3. Empirical Results and Discussion
DEAP2.1 software and an Excel planning method were used to solve the original DEA and ZSG-DEA efficiency. The last column of
Table 1 presents the results of the original DEA efficiency for 2020, which reveals that the average initial distribution efficiency is 0.731,
i.e., a medium-level average efficiency, and that the differences between provinces and cities are dramatic.
Table 1 indicates that the efficiency values of 15 provinces are under average levels, which accounts for 50 per cent of these values. Furthermore, the initial efficiency values for five provinces and cities reach 1, which demonstrates that the allocation for these five provinces and cities is DEA effective but that the other 25 provinces and cities are not DEA efficient. Some provinces, such as Shan Xi and Ning Xia, do not perform well in terms of efficiency. For provinces with abundant energy resources, such as Shan Xi, a low efficiency value means that there is greater potential to reduce carbon emissions.
Based on the original DEA model, we may adjust the emission rights of all provinces and cities based on their efficiency values and slack variables so that the lowest carbon emission with respect to the economy and the carbon dioxide emission with the greatest efficiency might be achieved. However, this adjustment does not consider specific allocation situations, which is not feasible. For example, the total amount of carbon dioxide emission is fixed, which means that when one DMU reduces the input of a variable, the input of this variable into another DMU will increase accordingly. The efficiency values of original DEA and slack variables are not consistent with restraining the fixed total amount and are not able to achieve reasonable reallocation of input. Therefore, we must assess the efficiency values of the ZSG-DEA model and make proper adjustments of carbon emission rights based on the efficiency values and slack variables of the ZSG-DEA model.
Fair and effective allocation results in effective allocative efficiencies for all participating provinces, whether in the original DEA model or in the ZSG-DEA model. As discussed above, the status quo of most provinces and cities is currently ineffective, and for that reason we must adjust the ZSG-DEA model. Based on Equation (2), the amount that carbon emission must be reduced in some areas and the amount of increase needed in other provinces and cities can be calculated to reach the efficient frontiers. The multiple iteration method is employed to allow all provinces and cities reach their efficient frontiers.
According to the results of the ZSG-DEA model in the initial allocation, we obtain the voluntary trade matrix for all provinces and cities, and the results of the adjusted allocation are shown in
Table A1,
Table A2,
Table A3,
Table A4 and
Table A5. Using the adjusted emission amount as the input variable and making another estimation of the efficiency values of the original DEA model, we find that the original DEA efficiency values increase significantly.
Given the initially allocated carbon dioxide emissions, consumption of NFFs (Non-fossil fuels) and the results of the ZSG-DEA model, we can obtain the increase and decrease matrix for the carbon allocations of all provinces and cities and can identify how to adjust the values to acquire a new set of adjusted carbon emission and NFF consumption, as shown by the first iteration in
Table A1.
In the next step, the adjusted carbon emission and the consumption of NFFs are used as input variables to calculate the efficiency values of the original DEA model. The average efficiency value of the original DEA model is shown to increase to 0.894, and the efficiency for all provinces and cities has improved significantly from their original state. Compared with the original CO2 emissions, the CO2 emissions in Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Shandong, Henan, Guizhou, Gansu, Qinghai, Ningxia and Xinjiang have all been reduced, in a total amount of 631,691,800 tons of carbon (t.c.). Meanwhile, another 11 provinces and cities, including Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang and Anhui, have accordingly increased their CO2 emissions by an overall volume of 631,691,800 t.c. The sum of the increased and reduced amounts is zero, guaranteeing the precondition of the fixed total amount. As for another input factor—energy consumption of NFFs—10 provinces and cities, including Tianjin, Hebei, Shanxi and Inner Mongolia, have also reduced their input amount by 158,109,600 t.c.; meanwhile, another 12 provinces and cities, such as Beijing, Liaoning, Jilin and Heilongjiang, have increased their input amount by 158,109,600 t.c., thereby assuring the precondition of fixed total energy consumption. Although the efficiency values of all the provinces and cities have increased following the first iteration, they remain under fair carbon emission allowances. Therefore, another iterative calculation is necessary. After the second iterative adjustment, the average value of the initial DEA efficiency has reached 0.962, with most provinces and cities close to 1. In comparison with the first adjustment, 10 provinces and cities, such as Hebei, Shanxi, Inner Mongolia and Liaoning, continue to reduce their CO2 emissions, whereas another 12 provinces and cities, including Beijing, Tianjin, Shanghai, and Jiangsu, continue to increase their emissions. In terms of NFF consumption, 10 provinces and cities, such as Tianjin, Shanxi and Inner Mongolia, further reduce their consumption, whereas 14 provinces and cities, such as Beijing, Hebei and Liaoning, must increase their consumption accordingly.
