On value efficiency analysis and cone-ratio data envelopment analysis models

Abstract In this paper we relate the Value Efficiency Analysis (VEA) efficiency scores with those of three different Cone-Ratio Data Envelopment Analysis (CR-DEA) models, when the chosen model Decision Making Units (DMUs) in CR-DEA jointly comprise the Most Preferred Solution (MPS) in VEA. In particular, we consider the cases where the set of feasible weight vectors is given respectively by (i) the weight vectors that are jointly optimal in DEA for all the model DMUs, (ii) every weight vector that is optimal in DEA for at least one of the model DMUs, and (iii) only those weight vectors with strictly positive input and output weights, each of which is jointly optimal in DEA for all the model DMUs. In each of these cases we show that the CR-DEA efficiency scores can be obtained or approximated by estimating either a VEA model or a series of VEA models, without the need of identifying a priori the set of feasible weight vectors. We illustrate the usefulness of our results by means of an empirical application using data on Japanese regional banks.