Does the EU emissions trading system help reduce PM2.5 damage? A research based on PSM-DID method

Air quality issues, especially haze pollution, have become an important aspect that threatens the sustainable development and health of human beings. Previous studies on the environmental effects of emissions trading system (ETS) mainly focused on carbon emission reduction, instead of focusing on the synergistic governance effect between carbon emission and PM2.5 reduction. Based on the PSM-DID method and the World Development Index (WDI) database, this paper examines whether the EU ETS has a spillover effect on PM2.5 damage reduction, and discusses the related impact mechanisms. The research results show that the EU ETS promotes the reduction of PM2.5 damage, and in different phases of implementation, the impact of the EU ETS on the reduction of PM2.5 damage has a dynamic effect. The robustness test results also show that the research conclusions of this paper are highly reliable. Finally, this paper gives relevant policy suggestions, which can encourage countries to achieve carbon emission reduction targets while helping to reduce PM2.5 damage, and eventually achieve a win–win situation between economic growth and environmental improvement.


Introduction
Air pollution has become an important issue that threatens the sustainable development and health of human beings. As an important component of air pollutants, PM 2.5 is the culprit. PM 2.5 is also the main air pollutant that causes haze (Dong et al., 2019a). A research report in the " Environmental Research Bulletin, 2013" showed that the number of deaths caused by air pollution in the world is about 2.1 million each year. The main cause of death is the increase in the concentration of suspended particulate matter such as PM 2.5 in the atmosphere. The "Global Environment Outlook 5" (2012) pointed out that nearly 2 million premature deaths were related to particulate pollution. The report from the European Union Environment Agency (2016) also pointed out that about 85% of Europeans are exposed to the harmful environment of PM 2.5 particles. Although these fine particles cannot be seen or smelled, they do have a devastating effect on the human body, including causing or aggravating heart disease, asthma, and lung cancer (Xu et al. 2019). The latest "European Air Quality Report 2020" released by the European Environment Agency shows that air pollution remains the biggest environmental health risk in Europe. The report shows that in order to curb the spread of the epidemic, European countries have generally implemented "cities closure" measures since last year, and the level of nitrogen dioxide has been greatly reduced, but the level of particulate matter in the air has not fallen much, and is still at a high level. Therefore, it is necessary to study and formulate effective environmental regulations to control and reduce the concentration of PM 2.5 in the air. In particular, to clarify the effect of the relevant ETS on the reduction of air pollutants is a research topic with important practical significance and theoretical value.
A properly designed ETS can not only promote the progress of energy saving and emission reduction, but also an important starting point for collaborative environmental management (Yan et al. 2020), it can effectively control air pollution and climate change, and promote the effectiveness of environmental and ecological governance (Zhang 2015;Li et al. 2019). The EU ETS is a cornerstone of the Responsible Editor: Ilhan Ozturk EU's policy to combat climate change and its key tool for reducing greenhouse gas emissions cost-effectively. Set up in 2005, it is the world's first major carbon market and remains the biggest one (European Commission 2021). The EU ETS is actually implemented step by step in three phases: The first phase is from 2005 to 2007, mainly for power production and energy-intensive industries in these countries. At the same time, all carbon emission allowances are issued for free; The second phase is from 2008 to 2012. During this phase, Iceland, Liechtenstein, and Norway joined, related emission requirements were further strengthened, for example, nitrous oxide emissions are included in the emission reduction target, and the fines for violating emission regulations have also increased from 40 euros/ton to 100 euros/ton; The third phase is from 2013 to 2020. Based on the previous implementation experience, significant adjustments have been made to the emissions trading system in this phase. The unified emission cap within the EU replaces the previous independent cap system of the participating countries, at the same time, it covers a wider range of emissions, for example, included CO 2 emissions from the aviation industry and perfluorocarbons (PFCs) from the aluminum production industry into the emissions trading system.
