Spatial distribution and regional difference of carbon emissions efficiency of industrial energy in China

The three-stage super-efficiency slack-based measure and data envelopment analysis (SBM-DEA) model with undesirable outputs is used to calculate carbon emissions efficiency of industrial energy (CEEIE) of 30 provinces in China from 2000 to 2017. Then ArcGIS software is used to illustrate the spatial distribution of CEEIE, and Dagum Gini ratio is calculated to decompose the regional difference. The results show that the spatial distribution of CEEIE changes from disorder to order and provinces characterized with high or low CEEIE cluster in space over time. The total Dagum Gini coefficient indicates that the interprovincial difference in CEEIE across China is gradually expanding, which is mainly induced by the difference between regions. Our findings attach more importance to interregional integration policies for carbon emissions reduction in China.

The Covid-19 pandemic resulted in the largest-ever decline in global emissions, which indicated that global energy-related CO 2 emissions fell by 5.8% in 2020. However, as the only major economy to record an increase in annual CO 2 emissions in 2020, China's emissions growth slows by just one percentage point compared with its average rate over the 2015-2019 period. The latest annual figures indicate that the country's overall CO 2 emissions in 2020 were 0.8% (or 75 Mt CO2) above the levels assessed at the end of 2019 1 . The country has entered a new normal in which development mode has changed largely, which has large impacts on carbon emissions 2 . In addition, China has committed to achieve carbon peak by 2030 and carbon neutrality by 2060. Ensuring economic growth and the realization of the two targets will be extremely challenging for Chinese government. As we know, industry always plays an important role in the economy and has been the dominant energy consumer and carbon emitter. In 2020, Chinese industry contributed 37.8% increments of GDP (National Bureau of Statistics of China 2021). Meanwhile, the proportion of energy consumption in the industrial sector is always higher than 65% and the carbon dioxide emissions by industry accounts for a share of over 70%. Therefore, reducing the carbon emissions of industrial energy consumption is a major challenge for China, which requires that the government pays more attention to carbon emissions efficiency of industrial energy (CEEIE).
As for how to implement the policies to curb the carbon emissions of industrial energy, first we should know the situation of carbon emissions efficiency. Kaya and Yokobori 3 and Sun 4 believe that the carbon emissions per unit of GDP can measure carbon emissions efficiency. Mielnik and Goldemberg 5 use the ratio of carbon emissions to energy consumption to measure carbon emissions efficiency. As direct measurement methods, these kinds of a single indicator have noticeable limitations, because it does not take a wide range of important external factors into consideration (Wang et al. 6 ; Cheng et al. 7 ). Although there are many methods for measuring carbon emissions efficiency from total factors perspective, data envelopment analysis (DEA, an efficiency evaluation method that provides a comprehensive evaluation of the relative effectiveness of similar decision-making units) has been the most widely used method (Ramanathan 8 ; Zhou et al. 9 ; Guo et al. 10 ; Meng et al. 11 ; Zhou et al. 12 ; Cheng et al. 13 ).
Second, it is vital to pay attention to regional difference of carbon emissions efficiency because of its variety across many regions in some countries, especially in those with many provincial regions like China. Guo et al. 10 use the DEA method to evaluate and compare the carbon emissions performance of 29 Chinese administrative regions at provincial level. Instead of DEA, Dong et al. 14 use a stochastic frontier analysis (SFA) method to measure and compare the carbon emissions efficiency of some provinces in China. Meng et al. 11 also use DEA to

Methodology and data sources
The method for measuring CEEIE. In this paper, we use the three-stage super-efficiency SBM-DEA method 17 with undesirable output to measure the CEEIE of the 30 provinces in China. It is necessary to point out that the carbon emission is regarded as an undesirable output in the process of the calculation of CEEIE. We divide the outputs into desirable output and undesirable output in terms of the classification method proposed by Wang and Luo 28 . The desirable output meets the expectation and is beneficial for society, but the undesirable output is just on the opposite. In addition, there are 34 provinces in China. For the reason of the lack of data, Tibet, Macau, Hong Kong and Taiwan are excluded from the sample. Therefore, the 30 provinces are Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi, Hainan, Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang. In the first stage, the super-efficiency SBM-DEA model is used to calculate the initial efficiency value and slack value of input/output for each DMU. Since there are zero values in our input data, we use the input-oriented super-efficiency SBM-DEA model  29 ; Meeusen and van den Broeck 30 ) is regression-based, and so has the virtue of being capable of isolating managerial inefficiency from both environmental effects and statistical noise, although it has the drawback of doing so within a parametric framework. Fried et al. 26 point out that the traditional DEA model cannot identify the inefficiency caused by managerial factors, environmental factors and random factors. Therefore, the way to solve this problem is to use SFA model at the second stage to screen out the impact of external environmental factors and random errors, and then the redundant input values are entirely caused by managerial inefficiency. The SFA regression model is where S ni is the redundancy of the n-th input of the i-th DMU, Z i is the environment variable vector and β n is the coefficient vector to be estimated. ε ni = v ni + µ ni represents the mixed error, in which v ni is the random error and µ ni is the managerial inefficiency, and the two terms are independent. v ~ N (0,σ 2 v ) means that v follows the normal distribution, while μ ~ N + (0, σ 2 µ ) means that μ follows the truncated normal distribution.γ = σ 2 v /(σ 2 v + σ 2 µ ) is the ratio of management inefficiency variance to the total variance. When the γ converges to 1, the managerial factor has the whole influence. When the γ converges to 0, µ ni equals 0 and the random model becomes a deterministic model, which can be estimated by ordinary least square. In order to adjust all the DMU to the same external environment and separate the random error from the mixed error terms, Frontier 4.1 is used to implement maximum likelihood estimation to get the estimation of β n , σ 2 and γ . Then the method proposed by Jondrow et al. 31 can be used to obtain the management inefficiency estimation.
