Increased inequalities of per capita CO2 emissions in China

Designing inter-regional and inter-provincial responsibility-sharing mechanisms for climate change mitigation requires the knowledge of carbon distributions. This study is the first to use a two-sector (i.e., productive and household sectors) inequality decomposition approach to examine the regional, provincial, and national inequalities of per capita CO2 emissions (CPC) in China, as well as their determinants. We show that the CPC inequality index in China increased from 1.1364 in 2000 to 2.3688 in 2017, with the productive sector accounting for 91.42% of this expansion and households responsible for the rest. The production-side per capita output level, energy efficiency, energy structure, and industrial structure explain 69.01%, 12.81%, 5.57%, and 4.03% of these inequalities, respectively. Further, the household per capita energy consumption and energy structure explain only 8.12% and 0.46%, respectively. Therefore, future responsibility-sharing mechanisms for climate mitigation need to be formulated taking mainly the productive sector into account.


Results
Regional and provincial per capita CO 2 emissions and their evolution. By investigating the regional and provincial CPC in China, we can draw the following conclusions.
First, from 2000 to 2017, the CPC of Ningxia, Inner Mongolia, Qinghai, and Xinjiang maintained at high levels, while those of Jiangxi, Hainan, Guangxi, and Anhui maintained at relatively low levels. Most provinces with higher CPC are located in the western region, likely due to the coal production bases, which generate large emissions. In combination with the small population, the CPC level of the region is high. Conversely, densely populated provinces, such as Henan, have lower CPC. However, there are still some provinces with sparse populations and relatively low CPC, such as Guangxi. Therefore, the CPC as a measurement objectively reflects the degree of carbon inequality.
Second, in 2017, the CPC of all 30 provinces experienced different growths compared with 2000. Inner Mongolia has seen the largest increase (16.4130), from 3.6763 to 20.0893, followed by Xinjiang, Ningxia, and Qinghai, with increases of 13.4314, 13.1316, and 12.0527, respectively. The change in the CPC of Beijing is the lowest, at only 0.4237. In general, the CPC growth in 12 provinces exceeded the national average level and that in four of these provinces exceeded 10 tCO 2 /capita (Fig. 1B).
Third, the inter-regional CPC inequalities from 2000 to 2017 are obvious. It can be seen that the CPC of the eastern region are higher than the national average, while the central region's CPC are lower than the national average. Except for 2017, CPC of the western region has been lower than the national average (Fig. 1A).
Fourth, except for a few provinces, the changes in CPC have shown significant regional inequalities (Fig. 1B). For instance, the changes (the value change in 2017 compared to 2000, same below) in the eastern region (5.8727) Inter-regional inequalities of per capita CO 2 emissions and their causes. By calculating the CPC difference of various regions (see "Methods" section for details), we obtained inter-regional CPC inequalities from 2000 to 2017, which show a specific trend over time. First, the CPC in the eastern region have always been higher than the national average level, and the difference has gradually expanded, from 0.6857 in 2000 to 1.2437 in 2017 within the range of (0.6857, 1.5253). The range refers to the value range of the calculation results, that is, the differences of CPC between each region and the national average level during the study period (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017). Second, the CPC in the central region have always been lower than the national average level, the difference between the central region and the national average expanded from -0.4373 in 2000 to -1.6947 in 2017. This shows that the central region experiences a yearly decline in CPC, which has lowered the national average level correspondingly. Third, the western region's CPC have been lower than the national average, with the difference first expanding and then narrowing, from -0.4284 in 2000 to -1.1119 in 2007 and -0.0764 in 2016. In 2017, it finally exceeded the national average by of 0.0471. This shows that the western region initially played a positive role in reducing the national CPC average level (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007), and then its positive effect gradually decreased (2008-2016), until it increased the national CPC average in 2017 (Fig. 2).
Interestingly, the eastern region has always shown a pulling effect on the national CPC average. Before 2008, the differences among the central region, western region, and national average remained basically the same. Until 2008, the absolute values of the differences between the two regions and the national average diverged significantly; while the difference between the central region and national average increased, the western region faced the opposite situation.
