Asymptotics for dea estimators in nonparametric frontier models. Discussion paper 0317, Institut de Statistique, Universitè Catholique de Louvain

Non-parametric data envelopment analysis (DEA) estimators based on linear program-ming methods have been widely applied in analyses of productive efficiency. The distri-butions of these estimators remain unknown except in the simple case of one input and one output. This paper derives the asymptotic distribution of DEA estimators under vari-able returns-to-scale. In addition, two bootstrap procedures (one based on sub-sampling, the other based on smoothing) are shown to provide consistent inference. The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing of the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on inputs levels and the mix of outputs in the case of output-oriented measures. ∗Research support from “Projet d’Actions de Recherche Concertées ” (No. 98/03–217) and from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government are acknowledged