where ∅ and ϕ are the distribution function and density function of the standard normal distribution, and e n is the error of maximum likelihood estimation. The estimation of v ni is And then the input data are adjusted by Eq. (5).
where X ni is the original input data, and X ′ ni is the adjusted input data. max f Z i ; β n − f Z i ; β n means that all DMUs are adjusted by the same environmental condition, and [max(v ni ) − v ni ] means that all DMUs are adjusted by the same random error.
In the third stage, X ni is replaced by X ′ ni , and then we can use the model (1) again to get CEEIE, which has excluded the impact of the environmental and random factors.
The method for decomposing regional difference of CEEIE. We use the Dagum Gini ratio method described by Peng et al. 17 to decompose the regional difference of CEEIE. Dagum Gini ratio is defined as In the formula (6), G is the total Gini ratio, which measures the total difference of CEEIE between provinces. K is the number of regions, including northern coast, eastern coast, southern coast, northeast, middle Yellow River, middle Yangtze River, southwest and northwest region in this paper. The eight regions are classified according and y jr are the CEEIE of provinces in the i-th and the j-th region, respectively, and i = 1,2 , …, K; j = 1, 2,…, K. μ is the average of CEEIE of all provinces, n is the number of all provinces, and n i and n j are the number of provinces in the i-th and the j-th region, respectively. Like the method of Dagum, the total Gini ratio can be decomposed as follows with measures the contribution of the difference of CEEIE within region to the total Gini coefficient G; measures the net contribution of the extended difference of CEEIE between regions to the total Gini coefficient G; measures the contribution of the transvariation intensity between regions to the total Gini coefficient G. λ i = n i /n and s i = λ i μ i /μ, μ i and μ j are the average of CEEIE of the i-th and the j-th region. In Eq. (10), is the relative economic affluence between the i-th and the j-th region, and the gross economic affluence d ij between the i-th and the j-th region, such as μ i > μ j , is where f i (y) and f j (y) are the probability density function of the i-th and the j-th region. d ij is by definition the weighted average of the CEEIE difference y ih -y jr for all CEEIE y ih of the members belonging to the i-th region with CEEIE greater than y jr of the members belonging to the j-th region, such that, μ i > μ j .
p ij is the first-order moment of transvariation between the i-th and the j-th region, such that μ i > μ j , is By definition p ij is the weighted average of the CEEIE difference y ih − y jr for all pairs of provinces, one taken from the i-th and the other from the j-th region, such that y ih > y jr and μ i > μ j . The word transvariation stands to the fact that the differences in CEEIE considered are of opposite sign than the difference in means of their corresponding region.
G ii is the Gini ratio within region and G ij is the Gini ratio between regions, i.e., Indicators and data sources. It's vital to construct a comprehensive and objective input-output indicator system for accurately measuring the CEEIE in China. According to the relevant literatures and the availability of data, the input indicators are composed of labor, capital stock (calculated with the method proposed by Shan 32 ) and energy consumption (the sum of all kinds of energy consumed by material production and non-material production sectors). We divide the output into desirable output (gross value of industrial output, the total amount of industrial products sold or available for sale produced by industrial enterprises in the form of currency) and undesirable output (carbon dioxide emissions, calculated according to the Guidelines for National Greenhouse Gas Inventories (Intergovernmental Panel on Climate Change (IPCC) 2006)). We use the following equation to calculation the CO 2 emissions from industrial energy combustion on the basis of China's provincial energy  33 attach more importance to the uncertainties in emission factors, we use the specific information in Table 1 for the formula (15) because of the limit of data. Many studies have found that carbon emissions efficiency is affected by many environmental factors. For example, technological progress can induce high carbon emissions efficiency 12 , and the level of economic development, economic capability, and energy structure also can lead to different carbon emissions efficiency 34 . We thus choose six environmental indicators from the perspective of economy, energy and institution.