As it is well known, greenhouse gas and air pollutant arise from the same source, both are mainly caused by the combustion of coal, oil, and natural gas. Therefore, the actions to reduce CO 2 and PM 2.5 emissions are consistent, and the realization of coordinated control of air pollutants and greenhouse gas emissions also has a realistic basis (Xian et al. 2018). In the process of reducing greenhouse gas emissions, the emission of atmospheric pollutants PM 2.5 can also be effectively controlled. The resulting environmental health benefits will offset the emission reduction costs and improve the cost efficiency of the implementation of ETS (Yang et al. 2013). A number of studies have confirmed that reducing greenhouse gas emissions has a synergistic effect on alleviating air pollution (Vennemo et al. 2009;Xue et al. 2015). Establishing an effective ETS can not only reduce carbon emissions, but also coordinate the treatment of air pollution and improve air quality. In addition, scholars have also confirmed that greenhouse gas reduction strategies can improve air pollution and bring public health benefits (Haines et al. 2009;Nemet et al. 2010;Groosman et al. 2011). Therefore, we have reason to believe that the implementation of ETS can also effectively reduce the damage of PM2.5, and we rarely see this kind of research. Based on this, studying the impact of the ETS on the reduction of PM 2.5 damage will be an effective supplement to the current research on the effectiveness of EU ETS collaborative governance, and it can also enrich the content and scope of current ETS research.
With the implementation of ETS, its impact has aroused widespread concern in previous studies. The initial research mainly focused on the environmental effects of ETS, for example, some studies focus on the role of ETS in carbon emission reduction (Laing et al. 2014;Muûls et al. 2016;Li et al. 2019). In addition, scholars continued to study the spillover effects of ETS, such as its impact on corporate profits (Smale et al., 2006), energy prices (Kara et al. 2008), industrial investment (Laing et al. 2014), and low-carbon consumption. There are also studies that focus on the role of ETS in the adjustment of industrial structure, such Zang et al. (2020) as investigated whether the implementation of ETS has spillover effect on the industrial structure upgrade. Although some scholars also have studied on PM 2.5 emission reduction from the perspective of policy tools, common policy tools include resource tax (Sancho 2010), sulfur tax (Xu and Masui 2009) and carbon tax (Allan et al. 2014). However, due to the lack of specific PM 2.5 emission data, the current research is mainly based on PM 2.5 concentration data (Dong et al. 2019b). This leads to the inability to effectively analyze the specific emission reduction path and impact mechanism of PM 2.5 . Only a few scholars such as Yan et al. (2020) have tested the cooperative control effect of the ETS on air pollution based on the ETS pilot with Chinese characteristics. Due to the short pilot time of ETS in China, current researches mostly employ forecast or simulation models to analyze its effect on emission reduction (Zhao et al. 2016). Therefore, given the maturity of the regulation, this study takes the EU EST as the core research subject. What is more, the existing studies on the synergistic effects of air pollutants and greenhouse gas emissions mostly use complex models for simulation analysis, there are too many assumptions and constraints, and the results of quantitative analysis can only be regarded as predicted values or theoretical values, there is often a lack of detailed analysis of historical data.
In summary, in order to fill the above research gaps, this paper selects PM 2.5 damage and other related data from the World Development Index (WDI) database, based on the PSM-DID method, we examined whether EU ETS has a spillover effect on the reduction of PM 2.5 damage. The structure of this article is as follows. The second section provides the literature review. The third section presents the research design, including the research method, data collection, variables, and the research model. The fourth section supplies the empirical analysis results, including regression analysis, robustness test results, and discussions. Finally, the fifth section gives the summary of this article, including implications, related deficiencies, and future research directions.

