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

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  • Yossi Hadad
  • Lea Friedman
  • Victoria Rybalkin
  • Zilla Sinuany-Stern

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Yossi Hadad & Lea Friedman & Victoria Rybalkin & Zilla Sinuany-Stern, 2013. "The relationship between DEA efficiency and the type of production function, the degree of homogeneity, and error variability," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 595-607, September.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:3:p:595-607
    DOI: 10.1007/s10100-012-0249-4
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    1. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    2. Banker, Rajiv D. & Chang, Hsihui, 1995. "A simulation study of hypothesis tests for differences in efficiencies," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 37-54, April.
    3. Toshiyuki Sueyoshi, 1997. "Measuring Efficiencies and Returns to Scale of Nippon Telegraph & Telephone in Production and Cost Analyses," Management Science, INFORMS, vol. 43(6), pages 779-796, June.
    4. Sueyoshi, Toshiyuki, 1994. "Stochastic frontier production analysis: Measuring performance of public telecommunications in 24 OECD countries," European Journal of Operational Research, Elsevier, vol. 74(3), pages 466-478, May.
    5. Zieschang, Kimberly D., 1984. "An extended farrell technical efficiency measure," Journal of Economic Theory, Elsevier, vol. 33(2), pages 387-396, August.
    6. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    7. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    8. Hisnanick, John J. & Kymn, Kern O., 1999. "Modeling economies of scale: the case of US electric power companies," Energy Economics, Elsevier, vol. 21(3), pages 225-237, June.
    9. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    12. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    13. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 151-157, September.
    14. Charnes, A. & Cooper, W. W. & Rhodes, E., 1979. "Measuring the efficiency of decision-making units," European Journal of Operational Research, Elsevier, vol. 3(4), pages 339-338, July.
    15. Charnes, A. & Cooper, W. W., 1984. "The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and Fare," European Journal of Operational Research, Elsevier, vol. 15(3), pages 333-334, March.
    16. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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