Skip to main content
SpringerLink
Log in

The relationship between DEA efficiency and the type of production function, the degree of homogeneity, and error variability

  • Original Paper
  • Published:
Central European Journal of Operations Research Aims and scope Submit manuscript

Abstract

In this paper, we use simulations to investigate the relationship between data envelopment analysis (DEA) efficiency and major production functions: Cobb-Douglas, the constant elasticity of substitution, and the transcendental logarithmic. Two DEA models were used: a constant return to scale (CCR model), and a variable return to scale (BCC model). Each of the models was investigated in two versions: with bounded and unbounded weights. Two cases were simulated: with and without errors in the production functions estimation. Various degrees of homogeneity (of the production function) were tested, reflecting a constant increasing and decreasing return to scale. With respect to the case with errors, three distribution functions were utilized: uniform, normal, and double exponential. For each distribution, 16 levels of the coefficient of variance (CV) were used. In all the tested cases, two measures were analysed: the percentage of efficient units (from the total number of units), and the average efficiency score. We applied a regression analysis to test the relationship between these two efficiency measures and the above parameters. Overall, we found that the degree of homogeneity has the largest effect on efficiency. Efficiency declines as the errors grow (as reflected by larger CV and of the expansion of the probability distribution function away from the centre). The bounds on the weights tend to smooth the effect, and bring the various DEA versions closer to one other. The type of efficiency measure has similar regression tendencies. Finally, the relationship between the efficiency measures and the explanatory variables is quadratic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arrow KJ, Chenery HB, Minhas BS, Solow RM (1961) Capital-labour sub-situation and economic efficiency. Rev Econ Stat 9(3): 225–250

    Article  Google Scholar 

  • Banker RD, Chang H (1995) A simulation study of hypothesis tests for differences in efficiencies. Int J Prod Econ 39(1–2): 37–54

    Article  Google Scholar 

  • Banker RD, Charnes A, Cooper WW (1984) Some models for scale inefficiencies in DEA analysis. Manag Sci 30(9): 1078–1092

    Article  Google Scholar 

  • Chambers RG, Chung Y, Färe R (1998) Profit directional distance functions and Nerlovian efficiency. J Optim Theory Appl 98(2): 351–364

    Article  Google Scholar 

  • Charnes A, Cooper WW (1984) The non-archimedean CCR ratio for efficiency analysis: a rejoinder to Boyyd and Fare. Eur J Oper Res 15(3): 333–334

    Article  Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision-making units. Eur J Oper Res 2(6): 429–444

    Article  Google Scholar 

  • Charnes A, Cooper WW, Rhodes E (1979) Short communication: measuring the efficiency of decision making units. Eur J Oper Res 3(4): 339

    Article  Google Scholar 

  • Charnes A, Cooper WW, Golany B, Seiford L, Stutz J (1985) Foundations of data envelopment analysis for Pareto–Koopmans efficient empirical production functions. J Econ 30(1–2): 91–107

    Google Scholar 

  • Debreu G (1951) The coefficient of the resource utilization. Econometrica 19(3): 273–292

    Article  Google Scholar 

  • Emrouznejad A, Barnett RP, Tavares G (2008) Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Socio Econ Plan Sci 42(3): 151–157

    Article  Google Scholar 

  • Färe R, Lovell CAK (1978) Measuring the technical efficiency of production. J Econ Theory 19: 150–162

    Article  Google Scholar 

  • Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc Ser A 120(3): 253–290

    Article  Google Scholar 

  • Hadad Y, Sinuany-Stern Z, Mehrez A (2003a) Effect of variations on efficiency of decision-making units with respect to output, output estimated by production functions, and output differences. Central Eur J Oper Res 11(4): 351–367

    Google Scholar 

  • Hadad Y, Sinuany-Stern Z, Mehrez A (2003b) DEA efficiency in relation to production function: a simulation study. Commun Dependability Quality Manag 6(3): 91–103

    Google Scholar 

  • Hadad Y, Friedman L, Sinuany-Stern Z, Ben-Yair A (2008) Ranking method based on the difference between weighted output and input. Comput Model New Technol 12(3): 55–65

    Google Scholar 

  • Hisnanick JJ, Kymn KO (1999) Modelling economies of scale: the case of US electric power companies. Energy Econ 21(3): 225–237

    Article  Google Scholar 

  • Hogg RV (1972) More light on the Kurtosis and related statistics. J Am Stat Assoc 67: 422–424

    Article  Google Scholar 

  • Mehrez A, Stulman A (1982) Some aspects of the distributional properties of the expected value of perfect information (EVPI). Oper Res Soc 33: 827–836

    Google Scholar 

  • Seiford LM (1994) Data envelopment analysis: the evolution of the state of the art (1978–1995). J Prod Anal 7(2–3): 99–137

    Google Scholar 

  • Sengupta JK, Sfeir RE (1988) Efficiency measurement by data envelopment analysis with econometric applications. Appl Econ 20(6): 285–293

    Article  Google Scholar 

  • Shephard RW (1970) Cost and production function. Princeton University Press, Princeton

    Google Scholar 

  • Simar L, Wilson PW (2007) Estimation and inference in two-stage, semi-parametric models of production processes. J Econ 136(1): 31–64

    Google Scholar 

  • Sueyoshi T (1994) Stochastic frontier production analysis; measuring performance of public telecommunications in 24 OECD countries. Eur J Oper Res 74: 466–478

    Article  Google Scholar 

  • Sueyoshi T (1997) Measuring efficiencies and returns to scale of Nippon telegraph telephone in production and cost analyses. Manag Sci 43(6): 779–796

    Article  Google Scholar 

  • Sueyoshi T, Sekitani K (2009) An occurrence of multiple projections in DEA-based measurement of technical efficiency: theoretical comparison among DEA models from desirable properties. J Oper Res 196(2): 764–794

    Article  Google Scholar 

  • Tavares G (2002) A bibliography of DEA (1978–2001), RRR 01-2002, RUTCOT-Rutgers Centre for OR. Rutgers University, New Jersey

    Google Scholar 

  • Thompson RG, Langemeier LN, Lee C-T, Lee E, Thrall RM (1990) The role of multiplier bounds in efficiency analysis with application to Kansas farming. J Econ 46(2): 93–108

    Google Scholar 

  • Varian HR (1992) Microeconomic analysis, 3rd edn. W.W. Norton, New York

    Google Scholar 

  • Zieschang KD (1984) An extended Farrell technical efficiency measure. J Econ Theory 33: 387–396

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, Shamoon College of Engineering (SCE), 84100, Beer-Sheva, Israel

    Yossi Hadad & Victoria Rybalkin

  2. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Lea Friedman & Zilla Sinuany-Stern

  3. Sapir College, Negev, Israel

    Lea Friedman

Authors
  1. Yossi Hadad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lea Friedman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Victoria Rybalkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zilla Sinuany-Stern
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yossi Hadad.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadad, Y., Friedman, L., Rybalkin, V. et al. The relationship between DEA efficiency and the type of production function, the degree of homogeneity, and error variability. Cent Eur J Oper Res 21, 595–607 (2013). https://doi.org/10.1007/s10100-012-0249-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10100-012-0249-4

Keywords

Search

Navigation