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

In this paper we examine a neglected aspect of Data Envelopment Analysis: cross-efficiency. We develop the concept of cross-efficiency in a number of new directions. We ground an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discuss the relative merits of each. We also present mathematical formulations of, and intuitive meanings for three possible implementations of aggressive and benevolent cross-efficiency. We have implemented two of these formulations in computer programs; their performance is compared empirically on a real data set. Finally, we suggest practical uses for cross-efficiency, illustrated with reference to the same data set