Driving Factors and Growth Potential of Provincial Carbon Productivity in China

: Climate change has become a global concern, and the development of a green economy has attracted wide attention. Understanding the driving factors and growth potential of provincial-level carbon productivity is crucial for China’s green economic development in the new normal phase. In this study, the logarithmic mean Divisia index (LMDI) is adopted to systematically investigate the driving factors of provincial carbon productivity and explore the growth potential of provinces’ carbon productivity based on the clustering analysis. The results show that: (1) China’s provincial carbon productivity presents an increasing trend in 2001–2017, but the differences in carbon productivity among provinces are widening. (2) Economic activity and industrial structure are key to push up regional carbon productivity in China, while energy intensity is the main factor pulling it down. (3) The potential for carbon productivity improvement varies greatly among provinces in the four groups. Speciﬁcally, in groups 1 and 2, the developed provinces have little potential for improving carbon productivity, while the developing provinces in group 4 are just the opposite. These ﬁndings can enlighten policymakers that the development of a green economy should focus on optimizing and upgrading industrial structure and reducing energy intensity, and provincial heterogeneity must be considered when formulating green economic development policies.


Introduction
Global climate change has been rendered an indisputable fact, with its main driving force being the rapid increase in CO 2 emissions that is caused by human activities. To meet the challenge of climate change, low-carbon sustainable development has become a common choice in the world. Both the micro-enterprises [1,2] and the macro-regions [3,4] actively explore sustainable development measures in the development process. A lowcarbon economy is the fundamental strategic choice to deal with climate change under the framework of sustainable development. As the world's largest CO 2 emitter, the Chinese government has put forward the development strategy of a low-carbon economy and ecological civilization. The core of low-carbon development is to achieve the dual goals of economic growth and carbon emission reduction, which requires an increase in carbon productivity. Therefore, production and lifestyle based on carbon productivity is not only the key to promote low-carbon development but also an important way to achieve sustainable development. Carbon productivity, termed by Kaya and Yokobori [5], refers to the ratio of gross domestic product (GDP) to CO 2 emissions of a country (region) over a certain period, thereby reflecting the economic benefits of CO 2 emissions. Carbon productivity is an important indicator to measure the level of green and low-carbon development [6]. The McKinsey Global Institute pointed out that humans must raise while FDI in surrounding areas has a negative impact on it. Zhang et al. (2014) [21] found that the growth rate of carbon productivity is determined by variables such as technological progress, substitution effect between capital and energy, and substitution effect between labor and energy, and the effects of technical efficiency, random difference, scale efficiency, and energy structure are limited.
In terms of research methods, index decomposition analysis (IDA) is the most commonly used method for studying the driving factors of carbon-emission-related indicators. Although IDA contains many methods, the choice in the present is essentially between the refined Laspeyres index method and the logarithmic mean Divisia index (LMDI) method [22]. In other words, the basic Laspeyres and the simple average Divisia methods have almost been abandoned because of their low performance. The formulae for the refined Laspeyres method are very complex, especially when the number of factors exceeds three, which is often the case in environmental decomposition studies, and the formula for different numbers of factor cases is very different. By comparison, LMDI has the advantage of leaving no residuals, easing interpretation of factor effects, and having consistent decomposition formulae for different numbers of factors [23]. Therefore, in practical application, the LMDI method has more extensive application [24]. For example, Liao et al. (2019) [25] adopted the LMDI method to analyze the driving factors of provincial-level CO 2 emissions from the power sector in China and found the change characteristics of each driving factor over time. Wen and Li (2020) [26] combined the LMDI method with the spectral clustering method to study industrial CO 2 emissions driving factors in 30 provinces of China and showed the difference of impact mechanisms on CO 2 emissions from the temporal and spatial angle. Cao et al. (2020) [3] used the LMDI method to examine the drivers of the growing environmental footprints in China's food system and revealed the impact mechanism of food consumption on the environment. Some studies have decomposed China's carbon productivity from regional and industrial perspectives based on the LMDI method. For example, Chen et al. (2018) [27] studied factors that drive the change in electric carbon productivity using LMDI. Lu et al. (2015) [28] analyzed China's carbon productivity driving factors using LMDI. These studies are valuable for understanding the driving factors of China's carbon productivity, but none of them has explored the growth potential of carbon productivity on the basis of decomposition of influencing factors. However, the growth potential of carbon productivity is the key problem to be solved urgently for the Chinese government to decompose the carbon productivity target from top to bottom.
