The carbon dioxide marginal abatement cost calculation of Chinese provinces based on stochastic frontier analysis

The Chinese government made a commitment to achieve a 40–45 % reduction in carbon emissions per unit of gross domestic product (GDP) by 2020 compared with 2005. Most provinces followed the national commitment due to unified task of 40–45 % reduction in carbon emissions. However, different industrial structures, energy consumption structures and natural resources endowment of each province vary the emission abatement costs. Each province should take the carbon dioxide abatement cost into consideration for the carbon dioxide reduction target. Data envelopment analysis (DEA) and linear programming (LP) methods were used to measure the marginal abatement cost in previous studies. In this paper, we built a quadratic parametric directional distance function (DDF) to measure the carbon dioxide marginal abatement cost of Chinese provinces. To overcome the flaw of ignoring random errors in previous research, this paper compared results of stochastic frontier analysis (SFA) method and DEA method. Because DEA method only considers the inefficiency and SFA method can distinguish the random error from inefficiency, the result of the average carbon dioxide marginal abatement cost of each province calculated by SFA was 55 % lower than DEA method. As the random error may be introduced by chosen function form, Spearman test and paired sample T test were used to test the correlation of two methods’ MAC results. The results show that the ranking order MAC results sequence of SFA method and DEA method is highly correlated. But the MAC value of SFA and DEA methods has significant difference. As half of the error comes from the random error, the MAC results calculated by SFA method are more precise than DEA method. So SFA method is more appropriate than DEA in this paper. This result reinforces the feasibility of the Chinese government carbon dioxide emission reduction target. However, this study proved that the carbon dioxide emissions and marginal abatement cost varied from province to province. Furthermore, there was no distinct correlation between carbon dioxide emissions and the marginal abatement cost. On the contrary, the marginal abatement cost was related to the industrial structures, energy consumption structures and natural resources endowment of each province. Therefore, two policy suggestions are proposed as CO2 emission reduction principle: First, central government should establish CO2 emission reduction targets based on MAC and local economic affordability. Second, resource endowments and embodied carbon transfer should be considered.


Introduction
The rapid development of Chinese economy has caused a large amount of carbon dioxide (CO 2 ) emission. CO 2 emission of China has increased quickly since 2000 (Song, 2010;Guo et al., 2010), as the proportion of Chinese CO 2 emission in the global emission has increased from 12.9% in 2000 to about 23% in 2010 (China Electricity Council, 2011). Besides, the proportion has sharply reached quintile in 2013 (Nyakundi et al., 2013). According to a scientific forecast, the proportion will drastically increase to one-third if no effective CO 2 emission restriction has imposed in China (Liao & Wei, 2011). Facing both the awareness of environmental protection and the international pressure on CO 2 emission reduction, Chinese government made a commitment that achieving a 40%-45% reduction in carbon emissions per unit of GDP by 2020 compared with 2005 in the Climate Conference in Copenhagen in 2009(China.com, 2009. Lacking central government's differentiation carbon dioxide reduction allocation, most provinces follow the national commitment. However, the industrial structure, energy consumption structure and natural resources of each province vary. Hence, it's not appropriate that all provinces 1 impose the identical CO 2 emission reduction criterion. To address this issue, previous studies researches on CO  . The MAC can express the complexity of CO 2 reduction more directly than macro abatement cost. Directional Distance Function (DDF) has been widely used by previous studies in calculation of CO 2 MAC. However, the different forms of DDF model will lead to different calculation results. In addition, the two methods commonly used by previous studies to solve DDF, data envelopment analysis (DEA) and linear programming (LP), also have flaws. Differentiable everywhere of function are required while using DEA method. Besides, different frontier of production function and direction vector of DEA method will lead to different CO 2 MAC results. LP method doesn't take measuring error and approximation error in to consideration. Therefore, the calculated results of CO 2 reduction cost varied in previous studies. DDF followed by stochastic frontier analysis (SFA) method can eliminate random error thereby is used to count accurate CO 2 MAC of Chinese provinces in this paper. The result shows that the average carbon dioxide marginal abatement cost of each province is 46% lower than previous studies. Accordingly policy suggestions considering each Chinese province's disparity of CO 2 MAC, industrial structure, energy consumption structure and natural resources are proposed. This paper is organized as follows. Section 2 introduces the literature review of carbon dioxide abatement cost. Section 3 describes the model and method. Section 4 constructs the direction distance model and stochastic frontier analysis. The conclusion and policy suggestions in section 5.

