Renewable Energy Green Innovation, Fossil Energy Consumption and Air Pollution--- Spatial Empirical analysis based on China

： The rapid development of China's economy has led to a rapid increase in energy production and use. Among them, the excessive consumption of coal in fossil energy consumption is the leading cause of air pollution in China. This paper incorporates renewable energy innovation, fossil energy consumption and air pollution into a unified analysis framework, and uses spatial measurement models to investigate the spatial effects of renewable energy green innovation and fossil energy consumption on air pollution in China, and decomposes the total impact into direct and indirect effects. influences. The empirical results show that China's air pollution, renewable energy green innovation and fossil energy consumption are extremely uneven in geographical space, generally showing the characteristics of high in the east and low in the west, and showing a strong spatial aggregation phenomenon. Fossil energy consumption will lead to increased air pollution, and the replacement of fossil fuels with clean and renewable energy is an important means of controlling pollution emissions. The direct and indirect effects of renewable energy green innovation on air pollution are significantly negative, indicating that renewable energy green innovation not only suppresses local air pollution, but also suppresses air pollution in neighboring areas. The consumption of fossil energy will significantly increase the local air pollution, and the impact on the SO2 and Dust&Smoke pollution in the adjacent area is not very obvious. It is recommended to strengthen investment in renewable energy green innovation, reduce the proportion of traditional fossil energy consumption, and pay attention to the spatial connection and spillover of renewable energy green innovation.


