Cross-evaluation in DEA: Improving discrimination among DMUs

There is a need to distinguish among efficient DMUs in Data Envelopment Analysis (DEA). The authors introduce cross-evaluation in DEA as a logical extension of the reference set count, an idea which is already well established in the literature as a way of discriminating among efficient DMUs. They argue that cross-evaluation is more general, and more powerful than the reference-set count. Next the authors describe four variants of cross-evaluation, each with its own particular meaning; then they describe their implementations as secondary goals to the usual DEA efficiency-maximising primary goal. The authors compare the performance of the four variants on a dozen data sets that have appeared in the DEA literature, paying particular attention to the effect of the different input-output structures among the data sets. They then illustrate, with one constructed example and one semi-realistic simulation, that cross-evaluation can give better results (in terms of robustly recovering unobserved ‘real’ efficiencies) than simple DEA efficiency itself. In the discussion the authors briefly touch on other uses of cross-evaluation that make it a useful addition to the DEA toolkit.