themselves to tell if and how they affect the performance.