Whether green technology innovation is conducive to haze emission reduction: empirical evidence from China

With the acceleration of industrialization, haze pollution has become a severe environmental pollution problem, and green technology innovation is one feasible way to alleviate it. Based on the PM2.5 concentration data of 30 provinces in mainland China from 2011 to 2017, we use a spatial panel model to investigate the spatial characteristics of haze pollution and examine the impact of green technology innovation on it. Results show that haze pollution has spatial correlation and a time lag. Its spatial correlation is associated with geographical distance as well as the compound influence of distance and economic development. Green technology innovation and foreign investment have inhibitory and negative spillover effects on haze pollution. Industrial structure and energy consumption structure play a partial intermediary role between green technology innovation and haze pollution, and the former has a significant negative spillover, while the latter has a positive effect. To reduce haze pollution, China should improve the level of green technology innovation, use foreign investment wisely, and enhance policy support and guidance. It should also promote the rationalization of industrial structure, optimize energy structure, and implement energy substitution. Finally, it is crucial that it should strengthen regional collaborative governance and build a multi-agent governance system.


Introduction
Due to the acceleration of China's industrialization and urbanization, environmental pollution has gradually become an important issue related to national development and people's life, especially haze pollution (Leeuwen and Mohen 2013). Haze pollution mainly consists of PM 2.5 , PM 10 , and other particles. Among them, PM 2.5 , which is more subtle, can enter the human lungs and cause more harm to the human body. Therefore, the research on haze pollution mainly focuses on PM 2.5 . Before 2007, the concentration of PM 2.5 emission in China increased rapidly, and since then it has basically stabilized in the range of 36-45μg/m 3 , but with large annual fluctuations ( Fig. 1). Unlike developed countries, the intensity and scope of environmental management in China is still relatively small, making haze pollution present the characteristics of Responsible Editor: Roula Inglesi-Lotz wide range, high frequency, heavy pollution, and serious harm. To some extent, the high level of pollutant emission caused by China's rapid economic development is the fundamental reason for the high incidence of haze (Xie et al. 2017), and the unreasonable economic development modes, such as unbalanced industrial structure, unreasonable energy structure, insufficient technological investment, and inefficient environmental governance, are also important reasons. Solving haze pollution and winning the battle against air pollution is one of the main tasks of China's economic and social development at this stage (Song et al. 2019).
Green technology innovation taking the realization of green development as the core pursuit and focusing on providing new products, processes, services and market solutions through innovations, reducing natural resource consumption, reducing ecological environmental damage, and improving resource allocation efficiency. It could provide power for China to achieve high-quality economic development. Based on the rapid development of green technology innovation and the above environmentally friendly characteristics of green technology innovation, combined with the affirmation of the existing research results on the haze reduction effect of green technology innovation, we focus on the study of green technology innovation on haze reduction to explore whether China's green technology innovation can indeed alleviate haze pollution? The research will enrich China's haze control methods and provide the necessary decision-making basis for the formulation of haze control policies. Fig. 2 shows the distribution of PM 2.5 and green technology innovation levels by province in mainland China in 2017, from which it can be seen that haze pollution in China is mainly concentrated in eight regions-Hebei, Tianjin, Shandong, Henan, Anhui, Jiangsu, Shanghai, and Xinjiang. And southwest China is less polluted. The regions with higher levels of green technology innovation are Beijing, Jiangsu, Zhejiang, and Guangdong. Therefore, the relationship between green technology innovation and haze pollution is not obvious intuitively, and a spatial econometric model needs to be constructed to investigate this issue.
The main contributions of this paper are as follows: First, based on three commonly used spatial measurement models, the spatial correlation effect of haze pollution at the provincial level in China is studied. Second, the haze abatement effect of green technology innovation in China is analyzed based on the weight matrix of geographical distance, economic weight matrix, and nested weight matrix of geographical and economic distance. Third, the green technology innovation of each province is measured by the number of green patent applications, and PM 2.5 refers to haze pollution, which is innovative.