To fill the above gap, this study estimates the potential of carbon productivity improvement in China's provinces from the perspective of convergence. This study not only clarifies the contributions of carbon productivity drivers but also explores the growth potential of carbon productivity in each province on the basis of decomposition and clustering. In this study, the provincial panel data of China from 2001 to 2017 were used to identify carbon productivity trends and driving factors between provinces, thereby intending to provide a basis for a region-oriented carbon productivity elevation strategy. First, carbon productivity in 30 provinces were calculated, and the LMDI was used to investigate the effect of drivers on regional carbon productivity. Second, the 30 provinces were clustered into four groups using the hierarchical clustering and K-means algorithm, according to carbon productivity features and driving mechanisms. Finally, provincial carbon productivity growth potentials were determined, and specific promotional strategies were put forward.
The rest of this study is organized as follows: Section 2 describes the carbon emission calculation method, LMDI decomposition model, K-means clustering, and the carbon productivity growth potential counting method that was used in this study as well as the corresponding data description. Section 3 presents the empirical results and discussion. Section 4 concludes the study and proposes corresponding implications.

Carbon Productivity Accounting
According to Kaya and Yokobori [5], carbon productivity is expressed as: where CP is carbon productivity, Y is GDP, and C is CO 2 emissions. As CO 2 emissions from fossil fuel combustion (i.e., energy-related emissions) account for more than 90% of the total CO 2 emissions in China [29], this study focuses on energyrelated CO 2 emissions. This study involves both provincial and sectoral levels; thus, a bottom-up sector-based approach is established for calculating the energy-related CO 2 emissions of a province. According to the Intergovernmental Panel on Climate Change (IPCC) guidelines, the formula for calculating provincial CO 2 emissions is as follows: where index k represents province, i represents sector, and j represents the type of fossil fuel. AD kij is the consumption of fossil fuel j in sector i in province k. NCV kj is the low calorific value of fossil fuel j. CC j is the carbon content of fossil fuel j. COF j is the carbon oxidation rate of fossil fuel j. The accounting includes 30 provinces in China, which means that Tibet, Hong Kong, Macao, and Taiwan are not considered (due to the problems of inconsistent statistical caliber or missing data). For sectoral division, the sector category in China's energy balance sheet issued by the official is adopted, that is, agriculture, forestry, animal husbandry, and fishery; industry; construction; transportation, storage, and post; wholesale and retail trades, hotels, and catering services; other sectors, shown in Table 1. In terms of the types of fossil fuel, 21 types were chosen from 26 types in China's energy statistical system. The types excluded from the CO 2 emission accounting system, such as Naphtha, Lubricants, Paraffin, White spirit, and Bitumen asphalt, are rarely used for combustion; in other words, the consumption of them can be almost considered to have no CO 2 emissions. The emission factors of different fossil fuel types are listed in Table 2. Please note that this study does not account for the indirect CO 2 emissions generated by inter-provincial electricity imports/exports. The energy input and CO 2 emissions in the process of thermal power generation and heating supply are included in the industrial sector. Accordingly, CO 2 emissions from the final consumption of electricity and heating are not considered to avoid double accounting. Meanwhile, the energy consumption used as raw materials and materials in the industrial sector should be deducted because they are non-energy use. In addition, energy consumption and CO 2 emissions in the household sector are integrated into the other sectors.

