Statistical Tests Based on DEA Efficiency Scores

  • Rajiv D. Banker
  • Ram NatarajanEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 164)


This chapter is written for analysts and researchers who may use data envelopment analysis (DEA) to statistically evaluate hypotheses about characteristics of production correspondences and factors affecting productivity. Contrary to some characterizations, it is shown that DEA is a full-fledged statistical methodology, based on the characterization of DMU efficiency as a stochastic variable. The DEA estimator of the production frontier has desirable statistical properties, and provides a basis for the construction of a wide range of formal statistical tests (Banker RD Mgmt Sci. 1993;39(10):1265–73). Specific tests described here address issues such as comparisons of efficiency of groups of DMUs, existence of scale economies, existence of allocative inefficiency, separability and substitutability of inputs in production systems, analysis of technical change and productivity change, impact of contextual variables on productivity, and the adequacy of parametric functional forms in estimating monotone and concave production functions.


Data envelopment analysis Statistical tests 


  1. Aigner DJ, Lovell CAK, Schmidt P. Formulation and estimation of stochastic frontier production function models. J Econom. 1977;6:21–37.CrossRefGoogle Scholar
  2. Anderson P, Petersen NC. A procedure for ranking efficient units in data envelopment analysis. Manage Sci. 1993;39:1261–64.CrossRefGoogle Scholar
  3. Banker RD. Estimating most productive scale size using data envelopment analysis. Eur J Oper Res. 1984;17:35–44.CrossRefGoogle Scholar
  4. Banker RD. Maximum likelihood, consistency and data envelopment analysis: a statistical foundation. Mgmt Sci. 1993;39(10):1265–73.CrossRefGoogle Scholar
  5. Banker RD. Hypothesis tests using data envelopment analysis. J Prod Anal. 1996;7:139–59.CrossRefGoogle Scholar
  6. Banker RD, Charnes A, Cooper WW. Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Manage Sci. 1984;30:1078–92.CrossRefGoogle Scholar
  7. Banker RD, Chang H, Natarajan R. Productivity change, technical progress and relative efficiency change in the public accounting industry. Manage Sci. 2005;51(2):291–304.CrossRefGoogle Scholar
  8. Banker RD, Chang H, Chang S. Statistical tests of returns to scale using DEA. Working paper. Temple University; 2010a.Google Scholar
  9. Banker RD, Chang H, Natarajan R. Estimating technical and allocative efficiency using DEA: an application to the U.S. Public Accounting Industry. J Prod Anal. 2007;27:115–21.CrossRefGoogle Scholar
  10. Banker RD, Das S, Datar S. Analysis of cost variances for management control in hospitals. Res Governmental Nonprofit Account. 1989;5:269–91.Google Scholar
  11. Banker RD, Janakiraman S, Natarajan R. Evaluating the adequacy of parametric functional forms in estimating monotone and concave production functions. J Prod Anal. 2002;17:111–32.CrossRefGoogle Scholar
  12. Banker RD, Janakiraman S, Natarajan R. Analysis of trends in technical and allocative efficiency: an application to Texas Public School Districts. Eur J Oper Res. 2004;154:477–91.CrossRefGoogle Scholar
  13. Banker RD, Natarajan R. Evaluating contextual variables affecting productivity using data envelopment analysis. Oper Res. 2008;56(1):48–58.CrossRefGoogle Scholar
  14. Banker RD, Natarajan R. DEA-based hypothesis tests to evaluate contextual variables affecting productivity. Working Paper. Temple University and the University of Texas at Dallas; 2009.Google Scholar
  15. Banker RD, Natarajan R, Parthasarathy S. Nonparametric Estimation and statistical tests of components of productivity change. Working paper. Temple University and the University of Texas at Dallas; 2009.Google Scholar
  16. Banker RD, Zheng Z, Natarajan R. DEA-based hypothesis tests for comparing two groups of decision making units. Eur J Oper Res. 2010b;206:231–8.CrossRefGoogle Scholar
  17. Berndt E, Wood D. Technology, prices and the derived demand for energy. Rev Econ Stat. 1975;57:259–68.CrossRefGoogle Scholar
  18. Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. Eur J Oper Res. 1978;2:429–44.CrossRefGoogle Scholar
  19. Färe R, Griffel-tatje E, Grosskopf S, Lovell CAK. Biased technical change and the Malmquist productivity index. Scand J Econ. 1997;99:119–27.CrossRefGoogle Scholar
  20. Førsund FR. The evolution of DEA – the economics perspective. University of Oslo, Norway: Mimeo; 1999.Google Scholar
  21. Førsund F, Kittelsen S. Productivity development of Norwegian electricity distribution utilities. Resour Energy Econ. 1998;20:207–24.CrossRefGoogle Scholar
  22. Greene WH. Maximum likelihood estimation of econometric frontier production functions. J Econom. 1980;13:27–56.CrossRefGoogle Scholar
  23. Gstach D. Another approach to data envelopment analysis in noisy environments: DEA+. J Prod Anal. 1998;9:161–76.CrossRefGoogle Scholar
  24. Iman RL, Conover WJ. The use of rank transform in regression. Technometrics. 1979;21:499–509.CrossRefGoogle Scholar
  25. Meeusen W, van den Broeck J. Efficiency estimation from Cobb–Douglas production functions with composed error. Int Econ Rev. 1977;18:435–44.CrossRefGoogle Scholar
  26. Ray S. Resource-use efficiency in public schools: a study of Connecticut data. Manage Sci. 1991;37:1620–28.CrossRefGoogle Scholar
  27. Ray S, Desli E. Productivity growth, technical progress, and efficiency change in industrialized countries: comment. Am Econ Rev. 1997;87:1033–9.Google Scholar
  28. Theil H. A rank-invariant method of linear and polynomial regression analysis. I Proc Kon Ned Akad V Wetensch. 1950;A53:386–92.Google Scholar
  29. Wooldridge JM. A test for functional form against nonparametric alternatives. Econom Theory. 1992;8:452–75.CrossRefGoogle Scholar
  30. Zhang D, Banker RD, Li X, Liu W. Performance impact of research policy at the Chinese Academy of Sciences. Res Policy. 2011;40(6):875–85.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fox School of Business and ManagementTemple UniversityPhiladelphiaUSA
  2. 2.School of ManagementThe University of Texas at DallasRichardsonUSA

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