Literature review
In recent years, with the rapid increase of energy consumption in China, the problem of air pollution caused by energy consumption has also intensified, which has led many scholars to pay attention to the problem of air pollution. Brunt, H et al (2016) found that air pollution, poverty and health issues are inseparable. If the local air pollution problems and solutions are considered in the context of broader health determinants, greater health benefits can be achieved (Reduce health risks and inequality) [10]。Dong K. et al (2019) found that respirable suspended particles (PM10) are a typical component of particulate matter, which can lead to increased morbidity and mortality of respiratory and cardiovascular diseases [11]. The findings of Signoretta et al(2019)show that the perception of major air pollution problems and worse mental wellbeing go hand in hand only in partial and established environmental States [12]. Gu Population Dynamics Survey with urban feature data and pollution data, and found that an increase in air pollution concentration significantly reduced residents' health. Men and urban residents are more sensitive to air pollution and are more adversely affected [13].
In these studies, scholars have paid more attention to the direct factors of air pollution.
Wang, X.-C. et al (2019) found that energy production and consumption caused air pollution, with 75% of global greenhouse gas emissions, 66 % Of NOx emissions and most PM emissions come from the energy sector [14]. Yuan, J. et al (2017) found that due to the largescale utilization of high-carbon carbide energy, a large amount of critical air pollutants (CAPs) and greenhouse gases (GHG) were emitted, resulting in increasing global climate change and local air pollution problems [15]. Zhang, S. et al (2015) found that the cement industry is China's second largest energy-consuming industry and a major emitter of carbon dioxide and air pollutants. The cement industry accounts for 7% of China's total energy consumption and 15% of CO %, 21% of PM, 4% of SO, 10% of NOx [16].
However, few scholars are currently concerned about the indirect factors of air pollution, especially the impact of renewable energy on air pollution. Boudri, J. et al (2002) studied the potential of using renewable energy in China and India and their cost-effectiveness in reducing air pollution in Asia, and found that increasing the use of renewable energy can reduce sulfur dioxide by 17-35% in China Emissions control costs can be reduced by more than two thirds in India [17].  found that technological innovations in renewable energy are conducive to reducing the concentration of nitrogen oxides (NOx) and respirable suspended particles (PM10) [18]. Xie, Y. et al (2018) concluded from scenario analysis that renewable energy has been more effective than taxis in reducing carbon dioxide and air pollutant emissions [19].The results of Alvarez et al (2017) confirmed the positive impact of the energy innovation process on air pollution, and pointed out that renewable energy contributes to improving air quality [20].
Although the above studies occasionally involve the temporal and spatial distribution of pollution, few studies have studied the spatial correlation and spatial spillover effects of air pollution, green innovation in renewable energy, and fossil energy consumption. Space models are rarely used to study the impact of renewable energy green innovation and fossil energy consumption on air pollution. Only a limited number of studies have involved this aspect. For example, Xie Q et al (2019) found that PM2.5 pollutants have strong spatial overflow characteristics [21].  discussed the temporal trends and spatial differences of air pollution in five hot spots in china, as well as the impact of macroinfluencing factors on four pollutants, and found that particulate matter exceeded standard in national-wide [22]. Zeng, et al (2019) found that provincial-level renewable energy policies have a positive impact on the reduction of SO2 and PM2.5. A province's energy policy will affect pollutant emissions from neighboring provinces [23].  found that atmospheric pollution emissions have a significant agglomeration effect. The spatial aggregation pattern of atmospheric pollution emissions is similar to that of fossil energy consumption. The proportion of clean energy consumption and the allocation of energy labor factors have suppressed atmospheric pollution emissions [24].
In recent years, renewable energy technologies represented by solar power generation and photovoltaic power generation have been applied on a large scale. Does renewable energy green innovation really improve air pollution? To what extent has air pollution been improved? What is the relationship between renewable energy green innovation, fossil energy consumption, and air pollution? Very few scholars have done research. Based on the previous research results, this article finds that there is room for the following: the traditional non-spatial econometric model needs to be expanded into a spatial econometric model for research. Spatial aggregation and spatial correlation effects of renewable energy green innovation, fossil energy consumption, and air pollution, and the effects of the former two on the latter. Therefore, the contribution of this study will be in the following aspects: First, the use of non-spatial and spatial measurement models to study the impact of renewable energy green innovation and fossil energy consumption on air pollution. Second, fully consider renewable energy green innovation, the spatial correlation of fossil energy consumption and space spillover effects, and quantify their impact on air pollution. Third, use visual methods to show the characteristics of the spatiotemporal evolution of renewable energy green innovation, fossil energy consumption, and air pollution. Fourth, expand the STIRPAT model to quantitatively study the impact of renewable energy green innovation, fossil energy consumption, environmental regulations, industrial structure, population, GDP and other factors on air pollution. (1)Air pollution: The most representative of air pollution is the amount of air pollutants. In previous studies, the concentration of PM2.5 was generally used as a proxy variable to measure the degree of air pollution, but PM2.5 cannot be used for a comprehensive evaluation on air pollution. Therefore, the main pollutant indicators for measuring air pollution in this paper are SO2, NOX, Dust&Smoke. And considering that each pollutant has its own limitations, this article specifically reduces the dimensions of these indicators to find a comprehensive pollution amount, so as to make the objective and comprehensive evaluation of air pollution to the greatest extent possible.。 This paper draws on the method of Liu et al (2015) for index dimensionality reduction.
First, the factor analysis method is used to uniformly reduce the three environmental output indicators. After the barlett sphere test, the statistic value is 56.077, the significance probability is 0.000, and the KMO value is 0.748. Therefore, the original hypothesis of irrelevance between indicators is rejected, and the indicator is suitable for factor analysis. At the same time, the corresponding weight of each indicator is calculated by the variance contribution rate of the factor score matrix and the common factor. The weights of the indicators for sulfur dioxide, nitrogen oxides, and smoke (dust) are 24%, 49%, and 27%, respectively. Combined with the weights of the three types of pollution indicators, comprehensive pollution can be calculated [25].The formula is as follows: Among them： is the weight of each pollutant， is the pollutant component. Hypothesis1-2 Renewable energy green innovation will reduce SO2 emissions.
Hypothesis1-3 Renewable energy green innovation will reduce NOx emissions.
(2)Fossil Energy Consumption (FEC): China's rapid development has led to a large amount of energy consumption, especially a significant increase in the consumption of fossil fuels. The main cause of pollution is the consumption of fossil fuels, while coal consumption accounts for more than 50% of China's fossil energy consumption [28],Therefore, coal consumption and pollutant emissions are closely related, so this paper selects coal consumption to represent fossil energy consumption.

Control variable
(1)Environmental regulation(ER)，There are many ways to measure the intensity of environmental regulation. Considering China's environmental pollution control policy, this article refers to the practice of Zhu Y et al (2019), and selects the number of environmental punishment cases as a proxy variable for the intensity of environmental regulation [29]. To a certain extent, environmental regulations will suppress pollutant emissions from micro-main bodies.
(2)Industrial Structure (IS): The proportion of the secondary industry is selected as the proxy variable. Hao et al (2016) empirical research shows that the correlation coefficient of the secondary industry's discharge of pollutants is positive [30].Therefore, this article assumes that there is a positive correlation between industrial structure and air pollution.
(3)GDP: Because there is a gap between the nominal GDP and the actual GDP of each province and municipality, this article uses the GDP of each province and municipality as the benchmark in 2000 to calculate the GDP deflator of each province and municipality, thus calculating the constant price GDP of each province and municipality .
(4)Population (POP). There is a direct link between population size and pollutant emissions. The increase in population will significantly increase energy consumption and pollutant emissions.

global correlation index
Here, the global spatial correlation is calculated according to the global Moran index： Among them： 、 denote spatial regional units i and j, respectively, and i≠j.
represents the spatial weight matrix； ̅ represents the average of provinces and municipalities. 2 means variance；( − ̅ )( − ̅ ) means the similarity of spatial units i and j; n means quantity.

