DEA方法的效率悖论与数据短尾现象
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摘要
通过实例分析发现许多重要DEA模型给出的评价结果都可能存在效率悖论,即随着评价标准的提高,一个决策单元的效率值反而会增大.为了探究DEA效率悖论产生的原因及解决办法,首先通过实例证明一些最重要DEA模型(包括CCR模型、BCC模型、FG模型、ST模型)给出的评价结果均可能存在效率悖论.然后,从理论上解释了DEA效率悖论产生的根源在于决策单元数据的短尾现象,并给出了判定存在数据短尾现象的方法.同时,给出了一种修正的DEA模型,该模型不仅可以克服DEA效率悖论的出现,而且还能有效提高DEA方法对效率测算的准确性.最后,应用2000-2014年的中国省级经济数据对相关模型进行了比较研究.
Some efficiency antinomies can be found by example analysis when most of important DEA models are used. Namely, the higher the evaluation standards is, the larger the efficiency value of a fixed decision-making unit. In order to explore the occurrence causes and solution method of DEA efficiency antinomy, this paper firstly proves that the efficiency antinomy exists when some most important DEA models(including CCR model, BCC model, FG model and ST model) are used by examples. Then, it is explained theoretically that the origin of the DEA efficiency paradox lies in the short-tail phenomenon of data in decision making units, and the method for judging whether there is the short tail phenomenon is provided. At the same time, a revised DEA model is given, which can not only overcome the emergence of DEA efficiency paradox, but also improve the accuracy of efficiency measurement. Finally, a comparative study of the related models is given by using the provincial economic data in China from 2000 to 2014.
Some efficiency antinomies can be found by example analysis when most of important DEA models are used. Namely, the higher the evaluation standards is, the larger the efficiency value of a fixed decision-making unit. In order to explore the occurrence causes and solution method of DEA efficiency antinomy, this paper firstly proves that the efficiency antinomy exists when some most important DEA models(including CCR model, BCC model, FG model and ST model) are used by examples. Then, it is explained theoretically that the origin of the DEA efficiency paradox lies in the short-tail phenomenon of data in decision making units, and the method for judging whether there is the short tail phenomenon is provided. At the same time, a revised DEA model is given, which can not only overcome the emergence of DEA efficiency paradox, but also improve the accuracy of efficiency measurement. Finally, a comparative study of the related models is given by using the provincial economic data in China from 2000 to 2014.
引文
[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 6(2):429-444.
[2]马占新.数据包络分析方法的研究进展[J].系统工程与电子技术,2002, 24(3):42-46.Ma Z X. Research on the data envelopment analysis method[J]. Systems Engineering and Electronics, 2002,24(3):42-46.
[3] Cook W D, Seiford L M. Data envelopment analysis(DEA)—Thirty years on[J]. European Journal of Operational Research, 2009, 192(1):1-17.
[4]马占新.数据包络分析(第一卷):数据包络分析模型与方法[M].北京:科学出版社,2010.Ma Z X. Models and methods of data envelopment analysis[M]. Beijing:Science Press,2010.
[5]马占新,马生昀,包斯琴高娃.数据包络分析(第三卷):数据包络分析及其应用案例[M].北京:科学出版社,2013.Ma Z X, Ma S Y, Bao S. Data envelopment analysis and its application cases[M]. Beijing:Science Press, 2013.
[6] Shephard R W. Theory of cost and production functions[M]. Princeton:Princeton University Press, 1970.
[7] Banker R D, Charnes A, Cooper W W. Some models for estimating technical and scale inefficiencies in data envelopment analysis[J]. Management Science, 1984, 30(9):1078-1092.
[8] Lovell C A K. The decomposition of Malmquist productivity indexes[J]. Journal of Productivity Analysis, 2003,20:437-458.
[9] Fare R, Grosskopf S, Lovell C A K. Production frontiers[M]. Cambridge:Cambridge University Press, 1994.
