Spatial-Temporal Analysis and Driving Factors Decomposition of (De)Coupling Condition of SO2 Emissions in China

China has a fast-growing economy and is one of the top three sulfur dioxide (SO2) emitters in the world. This paper is committed to finding efficient ways for China to reduce SO2 emissions with little impact on its socio-economic development. Data of 30 provinces in China from 2000 to 2017 were collected to assess the decoupling relationship between economic growth and SO2 emissions. The Tapio method was used. Then, the temporal trend of decoupling was analyzed and the Moran Index was introduced to test spatial autocorrelation of the provinces. To concentrate resources and improve the reduction efficiency, a generalized logarithmic mean Divisia index improved by the Cobb–Douglas function was applied to decompose drivers of SO2 emissions and to identify the main drivers. Results showed that the overall relationship between SO2 emissions and economic growth had strong decoupling (SD) since 2012; provinces, except for Liaoning and Guizhou, have reached SD since 2015. The decoupling indexes of neighboring provinces had spatial dependence at more than 95% certainty. The main positive driver was the proportion of the secondary sector of the economy and the main negative drivers were related to energy consumption and investment in waste gas treatment. Then, corresponding suggestions for government and enterprises were made.


Introduction
Since the 21st century, China's rapid economic growth and social development has given rise to a series of environmental problems. Air pollution has been identified as a high priority issue that must be addressed immediately. Among air pollutants, SO 2 has aroused wide concern from all parts of society. From an international perspective, SO 2 emission issues in China are still serious. In 2018, China's SO 2 emissions were 2578 thousand tons; it was the third highest in the world, just behind India and Russia (http://sputniknews.cn/economics/201908191029324285/). SO 2 emissions will not only lower the atmospheric quality, but also trigger health-related issues [1]. A 10µg/m 3 increase in SO 2 emissions was associated with an increase in out-of-hospital coronary deaths (of 0.88%) [2]. A significant long-term relationship between SO 2 and end-stage renal disease (ESRD)-related mortality was also found [3]. Therefore, it is essential for China to unceasingly reduce emissions of SO 2 while developing the economy. To achieve this "win-win" condition between economic growth and SO 2 emissions, the relationship between economic development and SO 2 emissions should be studied intensively and deeply.
The purpose of this paper is to find efficient ways for China to reduce SO 2 emissions with as little impact on its socio-economic development as possible. Therefore, this paper collected data of 30 provinces of China (excluding Hong Kong, Macao, Taiwan, and Tibet) from 2000 to 2017. Firstly, the annual decoupling index of each province was calculated for temporal analysis. The focus of this part was to analyze the dynamic change trend of decoupling conditions from both national and provincial perspectives. Secondly, spatial analysis was done by making comparisons among provinces over the entire time period, and by studying the spatial autocorrelation between neighboring provinces. The focus of this part was to compare the state of provinces over the whole time period and to find out the interaction patterns between neighboring areas. Thirdly, to decompose the effect of different driving factors comprehensively, this paper used the Cobb-Douglas (C-D) production function to improve the LMDI model. The C-D production function was introduced by Cobb and Douglas in 1928 [19], it takes labor and capital as the main factors to establish an exponential relationship model. Thus, using the C-D production function can make up for the lack of capital and labor in LMDI. Based on the C-D production function and the LMDI method, a GLMDI method was constructed, referring to research by Wang et al. [20]. Then, effects of 10 representative driving factors were decomposed by the GLMDI method; their impacts on SO 2 emissions were discussed and compared. The task, of this part, was to analyze the influence of each driving factor on SO 2 emissions; thus, the main drivers could be found out, which should be focused on by the Chinese government to improve the efficiency of SO 2 emissions reduction.
The rest of this paper is organized as follows. Section "Materials and Methods" presents the research methods and relevant data sources. Section "Results and Discussion" analyzes the decoupling conditions from a spatial-temporal perspective and decomposes driving factors of SO 2 emissions in China over years. The main conclusions of this paper are in Section "Conclusions".