As we all known, China's opening up policy has gone through several stages, from special economic zones to coastal open cities, opening along the river, and finally opening to the outside world. Based on their geographical location, the eastern coastal areas are opening up at a higher rate, while the western border areas still account for a small proportion of the total imports and exports of the country. Therefore, the eastern coastal cities were the first to develop, which increased their CO 2 emissions and caused their CPC to be higher than the national average. Given the continuous development, this difference is increasing. At the same time, the central and western regions are lagging behind in terms of economic development compared to the eastern region, and their CPC are generally lower than the national average.
The 'One Belt and One Road' policy of 2013 covered most of the central and western China, transforming their vast territories from the original 'inland hinterland' to 'open frontier' , which further improved their opening-up levels and the sustainable development of the economy. Compared with the western region, the development of the central region is moving more rapidly, especially in Hunan and Hubei, the development of which has led the entire economy of the central region and resulted in a large amount of CO 2 emissions. The geographical disadvantage of the western region has led to scarce population and loss of talent, which lead to low levels of economic activity. Although western provinces such as Chongqing and Sichuan show promising development, this is not enough to stimulate the entire western region. In sum, it confirms the interesting phenomenon we found before that the absolute values of the differences between the central region, western region and the national average diverged significantly after 2008.
After 40 years of reform and 'opening up' , China's economy has made great progress, such economic growth, however, has been accompanied with huge CO 2 emissions 24 . Among them, the main drivers of energy-related CO 2 emissions were economic growth (176%), population growth (16%), while the effects of energy intensity (-79%) and carbon intensity (-13%) slowed the growth of carbon emissions 25 .
To explore the causes of inter-regional inequalities in CPC, we divide the differences into eight factors using the two-sector inequality decomposition method, among which five factors belong to the productive sector and three belong to the household sector (see "Methods" section for details). As part an element of our definition, regardless of whether the CPC in a certain region are higher or lower than the national average level (positive or negative value), if the decomposition result of a factor is shown to be positive, that factor promotes an increase in the CPC difference. That is, as long as the decomposition result of a certain factor is positive, that factor hinders the balanced development of CPC and shows a negative impact, and vice versa.
This figure is used to compare the differences in CPC (Δtot) and their drivers (ΔpCF et. al) among the eastern, central, and western regions (Fig. 3). Taking year 2000 as an example, the CPC in the eastern region is 0.6857 higher than the national average (Fig. 2), and the main reasons are the per capita gross domestic product (GDP) (ΔpED, 1.1180, negative effect), followed by energy intensity (ΔpEI, − 0.6514, positive effect), industrial structure (ΔpIS, 0.1147, negative effect), energy consumption structure (ΔpES, 0.0527, negative effect), energy consumption per capita (ΔlPE, 0.0289, negative effect) and energy consumption structure (ΔlES, 0.0229, negative effect,  www.nature.com/scientificreports/ The situation is similar for the other 17 years. Furthermore, the above factors almost have the opposite effects in the eastern, central, and western regions. That is, in the eastern region, the factors of the household sector are almost all above the horizontal axis (negative effect). Except for the the per capita GDP and the energy consumption structure, the factors of the productive sector are almost all below the horizontal axis (positive effect), while in the central and western regions, the situation is just the opposite (Fig. 3A-C). The statistical characteristics of each factor (range, mean, plus/minus one standard error) between the three regions numerically confirmed not

Inter-provincial inequalities of per capita CO 2 emissions and their causes.
To accurately implement policies, further analysis of the characteristics of inter-provincial CPC inequalities is required. We calculated the difference between the CPC of each province and the national average, and the calculation result is shown in Fig. 4 (see "Methods" section for details). Between 2000 and 2017, several provinces in the western region performed the worst, and the CPC inequalities increased across the country (Fig. 4). Specifically, first, the differences between 30 provinces and the national average were not obvious in 2000. The overall colour of China's map in 2000 was lighter, without striking differences, while the 2017 map showed a variety of colours, and the inequalities among provinces became increasingly obvious.
