Statistical inference in nonparametric frontier models: the state of the art

Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determinion of the statistical properties of the non-parametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situation. Consequently, statistical inference in DEA/FDH-type models is now available. These techniques allow correction for the bias of the efficiency estimators and construction of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Stressing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes.