Statistical inference in nonparametric frontier models: recent developments and perspectives

This chapter recasts the parametric and statistical approach of Chapter 2, and the nonparametric and deterministic approach of Chapter 3 into a nonparametric and statistical approach. It presents in a unified notation the basic assumptions needed to define the data-generating process (DGP) and shows how the nonparametric estimators [free disposal hull (FDH) and data envelopment analysis (DEA)] can be described easily in this framework. It then discusses bootstrap methods for inference based on DEA and FDH estimates. After that it discusses two ways FDH estimators can be improved, using bias corrections and interpolation. The chapter proposes a way for defining robust nonparametric estimators of the frontier, based on a concept of “partial frontiers” (order-m frontiers or order-α quantile frontiers). The next section surveys the most recent techniques allowing investigation of the effects of these external factors on efficiency. The two approaches are reconciled with each other, and a nonparametric method is shown to be particularly useful even if in the end a parametric model is desired. This mixed “semiparametric” approach seems to outperform the usual parametric approaches based on regression ideas. The last section concludes with a discussion of still-important, open issues and questions for future research.