Double Effects of Environmental Regulation on Carbon Emissions in China: Empirical Research Based on Spatial Econometric Model

,is paper theoretically analyzes the direct impact of environmental regulation on carbon emissions and its indirect effects on carbon emissions through foreign direct investment (FDI), energy consumption, industrial structure, and technological innovation.,en, this paper constructs a spatial lag model to empirically test the dual effects of environmental regulation on carbon emissions based on the provincial panel data of 2003–2017 in China. ,e results show that the average Moran’s I value of carbon emissions during 2003–2017 is 0.2506, passing the significance test at 1% level, and carbon emissions have spatial correlation characteristics. ,e direct impact of environmental regulation on carbon emissions is significant and positive. Environmental regulation could indirectly influence carbon emissions by influencing FDI, energy consumption, and technological innovation, and meanwhile, FDI, energy consumption, and technological innovation help to reduce carbon emissions under the constraint of environmental regulation, specifically. However, the impact of environmental regulation on carbon emissions through industrial structure is not significant.


Introduction
China is a major emitter of carbon pollution. In order to address the increasingly serious climate change issues, the government has promised to reduce the CO 2 per unit of GDP by 40%∼50% in 2020 compared to that of 2005, and the emission is estimated to peak in 2030 [1][2][3]. erefore, the country absorbs more stringent environmental regulation policy for the transition from the environmental-unfriendly extensive development mode to the green development mode [3][4][5]. e Chinese government has promulgated a number of laws and regulations, including the " ree-Year Action Plan to Win the Blue Sky Defense War" and the "Water Pollution Prevention Action Plan" in 2018 [6]. e total investment in environmental pollution control increased from 116.6 billion yuan in 2001 to 953.9 billion yuan in 2017; there were 186,000 yuan penalty for environmental pollution in the country, with fines of 15.28 billion yuan in 2018, which is 1.32 times that in 2017 and 4.8 times that in 2014 when the new Environmental Protection Law was implemented [6].
Does stricter environmental regulation play a role in reducing carbon emissions? is issue has received extensive attention and heated discussion from the academic circles. Some scholars believe that more stringent environmental regulation will force enterprises to carry out technological innovation, which can not only reduce carbon emissions, but also promote economic growth [7][8][9][10][11][12][13]. Some scholars point out that strict environmental regulation may increase business costs and weaken the competitiveness of enterprises [14][15][16][17][18][19][20]. How does environmental regulation affect carbon emissions in China? Does environmental regulation directly reduce carbon emissions or indirectly affect carbon emissions through other factors? Bearing these questions in mind, the purposes of this study can be divided into three parts. First, the theoretical framework of indirect effects of environmental regulation on carbon emissions is built. Second, the spatial data analysis technology is used to analyze the spatial correlation between environmental regulation and carbon emissions to test the spatial spillover characteristics of the two. ird, spatial econometric model is used to test the direct and indirect effects of environmental regulation on carbon emissions.
is paper attempts to extend the existing research from two aspects. First, when analyzing the impact of environmental regulation on carbon emissions, this article not only analyzes the direct impacts, but also further analyzes the indirect effect of environmental regulation on carbon emissions through FDI, energy consumption, industrial structure, and technological innovation, which is more comprehensive than previous studies that only considered the direct relationship between the two. e second is the introduction of spatial econometric methods in this paper, which takes into account the spatial correlation characteristics of research variables, making the research conclusions more robust.