Literature review
Previous studies on the evaluation of ETS implementation results mainly followed four clues. The first clue is its direct effects on emission reductions (e.g., Laing et al., 2014;Muûls et al., 2016;Li and Jia, 2016). The second clue focuses on the contingent effect of ETS on economic indicators (Wang 2012;Hoffmann 2007;Abrell et al. 2011;Anger and Oberndorfer 2008;Zhang and Wei 2010). The third clue focuses on its positive impact on carbon productivity (Cui et al. 2014;Zhang et al. 2017). The fourth clue mainly studies the potential impact of ETS on technology innovation (Porter 1991;Porter and Linde 1995;Cerin 2006; Van Leeuwen and Mohnen 2017). As PM 2.5 governance is an important part of environmental regulation; however, few scholars have studied it from the perspective of environmental regulation theory. In particular, there are few studies on the relationship between EU ETS and PM 2.5 emission reduction (Lv et al. 2015;Liu et al. 2020).
Through combing the literature on PM 2.5 , we found that current researches mainly focus on the influencing factors, composition, harm, and pathogenic mechanism of PM 2.5 . Such as Shao et al. (2016) found that although the frequent occurrence of haze pollution is affected by climatic factors to some extent, the extensive economic development mode, unbalanced industrial structure, low energy efficiency, and low environmental governance efficiency are the ultimate influencing factors. Therefore, to analyze the causes of haze from the perspective of socio-economic influencing has gradually become the mainstream direction. Based on the STIRPAT model, Xu and Lin (2016) found that factors such as economic development, urbanization, private car ownership, coal consumption, and energy efficiency have significant differences in the impact of PM 2.5 emissions in different regions.
At the same time, a number of studies have confirmed that reducing greenhouse gas emissions has a synergistic effect on alleviating air pollution. Xue et al. (2015) quantitatively evaluated the synergistic benefits of wind power generation based on the life cycle analysis method. Vennemo et al. (2009) compared the benefits and costs of three different CO 2 emission strategies (including intensity, total emission, and industry intensity), and concluded that intensity control has the greatest environmental synergy. In addition, a number of studies also have confirmed that greenhouse gas reduction strategies can improve air pollution and bring public health benefits (Haines et al. 2009;Nemet et al. 2010;Groosman et al. 2011). However, previous studies on the environmental effects of ETS focused on carbon reduction, rather than on the collaborative governance effects of ETS on PM 2.5 .
Up to now, the research on PM 2.5 governance from the perspective of environmental regulation theory is still a gap that needs to be filled urgently, and it is rarely to find studies that use ETS as an explained variable. Preliminary studies such as Lv et al. (2015) have analyzed the dilemma of PM 2.5 governance in China based on the perspective of environmental regulation theory, they pointed out that the problem of PM 2.5 governance is manifested as weak environmental law enforcement. Zhang (2017) built a spatial interaction model of urban pollutant emissions, he found that although the total amount of pollutant emissions in Chinese cities has been reduced, the concentration of PM 2.5 in the air has not shown a significant decline. Liu et al. (2020) studied the relationship between environmental regulations and urban air pollution by constructing a spatial Dubin model, they have identified the effectiveness of air pollution control in the city. It can be seen that most previous studies have studied the effects of PM 2.5 governance based on the perspective of general environmental regulation. Only a few scholars, such as the latest research by Yan et al. (2020), they have studied the relationship between China's ETS and air pollution by constructing an empirical model. As mentioned above, the implementation time of Chinese ETS is shorter than that of EU ETS, and its content, coverage, and maturity are far less than EU ETS at the current stage. Moreover, the PM 2.5 data used in the study by Yan et al. are speculative data, not actual emission data. Therefore, based on the historical data of PM2. 5 damage of the World Bank, this paper constructs a regression model to quantitatively analyze the impact of ETS on PM 2.5 damage reduction, we believe that more convincing evidence will be obtained.

