基于前沿分析方法的全要素能源效率研究
|
摘要
近些年,由于能源短缺以及能源消费所带来的环境问题日益严重,能源效率研究逐渐成为科学研究者们关注的焦点。而能源效率的评价及影响因素分析是能源效率研究的主要内容。
本文以能源效率的评价及影响因素分析作为研究内容,首先对国内外能源效率研究文献进行了详细的综述。综述发现:目前能源效率的评价模型已加入环境污染作为非合意产出变量,但对环境污染变量的处理仍不成熟;能源效率的评价方法主要有数据包络分析(DEA)和随机前沿分析(SFA)两种,两者各有优缺点,还没有一种将两者整合的方法;能源效率的影响因素研究主要集中于外部因素的分析,对内部因素的分析较少。本文基于DEA和SFA提出了综合分析法(D&S),利用全球49个国家1999–2008年的数据对这三种评价模型进行了实证检验,并分析了三种实证结果的相关性、一致性以及稳定性,同时通过对能源效率差异的因素分解,分析和阐明了各内部因素对能效差异的影响机理及贡献值。
实证结果表明,通过配对T检验和Spearman和Kendall等级相关系数检验,DEA、SFA与D&S三种方法的评价结果具有显著的相关性和排序上的一致性。从稳定性来看,SFA评价结果的稳定性明显优于DEA,D&S稳定性介于两者之间,但也明显优于DEA,这说明通过SFA剔除随机因素对提高DEA评价结果的稳定性效果显著。样本总体的能源效率值有随时间提升的趋势,中国与样本总体的能源效率存在较大的差距,但中国的能效提升速度略快于样本总体,能源效率差距在不断缩小。通过能源效率差异的因素分解,将能效差异产生的内因归结为能源强度差异、资本–能源比率差异、人力–能源比率差异以及污染–能源比率差异四个部分,皆与能源效率差异负相关。能源强度差异和人力–能源比率差异的对能效差异的贡献率大于资本–能源比率差异和污染–能源比率差异。
In recent years, due to energy shortages and increasingly serious environmental problems posed by energy consumption,energy efficiency attracts more and more researchers’attention. The evaluation of energy efficiency and related factors to energy efficiency are the most important aspects in energy efficiency studies.
In this paper, the evaluation of energy efficiency and analysis of related factors are the main research content. First of all, domestic and international literature of energy efficiency is reviewed in detail. It is found that: the current evaluation model of energy efficiency has taken the environmental pollution as a non-consensual output variable, but it is still immature when processing environmental pollution variable. Data envelopment analysis (DEA) and Stochastic Frontier Analysis (SFA) are two main methods of energy efficiency evaluation, both of which have advantages and disadvantages, and there is no method to integrate them. Previous studies on related factors to energy efficiency are mostly focused on the analysis of external factors, and less can be seen on internal factors. Based on DEA and SFA, a new integrated analysis method (D&S) was proposed. Panel data from 49 countries during the period of 1999-2008 are used to compute energy efficiency in these three methods. Then, relevance, consistency and stability of the results were analyzed. Through the differentiation decomposition of internal factors of energy this paper further illustrates its mechanism and contribution.
The empirical results show as follow: By the paired T test, Spearman and Kendall rank correlation coefficient test, it is proved that evaluation results of DEA, SFA and D&S are significantly relevant and orderly consistent. From the point of view of stability, SFA is much better than D&S, and followed by DEA, which indicate that the stability of evaluation results of DEA is improved obviously by removing random factors via SFA. There is a tendency that energy efficiency values of the overall sample is increasing over time, while, a big gap about this value still do exist between China and overall sample and this gap tends to gradually narrow, meanwhile, China’s efficiency increases faster than that of over sample. Differences in energy efficiency are decomposed into four factors, that is, energy intensity, capital-energy ratio, human-energy ratio and energy-pollution ratio. All factors are negatively correlated with energy efficiency, and their contribution rate of energy intensity and human-energy ratio to the differences in energy efficiency is greater than capital-energy ratio and energy-pollution ratio.