Literature review
Haze is the result of the interaction between specific climatic conditions and human activities. With the increasing pollution of the atmosphere caused by human activities, haze pollution has become a key issue of social concern. In 1995-1999, the international scientific cooperation project "INDOEX" conducted a comprehensive study on atmospheric brown cloud (ABC) and its impact on climate for the first time. It was found that the haze layer over the Indian Ocean, South Asia, Southeast Asia, and East Asia has a high content of soot, which mainly comes from the combustion of fossil fuels and biofuels. Based on this experiment, in August 2002, the United Nations Environment Program officially launched the international ABC research project (Ramanathan et al. 2001). The research results of Chun-Chung and Vernon (2006) show that haze pollution will affect China's economic development by influencing the process of urbanization. Chen and Chen (2018) further found that haze pollution greatly reduces the quality of China's economic development and  (except Tibet) has a particularly significant impact on large cities. Guan et al. (2014) studied the drivers of haze pollution in China by using structural analysis method, and found that capital formation and export production are important causes of haze pollution. It has also been empirically verified that haze pollution has significant spatial characteristics (Ma and Zhang 2014). Based on the spatial Durbin model, Ma et al. (2016) found that China's coal-based energy consumption structure is an important factor that affects haze pollution.
Green technological innovation is also called ecological technological innovation. It is a technological innovation that promotes the coordinated development of man, natur, and society for the purpose of saving resources and energy and protecting the environment. In 1994, Braun and Wield first proposed the concept of "green technology innovation" (Braun and Wield 1994). And then the concept was introduced to China. Chinese scholars Chen and Wang (1998) first investigated the incentive mechanism of green technology innovation. The "Green Economy Initiative" of the United Nations Environment Program in 2008 and the Copenhagen Conference in 2009 and other related events have made green technology innovation a topic of global concern, and the relevant literature has also been enriched. Although China's green technology innovation has made great progress in recent years, it is still in a stage of insufficient development, and it is far from completely relying on green technology to develop production (Wang et al. 2019); Luo and Liang (2016) calculated the technological innovation efficiency of China's industrial enterprises through principal component analysis and found that there is a significant regional gap between the eastern, central, and western regions, and the gap is still widening.
There are direct and indirect relationships between green technological innovation and haze pollution. Existing studies by domestic and foreign scholars have directly discussed the effects of technological innovation on haze emission reduction and have also studied technological innovation on carbon emissions and energy efficiency. The intermediary factors of the indirect impact of pollution are used to explore the emission reduction effect of green technological innovation.
In the research on the direct relationship between green technological innovation and haze pollution, Liu (2018a) used the nuclear density method to analyze the dynamic evolution and spatial spillover effects of China's technological innovation and haze pollution. The results showed that technological innovation can not only reduce the province's haze pollution but can also indirectly lead to a decrease in the degree of haze pollution in neighboring provinces through knowledge spillover effects. Liu (2018b) used the spatial Dubin model to analyze the impact of technological innovation on China's PM 2.5 . The empirical results showed that technological innovation could significantly reduce PM 2.5 emissions in the region, neighboring regions, and the world. Yi et al. (2020) considered the heterogeneity of technological progress and analyzed the impact of different technological advances on haze pollution and found that due to the cost reduction effect and income effect, neutral technological progress and technological progress that reduce labor input are beneficial to the haze. However, technological progress that reduces resource input has no significant impact on haze pollution. In addition, due to the energy rebound effect, energy-saving technological progress cannot effectively reduce haze pollution.
In exploring the indirect impact of green technological innovation on haze pollution, scholars often conduct research on the influence of green technological innovation on intermediary factors such as carbon emissions or energy efficiency. Regarding carbon emissions, Honjo (1996) came to the conclusion that green technology innovation reduced carbon emissions through research. Apergis et al. (2013) believed that through green technology innovation, enterprises obtained gr een technology and produced green products to reduce carbon emissions. Carbon emissions in the production process, thereby reducing environmental pollution. Du  (2019) found that in economies with income levels above the critical value, green technology innovation has a significant effect on carbon emissions reduction. Regarding energy efficiency, Garbaccfio et al. (1999) studied the reasons for the sharp decline in China's energy output ratio from 1978 to 1995 and decomposed the reduction in energy consumption into technological changes and various types of structural changes, and found that technological changes were the main reason. The structural changes have increased energy use. Fisher Vanden et al. (2006) also studied the reasons for the increase in energy productivity in China's industrial sector and came to a conclusion similar to Garbaccfio that technological progress and industrial structure optimization are both important factors. Wurlod and Noailly (2018) studied green technology innovation in the industrial sector of OECD countries. Results showed that green patent activities in a specific sector increased by 1% and energy intensity decreased by 0.03%, and the phenomenon has become more pronounced in recent years. Therefore, existing studies proved that green technological innovation could improve energy efficiency and effectively reduce carbon emissions in production activities. Carbon emission itself has little effect on haze pollution, but its by-products, such as the production of particulate matter in combustion, will aggravate haze pollution. In addition, low energy use efficiency is the root cause of air pollution. It may be possible to improve energy efficiency through technological innovation which effectively improves haze pollution, which also shows to a certain extent that green technological innovation has the effect of mitigating and inhibiting environmental pollution.
To sum up, most of the existing literature on green technology innovation and haze pollution researches focus on the indirect impact of green technology innovation on haze pollution, and the research literature in this area is relatively abundant. There are relatively few documents that specifically explore the direct relationship between green technological innovation and haze pollution or model the two together to study the haze reduction effect of green technological innovation. Based on the above practical reasons and research background, we take the main "culprit" of haze pollution-PM 2.5 and the core indicator of green technology innovation research-the number of green patent applications (Brunnermeier and Cohen 2003) as the research object. A spatial panel data model is used to empirically test the haze reduction effects of China's inter-provincial green technology innovations to find out the specific effects of green technology innovations on haze pollution, and to find other ways to reduce haze pollution and effectively prevent haze pollution. The research perspective of this paper is relatively innovative, which enriches the empirical research in this field to a certain extent and provides corresponding theoretical reference for China's haze reduction.

