Does the Distribution of Efficiency Scores Depend on the Input Mix?

In this paper we examine the possibility of using the standard Kruskal-Wallis
rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input
(or output) mix. Recently, a general data generating process (DGP) suiting the DEA methodology has been formulated and some asymptotic properties of the DEA estimators have been established. In line with this generally accepted DGP, we formulate a conditional test for the assumption of mix independence. Since the DEA frontier is estimated, many standardl assumptions for evaluating the test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, as shown here, is applicable for models with multiple inputs and one output with constant returns to scale when comparing distributions of efficiency scores in two or more groups. The approach is illustrated in an empirical case of demolition projects where we reject the assumption of mix independence. This means that it is not meaningful to perform a complete ranking of the projects based on their efficiency score. Thus the example illustrates how common practice can be
inappropriate.