Literature Review
The existing studies show that a multitude of quantitative models are used to measure

Comments on Literature
All above-mentioned models have room for improvement. Although the marginal cost curve model is simple in computation, the form of cost curve will lead to fitting error. GDP was treated as input in VAR model and MARKAL model while distance function model consider GDP as output. Thereby, GDP and CO 2 emission can be treated equally in distance function model. Therefore, distance function model is more suitable as MAC have close relationship with economic loss. Parametric distance function and nonparametric distance function were two popular methods used to measure CO 2 MAC (Liu et al., 2011). Parametric distance function needs to pre-establish a function which is differentiable everywhere while specific function is not needed in nonparametric distance function. The parametric distance function has the advantage of manipulate algebraically (Choi et al., 2012). In 1990s, Shephard output distance function was first used to measure the MAC of pollutants (Shephard, 1970

Model And Method
DDF model measuring MAC of undesirable output was proposed by Chambers and Färe separately. DDF depicts an input-output process with multiple input and outputs based on production function. Then a production possibility curve (PPC) in the two-dimensional space was built. However, PPC boundary optimal cannot be touched as the restriction of technology. Hence, MAC can be measured by distance between output set and PPC boundary.

Establishment of DDF
In a certain Chinese province, consider a production process employs three inputs capital (X k ), labor (X L ) and energy (X E ) and one desirable output GDP (y) and one undesirable output CO 2 emission (b). The production technology set P can be defined as: P= {(y,b):X can produce (y,b)} The set has following properties: (1) Inputs are free disposability: The increase of inputs will lead to increased output, (2) Undesirable outputs are weak free disposability: Proportionate reduction of desirable and undesirable outputs simultaneously is possible with given inputs, in other words, (y,b)∈P,0≤θ≤1,then (θy,θb)∈P.
(4) Null-jointness: desirable output must be accompanied by the generation of undesirable and the only way to avoid desirable and undesirable outputs is to stop all production activities which means (y,b)∈P, and b=0, then y=0. Let g=(g y ,g b ) as the directional vector which indicates the expansion of GDP in the direction of g y and the reduction of CO 2 in the direction of g b , then the DDF can be defined as: (1) β presents the maximum proportion of expansion or reduction. β=0 when the decision making unit lies on the production frontier. Point A stands for a certain region in the production technology set P, while coordinate axis y and b represent GDP and CO 2 emission in this region respectively. A moves toward point B, which not only reduces undesirable output (CO 2 emission) but also increase desirable output (GDP).Hence, DDF is measured by β=AB/Og.  The revenue of a certain region can be defined as:

Calculation of DDF
p represents price of GDP. Let p=1. p b represents price of CO 2 and indicate MAC in this paper. MAC express by Eq. 6 after taking partial derivation of b and y on Eq. 5.
Eq.2 is the first-order homogeneous equation which contains desirable and undesirable outputs. To measure MAC, natural logarithm was taken as normalization process on Eq.2. Hence, 0<D 0 <1,then lnD 0 <0. According to Eq. 3 and numerical value of inputs and outputs, MAC can be expressed as: The Measurement of CO 2 emission factor IPCC proposed is showed by Eq.11. δ j =M j ×β j ×ε j ×ω (11) M j presents net calorific value of energy j. β j presents carbon content of the unit heat value of energy j. ε j presents carbohydrate oxidation of energy j. ω presents gasification coefficient of CO 2 and has constant value of 44/12. According to standard coal coefficient, net calorific power, carbon content and oxygenation efficiency in 2014 China Energy Statistic Yearbook and Eq. 11, CO 2 emission factors are measured in Table 2.  Hence, SFA method is necessarily used in this paper. Meanwhile, coefficient of Eq.9, standard deviation and statistical tests at 1% significance were shown in Table 4.  Table 4 is greater than the critical value which means the t-test of coefficient is significant and the coefficient result is reliable.