Influence mechanism
The effect of green technological innovation on the prevention and treatment of environmental pollution is self-evident. From the perspective of product life cycle analysis, green technology innovation follows ecological principles and ecological economic laws, and integrates environmental principles at each stage of the innovation process, which not only pays attention to the production cost of the product, but also pays attention to the social and ecological costs of the product to realize the product .The goal is to minimize the total cost of the entire life cycle, which has the characteristics of saving resources and energy and conforming to sustainable development.
The impact of green technological innovation on haze pollution mainly comes from two aspects (Fig. 3). On the one hand, green technological innovation has a "prevention effect" on haze pollution, which can reduce haze pollution and improve environmental quality. First, green technology innovation improves production methods, optimizes corporate production structure, and develops cleaner production technologies to solve the problem of haze pollution at the source and reduce the difficulty of back-end governance. Second, green technology innovation improves energy utilization in the production process to reduce the use of high-polluting energy so as to improve enterprise production efficiency and reduce enterprise pollution emissions (Cai and Li 2018). The above two methods could reduce the main pollutants that form haze from the source emissions, such as PM 2.5 . Third, through green technological innovation, it improves the efficiency of the treatment of pollution that has already occurred, alleviates the degree of haze pollution, and achieves the goal of treating haze pollution.
On the other hand, technological innovation may also hinder the treatment of haze pollution to a certain extent. Research by Sun et al. (2012) found that technological progress has increased haze pollution since the 1990s. Li and Zhou (2006) believed that the phenomenon was caused by the "rebound effect" of energy caused by technological progress, that is, on the basis of constant energy prices, green technological innovation has reduced energy consumption per unit of output. However, it will stimulate enterprises to increase the use of energy, resulting in an increase in the final consumption of energy, leading to an increase in pollutant emissions and aggravating haze pollution. Based on the above discussion, it can be seen that the impact of green technological innovation on haze pollution has two sides, and its final impact depends on the combined effect of the "prevention effect" and the "rebound effect."