Further adjustments are necessary as a fair and effective carbon emission allocation has not been achieved. After the third iteration, the initial DEA efficiency value reaches 0.991, and almost all the allocative efficiency values nearly reach 0.99. However, further adjustments are undertaken to achieve the most effective efficiency value as expected. The fourth iteration shows that the vast majority of provinces and cities have achieved fair and effective initial efficiency values (reached at 1), apart from a few provinces such as Jiangsu, Fujian, Hubei, Hunan, Guangdong
etc. Therefore, a fifth iteration was carried out, as shown in
Table 2,
Table A5 and
Figure 1.
After the fifth iteration, the DEA efficiency values of all 30 provinces and cities have become 1. Comparing the initial allocation with the allocation after the fifth iteration, provinces such as Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Shandong, Henan, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang all must reduce their carbon emissions, whereas the remaining provinces must increase their carbon emissions; Guangxi, Hainan,
etc. demonstrate the most significant increases. Guangxi’s carbon emission increases from 81,762,900 t.c. to 160,709,800 t.c., as shown in
Table 1,
Table 3 and
Table A5.
For non-fossil energy consumption, Tianjin, Hebei, Shanxi, Inner Mongolia, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Hubei, Guizhou, Gansu, Qinghai and Ningxia must reduce their consumption, and the rest of the provinces must increase their consumption; Beijing must increase most. The consumption assigned after five iterations is 1.18 times that of the initial allocation.
Next, we compare our results with past work. Miao
et al. [
23] researched CO
2 emissions allowances among provinces in 2010 in China but did not research CO
2 emissions allowances among provinces in 2020 in China. References [
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36] did not use the ZSG-DEA model and/or did not research the CO
2 emissions allowance among provinces in China.
Wang
et al. [
22] researched CO
2 emission allowances among provinces in 2020 in China using the ZSG-DEA model. Thus, our results are most comparable with Wang
et al. [
22], and the CO
2 emissions difference values after the 5th iteration in 2020 from both papers are illustrated in
Figure 2. Although not all the input and output variables used in Wang
et al. [
22] are the same as those used in this paper, both papers reveal similar trends in CO
2 emissions difference values for 2020 after the 5th iteration. However, in this paper, the CO
2 emissions difference value in most provinces and cities after the 5th iteration in 2020 is smaller than that in Wang
et al. [
22]. We investigate the reasons for this difference.
We believe that the main reason for this difference is that the input and output variables in Wang
et al. [
22] and this paper are not all the same. The input variables used in Wang
et al. [
22] are total energy consumption, CO
2 emissions and non-fossil energy consumption. All three inputs in Wang
et al. [
22] have constant total amounts that must be reallocated among China’s regions. The output variables used in Wang
et al. [
22] are GDP (based on 2005 prices) and POP. Our article uses CO
2 emissions and non-fossil energy consumption as input variables; we do not use total energy consumption because we posit that this variable is changeable. The output variables used in our article are total energy consumption, gross domestic product (based on 2010 prices) and POP.
5. Data Sources and Processing
This paper examines the carbon emission allowance allocation mode of all Chinese provinces in terms of efficiency. Therefore, the allocation allowance of all provinces must be first affirmed, and then the efficiency of the allocation mode may be examined. This study assumes that overall carbon emission in 2015 is 17% less than that in 2010, which is consistent with the goal of carbon emission reduction in the “12th Five Year Plan”. At the Copenhagen United Nations Climate Change Conference, the Chinese government pledged that its carbon emission in 2020 would be reduced by 40%–45% from that its 2005 levels.