Second, in 2000, there were 17 provinces with CPC higher than the national average, and this number dropped to 12 by 2017. In addition, the differences in CPC in ten of these 12 provinces increased compared to 2000 (increase in value).
Third, compared with national CPC average, from 2000 to 2017, the provinces with higher changes in differences are Inner Mongolia, Qinghai, Ningxia, and Xinjiang. Moreover, the differences of these provinces have grown tremendously. In 2017, Ningxia's value reached its maximum of 16.0075, and Inner Mongolia has seen the largest increase, 11.9819 in 2017 (see Supplementary Table S2).
Fourth, the difference of CPC in Beijing has gradually decreased, from 4.6426 in 2000 to -0.2483 in 2017. Similarly, the provinces for which the values eventually fell include Tianjin, Shanghai, Jilin, Heilongjiang, Hubei, Chongqing, and Gansu; five of these seven provinces started from higher than the national average in 2000 to lower than that in 2017 (among them, the values of some provinces have fallen below 2, so Fig. 4 cannot reflect this change). Finally, since 2010, the difference of CPC of Sichuan, Yunnan, Guangxi, Hunan, Jiangxi, and Anhui have remained within the same changing range, namely from − 2 to − 4 (see Supplementary Table S2).
Considering that the decomposition results involve 30 provinces between 2000 and 2017, and each province has eight factors each year. The large amount of data restricts our ability to display all results as charts, so we analyse the decomposition results only in text. The results show that the main factors driving the differences of CPC are per capita GDP (ΔpED), energy intensity (ΔpEI), industrial structure (ΔpIS), and energy consumption per capita (ΔlPE), consistent with the results for the regional differences. Moreover, the energy consumption per capita (ΔlPE) has become more important in the discussion of provincial CPC differences. Overall, the impact of the productive sector on provincial differences is far greater than that of the household sector. Consistent with the definition of regional CPC differences, as long as the decomposition result of a certain factor is positive, the factor will have a negative impact on the balanced CPC development. The results showed that whether each factor is positive or negative depends on both the province and the time period, and it is difficult to conclude a definite conclusions.   www.nature.com/scientificreports/ ing factors of the inequality index are the per capita GDP (I pED ), which contributes most to the inequality index, followed by energy intensity (I pEI ), energy consumption per capita (I lPE ), energy structure (I pES ), and industrial structure (I pIS ); the energy consumption structure (I lES ) has a negligible impact (Fig. 5C).
Because the national CPC inequality index is always above zero, the higher its value, the worse the national CPC situation is. Therefore, when the decomposition result of a factor is positive, the factor will promote CPC inequalities via a negative effect and vice versa. Consistent with the definition before, in the productive sector, per capita GDP (I pED , negative effect) and industrial structure (I pIS , negative effect) always hinder the balanced development of CPC and promote inequality; that is, they have negative effect. Both energy intensity (I pEI , positive and negative effects) and energy structure (I pES , positive and negative effects) have positive and negative effects on the inequality index. Energy structure (I pES ) only promoted the balanced development of CPC in 2000 (− 0.0279, positive effect), while contributing to the increase in the inequality index in the other years. At the same time, the number of years with a negative effect (15 years) of energy intensity (I pEI ) was greater than that with a positive effect (3 years). Overall, the impact of the five factors pertaining to the productive sector on the inequality index is greater than the impact of the three factors from the household sector (Fig. 5C). Among the factors related to the household sector, only the energy consumption per capita (I lPE , negative effect) had a significant negative impact on the inequality index (see Supplementary Table S3).
Studies have shown that, in 2010, the 10% of the population with the highest income accounted for 36% of the global carbon emissions, while the extreme poor (12% of the global population) only accounted for 4% 26 . In China, more than 58% of the indirect carbon emissions of urban households was from higher-income groups 27 . Between 2007 and 2012, the total household footprint increased by 19%, with 75% of this increase being attributed to increased consumption by the urban middle and upper classes, who are the most important consumers of services and mobility 28 . Although this phenomenon is weakening, carbon inequality declined with economic growth in China 29 . Wealth and income levels have remained the root cause of CO 2 emissions and thus CPC since 2000. As such, income inequality and income levels are key factors to consider when formulating carbon reduction policies 30 .