Tapio Elastic Analysis Method
As research on decoupling grows, various methods for determining and analyzing decoupling status has been developed, including the OECD decoupling factor method, the variation analysis (VA) method, and the Tapio elastic analysis (TEA) method. Although all three methods are workable, they have some limitations. The OECD decoupling factor model cannot distinguish the decoupling states in an expanding and recessive economy [21]; the VA method cannot distinguish between non-decoupling and re-decoupling [22]; and the TEA method defines much decoupling states. Wu et al. summarized these decoupling methods and compared their advantages and disadvantages; the result showed that the TEA model was more accurate and not limited by the length of time [23]. Therefore, this paper selects the TEA method to assess the decoupling relationship between economic growth and SO 2 emissions in China. Based on the general concept of the TEA model, the decoupling elasticity index between SO 2 Emissions and economic growth can be written as: where, e t+1 denotes the decoupling index between year t and year t + 1. ∆S t+1 , ∆G t+1 represent the change rate of SO 2 emissions and economic growth from year t to year t+1 separately. S t+1 , G t+1 , respectively, denote SO 2 emissions and economic growth in year t + 1 while S t , G t denotes those conditions in year t. In this paper, the Gross Regional Product (GRP) of each province, converted to comparable prices based on the year 2000, was used to measure economic growth level. The data of provincial GRP figures, GRP indices, and SO 2 emissions were derived from the National Bureau of Statistics of China.
On the basis of definition, classification, and empirical analysis mentioned by Tapio [24], the decoupling relationship between air pollutant emissions and economic growth can be divided into three states, namely, decoupling, coupling, and negative decoupling, which can be further subdivided into eight logical possibilities, as shown in Table 1. According to Tapio's research [24], in order not to over-interpret slight changes as significant, ±20% variation of the e t+1 values around 1.0 are still regarded, here, as coupling. Thus, coupling is defined as e t+1 values from 0.8 to 1.2, which is an empiric value. On the other hand, the growth of the variables can be positive or negative, expressed as expansive coupling and recessive coupling.

Moran Index
At present, there are two commonly used methods to test spatial dependence, which are Geary's coefficient [25] and the Moran Index (Moran's I) test [26]. Both of them have limitations. The Geary's coefficient could be sensitive to high values, which means that it has a better ability to detect high-value spatial clustering than low-value spatial clustering. The Moran's I could be mainly affected by the size of the aggregation area, which means that it will increase with the expansion of the spatial clustering range. However, researchers have found that it is more reliable to use Moran's I to judge whether there is spatial clustering in a region [27]. Our main purpose was to determine whether there is spatial correlation between provinces; the Moran's I was adopted. The expression of Moran's I is as follows: where, n represents provinces in China. x i , x j are the decoupling indicators from 2000 to 2017 of i province, j province, respectively. x denotes the mean of decoupling indexes. ω ij denotes the spatial weight, which represents the strength of potential interaction between individual provinces. There are various approaches to generate a spatial weight matrix including queen contiguity [28], rook contiguity [29], distance weight [30], and k-nearest neighbors [31]. The matrixes generated by the first two methods are composed of 0 and 1. Rook contiguity stipulates that if two provinces have a common boundary, they are considered adjacent, and the corresponding value in the spatial weight matrix is 1, otherwise, the value in matrix is 0. Queen contiguity stipulates that if two provinces have a common boundary or a common point, they are considered adjacent. Within the scope of this study, Hainan has neither a common border nor a common point with other provinces. In order not to ignore the relationship between Hainan and other provinces, the first two methods were not adopted in this paper. The latter two methods construct the matrix according to the geographical distance between provinces. The k-nearest neighbors method is to calculate the distance between each province and its nearest k provinces, k is the number of neighbors, which needs to be set by scholars. In this method, each province has the same number of neighbors, which is subjective to some extent. For the distance weight theory, the threshold of a minimum space range is calculated to ensure that each province has at least one neighbor. Then, the distances between each province and its neighbors are calculated to generate the spatial weight matrix. This approach is more objective and can make the influence scope of each province consistent, so, this paper adopts distance weight matrix method. The provincial longitude and latitude data were derived from the National Bureau of Statistics of China.