Research model design
Based on the above theories, a spatial panel model is constructed to empirically estimate the impact of green technology innovation on haze pollution. It is noteworthy that haze pollution is expected to spatially correlate across regions due to atmospheric circulation, industrial transfer, and interregional traffic flow. Thus, we should consider the spatial characteristics of haze pollution. The results of Xiao et al. (2019) show that there is an apparent spatial correlation of green innovation among provinces in China. Moran's I index is used to test whether haze pollution has spatial correlation, and its calculation formula is as follows.
where n is the 30 provinces in mainland China except Tibet. w ij is the spatial weight matrix.
x and x are PM 2.5 concentrations and their mean values for each province, respectively.

Construction of spatial weight matrix
In this paper, three spatial weight matrices are structured to measure the spatial correlation of haze pollution (Getis 2009). Geographic distance weight matrix considers the geographic distance between provinces, which is the reciprocal square of the distance between the geographical centers of provinces i and j (Zhang et al. 2020b): where d ij is the distance between the geographic centers of provinces i and j.
Economic weight matrix considers the differences in economic development levels between provinces (Du et al. 2018). The more similar the level of economic development is, the greater the spatial weight coefficient is. The formula is as follows: where Y represents the economic development level of each province, and it is usually expressed by GDP per capita. Nested weight matrix of geographical and economic distance considers the radiation effect of geographic distance and economic factors. The formula is as follows: where φ represents the proportion of the geographic distance weight matrix, between 0 and 1. In order to simplify the analysis, in this paper, the value of φ is 0.5.

Basic model setting
In order to better empirically test the impact of green technology innovation on haze emission reduction, on the basis of the above theoretical model, the following basic panel model is constructed in this paper: In the above equation, lnPM i,t is the explained variable, indicating the natural logarithm of haze pollution for province i in year t, which is measured by PM 2.5 concentration in this paper. GP is the core explanatory variable, indicating the degree of green technology innovation, which is measured by the number of green patent applications. The remaining five variables are control variables, respectively: PD is the population density of each province (Liu et al. 2017). AFC represents the air circulation coefficient, which measures the degree of atmospheric circulation between regions. ISI represents the industrial structure advanced index, reflecting the level of industrial structure advanced in each province. EC represents energy consumption structure, that is, the proportion of coal consumption in total energy consumption. FDI refers to the proportion of actual use of foreign direct investment in local GDP, which measures the level of regional openness. γ 0 represents the constant term and γ 1 to γ 6 respectively represent the regression coefficient of each variable. ε represents the random disturbance term. The purpose of this paper is to empirically test green technological innovation, that is, whether the core explanatory variable GP can inhibit haze pollution (PM 2.5 ).

Construction of spatial econometric model
Spatial lag model (SLM), spatial error model (SEM), and spatial Durbin model (SDM) are commonly used spatial econometric models of panel data. They respectively focus on measuring the spatial effects caused by the spatial correlation of the explained variables, error terms, and explanatory variables. Their basic forms are as follows (Elhorst 2014): (ii) Spatial error model (SEM) The generating process of the disturbance term u is as follows: (iii) Spatial Durbin model (SDM) In the above equations, y is the N × 1 dimensional vector composed of the explanatory variables. W is the spatial weight matrix, and Wy is the endogenous interaction effect between dependent variables. X is the independent variable, which is an N × K dimensional vector. WX is the exogenous interaction effect between independent variables. ρ is the spatial autoregressive coefficient and represents the degree of spatial relevance, which measures the impact Wy on y. τ N represents the order unit matrix, which is an N × 1 dimensional vector associated with the constant parameter α to be estimated. θ and β are K × 1 dimensional vectors with fixed parameters to be estimated. δ is the spatial autocorrelation coefficient, and ε is the random error term.

Variable description and data source
This paper selects panel data from 30 provinces in mainland China for 2011-2017 to conduct an empirical study (Tibet has not been included in the study due to lack of data) (see Appendix). Due to the late start of PM 2.5 monitoring in China, the PM 2.5 data used in this paper are from the atmospheric composition analysis group of the USA. Green patent authorization data are from China patent database. The industrial structure advanced index is calculated by using the original data of China Statistical Yearbook and referring to the calculation method proposed by Fu (2010). Other data source from the National Bureau of Statistics of China (NBS), the China Statistical Yearbook (2011)(2012)(2013)(2014)(2015)(2016)(2017), and the EPS (Easy Professional Superior) data platform. Table 1 describes these variables. Table 2 presents the corresponding descriptive statistics of variables.