Direct Effect of Environmental Regulation on Carbon
Emissions. Environmental regulation refers to discharge permit system, administrative penalties, and emission taxes put forward by government to adjust the production and business activities of manufacturers in order to achieve the sustainable environment and economic development [21]. Environmental regulation is the most effective way to protect resources and control pollution, and it is very important for China to realize energy-saving and emissionreduction targets which construct a rational environmental regulation policy system [7,8]. Huang and Xiu found that environmental regulation had an important impact on regional emissions reduction [9,10]. Hampf and Rødseth analyzed the economic effects of implementing EPA's newly proposed regulations for carbon dioxide (CO 2 ) on existing US coal-fired power plants, by using nonparametric methods on a sample of 144 electricity generating units, and found that, by adopting best practices, current profits could be maintained even if an intensity standard of 0.88 tons of CO 2 per MWh was implemented [11]. Huang showed that environmental regulation had an inverted "U"-shaped impact on the efficiency of energy conservation and emission reduction [12]. Zhang et al. indicated that environmental policies helped to achieve the objective of reducing carbon emissions [13].
However, some scholars have found that environmental regulation offers no reward for conducting pollution prevention and creates "green paradox," which means that a gradual expansion of demand-reducing public policies, such as increasing ad valorem taxes on carbon consumption and increasing subsidies for replacement technologies, may exacerbate the problem as it gives resource owners the incentive to avoid future price reductions by anticipating their sales [14]. Gani pointed out the significant negative correlation between the level of legal regulation and CO 2 emission [15]. Werf and Maria explored that climate policies typically reduced oil demand only in some geographic areas [16]. Grafton et al. used energy data over the period of 1981-2011 and found that US biofuels subsidies and production had provided a perverse incentive for US fossil fuel producers to increase their rate of extraction that had generated a weak green paradox [17]. Allaire and Brown explored that the subsidies for ethanol increased greenhouse gas emissions, while those for biodiesel had an ambiguous effect [18]. Sterner et al. considered several factors that affected the implementation of environmental regulation policy and product green paradox, including potential spatial carbon leakage to countries [19]. Shao et al. believed that the introduction of renewable energy sources intensified the promotion effect of R&D efficiency as a result of the "green paradox" effect [20].
In addition, some scholars believed that the relationship between the two is uncertain. Wang et al. thought that the impact of environmental regulation on carbon emissions had a threshold effect [22]. Liu et al. suggested that the impact of environmental regulation on environmental pollution was nonlinear [23]. e effect of regulations on carbon emissions was inconsistent [24]. Environmental regulation may have a direct effect on regional carbon emissions, and this effect may be positive and may also be the recurrence of green paradox. Based on the above literature, this paper proposes the following hypothesis: Hypothesis 1. Environmental regulation has a direct impact on regional carbon emissions.

Indirect Effects of Environmental Regulation on Carbon
Emissions. Environmental regulation would not only have a direct impact on carbon emissions, but also exert an indirect impact through four transmission channels of the energy consumption structure, industrial structure, technological innovation, and FDI [21].

Environmental Regulation, FDI, and Carbon
Emissions.
e introduction of FDI may lead to "pollution halo" effect or "pollution heaven" effect, which may lead to "forced effect" or "reverse effect" of environmental regulation on regional emission reduction. "Pollution halo" effect holds that foreign-invested enterprises with advanced technologies can deliver green and clean production technologies to enhance environmental protection in production, and thus reduce carbon emissions of the host country [25]. If foreign firms do transfer advanced technology and management know-how to domestic firms, they will thereby help to reduce industrial pollution in developing countries since they are generally believed to be cleaner than the domestic counterparts [26]. e pollution heaven hypothesis (PHH) posits that production within polluting industries will shift to locations with lax environmental regulation [27]. In the light of heavy economic performance as the target function, the local government has to relax the environmental regulation in order to fight the mobility factor motivation [28]. Chung, Chung, and Zhou et al. found strong evidence that polluting industries tended to invest more in countries with laxer environmental regulation [29][30][31]. Xu et al. explored the relationship among FDI, environmental regulation, and energy consumption and showed that environmental regulation had a negative effect on FDI in both the long and short term [32]. Based on the above literature, this paper proposes the following hypothesis: Hypothesis 2. Environmental regulation will indirectly affect regional carbon emissions by affecting FDI.