Per capita GDP is an important indicator of economic development, and in China, it grew rapidly from 2000 to 2017, affecting the country's service consumption and mobility, which in turn led to the growth of CO 2 emissions. Simultaneously, since 2000, China has witnessed a significant lifestyle change due to technological progress, and this change has affected CO 2 emissions as well. For example, online shopping supported by physical stores is likely to reduce the greenhouse gas footprint of traditional shopping, while online shopping without physical stores usually has a higher greenhouse gas footprint 31 . Although the action mechanism has not been proven, the new lifestyle has increased CO 2 emissions, and the lifestyle changes contributed 74.9% of the total increase in household consumption and household carbon emissions during 2012-2016 in China 32 . Economic development is important, but we should also consider that economic growth alone cannot lead to environmental sustainability and that the current trajectories of resource use cannot be sustained without breaking the feedback loops between the national and international economies 33 .
We discuss the specific effects of various factors on the inequality index (Fig. 5C). By reusing and recalculating the decomposition results, except for 2003, in which the productive sector and the household sector accounted for 77% and 23% of the inequality index respectively. In other 17 years, the productive sector determined about In order to study the average effect, we calculate the average value of this 18 calculated results and find that, from 2000 to 2017, the productive sector determined 91.42% of the inequality index, while the household sector determined the remaining 8.58%. Specifically, per capita GDP (I pED ), energy intensity (I pEI ), energy structure (I pES ), and industrial structure factor (I pIS ) accounted for 69.01%, 12.81%, 5.57%, and 4.03%, respectively, of the inequality index. The per capita energy consumption (I lPE ) and energy structure (I lES ) accounted for 8.12% and 0.46% of the inequality index, respectively, which validates the previous results.

Dynamic evolution of China's per capita CO 2 emissions inequalities. The dynamic evolution of
the inequality index is calculated as the change in the index over two consecutive years (Fig. 5B), which reflects the trend of the inequality index. The dynamic evolution of the inequality index fluctuates, taking an irregular W-shape (Fig. 6A). The determinants of this dynamic evolution show that, unlike the inequality index, it is difficult to determine the effects of each factor on the evolution (Fig. 6C). In addition, except for some factors (i.e., ΔI pEI , ΔI pED , and ΔI lPE ), which have large positive and negative fluctuations, the magnitude of the other factors is within a certain range (Fig. 6B). This means that the dynamic evolution of the inequality index is not determined by the single actions of some factors but is, rather, the result of the combined actions of multiple factors. Among the driving factors in the productive sector, the number of years in which the energy structure (ΔI pES ) has a negative effect (13) is greater than the number of years in which it has a positive effect (4); energy intensity (ΔI pEI ) has a negative effect in 12 years and a positive effect in 5 years; per capita GDP (ΔI pED ) has a negative effect in 11 years and a positive one in 6 years; industrial structure (ΔI pIS ) is the opposite, with 10 years of positive effect and 7 years of negative effect. Among the driving factors in the household sector, energy structure (ΔI lES ) promoted the balanced development of CPC in China in 9 years (positive effect) and blocked it in 8 years (negative effect). Energy consumption per capita (ΔI lPE ) impeded the balanced development of CPC in 14 years (negative effect, see Fig. 6C, Supplementary Table S4). It should be noted that only the numbers of years of positive and negative effects were used for discussion. That's because, we mainly want to know which effect of each factor is greater, the positive or the negative effect.
