中国工业二氧化碳影子价格的稳健估计与减排政策
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摘要
二氧化碳影子价格的稳健估计是评估边际减排成本、设定环境税框架以及评价碳排放权交易体系有效程度的基础性工作。本文在采用自体抽样方法(bootstrap method)的基础上,通过构建二氧化碳影子价格的稳健估计模型,测算了中国36个工业行业1998～2011年的二氧化碳影子价格。研究结果表明:(1)在参数线性规划模型下,忽视随机因素对生产前沿的影响,会低估二氧化碳影子价格。稳健估计得到中国工业行业二氧化碳影子价格平均值为5480元/吨,远低于现有研究估计结果。(2)二氧化碳影子价格在不同行业间存在较大差异并呈扩大趋势,表明行业间存在巨大的碳排放权交易空间,但是36个行业中有越来越多的行业已经向"清洁型"生产技术转变。(3)二氧化碳边际减排成本与碳排放强度之间具有显著的"倒U形"关系,行业碳排放强度的临界值为10.37吨/万元。行业的碳排放强度控制在临界值以下时,可以实现有效减排和生产技术清洁化。(4)我国未来二氧化碳减排政策应采取数量机制和价格机制相结合的策略,价格机制控制碳排放强度较高的行业,数量机制实现行业间边际减排成本的趋同。
The robust estimation of the shadow price of CO_2 is fundamental for the evaluation of marginal abatement cost of CO_2, the effectiveness of CO_2 emission permits trading system and the setup of CO_2 tax framework. By proposing a robust estimation framework, we estimate the shadow price of 36 Chinese industrial sectors' CO_2 from 1998 to 2011, and the results show that:(1)The traditional parametric programming model neglects the stochastic effect on production frontier, which results in a downward bias in the estimation of the shadow price of CO_2. Under the robust model, we find that the shadow price is 5480 Yuan/ton on average;(2)The shadow price of CO_2 between industrial sectors is large and exhibits a divergence tendency, which implies a great trading potential among sectors while more and more industries convert to a cleaner production technology;(3)The estimation of MACC shows that, there is a significant inverse U-shape relationship between MAC and carbon intensity, with a critical value of the industry's carbon emission intensity being 1.037 ton per thousand Yuan. When the sector's carbon intensity is below the critical value, it is possible to achieve effective emission reduction and make the production cleaner;(4)China's future carbon abatement policy should adopt a combination of quantitative mechanism and price mechanism. We should use price mechanism to control higher level carbon emission industries, while usequantitative mechanisms to achieve inter-industry convergence of marginal abatement costs.
The robust estimation of the shadow price of CO_2 is fundamental for the evaluation of marginal abatement cost of CO_2, the effectiveness of CO_2 emission permits trading system and the setup of CO_2 tax framework. By proposing a robust estimation framework, we estimate the shadow price of 36 Chinese industrial sectors' CO_2 from 1998 to 2011, and the results show that:(1)The traditional parametric programming model neglects the stochastic effect on production frontier, which results in a downward bias in the estimation of the shadow price of CO_2. Under the robust model, we find that the shadow price is 5480 Yuan/ton on average;(2)The shadow price of CO_2 between industrial sectors is large and exhibits a divergence tendency, which implies a great trading potential among sectors while more and more industries convert to a cleaner production technology;(3)The estimation of MACC shows that, there is a significant inverse U-shape relationship between MAC and carbon intensity, with a critical value of the industry's carbon emission intensity being 1.037 ton per thousand Yuan. When the sector's carbon intensity is below the critical value, it is possible to achieve effective emission reduction and make the production cleaner;(4)China's future carbon abatement policy should adopt a combination of quantitative mechanism and price mechanism. We should use price mechanism to control higher level carbon emission industries, while usequantitative mechanisms to achieve inter-industry convergence of marginal abatement costs.
引文
(1)Ackerberg D. A. Caves K. and Frazer G.,2015,“Identi-fication Properties of Recent Production Function Estimators,Econometrica,Vol.83(6),pp.2411~2451.
(2)Aigner D.J.and Chu S.F.,1968,“On Estimating the Industry Production Function”,American Economic Review,Vol.58(4),pp.826~839.