LMDI Decomposition Model of Carbon Productivity
The decomposition model decomposes a total indicator into several driving factors and quantifies the contribution of each driving factor. This method is widely used to study the driving force of CO 2 emissions [30]. This paper adopts the LMDI method to decompose the driving factors of provincial-level carbon productivity, and the formula is as follows: where Y ki is the value added of sector i in province k; C ki is the CO 2 emissions of sector i in province k; E ki is the fossil fuel consumption of sector i in province k; and E k , Y k , and P k are the energy consumption, value added, and population in province k, respectively. Accordingly, ICP ki denotes the industrial structure from the perspective of carbon productivity; CE ki is the carbon intensity effect of energy consumption; ES ki is the energy structure effect; EI k is the energy intensity effect; PCG k represents the economic activity effect; and PC k is the ratio of population to CO 2 emissions.
The change of provincial carbon productivity from the period of 0 to T can be expressed by the definite integral of its first derivative versus time in an interval (0, T), as shown in Equation (4).
In order to eliminate the influence of time, t, on all factors, the logarithmic average function proposed by Ang and Choi (1997) [31] is used as a weighting factor, as shown in Equation (11). The contribution values of various driving factors on carbon productivity between the base year 0 and the target year T for province k can be calculated using the following equations:

Carbon Productivity Growth Potential Analysis Method
Referring to the method adopted in determining energy intensity conservation potential, this paper calculates the growth potential of provincial carbon productivity. The conservation potential of energy intensity is defined as the difference between the current value and the target energy efficiency value. The environmental convergence has been confirmed, including the convergence between developed and developing countries [4] and provinces within a country [32]. Based on the convergence theory, the energy efficiency of each province converges to the highest value in the region; therefore, the highest value in the region is set as the target of intensity conservation [32]. Drawing on this idea, this paper classifies provinces with similar characteristics of carbon productivity into one group.
On this basis, the highest carbon productivity value of each group is set as the target of carbon productivity promotion in provinces of this group. The carbon productivity growth potential for province k can be expressed as follows: where CPP k is the carbon productivity growth potential for province k and CP gmax is the maximum carbon productivity in group g, to which the province k belongs. Based on the decomposition of carbon productivity driving factors, the K-means clustering algorithm is used to classify the 30 provinces in China, to clarify and compare the carbon productivity characteristics of each province. The K-means clustering algorithm is a type of automated clustering algorithm that seeks the optimal solution through iteration. First, K initial cluster centers are selected from the given data sample, X. By calculating the distance between each point and the cluster center, each point is assigned to the cluster where the nearest cluster center is located. After the distribution, the center points of each cluster are determined again, then the points are distributed again, and the cluster centers are updated, iterating until the change of the cluster center points is very small. Suppose there are M clustering objects and N clustering variables. The cluster object is expressed as For any two objects X i and X j , the Euclidean distance d X i X j is calculated as follows: According to the study of Liao et al. (2019) [20], the objective function is defined as: With the sample data of 30 provinces, ICP ki , CE ki , ES ki , EI ki , PCG k , PC k , carbon productivity in 2017, and annual growth rate of carbon productivity from 2001 to 2017 are taken as clustering variables. In addition, according to hierarchical clustering results, this paper adopts k = 4 as the best clustering number.

Data
The latest release of the China Energy Statistical Yearbook only counts the data of 2017, which leads to the carbon emission calculating only up to 2017; therefore, this paper investigates until 2017 (The latest release of the China Energy Statistical Yearbook was checked in September 2020). Considering the influences of government planning on carbon productivity, the studied period is from 2001 to 2017, which covers China's most recent four five year plan periods (FYPP). The fossil fuel consumption data are extracted from the "energy balance sheet" in the "China Energy Statistical Yearbook" (National Bureau of Statistics, 2001-2017). To calculate the industrial structure of energy consumption in 30 provinces, the physical energy consumption of each sector is converted into standard coal, and the standard coal conversion coefficient adopted is extracted from the China Energy Statistics Yearbook. The low calorific value of most energy types is extracted from the China Energy Statistics Yearbook, while a few that are missing in the China Energy Statistics Yearbook are taken from the China Emission Accounts and Datasets (CEADs) [33]. Carbon content and carbon oxidation rate are taken from the China Low-Carbon Development Report (2017). The data on GDP and provincial value added come from the Energy Statistical Yearbook of each province, and the regional GDP index (previous year = 100) is used to adjust the nominal GDP of all provinces in each year to the actual GDP at constant price in 2001. In addition, the population at the end of each year is chosen as the population data for the 30 provinces, which are extracted from the China Statistical Yearbook.  Although the government had issued an energy development plan, China was in a period of rapid growth in terms of both economic development and energy consumption demand. Therefore, China's carbon productivity grew slightly at this stage. In the 12th FYPP (2011-2015), the Chinese government issued the "Comprehensive Work Plan for Energy Conservation and Emission Reduction" and began to implement dual control measures for energy consumption and energy intensity. The growth of carbon emissions from fossil fuel combustion was gradually controlled. In 2014, China's economic development entered a new stage, paying more attention to the quality and efficiency of economic development, achieved remarkable energy conservation and emission reduction, and maintained medium-and high-speed economic growth. China kept economic growth while controlling carbon emission; therefore, its carbon productivity in this stage accelerated significantly (12-13th five year plan).