The driving factors' influence on the dynamic evolution of the inequality index varies by year and is difficult to generalize. Therefore, we calculated the average influence of all factors on the inequality index over the 18 years. The five factors in the productive sector determined 82.54% of the dynamic evolution of the inequality index, while the three factors in the household sector determined only 17.46% of that change. Specifically, if the inequality index changes by one point, the energy intensity (ΔI pEI ) determines 46.31% of that change, followed by www.nature.com/scientificreports/ the per capita GDP (ΔI pED ), per capita energy consumption (ΔI lPE ), and energy structure (ΔI pES ), which account for 34.50%, 19.12%, and 17.40% of the change, respectively. By contrast, the one-point change is hindered by the industrial structure (ΔI pIS , − 15.63%) and the energy consumption structure (ΔI lES , − 1.66%, see the horizontal histogram in Fig. 6C). Energy intensity (ΔI pEI ) exceeds per capita GDP (ΔI pED ) as the primary factor determining the dynamic evolution of the inequality index. Interestingly, there seems exist a paradox between the claim that 91.42% of the contribution in the inequality index comes from the productive sector and the claim that when we employ a dynamic evolution analysis, the productive sector accounts for 82.54% of its change. In fact, these two conclusions are actually not in conflict. The reason for the difference is the result of using two different variables as the research object. First, this study studies the determinants of the inequality index constructed based on CPC data. The other is to take the change of the inequality index as a new research object. When the inequality index moves, the importance of the productive sector drops to 82.54%, which shows that when viewed from the perspective of time changes, the harm (increased inequality of CPC) caused by the productive sector will indirectly weakened, which also proves the ridiculousness of completely stopping productive activities because of carbon reduction.

Conclusion and discussion
Inequalities of CPC are crucial for low-carbon development research in China. By studying inter-regional and inter-provincial inequalities, we find that: its driving factors are difficult to determine, after reusing and recalculating the decomposition results, we find that the productive sector determined about 82.54% of the changes of the inequality index, while the household sector determined about 17.46% of that change, and the importance of energy intensity (I pEI ) exceeds that of per capita GDP (I pED ) for the first time.
Based on the results, we put forward the following suggestions. The first is energy transition, which is one of the most important measures for reducing CPC inequalities, should be used to improve the environmental climate and to gradually reduce pollutant emissions, such as atmospheric CO 2 concentration, the increase of which may lead to health risks 34 . Currently, many countries are taking relevant measures in this respect, such as, the United States suspended coal-fired installations between 2005 and 2016, which was related to reducing pollution concentrations and mortality and increasing crop production 35 . Another example shows that reduced household solid-fuel consumption was the leading contributor to the rapid decrease in the integrated exposure to ambient and household PM2.5 pollution during 2005-2015 36 . There are further examples confirm that the reduction of fossil energy consumption can increase the solar radiation on China's surface. If China's solar radiation level returns to the 1960s level, it can increase power generation by 12%-13% 37 . In other words, energy transition is the primary means to reduce CO 2 emissions. Regarding the research and development of new renewable clean energy, as traditional energy will eventually be phased out, we need to prevent problems before they occur, focus on safety and security, and prepare for energy transition.
The next step is to formulate different environmental regulations based on the main determinants of CPC inequalities in each province. Environmental regulations affect CO 2 emissions not only directly but also indirectly through the energy consumption structure 38 . In the implementation of local policies, attention should be paid to the regulation intensities of various provinces, which can cause carbon emission transfer within regions 39 . At the same time, vulnerable groups should also be considered separately in the demand-side response rate design, and future studies should determine which designs avoid exacerbating existing energy injustices or create new ones most effectively 40 .
At last, future responsibility-sharing mechanisms for climate mitigation need to be formulated mainly based on the productive sector, and much attention needs to be paid to decarbonization management in industrial sectors. The energy-saving and emission-reduction potentials of the 35 industrial sectors are significantly different, and technological progress has a large positive impact on emissions reduction in the industrial sector 41  www.nature.com/scientificreports/ example, energy storage technology can help with the decarbonization of the power industry 42 , and improving energy efficiency and reducing greenhouse gas emissions of energy infrastructure is of great significance for the decarbonization of the industrial park and thus boosting the country's low-carbon development 43 . The population data are collected from the National Bureau of Statistics of China (NBSC). The GDP data of the three industries (i.e., primary, secondary and tertiary industry) are from the NBSC, and the unit is 100 million RMB. This study covers 19 types of energy consumption (i.e., raw coal, washed coal, other coal washing, briquette, coke, coke oven gas, other coal, crude oil, gasoline, kerosene, diesel, fuel oil, liquefied petroleum gas, refinery dry gas, natural gas, other petroleum products, other coking products, electricity, and heat), and the data are come from the China Energy Statistical Yearbook, the unit of energy consumption is 10,000 tonnes of standard coal.