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(7)Chung Y.H.,F?re R.and Grosskopf S.,1997,“Productivity and Undesirable Outputs:A Directional Distance Function Approach”,Microeconomics,Vol.51(3),pp.229~240.
(8)Coggins J.S.and Swinton J.R.,1996,“The Price of Pollution:A Dual Approach to Valuing SO2Allowances”,Journal of Environmental Economics and Management,Vol.30(1),pp.58~72.
(9)Davidson R.and MacKinnon J.G.,2000,“Bootstrap Tests:How Many Bootstraps?”,Econometric Reviews,Vol.19(1),pp.55~68.
(10)Du L.and Mao J.,2015,“Estimating the Environmental Efficiency and Marginal CO2Abatement Cost of Coal-Fired Power Plants in China”,Energy Policy,Vol.85,pp.347~356.
(11)Du L.,Hanley A.and Wei C.,2015,“Estimating the Marginal Abatement Cost Curve of CO2Emissions in China:Provincial Panel Data Analysis”,Energy Economics,Vol.48,pp.217~229.
(12)F?re R.and Lundberg A.,2006,“Parameterizing the Shortage Function”,Mimeo.Department of Economics,Oregon State University.
(13)F?re R.,Grosskopf S.,Hayes K.J.and Margaritis D.,2008,“Estimating Demand with Distance Functions:Parameterization in The Primal and Dual”,Journal of Econometrics,Vol.147(2),pp.266~274.
(14)F?re R.,Grosskopf S.,Lovell C.A.K.and Yaisawarng S.,1993,“Derivation of Shadow Prices for Undesirable Outputs:A Distance Function Approach”,Review of Economics and Statistics,Vol.75(2),pp.374~380.
(15)F?re R.,Grosskopf S.,Noh D.and Weber W.,2005,“Characteristics of A Polluting Technology:Theory and Practice”,Journal of Econometrics,Vol.126(2),pp.469~492.
(16)F?re R.,Grosskopf S.and Weber W.L.,2006,“Shadow Prices and Pollution Costs in U.S.Agriculture”,Ecological Economics,Vol.56(1),pp.89~103.
(17)F?re R.,Martins-Filho C.and Vardanyan M.,2010,“On Functional Form Representation of Multi-output Production Technologies”,Journal of Productivity Analysis,Vol.33(2),pp.81~96.
(18)Hsieh C.,Hurst E.,Jones C.I.and Klenow P.J.,2013,“The Allocation of Talent and U.S.Economic Growth”,NBERWorking Papers,No.W18693.
(19)Jones C.I.,2016,“The Facts of Economic Growth”,Handbook of Macroeconomics,Vol.2,pp.3~69.
(20)Lee J.D.,Park J.B.and Kim T.Y.,2002,“Estimation of the Shadow Prices of Pollutants with Production/Environment Inefficiency Taken into Account:ANonparametric Directional Distance Function Approach”,Journal of Environmental Management,Vol.64(4),pp.365~375.
(21)Lee M.and Zhang N.,2012,“Technical Efficiency,Shadow Price of Carbon Dioxide Emissions,and Substitutability for Energy in the Chinese Manufacturing Industries”,Energy Economics,Vol.34(5),pp.1492~1497.
(22)Li K.and Lin B.,2015,“Metafroniter Energy Efficiency with CO2Emissions and Its Convergence Analysis for China”,Energy Economics,Vol.48,pp.230~241.
(23)Murty M.N.and Kumar S.,2002,“Measuring the Cost of Environmentally Sustainable Industrial Development in India:A Distance Function Approach”,Environment and Development Economics,Vol.7(03),pp.467~486.
(24)Murty M.N.,Kumar S.and Dhavala K.K.,2007,“Measuring Environmental Efficiency of Industry:A Case Study of Thermal Power Generation in India”,Environmental and Resource Economics,Vol.38(1),pp.31~50.
(25)Ouyang X.and Sun C.,2015,“Energy Savings Potential in China's Industrial Sector:From the Perspectives of Factor Price Distortion and Allocative Inefficiency”,Energy Economics,Vol.48,pp.117~126.
