Drivers and Decoupling Effects of PM2.5 Emissions in China: An Application of the Generalized Divisia Index

Although economic growth brings abundant material wealth, it is also associated with serious PM2.5 pollution. Decoupling PM2.5 emissions from economic development is important for China’s long-term sustainable development. In this paper, the generalized Divisia index method (GDIM) is extended by introducing innovation indicators to investigate the main drivers of PM2.5 pollution in China and its four subregions from 2008 to 2017. Afterwards, a GDIM-based decoupling index is developed to examine the decoupling states between PM2.5 emissions and economic growth and to identify the main factors leading to decoupling. The obtained results show that: (1) Innovation input scale and GDP are the main drivers for increases in PM2.5 emissions, while innovation input PM2.5 intensity, emission intensity, and emission coefficient are the main reasons for reductions in PM2.5 pollution. (2) China and its four subregions show general upward trends in the decoupling index, and their decoupling states turn from weak decoupling to strong decoupling. (3) Innovation input PM2.5 intensity, emission intensity, and emission coefficient contribute largely to the decoupling of PM2.5 emissions. Overall, this paper provides valuable information for mitigating haze pollution.


Introduction
Over recent decades, China has seen enormous economic growth, but also suffered from frequent and widespread haze pollution [1,2]. Fine particulate matter, i.e., PM 2.5 (≤ 2.5 µm in aerodynamic diameter), is the primary cause of haze episodes in China [3,4]. Despite being small in size, PM 2.5 has a strong capacity to absorb various toxic substances and may induce a variety of diseases [5][6][7]. In China, the estimated number of PM 2.5 -related deaths reached 1.1 million in 2015, increasing by 0.15 million compared with 1990 [8]. In addition to adverse effects on human health, PM 2.5 pollution also contributes significantly to visibility degradation, climate change, and economic loss [9][10][11]. As revealed in previous research, the PM 2.5 -related economic loss in China in 2016 reached USD 101 billion, which was nearly 1% of China's GDP [12]. Thus, PM 2.5 pollution has threatened sustainable development in China, and how to alleviate PM 2.5 pollution has become a vital and challenging task for the government.
Aiming to improve air quality, the Chinese government has formulated a range of policies since 2013, such as "The Air pollution prevention and control action plan" and "The Three-Year Action Plan for Winning the Battle Against Air Pollution" [13][14][15][16]. As a result of these tough policies, the annual average PM 2.5 concentration of 339 Chinese cities dropped to 30 µg/m 3 in 2021, a decrease of 58% (42 µg/m 3 ) compared with 2013. However, the overall air quality is still poor in China; in 2021, only 1% of 339 cities met the national Grade I air quality standard (15 µg/m 3 ). Particles released by the combustion of fossil fuels are the principal source of PM 2.5 pollution; however, fossil fuels are the dominant energy upon which the Chinese economy relies [17][18][19][20][21]. To achieve the Sustainable Development three innovation factors (i.e., innovation input scale, innovation input PM 2.5 intensity and innovation input efficiency) were introduced to the existing GDIM model. For the first time, the contributions of innovation factors to changes in PM 2.5 emissions are comprehensively examined. (2) To disclose the regional and temporal heterogeneity of the relationship of PM 2.5 emissions with economic growth or other factors, China was divided into four subregions and the whole period was divided into several subperiods.
The rest of the paper is arranged as follows: Section 2 describes the research methods and data sources used. Section 3 states and discusses the empirical results. Section 4 presents the conclusions and policy implications.

GDIM Method
Index decomposition analysis (IDA) is a mature decomposition analysis method that has been widely used to identify the effects of different drivers on changes in PM 2.5 emissions [8,28,42]. Among the specific IDA methods, the GDIM method proposed by Vaninsky [37] has the following advantages over other IDA methods. First, GDIM allows multiple absolute and relative indicators to be incorporated simultaneously into the target variable [38,48,49]. Second, GDIM can solve factor interdependence problems that occur in other IDA methods [39,50,51]. According to Vaninsky [37], the mapping relationship between the target variable Z and factor variables X can be expressed as: where ∆Z is the change in the target variable from the current time to the reference time, ∆Z(X i ) is the contribution of X i to Z, and L represents the time. f i is the partial derivative of f (X 1 , X 2 , · · · , X n ) with respect to X i . Given X i = X i (t), it follows that Equation (2) can be expressed in vector form: where ∇Z =< f 1 , · · · , f n > is a column gradient vector of f (X 1 , X 2 , · · · , X n ). As Vaninsky [37] points out, the decomposition above does not fully take interdependence into account. Therefore, Equation (5) is added to restrict the relationship between the decomposition factors.
Φ j (X 1 , X 2 , · · · , X n ) = 0, j = 1, · · · , k Equation (5) can be rewritten in vector form: As a result, the GDIM decomposition of the target variable Z is where Φ X is the Jacobian matrix of Φ(X), I is the unit matrix, and Φ + X is the generalized inverse of Φ X . If Φ X has full column rank, then Φ +