Analysis of empirical results
Based on model (5), combined with the spatial panel data model, the following investigate the impact of green technology innovation on haze pollution.

Spatial correlation test
Moran's I test is used to check the existence of spatial autocorrelation in lnPM. The Lagrange Multiplier (LM) test (Anselin 1988) and the robust LM test (Anselin et al. 1996) are used to justify whether we select a spatially lagged term of lnPM or a spatial error term. Table 3 reports the test results under three weight matrices, i.e., the geographic distance weight matrix (W 1 ), the economic weight matrix (W 2 ), and the nested weight matrix of geographical and economic distance (W 3 ). The test results show that the Moran's I test statistics are significant at the 1% level of significance, indicating that haze pollution has significant spatial correlation, in relation to geographical space, economic development level, and the comprehensive impact of the two. Under W 1 and W 3 , both LM and robust LM tests show that the null hypotheses of no spatially lagged lnPM and no spatially lagged error term are rejected at the 1% level of significance. Under W 2 , the LM test results further show that the null hypothesis of no spatially lagged lnPM cannot be rejected, and no spatially lagged error term must be rejected, justifying that the spatial error model should be selected.

Model selection
As in the previous analysis, there are mainly three spatial measurement models: SLM, SEM, and SDM. In order to choose a more suitable model, a spatial diagnostic test is required. Table 4 shows the parameter estimation results of SLM, SEM, and SDM models based on W 1 , W 2 , and W 3 , respectively. Take the matrix W 3 as an example. Firstly, the Hausman test is used to determine whether to choose a random effect or a fixed effect. The results show that the SLM model accepts the null hypothesis of random effects, while the SEM model and SDM model significantly reject the null hypothesis of random effects and fixed effects should be selected. Secondly, based on the choice of fixed effects, a joint significance test should also be performed to further determine whether the model should choose individual fixation, time fixation, or dual fixation.  (Lian et al. 2014). Under the matrix W 2 , the dual-fixed SLM model fits better, which is contrary to the conclusion of the LM test above. Moreover, the value of spatial ρ of the SLM model is not significant. It can be concluded that under the matrix W 2 , the possibility of the spatial correlation of haze pollution is low. Therefore, the subsequent analysis of the SLM model under the matrix W 2 will not be done in the following, but the analysis will be focused on the SDM model under the matrix W 1 and W 3 . Based on the above analysis, regression analysis is performed on models with a higher degree of fit under the matrix W 1 and W 3 respectively to explore the haze reduction effect of green technological innovation.