(26)Park H.and Lim J.,2009,“Valuation of Marginal CO2Abatement Options for Electric Power Plants in Korea”,Energy Policy,Vol.37(5),pp.1834~1841.
(27)Rezek J.P.and Campbell R.C.,2007,“Cost Estimates for Multiple Pollutants:A Maximum Entropy Approach”,Energy Economics,Vol.29(3),pp.503~519.
(28)Rezek J.and Blair B.F.,2005,“Abatement Cost Heterogeneity in Phase I Electric Utilities”,Contemporary Economic Policy,Vol.23(3),pp.324~340.
(29)Simar L.and Wilson P.W.,1998,“Sensitivity Analysis of Efficiency Scores:How to Bootstrap in Nonparametric Frontier Models”,Management Science,Vol.44(1),pp.49~61.
(30)Simar L.and Wilson P.W.,2011,“Performance of the Bootstrap for DEA Estimators and Iterating the Principle”,Handbook on Data Envelopment Analysis,Springer,US.
(31)Vardanyan M.and Noh D.W.,2006,“Approximating the Cost of PollutionAbatement via Alternative Specifications of A Multi-Output Production Technology:A Case of the U.S.Electric Utility Industry tric Utility Industry”,Journal of Environmental Management,Vol.80,pp.177~190.
(32)Wei C.,L?schel A.and Liu B.,2013,“An Empirical Analysis of the CO2Shadow Price in Chinese Thermal Power Enterprises”,Energy Economics,Vol.40(18),pp.22~31.
(33)Xiao B.,Niu D.,Wu H.and Wang H.,2017,“Marginal Abatement Cost of CO2in China Based on Directional Distance Function:An Industry Perspective”,Sustainability,Vol.9(1),pp.138.
(34)Yang H.and Pollitt M.,2010,“The Necessity of Distinguishing Weak and Strong Disposability among Undesirable Outputs in DEA:Environmental Performance of Chinese Coal-Fired Power Plants”,Energy Policy,Vol.38(8),pp.4440~4444.
(35)Yuan P.,Liang W.and Cheng S.,2012,“The Margin Abatement Costs of CO2in Chinese Industrial Sectors”,Energy Procedia,Vol.14,pp.1792~1797.
(36)Zhang X.,Xu Q.,Zhang F.,Guo Z.and Rao R.,2014,“Exploring Shadow Prices of Carbon Emissions at Provincial Levels in China”,Ecological Indicators,Vol.46(11),pp.407~414.
(37)Zhou P.,Zhou X.and Fan L.W.,2014,“On Estimating Shadow Prices of Undesirable Outputs with Efficiency Models:A Literature Review”,Applied Energy,Vol.130(5),pp.799~806.
(38)Zhou X.,Fan L.W.and Zhou P.,2015,“Marginal CO2Abatement Costs:Findings from Alternative Shadow Price Estimates for Shanghai Industrial Sectors”,Energy Policy,Vol.77,pp.109~117.