Decomposition of PM 2.5 Emission Factors
The generalized Divisia index method (GDIM) is an effective decomposition approach that links the changes in pollutant emissions with socio-economic factors through the deformation of Kaya identity [28,42,43]. In contrast to classical econometric models, the GDIM approach mainly decomposes PM 2.5 emissions based on time-series data into different influencing factors without residual terms. In this paper, the GDIM model is used to investigate the impacts of the following socio-economic drivers on PM 2.5 emissions. According to the basic principles of GDIM, PM 2.5 emissions can be decomposed into the following forms:  (8)- (10). Among these factors, G, E, PMG, PME, and EI have been frequently examined in previous relevant studies [8,28,52], but R, PMR, and RE have been somewhat overlooked in the existing index decomposition literature on PM 2.5 emissions. In the GDIM model, G, E, and R are absolute quantitative factors, while PMG, PME, PMR, EI, and RE are relative quantitative factors. Then, Equations (8)-(10) can be transformed into the following forms: Let the function PM(X) denote the response of indicator X to variations in PM 2.5 emissions; then, the gradient of PM(X) and the Jacobean matrix consisting of the relevant impact indicators can be constructed using Equations (11)-(15): The Jacobean matrix Φ X is composed of the partial derivative of function PM(X), which can reflect the marginal impacts of different drivers on PM 2.5 emissions.
Following the GDIM calculation method, the changes in PM 2.5 emissions are decomposed as follows: where L denotes the study period, I denotes a matrix with all diagonal elements being 1, and According to Equation (18), the variations in PM 2.5 emissions over different time spans can be decomposed into the sum of eight effects: ∆G, ∆E, ∆R, ∆PMG, ∆PME, ∆PMR, ∆EI, and ∆RE. A detailed description of the eight effects is given in Table 1. It can be found that the sum of the results of the additive decomposition of the eight factors over the same period is about the same as total variations in PM 2.5 emissions. Therefore, the degree of influence of each driver on PM 2.5 emissions can be calculated separately. At the same time, the primary drivers influencing the change in PM 2.5 emissions can be found.

Decoupling Model Based on GDIM
This paper uses the GDIM model to calculate the contribution of each driver to the changes in PM 2.5 emissions, but it does not provide a direct measure of the dependence of PM 2.5 emissions on economic growth. Therefore, the decoupling method is used to investigate the economic dependence of PM 2.5 emissions. Using the methods found in [22,[52][53][54][55][56], the decoupling effect between GDP and PM 2.5 is defined as: where, PM t (GDP t ) and PM t−1 (GDP t−1 ) represent the PM 2.5 emissions (GDP) during time t and t − 1, respectively. Based on Equation (18), ∆PM can be expressed as Excluding the impact of economic growth on the changes in PM 2.5 emissions, Equation (18) can be written as Finally, the decoupling index between PM 2.5 emissions and economic growth is defined as where DI is called the decoupling effort index. DI ≤ 0 denotes "no decoupling", 0 < DI < 1 refers to "weak decoupling", and DI ≥ 1 represents "strong decoupling". ∆F means the changes in PM 2.5 emissions due to the remaining drivers after the exclusion of GDP. DI E , DI R , DI PMG , DI PME , DI PMR , DI EI , and DI RE indicate the contributions of energy consumption scale, innovation input scale, emission intensity, emission coefficient, innovation input PM 2.5 intensity, energy intensity, and innovation input efficiency, respectively, to the decoupling of PM 2.5 emissions. The DI index has the following advantages: (1) Combining the strengths of the OECD and Tapio approaches, it measures the decoupling of socio-economic development and PM 2.5 emissions. (2) The effect of GDP on changes in PM 2.5 emissions is eliminated during the calculation of the DI index. (3) From Equation (22), the contributions of various factors (e.g., energy consumption scale) to the decoupling of PM 2.5 emissions can be obtained.