The environmental indicators related to economy compose of GDP per capita (for measuring economic development) and the ratio of GDP of tertiary industry to GDP (for measuring industrial structure). On one hand, economic development means greater energy consumption and more carbon emissions. One other hand, infrastructure, energy utilization and pollutant treatment capacity will be improved with economic development. Therefore, the impact of economic development on CEEIE is not clear. As for industrial structure, it can affect CEEIE through energy consumption and energy intensity. For example, the optimization of industrial structure can promote the development of low-carbon industry to induce carbon dioxide emissions. The environmental indicator related to energy is the ratio of coal consumption to total energy consumption (for measuring energy consumption structure). According to the statistics of IPCC (2006), the carbon emissions per unit coal consumption is 1.33 times that of oil and 1.73 times that of natural gas. Therefore, a high coal consumption rate means low carbon emissions efficiency or a poor energy consumption structure. The environmental indicators related to institution compose of the ratio of government investment in environmental governance to GDP (for government environmental governance), the ratio of R&D expenditure to GDP (for measuring technological innovation ability) and the ratio of total import and export to GDP (for measuring the degree of opening up). The expenditure in government environmental governance and technological innovation can curb energy consumption of enterprises and promote the production and use of clean energy. With the increasing degree of opening up, the international organizations require China to make more contribution to carbon reduction. Besides, the effect of technology spillover brought by opening up should enhance energy efficiency.
The above-mentioned indicators are described in

Results
The situation of CEEIE. Table 3 reports the averages of CEEIE of China and the eight regions. From 2000 to 2019, the CEEIE of China is increasing significantly, and the average annual growth rate is 1.27%. Besides, the CEEIE of China ranges from 0.818 to 1.041, which implies a high level of carbon emissions efficiency. As for the regional CEEIE, northern coast region has the highest average annual growth rate (3.42%), while northeast region has the lowest (0.11%). In 2000, only the southern coast region has DEA effective CEEIE. But in 2019, there are five regions with DEA effective CEEIE and most of them (three out of five) cluster in coast. As we know, coastal regions in China have high level of economic development and advanced production technology, which means that they have greater abilities to reduce the carbon emissions.
The spatial distribution of CEEIE. As graphical supplements to CEEIE in Table 3, Figures 1, 2 The CEEIE varies substantially across provinces and tends to cluster in space over time, which means that the spatial distribution of CEEIE is being from disorder to order. Specifically, provinces characterized by high CEEIE are shown to cluster in the coastal regions with developed economy or region attaching more importance to environmentfriendly industries from 2000 to 2019. In China, developed provinces have transformed from deep industrialization to service-oriented industries and then realized sustainable emission reduction. For example, Beijing in northern coast region has been focusing on developing new energy utilization and cultivating industries related new energy, which also promotes the reduction of industrial carbon emissions. While Hunan in middle Yangtze River region has paid more attention to the environmental impact of the industry and tended to introduce lowcarbon emission and environment-friendly industries.
The regional difference of CEEIE. Figure  These results indicate that the total difference of CEEIE has a fluctuating and upward trend in the research period. As shown in Table 3, the provinces with high CEEIE also have high average annual growth rate, while the provinces with low CEEIE also have low average annual growth rate. Therefore, the gap of CEEIE among provinces in China is expanded over time.  Table 4. We can find that the Gini ratio within region is increasing in northern coast and southern coast region, but deceasing in other six regions. From 2000 to 2019, the average annual growth rate of the Gini ratio of CEEIE within region is negative (− 0.61%). These results imply that the differences of CEEIE within region have been narrowed. We believe that the implementation of regional coordinated development strategy and the gap of economic development of provinces in a region are the two key factors affecting the Gini ratio within region. For example, eastern coast region has implemented regional integration development strategy of Yangtze River Delta since 2010 and economic development of Shanghai, Zhejiang and Jiangsu has always been very balanced, which make that eastern coast region has the lowest Gini ratio within region.