Analysis of regression results
Based on the results of the spatial diagnostic test, the SDM model under the matrix W 1 and the matrix W 2 has batter fitting degree for sample data. Therefore, the regression results of the SDM model under the matrix W 1 and the matrix W 3 are listed, and compared with the OLS results. The specific results are shown in Table 5. According to the above regression results, it is found that: First, ignoring the spatially related effects affects the effect of the explanatory variables on the explained variables and the extent of their effect. First of all, on the coefficient signs of the core explanatory variables, the SDM model based on the matrix W 3 has consistent and opposite variable coefficient signs to the OLS model, which shows that when considering the spatial effect, the core explanatory variables will have a completely opposite impact on the explained variables by adding the spatial effect, indicating that the variables and sample data in this study have obvious and non-negligible spatial correlation. And then, on the absolute values of the coefficients of the core explanatory variables, the estimates of the SDM model are greater than those of the OLS model, indicating that the simple non-spatial OLS model underestimates the degree of influence of the core explanatory variables on haze pollution because of ignoring the spatial correlation between the variables.
Second, the spatial correlation of China's haze pollution is significant. The spatial ρ is significantly positive, indicating that the haze pollution between regions has significant spatial correlation and strong spillover effects. Geographical distance and the combined factors of geography and economy are both important factors that affect the degree of regional haze pollution: when the two places are geographically close, the exchange of production and other activities between the two places makes them have more similar haze pollution conditions. It is precisely because of the spillover effect of haze pollution that it is impossible for a region to complete haze control work alone, nor can it be deliberately to improve the local atmospheric environment simply by transferring pollution-intensive industries to neighboring regions. Although this method may temporarily improve the local environmental quality, pollution from neighboring areas will Note: ** , *** denote statistical significant at 5% and 1% confidence levels respectively inhibit this improvement. Therefore, the management of haze pollution requires the coordinated participation of multiple entities. Third, GP, EC, and FDI are all conducive to haze reduction. The core explanatory variable GP has a significant inhibitory effect on haze pollution. The estimated results of the SDM model based on the matrix W 3 show that for every 1% increase in regional green technology innovation, local haze pollution will be reduced by 0.1323%. In addition, EC and FDI also have different effects on haze pollution: the optimization of EC can effectively reduce haze pollution. For every 1% reduction in the proportion of coal consumption in total energy consumption, haze pollution is reduced by 0.1484%. This is the same as the research conclusion of Shao et al. (2016). And every 1% increase in FDI will reduce haze pollution by 0.0489%, which is in line with the "pollution halo" hypothesis: FDI can be achieved by introducing environmentally friendly technologies and products which improve the environmental quality of a country. In general, the effect of GP on haze pollution is limited. On the one hand, China's GP is still in the development stage; the level still needs to be improved, and the scale still needs to be expanded. On the other hand, the haze pollution control measures need to be optimized. In the treatment of haze pollution, a multipronged approach is needed to coordinately optimize the energy consumption structure and increase the positive spillover of foreign capital to achieve significant results. Fourth, the time lag of the explanatory variables is significantly positive. Considering that the pollutants of air pollution such as haze are often cumulative, there is a certain "time lag" between cause and effect, that is, when the current haze pollution is at a high level, the haze pollution level of next phase may continue to rise, thus showing a "snowball effect" (Shao et al. 2016). Therefore, the time lag term of the explanatory variable haze pollution is added to the SDM model as an explanatory variable. The results show that haze pollution has a significant time lag. At a significance level of 1%, the previous haze pollution significantly affected the current pollution level, which is manifested in that for every 1% increase in the previous haze pollution, the current haze pollution will increase by 0.3397% and 0.3275% respectively.

Analysis of spillover effects
Since the coefficients of the explanatory variables in the spatial panel data model do not reflect the spatial effects, the spatial spillover effects of each variable on haze pollution are listed below. The results are shown in Table 5. As we can see: First, the symbol correspondence of spillover effect of the two models is consistent, which indicates that the spillover effect is relatively stable and the model has good robustness.
Second, GP has obvious negative spillover effect. The direct effect of GP on haze pollution is not significant in matrix W 1 . But the spillover effect of it is significant in both matrices, indicating that local GP has a significant inhibitory effect on haze pollution in adjacent regions. GP has the positive externalities of knowledge and technology spillover, and the government should guide it with policies and regulations to give full play to its positive externalities.
Third, PD, AFC, ISI, EC, and FDI have significant spillover effects on haze pollution. Firstly, the accumulation of population often aggravates haze pollution through consumption, travel, production, and so on. The regression results show that PD has a significant positive spillover effect on haze pollution under W 3 , indicating that population has aggravated Note: * , ** , *** denote statistical significant at 10%, 5%, and 1% confidence levels respectively haze pollution, which is the same as the research conclusion of Shao et al. (2019). Secondly, AFC promotes similar haze pollution in neighboring areas. Thirdly, changes in industrial structure has obvious spillover effect on haze pollution. When Zhang et al. (2020a) studied the spatial impact of industrial structure on haze pollution, they also came to the conclusion that industrial structure has an inhibitory effect on haze pollution, and further divided industrial structure changes into two major categories: rationalization and upgrading. During the sample period, only the rationalization of the industrial structure played a role in reducing haze. In this paper, due to the rationalization of the industrial structure, every 1% increase in the local ISI will reduce the haze pollution in neighboring areas by 7.3341%, and reduce the haze pollution in neighboring areas with similar economic development levels by 22.9147%, which has a profound impact. We believe that this is due to the differences in the level of economic and technological development between regions, and the transfer of pollution by the industrial echelon will cause transboundary pollution between regions. The development of local green technology innovation has promoted the higher level of local industrial structure, reduced highpolluting industries transferred to neighboring areas, and reduced haze pollution (Li and Mao 2020). Fourthly, the spillover effect of EC on haze pollution is significant. The results of SDM model based on W 1 and W 3 respectively show that a 1% decrease in the proportion of coal consumption in total energy consumption will reduce the haze pollution in neighboring areas by 0.2680%, and the decline in neighboring areas with similar economic development levels will be even higher, reaching 1.0582%. Currently, coal ranks first in China's energy consumption structure. In the long run, changing the energy consumption structure is the key, but it is difficult to change it in the short term. Then increasing the use of high-quality energy, especially the use of high-quality coal, is the main way to reduce haze in the short term (Ma and Zhang 2014). Finally, FDI also has a negative spillover effect on haze pollution. For every 1% increase in FDI, haze pollution in neighboring areas with similar economic development levels will be reduced by 0.4255%. The behavior of attracting investment in adjacent areas is conducive to improving environmental quality (Xu and Deng 2014).