Moran's I ranges from −1 to 1. If it is greater than 0, there is positive spatial autocorrelation. The larger the value, the stronger the positive spatial dependence. If the index is less than 0, there is no similar attributes between adjacent provinces, and the smaller the value, the greater the difference of each spatial unit. If the value is 0, the situation is subject to random distribution.

Generalized LMDI Method
For further analysis of the SO 2 emissions drivers, this paper adopts a GLMDI decomposition method based on an extended Kaya identity [32]. The SO 2 emission (SE t ) in period t can be expressed as follows.
which is the proportion of the province i's GRP (GRP t i ) to the whole country (GDP t ), represents the economic growth level of province i. , which is the urban fixed assets investment (IN t i ) per urban population (C t i ), represents the intensity of urban fixed assets investment in province i.
, which is the ratio of energy consumption (E t i ) to secondary industrial output (I t i ) in province i, was used to denote the energy intensity. In China, energy consumption is mainly generated by the secondary industry. According to data from the National Bureau of Statistics (https://data.stats.gov.cn/easyquery.htm?cn=C01), in 2017, the energy consumption of the secondary industry in China was 294,488.04 × 10 4 tons of coal equivalent (tce), while the consumption of the primary and thirdly industry were only 8931.23 × 10 4 tce and 24,268.83 × 10 4 tce, respectively. Therefore, to some extent, the more energy consumed per unit of the secondary industrial output, the greater the intensity of the province i's energy consumption.
, is the ratio of population (P t i ) to energy consumption (E t i ) in province i. Commonly, industries sustain peoples' lives by consuming energy to make products and generate income. At the same level of energy consumption, if industries in an area can sustain more people, that area is more energy efficient. The implication of this indicator is that the larger the population per unit of energy consumed, the more efficient the province i's energy consumption.
, represents province i's investment strength on waste gas treatment. WG t i denotes the investment for industrial waste gas treatment projects. In China, this investment mainly concentrates on the old industrial pollution source treatment, such as desulfurization and denitrification. Old industrial pollution sources are mostly located in urban areas; the proportion of this investment to urban fixed assets investment (IN t i ) was used to estimate the investment strength.
, is the ratio of SO 2 emissions to investment on waste gas treatment projects in province i. The implication of this indicator is that the more the SO 2 emissions per unit of investment, the higher the investment efficiency requirement in province i. Generally, the waste gas treatment investment varied from province to province, and the SO 2 emissions of each province was also different. For provinces with high emissions but low investment, the pressure to reduce SO 2 will be greater because of a lack of funds. For these provinces, the demand for investment efficiency will be higher. As a result, they are likely to increase the efficiency of their investment through various ways, such as technological innovation. Therefore, it is uncertain whether the higher requirement for investment efficiency will contribute to or inhibit SO 2 emissions. To study this mechanism, the ratio of SO 2 emissions to investment on waste gas treatment projects was adopted.
In order to assess the impact of capital and labor input on SO 2 emissions, the C-D production function was introduced. The general formula of the C-D production function is as follows.
where, A, α, β are uncertain constant parameters, in general, A>0, 0 < α < 1, 0 < β < 1. K denotes capital input, measured by fixed asset investment. L denotes labor input, measured by the number of employed. A represents the level of technological progress to some extent but it was not considered in this study, see formula (18). Many methods have been used to calculate α and β of C-D production function, such as wage share in Gross Domestic Product (GDP), international experience reference, regression, etc. Among them, the regression method proved to be more scientific and accurate [33].
In the context of China's rapid development, the parameter values over the years were likely to be different. In order to reflect this difference, the cross-sectional regression method was adopted in this paper to estimate the α and β of C-D function over the years, see Table 2, all the results were statistically significant. The formula of GLMDI model is as follows: The symbolism of each variable in GLMDI model is shown in Table 3. Table 3. Meaning of variables in the generalized logarithmic mean Divisia index (GLMDI) model.

Variable
Meaning Unit The economic growth level of province i.
The energy consumption intensity in province i.
The energy consumption efficiency in province i.
