Data Envelopment Analysis Journal > Vol 4 > Issue 1

Cross Efficiency Analysis and Extended Facets

Ole Bent Olesen, Department of Business and Economics, University of Southern Denmark, Denmark,
Suggested Citation
Ole Bent Olesen (2018), "Cross Efficiency Analysis and Extended Facets", Data Envelopment Analysis Journal: Vol. 4: No. 1, pp 27-65.

Publication Date: 18 Sep 2018
© 2018 O. B. Olesen
Productivity measurement and analysis
Data envelopment analysis (DEA)simple efficiencyself-appraisalpeer-appraisalcross-efficiency


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In this article:
1. Introduction to Cross-Efficiency
2. Partial Cross-Efficiency Scores and their Relation to Extended Facets, A Numerical Example
3. Partial Cross-Efficiency Scores and Their Relation to Extended Exterior Facets
4. The Average of the Peers' Appraisal of Unit j, ECOL(j)
5. Secondary Goals
6 Conclusion
Appendix A: A Short Introduction to Extended Facet Analysis in the CCR DEA Model
A1. Primal and Dual Description of the Production Possibility Set TCCR
A2. Definition of Concepts Like Faces and Facets of the Production Possibility Set TCCR
A3. An Efficiency Evaluation Relative to a Technology Spanned by Extended Facets Based on FDEFs


The purpose of this paper is to discuss some of the conclusions in a recent paper by Finn Førsund entitled "Cross Efficiency: A Critique". Finn Førsund is criticizing cross-efficiency for lack of economic foundation. I build on extended facet analysis to provide an economic interpretation of each of the different cross-efficiency scores that enters into the "peers' appraisal cross-efficiency averages" of unit j, denoted ECOL(j) in the paper. However, when I consider this new economic interpretation, I end up agreeing with Finn Førsund that it is very difficult to see any meaningful interpretation of these "peers' appraisal cross-efficiency averages".