Trends of Carbon Productivity
There is a significant degree of variation in the carbon productivity of the 30 provinces in China; further, this gap is widening. In 2017, Beijing's carbon productivity was significantly more, thereby exceeding 2 million yuan/100 tons, whereas those of the other provinces were lower than 1.5 million yuan/100 tons. Moreover, Ningxia has the lowest carbon productivity of only 0.11 million yuan/100 tons. Beijing's carbon productivity is 19.03 times that of Ningxia. More than half of the 30 provinces have a higher carbon productivity than the national average. Beijing, Shanghai, Guangdong, Tianjin, Fujian, Sichuan, Chongqing, Shandong, Jiangsu, Hainan, Hubei, Hunan, Guangxi, Henan, Yunnan, and Jiangxi contribute to China's carbon productivity growth, while other provinces produce a negative effect. From 2001 to 2017, carbon productivity in Beijing, Shanghai, Guangdong, and Tianjin has shown rapid growth. In 2001, Beijing's carbon productivity was only 0.52 million yuan/100 tons, which increased to 1.12 million yuan/100 tons in 2010 and reached 2.16 million yuan/100 tons in 2017. Beijing's average annual growth rate of carbon productivity was 9.29% in 2001-2017. However, the growth of carbon productivity in Xinjiang, Ningxia, and some other provinces has been minor. Different growth rates of carbon productivity aggravate the gap of carbon productivity between regions. Figure 2 shows the driving factors of carbon productivity change in China's provinces in four FYPPs. It can be seen that the contributions of various factors to carbon productivity change varied considerably across provinces and over time, while presenting some consistency on the whole. More specifically as follows:

Driving Factors of Carbon Productivity
With the development of the economy, the inhibiting effect of energy intensity on carbon productivity is obviously enhanced.  Figure 2c), indicating that energy intensity becomes a key factor hindering the improvement of provincial carbon productivity in this stage. In addition, the contribution values of energy intensity in a few provinces, such as Ningxia, Inner Mongolia, Xinjiang, Shanxi, and Liaoning, switch from negative to positive in the 13th FYPP (2016-2017) (see Figure 2d). One explanation could be that the economic growth of these resource-based provinces is in a bottleneck, while the growth rate of energy consumption has not slowed down.