本文以能源效率的评价及影响因素分析作为研究内容,首先对国内外能源效率研究文献进行了详细的综述。综述发现:目前能源效率的评价模型已加入环境污染作为非合意产出变量,但对环境污染变量的处理仍不成熟;能源效率的评价方法主要有数据包络分析(DEA)和随机前沿分析(SFA)两种,两者各有优缺点,还没有一种将两者整合的方法;能源效率的影响因素研究主要集中于外部因素的分析,对内部因素的分析较少。本文基于DEA和SFA提出了综合分析法(D&S),利用全球49个国家1999–2008年的数据对这三种评价模型进行了实证检验,并分析了三种实证结果的相关性、一致性以及稳定性,同时通过对能源效率差异的因素分解,分析和阐明了各内部因素对能效差异的影响机理及贡献值。
实证结果表明,通过配对T检验和Spearman和Kendall等级相关系数检验,DEA、SFA与D&S三种方法的评价结果具有显著的相关性和排序上的一致性。从稳定性来看,SFA评价结果的稳定性明显优于DEA,D&S稳定性介于两者之间,但也明显优于DEA,这说明通过SFA剔除随机因素对提高DEA评价结果的稳定性效果显著。样本总体的能源效率值有随时间提升的趋势,中国与样本总体的能源效率存在较大的差距,但中国的能效提升速度略快于样本总体,能源效率差距在不断缩小。通过能源效率差异的因素分解,将能效差异产生的内因归结为能源强度差异、资本–能源比率差异、人力–能源比率差异以及污染–能源比率差异四个部分,皆与能源效率差异负相关。能源强度差异和人力–能源比率差异的对能效差异的贡献率大于资本–能源比率差异和污染–能源比率差异。
In recent years, due to energy shortages and increasingly serious environmental problems posed by energy consumption,energy efficiency attracts more and more researchers’attention. The evaluation of energy efficiency and related factors to energy efficiency are the most important aspects in energy efficiency studies.
In this paper, the evaluation of energy efficiency and analysis of related factors are the main research content. First of all, domestic and international literature of energy efficiency is reviewed in detail. It is found that: the current evaluation model of energy efficiency has taken the environmental pollution as a non-consensual output variable, but it is still immature when processing environmental pollution variable. Data envelopment analysis (DEA) and Stochastic Frontier Analysis (SFA) are two main methods of energy efficiency evaluation, both of which have advantages and disadvantages, and there is no method to integrate them. Previous studies on related factors to energy efficiency are mostly focused on the analysis of external factors, and less can be seen on internal factors. Based on DEA and SFA, a new integrated analysis method (D&S) was proposed. Panel data from 49 countries during the period of 1999-2008 are used to compute energy efficiency in these three methods. Then, relevance, consistency and stability of the results were analyzed. Through the differentiation decomposition of internal factors of energy this paper further illustrates its mechanism and contribution.
The empirical results show as follow: By the paired T test, Spearman and Kendall rank correlation coefficient test, it is proved that evaluation results of DEA, SFA and D&S are significantly relevant and orderly consistent. From the point of view of stability, SFA is much better than D&S, and followed by DEA, which indicate that the stability of evaluation results of DEA is improved obviously by removing random factors via SFA. There is a tendency that energy efficiency values of the overall sample is increasing over time, while, a big gap about this value still do exist between China and overall sample and this gap tends to gradually narrow, meanwhile, China’s efficiency increases faster than that of over sample. Differences in energy efficiency are decomposed into four factors, that is, energy intensity, capital-energy ratio, human-energy ratio and energy-pollution ratio. All factors are negatively correlated with energy efficiency, and their contribution rate of energy intensity and human-energy ratio to the differences in energy efficiency is greater than capital-energy ratio and energy-pollution ratio.