The intensity of urban fixed assets investment in province i. Taking SO 2 emissions in period 0 as the benchmark to investigate the change of SO 2 emissions in period t, the summation decomposition of the GLMDI model is as follows.
The calculation method of decomposition factors in formula (6) are as follows. where, This study gave no consideration on it. National data, such as GDP, fixed asset investments, employed numbers, and provincial data, such as GRP, industrial output, fixed asset investments, total population, urban population

Spatial-Temporal Analysis of (De)Coupling Conditions
According to the results of decoupling indexes assessment, as shown in Table 1, there were five decoupling states within the scope of this study, namely, strong decoupling (SD), weak decoupling (WD), expansive negative decoupling (END), expansive coupling (EC), and recessive coupling (RC), sorting from most to least. Based on the decoupling state classification, see Table 1, SD is the most desirable condition where SO 2 emissions decline along with economic development. Therefore, the frequent emergence of SD indicated that the overall decoupling status of provinces in China was favorable.
From the perspective of temporal contrast, as shown in Figure 1, the overall decoupling condition in China was improving. At the beginning of the 21st country, the GDP and SO 2  However, the situation varies from province to province; see Table 4. From 2001 to 2014, there were many changes and fluctuations of the decoupling state. After 2015, 28 provinces reached the SD state, accounting for 93.3% of the provinces studied. Among all the administrative units, Beijing was in the best state, which had almost achieved SD in all periods within this study, except 2004. This situation shows that Beijing's decoupling condition had been relatively stable.
On the contrary, some provinces should be focused on. As shown in Table 4, Guizhou was in WD scenario in 2017, where the SO2 emissions grows more slowly than the economy, which was not the best, but an acceptable condition. The condition in Liaoning became RD in 2016, which means the economy was in recession while the SO2 emissions decreased even more significantly. Although this condition was good from an environmental point of view, emission reduction at the cost of economic recession was not acceptable. To achieve the goal of sustainable development, the situation in Liaoning province needed to be carefully considered. Moreover, Hainan, Qinghai, and Xinjiang had the fewest SD states among the provinces studied, only six times from 2001 to 2017, which means their situations were precarious and complicated in former years. However, these three provinces reached SD state after 2015, which suggested that their situations were expected to gradually stabilize. For these provinces, recent experience could be referenced and efforts should be made to consolidate their SD situations. However, the situation varies from province to province; see Table 4. From 2001 to 2014, there were many changes and fluctuations of the decoupling state. After 2015, 28 provinces reached the SD state, accounting for 93.3% of the provinces studied. Among all the administrative units, Beijing was in the best state, which had almost achieved SD in all periods within this study, except 2004. This situation shows that Beijing's decoupling condition had been relatively stable.
On the contrary, some provinces should be focused on. As shown in Table 4, Guizhou was in WD scenario in 2017, where the SO 2 emissions grows more slowly than the economy, which was not the best, but an acceptable condition. The condition in Liaoning became RD in 2016, which means the economy was in recession while the SO 2 emissions decreased even more significantly. Although this condition was good from an environmental point of view, emission reduction at the cost of economic recession was not acceptable. To achieve the goal of sustainable development, the situation in Liaoning province needed to be carefully considered. Moreover, Hainan, Qinghai, and Xinjiang had the fewest SD states among the provinces studied, only six times from 2001 to 2017, which means their situations were precarious and complicated in former years. However, these three provinces reached SD state after 2015, which suggested that their situations were expected to gradually stabilize. For these provinces, recent experience could be referenced and efforts should be made to consolidate their SD situations. Figure 2a-from the perspective of spatial analysis. In the context of positive economic growth in all provinces, SO 2 emissions increased in only three provinces (Qinghai, Xinjiang, and Ningxia) and fell in all others, so that Qinghai, Xinjiang, and Ningxia failed to achieve SD condition; see Figure 2b.