Economic activity has always played a leading role in the elevation of provincial carbon productivity in China. Figure 2 represents that GDP per capita has positive and significant effects on the provincial carbon productivity changes in four FYPPs. A rapid and steady economic growth is crucial for increasing carbon productivity. In the 10th FYPP  The industrial structure is another key factor driving the growth of carbon productivity in China's provinces. Figure 2 shows that the provincial sectorial structure's contribution to carbon productivity was negative over the period 2001-2005. Since 2006, provincial sectorial structure' contribution values had shifted from negative to positive, and the contribution values show a growth trend. In the 10th FYPP (2001-2005), sectorial carbon productivity had an adverse influence on the growth of carbon productivity in the less developed provinces, such as Guizhou and Jiangxi (see Figure 2a). The contribution values of Guizhou and Jiangxi were −0.74 million yuan/100 tons and −0.59 million yuan/100 tons, respectively. In the 11th FYPP (2006-2010), the sectorial carbon productivity factor of each province is one of the main driving factors in increasing regional carbon productivity, except in Ningxia (see Figure 2b). Beijing and Shanghai's industrial structure contributed substantially to the carbon productivity changes, with 0.33 million yuan/100 tons and 0.22 million yuan/100 tons, respectively. In the 12th FYPP (2011-2015), the industrial structure greatly influenced regional carbon productivity changes, which has become the core driving factor (see Figure 2c). Sectorial structure's influences on Beijing, Fujian, Tianjin, and Shanghai were strong and strengthened significantly in Guangdong, Hunan, and Zhejiang. In the 13th FYPP (2016-2017), the effects of sectorial structure on developed provinces, such as Beijing, Tianjin, Shanghai, and Guangdong, remained outstanding (see Figure 2d). In addition, the contribution of each industry to carbon productivity changes is different and changing. Figure 3a shows that in 10th FYPP (2001)(2002)(2003)(2004)(2005), provincial agriculture, forestry, animal husbandry, and fishery; wholesale and retail trades, hotels and catering services, and other sectors have negative contributions to carbon productivity changes, and agriculture, forestry, animal husbandry, and fishery's contribution is greater than other sectors. Figure 3b,d shows that since 2006, with the acceleration of industrialization, regional industrial contributions in China have increased significantly, and other service and wholesale and retail trades, hotels, and catering services' effects on carbon productivity changes have switched from negative to positive, which played a major role in promoting carbon productivity. The transportation, storage, and post industries, wholesale and retail trades, and hotels and catering services contributed less in driving the carbon productivity growth. Thus, elevating carbon productivity needs to focus on increasing the contribution of transportation, storage, and post industries, wholesale and retail trades, and hotels and catering services. In summary, the industrial structure is the core factor in improving regional carbon productivity. This factor reflects the comprehensive effects of industrial structure and technical level in a region. China's provinces should optimize their industrial structure according to their resource endowment, accelerate the transformation of new and old kinetic energy, cultivate new industries and stimulate industrial vitality, so as to reduce carbon emissions while improving industrial efficiency.
Carbon intensity, energy structure, and population scale have a limited effect on regional carbon productivity in China. Figure 2 shows that the carbon intensity of energy consumption and energy structure has little contribution to regional carbon productivity changes. In Figure 2a The results of this paper show that China's carbon productivity has regional heterogeneity, which is consistent with the research of Li et al.  [16,21,34]. This paper finds that economic activity, industrial structure, and energy intensity are the main factors affecting China's regional carbon productivity. This result is consistent with Li et al. (2018) [34]. However, Zhang et al. (2014) believe that increasing China's carbon productivity level should focus on technological progress, capital energy substitution effect, and labor energy substitution effect. This is mainly due to the different decomposition methods of carbon productivity drivers [21].
This study analyzes the changes in China's carbon productivity driving factors. China's carbon productivity in 2011-2017 shows a trend of accelerating growth as compared to that in 2001-2010. This is because China's economic development has entered a new normal. After entering the new normal, the improvement in China's carbon productivity is mainly due to the optimization and upgradation of industrial structures. In the new normal stage, China has been actively seeking economic transformation, focusing on the transformation to a knowledge civilization. China no longer emphasizes development through reliance on low-value-added industries, high consumption, high pollution, and high-emission industries, and encourages economic growth to rely more on strategically emerging industries, vigorously developing green industries, and circular economies. Therefore, the improvement in industrial structure offsets China's carbon dioxide emissions, while significantly contributing to emission reduction via an intensive and sustainable development model in the new normal stage. China needs to eliminate backward production capacity through structural reforms on the supply side of operations and adjust industrial structure at the regional level.

Clustering Results
The hierarchical clustering and K-means clustering algorithm are used to classify China's 30 provinces into four groups. According to hierarchical clustering results (see Figure 4), this paper adopts k = 4 as the best clustering number. The clustering results are shown in Table 3.  Additionally, this paper calculates the average contribution value of each driving factor to the carbon productivity in each group, and the mean value of carbon productivity (denoted by CP) and its growth rate (denoted by R CP ) in each group, as shown in Table 4.

