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

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.

[1]  R. Färe,et al.  Profit, Directional Distance Functions, and Nerlovian Efficiency , 1998 .

[2]  William W. Cooper,et al.  SHORT COMMUNICATION: MEASURING EFFICIENCY OF DECISION MAKING UNITS , 1979 .

[3]  Kern O. Kymn,et al.  Modeling economies of scale: the case of US electric power companies , 1999 .

[4]  R. Hogg.  More Light on the Kurtosis and Related Statistics , 1972 .

[5]  Kazuyuki Sekitani,et al.  An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties , 2009, Eur. J. Oper. Res..

[6]  K. Arrow,et al.  Capital-labor substitution and economic efficiency , 1961 .

[7]  Toshiyuki Sueyoshi,et al.  Measuring efficiencies and returns to scale of Nippon telegraph & telephone in production and cost analyses , 1997 .

[8]  Alan Stulman,et al.  Some Aspects of the Distributional Properties of the Expected Value of Perfect Information (EVPI) , 1982 .

[9]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[10]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[11]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[12]  Rajiv D. Banker,et al.  A simulation study of hypothesis tests for differences in efficiencies , 1995 .

[13]  J. Sengupta,et al.  Efficiency measurement by data envelopment analysis with econometric applications , 1988 .

[14]  A. Charnes,et al.  The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and Färe☆ , 1984 .

[15]  Lawrence M. Seiford,et al.  Data envelopment analysis: The evolution of the state of the art (1978–1995) , 1996 .

[16]  Ali Emrouznejad,et al.  Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years , 2008 .

[17]  Russell G. Thompson,et al.  The role of multiplier bounds in efficiency analysis with application to Kansas farming , 1990 .

[18]  Z. Sinuany-Stern,et al.  RANKING METHOD BASED ON THE DIFFERENCE BETWEEN WEIGHTED OUTPUT AND INPUT , 2008 .

[19]  R. Shephard.  Cost and production functions , 1953 .

[20]  Rolf Färe,et al.  Measuring the technical efficiency of production , 1978 .

[21]  Toshiyuki Sueyoshi,et al.  Stochastic frontier production analysis: Measuring performance of public telecommunications in 24 OECD countries , 1994 .

[22]  M. Farrell.  The Measurement of Productive Efficiency , 1957 .

[23]  Boaz Golany,et al.  Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions , 1985 .

[24]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[25]  K. Zieschang.  An extended farrell technical efficiency measure , 1984 .

[26]  P. W. Wilson,et al.  Estimation and inference in two-stage, semi-parametric models of production processes , 2007 .