Environmental Regulation, Energy Consumption, and
Carbon Emissions. Strengthening the implementation of environmental regulation is one of the key measures to prevent further energy depletion and environmental deterioration [33]. Zhang, Zhang, and Dirckinck-Holmfeld also believed that the intensity of environmental regulation usually affected the energy consumption [34][35][36]. Zhou et al. discovered that the introduction of regulations would actually curb air emissions and energy consumption [37]. e increasingly intensified environmental regulation will intend to promote corporate change from passive management to active control and from end-of-pipe treatment to cleaner production [38]. As mentioned above, the implementation of government environmental regulation is forcing the enterprises to use emission reduction technologies and clean energy to reduce the demand for high carbon energy and optimize energy consumption structure, which will ultimately reduce energy consumption and carbon emissions. However, the response of energy owners to environmental regulation increases the use of high carbon energy [21]. Zhou and Feng found that energy-saving effects of environmental regulation in China were dynamic and yielded complex results of the "green paradox" and "compliance cost" [33]. Chen and Gong integrated the coupling effects of environmental regulation on energy consumption intensity and energy consumption structure and revealed that energy efficiency policy intensity was not the major effect on the development of low or moderate energy consumption industries [39]. Research shows that the effects of environmental regulation on energy consumption are double-sided. It may lead to low-carbon energy consumption as well as high carbon energy consumption. erefore, the result of using environmental regulation to affect carbon emissions by adjusting the energy consumption structure is also double-sided, which may reduce or increase carbon emissions. Based on the above literature, this paper proposes the following hypothesis: Hypothesis 3. Environmental regulation will indirectly affect regional carbon emissions by affecting energy consumption.

Environmental Regulation, Industrial Structure, and
Carbon Emissions. Environmental regulation has become one of the most important driving forces underlying sustainable development and the transformation of the pattern of economic development [40]. Environmental regulation expenditures have statistically significant effects on the probabilities of a company's capacity moving to a larger company-size category, so industry structure is affected by environmental regulation [41]. However, the impact of environmental regulation on industrial transformation presented a comparison of distortion effect of resource allocation and technology effect [42]. Environmental regulation will promote industrial transformation when technology effect of environmental regulation is stronger than distortion effect of resource allocation [42]. Particularly, command-control environmental regulation has a significant incentive effect and spillover effect of technological innovation on cleaning industries, but these effects do not exist in pollution-intensive industries [42]. Gao et al. showed that environmental regulation manifested through constraining the entrance of enterprises into the pollution sectors and encouraging high-efficiency technologies has resulted in the optimization of manufacturing industries and the productivity improvement in Wuxi, which also countered the negative impact of rising production costs brought by regulation [40]. Yuan and Xie believed that formal environmental regulation can effectively drive industrial restructuring and can be used as a new impetus for carbon emissions [43]. Zhong et al. revealed that environmental regulation forced the adjustment of the corporate behavior caused by the rising price of pollution-producing factors, which will drive the transformation of the polluting industry to the direction of the low carbon [44]. Azzam et al. developed a comparative statics model of long-run industry equilibrium in the presence of size-based environmental regulation stringency and found environmental regulation has different effect on different sizes of companies [45]. Zhang and Xu found that, compared with technical progress, environmental regulation impacts carbon productivity more significantly [46]. Based on the above literature, this paper proposes the following hypothesis: Hypothesis 4. Environmental regulation will indirectly affect regional carbon emissions by affecting industrial structure.