Analysis of the Growth Potential of Provincial Carbon Productivity
The results of carbon productivity's growth potential in 30 provinces are reported in this sub-section (see Table 5). Moreover, the measures to improve carbon productivity in different types of provinces are discussed. Group 1 includes Beijing, Shanghai, and Tianjin, which are characterized by the highest level and growth rate of carbon productivity in China. In these three municipalities, industrial structure and economic activity play a leading role in carbon productivity growth. The influence of industrial structure optimization and economic activity expansion on promoting carbon productivity is stronger than that of energy intensity on hindering carbon productivity. This group has significantly raised the national average level of carbon productivity. The Blue Book of Industrialization: China's Industrialization Progress Report  states that Beijing, Shanghai, and Tianjin represent the post-industrialization stage; in 2017, the industrial structure proportions of the three municipalities were 0.4:19.0:80.6, 0.4:29.1:70.5, and 1.2:40.8:58.0, respectively. Since Beijing, Shanghai, and Tianjin have reached a high level of economic development and industrialization, these three provinces can take the lead in exploring ways to improve China's carbon productivity in the post-industrial period. Table 5 shows that Beijing's carbon productivity is highest among group 1, with 2.16 million yuan/100 tons. Taking this as the target, the growth potential of carbon productivity in Shanghai and Tianjin are 33.16% and 41.5%, respectively. Compared to other provinces, the potential for an increase in carbon productivity in these two regions is low. Considering the regional characteristics in group 1, carbon productivity can be elevated in service sectors such as transportation, storage, and post industries. Differing from Beijing and Shanghai, Tianjin still has a high proportion of secondary industry. Therefore, Tianjin should increase carbon productivity by improving industrial energy efficiency and promoting high-tech industries.
Group 2 covers Chongqing, Fujian, Guangdong, Jiangsu, Shandong, Sichuan, and Zhejiang, with higher carbon productivity and slower carbon productivity growth. Table 5 shows that Guangdong has the maximum carbon productivity in group 2, with 12,700 tons/100 million yuan. To reach this target maximum, the carbon productivity growth potentials of Chongqing, Fujian, Zhejiang, Sichuan, Shandong, Jiangsu, and Zhejiang are less than 40%, especially in Fujian, which is only 8.66%. Chongqing, Zhejiang, Sichuan, Shandong, and Jiangsu's potential for carbon productivity improvement is 28.35%, 16.54%, 26.77%, 30.71%, and 31.50%, respectively. These provinces are economically developed. In 2017, Chongqing's GDP growth rate was 9.3%, ranking fourth in the country. The other six regions' GDP ranked in the top 10 in China. Therefore, economic activity has the greatest effect on this group of carbon productivity. Economically developed regions, such as Guangdong, Zhejiang, Shandong, and Jiangsu have high-carbon productivity. These areas need to focus on tackling the contradiction between economic development and energy demand. Thus, they could develop a circular economy and build low-carbon cities.
Group 3 is characterized by low-carbon productivity and higher growth. This feature determines that group 3 should be a major focus for China to raise carbon productivity. This group includes Anhui, Heilongjiang, Henan, Hubei, Hunan, Jilin, Liaoning, Shaanxi, and Yunnan. The average annual growth rate of carbon productivity in this group is 4.56%, second only to group 1. Table 5 shows that Hunan has the highest carbon productivity, which is 0.77 million yuan/100 tons. Taking this value to be the target, the potentials for carbon productivity growth in Anhui, Heilongjiang, Henan, Hubei, Jilin, Liaoning, Shaanxi, and Yunnan are 28.21%, 32.05%, 8.97%, 1.28%. 25.64%, 42.31%, 21.79%, and 8.97%, respectively. The carbon productivity growth potentials of these regions are less than 50%, especially in Hubei, Henan, and Yunnan, which are no more than 10%. Areas rich in renewable energy, such as Yunnan, ought to optimize hydropower resources' allocation, promote the transformation and upgrade of energy structures, and develop tourism to lead the tertiary industry. For these areas, renewable energy and tourism are important ways to stimulate economic vitality and improve carbon productivity.