Analysis of mediating effects
Mediating effect means that the influence relationship between variables (X to Y) is not a direct causal chain relationship, but is produced through the indirect influence of one or more variables (M). In this case, we call M as a mediating variable, and through M, the indirect influence X on Y is called the mediation effect. Based on the regression results of the above spatial panel model, the direct impact of GP on haze pollution is not significant or the degree of impact is not obvious, while the control variables of ISI, EC, and FDI have considerable impact on haze pollution. Can GP influence changes in the ISI, EC, and FDI to promote the development of haze emission reduction? Combining the "prevention and control effect" and "rebound effect" of GP on the impact mechanism of haze pollution-the "prevention effect" brought by the development of cleaner production technologies, the improvement of energy utilization efficiency and the improvement of pollution control methods can reduce haze pollution. The increase in energy use efficiency leads to a reduction in unit energy consumption and a reduction in costs. On the contrary, it stimulates the "rebound effect" brought about by the increase in energy demand, which will expand haze pollution. The following applies the intermediary effect model, using ISI, EC, and FDI as intermediary variables to explore the transmission mechanism between GP and haze pollution, and broaden the ways to prevent haze pollution.
Simulation study has found that "Bootstrap method" has higher statistical power than other methods of intermediary effect test (Song et al. 2012). Therefore, based on this method, this paper uses Stata14 to test the intermediary effect of sample data. The original hypothesis is that there is no mediating effect. The results are shown in Table 6.
It can be seen from the results that the direct and indirect effects of I and EC on haze pollution are both significant, indicating that ISI and EC play a part of the mediating role in green technological innovation and haze pollution. The indirect effect of FDI on haze pollution is not significant, but the direct effect is significant, indicating that there is no intermediary effect. The proportion of secondary industry in China's industrial structure and the abnormally high proportion of coal in the energy consumption structure are the important reasons for haze pollution. Therefore, promoting the rationalization of industrial structure, reducing the proportion of pollution-intensive enterprises and increasing energy technology innovation, reducing the use of disposable energy such as coal, realizing energy substitution, and adjusting the energy consumption structure are the keys to achieve haze control (Wei and Ma 2015). Note: * , ** , *** denote statistical significant at 10%, 5%, and 1% confidence levels respectively

Robustness test
Considering the robustness of the model and preventing accidental conclusion, another measurement model, the GMM model, was chosen to re-estimate the model in this paper, and the results are shown in Table 7.
The results show that under the GMM model, the coefficient signs and statistical significance of the core explanatory variables are completely consistent with the SDM model under matrix W 3 , and the signs of other control variables are basically the same, meanwhile the significant differences are small. The GMM model passes the over-recognition test, indicating that the instrumental variable PD is appropriate. The Hausman test results indicate that the other explanatory variables are all exogenous, and there is no influence of heteroskedasticity. The results have high reliability. Therefore, the results show that the original model has good robustness, and the estimation results have high credibility.