The Moran Index scatter plot was used to further assess the spatial relationship among provinces, as shown in Figure 3a. The x-axis represents the normalized provincial decoupling index (e t+1 ) and the y-axis represents the lagged value, that is, the normalized e t+1 of adjacent units of each province. The diagonal in the graph can be regarded as the linear fitting of the scatters. The Moran's I is the slope of the diagonal, which is greater than 0, representing positive spatial autocorrelation. This result was permutated 999 times to test its significance and the p value was 0.001, indicating at least 99% certainty that the results were significant. Moreover, it is worth noting that there is an upper-right outlier in Figure 3a. To exclude its influence on the result, Moran's I was recalculated after removing the outlier for robust check, as shown in Figure 3b. The recalculated Moran's I was still greater than 0, and its p value after 999 times permutating was 0.028, which was lower than 0.05, indicating that the results were significant at least 95% certainty. That is, generally, the outlier did not have a decisive influence on the results; the decoupling conditions of neighboring provinces would affect each other. Table 4. Annual decoupling condition of each province.

Provinces in favorable stages
Beijing SD  SD  SD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Tianjin  SD  SD  WD  SD  EC  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Hebei  SD  SD  EC  WD  WD  WD  SD  SD  SD  SD  END  SD  SD  SD  SD  SD  SD  Shanxi  SD  WD  EC  WD  WD  SD  SD  SD  SD  SD  EC  SD  SD  SD  SD  SD Hunan  SD  SD  END  WD  WD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Guangdong  WD  WD  WD  WD  EC  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Guangxi  SD  SD  END  WD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Chongqing  SD  SD  EC  WD  WD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Sichuan  SD  SD  WD  WD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  Yunnan  SD  WD  END  WD  EC  WD  SD  SD  SD  WD  END  SD  SD  SD  SD  SD  SD  Shaanxi  SD  WD  END  WD  EC  WD  SD  SD  SD  SD  END  SD  SD  SD  SD  SD  SD  Gansu  WD  END  END  SD  END  SD  SD  SD  SD  EC  EC  SD  SD  WD  SD  SD  SD  Ningxia  SD  EC  END  WD  END  EC  SD  SD  SD  SD  END  SD  SD  SD  SD SD SD Liaoning  SD  SD  WD  WD  END  WD  SD  SD  SD  SD  EC  SD  SD  SD  SD  RD  SD  Guizhou  SD  SD  SD  SD  WD  WD  SD  SD  SD  SD  SD  SD  SD  SD  SD  SD  WD  Hainan  WD  EC  WD  WD  SD  WD  WD  SD  WD  END  EC  WD  SD  WD  SD  SD  SD  Qinghai  EC  SD  END  END  END  WD  WD  WD  WD  WD  WD  SD  WD  SD  SD  SD  SD  Xinjiang  SD  SD  EC  END  WD  WD  WD  WD  WD  SD  END  WD  WD  WD  SD SD SD Figure 2a-from the perspective of spatial analysis. In the context of positive economic growth in all provinces, SO2 emissions increased in only three provinces (Qinghai, Xinjiang, and Ningxia) and fell in all others, so that Qinghai, Xinjiang, and Ningxia failed to achieve SD condition; see Figure  2b. The Moran Index scatter plot was used to further assess the spatial relationship among provinces, as shown in Figure 3a. The x-axis represents the normalized provincial decoupling index ( ) and the y-axis represents the lagged value, that is, the normalized of adjacent units of each province. The diagonal in the graph can be regarded as the linear fitting of the scatters. The Moran's I is the slope of the diagonal, which is greater than 0, representing positive spatial autocorrelation. This result was permutated 999 times to test its significance and the p value was 0.001, indicating at least 99% certainty that the results were significant. Moreover, it is worth noting that there is an upper-right outlier in Figure 3a. To exclude its influence on the result, Moran's I was recalculated after removing the outlier for robust check, as shown in Figure 3b. The recalculated Moran's I was still greater than 0, and its p value after 999 times permutating was 0.028, which was lower than 0.05, indicating that the results were significant at least 95% certainty. That is, generally, the outlier did not have a decisive influence on the results; the decoupling conditions of neighboring provinces would affect each other.