Group 4 is composed of Gansu, Guangxi, Guizhou, Hainan, Hebei, Inner Mongolia, Jiangxi, Ningxia, Qinghai, Shanxi, and Xinjiang. This group's typical feature is a slow rise in carbon productivity, and Xinjiang has even experienced negative growth. The average growth rate of national carbon productivity is 3.09%, while that of Hainan and Ningxia are 0.9% and 0.79%, respectively and in Xinjiang growth is −0.88%. Furthermore, this group's carbon productivity is lower than other groups. There is substantial room to elevate carbon productivity in this group, but it is also difficult to achieve. This because Gansu, Guangxi, Guizhou, Hainan, Hebei, Inner Mongolia, Jiangxi, Ningxia, Qinghai, Shanxi, and Xinjiang are all developing regions. In 2017, the GDP of these 11 provinces accounted for only 18.39% of China. The industrial structure needs to be optimized in the 11 places, especially in Hainan, Xinjiang, and Ningxia, which are 22.0:22.3:55.7, 15.5:39.3:45.2, and 7.6:46.8:45.6, respectively in 2017. Typically, the industrial structure of Xinjiang has a negative influence on carbon productivity. In addition, the positive effects of economic activities on carbon production in these three provinces are not strong. The growth rate of carbon productivity is far lower than the national average. Table 5 shows that Hainan's carbon productivity is the highest in this group, with 0.8 million yuan/100 tons, but this level is only the national average. Taking Hainan's carbon productivity as the target, Gansu, Guangxi, Guizhou, Hebei, Inner Mongolia, Jiangxi, Ningxia, Qinghai, Shanxi, and Xinjiang's carbon productivity growth potential are 48.75%, 10%, 57.5%, 47.5%, 70%, 11.25%, 86.25%, 53.75%, 70%, and 75%, respectively. Hainan, Gansu, Guizhou, Ningxia, Qinghai, and Xinjiang's GDP ranked in the bottom 10 of the whole country. Hebei, Shanxi, and Inner Mongolia have heavy industrial structures. This group should bring its advantages into full play based on regional resource endowment to elevate the carbon productivity growth rate.
Energy-dependent regions, such as Shanxi, Inner Mongolia, and Hebei, are rich in coal resources. The carbon emissions brought by the rapid development of the energy industry are major factors inhibiting carbon productivity elevation. Therefore, these provinces need to adopt advanced energy-saving technologies, improve energy efficiency, promote clean and efficient utilization of coal, and reduce energy intensity. The provinces in this group should seize the opportunity to maintain rapid economic growth. At the same time, they should also pay attention to enhancing low-carbon innovation to reduce carbon emissions.
In short, through the above analysis, the following results are obtained. During 2001-2017, China's carbon productivity continued to rise, and the difference in carbon productivity between provinces gradually widened. China's carbon productivity showed an upward trend, and the growth accelerated sharply in the new normal. The annual growth rate of China's carbon productivity grew greatly from 1.74% in 2001-2010 to 6.86% in 2010-2017. There are great variations in carbon productivity between provinces. In 2017, the highest provincial carbon productivity was 19.03 times the lowest provincial carbon productivity.
Economic activity and industrial structure are key to push up regional carbon productivity in China, while energy intensity is the main factor pulling it down. In the four (10th-13th) FYPPs, economic activity plays a leading role in improving carbon productivity. After entering the new normal, the improvement of China's carbon productivity is mainly due to the optimization and upgrading of industrial structures. Since 2006, energy intensity became the major factor hindering carbon productivity growth in all provinces.
China's 30 provinces are classified into four groups. Group 1 includes Beijing, Shanghai, and Tianjin, with the highest level and growth rate of carbon productivity. Group 2 covers Chongqing, Fujian, Guangdong, Jiangsu, Shandong, Sichuan, and Zhejiang, with higher carbon productivity and slower carbon productivity growth. Group 3 is characterized by low-carbon productivity and higher growth. This feature determines that group 3 should be a major focus for China to raise carbon productivity. This group includes Anhui, Heilongjiang, Henan, Hubei, Hunan, Jilin, Liaoning, Shaanxi, and Yunnan. Group 4 is composed of Gansu, Guangxi, Guizhou, Hainan, Hebei, Inner Mongolia, Jiangxi, Ningxia, Qinghai, Shanxi, and Xinjiang.