Research method
This paper uses the DID method based on PSM to study the spillover effect of ETS on PM 2.5 damage reduction. DID is a commonly used quasi-experimental method to estimate the causal effects of specific public policies (Stuart et al. 2014). Since the implementation of a public policy is usually not affected by the subject, therefore, the implementation of the policy can be regarded as an exogenous "intervention" for the subject, and it can also be regarded as a quasi-experiment. The DID method is to estimate the net effect of a policy by comparing the result changes between the intervention group and the control group before and after its implementation. DID method can eliminate the estimation bias caused by time-varying factors (Stuart et al. 2014). However, DID method also faces the endogenous problem caused by sample selection bias, that is, the samples in the control group are usually selected randomly. If the result trend or sample composition varies over time due to various confounding variables, it will lead to estimation bias.
The PSM-based DID method can solve the problem of sample selection bias caused by confounding factors (Caliendo and Kopeinig 2008). PSM is a counterfactual causal inference method, it uses the common characteristics of a set of intervention group and control group, and match the intervention group to a similar control group sample as a new control group. This can reduce the estimation bias caused by the confounding factor, and can make the comparison of the DID regression results of the intervention group and the new control group more reasonable. Therefore, the PSMbased DID method can effectively estimate the impact of specific policies.

Data collection
This paper mainly involves objective data such as PM 2.5 emission damage and related economic indicators in various countries, these data come from the World Development Indicators (WDI) database of the World Bank. The WDI database collects and compiles hundreds of indicator data related to global development, covering various countries and regions around the world, and the data source is authoritative and accurate. The economic development indicators of the countries (regions) involved in this research include gross domestic product (GDP), per capita GDP, gross domestic income (GDI), consumer price index (CPI), the proportion of secondary and tertiary industry output in GDP, employment status, and airborne fine particulate matter (PM 2.5 ) emissions index. Due to the availability of WDI data, the time span of the panel data involved in this research is from 2000 to 2017. After excluding countries or regions with missing data, a total of 147 countries and regions remain as backup samples.

Dependent variable
The dependent variable of this study is the damage caused by airborne fine particulate matter emissions, which referred to as PM 2.5 emission damage. It is calculated according to the natural logarithm of PM 2.5 emission damage (priced in US dollars). The World Bank's specific description of PM 2.5 emission damage is "Particulate emissions damage is the damage due to exposure of a country's population to ambient concentrations of particulates measuring less than 2.5 microns in diameter (PM 2.5 ), ambient ozone pollution, and indoor concentrations of PM 2.5 in households cooking with solid fuels. Damages are calculated as foregone labor income due to premature death. Estimates of health impacts from the Global Burden of Disease Study 2016. Data for other years have been extrapolated from trends in mortality rates."

Independent variable
The independent variable of this study is the implementation of the ETS. Refer to the DID method, we construct two dummy variables Treat i and D t . Among them,Treat i indicates that the sample country or region belongs to the intervention group or control group. If the i-th country or region joins the ETS, then the country's Treat i is equal to 1. On the contrary, if the country or region has not joined the ETS, the country's Treat i is equal to 0.D t indicates the time dummy variable for the implementation of the ETS. If the ETS is implemented in year t, D t in the current year and the subsequent years is equal to 1, and D t in the previous year is equal to 0. It should be pointed out that since the EU ETS was implemented step by step in three phases from 2005 to 2017, the specific content of implementation of each phase was gradually deepened, and a small number of non-EU countries have joined the EU ETS in each implementation phase. Therefore, for these countries that join in the later phase, their Treat i in the early phase is equal to 0, and after joining the ETS, their Treat i is correspondingly equal to 1. According to this, the independent variable of the DID regression analysis is the cross product of Treat i and D t , namely Treat i *D t .

Control variables
With reference to previous researches, this paper controls for economic variables related to outcome variable (Apergis 2016;Cheng et al. 2017;Li and Lin 2015;Yang et al. 2015). Firstly, the economic scale and degree of development of a country are often closely related to the emission of air pollutants, which will affect PM 2.5 emissions. Therefore, we control the gross national product (GDP), per capita gross national product (per capita GDP), gross domestic income (GDI), urbanization rate (Urban), and consumer price index (CPI) of each country. In order to reduce the dimensional influence, the natural logarithm of GDP, GDP per capita, and GDI is taken. Secondly, the industrial structure level of a country is also an important factor that affects the emission of air pollutants. Therefore, this paper controls the proportion of the output value of the secondary and the tertiary industries and the employment situation (measured by the employment rate). Thirdly, it should be pointed out that, consistent with previous studies, this paper also uses these control variables as covariates for the propensity score matching analysis (Table 1).

Regression model
According to the introduction of EU ETS in the introduction section, it can be seen that different implementation phases may have significantly different consequences. Therefore, it is necessary to study the environmental governance effects of the EU ETS on PM 2.5 emissions damage according to the specific conditions of each phase. Refer to the research of Zang et al. (2020), regarding the environmental governance effects before and after the implementation of the EU ETS in each phase (i.e., PM 2.5 emission damage), this paper uses DID regression, and the regression model is as follows: In the above formula, Y it represents the outcome variable, that is, the PM 2.5 emission damage of each sample country or region before and after the implementation of the ETS, it is expressed as the natural logarithm of PM 2.5 emission damage (priced in US dollars) and the proportion of PM 2.5 emission damage to gross national income. As mentioned earlier, Treat i * D t is a dummy variable that reflects the implementation of ETS. γ i , μ t respectively represent the individual fixed effect and time fixed effect of the country or region. Control it is the control variable mentioned above, including the gross national product (GDP), per capita gross national product (per capita GDP), gross domestic income (GNI), consumer price index (CPI), the proportion of the output value of the second/tertiary industry, and the employment situation. ε it represents the random interference items.
In addition, in the regression model of each phase, the time range of the sample panel data is from the first five years of the intervention year of this phase to the year before the intervention year of the next phase (due to the limitation of WDI data accessibility). Therefore, the time range of the first phase regression panel data is from 2000 to 2007, the time range of the second phase regression panel data is from 2003 to 2012, and the time range of the third phase regression panel data is from 2008 to 2017. At the same time, the intervention group and control group samples added to formula (1) are all samples after the propensity score matching. Figure 1 shows the overall changes in PM 2.5 emission damage (lnEMD) in the intervention group and control group countries or regions during the observation period.