Data Sources
Due to the fact that PM 2.5 emission data are not easily obtained, 30 provincial-level regions in mainland China from 2008 to 2017 were selected as the study area for this paper (Tibet was excluded due to a lack of data). Socio-economic data, including GDP, energy consumption, and R&D expenditure, are taken from the China Statistical Yearbook  [55,[57][58][59].
To remove the effect of price volatility, GDP and R&D expenditure are expressed at 2008 constant prices. In particular, following the principles of classification in the literature [52], the whole of China is divided into four subregions, namely, Eastern, Central, Western and Northeastern China.

Year-by-Year Decomposition of PM 2.5 Emissions
In order to identify the main drivers influencing the variations in PM 2.5 emissions, the contributions of eight drivers (e.g., GDP (∆G), energy consumption scale (∆E), and innovation input scale (∆R), etc.) were calculated using the R software according to Equation (18). The year-by-year decomposition of PM 2.5 emissions in China and its four subregions are shown in Figure 1 (Table A1)    As shown in Figure 1 (Table A1), the contribution of innovation input scale (∆R) to PM 2.5 emissions is positive for the 2008-2017 period, and its annual average contribution is 506,105.6 Mg, which shows that innovation input scale (∆R) has resulted in a significant increase in PM 2.5 emissions [60]. This is due to the fact that during the 2008-2017 period, R&D expenditure may have been spent more on promoting technological advances in production than on green technologies, stimulating the expansion of production and leading to increases in PM 2.5 emissions [44]. Furthermore, GDP (∆G) plays a crucial role in increasing PM 2.5 emissions, and its annual average contribution is 337,518.7 Mg. In contrast, the energy consumption scale (∆E) is observed to play a minor role in promoting PM 2.5 emissions, and its annual average contribution is 134,278 Mg, except for 2012-2013. Figure 1 ( Table A1) shows that the major drivers for reductions in PM 2.5 emissions are innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG), and emission coefficient (∆PME). Innovation input PM 2.5 intensity (∆PMR) plays the most important role in reducing PM 2.5 emissions from 2008 to 2017. It is found that from 2008 to 2009, innovation input PM 2.5 intensity (∆PMR) has led to a significant reduction in PM 2.5 emissions equal to the amount of 1,069,357 Mg. Subsequently, the contribution of innovation input PM 2.5 intensity (∆PMR) presents a stable trend, with an average annual decrease of 638,940.9 Mg from 2009 to 2016. After 2016, the reduction in PM 2.5 emissions attributed to innovation input PM 2.5 intensity (∆PMR) decreases slightly. With increasing R&D expenditure, the technology innovations of enterprises have been improved, in turn increasing the efficiency of factor utilization and reducing PM 2.5 emissions [44,45]. In line with previous studies, emission intensity (∆PMG) also has a negative impact on PM 2.5 emissions [30,35,53]. Specifically, the reduced level of PM 2.5 emissions due to emission intensity (∆PMG) is 51,253,335 Mg per year on average, implying that reducing emission intensity (∆PMG) can effectively improve air quality. In addition, the emission coefficient (∆PME) is another significant driver of PM 2.5 emission reduction, in line with the findings in the literature [35]. It is observed that the emission coefficient (∆PME) reduced PM 2.5 emissions for this entire term by an average of 354,372.4 Mg a year, except for 2012-2013. This is because the government of China has undertaken a tremendous amount of work on energy transformation. For instance, the government implemented the Golden Sun Demonstration Project in 2009, increasing the applications of solar energy [61].
Overall, energy intensity (∆EI) has a relatively small effect on the reduction in PM 2.5 emissions. However, it led to a relatively large reduction in PM 2.5 emissions from 2012 to 2013, with a reduction of 32,855.3 Mg. The reason for this may be that, in 2011, the Chinese government established a national mandatory goal of reducing energy intensity (∆EI) by 16% by 2015 [62,63]. Similarly, innovation input efficiency (∆RE) makes a small contribution to the reduction in PM 2.5 emissions. These findings imply that there is still much room for improvement in energy intensity (∆EI) and innovation input efficiency (∆RE). Since the 12th Five-Year Plan, China's government has implemented a wide range of policies to curb pollution, for example, setting strict PM 2.5 emission reduction targets, optimizing energy structure, and promoting the clean utilization of coal [22], which helps to decrease PM 2.5 emissions [64]. In contrast, the influences of energy intensity (∆EI) and innovation input efficiency (∆RE) are relatively small. contribution to the reduction in PM2.5 emissions. These findings imply that there is still much room for improvement in energy intensity (ΔEI) and innovation input efficiency (ΔRE).

Comparison of Decomposition Results of the Changes in PM2.5 Emissions for China and Its Four Subregions over Different Time Periods
China's "Five-Year Plan" proposes medium targets for socio-economic development.     contribution to the reduction in PM2.5 emissions. These findings imply that there is still much room for improvement in energy intensity (ΔEI) and innovation input efficiency (ΔRE).

