On the comparability of efficiency scores in nonparametric frontier models

Data Envelopment Analysis (DEA) is widely used in the field of academic research, in business consulting and in a regulatory context. Usually it is the aim to estimate efficiency scores of decision making units (DMU). The attempt to infer from a sample on the true, but unknown production technology makes it a typical estimation procedure. Banker (1993) and Kneip, Park and Simar (1998) prove that the estimators obtained by DEA are biased, but under certain assumptions are consistent. Efficiency estimates obtained by DEA therefore seem to be suited for hypothesis testing, e.g. for comparison of mean efficiency between groups of observations. However, under certain circumstances - that will be analyzed in this paper - mean efficiency of groups of observations are biased to a different degree and thus differences in mean efficiency are also biased. Without bias correction, hypothesis tests of mean efficiencies between groups are then erroneous. In this paper an indicator is proposed to detect non-comparable mean efficiency scores. The procedure is illustrated in Monte Carlo simulations and applied to a real world data set.