Materials and methods
The CO 2 emissions discharged by the 19 types of fossil energy consumption are calculated based on the guidelines of the Intergovernmental Panel on Climate Change 44 , while the direct CO 2 emissions caused by electricity consumption are estimated by the CO 2 emission coefficient of thermal power generation. The unit of CO 2 emissions is 10,000 tonnes.
Decomposition of per capita CO 2 emissions. By using the logarithmic mean Divisia index (LMDI) decomposition method [45][46][47] , the CPC of each province can be decomposed into eight factors, as show in Eq. (1): where PC denotes per capita CO 2 emissions (CPC), CE are the CO 2 emissions, and P the population. pCE indicates CO 2 emissions generated by the energy consumption for productive activities, lCE indicates CO 2 emissions generated by the energy consumption in the household sector, and prefixes p and l denote the productive sector and the household sector, respectively. i, j, and k represent the i-th energy, j-th industry, and k-th province, respectively. Specifically, E is the energy consumption, and Y is the GDP.
CF denotes the carbon emission coefficient, and it is the CO 2 emissions per unit of energy consumption. ES is energy consumption structure (energy structure), which can be determined by the proportion of each type of energy in the total energy use in each province. EI is energy intensity, or energy efficiency (energy consumption required per unit of GDP). IS is industrial structure (the proportion of the output of the j-th industry in the total output), and ED is GDP per capita. Therefore, pCF, pES, pEI, pIS and pED represent the corresponding factor in the productive sector, respectively. lCF, lES and lPE are the carbon emission coefficient, energy consumption structure and energy consumption per capita of the household sector, respectively.
Mentioned in the INTROTUCTION section, the scientific basis of dividing the production-and consumption-based CO 2 emissions is that the productive sector contributes to both production and CO 2 emissions, while the household sector does not involve any productive activities and have no contribution to production, with only generates CO 2 emissions. This makes the roles of the productive sector and the household sector essentially different in the social process, and thus provides a very convincing basis for distinguishing between the two sectors.
Of course, it also needs to be pointed out that whether it is agricultural enterprises, manufacturing enterprises or service industry enterprises, they all have a direct contribution to GDP, and they are divided into the productive sector without doubt. However, although most non-profit institutions are not directly involved in production in most cases, such as government management departments and university scientific research institutes, their ultimate goal is to produce services. Thus, in this consideration, we only select the household sector as the consumption-based sector.
In addition to the support of theoretical basis, that is, on the basis of LMDI application researches 48 , this study subdivides the decomposition factors from the new perspective of productive and household sectors creatively.
Decomposition of the difference in per capita CO 2 emissions. Based on Eq. (1), we can obtain the decomposition formula for the differences in the CPC of each province as:

Measurement and decomposition of inequalities in per capita CO 2 emissions. To reveal CPC
inequalities, an inequality index was constructed: where I(PC) is the inequality index, φ k indicates the proportion of the total output value of the k-th province and ∑φ k = 1. I pCF , I pES , I pEI , I pIS , I pED , I lCF , I lES , and I lPE are the factors determining the inequality index. According to Eq. (3), the smaller the index is, the smaller the CPC inequalities are. Note that the carbon emission coefficient of each energy type is fixed; therefore, the carbon emission coefficient factors (I pCF and I lCF ) in Eq. (3) have almost no impact on the inequality index, and the same is true for carbon emission coefficient factors (ΔI pCF and ΔI pCF ) in Eq. (4)  Dynamic evolution of inequalities in per capita CO 2 emissions. The dynamic evolution process is characterized by the changes in the inequality index over two consecutive years, which reflects the evolutionary trend of CPC inequalities in China.
where ΔI pCF , ΔI pES , …, and ΔI lPE are the determinants of the dynamic evolution, respectively. In addition, we summarize the definitions of variables and characters appearing in equations, as shown in Table 1.

Data availability
All data needed to evaluate the conclusions in this study are present in the Supplementary Materials.