Comparison of Decomposition Results of the Changes in PM2.5 Emissions for China and Its Four Subregions over Different Time Periods
China's "Five-Year Plan" proposes medium targets for socio-economic development.      Considering the regional heterogeneity of factors impacting PM 2.5 emissions, this paper further breaks down the PM 2.5 emissions of the four subregions over three subperiods ( Figure 3). It can be observed that PM 2.5 emissions in the four subregions show similar changing trends. Specifically, since the 12th Five-Year Plan, PM 2.5 emissions in all four subregions have shown obvious downward trends, with similar decreasing rates. Furthermore, the main factors increasing or decreasing PM 2.5 pollution are also similar in the four subregions, although regional variations are found regarding the magnitude of each factor driving PM 2.5 emission changes.
As illustrated in Figure 3 (Table A3) [65], leading to a considerable number of energy-intensive enterprises shifting from eastern regions to western regions [66]. Innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG), and emission coefficient (∆PME) are the primary drivers of PM 2.5 pollution reduction for the four subregions, with innovation input PM 2.5 intensity (∆PMR) having the strongest inhibitory effect, followed by emission intensity (∆PMG) and emission coefficient (∆PME). In detail, PM 2.5 emission reductions due to innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG) and emission coefficient (∆PME) are significantly lower in Northeast China than in the other three economic regions throughout the period. This is because economic development in Northeast China relies heavily on heavy and energyintensive industries, and PM 2.5 pollution is more serious in this region [67]. Innovation input efficiency (∆RE) and energy intensity (∆EI) both have little influence on reducing PM 2.5 pollution in all subregions. During the 2010-2015 period, the highest PM 2.5 emission reductions caused by innovation input efficiency (∆RE) and energy intensity (∆EI) occur in Eastern China (2.8 Mg) and Central China (5.8 Mg), respectively.

emissions in Northeast
China over this period cannot curb the intensification of PM 2.5 pollution due to economic growth [22]. From 2011 to 2015, across China and its four subregions, the decoupling indexes gradually increase and the decoupling states change from weak decoupling to strong decoupling. This can be explained by the fact that during the 2011-2015 period, the Chinese government made a great effort to reduce emissions [22,64], mitigating PM 2.5 pollution effectively. From 2015 to 2016, all the decoupling indexes are greater than 1, indicating that China and its four subregions achieved strong decoupling. In particular, the decoupling index of Northeast China reaches the peak (5.47) during this period, which means that PM 2.5 emissions were increasing at a much slower rate than economic growth. From 2016 to 2017, although the decoupling indexes show downward trends again, China and its four subregions still present strong decoupling.
China over this period cannot curb the intensification of PM2.5 pollution due to economic growth [22]. From 2011 to 2015, across China and its four subregions, the decoupling indexes gradually increase and the decoupling states change from weak decoupling to strong decoupling. This can be explained by the fact that during the 2011-2015 period, the Chinese government made a great effort to reduce emissions [22,64], mitigating PM2.5 pollution effectively. From 2015 to 2016, all the decoupling indexes are greater than 1, indicating that China and its four subregions achieved strong decoupling. In particular, the decoupling index of Northeast China reaches the peak (5.47) during this period, which means that PM2.5 emissions were increasing at a much slower rate than economic growth. From 2016 to 2017, although the decoupling indexes show downward trends again, China and its four subregions still present strong decoupling.