Provinces in need of attention
(a) (b) To give a more comprehensive analysis of spatial relationships between provinces, Figure 3a takes all provinces into account. Specific to each province's situation, the four quadrants identify four kinds of spatial relationships and they can be further categorized into two groups: positive and negative spatial autocorrelation [34]. Provinces in the first and third quadrants, respectively, exhibited high-high (H-H) and low-low (L-L) aggregation, indicating that these provinces tended To give a more comprehensive analysis of spatial relationships between provinces, Figure 3a takes all provinces into account. Specific to each province's situation, the four quadrants identify four kinds of spatial relationships and they can be further categorized into two groups: positive and negative spatial autocorrelation [34]. Provinces in the first and third quadrants, respectively, exhibited high-high (H-H) and low-low (L-L) aggregation, indicating that these provinces tended to be adjacent to provinces with similar decoupling indexes, that is, positively autocorrelated. Provinces in the second and fourth quadrants exhibited low-high (L-H) and high-low (H-L) aggregation separately, indicating that these provinces tended to be adjacent to provinces with opposite decoupling indexes, which is called negative autocorrelation. The map of Local Indications of Spatial Association (LISA) aggregation was applied to analyze the spatial correlation and the significance of each province. The LISA is a space-based statistical technique; it gives an indication of the extent to which a significant spatial clustering of homogeneous values existing around a particular observation [35,36]. The results of LISA, which indicate spatial correlation of decoupling index in 30 provinces, can be calculated through software GeoDa, as shown in Table 5. Table 5. Spatial correlation of decoupling index in 30 provinces. Four provinces, Xinjiang, Jiangxi, Anhui, and Fujian showed significantly positive autocorrelation. Cross-regional coordination could be considered in these regions. Among these provinces, Xinjiang did not, overall, reach SD state; see Figure 2. Its conditions could have a bad effect on neighboring provinces. Therefore, in order to maintain favorable decoupling status, the provinces adjacent to Xinjiang should give Xinjiang the necessary assistance to make it achieve SD faster. Moreover, there were four provinces in states of significantly negative autocorrelation, Shanghai, Jiangsu, Zhejiang, and Shaanxi; they were all in H-L condition. All of these provinces had, overall, reached SD state; see Figure 2. However, their developments might have dampening effects on the surrounding areas. For these provinces, there might be trade-offs with their neighbors. Therefore, these provinces should learn the decoupling trends of neighbors and complement each other when seeking self-development.

Driving Factors Decomposition of SO 2 emissions
Nevertheless, the understanding of decoupling conditions alone cannot maximize the efficiency of SO 2 reduction. Therefore, panel data of 30 provinces from 2000 to 2017 were used to identify the effect of each driving factor on SO 2 emissions. Decomposition and analysis were carried out according to Equations (7)- (17). For the whole country, decomposition factors were calculated, taking the year 2000 as the benchmark; the results are shown in Table 6.
In general, the impact of elements on SO 2 emissions was negative within this study; see row ∆SE tot , indicating that SO 2 emissions had been overall suppressed in China from 2000 to 2017. The driving factors can be categorized into two groups: the positive factors, which would cause emissions increase, and the negative factors, which could facilitate emissions reduction. As shown in Table 6, the capital (∆SE t K ), the labor (∆SE t L ), the economic growth level (∆SE t Q ), the proportion of secondary sector of economy to GRP (∆SE t SI ), the urbanization rate (∆SE t UR ) and the fixed assets investment (∆SE t FA ) were positive drivers. Obviously, all of these positive drivers are important factors to promote social and economic development, which means that China's socio-economic development, indeed, led to an increase in SO 2 emissions. On the contrary, the energy consumption intensity (∆SE t EI ), the energy efficient (∆SE t EE ), the waste gas treatment investment (∆SE t WI ), and the investment efficiency requirement (∆SE t SR ) were negative drivers. The first two negative factors are related to energy consumption, which shows that China's energy management has played a beneficial role in reducing SO 2 emissions. The negative impact of these energy factors is favorable for China, because China remained the world's largest energy consumer in 2017, accounting for 23.2% of global energy consumption and 33.6% of global energy consumption growth, according to the 2018 British Petroleum (BP) World Energy Statistical Yearbook (http://www.199it.com/archives/767423.html). As China develops further, it will be difficult for