Confidence Intervals for Efficiency Scores in Non-convex Technologies

Luiza Bădin | Bucharest University of Economic Studies

The envelopment estimators popular in efficiency analysis rely on the assumption that all the observations fall on the same side of the frontier. The nonparametric Free Disposal Hull (FDH) estimator introduced by Deprins et al. (1984) represents the smallest free disposal set covering all the observations and the technical efficiency of an arbitrary producer is measured with respect to the boundary of the free disposal hull of the whole sample. The asymptotic sampling distribution of the FDH estimator derived in Park et al. (2000) is Weibull  where p + q is the dimension of the input⇥output space and ^μNW,0 is a parameter which has to be estimated. Park et al. (2000) propose a consistent estimator for ^μNW,0, but their Monte-Carlo experiments show rather poor performances of the estimator in terms of accuracy. These poor performances jeopardize the precision of the resulting confidence intervals for the efficiency scores. Jeong and Simar (2006) propose a consistent bootstrap based on subsampling for building confidence intervals for the efficiency scores, but the procedure needs large samples to give reasonable results and still no practical rules to select the appropriate subsample size are available.

The objective of our paper is to provide alternative estimators of ^μNW,0 and asymptotic confidence intervals for the efficiency scores easy to implement and fast to compute in practical situations. We investigate and compare by Monte-Carlo experiments the behavior of the resulting estimators, and their effect on the achieved coverage of the confidence intervals for efficiency scores. Our framework is the general multivariate setup of Park et al. (2000), assuming a jump of the joint density of the input⇥output pairs at frontier points, i.e. a strictly positive probabilty of observing firms in any neighborhood of the optimal frontier.