Abstract |
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In productivity analysis, the efficiency scores of economic producers are evaluated by measuring their distance toward a production frontier. This frontier is deﬁned as the set of the most efficient alternatives among all possible combinations in the input-output space, and it has to be estimated from a random sample of ﬁrms. The nonparametric envelopment estimators rely on the assumption that all the observations fall on the same side of the frontier. Therefore any deviation from the frontier is due only to inefficiency. The Free Disposal Hull (FDH) estimator of the attainable set, introduced by Deprins, Simar and Tulkens (1984), is the smallest free disposal set covering all the observations. However, by construction, the FDH estimator is an inward-biased estimator of its theoretical correspondent. In this paper we consider the univariate extreme values representation of the FDH estimators and we propose a bias corrected estimator for the efficient frontier or for the efficiency scores, based on order statistics and closely related to FDH. The presentation is based on a probabilistic formulation of the model where the input-output pairs are realizations of independent random variables drawn from a joint distribution whose support is the production attainable 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. |