A Bias-corrected Nonparametric Envelopment Estimator of Frontiers

In efficiency analysis, the production frontier is defined as the set of the most efficient alternatives among all possible combinations in the input-output space. The nonparametric envelopment estimators rely oil the assumption that all the observations fall oil the same side of the frontier. The free disposal hull (FDH) estimator of the attainable set is the smallest free disposal set covering all the observations. By construction, the FDH estimator is an inward-biased estimator of the frontier. The univariate extreme values representation of the FDH allows us to derive a bias-corrected estimator for the frontier. The presentation is based on a probabilistic formulation where the input-output,pairs are realizations of independent random variables drawn from a joint distribution whose support is the production set. The bias-corrected estimator shares the asymptotic properties of the FDH estimator. But in finite samples, Monte Carlo experiments indicate that our bias-corrected estimator reduces significantly not only the bias of the FDH estimator but also its mean squared error, with no computational cost. The method is also illustrated with a real data example. A comparison with the parametric stochastic frontier indicates that the parametric approach can easily fail under wrong specification of the model.