The potential for carbon productivity improvement varies greatly among provinces in the four groups. Beijing has the maximum carbon productivity in group 1, and the growth potential of those in Shanghai and Tianjin are 33.16% and 41.5%, respectively. Guangdong's carbon productivity is the highest in group 2, and the carbon productivity growth potentials of other regions are less than 40%. Hunan has the highest carbon productivity in group 3, which is 0.77 million yuan/100 tons. The carbon productivity growth potentials of these regions are less than 50%. Hainan's carbon productivity is the highest in group 4, and other provinces' carbon productivity growth potential are 48.75%, 10%, 57.5%, 47.5%, 70%, 11.25%, 86.25%, 53.75%, 70% and 75%, respectively.

Conclusions
Carbon productivity can be used as an important indicator to measure a country's efforts and effectiveness in coping with climate change. In order to better understand the change in China's carbon productivity, this paper first conducts decomposition analysis to study the driving factors of carbon productivity. Then, this study further calculates the growth potential of carbon productivity in each province, so as to explore the growth target and promotion path of carbon productivity in each province. The main conclusions are as follows.
The study finds that economic activity, industrial structure, and energy intensity are the main driving factors of regional carbon productivity changes in China during 2001-2017. The former two factors increased China's carbon productivity growth, whereas the latter reduced it. Thus, the policy should focus on optimizing and upgrading industrial structure and reducing energy intensity. Supply-side structural reform needs to be pushed up further, accelerating the conversion of new and old kinetic energy, and realizing the green and low-carbon economic transformation.
The study also shows that in China, there are differences in the growth potential of carbon productivity between provinces. This finding implies that China's low-carbon policy should consider regional heterogeneity. Policies are needed to highlight the developmental advantages of each region, relying on resource endowments. Economically developed regions, such as Beijing and Shanghai, should focus on the promotion of carbon productivity in service sectors. Shanxi, Inner Mongolia, Shaanxi, Hebei, and other energy-dependent areas need to adopt advanced energy-saving technologies, promote clean and efficient utilization of coal, and reduce energy intensity. Sichuan and Yunnan can make full use of the advantages of renewable energy. Developing provinces should raise carbon productivity by optimizing and upgrading industrial structure, developing characteristic industries to increase added value and stimulate regional economic development.
In addition, due to the strong regional heterogeneity, the impact of these heterogeneities should be considered in the establishment of the national carbon market and the formulation of carbon prices in the future. Regional heterogeneity has led to significant differences in the transaction prices of different carbon market pilots. Therefore, in the process of establishing a unified national carbon market, it is necessary to consider regional heterogeneity, balance the economic development, carbon emissions, and emission reduction needs of each region, and repeatedly adjust the carbon price to achieve market stability.
Finally, China's current regional carbon emission reduction research is facing the problem of insufficient data acquisition. The calculation of greenhouse gas emission statistics is the basis for determining national carbon emission reduction targets and for regional and industry decomposition. It is recommended to establish a carbon-emission-related statistical verification system in the future, regularly compile national and provincial greenhouse gas emission inventories, implement a carbon emission accounting and reporting system for key units, and further improve government assessment and promote scientific research.
This paper can also provide reference for developing countries in the stage of industrialization and urbanization. Economic activities, industrial structure, and energy intensity are important factors affecting carbon productivity. The annual growth rate of GDP in developing countries is high. The improvement of carbon productivity must first offset the carbon emissions brought by economic growth. Carbon emission reduction can be achieved through the optimization and upgrading of industrial structure and the reduction of energy intensity. In addition, regional heterogeneity is an important factor that a country needs to consider to improve carbon productivity. Due to the differences of economic development stage, scientific and technological level, resource endowment and other factors, the influencing factors of regional carbon productivity are also different. When implementing carbon emission reduction policies, regional heterogeneity should be considered and measures should be adapted to local conditions.

Conflicts of Interest:
The authors declare no conflict of interest.