TY - JOUR
T1 - The relationship between DEA efficiency and the type of production function, the degree of homogeneity, and error variability
AU - Hadad, Yossi
AU - Friedman, Lea
AU - Rybalkin, Victoria
AU - Sinuany-Stern, Zilla
N1 - Funding Information:
Acknowledgments The authors would like to express gratitude for the contribution of the CJOR referees to the quality of this paper and for their constructive and helpful comments to the paper. Their comments and remarks truly assisted in enhancing the readability and the quality of this paper. This research has been partially supported by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev.
PY - 2013/9/1
Y1 - 2013/9/1
N2 - 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.
AB - 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.
KW - Coefficient of variance (CV)
KW - Data envelopment analysis (DEA)
KW - Efficiency
KW - Goodness of DEA in simulations
KW - Kurtosis
KW - Production functions
KW - Regression analysis
KW - Simulation
UR - http://www.scopus.com/inward/record.url?scp=84881044119&partnerID=8YFLogxK
U2 - 10.1007/s10100-012-0249-4
DO - 10.1007/s10100-012-0249-4
M3 - Article
AN - SCOPUS:84881044119
VL - 21
SP - 595
EP - 607
JO - Central European Journal of Operations Research
JF - Central European Journal of Operations Research
SN - 1435-246X
IS - 3
ER -