Efficiency and cross-efficiency in DEA: Derivations, meanings and uses

This paper examines a neglected aspect of Data Envelopment Analysis: cross-efficiency. It develops the concept of cross-efficiency in a number of new directions. It grounds an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discusses the relative merits of each. It also presents mathematical formulations of, and intuitive meanings for, three possible implementations of aggressive and benevolent cross-efficiency. Two of these formulations in computer programs have been implemented; their performance is compared empirically on a real data set. Finally, practical uses for cross-efficiency, illustrated with reference to the same data set, are suggested.