Environmental Regulation, Technological Innovation, and Carbon Emissions.
A general conclusion is that aggregate policy feedback mechanisms tend to make current climate policies much less effective than is generally assumed. In fact, various policy measures involve a definite risk of "backfiring" and actually increase carbon emissions [47].
is risk is particularly pronounced once effects of climate policies on the pace of innovation in climate technology are considered. Lee examined the effect of environmental regulation on green technology innovation through the supply chain integration, using a multi-industry sample of manufacturing organisations, and found that environmental regulation has an important effect on green technology innovation. Ma et al. explored that environmental regulation can motivate coal enterprises' technology innovation by adding variable [48]. Sun et al. found that the short-term decision of enterprise technological innovation was influenced by the additional cost caused by the environmental regulation, and the long-term decision of enterprise was technological innovation [49]. Chen and Xu Discrete Dynamics in Nature and Society showed that environmental regulation has a significant positive effect on research expenditure [50]. Du and Peng explored that the environmental regulation intensity positively moderated the relationship between both of related technological diversification, unrelated technological diversification, and firm's technological innovation performance [51]. Guo et al. discovered that environmental regulation positively influenced technological innovation [52]. Environmental regulation has an important impact on enterprise green technological progress [53,54]. en, technological innovation is an important factor impacting carbon emissions, and environmental regulation can effect carbon emissions through technological innovation. Zhang et al. revealed that China's current environmental regulation has not yet been able to effectively reduce carbon emissions by promoting technological innovation [55]. Huang and Xie explored that only when technological innovation level is between the first and second threshold value can stringent environmental regulation improve total factor energy efficiency [56]. Lu and Feng revealed that the environmental regulation does not produce significantly direct impact on carbon emissions performance, but in the lag of 1-3 years; environmental regulation has a significantly indirect effect on carbon emissions performance through technology progress, and this effect is higher than the technological progress itself [57]. Tang et al. found that environmental regulation significantly and positively influenced technological innovation, and technological innovation has a positive impact on regional green growth performance [58]. Wang et al. discovered that environmental regulation regulated the relationship between technological innovation and carbon emissions [59]. Based on the above literature, this paper proposes the following hypothesis: Hypothesis 5. Environmental regulation will indirectly affect regional carbon emissions by affecting technological innovation.

Model Building.
e spillover characteristic of carbon emissions in space has been proven by many scholars, which should not be ignored when analyzing the relationship between environmental regulation and carbon emissions [3,5,[60][61][62][63][64]. So, this paper will use spatial metrological method to study the impact of environmental regulation on carbon emissions. e spatial econometric model has three advantages: it can visually present the spatial distribution characteristics of social issues firstly, then, it considers the dynamic characteristics of various influencing factors, and it can use the spatial econometric method to regress when analyzing the influencing factors on social issues, and the results are more robust [65]. According to the research of Anselin, classical spatial metrological model includes spatial lag model (SLM) and spatial error model (SEM). e direct effects of environmental regulation on carbon emissions by the SLM and SEM model can be expressed as equations (1) and (2): where wlnCO 2 is spatial lag variable; ρ is the spatial autoregressive coefficient; λ is spatial error autoregressive coefficient; w is the spatial weight matrix; lnER denotes urbanization level; and lnX represents the collection of control variables. In the spatial econometric model, the spatial weight matrix(w ij ) reflects the spatial connection between variables, representing the neighboring relations between the area i and the area j. is paper establishes the spatial weight matrix based on spatial adjacency relation, which is expressed as follows [66]: In order to analyze the indirect influence of environmental regulation on carbon emissions, this paper introduces the cross terms of environmental regulation and energy consumption structure, industrial structure, technological innovation, and FDI to explore the effects of the four factors on carbon emissions. e SLM and SEM models can be expressed as equations (3) and (4): ln CO2 it � ρw ln CO2 it + θ 0 + θ 1 ln ER it * ln fdi it + θ 2 ln ER it * ln fdi it + θ 3 ln ER it * ln ec it + θ 4 ln ER it * ln ic it + θ 5 ln ER it * ln tec it + θ 6 ln X it + ε i . (4) ln CO2 it � ω 0 + ω 1 ln ER it * ln fdi it + ω 2 ln ER it * ln fdi it + ω 3 ln ER it * ln ec it + ω 4 ln ER it * ln ic it Where lnfdi means foreign direct investment, lnec expresses energy consumption, lnic denotes industrial structure, and lntec represents technological innovation. In addition, economic growth is an important factor that leads to environmental degradation and increases carbon emissions [3,67]. Based on the research results of Grossman and Krueger and Gani, who believe that there is an inverted U-shaped relationship between economic growth and environmental pollution, gdp and its square term are considered as control variables in the model [15,68]. e increasing of urban population has led to urban expansion and industrial agglomeration, which will increase the consumption of petrochemical energy and carbon emissions, and population is considered in the model [69]. 4 Discrete Dynamics in Nature and Society

Carbon Emissions.
Carbon emissions are mainly calculated by the method of Intergovernmental Panel on Climate Change (IPCC). Since fossil energy consumption is the main source of carbon emissions, this paper computes the carbon emissions in light of the energy consumption data of the provinces over the years. According to the China Energy Statistical Yearbook, there are ultimately 9 major categories of energy consumption, which includes coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, natural gas, and electricity [3]. Electricity is produced through the consumption of other types of energy, which is not computed to avoid duplication, and the total energy consumption of the eight types of energy is multiplied by the respective carbon emissions coefficient [3]. e formula is as follows: where C it is the total CO 2 emission of province i in year t; E ijt is the consumption of the j-th type of energy of province i in year t; and η j is the carbon emissions coefficient of the j-th type of energy.