Influence factor analysis of MAC
The composition of CO 2 emission and comparison between CO 2 emission and MAC are shown in Fig.4 and Fig. 5. (1)Industrial structures Fig.4 shows that large CO 2 emitters like Shandong, Hebei, Shanxi and Inner Mongolia are highly-developed industry provinces. According to 2014 China Statistic Yearbook, the ratios of secondary industry of large emitters are more than 50%. Especially, high-carbon secondary industry like steel industry and mining industry are the leading industry in those large emitters. Hence, the MACs of large emitters are low. Small emitters can be divided into two groups. First group is provinces with highly-developed but low-carbon tertiary industry like financial industry wholesale and retail trade industry and catering accommodation industry. Beijing, Tianjin, Shanghai and Hainan are in the first group. The ratios of low-carbon industry in those provinces are more than half of total ratio of tertiary industry. As low-carbon industries emit little CO 2 , it will cost large economic loss to reduce CO 2 emission. Therefore MACs of first group of small emitters are low. The other group of small emitters includes Western provinces like Ningxia, Gansu and Qinghai with rising new energy industry. However, there are still metallurgy industries with large CO 2 emission in those provinces. Hence, with relatively small CO 2 emission, MACs of second group provinces are low.
(2) Energy consumption structures From Fig.4, Coal is main emitter of CO 2 emission in the whole country. The average ratio of CO 2 emission from coal combustion of 30 Chinese provinces is 80%. Coal is mainly used for power generation, production of building materials and domestic-use coal. Besides, Coke, mainly used in metal smelting, is the second large CO 2 emission.
Hebei province, one of the large steel provinces in China, consume large amount of coke for metal smelting. 23% of CO 2 emission came from coke. Diesel oil is mainly used as fuel for large vehicle and vessel. Gasoline is the fuel for compact cars. Blooming trade and large demand in transportation in Shanghai, Guangdong and Zhejiang consume large amount of diesel oil and gasoline. Small amount of kerosene and fuel oil were consumed natural gas is a relatively clean energy. The CO 2 emissions from these three energies were low. It's easier to reduce high-carbon energy's CO 2 emission. Therefore, MAC of Hebei province and Shandong province are low while Beijing and Shanghai are high.
(3)Natural resources Southern provinces as Hubei, Sichuan and Yunnan provinces have abundant hydro-power. The ratio of hydropower in these three provinces contains 16%, 17% and 14% in 2012. Inner Mongolia Autonomous Region, Hebei and Liaoning provinces have affluent wind power resources as the ratios of installed capacity of wind-driven power are 35%, 10% and 9%. Hydropower and wind power are clean energy and will not produce CO 2 emission. Hence, the MACs of above-mentioned provinces are high.

Conclusion and the policy suggestions 5.1 Conclusion
(1) Applying SFA method, MAC results are precise but are 46% less than LP method in this paper as random errors were taken into concerned.
(2) There are no distinct correlation between CO 2 emission and MAC.
(3) Because of different industrial structures, energy consumption structures and natural resources among Chinese provinces, the CO 2 emission and MAC of each province varied.

Policy suggestions
From the national level, high MAC provinces should reduce more CO 2 emission while the low MAC provinces reduce less CO 2 emission. Therefore, a fair but distinct policy should be proposed. 5.2.1 Change energy production and consumption structures Coal which contains more than 70% of total primary energy is the dominating energy in Chinese production structure. Crude oil and natural gas only holds less than 10% of total energy. Clean energy which contains hydroelectric, wind electricity and nuclear power attains 10% of all energy. The abundant hydroelectricity resources in Hubei, Sichuan and Yunnan provinces, wind electricity resources in Inner Mongolia, Hebei and Liaoning provinces and the solar power energy which is in a stage of development in lots of Chinese provinces made energy production structure transformation capable. Coal is also the main consumption energy in all Chinese provinces. Coal combustion caused large amount of CO 2 emission. According to the calculation in this paper, the ratio of CO 2 emission from coal is 88.37%, 92.2% and 91.75% in Shanxi province, Ningxia Hui Autonomous Region and Inner Mongolia Autonomous Region. And it's not restricts in provinces with abundant coal industry. The average value of ration of CO 2 emission from coal among nationwide is 80.17%. High CO 2 emission from coal combustion is a nationwide issue. Hence, transform energy consumption structures in all Chinese provinces should be proposed. 5.2.2 Synergetic development in industry structure and economy among provinces Different industrial structure is one of the reasons that lead to different CO 2 emission and MAC in Chinese provinces. Thermal power, steel and chemical engineering industries are the leading industry in high MAC provinces in Central and Western China. These high CO 2 industries are second industries with low added value. And the MACs are relatively low. Economic development will be destructed if simply reduce large industry production. Synergetic development in industry structure and economy among provinces is more reasonable. Labor, market, environment and policy are the factors which will bring to the industrial transfer. During the development, relatively developed region will prioritize tertiary industry with high additional value and transfer the secondary industry with low additional value into relatively developing region. Pollutions are also move to the developing region. Therefore, policy of synergetic development among developed and developing regions should be proposed. Developed region should compensate developing region which undertake more pollution.