Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models

Non-parametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proved consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns-to-scale. This result is used to prove consistency of two different bootstrap procedures (one based on subsampling, the other based on smoothing). The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing 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. ∗Kneip: Institut für Gessellschaftsund Wirtschaftswissenschaften, Statistische Abteilung, Universität Bonn, Adenauerallee 24-26, 53113 Bonn, Germany; email [email protected]. Simar: Institut de Statistique, Université Catholique de Louvain, Voie du Roman Pays 20, Louvain-la-Neuve, Belgium; email [email protected]. Wilson: The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634–1309, USA; email [email protected]. Research support from the Texas Advanced Computation Center, and from the “Interuniversity Attraction Pole,” Phase V (no. P5/24) and Phase IV (no. P6/03) from the Belgian Government (Belgian Science Policy) is gratefully acknowledged.