Environmental
Regulation. e indicators of environmental regulation can be roughly divided into inputoriented indicators and performance-oriented indicators in the existing literature [5]. e former include pollution abatement costs, pollution control investment, frequency of supervision, and inspection and governmental expenditure on environmental protection, while the latter include sewage charges and emissions of major pollutants [5,50,57,64,70,71]. is paper focuses on investigating the intensity of environmental regulation of each region, referencing the practice of Li and Zhang, Zhang, and Zhang, and the amount of investment in the pollution control in each region is selected to measure environment regulations [5,64,70].

Other Variables.
Referring to the study of Zhang, Sun et al., and Ding et al., energy consumption is measured by total energy consumption at the end of the year for each region, and FDI is measured by the amount of the actually used foreign capital [5,72,73]. e data of FDI on the yearbook are measured in US dollars, and they are converted into the amount in RMB according to the annual average exchange rate of the year [72]. Learning from Li and Wang and Yang et al., industrial structure is measured by the proportion of the secondary industry in the total industrial output. [74,75] Drawing lessons from Liu and Feng and Zhang, technological innovation level is measured by the ratio of R&D expenditure to GDP for each region [64,70]. According to Gani, Zhang, and Zhang, Gross Domestic Product (GDP) is indicated by actual GDP per capita, and population size is indicated by population density of each region [13,15,21].  Table 1. Table 2  ere exists obvious spatial dependence, which means significant spatial spillovers and spatial agglomeration effects exist between regional environmental regulation and carbon emissions. e paper uses Moran scatterplots to further test the spatial correlation between environmental regulation and carbon emissions. Meanwhile, the numbers of the scattered points of carbon emissions in the three years locating in the first and the third quadrants are 17, 17, and 18, which indicates that significant spatial autocorrelation exists between environmental regulation and spatial distribution of carbon emissions.

Model Selection.
Before the empirical study, SLM and SEM models are compared and the results are shown in Table 3. e analysis results show that both the SLM and SEM models pass the significance test, while the spatial lag characteristics of the model are more significant than the spatial error characteristics; finally, the spatial lag model is chosen to conduct the empirical research. Furthermore, according to the Hausman test, the test value is 7.7822, degrees of freedom value is 17, and does not pass the significance test, demonstrating that the fixed effect model is superior to the random effect model. erefore, the fixed effect SLM model is selected to start the empirical analysis.
Discrete Dynamics in Nature and Society