(39)陈诗一:《工业二氧化碳的影子价格:参数化和非参数化方法》,《世界经济》,2010年第8期。
(40)陈诗一:《边际减排成本与中国环境税改革》,《中国社会科学》,2011a年第3期。
(41)陈诗一:《中国工业分行业统计数据估算:1980~2008》,《经济学(季刊)》,2011b年第3期。
(42)刘春梅、高阳:《碳交易下我国工业部门间碳减排成本研究》,《软科学》,2016年第3期。
(43)刘明磊、朱磊、范英:《我国省级碳排放绩效评价及边际减排成本估计:基于非参数距离函数方法》,《中国软科学》,2011年第3期。
(44)马赞甫:《线性规划中影子价格的“非唯一性”》,《系统工程》,2007年第4期。
(45)涂正革:《工业二氧化硫排放的影子价格:一个新的分析框架》,《经济学(季刊)》,2009年第1期。
(46)魏楚:《中国城市CO2边际减排成本及其影响因素》,《世界经济》,2014年第7期。
(47)吴力波、钱浩祺、汤维祺:《基于动态边际减排成本模拟的碳排放权交易与碳税选择机制》,《经济研究》,2014年第9期。
(48)吴英姿、闻岳春:《中国工业绿色生产率、减排绩效与减排成本》,《科研管理》,2013年第2期。
(49)袁鹏、程施:《我国工业污染物的影子价格估计》,《统计研究》,2011年第9期。
(50)朱宁、王兵、于之倩:《基于风险偏好的中国商业银行不良贷款影子价格研究》,《金融研究》,2014年第6期。
(1)关于各类方法优缺点及适用性的讨论可以参见魏楚(2014)。
(2)由于不可观察的生产技术会影响企业的投资决策,进而影响企业的资本存量变化,由此带来的内生性问题会使得资本及劳动投入的OLS估计系数有偏。对于生产函数参数估计的内生性问题的详细讨论可以参见Ackerberg等(2015)发表于《Econometrica》的文章。
(3)该假设表明经济资源具有稀缺性,在生产前沿面上无法同时增加所有产出,若要增加某种产出就需要减少另一种产出,生产前沿面上点的斜率即为两种产出的边际转换率。达到均衡时,各项产出间的边际转换率(MRT)等于其相对应的价格(亦或是影子价格)之比。
(4)关于生产技术性质的更多介绍可以参见F?re等(2006)。
(5)本文用二氧化碳影子价格作为二氧化碳边际减排成本的近似,下文分析中,这两个概念将会交替使用。
(6)Aigner和Chu(1968)最早采用二次型函数将生产前沿面参数化,F?re和Lundberg(2006)证明了二次型函数是可以通过施加约束条件而满足传递性的两种函数之一,且F?re等(2008)指出只有二次型函数同时拥有计算边际效应的一阶以及二阶参数。F?re等(2010)用蒙特卡罗方法分析了二次型函数与超越对数函数在不同技术设定下的表现,结果发现无论生产技术如何设定,二次型的表现都要优于超越对数函数的表现。
(7)朱宁等(2014)研究表明,不同方向向量的选取可以代表决策单元的不同风险偏好。
(8)由于2011年以后国家统计局不再报告分行业的工业总产值,使得本文样本期只能更新至2011年。此外,2011年以后,《中国能源统计年鉴》对部分行业分类进行了调整,例如将橡胶与塑料制品归为一个行业等,为保持数据口径的一致性,本文最终将样本期更新到2011年。
(9)在方向向量的选择上,Chaffai等(2008)与朱宁等(2014)对不同偏好下方向向量的选择进行了讨论。
(10)Davidson和Mackinnon(2000)认为,在0.05的显著性水平下,自体抽样次数不应该小于399次,而次数的增加并不能对结果产生显著的影响。在本文的框架下,每做一次自体抽样都需要对样本求解非线性规划问题,从而增加不必要的自体抽样次数会大大增加计算复杂度,综合考虑之下本文最终将自体抽样次数设定为1000次。采用Matlab的优化工具箱,将抽样次数设定为1000时,需要计算6小时左右。
(11)为进一步考察二氧化碳影子价格变化规律,本文按照图2的结果将整个样本期分为3个子样本,并计算了不同行业二氧化碳影子价格在不同子样本中的平均值,结果参见本文附录B。
(12)有兴趣的读者可以参考Ouyang和Sun(2015)的论文,他们在这一领域做了较为有意义的探索。
(13)这里注意区分二氧化碳影子价格本身和二氧化碳影子价格的变化趋势。二氧化碳影子价格高,表示边际减排成本大,降低一单位二氧化碳导致好产出下降多;而二氧化碳影子价格上升,表示边际减排成本越来越大,降低一单位二氧化碳导致的好产出的下降越来越多,同时说明此时的生产技术越来越“清洁”。
(14)现有文献在解释随着效率的提高(生产技术更为清洁),二氧化碳影子价格将呈现出上升趋势时,认为随着技术的提高,进一步改善技术的空间将越来越小,即实现更为清洁的生产技术难度加大,从而导致为此付出的成本增加(Lee etal.,2002;F?re et al.,2005;朱宁等,2014)。
(15)当生产达到帕累托最优时,产出边际转化率等于产品相对价格之比。由于本文假定好产出的价格为pm=1,则边际碳排放强度可以表示为d CO2/dy=1/MRTCO2,y=py/pCO2=1/pCO2,即在均衡条件下边际碳排放强度等于二氧化碳影子价格的倒数。
(2)Aigner D.J.and Chu S.F.,1968,“On Estimating the Industry Production Function”,American Economic Review,Vol.58(4),pp.826~839.