The differences of CEEIE between regions from 2000 to 2019 are reported in Table 5. There are maximum gap between southern coast region and northwest region, while the minimum gap emerges between northern coast region and eastern coast region. These findings are consistent with the difference of economic development  www.nature.com/scientificreports/ between the two regions in China. For the variation of Gini ratio of CEEIE between regions over time, it shows that the differences of CEEIE between adjacent regions are decreasing but increasing between distant regions. For example, the lowest average annual growth rate of Gini ratio of CEEIE between regions (− 3.46%) is for eastern coast region and middle Yangtze River region, while the highest (5.63%) is for northern coast region and northwest region. Therefore, we can conclude that CEEIE may have spatial spillover effect and the regions with high CEEIE or the regions with low CEEIE may cluster in space, which is consistent with the results of spatial distribution analysis. The sources of the regional difference of CEEIE are shown in Table 6 and Fig. 7. From 2000 to 2019, the Gini inequality within region contributes with a 7.58% to the total Gini ratio on average, the Gini inequality between regions contributes with a 71.59%, and the contribution of the transvariation intensity between regions is a 20.83%. As shown in Fig. 7, the contribution rate (CR) of the Gini inequality within region is stable, but the CR between regions is increasing and the CR of transvariation intensity is decreasing. These findings indicate that there are great differences between regions, which are the greatest sources of CEEIE inequality. Because the CR of transvariation intensity is the impact of the interaction of the difference within region and between regions on the total difference, its second largest CR means that the spatial dependence of the carbon emissions reduction behavior of local government also is an important source of the regional difference of CEEIE in China.

Conclusions and implications
This paper uses the three-stage super-efficiency SBM-DEA model with undesirable output to evaluate CEEIE of 30 provinces in China from 2000 to 2017, and analyzes the spatial distribution and regional difference of CEEIE. We find that there is a big difference of CEEIE between provinces and between regions and the CEEIE of most provinces and regions are low. The analysis of spatial distribution indicates that the provinces characterized with high or low CEEIE cluster in space and the spatial distribution of provincial CEEIE is being from disorder to order over time. But the results of total Dagum Gini ratio indicate that the difference of CEEIE among provinces is expanded over time, which means that there are great gaps among the carbon emissions reduction capability of local government. Especially, the provinces with good economic foundation always have higher CEEIE. Furthermore, the decomposition of the total Dagum Gini ratio shows that the differences of CEEIE within region have been narrowed. Because the provinces in a same region have similar emissions reduction capability and it is more convenient for them to carry out carbon emission cooperation, the decreasing trend of the differences of CEEIE within region occurs. Besides, the differences between regions and its greatest contribution to the total difference of CEEIE imply that other than interprovincial carbon emission cooperation, interregional cooperation can play an important role in the regional difference of CEEIE. Finally, all the findings mean that the spatial dependence of carbon emissions reduction behavior of local government has a vital influence on CEEIE.
The findings of this study have some important policy implications for improving carbon emissions efficiency and promoting the balance of regional carbon emissions. First of all, the governments should implement www.nature.com/scientificreports/ differentiated schemes based on the actual situation of each region when formulating carbon emissions reduction policies. For example, the coast regions, as economic leading and industrial transfer out regions, have high degree of industrialization and economic development and strong demand for industrial upgrading and environmental improvement. Therefore, the governments in these regions should strengthen the current governance Table 5. The difference of CEEIE between regions. 1 is northern coast region; 2 is eastern coast region; 3 is southern coast region; 4 is northeast region; 5 is middle Yellow River region; 6 is middle Yangtze River region; 7 is southwest region; 8 is northwest region. www.nature.com/scientificreports/ and intervention means to formulate more stringent carbon emissions reduction standards and promote the optimization of industrial structure and industrial carbon emissions. Nevertheless, the economic zones located in the center and west (such as middle Yellow River region) have relatively low level of economic development, and they are also the main areas for undertaking industrial transfer. They thus bear the dual pressures of economic development and environmental improvement. The governments in these regions should play better roles in supervision and guidance, and take into account the obligation of carbon emissions reduction when pursuing economic growth. For example, formulating scientific industrial development plans based on regional characteristics and functional positioning, and effectively screening the transferred industries through reasonable guidance and intervention may avoid the possible negative effects of industrial transfer on environmental pollution in the process of economic development.  www.nature.com/scientificreports/ Second, the interregional integration policies for carbon emissions reduction should be made by central government to enhance the CEEIE. Most importantly, it is necessary to establish an effective interregional cooperative mechanism to draw up a long-range carbon emissions reduction plan. For example, it is practicable to establish an integrated management organization for interregional environmental management, or establish an interregional environmental protection organization. The agency should formulate a clear action plan for interregional integration of carbon emissions reduction policy, which is not only a comprehensive plan, but must be implemented into environmental protection policy of each province in different regions.
Third, the provinces in China should regularly share energy saving and emissions reduction technology and exchange the carbon emissions reduction policies. Green technology innovation activities are mainly concentrated in the developed regions of China, in which there are better capitals and technology endowment advantages. Therefore, the realization of high-efficiency carbon emissions reduction depends on the deep integration of technical endowment between the developed regions and the underdeveloped regions. The conventional sharing of the experiences of carbon emissions reduction can make green technologies spread rapidly, which should give fully positive role for spillover effects of science and technology of industrial carbon emissions reduction.