Propensity score matching analysis results
As mentioned above, it is necessary to measure the effect of EU ETS on PM 2.5 emission damage according to the actual conditions in three different phases, and in the three phases, the countries of the intervention group also changed. Therefore, it is necessary to conduct propensity score matching  . 1 The overall change trend of lnEMD. The solid line with dots represents the situation of the intervention group. The dotted line with a quadrilateral represents the situation of the control group analysis for the three phases to obtain the control group samples. K-nearest neighbor matching (K = 4) is used here, and the covariates of propensity score matching are as described in the previous section. After propensity score matching analysis, the intervention group and control group countries of the three phases of EU ETS implementation are shown in Table 2. It needs to be further explained that in the three-stage regression model, the number of samples in each stage is different, specifically: In the first phase (the intervention year is 2005), after matching, there are 15 countries in the intervention group and 36 countries in the control group. In the second phase (the intervention year is 2008), after matching, there are 18 countries in the intervention group and 20 countries in the control group. In the third phase (the intervention year is 2013), after matching, there are 20 countries in the intervention group and 25 countries in the control group.
After propensity score matching analysis, it is usually necessary to perform a balance test on the samples of the intervention group and the control group to ensure that there is no sample selection bias. Zang et al. (2020) pointed out that after matching, the difference between the intervention group and the control group should be significantly reduced, and the absolute value of the deviation of the sample on each covariate should not exceed 20. At the same time, the t-test after matching should not be significant (that is, the p-value corresponding to the t-statistic is greater than 0.05). It can be seen from Table 3 that after the matching analysis of the three phases, the absolute value of the deviation value of each covariate is basically less than 20, and the p-values all exceed 0.05, which meets the requirements of the balance test. Therefore, after matching, there is no significant difference between the intervention group and the control group, which meets the requirements for further analysis.

DID regression analysis results
Based on the samples of the intervention group and the control group obtained by propensity score matching, by using DID regression, this section analyzes the environmental governance effects of the EU ETS on PM2.5 emissions damage. In this section, first we conduct an overall regression analysis of the effects of each phase, then we analyze the dynamic effects of each phase, at last we show the robustness test results. The specific empirical analysis results are as follows.  The spillover effect of ETS on PM 2.5 damage reduction The results of DID regression based on propensity score matching are shown in Table 4. Models 1, 2, and 3 respectively correspond to the first, second, and third phase of the implementation of the EU ETS. The results of Model 1 show that after the implementation of the first phase of the trading system, the degree of damage caused by PM 2.5 emissions in EU countries has increased compared to before the implementation ( β = 0.08 , p<0.01). The results of Model 2 show that the second phase of EU ETS implementation has no significant impact on the reduction of PM2.5 damage. The results of Model 3 show that after the implementation of the EU ETS in the third phase, the PM 2.5 emission damage due to each member country has been significantly reduced ( β = −0.07 , p<0.01). At the same time, in order to reduce the estimation error and avoid the overlap of effects across policy periods, we also connect the data for all phases of EU ETS. After propensity score matching analysis, the intervention group and control group countries of the Phase1-3 of EU ETS implementation are shown in Table 5. In the phase 1-3 (the intervention year is 2005), after matching, there are 23 countries in the intervention group and 23 countries in the control group.
The results of DID regression based on propensity score matching are shown in Table 6, and the model used here is the same as the model used above. At the same time, in order to avoid the problem of multicollinearity of control variables, we rediscover the appropriate control variables, that is lnpergdp, labour, service, industry, CPI, and urban. The results also show that after the implementation of the EU ETS, the PM 2.5 emission damage due to each member country has been significantly reduced ( β = −0.08 , p<0.05).

