Introducing external factors in nonparametric frontier models: a unifying approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In literature mainly three approaches have been developed: a one-stage approach, a two-stage approach and a bootstrap-based approach. Daraio and Simar (2003) propose a full nonparametric methodology based on conditional FDH and conditional order-m frontiers. In this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models. Developing further the work done in Daraio and Simar (2003) we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this convex conditional estimator is also proposed. Convexity has always been assumed in mainstream production theory and general equilibrium. Moreover, in many empirical applications, as is the case for the mutual funds industry, the convexity assumption can be reasonable and sometimes natural. The paper, completing the tools available for practitioners, offers a whole set of efficiency measures useful to explain efficiency differentials in several different empirical contexts.