Combining ranking scales and selecting variables in the DEA context: The case of industrial branches

In this paper we use various recent scale ranking methods in the DEA (Data Envelopment Analysis) context. Two methods are based on multivariate statistical analysis: canonical correlation analysis (CCA) and discriminant analysis of ratios (DR/DEA), while the third is based on the cross efficiency matrix (CE/DEA) derived from the DEA. This multirank approach is necessary for rank validation of the model. Their consistency and goodness of fit with the DEA are tested by various nonparametric statistical tests. Once we had validated the consistency among the ranking methods, we constructed a new overall rank combining all of them. Actually, given the DEA results, we here provide ranks that complement the DEA for a full ranking scale beyond the mere classification to two dichotomic groups. This new combined ranking method does not replace the DEA, but it adds a post-optimality analysis to the DEA results. In this paper, we combine the ranking approach with stochastic DEA: each approach is in the forefront of DEA. This is an attempt to bridge between the DEA frontier Pareto Optimum approach and the average approach used in econometrics. Furthermore, the quality of this bridge is tested statistically and thus depends on the data. We demonstrate this method for fully ranking the Industrial Branches in Israel. In order to delete unmeaningful input and output variables, and to increase the fitness between the DEA and the ranking, we utilize the canonical correlation analysis to select the meaningful variables. Furthermore, we run the ranking methods on two sets of variables to select the proper combination of variables which best represents labor.