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

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)595-607
Number of pages13
JournalCentral European Journal of Operations Research
Volume21
Issue number3
DOIs
StatePublished - 1 Sep 2013

Keywords

  • Coefficient of variance (CV)
  • Data envelopment analysis (DEA)
  • Efficiency
  • Goodness of DEA in simulations
  • Kurtosis
  • Production functions
  • Regression analysis
  • Simulation

ASJC Scopus subject areas

  • Management Science and Operations Research

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