(1). Direct Effect of Environmental Regulation on Carbon
Emissions. Table 4 shows the direct effect of environmental regulation on carbon emissions. e Adjusted R 2 value is 0.9050 and the log likelihood value is 35.3657, which shows the model fits well.
First, carbon emissions have significant spatial correlation characteristics, and the level of carbon emissions in the region will affect the level of carbon emissions in surrounding areas. Table 4 shows that the spatial lag coefficient ρ value which is used to detect the special effect of carbon emissions is 0.242996 and has passed the significance test of 1%, which means carbon emissions have significant spatial positive correlation characteristics, and when carbon emissions of surrounding area increase by 1%, the carbon emissions in the region will increase by 0.242996% in average under the control of other influencing factors. e results of this study are consistent with Yang et al.; the existence of space spillover phenomenon of carbon emissions is proved again, so are the correctness and necessity of choosing a spatial measurement model [3]. e space spillover phenomenon of carbon emissions is attributed to the natural geographical reasons and socioeconomic factors [42,60]. Natural factors such as wind direction and rain will spread carbon emissions to the surrounding areas, which lead to carbon emissions of the surrounding area to be affected by the area [76]. In addition, industrial transfer as an important socioeconomic factor has led to heavy polluting industries transferring from east to middle and west region, which has enhanced the spatial correlation of regional carbon emissions.
Second, the relationship between environmental regulation and carbon emissions is positive and significant. As can be seen from Table 4, the coefficient of environmental regulation and carbon emissions is 0.081296, which meets the demand of significance test, showing that the correlation between environmental regulation and carbon emissions is significant. e correlation coefficient between them is positive, indicating that strengthening of environmental regulation leads to the increase of carbon emissions, which supports the opinion of Sinn, Allaire et al., and Zhang et al., that green paradox phenomenon happens, and the response of the suppliers to environmental regulation makes energy owners speed up the exploitation and thus aggravate energy consumption, resulting in the increasing of carbon emissions [13,14]. A large-scale hidden economy exists in China; the increasingly intensified environmental regulation in China will expand the scale of the hidden economy, thereby raising the overall level of pollution [77]. With the strengthening of the government's environmental regulation, in order to save production costs, companies tend to gradually shift export production to hidden economic sectors where there is less government supervision [78]. Because the pollution emissions of hidden economic sectors are not controlled, the overall pollution emission level has risen. Based on the above, it is said that environmental regulation has a direct impact on regional carbon emissions and Hypothesis 1 is confirmed.
In addition, FDI, energy consumption, and technological innovation are important factors affecting carbon emissions, and all of them pass the significance test at the 1% level. According to the values of regression coefficient, FDI and technological innovation are conducive to reducing carbon emissions, while energy consumption increases carbon emissions [79]. e impact of industrial structure on carbon emissions is not significant. e linear term of GDP per capita is positively related to carbon emissions while the quadratic term of GDP per capita is negatively related to carbon emission; both of them do not pass the significance test, which shows that there is not an inverted U relation  Discrete Dynamics in Nature and Society between GDP per capita and carbon emissions. ere is a positive but not significant correlation between regional population and carbon emissions.
(2). Indirect Effects of Environmental Regulation on Carbon Emissions. Table 5 shows the indirect effects of environmental regulation on carbon emissions. is paper gradually adds the cross terms of environmental regulation and FDI, energy consumption, industrial structure, and technological innovation in models 1-4 of Table 5 to observe how environmental regulation indirectly influences carbon emissions through those four ways. Regarding the adjusted R 2 values and log likelihood values of models 1-4, those models fit well.
First, the cross term of environmental regulation and FDI has negative impact on carbon emissions, and all coefficients in models 1-4 pass the significant test of 1%. It is shown that FDI helps to reduce carbon emissions under the constraint of environmental regulation, which to some extent confirms the existence of "pollution halo" effect [32]. Foreign enterprises with advanced technology can transfer   Note: * * * , * * , and * indicate the significance at 1%, 5%, and 10% level, respectively. Note: * * * , * * , and * indicate the significance at 1%, 5%, and 10% level, respectively.
Discrete Dynamics in Nature and Society more green and clean production technology to the host country under the constraint of environmental regulation, enhancing environmental protection, and thus reduce carbon emissions of host country [21]. Meanwhile, by raising the level of environmental regulation, the government plays a role in preventing pollution-intensive industries of the developed countries from entering the market and forcing foreign companies to flee form the Chinese market, which helps prevent the host country from becoming the "pollution heaven" of developed countries [32]. e results show that environmental regulation indirectly affects regional carbon emissions by affecting FDI, which confirms Hypothesis 2, and supports the views of Ong [25]. Second, the cross term of environmental regulation and energy consumption is positively related to carbon emissions. As Table 5 shows, the correlation coefficients are 0.0873, 0.0818, and 0.0968 in models 2-4, which are statistically significant at the 1% level indicating that energy consumption is the main cause of the increase of carbon emissions. Firstly, the situation of "rich in coal and poor in oil" determines the domination of the coal in energy consumption structure in China, which is difficult to change in the short term, and restricts the reduction targets [5]. en, compared with fossil energy, the cost of clean energy is high and is not easy to establish a complete market trading system, leading to the domination of fossil energy in the market [5,13].
However, comparing the direct impact coefficient of energy consumption on carbon emissions which is 1.016869 in Table 4 and the cross term coefficients of environmental regulation and energy consumption in Table 5, it is found that the latter is much smaller than the former, which means that the role of energy consumption in promoting carbon emissions has been weakened under the constraints of environmental regulation. e introduction of environmental regulation helps enterprises to introduce low-carbon production processes and cleaner production technologies to reduce energy consumption and ultimately reduce carbon emissions [36][37][38]. erefore, environmental regulation could indirectly affect regional carbon emissions by affecting energy consumption, which confirms Hypothesis 3. ird, the cross term of environmental regulation and industrial structure on carbon emissions is not significant. e correlation coefficients of the cross terms from models 3 and 4 are 0.0164 and -0.0045, respectively, failing to pass the significance test, which means that the impact of industrial structure on carbon emissions is not significant under the constraints of environmental regulation. erefore, environmental regulation cannot indirectly affect regional carbon emissions by affecting industrial, which is unable to prove Hypothesis 4. e main reasons for this result are as follows. Environmental regulation has an important stimulating effect on technological innovation and technology spillovers in clean industries, but the effect is limited confined within highly polluting industries [42,45]. Simultaneously, environmental regulation leads to higher prices of production factors and higher production costs for polluting enterprise; only when the environmental regulation reaches the threshold can it drive the transfer of polluting industries to low-carbon industries [41,46]. Fourth, the cross term coefficient of environmental regulation and technological innovation on carbon emissions is −0.0558 in model 4 and passes the significance test at 1% level, which indicates that technological innovation can effectively suppress carbon emissions under the restriction of environmental regulation. erefore, environmental regulation could indirectly affect regional carbon emissions by affecting technological innovation where Hypothesis 5 is confirmed. By comparing the direct impact coefficient of technological innovation on carbon emissions and the coefficient of the cross term of environmental regulation and technological innovation, it can be found that the former, −0.137021, is much smaller than the latter, −0.0558. Environmental regulation has cost effect and compensation effect on technological innovation, where cost effect means environmental regulation will increase the pollution management cost of an enterprise, and compensation effect means that enterprises will improve their production processes and improve their pollution control capabilities Note: * * * , * * , and * indicate the significance at 1%, 5%, and 10% level, respectively. 8 Discrete Dynamics in Nature and Society through optimizing the production process and increasing productivity and ultimately reduce or offset the environmental costs that the government's environmental regulation adds to the enterprise [80]. From the above, it can be found that environmental regulation has played a compensation effect on technological innovation.