The dynamic effect of ETS on PM 2.5 damage reduction
The dynamic effect analysis of DID regression is to test the changes in the results of policy implementation over time, which helps to grasp the effect of policy implementation more clearly. Through the regression analysis of the dynamic effects of the three implementation phases of the EU ETS (see Table 7  year, and both are significant at the 5% confidence level. In addition, from the regression coefficient in the third phase, it can be found that the absolute value of the coefficient is increasing year by year, and the degree of significance also shows an upward trend. This shows that EU ETS has gradually played a role in reducing PM 2.5 damage in the third phase, and it is more and more conducive to the reduction of PM 2.5 damage. From the results of the above-mentioned holistic analysis and dynamic effect analysis, it can be seen that the results of the dynamic analysis further support the conclusion of the holistic analysis. Specifically, the impact of EU ETS on PM 2.5 damage did not play its due role in the first phase, and the degree of PM 2.5 damage has increased. In the second phase of ETS implementation, it can be seen from the analysis result that this phase is a transitional phase. Although the regression analysis results are not significant, the degree of PM 2.5 damage still changes from rising to falling, and in the later phase of the second phase implementation, ETS began to exert an inhibitory effect on PM 2.5 damage, and it becomes significant at the end of the second phase. The third phase is the phase when ETS is fully functional. No matter from the point of view of significance or from regression coefficient, ETS has played a significant effect on the reduction of PM 2.5 damage. Figure 2 shows the parallel trend test results of the policy effect of the implementation of the EU ETS. It can be seen from the following three figures that the estimated coefficients before the implementation of the EU ETS at each phase fluctuate around 0 (the 95% confidence interval also contains a value of 0), in the year of policy implementation and the following years, the coefficient is significantly negative. This shows that the difference between the intervention group and the control group before the implementation of the policy in the three phases is not obvious, that is, the premise hypothesis of parallel trends is met.

Placebo test results
In order to ensure the robustness of the results of the effect of the EU ETS on PM2.5 damage reduction, we conduct the placebo test of the policy implementation time. To do the placebo test, scholars generally use virtual policy implementation time. For example, Liu and Zhao (2015) advanced the policy implementation time by 2-3 years in the placebo test. According to the actual situation of the research object in this paper, we respectively advance the policy implementation point to 2003 and 2004. If the virtual variable of EU ETS is still significantly positive, then it shows that the reduction of PM 2.5 damage is likely to come from other policy changes or random factors rather than the implementation of EU ETS. Finally, the results of the placebo test can be found that the interaction coefficient is not significant, and the results of the placebo   Table 8, which shows that the DID estimation results are not affected by other factors. Counterfactual analysis results: In order to further test the robustness of the results, we also learn from existing research (Fan and Tian 2013), and conduct counterfactual testing by delaying the implementation of the policy. The DID regression results are shown in Table 9. We can see that by lagging the implementation time of EU ETS by 1 year, 2 years, and 3 years respectively. The results of the counterfactual analysis can be found that the interaction coefficient is also significant, which shows that the DID estimation results are not affected by other factors. Therefore, we can consider the previous results to be robust.

Heterogeneity analyses results
Due to a series of social progress accompanying urbanization, researchers believe that urbanization provides necessary conditions for containing or even improving environmental problems (Clement 2010). At the same time, numerous studies have shown that there is a significant relationship between the level of urbanization and PM 2.5 emissions (Luo et al. 2021). Therefore, this paper further analyzes whether there are differences in the impact of  ETS on the reduction of PM2.5 emission damage under different levels of urbanization. Table 10 shows the results of the effects of EU ETS interaction with country (region) urbanization level on the reduction of PM 2.5 damage. It can be seen that the coefficient of the interaction term is positive at the 1% significance level, indicating that the urbanization level negatively moderates the relationship between EU ETS and PM 2.5 damage reduction. This is because, on the basis of comprehensive calculation of costs and benefits, urbanization can improve the availability of public facilities, improve the efficiency of the use of infrastructure, promote the use of public transportation, and reduce environmental externalities (Wang 2017). When the level of urbanization is high, urban agglomerations and technological progress reduce the PM 2.5 density in the later stages of urbanization (Dong et al. 2020;Martínez-Zarzoso and Maruotti 2011). The overall level of urbanization in EU countries is at a relatively high level and is in the later stage of urbanization development. Therefore, the higher the level of urbanization, the effect of EU ETS in reducing PM 2.5 emission damage is restrained to a certain extent.