[10] Ray S C, Desli E. Productivity growth, technical progress, and efficiency change in industrialized countries:Comment[J]. American Economic Review, 1997, 87(5):1033-1039.
[11]章祥荪,贵斌威.中国全要素生产率分析:Malmquist指数法评述与应用[J].数量经济技术经济研究,2008(6):111-122.Zhang X S,Gui B W. The analysis of total factor productivity in China:A review and application of Malmquist index approach[J]. The Journal of Quantitative&Technical Economics, 2008(6):111-122.
[12] Fare R, Grosskopf S. A nonparametric cost approach to scale efficiency[J]. The Scandinavian Journal of Economics, 1985, 87(4):594-604.
[13] Seiford L M, Thrall R M. Recent development in DEA, the mathematical programming approach to frontier analysis[J]. Journal of Econometrics, 1990, 46(1/2):7-38.
[14] Charnes A, Cooper W W, Wei Q L, et al. Cone ratio data envelopment analysis and multi-objective programming[J]. International Journal of Systems Science, 1987, 20(7):1099-1118.
[15]马占新.综合数据包络分析模型及其软件系统设计[J].系统工程与电子技术,2004, 26(12):1917-1922.Ma Z X. Analysis model and software design of data envelopment[J]. Systems Engineering and Electronics, 2004,26(12):1917-1922.
[16] Sengupta J K. A dynamic efficiency model using data envelopment analysis[J]. International Journal of Production Economics, 1999, 62(3):209-218.
[17] Sengupta J K. Data envelopment analysis for efficiency measurement in the stochastic case[J]. Computers&Operations Research, 1987, 14(2):117-129.
[18]马占新,郑雪琳,安建业,等.一种含有中性指标的数据包络分析方法[J].系统工程理论与实践,2017, 37(2):418-430.Ma Z X, Zheng X L, An J Y, et al. Data envelopment analysis method with some neutral indexes[J]. Systems Engineering—Theory&Practice, 2017, 37(2):418-430.
[19]马占新.广义参考集DEA模型及其相关性质[J].系工程与电子技术,2012, 34(4):709-714.Ma Z X. DEA model with generalized reference set and its properties[J]. Systems Engineering and Electronics,2012, 34(4):709-714.
[20] Cullinane K, Song D W, Ji P, et al. An application of DEA windows analysis to container port production efficiency[J]. Review of Network Economics, 2004, 3(2):184-206.
[21]马占新.数据包络分析(第四卷):偏序集与数据包络分析[M].北京:科学出版社,2013.Ma Z X. Partially ordered set and data envelopment analysis[M]. Beijing:Science Press, 2013.
[22]马占新.数据包络分析(第二卷):广义数据包络分析方法[M].北京:科学出版社,2012.Ma Z X. Generalized data envelopment analysis[M]. Beijing:Science Press,2012.
[23]马生昀,马占新.数据包络分析(第五卷):广义数据包络分析方法II[M].北京:科学出版社,2017.Ma S Y,Ma Z X. Generalized data envelopment analysis II[M]. Beijing:Science Press, 2017.
[24]马占新.一种基于样本前沿面的综合评价方法[J].内蒙古大学学报,2002, 33(6):606-610.Ma Z X. An evaluation method based on some sample units[J]. Journal of Inner Mongolia University, 2002, 33(6):606-610.
[25]马占新.样本数据包络面的研究与应用[J].系统工程理论与实践,2003, 23(12):32-37.Ma Z X. Frontier that formed by some sample units and its applying[J]. Systems Engineering—Theory&Practice, 2003, 23(12):32-37.
[26]马占新,吕喜明.带有偏好锥的样本数据包络分析方法研究[J].系统工程与电子技术,2007,29(8):1275-1282.Ma Z X, Lii X M. Study on sample data envelopment analysis method with restrain cone[J]. Systems Engineering and Electronics, 2007, 29(8):1275-1282.
