Journal of Business Economics

, Volume 89, Issue 1, pp 53–77 | Cite as

Measuring potential sub-unit efficiency to counter the aggregation bias in benchmarking

  • Heinz AhnEmail author
  • Peter Bogetoft
  • Ana Lopes
Original Paper


The paper deals with benchmarking cases where highly aggregated decision making units are in the data set. It is shown that these units—consisting of sub-units which are not further known by the evaluator—are likely to receive an unjustifiable harsh evaluation, here referred to as aggregation bias. To counter this bias, we present an approach which allows to calculate the potential sub-unit efficiency of a decision making unit by taking into account the possible impact of its sub-units’ aggregation without having disaggregated sub-unit data. Based on data envelopment analysis, the approach is operationalized in several ways. Finally, we apply our method to the benchmarking model actually used by the Brazilian Electricity Regulator to measure the cost efficiency of the Brazilian distribution system operators. For this case, our results reveal that the potential effect of the aggregation bias on the operators’ efficiency scores is enormous.


Benchmarking Data envelopment analysis DEA Aggregation bias Potential sub-unit efficiency Regulation 

JEL Classification

C14 C61 C67 



The authors would like to thank the reviewers for their helpful comments. The first author gratefully acknowledges that this work was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant AH 90/5-1. The third author appreciates that this work was supported by the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) and the Companhia Energética de Minas Gerais (CEMIG) under Grant APQ-03165-11; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under Grant 999999.000003/2015-08; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grant 444375/2015-5.


This work was supported by Deutsche Forschungsgemeinschaft (DFG) under Grant AH 90/5-1, Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) and Companhia Energética de Minas Gerais (CEMIG) under Grant APQ-03165-11, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under Grant 999999.000003/2015-08, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grant 444375/2015-5.

Compliance with ethical standards

Conflict of interest

Although one of the funds is supported by a company, there is no conflict of interest. The developed approach is universally applicable and of general interest for any benchmarking study.


  1. Afsharian M, Ahn H, Thanassoulis E (2017) A DEA-based incentives system for centrally managed multi-unit organisations. Eur J Oper Res 259:587–598CrossRefGoogle Scholar
  2. Ahn H, Le MH (2015) DEA efficiency of German savings banks: evidence from a goal-oriented perspective. J Bus Econ 85:953–975CrossRefGoogle Scholar
  3. Andersen J, Bogetoft P (2007) Gains from quota trade: theoretical models and an application to the Danish fishery. Eur Rev Agric Econ 34:105–127CrossRefGoogle Scholar
  4. ANEEL (Agẽncia Nacional De Energia Elétrica) (2015) Metodologia de custos operacionais [operational costs methodology]. Technical note 66/2015. BrasiliaGoogle Scholar
  5. Bogetoft P (2000) DEA and activity planning under asymmetric information. J Prod Anal 13:7–48CrossRefGoogle Scholar
  6. Bogetoft P (2012) Performance benchmarking: measuring and managing performance. Springer, New YorkCrossRefGoogle Scholar
  7. Bogetoft P, Lopes A (2015) Comments on the Brazilian benchmarking model for energy distribution regulation: fourth cycle of tariff review—technical note 407/2014. Accessed 16 Dec 2017
  8. Bogetoft P, Otto L (2011) Benchmarking with DEA, SFA, and R. Springer, New YorkCrossRefGoogle Scholar
  9. Bogetoft P, Pruzan P (1991) Planning with multiple criteria. North-Holland, AmsterdamGoogle Scholar
  10. Bogetoft P, Wang D (2005) Estimating the potential gains from mergers. J Prod Anal 23:145–171CrossRefGoogle Scholar
  11. Bogetoft P, Boye K, Neergaard-Petersen H, Nielsen K (2007) Reallocating sugar beet contracts: can sugar production survive in Denmark? Eur Rev Agric Econ 34:1–20CrossRefGoogle Scholar
  12. Charnes A, Neralic L (1990) Sensitivity analysis of the additive model in data envelopment analysis. Eur J Oper Res 48:332–341CrossRefGoogle Scholar
  13. Charnes A, Rousseau J, Semple J (1996) Sensitivity and stability of efficiency classifications in data envelopment analysis. J Prod Anal 7:5–18CrossRefGoogle Scholar
  14. Färe R, Grosskopf S (2000a) Network DEA. Socio Econ Plan Sci 34:35–49CrossRefGoogle Scholar
  15. Färe R, Grosskopf S (2000b) Outfoxing a paradox. Econ Lett 69:159–163CrossRefGoogle Scholar
  16. Färe R, Zelenyuk V (2002) Input aggregation and technical efficiency. Appl Econ Lett 9:635–636CrossRefGoogle Scholar
  17. Färe R, Grosskopf S, Zelenyuk V (2004) Aggregation bias and its bounds in measuring technical efficiency. Appl Econ Lett 11:657–660CrossRefGoogle Scholar
  18. Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc 120:253–281Google Scholar
  19. Fox KJ (1999) Efficiency at different levels of aggregation: public vs. private sector firms. Econ Lett 65:173–176CrossRefGoogle Scholar
  20. Fox KJ (2012) Problems with (dis)aggregating productivity, and another productivity paradox. Ann Oper Res 37:249–259Google Scholar
  21. Frank CR Jr (1969) A generalization of the Koopmans–Gale theorem on pricing and efficiency. Int Econ Rev 10:488–491CrossRefGoogle Scholar
  22. Hackman ST (2010) Production economics: integrating the microeconomic and engineering perspectives. Springer, BerlinGoogle Scholar
  23. Imanirad R, Cook WD, Zhu J (2013) Partial input to output impacts in DEA: production considerations and resource sharing among business subunits. Nav Res Logist 60:190–207CrossRefGoogle Scholar
  24. Kao C, Hwang S-N (2008) Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. Eur J Oper Res 185:418–429CrossRefGoogle Scholar
  25. Lozano S, Villa G (2004) Centralized resource allocation using data envelopment analysis. J Prod Anal 22:143–161CrossRefGoogle Scholar
  26. Ma J, Chen L (2018) Evaluating operation and coordination efficiencies of parallel-series two-stage-system: a data envelopment analysis approach. Expert Syst Appl 91:1–11CrossRefGoogle Scholar
  27. Rockafellar RT (1970) Convex analysis. Princeton University Press, PrincetonCrossRefGoogle Scholar
  28. Simar L, Wilson PW (1999) Estimating and bootstrapping Malmquist indices. Eur J Oper Res 115:459–471CrossRefGoogle Scholar
  29. Sung T-J, Lu Y-T, Ho S-S (2010) Time-based strategy and business performance under environmental uncertainty: an empirical study of design firms in Taiwan. Int J Des 4(3):29–42Google Scholar
  30. Tauer LW (2001) Input aggregation and computed technical efficiency. Appl Econ Lett 8:295–297CrossRefGoogle Scholar
  31. Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130:498–509CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Management Control and Business AccountingTechnische Universität BraunschweigBrunswickGermany
  2. 2.Department of EconomicsCopenhagen Business SchoolFrederiksbergDenmark
  3. 3.Center for Efficiency, Sustainability and Productivity – NESPUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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