(3)Auffhammer M.and Carson R.T.,2008,“Forecasting The Path of China's CO2Emissions Using Province-level Information”,Journal of Environmental Economics and Management,Vol.55(3),pp.229~247.
(4)Chaffai M.E.,Dietsch M.and Godlewsky C.,2008,“The Price of Bad Loans:An International Banking Comparison”,ASSA,Annual Meeting,January,New Orleans.
(5)Chambers R.G.,Chung Y.and F?re R.,1998,“Profit,Directional Distance Functions and Nerlovian Efficiency”,Journal of Optimization Theory and Applications,Vol.98(2),pp.351~364.
(6)Choi Y.,Zhang N.and Zhou P.,2012,“Efficiency and Abatement Costs of Energy-Related CO2Emissions in China:ASlacks-Based Efficiency Measure”,Applied Energy,Vol.98(5),pp.198~208.
(7)Chung Y.H.,F?re R.and Grosskopf S.,1997,“Productivity and Undesirable Outputs:A Directional Distance Function Approach”,Microeconomics,Vol.51(3),pp.229~240.
(8)Coggins J.S.and Swinton J.R.,1996,“The Price of Pollution:A Dual Approach to Valuing SO2Allowances”,Journal of Environmental Economics and Management,Vol.30(1),pp.58~72.
(9)Davidson R.and MacKinnon J.G.,2000,“Bootstrap Tests:How Many Bootstraps?”,Econometric Reviews,Vol.19(1),pp.55~68.
(10)Du L.and Mao J.,2015,“Estimating the Environmental Efficiency and Marginal CO2Abatement Cost of Coal-Fired Power Plants in China”,Energy Policy,Vol.85,pp.347~356.
(11)Du L.,Hanley A.and Wei C.,2015,“Estimating the Marginal Abatement Cost Curve of CO2Emissions in China:Provincial Panel Data Analysis”,Energy Economics,Vol.48,pp.217~229.
(12)F?re R.and Lundberg A.,2006,“Parameterizing the Shortage Function”,Mimeo.Department of Economics,Oregon State University.
(13)F?re R.,Grosskopf S.,Hayes K.J.and Margaritis D.,2008,“Estimating Demand with Distance Functions:Parameterization in The Primal and Dual”,Journal of Econometrics,Vol.147(2),pp.266~274.
(14)F?re R.,Grosskopf S.,Lovell C.A.K.and Yaisawarng S.,1993,“Derivation of Shadow Prices for Undesirable Outputs:A Distance Function Approach”,Review of Economics and Statistics,Vol.75(2),pp.374~380.
(15)F?re R.,Grosskopf S.,Noh D.and Weber W.,2005,“Characteristics of A Polluting Technology:Theory and Practice”,Journal of Econometrics,Vol.126(2),pp.469~492.
(16)F?re R.,Grosskopf S.and Weber W.L.,2006,“Shadow Prices and Pollution Costs in U.S.Agriculture”,Ecological Economics,Vol.56(1),pp.89~103.
(17)F?re R.,Martins-Filho C.and Vardanyan M.,2010,“On Functional Form Representation of Multi-output Production Technologies”,Journal of Productivity Analysis,Vol.33(2),pp.81~96.
(18)Hsieh C.,Hurst E.,Jones C.I.and Klenow P.J.,2013,“The Allocation of Talent and U.S.Economic Growth”,NBERWorking Papers,No.W18693.
(19)Jones C.I.,2016,“The Facts of Economic Growth”,Handbook of Macroeconomics,Vol.2,pp.3~69.
(20)Lee J.D.,Park J.B.and Kim T.Y.,2002,“Estimation of the Shadow Prices of Pollutants with Production/Environment Inefficiency Taken into Account:ANonparametric Directional Distance Function Approach”,Journal of Environmental Management,Vol.64(4),pp.365~375.