[27]马占新,马生昀.基于C~2W模型的样本数据包络分析方法研究[J].系统工程与电子技术,2009, 31(2):366-372.Ma Z X, Ma S Y. Generalized data envelopment analysis method based on C~2W model[J]. Systems Engineering and Electronics, 2009, 31(2):366-372.
[28]马占新,马生昀.基于C~2WY模型的广义数据包络分析方法研究[J].系统工程学报,2011, 26(2):251-261.Ma Z X, Ma S Y. Generalized data envelopment analysis method based on C2WY model[J]. Journal of Systems Engineering, 2011, 26(2):251-261.
[29] Wei Q L, Yan H. A data envelopment analysis(DEA)evaluation method based on sample decision making units[J]. International Journal of Information Technology and Decision Making, 2010(9):601-624.
[30]马占新,赵春英.一种用于广义DEA有效性的度量方法[J].系统工程与电子技术,2016, 38(11):101-114.Ma Z X, Zhao C Y. Measure method for efficiency of generalized DEA[J]. Systems Engineering and Electronics,2016, 38(11):101-114.
[31]中国统计局.中国统计年鉴[M].北京:中国统计出版社,2012.National Bureau of Statistics. China statistical yearbook[M]. Beijing:China Statistics Press, 2012.
[2]马占新.数据包络分析方法的研究进展[J].系统工程与电子技术,2002, 24(3):42-46.Ma Z X. Research on the data envelopment analysis method[J]. Systems Engineering and Electronics, 2002,24(3):42-46.
[3] Cook W D, Seiford L M. Data envelopment analysis(DEA)—Thirty years on[J]. European Journal of Operational Research, 2009, 192(1):1-17.
[4]马占新.数据包络分析(第一卷):数据包络分析模型与方法[M].北京:科学出版社,2010.Ma Z X. Models and methods of data envelopment analysis[M]. Beijing:Science Press,2010.
[5]马占新,马生昀,包斯琴高娃.数据包络分析(第三卷):数据包络分析及其应用案例[M].北京:科学出版社,2013.Ma Z X, Ma S Y, Bao S. Data envelopment analysis and its application cases[M]. Beijing:Science Press, 2013.
[6] Shephard R W. Theory of cost and production functions[M]. Princeton:Princeton University Press, 1970.
[7] Banker R D, Charnes A, Cooper W W. Some models for estimating technical and scale inefficiencies in data envelopment analysis[J]. Management Science, 1984, 30(9):1078-1092.
[8] Lovell C A K. The decomposition of Malmquist productivity indexes[J]. Journal of Productivity Analysis, 2003,20:437-458.
[9] Fare R, Grosskopf S, Lovell C A K. Production frontiers[M]. Cambridge:Cambridge University Press, 1994.
[10] Ray S C, Desli E. Productivity growth, technical progress, and efficiency change in industrialized countries:Comment[J]. American Economic Review, 1997, 87(5):1033-1039.
[11]章祥荪,贵斌威.中国全要素生产率分析:Malmquist指数法评述与应用[J].数量经济技术经济研究,2008(6):111-122.Zhang X S,Gui B W. The analysis of total factor productivity in China:A review and application of Malmquist index approach[J]. The Journal of Quantitative&Technical Economics, 2008(6):111-122.
[12] Fare R, Grosskopf S. A nonparametric cost approach to scale efficiency[J]. The Scandinavian Journal of Economics, 1985, 87(4):594-604.
[13] Seiford L M, Thrall R M. Recent development in DEA, the mathematical programming approach to frontier analysis[J]. Journal of Econometrics, 1990, 46(1/2):7-38.
[14] Charnes A, Cooper W W, Wei Q L, et al. Cone ratio data envelopment analysis and multi-objective programming[J]. International Journal of Systems Science, 1987, 20(7):1099-1118.
[15]马占新.综合数据包络分析模型及其软件系统设计[J].系统工程与电子技术,2004, 26(12):1917-1922.Ma Z X. Analysis model and software design of data envelopment[J]. Systems Engineering and Electronics, 2004,26(12):1917-1922.