引文
1 R. Ramanathan.A holistic approach to compare energy efficiencies of different transport modes. Energy Policy.2000, (15):743~747
2 Ramakrishnan Ramanathan.A multi-factor efficiency perspective to the relationships among world GDP, energy consumption and carbon dioxide emissions. Technological Forecasting & Social Change . 2006, (73) :483~494
3 Satoshi Honma, Jin-Li Hu.Total-factor energy efficiency of regions in Japan. Energy Policy. 2008, (36):821~833
4 Kankana Mukherjee.Energy use efficiency in U.S. manufacturing:A nonparametric analysis. Energy Economics.2008, (30) :76~96
5 Sebastián Lozano, Ester Gutiérrez.Non-parametric frontier approach to modelling therelationships among population, GDP, energy consumptionand CO2 emissions. Ecological economics.2008, (66):687~ 699
6 Per J.Agrell, Peter Bogetoft.Economic and environmental efficiency of district heating plants. Energy Policy.2005, (33):1351~1362
7 Fabrizio Erbetta, Luca Rappuoli.Optimal scale in the Italian gas distribution industry using data envelopment analysis. Omega. 2008, (36): 325~ 336
8 Rafael A. Cuesta, C.A. Knox Lovell, JoséL. Zofío.Environmental efficiency measurement with translog distance functions:A parametric approach. Ecological Economics. 2009, (68): 2232~2242
9 Toshiyuki Sueyoshi, TakahiroUeno.Performance analysis of US coal-fired power plants by measuring three DEA efficiencies. Energy Policy. 2010, (38):1675~1688
10王庆一.中国的能源效率及国际比较.研究探讨.2003,(8):5~7
11耿诺,王高尚.我国能源效率分析.中国能源.2008, 130 (7):32~36
12葛莹玉.基于DEA的东部地区全要素能源效率变动的实证分析.统计教育.2008,(9):21~25
13严菲,谭忠富.基于DEA方法的全要素能源效率分析.华东电力.2009,37(9): 1568~1571
14魏楚,沈满洪.能源效率研究发展及趋势:一个综述.浙江大学学报,2009,(03)
15唐玲,杨正林.能源效率与工业经济转型.数量经济技术经济研究.2009, (10):34~48
16李世祥,成金华.中国主要工业省区能源效率分析:1990～2006年.数量经济技术经济研究.2008,(10):32~42
17王群伟,周德群,王思斯.考虑非期望产出的区域能源效率评价研究.中国矿业. 2009,(9):36~40
18袁晓玲,张宝山,杨万平.基于环境污染的中国全要素能源效率研究.中国工业经济.2009,(2):76~86
19吴琦,武春友.基于DEA的能源效率评价模型研究.管理科学.2009,(01):103~112
20 P.J.Agrell,Peter Bogetoft.Economic and environmental efficiency of district heating plants.Energy Policy. 2005, (33):1351~1362
21 Alexander Vaninsky. Efficiency of electric power generation in the United States: Analysis and forecast based on data envelopment analysis. Energy Economics. 2006, (28) :326~338
22 Kemal Sar?ca Ilhan Or Efficiency assessment of Turkish power plants using dataenvelopment analysis. Energy.2007, (32):1484~1499
23 Carlos Pestana Barros.Efficiency analysis of hydroelectric generating plants: A case study for Portugal. Energy Economics.2008, (30):59~75
24 Seyed Mehdi Nassiri, Surendra Singhb.Study on energy use efficiency for paddy crop using data envelopment analysis (DEA) technique. Applied Energy.2009,(86): 1320~1325
25 Kevin Cullinane,Dong-Wook Song.Estimating the relative efficiency of european container ports: a stochastic frontier analysis. Research in Transportation Economics. 2006, 16:85~115
26 Eric C. Wang. R&D efficiency and economic performance: A cross-country analysis using the stochastic frontier approach. Journal of Policy Modeling.2007,29:345~360.