Discussions
By reviewing the specific system design content and actual implementation of the three phases of EU ETS, and combined with previous studies, we further explain the above analysis results. On the whole, the analysis results show that after the implementation of the EU ETS, the PM 2.5 emission damage due to each member country has been significantly reduced. Specifically, the first phase is the pilot phase, and the EU's emission limits are also difficult to determine; At the same time, most of the emission allowances allocated by member states to market entities are free (about 95%), most allowances (especially those in Eastern Europe) cannot enter the market, and the allowance prices was fluctuate (Wng 2009). At the same time, its initial scope of implementation was limited to large energy-consuming companies and carbon dioxide emissions, and did not expand to more industrial fields, smaller-scale production companies, and other types of greenhouse gases. This may be the main reason why the first phase of ETS did not work (Zang et al. 2020).
With the implementation of the second phase, related emission requirements have been further strengthened, more countries and greenhouse gas emissions have also been included in the scope, and the degree of punishment has been increased. As a result, it led to a change in the degree of Table 9 The results of the counterfactual analysis *, **, and *** denote significance at the 10%, 5%, and 1% levels. Standard errors are in parentheses (clustered to the individual level).
(1)  PM 2.5 damage in the second phase. After the accumulation of experience in the first two phases of implementation, the ETS in the third phase has been greatly improved, and the system has gradually matured. Therefore, in the third phase, its effect of reducing PM2.5 damage is the most effective (Yan et al. 2020).
The empirical results of the study indicate that the EU ETS pilots can not only serve as an important market-based environment regulation instrument for ameliorating climate change but also effectively lowers PM 2.5 damage. This also indirectly indicates that EU ETS has great potential in maximizing the collaborative governance efficiency of climate change and air pollution. Which shows that EU ETS can not only achieve its original purpose of controlling carbon emission reduction, but also improve social welfare (reduction of medical expenses) and achieve additional economic benefits. Therefore, for other countries that have not implemented ETS, in addition to encourage ETS pilots to explore innovation, it is also necessary to carefully consider how ETS can play the greatest value in reducing PM 2.5 in the initial toplevel design. In terms of the internal design of the system, it can also consider including an upper PM 2.5 limit in the national carbon trading quota allocation scheme, on the one hand, this can expand the collaborative governance of ETS on air pollution, on the other hand, it can incentivize emitters to upgrade and transform their green technology, thus contributing to lowering PM 2.5 concentration levels (Yan et al. 2020). At the same time, the analysis results of the poor effectiveness of the first two phases of EU ETS in reducing PM2.5 damage also show that it is necessary to design punishment in measures the national carbon market, a certain amount of fines should be imposed emitters that fail to fulfil their emission reduction obligations. The results of heterogeneity analyses suggest that ETS has different effects under different levels of urbanization, the flexible application of the "common but differentiated responsibilities" principle among EU member states can provide a reference for other countries with uneven domestic development.
So what is the possible impact mechanism of ETS on PM 2.5 damage reduction? Based on previous studies, the authors believe that the effect of ETS on PM 2.5 damage reduction is mainly through the following two approaches. 1. Industrial transfer and industrial structure upgrade approach. EU ETS is an effective market-based environmental regulation, which will follow the "pollution paradise" hypothesis. That is to say, its implementation will directly affect the industrial transfer of relevant heavy pollution industries, transfer to other countries or regions with lower environmental requirements, or directly cause the shutdown of relevant heavy pollution enterprises (Fan et al. 2017). At the same time, related studies have also confirmed that the implementation of EU ETS can promote the upgrading of the industrial structure of EU member states, prompt enterprises to increase green total factor productivity, and thereby reduce polluting gas emissions (Zang et al. 2020;Xian et al. 2018;Yang et al. 2013). As mentioned in the introduction and the review section of this paper, carbon reduction, greenhouse gas reduction, and PM 2.5 reduction have a synergistic effect. Therefore, it is necessary to believe that the transfer of polluting industries and the upgrading of industrial structure will promote the reduction of PM 2.5 damage. 2. Green technology innovation approach. Green technological innovation can be said to be the essential factor of ETS affecting PM 2.5 emission reduction. Previous research has shown that market-based environmental policy tools have a stronger effect of technological progress. Studies from many countries have also proved that environmental regulation will force companies to further optimize resource allocation, improve energy efficiency and productivity by promoting green innovation, for example, studies from the European Union, the United States, and China, and the latest research by Yan et al. (2020) also directly proves that green technology innovation plays a completely intermediary role between ETS and air pollution reductions.