[16] Sengupta J K. A dynamic efficiency model using data envelopment analysis[J]. International Journal of Production Economics, 1999, 62(3):209-218.
[17] Sengupta J K. Data envelopment analysis for efficiency measurement in the stochastic case[J]. Computers&Operations Research, 1987, 14(2):117-129.
[18]马占新,郑雪琳,安建业,等.一种含有中性指标的数据包络分析方法[J].系统工程理论与实践,2017, 37(2):418-430.Ma Z X, Zheng X L, An J Y, et al. Data envelopment analysis method with some neutral indexes[J]. Systems Engineering—Theory&Practice, 2017, 37(2):418-430.
[19]马占新.广义参考集DEA模型及其相关性质[J].系工程与电子技术,2012, 34(4):709-714.Ma Z X. DEA model with generalized reference set and its properties[J]. Systems Engineering and Electronics,2012, 34(4):709-714.
[20] Cullinane K, Song D W, Ji P, et al. An application of DEA windows analysis to container port production efficiency[J]. Review of Network Economics, 2004, 3(2):184-206.
[21]马占新.数据包络分析(第四卷):偏序集与数据包络分析[M].北京:科学出版社,2013.Ma Z X. Partially ordered set and data envelopment analysis[M]. Beijing:Science Press, 2013.
[22]马占新.数据包络分析(第二卷):广义数据包络分析方法[M].北京:科学出版社,2012.Ma Z X. Generalized data envelopment analysis[M]. Beijing:Science Press,2012.
[23]马生昀,马占新.数据包络分析(第五卷):广义数据包络分析方法II[M].北京:科学出版社,2017.Ma S Y,Ma Z X. Generalized data envelopment analysis II[M]. Beijing:Science Press, 2017.
[24]马占新.一种基于样本前沿面的综合评价方法[J].内蒙古大学学报,2002, 33(6):606-610.Ma Z X. An evaluation method based on some sample units[J]. Journal of Inner Mongolia University, 2002, 33(6):606-610.
[25]马占新.样本数据包络面的研究与应用[J].系统工程理论与实践,2003, 23(12):32-37.Ma Z X. Frontier that formed by some sample units and its applying[J]. Systems Engineering—Theory&Practice, 2003, 23(12):32-37.
[26]马占新,吕喜明.带有偏好锥的样本数据包络分析方法研究[J].系统工程与电子技术,2007,29(8):1275-1282.Ma Z X, Lii X M. Study on sample data envelopment analysis method with restrain cone[J]. Systems Engineering and Electronics, 2007, 29(8):1275-1282.
[27]马占新,马生昀.基于C~2W模型的样本数据包络分析方法研究[J].系统工程与电子技术,2009, 31(2):366-372.Ma Z X, Ma S Y. Generalized data envelopment analysis method based on C~2W model[J]. Systems Engineering and Electronics, 2009, 31(2):366-372.
[28]马占新,马生昀.基于C~2WY模型的广义数据包络分析方法研究[J].系统工程学报,2011, 26(2):251-261.Ma Z X, Ma S Y. Generalized data envelopment analysis method based on C2WY model[J]. Journal of Systems Engineering, 2011, 26(2):251-261.
[29] Wei Q L, Yan H. A data envelopment analysis(DEA)evaluation method based on sample decision making units[J]. International Journal of Information Technology and Decision Making, 2010(9):601-624.
[30]马占新,赵春英.一种用于广义DEA有效性的度量方法[J].系统工程与电子技术,2016, 38(11):101-114.Ma Z X, Zhao C Y. Measure method for efficiency of generalized DEA[J]. Systems Engineering and Electronics,2016, 38(11):101-114.
[31]中国统计局.中国统计年鉴[M].北京:中国统计出版社,2012.National Bureau of Statistics. China statistical yearbook[M]. Beijing:China Statistics Press, 2012.
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