its energy consumption to decline in short-term. Therefore, energy management will continue to be important to SO 2 emissions reduction; the inhibitory effect of energy factors can be good to China's atmospheric environment protection in the long run. The latter two negative factors are related to investment in waste gas treatment projects, indicating that China's investment in waste gas treatment has made achievement in reducing SO 2 emissions. The most significant negative driver is ∆SE t SR , which denotes the requirement of waste gas reduction investment efficiency. In order to meet the investment efficiency requirement, the Chinese government and enterprises accelerated technological innovation of SO 2 emission reduction and adopted a series of mandatory emission reduction policies. At the second National Conference on Environmental Science and Technology of China, the minister of Ministry of Environmental Protection (now the Ministry of Ecology and Environment) said that technological progress accounted for 66% of sulfur dioxide emissions reduction (http://www.cinic.org.cn/zgzz/cx/136582.html). Moreover, China issued at least 237 air pollution control regulations at the national level from 2000 to 2017 (data were obtained from the websites of the Ministry of Ecology and Environment (http://www.mee.gov.cn/), Ministry of Finance (http: //www.mof.gov.cn/index.htm), Resource Conservation and Environmental Protection division of National Development and Reform Commission (https://www.ndrc.gov.cn/fzggw/jgsj/hzs/), and the Laws and Regulations Database of Peking University), which urged and guided the emission reduction of SO 2 and other air pollutants. All of these reasons made ∆SE t SR become the most important emission reduction driver.
However, only a macro analysis of the overall situation of China cannot reveal the changes of each factor over the years. For a rapidly developing country, the effects of each factor are likely to be different at different development stages. Therefore, the analysis of the changes in the impact of various factors in different years will provide a more specific reference for China's SO 2 emission reduction. To compare the changes of decomposition factors over the years, this study calculated each decomposition factor taking the previous year as the benchmark, the results are shown in Table 7.  Figure 1, which was the result of multifactorial interaction. To find out the key factors, as shown in row 2002-2003, the positive effect of the fixed assets investment per person (∆SE t FA ) was relatively high, while the negative effect of the energy intensity (∆SE t EI ) was the lowest compared to other periods. In other words, the fixed assets investment per person significantly contributed to SO 2 emissions increase, while the industrial energy intensity control did not have adequate restraining effect on SO 2 emissions from 2002 to 2003. From 2004 to 2005, the urbanization rate (∆SE t UR ) was much greater than that in other periods, while the contribution of ∆SE t EI was still relatively low, which means that rapid urbanization contributed significantly to SO 2 emissions while the inhibition effect of industrial energy intensity control on SO 2 was relatively weak compared with other stages.
From the perspective of positive factorization, there were two factors that always behaved as positive drivers, the labor (∆SE t L ) and the economic growth level (∆SE t Q ), indicating that labor and economic development always contributed to higher SO 2 emissions in China. Besides, the capital (∆SE t K ), the proportion of secondary sector of economy to GRP (∆SE t SI ), the urbanization rate (∆SE t UR ), and the fixed assets investment per person (∆SE t FA ) exhibited acceleration impact on SO 2 emissions in no less than 14 years. Among all the positive drivers, the labor (∆SE t L ), the economic growth level (∆SE t Q ), the capital (∆SE t K ), the urbanization rate (∆SE t UR ), and the fixed assets investment per person (∆SE t FA ) are key indicators of national progress, and cannot be suppressed just for the sake of SO 2 emission reduction. While, the proportion of secondary sector of economy to GRP can be weighed in the future. In fact, the adjustment of economic structure has been attached great importance by the Chinese government, and great breakthroughs have been made in the past period of time. However, according to data from the World Bank World Development Indicator (WDI) database, in 2017, the proportion of secondary industry was 40.5% in China, while this proportion was less than 30% in developed countries, such as the United States, Japan, and Canada, which means that China's economic structure still has potential for optimization. To reduce the proportion of secondary industry and, thus, its impact on SO 2 emissions, the Chinese government should continue to encourage non-industrial enterprises to drive the economy. For example, the government could sequentially improve the proportion of primary and tertiary industry in GRP to optimize the structure of enterprises in China.