The role of Different Drivers in Decoupling
Decoupling emphasizes the stable and sustained separation of economic development and air pollution in the relatively long term, but not the short term. For the purpose of identifying the key drivers influencing the decoupling of PM 2.5 emissions, this paper develops a decoupling effort model based on the GDIM method. Using Equation (22), the contribution of each factor to the decoupling index is calculated. Detailed results can be found in Tables 2 and 3.  Note: DI PMG , DI R , DI PMR , DI RE , DI E , DI PME and DI EI indicate the contributions of emission intensity, innovation input scale, innovation input PM 2.5 intensity, innovation input efficiency, energy consumption scale, emission coefficient, and energy intensity to the decoupling of the PM 2.5 emissions, respectively. DI denotes the decoupling index between PM 2.5 emissions and economic growth.
As presented in Table 2, from 2008 to 2017, the contributions of innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG) and emission coefficient (∆PME) are positive and large, implying their prominent roles in promoting the decoupling process. Meanwhile, a remarkable increase can be observed in the decoupling index across China for the 2008-2017 period, from 0.47 (2008-2010) to 1.39 (2015-2017). This may be related to the increasing contributions of the aforementioned three factors to decoupling index. During the 2015-2017 period, the contribution values of innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG), and emission coefficient (∆PME) reached 0.64, 0.72, and 0.47, respectively, which are much higher rates than in the previous periods. In contrast, the innovation input scale (∆R) and energy consumption scale (∆E) have adverse impacts on decoupling for the whole period. During the past few years, R&D funds may have been used primarily to improve production technology [44], stimulating the expansion of production scale and thereby hindering the decoupling process in China [22]. Table 3 illustrates the roles of multiple drivers for the decoupling of PM 2.5 emissions from economic growth in different regions over the 2008-2017 period. The four subregions present similar decoupling processes, transforming from weak decoupling to strong decoupling. It is obvious that innovation input PM 2.5 intensity (∆PMR) is the leading factor affecting the decoupling states of the four subregions in the three subperiods, except for in Northeast China from 2010 to 2015. In addition, emission intensity (∆PMG) and the emission coefficient (∆PME) are also dominant drivers for the decoupling of PM 2.5 emissions in different regions over this period. Accordingly, more efforts should be focused on technological innovation, adjusting industrial structure, and promoting clean energy.

Conclusions
The present study investigates the main drivers of PM 2.5 emissions in China and its four subregions from 2008 to 2017. Then, the decoupling states between PM 2.5 emissions and economic growth are examined and compared for China and its four subregions. Finally, the contributions of different factors to the decoupling index are quantified.
(1) Innovation input scale (∆R) and GDP (∆G) are the main factors for the increase in PM 2.5 emissions. In contrast, innovation input PM 2.5 intensity (∆PMR) contributes most for the reduction in PM 2.5 emissions, followed by emission intensity (∆PMG) and emission coefficient (∆PME). (2) In the four subregions, PM 2.5 emissions show similar changing trends, with obvious downward trends with similar rates since the implementation of 12th Five-Year Plan. In addition, the major factors increasing or mitigating PM 2.5 pollution are also similar in the four subregions, though the magnitudes of increases or decreases shows regional variations. (3) From 2008 to 2017, the decoupling indexes for China and its four subregions first decrease, then rise, and finally decrease again, showing overall upward trends, and the decoupling states turn from weak decoupling to strong decoupling. (4) During the whole period, the contributions of innovation input PM 2.5 intensity (∆PMR), emission intensity (∆PMG) and emission coefficient (∆PME) to the decoupling are positive and large, implying their prominent roles in promoting the decoupling process. (5) This paper has a few limitations. Firstly, due to the limitation in data availability, the effects of different types of technological innovation (e.g., production technology innovation and abatement technology innovation) on PM 2.5 emissions are not examined precisely. To obtain more accurate results, the total R&D funds should be divided into funds for production technology and abatement technology when data is available. Secondly, factors that are not easily measured, e.g., environmental regulation, are not incorporated into the GDIM model. Considering that a variety of policies and strategies have been implemented for controlling air pollution in China, quantifying the impacts of these policies and strategies on PM 2.5 emissions is our next concern. Lastly, the study only concentrates on China and its four subregions, without special consideration for heavily polluted areas, e.g., the Fenwei Plain. The investigation of heavily polluted areas should be considered in future work.

Policy Implication
Based on the above empirical results, several policy implications can be drawn as follows: (1) The results revealed in this study suggest that the innovation input PM 2.5 intensity (∆PMR) can mitigate PM 2.5 emissions and promote the decoupling of PM 2.5 emissions and economic growth. Therefore, the government should provide sufficient financial and tax support, such as raising R&D expenditure on energy saving and emission reduction and encouraging enterprises to increase R&D investment in green technology innovation, so as to reduce PM 2.5 emissions. (2) As emission intensity (∆PMG) plays a significant role in reducing PM 2.5 emissions, it is necessary to reduce the use of traditional energy by adjusting and optimizing the industrial structure. On one hand, the government should develop high-technology industries which have low energy consumption and vigorous high-value addition. On the other hand, energy-intensive industries with high air pollutant emission intensity and backward technology should be gradually eliminated.
(3) More attention should be paid to improvements in energy structure. This is because the emission coefficient (∆PME) has a significant impact on reducing PM 2.5 pollution. Thus, promoting the utilization of cleaner and renewable energies (e.g., wind and solar energy) is an effective way to mitigate PM 2.5 pollution. Data Availability Statement: The data are not publicly available due to privacy restrictions.

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