Title: Statistical inference in nonparametric frontier estimation: Recent developments and dynamic extensions
Authors: Leopold Simar - Universite Catholique de Louvain (Belgium) [presenting]
Alois Kneip - University of Bonn (Germany)
Paul Wilson - Clemson University (United States)
Abstract: Nonparametric frontier estimation has been popularized by the use of envelopment estimators in the family of FDH/DEA estimators. Once the efficient frontier has been estimated, the efficiency of each firm is evaluated by gauging its distance to the estimated efficient frontier. When general features of the production set is the focus, like mean of groups, shape of the production set (convexity or not), returns to scale assumptions, testing separability, etc. a test statistics has to be provided which is often a function of averages of efficiency scores. Basic results have been obtained to derive central limit theorems for means of efficiency scores, where the inherent bias of the FDH/DEA estimators jeopardize the properties of simple, naive averages. Still it is possible to correct this problem by estimating the bias term. This has been used in various testing situations (equality of means of groups of firms, returns to scale assumptions, convexity, separability with respect to some environmental variables, etc.). New direction try to extend now these ideas to dynamic setups, where the Malmquist index is one of the basic tools used to analyze the evolution over time of the production sets. New theoretical developments allow indeed to extend the previous results to Malmquist indices. New version of central limit theorems are available and some Monte-Carlo experiments analyze the behavior of group means of these Malmquitst indices in finite samples.