These results show that China’s carbon emission reduction goal for 2020 will be approximately 31.3% if the 2010 value is taken as the benchmark. After affirming the total amount of the allocation, the carbon emissions allowance for each province can be simulated in terms of the optimum allocation of efficiency.
Using 2010 as the base year, the total amount of carbon emissions in 2020 and its allocation to each province and city can be estimated and predicted with optimal efficiency. The table below presents the carbon emissions, energy consumption, GDP, POP,
etc., in all provinces and cities in 2010, which are used as the initial data (see
Table 4).
The calculation of actual carbon emission in each province and city is derived from the amount of energy consumption in the energy balance sheets for all provinces and cities in the China Energy Statistical Yearbook 2011 [
38,
39,
40,
41,
42,
43,
44]. The detailed calculation methods for carbon emission are described in the Guidelines for the Provincial Greenhouse Gas List [
45], which is also called IPCC Method 1. According to this method, actual carbon emission is derived from the consumption of various fossil fuels, the heat per unit and carbon content per unit of various types of fuels plus the average oxidation rate of the main equipment used to burn various fuels, after deducting fixed carbon content and other parameters of fossil fuels used for non-energy purposes. However, it has been proven that it is difficult to acquire certain data in the calculation process, such as the number of products with fixed carbon content,
etc. Therefore, an alternative method is employed in this study and is demonstrated below.
First, the energy consumption of different types of fossil fuels is converted into that of standard coal, and then the carbon emission factor, fixed carbon rate, oxidation rate of carbon and other parameters are used to calculate the emission amount of carbon and carbon dioxide in different types of fuels. The specific equation for the calculation is as follows:
Xi = Σproduction + import − export ± increase or decrease of stock ± others (mainly adding fuels overseas)
The emission amount of carbon (
PC) is as follows:
where
k is the carbon oxidation rate; λ is the conversion coefficient of standard coal; φ is the potential carbon emission factors; and θ is the solid carbon rate.
Xi represents the total energy consumption in the
ith province or city. The parameters of other models also can be found in
Table 5 [
46]. Because the molecular weight of CO
2 is 44 and the molecular weight of carbon is 12, the total carbon emission of each province calculated above can be converted into CO
2 emission, based on this ratio. For the energy conversion, the conversion coefficient used in this study is 29,307.6 MJ of heat of standard coal per ton (see
Table 5).
The data regarding NFFs are calculated on the basis of the Annual Development Report of China’s Power Sector 2011 [
47], issued by the China Electricity Council. NFFs refer to energy resources that are not coal, petroleum, natural gas or others; thus, NFFs consist of those resources that are not formed through long-term geological transformation that can only be consumed once and instead include current new energies and renewable energies such as nuclear energy, wind energy, solar energy, water energy,
etc. According to the actual praxis and the available data, the hydroelectric and thermal energy data of NFFs are calculated for the consumption of non-fossil energy and converted into standard coal, derived from the conversion standard of 0.1229 standard coal/KW that is based on the national standard found in GB-2008 [
48].
The data for GDP and the populations of provinces in 2010 are obtained from the China Statistical Yearbook 2011. According to the Energy Information Administration (EIA), the United States energy information administration website and the International Energy Outlook [
49], the predicted average annual growth rate of GDP for China is 6.6% from 2010 to 2030, which is used in this study for projecting GDP in 2020. Moreover, China’s population will reach 1.43 billion by 2020 in accordance with World Population Prospects [
50], published by the United Nations Department of Economic and Social Affairs (UNDESA). The prediction of total energy consumption in 2020 is calculated using the energy/GDP elasticity coefficient. As for the energy consumption goal of NFFs, based on the medium- and long-term plans of national renewable energy development, non-fossil energies should account for 15% of primary energy consumption by 2020. The consumption ratio of NFFs over primary energy equals the energy consumption of NFFs/the total consumption of primary energy (fossil fuels + consumption of NFFs). This calculation is used to predict the energy consumption of NFFs in 2020.
The total amount of national carbon dioxide emission in 2020 is predicted to be 5,711,350,300 t.c. Taking the carbon emission of all provinces and cities from 2010–2014 and the overall allowance into consideration, the predicted values of initial allowance allocation results and other variables are shown in
Table 1.