27 Paul Fenn,Dev Vencappa,Stephen Diacon, Paul Klumpes hris O’rien.Market structure and the efficiency of European insurance companies: A stochastic frontier analysis. Journal of Banking & Finance. 2008,(32):86~100
28 Rafael A. Cuesta, C.A. Knox Lovell, JoséL. Zofío. Environmental efficiency measurement with translog distance functions: A parametric approach. Ecological Economics. 2009, (68):2232~2242
29 Guillermo Iglesias, Pablo Castellanos, Amparo Seijas. Measurement of productive efficiency with frontier methods: A case study for wind farms. Energy Economics. 2010, (32):1199~1208
30 A. Azadeh, S. F. Ghaderi, H. Omrani, H. Eivazy. An integrated DEA–COLS–SFA algorithm for optimization and policy making of electricity distribution units. Energy Policy. 2009, (37): 2605~2618
31魏楚,沈满洪.能源效率与能源生产率:基于DEA方法的省际数据比较.数量经济技术经济研究.2007,(09)
32李世祥,成金华.中国工业行业的能源效率特征及其影响因素:基于非参数前沿的实证分析.财经研究. 2009,(07):134~143
33武春友,吴琦.基于超效率DEA的能源效率评价模型研究.管理学报.2009, (11):1460~1465
34袁晓玲,屈小娥.中国工业部门能源消费的面板协整分析.产业经济研究.2008, (06):10~15
35吴庆文,李双杰.中国电子行业上市公司效率的随机前沿分析.数量经济技术经济研究.2003,(01):112~116
36陈祖海,熊焰,刘倩.环境持续性的经济效率随机前沿分析.统计与决策.2006, (08):44~45
37刘玲利,李建华.基于随机前沿分析的我国区域研发资源配置效率实证研究.科学学与科学技术管理.2007,(12):39~44
38杜文杰.农业生产技术效率的政策差异研究-基于时不变阈值面板随机前沿分析.数量经济技术经济研究.2009,(09):107~118
39盛垒.跨国公司在华R&D投资的溢出效应研究-基于随机前沿分析方法(SFA)的检验.世界经济研究.2010,(06):68~74
40许晓雯,时鹏.基于DEA和SFA的我国商业银行效率研究.数理统计与管理.2006,(01):68~72
41王学渊.基于DEA和SFA方法的农户灌溉用水效率比较研究-以西北地区的实地调查数据为例.中国农村水利水电.2010,(01):8~13
42 Ian Sue Wingetal. Explaining Long-Run changes in the energyintensity of the U. S. economy. Working Paper, 2004
43 Rebecca and David. Energy transitions in developing countries:of concepts and literature. Working Paper, 2005
44 Hang and Tu. The impacts of energy prices on energy intensity:Evidence from China. Energy Policy.2007, (35): 2978~2988
45 Fan, Laao and Wei. Can market oriented economic reforms to energy efficiency improvement? Evidence from China. Energy Policy.2002,(35): 2287~2295
46 Leon Clarke, Weyant John, Birky Alicia. On the technological change: Assessing the evidence. Energy Economics.2006,(28): 579~595
47 Moore, Arent , Norland. R&D advancement, technology and impact on evaluation of public R&D. Energy Policy.2007,(35):1464~1473
48朱文宇.技术进步、资源配置与能源效率—基于中国的实证分析.经济研究导刊.2009,(09):30~32
49陈军,徐士元.技术进步对中国能源效率的影响:1979~2006.科学管理研究.2008,(01):9~13
50吴巧生,成金华.中国能源消耗强度变动及因素分解:1980~2004经济理论与经济管理.2006,(10)
51史丹.中国经济增长过程中能源利用效率的改进.经济研究.2002,(09)
52魏楚,沈满洪.能源效率及其影响因素:基于DEA的实证分析.管理世界.2007,(08)
53袁晓玲,张宝山.杨万平基于环境污染的中国全要素能源效率研究.中国工业经济.2009,(02):76~86
54史丹,吴利学,傅晓霞,吴滨.中国能源效率地区差异及其成因研究—基于随机前沿生产函数的方差分解.管理世界.2008,(02):35~43
55魏一鸣,廖华.能源效率的七类测度指标及其测度方法.中国软科学.2010,(1): 128~137
56刘晓宏,杨倩.随机边界分析.复旦大学出版社,2007:6~97
57 Aigner, D.J., C.A.K. Lovell, Schmidt. Formulation and estimation of Stochastic frontier production function model. Journal of Econometrics.1977,(13)
58 Jondrow.On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics.1982,(19):223~238
59 Schnidt, R.C.Sickles.Production frontier and panel data. Journal of Business and Economic Statistics.1984,(02):83~100
60 Charnes, W.W.Cooper. Measuring the efficiency of decision making units.European Journal of Operational Research.1978,(02):429~444