Conclusions and policy implications
Using the panel data of 30 provinces in mainland China in 2011-2017, we apply spatial models to estimate the impact of GP on haze pollution and its transmission mechanism under alternative spatial weight matrices. Results show that China's haze pollution has a significant spatial correlation. Every 1% increase in local haze pollution increases haze pollution by 0.5257% in adjacent areas and by 0.4132% in the geographically close region with similar economic development. In addition, the time lag of haze pollution will lead to "snowball effect," which means the current haze pollution will have an impact on the next phase of haze pollution. GP is an effective means to prevent and control haze pollution. Every 1% increase in GP can reduce haze pollution by 0.1323%. Its spatial spillover effect is significant. The improvement of local GP has an evident radiation impact on haze pollution in adjacent areas, specifically manifested in a 0.4436% reduction in haze pollution in geographically adjacent areas and a 1.9346% reduction in geographically adjacent areas with similar economic development. The spillover effects of EC, FDI, and IS on haze pollution are negative and significant, indicating that the optimization of EC, the increase of foreign investment, and the rationalization of industrial structure contributed to the reduction of haze pollution. ISI and EC play a partially mediating role in green technological innovation and haze pollution. PD and AFC have significant positive spatial spillover effects on haze pollution.
The policy implications of this paper are to understand the role of haze pollution inhibition factors, and emphasize the importance of the strengthening of haze pollution contributory factors, which means to better play the role of "prevention and control effect" of green technology innovation and to reduce the negative impact of the "rebound effect." In terms of promoting the enhancement of inhibiting factors, first, vigorously promote green technology innovation. Second, encourage the private sector, such as enterprises, to engage in green technology innovation and give full play to the role of environmental policy tools to the externalities of environmental innovation (Liao 2018), and to reduce barriers to innovation (Gupta and Barua 2018). Third, increase support for green technology innovation in public institutions, higher education institutions, and other departments. Fourth, introduce high-quality foreign investment and appropriately increase the guidance in the use of foreign capital. Fifth, guide foreign investment in favor of environmentally friendly technologies and high value-added products. Finally, give full play to regional synergies, and undertake joint efforts to prevent and control haze pollution, and build a collaborative governance system with the participation of multiple entities (Shi and Lai 2013;Yin et al. 2020). With local governments in the leading role, cooperation in haze control among regions should be strengthened. At the Note: * , ** , *** denote statistical significant at 10%, 5%, and 1% confidence levels respectively same time, the power of enterprises should be connected, the common interest network of all subjects established, and knowledge sharing realized (Arfi et al. 2018). In terms of inhibiting the enhancement of pollution contributory factors, efforts should be directed towards reducing the generation of haze pollution in production and promoting the rational upgrading of industrial structure. Rational upgrading does not constitute blind demand for the reduction of secondary industry and the expansion of tertiary industry, but aims to make secondary industry more environmentally friendly and reduce the damage of industrial pollution to the atmospheric environment. By optimizing the energy structure, reducing the consumption of fossil energy, developing clean energy and increasing the promotion and popularization of clean energy, and realizing energy substitution earlier.
In addition, the aim should be to reduce the generation of haze pollution in daily life: raising public awareness of energy conservation and environmental protection, improve the utilization rate of public transport, and reduce the pollution of the atmosphere caused by automobile exhaust. This paper studies the impact of green technology innovation on haze pollution, and puts forward corresponding policy suggestions according to the research conclusions, but we believe that there are still the following areas to be improved: Firstly, due to the availability of data, our sample range is 2011-2017, and it would be better to extend the research period to 2019 or even newer years. Secondly, due to limitations such as article length, more factors affecting haze pollution are not considered as control variables. Thirdly, we appreciate the reviewers for their comments on the core explanatory variables. In future research, we will strive to use indicators that can more accurately measure green technology innovation than the amount of patent authorization. We will try our best to improve this problem.