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

Efficiency scores of firms are measured by their distance to an estimated p roduction frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-t ype estimators). Many have claimed that FDH and DEA techniques are non-stat istical, as opposed to econometric approaches where particular parametric e xpressions are posited to model the frontier. We can now define a statistic al model allowing determination of the statistical properties of the nonpar ametric estimators in the multi-output and multi-input case. New results pr ovide the asymptotic sampling distribution of the FDH estimator in a multiv ariate setting and of the DEA estimator in the bivariate case. Sampling dis tributions may also be approximated by bootstrap distributions in very gene ral situations. Consequently, statistical inference based on DEA/FDH-type e stimators is now possible. These techniques allow correction for the bias o f the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now availa ble, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or a dapted for practical purposes.