61 Banker, A.Charnes. Some models for estimating technical and scale inefficiencies in data envelopment analysis.Management Science.1984,(30):1078~1092
62 Charnes, W.W.Cooper. A development study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces. Annals of Opreations Research.1985,(02):95~112
63李双杰,范超.随机前沿分析与数据包络分析方法的评析与比较.统计与决策. 2009, (7):25~28
2 Ramakrishnan Ramanathan.A multi-factor efficiency perspective to the relationships among world GDP, energy consumption and carbon dioxide emissions. Technological Forecasting & Social Change . 2006, (73) :483~494
3 Satoshi Honma, Jin-Li Hu.Total-factor energy efficiency of regions in Japan. Energy Policy. 2008, (36):821~833
4 Kankana Mukherjee.Energy use efficiency in U.S. manufacturing:A nonparametric analysis. Energy Economics.2008, (30) :76~96
5 Sebastián Lozano, Ester Gutiérrez.Non-parametric frontier approach to modelling therelationships among population, GDP, energy consumptionand CO2 emissions. Ecological economics.2008, (66):687~ 699
6 Per J.Agrell, Peter Bogetoft.Economic and environmental efficiency of district heating plants. Energy Policy.2005, (33):1351~1362
7 Fabrizio Erbetta, Luca Rappuoli.Optimal scale in the Italian gas distribution industry using data envelopment analysis. Omega. 2008, (36): 325~ 336
8 Rafael A. Cuesta, C.A. Knox Lovell, JoséL. Zofío.Environmental efficiency measurement with translog distance functions:A parametric approach. Ecological Economics. 2009, (68): 2232~2242
9 Toshiyuki Sueyoshi, TakahiroUeno.Performance analysis of US coal-fired power plants by measuring three DEA efficiencies. Energy Policy. 2010, (38):1675~1688
10王庆一.中国的能源效率及国际比较.研究探讨.2003,(8):5~7
11耿诺,王高尚.我国能源效率分析.中国能源.2008, 130 (7):32~36
12葛莹玉.基于DEA的东部地区全要素能源效率变动的实证分析.统计教育.2008,(9):21~25
13严菲,谭忠富.基于DEA方法的全要素能源效率分析.华东电力.2009,37(9): 1568~1571
14魏楚,沈满洪.能源效率研究发展及趋势:一个综述.浙江大学学报,2009,(03)
15唐玲,杨正林.能源效率与工业经济转型.数量经济技术经济研究.2009, (10):34~48
16李世祥,成金华.中国主要工业省区能源效率分析:1990～2006年.数量经济技术经济研究.2008,(10):32~42
17王群伟,周德群,王思斯.考虑非期望产出的区域能源效率评价研究.中国矿业. 2009,(9):36~40
18袁晓玲,张宝山,杨万平.基于环境污染的中国全要素能源效率研究.中国工业经济.2009,(2):76~86
19吴琦,武春友.基于DEA的能源效率评价模型研究.管理科学.2009,(01):103~112
20 P.J.Agrell,Peter Bogetoft.Economic and environmental efficiency of district heating plants.Energy Policy. 2005, (33):1351~1362
21 Alexander Vaninsky. Efficiency of electric power generation in the United States: Analysis and forecast based on data envelopment analysis. Energy Economics. 2006, (28) :326~338
22 Kemal Sar?ca Ilhan Or Efficiency assessment of Turkish power plants using dataenvelopment analysis. Energy.2007, (32):1484~1499
23 Carlos Pestana Barros.Efficiency analysis of hydroelectric generating plants: A case study for Portugal. Energy Economics.2008, (30):59~75
24 Seyed Mehdi Nassiri, Surendra Singhb.Study on energy use efficiency for paddy crop using data envelopment analysis (DEA) technique. Applied Energy.2009,(86): 1320~1325
25 Kevin Cullinane,Dong-Wook Song.Estimating the relative efficiency of european container ports: a stochastic frontier analysis. Research in Transportation Economics. 2006, 16:85~115
26 Eric C. Wang. R&D efficiency and economic performance: A cross-country analysis using the stochastic frontier approach. Journal of Policy Modeling.2007,29:345~360.