local correlation index
However, the global correlation index cannot measure the local correlation, so the local Moran index needs to be quoted： (2) Whether it is global spatial autocorrelation and local spatial autocorrelation, the establishment of spatial weight matrix is very important. In this paper, the spatial adjacency weight matrix is selected.
The spatial adjacency weight matrix is a spatial weight matrix that reflects the spatial adjacency relationship. It can be set as that there is a significant mutual influence relationship between the areas that are adjacent to each other, and the interaction between the areas that are not adjacent is not significant. The spatial adjacency weight matrix can reflect the spatial role relationship of the development indicators between provinces and municipalities.
Therefore, the spatial adjacency weight matrix of provinces and municipalities is introduced to make the spatial relationship of development indicators concrete.

spatial econometric model
Based on the above regression model, we set a general provincial pollutant emission regression model： The IPAT model is used to explore the complex social dynamics mechanisms generated by environmental problems. The original IPAT model was proposed by the famous American Where a is a constant term, b, c, and d are exponential terms of P, A, and T, respectively, and e is an error term.
Take the logarithm of the left and right sides of the equation： Applied to this article, you can get the following formula： However, the general regression model does not take into account the spatial influence between variables. The spatial economic model incorporates the spatial influence on the basis of the ordinary regression model [35].The spatial lag model (SLM) can be expressed as： y = ρWy + Xβ + ε (6) Where y is the vector of the dependent variable; X represents a matrix of explanatory variables; W is the spatial weight matrix; Wy is the vector of the spatial lag dependent variable; ρ is the spatial regression coefficient, reflecting the spatial correlation of the dependent variable; β is a parameter vector, reflecting the influence of explanatory variables on the dependent variable; ε is a vector of disturbance terms.
By distinguishing the spatial correlation error ε and the spatial independent error μ, the spatial error model (SEM) can be expressed as [36]: Where is the spatial autocorrelation coefficient on the error term, which reflects the influence of the residual in the nearby area on the residual; μ is the interference term of a vector. The values of other variables and parameters are the same as the SLM formula. In Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 9 July 2020 doi:10.20944/preprints202007.0167.v1 addition, in order to estimate the spatial spillover effect of pollutants in provinces and municipalities, this study examines the direct and indirect effects of explanatory variables.
Due to the mutual influence of air pollution, innovation factors and energy factors between regions. Therefore, when measuring their impact from a spatial perspective, the spatial measurement model is generally used. In order not to lose the generality, this article uses the spatial dubin model (SDM), which is the spatial lag model (SLM) and the spatial error model (The general form of SEM), the expression is.： Among them， is the explanatory variable， is the explanatory variable， is the constant term， is the spatial autoregressive coefficient， and are the coefficients to be estimated， is the residual term. is the influence of regional independent variable on dependent variable， ∑ =1 is a space lag item, represents the dependent variable composed of the observation values of the explanatory variables of each spatial unit( i = 1,… ，n) at time t( t = 1,…,T). is an independent and identically distributed random error term; and represent the spatial and temporal effects, respectively. This paper constructs a spatial variable W·dependent variable to characterize the spatial spillover effects of pollutant emissions, renewable energy green innovation, and fossil energy consumption. W is expressed as a spatial weight, which is used to calculate the degree of correlation and mutual influence between various spatial elements.

Direct and indirect spatial influence
In the spatial econometric model, the independent variables usually have an indirect effect on the dependent variables in the surrounding non-local areas (spatial spillovers). We estimated the direct, indirect, and total spatial effects based on the estimated spatial regression coefficients [37] [38].Further quantify the spatial spillover effects of renewable energy green innovation, energy consumption and other socio-economic indicators on air pollution. Determine the direct and indirect spatial effects according to the determined spatial correlation coefficient ρ, as shown in the formula below： Where X represents the explanatory variable， represents the constant vector, αis the parameter of the intercept term. In the above formula (10), the average value of the sum of the values of the matrix elements on the right is defined as the direct effect, and the average value of the sum of all the row and column elements of the non-diagonal elements is the indirect effect, reflecting the influence of other regional independent variables on the regional dependent variable.