Conclusions and implications
To study and formulate effective environmental regulations to control and reduce the concentration of PM 2.5 in the air, especially to clarify the effect of the relevant ETS on the emission reduction of air pollutants is a research topic with important practical significance and theoretical value. Based on the PSM-DID method, this paper selects PM 2.5 damage and other related data from the World Development Index database. This paper examines whether the EU ETS has a spillover effect on PM 2.5 damage reduction, clarifies the ETS impact effect at its different implementation phases, and further explores the related impact mechanisms and approaches. The following research conclusions are obtained: This study finds that the degree of PM 2.5 damage in countries participating in the EU ETS has changed from an increase in the first phase to a transition in the second phase then to a significant reduction in the third phase. Therefore, the EU ETS has a spillover effect on the reduction of PM 2.5 damage in the pilot areas. Meanwhile, in each phase, the EU ETS has a dynamic effect on the reduction of PM 2.5 damage. Looking at it separately, with the passage of policy implementation time, the effect of the EU ETS on the reduction of PM 2.5 damage has shown a slow increase until it stabilizes. The policy effect also changed from the weak effect in the first phase to the strong effect in the third phase.
We can also draw some useful policy implications from these conclusions: Firstly, the research conclusions of this paper are an effective supplement to the previous researches, indicating that the implementation of EU ETS can not only be used as an important market-based environmental regulatory tool to solve the problem of CO 2 emissions, an effective ETS can also realize the reduction of PM 2.5 emissions damage in the natural environment. Therefore, other countries can follow the implementation experience of the EU ETS, vigorously promote the exploration and innovation of ETS, and form a unified national carbon market trading system as soon as possible, so can enjoy the effective role of ETS in reducing PM 2.5 damage as soon as possible. Secondly, combined with an in-depth study of the phased implementation of the EU's ETS, it is found that there is only a relatively strict ETS (such as covering more energy-consuming industries, more air emissions, and stricter emission targets, etc.) can really play a role in reducing PM 2.5 damage. Otherwise, it will not really effectively reduce PM 2.5 damage. Therefore, it is necessary to adhere to the pilot work of ETS, further improve and enrich the connotation and scope of the ETS. It also has important reference value for other countries outside EU, especially for developing countries. Finally, we should to know that the prerequisite for environmental regulation to produce economic or environmental effects is the effective implementation of policy tools. The effectiveness of the effects of the ETS is also related to differences in economic characteristics such as resource endowments and regional development levels. At the same time, the government should focus on improving the supporting policies and infrastructure for the operation of the ETS to fully activate the emissions trading market.
This research still has certain shortcomings. This paper examines the EU ETS policy and its effects from the national level; however, compared with the country as the main body of PM 2.5 emissions, various industries, especially different types of enterprises, and even different types of lifestyles, should be directly studied and analyzed, we believe that the conclusion of the analysis will be more objective and universal. In addition, although this paper discusses the possible ways that ETS affects PM 2.5 emission reduction, due to space and data, this paper does not construct an analysis model for further testing. Meantime, as we know, there is no policy that has no costs and only benefits, and the same is true for EU ETS. There are also potential risks and negative effects in the implementation of EU ETS, such as more serious negative impact on the new Member States' economies, potential welfare loss, and carbon leakage (Brink et al. 2016;Cludius et al. 2020). Future research needs to emphasize a cost-benefit analysis and in-depth analysis of its impact on PM2.5 damage reduction. At last, as mentioned above, the effectiveness of the effects of the ETS is also related to differences in economic characteristics, subsequent research can supplement the analysis of heterogeneity in the empirical research section to verify the role of spatial heterogeneity in ETS's impact on PM2.5 damage. We believe that when the data is available in the follow-up research, the above discussions of this research can be further explored in order to obtain stronger evidence.