(21)Lee M.and Zhang N.,2012,“Technical Efficiency,Shadow Price of Carbon Dioxide Emissions,and Substitutability for Energy in the Chinese Manufacturing Industries”,Energy Economics,Vol.34(5),pp.1492~1497.
(22)Li K.and Lin B.,2015,“Metafroniter Energy Efficiency with CO2Emissions and Its Convergence Analysis for China”,Energy Economics,Vol.48,pp.230~241.
(23)Murty M.N.and Kumar S.,2002,“Measuring the Cost of Environmentally Sustainable Industrial Development in India:A Distance Function Approach”,Environment and Development Economics,Vol.7(03),pp.467~486.
(24)Murty M.N.,Kumar S.and Dhavala K.K.,2007,“Measuring Environmental Efficiency of Industry:A Case Study of Thermal Power Generation in India”,Environmental and Resource Economics,Vol.38(1),pp.31~50.
(25)Ouyang X.and Sun C.,2015,“Energy Savings Potential in China's Industrial Sector:From the Perspectives of Factor Price Distortion and Allocative Inefficiency”,Energy Economics,Vol.48,pp.117~126.
(26)Park H.and Lim J.,2009,“Valuation of Marginal CO2Abatement Options for Electric Power Plants in Korea”,Energy Policy,Vol.37(5),pp.1834~1841.
(27)Rezek J.P.and Campbell R.C.,2007,“Cost Estimates for Multiple Pollutants:A Maximum Entropy Approach”,Energy Economics,Vol.29(3),pp.503~519.
(28)Rezek J.and Blair B.F.,2005,“Abatement Cost Heterogeneity in Phase I Electric Utilities”,Contemporary Economic Policy,Vol.23(3),pp.324~340.
(29)Simar L.and Wilson P.W.,1998,“Sensitivity Analysis of Efficiency Scores:How to Bootstrap in Nonparametric Frontier Models”,Management Science,Vol.44(1),pp.49~61.
(30)Simar L.and Wilson P.W.,2011,“Performance of the Bootstrap for DEA Estimators and Iterating the Principle”,Handbook on Data Envelopment Analysis,Springer,US.
(31)Vardanyan M.and Noh D.W.,2006,“Approximating the Cost of PollutionAbatement via Alternative Specifications of A Multi-Output Production Technology:A Case of the U.S.Electric Utility Industry tric Utility Industry”,Journal of Environmental Management,Vol.80,pp.177~190.
(32)Wei C.,L?schel A.and Liu B.,2013,“An Empirical Analysis of the CO2Shadow Price in Chinese Thermal Power Enterprises”,Energy Economics,Vol.40(18),pp.22~31.
(33)Xiao B.,Niu D.,Wu H.and Wang H.,2017,“Marginal Abatement Cost of CO2in China Based on Directional Distance Function:An Industry Perspective”,Sustainability,Vol.9(1),pp.138.
(34)Yang H.and Pollitt M.,2010,“The Necessity of Distinguishing Weak and Strong Disposability among Undesirable Outputs in DEA:Environmental Performance of Chinese Coal-Fired Power Plants”,Energy Policy,Vol.38(8),pp.4440~4444.
(35)Yuan P.,Liang W.and Cheng S.,2012,“The Margin Abatement Costs of CO2in Chinese Industrial Sectors”,Energy Procedia,Vol.14,pp.1792~1797.
(36)Zhang X.,Xu Q.,Zhang F.,Guo Z.and Rao R.,2014,“Exploring Shadow Prices of Carbon Emissions at Provincial Levels in China”,Ecological Indicators,Vol.46(11),pp.407~414.
(37)Zhou P.,Zhou X.and Fan L.W.,2014,“On Estimating Shadow Prices of Undesirable Outputs with Efficiency Models:A Literature Review”,Applied Energy,Vol.130(5),pp.799~806.
(38)Zhou X.,Fan L.W.and Zhou P.,2015,“Marginal CO2Abatement Costs:Findings from Alternative Shadow Price Estimates for Shanghai Industrial Sectors”,Energy Policy,Vol.77,pp.109~117.