From the perspective of negative factorization, the intensity (∆SE t EI ) and the efficiency (∆SE t EE ) of energy consumption had suppression impact on SO 2 emissions in 16 years, and they all remained negative after year 2013, indicating that the inhibition of SO 2 emissions by energy management was stable over years, which is beneficial for China, referring to the macro analysis of the whole country above. For the waste gas treatment investment (∆SE t WI ), and the investment efficiency requirement (∆SE t SR ), the conditions before 2015 were unstable, while these two factors remained negative from 2015 to 2017. Whether they will change next is still uncertain; thus, the government and enterprises need to take necessary measures to stabilize their negative influence.

Limitations
Due to the lack of public data, some factors affecting sulfur dioxide emissions, such as indicators measuring the development of SO 2 filtration technology, were not taken into account in the model. This issue also made some indicators be not straightforward. As there is no available public data on investments specifically for SO 2 treatment, the investment in industrial waste gas treatment projects was used to estimate the investment strength of waste gas treatment and the investment efficiency requirement. However, the waste gas projects mainly include desulfurization and denitrification, they do not solely consider SO 2 . In addition, at the provincial level, comprehensive energy consumption data for the secondary industry are not directly disclosed in China. For China's energy consumption is mainly generated by the secondary industry, the total energy consumption, instead of the energy consumption for the secondary industry, was used to measure the energy intensity and efficiency.
Moreover, this paper used the data of each province in China to study the factorization of the whole country, and the analysis was relatively macro, while the situation of each province was different, so the factorization of each province would be more targeted. However, according to the principle of the GLMDI model, more microscopic data are needed to realize the factor decomposition at the provincial level, such as the data of cities within the jurisdiction of each province. At present, some data of key driving factors, such as the investment data of waste gas treatment, are not publicly available at the city level, which limits further refinement of the study. In future research, further optimization of index selection can be considered, and different theoretical models can be tried to achieve the impact factor decomposition at the provincial level.

Conclusions
According to the spatial-temporal analysis of (de)coupling condition, China's decoupling scenario had become better from 2000 to 2017. Over the entire time period, Qinghai, Xinjiang, and Ningxia failed to achieve SD condition. The overall relationship between SO 2 emission and economic growth had achieved the SD stage since 2012. Provinces, except Liaoning and Guizhou, had all reached SD state since 2015. Among the provinces, Beijing has the most stable decoupling condition, which can provide reference for other provincial administrative units. While, Liaoning and Guizhou need to be paid more attention to by the Chinese government in the future, as their decoupling situations were still unstable in recent years. The decoupling indexes of neighboring provinces indicated significant spatial dependence at more than 95% certainty. Coordinated development across provinces could be taken into account in Xinjiang, Jiangxi, Anhui, and Fujian. In particular, the provinces adjacent to Xinjiang should give Xinjiang the necessary assistance for maintaining their own SD state. Complementary development with neighboring provinces should be considered in Shanghai, Jiangsu, Zhejiang, and Shaanxi.
According to the driving factors decomposition, as a whole, SO 2 emissions suppression in China was relatively stable, while the driving factors demonstrated different impacts on SO 2 emissions over the years. Thus, China should examine the influence of various factors from a dynamic perspective to make correct decisions in SO 2 emission reduction. The positive driver that should be paid most attention to is the proportion of the secondary sector of the economy to GRP. This is not only because of the adjustment potential of this driver, but also because optimizing this factor to reduce SO 2 emissions will not be at the expense of the country's socio-economic development. The main negative drivers were related to energy consumption and investment in waste gas treatment. The inhibitory effect of energy factors can be beneficial to China's SO 2 emissions reduction in the long run. Moreover, the negative drivers that should be focused on are waste gas treatment investment and investment efficiency requirement, because their effects are still uncertain. To stabilize the negative effect of these factors, the direction of investment in waste gas treatment should be optimized. The government should focus on the support of low-cost and high-efficiency technologies for SO 2 reduction. The enterprises should speed up the elimination of backward production and invest more in environmentally friendly production.