27 Paul Fenn,Dev Vencappa,Stephen Diacon, Paul Klumpes hris O’rien.Market structure and the efficiency of European insurance companies: A stochastic frontier analysis. Journal of Banking & Finance. 2008,(32):86~100
28 Rafael A. Cuesta, C.A. Knox Lovell, JoséL. Zofío. Environmental efficiency measurement with translog distance functions: A parametric approach. Ecological Economics. 2009, (68):2232~2242
29 Guillermo Iglesias, Pablo Castellanos, Amparo Seijas. Measurement of productive efficiency with frontier methods: A case study for wind farms. Energy Economics. 2010, (32):1199~1208
30 A. Azadeh, S. F. Ghaderi, H. Omrani, H. Eivazy. An integrated DEA–COLS–SFA algorithm for optimization and policy making of electricity distribution units. Energy Policy. 2009, (37): 2605~2618
31魏楚,沈满洪.能源效率与能源生产率:基于DEA方法的省际数据比较.数量经济技术经济研究.2007,(09)
32李世祥,成金华.中国工业行业的能源效率特征及其影响因素:基于非参数前沿的实证分析.财经研究. 2009,(07):134~143
33武春友,吴琦.基于超效率DEA的能源效率评价模型研究.管理学报.2009, (11):1460~1465
34袁晓玲,屈小娥.中国工业部门能源消费的面板协整分析.产业经济研究.2008, (06):10~15
35吴庆文,李双杰.中国电子行业上市公司效率的随机前沿分析.数量经济技术经济研究.2003,(01):112~116
36陈祖海,熊焰,刘倩.环境持续性的经济效率随机前沿分析.统计与决策.2006, (08):44~45
37刘玲利,李建华.基于随机前沿分析的我国区域研发资源配置效率实证研究.科学学与科学技术管理.2007,(12):39~44
38杜文杰.农业生产技术效率的政策差异研究-基于时不变阈值面板随机前沿分析.数量经济技术经济研究.2009,(09):107~118
39盛垒.跨国公司在华R&D投资的溢出效应研究-基于随机前沿分析方法(SFA)的检验.世界经济研究.2010,(06):68~74
40许晓雯,时鹏.基于DEA和SFA的我国商业银行效率研究.数理统计与管理.2006,(01):68~72
41王学渊.基于DEA和SFA方法的农户灌溉用水效率比较研究-以西北地区的实地调查数据为例.中国农村水利水电.2010,(01):8~13
42 Ian Sue Wingetal. Explaining Long-Run changes in the energyintensity of the U. S. economy. Working Paper, 2004
43 Rebecca and David. Energy transitions in developing countries:of concepts and literature. Working Paper, 2005
44 Hang and Tu. The impacts of energy prices on energy intensity:Evidence from China. Energy Policy.2007, (35): 2978~2988
45 Fan, Laao and Wei. Can market oriented economic reforms to energy efficiency improvement? Evidence from China. Energy Policy.2002,(35): 2287~2295
46 Leon Clarke, Weyant John, Birky Alicia. On the technological change: Assessing the evidence. Energy Economics.2006,(28): 579~595
47 Moore, Arent , Norland. R&D advancement, technology and impact on evaluation of public R&D. Energy Policy.2007,(35):1464~1473
48朱文宇.技术进步、资源配置与能源效率—基于中国的实证分析.经济研究导刊.2009,(09):30~32
49陈军,徐士元.技术进步对中国能源效率的影响:1979~2006.科学管理研究.2008,(01):9~13
50吴巧生,成金华.中国能源消耗强度变动及因素分解:1980~2004经济理论与经济管理.2006,(10)
51史丹.中国经济增长过程中能源利用效率的改进.经济研究.2002,(09)
52魏楚,沈满洪.能源效率及其影响因素:基于DEA的实证分析.管理世界.2007,(08)
53袁晓玲,张宝山.杨万平基于环境污染的中国全要素能源效率研究.中国工业经济.2009,(02):76~86
54史丹,吴利学,傅晓霞,吴滨.中国能源效率地区差异及其成因研究—基于随机前沿生产函数的方差分解.管理世界.2008,(02):35~43
55魏一鸣,廖华.能源效率的七类测度指标及其测度方法.中国软科学.2010,(1): 128~137
56刘晓宏,杨倩.随机边界分析.复旦大学出版社,2007:6~97
57 Aigner, D.J., C.A.K. Lovell, Schmidt. Formulation and estimation of Stochastic frontier production function model. Journal of Econometrics.1977,(13)
58 Jondrow.On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics.1982,(19):223~238
59 Schnidt, R.C.Sickles.Production frontier and panel data. Journal of Business and Economic Statistics.1984,(02):83~100
60 Charnes, W.W.Cooper. Measuring the efficiency of decision making units.European Journal of Operational Research.1978,(02):429~444
61 Banker, A.Charnes. Some models for estimating technical and scale inefficiencies in data envelopment analysis.Management Science.1984,(30):1078~1092
62 Charnes, W.W.Cooper. A development study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces. Annals of Opreations Research.1985,(02):95~112
63李双杰,范超.随机前沿分析与数据包络分析方法的评析与比较.统计与决策. 2009, (7):25~28