Spatio-temporal distribution characteristics of pollutant emissions, RETI, fossil energy consumption
In order to visualize the spatial and temporal distribution characteristics, we used Arcgis

Global spatial correlation analysis
As shown in Table 3, it is the global Moran index of pollutant emissions, renewable energy green innovation, and fossil energy consumption in 26 provinces and 4 municipalities in China. It can be seen from them that they all have a very significant spatial correlation.
However, with the evolution of time, the spatial correlation of environmental pollution has gradually weakened, and its significance has also decreased. It may be that the pollution control measures of the provincial government are working. On the one hand, the discharge of pollutants is reduced, and on the other hand, the spatial diffusion of pollutants between provinces is controlled. However, the overall correlation and significance of renewable energy green innovation and fossil energy consumption among provinces are still very high. Notes: z-statistics in parenthesis. *, **, and *** indicate that p values is less than 0.1, 0.05, and 0.01 levels, respectively.  Undertaken. The motivation and opportunity for the private sector to fully participate in retechnology innovation seem insufficient [40]. In general, it shows the characteristics of high in the east and low in the west, and shows a strong spatial aggregation phenomenon. Therefore, spatial factors cannot be ignored in analyzing the role of renewable energy green innovation and fossil energy consumption in air pollution in China. Next, we will use spatial measurement models to analyze.

Analysis of non-spatial panel model results
First, in order to compare with the spatial panel model, we first use the non-spatial panel model to analyze, the results are shown in Table 4. Renewable energy green innovation, environmental regulation and comprehensive air pollution, NOx, SO2, Dust&Smoke show a significant negative correlation, which is significant at the 1% level, thus confirming Hypothesis1-1,1-2,1-3,1-4 This is consistent with the findings of Alvarez et al [43].  [44].But do they still exist spatially? We need to further verify through the spatial Dubin model.

Spatial Dubin model
We construct a spatial Dubin model and use the spatial adjacency matrix for regression.
The results are shown in Table 5, where the Wald and LR test results are both significant at the 1% level, indicating that the spatial Durbin model cannot be replaced by SEM and SLM.
Judging from the results of the SDM model, there is a negative correlation between renewable energy green innovation and emissions of comprehensive pollutants, NOx, and SO2, which supports Hypothesis 1-1, 1-2, 1-3. The fossil energy consumption is negatively correlated with the emissions of comprehensive pollutants, NOx, SO2, Dust&Smoke, especially the negative correlation between SO2 and Dust&Smoke emissions at 1% level, which confirms our Hypothesis1-1, 1-2 , 1-3, 1-4. The coefficients of lnGDP and (lnGDP)2 under different air pollutants are positive and negative, respectively, but they do not pass the significance level test, so they do not support EKC hypothesis. Under 4 explanatory variables (composite pollution, NOx, SO2, dust&smoke), the coefficients of ρ are 0.6408 (t=0.0564, p=0.000), 0.5248 (t=0.0680, p=0.000), 0.6043 (t=0.0592, p =0.000), 0.6320 (t=0.0543, p=0.000), which shows that there is a significant provincial space spillover effect of air pollution in China. In addition, we use partial differential methods to study the direct, indirect and total impact of renewable energy green innovation and fossil energy consumption on air pollution in China (see table   6). .62*** Note: Standard errors in parentheses."* p<0.10 ** p<0.05 *** p<0.001"cppg,so2pg, noxpg,dspg are emissions unit currency

Direct action, indirect action and total action
Space spillover effects include direct and indirect effects. Table 6  However, this effect is spatially heterogeneous. The impact of population size on air pollution in the eastern region is much smaller than that in the central and western regions [49].Environmental regulations have a negative impact on the emission of pollutants in various provinces, especially the control effects of NOx and SO2 are more significant.

Conclusion and policy implication
The air pollution problem in China is complex and comprehensive, and involves many factors. The distribution of air pollution is spatially related, and air pollution also has a strong spatial spillover effect. Renewable energy green innovation and fossil energy consumption have a profound impact on air pollution in space. The discussion mainly reached the following conclusions:  Based on the above analysis, the following suggestions are made to mitigate air pollution： (1)According to the spatial overflow characteristics of pollutant discharge, it is recommended to establish a mechanism for regional cooperative governance, especially in areas with high pollution concentration. Neighboring provinces should work together to control pollution, and establish environmental governance exchanges and cooperation between regions. When formulating environmental policies, strengthen coordination and communication between regions, and fully consider the environmental impact of air pollution in one province on surrounding provinces.
(2)It is recommended to strengthen the space diffusion of renewable energy green innovation, to allow scientific and technological innovation factors to fully flow, so that renewable energy green innovation in one province can fully serve the surrounding provinces. The government should encourage the flow of regional innovation factors to allow the full flow of technological innovation, and the state should build a platform for provinces with backward innovation to easily introduce advanced energy technologies. Renewable energy green innovation is widely used, will make renewable energy technology more applied, thereby increasing the proportion of renewable energy consumption, to achieve the purpose of effectively reducing air pollutant emissions. Increase investment in research and development of renewable energy technologies, the development of renewable energy green innovation in one province will reduce pollutant emissions from neighboring provinces.