(39)陈诗一:《工业二氧化碳的影子价格:参数化和非参数化方法》,《世界经济》,2010年第8期。
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(1)关于各类方法优缺点及适用性的讨论可以参见魏楚(2014)。
(2)由于不可观察的生产技术会影响企业的投资决策,进而影响企业的资本存量变化,由此带来的内生性问题会使得资本及劳动投入的OLS估计系数有偏。对于生产函数参数估计的内生性问题的详细讨论可以参见Ackerberg等(2015)发表于《Econometrica》的文章。
(3)该假设表明经济资源具有稀缺性,在生产前沿面上无法同时增加所有产出,若要增加某种产出就需要减少另一种产出,生产前沿面上点的斜率即为两种产出的边际转换率。达到均衡时,各项产出间的边际转换率(MRT)等于其相对应的价格(亦或是影子价格)之比。
(4)关于生产技术性质的更多介绍可以参见F?re等(2006)。
(5)本文用二氧化碳影子价格作为二氧化碳边际减排成本的近似,下文分析中,这两个概念将会交替使用。
(6)Aigner和Chu(1968)最早采用二次型函数将生产前沿面参数化,F?re和Lundberg(2006)证明了二次型函数是可以通过施加约束条件而满足传递性的两种函数之一,且F?re等(2008)指出只有二次型函数同时拥有计算边际效应的一阶以及二阶参数。F?re等(2010)用蒙特卡罗方法分析了二次型函数与超越对数函数在不同技术设定下的表现,结果发现无论生产技术如何设定,二次型的表现都要优于超越对数函数的表现。
(7)朱宁等(2014)研究表明,不同方向向量的选取可以代表决策单元的不同风险偏好。
(8)由于2011年以后国家统计局不再报告分行业的工业总产值,使得本文样本期只能更新至2011年。此外,2011年以后,《中国能源统计年鉴》对部分行业分类进行了调整,例如将橡胶与塑料制品归为一个行业等,为保持数据口径的一致性,本文最终将样本期更新到2011年。
(9)在方向向量的选择上,Chaffai等(2008)与朱宁等(2014)对不同偏好下方向向量的选择进行了讨论。
(10)Davidson和Mackinnon(2000)认为,在0.05的显著性水平下,自体抽样次数不应该小于399次,而次数的增加并不能对结果产生显著的影响。在本文的框架下,每做一次自体抽样都需要对样本求解非线性规划问题,从而增加不必要的自体抽样次数会大大增加计算复杂度,综合考虑之下本文最终将自体抽样次数设定为1000次。采用Matlab的优化工具箱,将抽样次数设定为1000时,需要计算6小时左右。
(11)为进一步考察二氧化碳影子价格变化规律,本文按照图2的结果将整个样本期分为3个子样本,并计算了不同行业二氧化碳影子价格在不同子样本中的平均值,结果参见本文附录B。
(12)有兴趣的读者可以参考Ouyang和Sun(2015)的论文,他们在这一领域做了较为有意义的探索。
(13)这里注意区分二氧化碳影子价格本身和二氧化碳影子价格的变化趋势。二氧化碳影子价格高,表示边际减排成本大,降低一单位二氧化碳导致好产出下降多;而二氧化碳影子价格上升,表示边际减排成本越来越大,降低一单位二氧化碳导致的好产出的下降越来越多,同时说明此时的生产技术越来越“清洁”。
(14)现有文献在解释随着效率的提高(生产技术更为清洁),二氧化碳影子价格将呈现出上升趋势时,认为随着技术的提高,进一步改善技术的空间将越来越小,即实现更为清洁的生产技术难度加大,从而导致为此付出的成本增加(Lee etal.,2002;F?re et al.,2005;朱宁等,2014)。
(15)当生产达到帕累托最优时,产出边际转化率等于产品相对价格之比。由于本文假定好产出的价格为pm=1,则边际碳排放强度可以表示为d CO2/dy=1/MRTCO2,y=py/pCO2=1/pCO2,即在均衡条件下边际碳排放强度等于二氧化碳影子价格的倒数。