Robustness Test.
is paper uses the ratio of investment in pollution treatment to GDP as the proxy for environmental regulation and analyzes the direct and indirect effects of environmental regulation on carbon emissions again to perform the robustness test. e test results are shown in Table 6. As shown in Table 6, although the cross term of environmental regulation and industrial structure on carbon emissions is more significant than the above results, the direct and indirect effects results between environmental regulation and carbon emissions are basically coincident with the above results; namely, environmental regulation has significant direct impact on carbon emissions, and environmental regulation also can indirectly influence carbon emissions by influencing FDI, energy consumption, and technological innovation.

Conclusions
Based on the panel data of 30 provinces in China from 2003 to 2017, this paper systematically analyzes the direct and indirect effects of environmental regulation on carbon emissions. First, the average Moran's I value of carbon emissions during 2003-2017 is 0.2506 and passes the significance test at 1% level, implying that there is a significant spatial correlation and cluster effect of carbon emissions, which means the level of carbon emissions in the surrounding areas will affect the level of carbon emissions in this region. Second, the direct relationship between environmental regulation and carbon emissions is positive and significant, indicating that environmental regulation has exacerbated regional carbon emissions in China. ird, the cross terms of environmental regulation and FDI, energy consumption, and technological innovation have significant impact on carbon emissions, which implies environmental regulation could indirectly influence carbon emissions by influencing FDI, energy consumption, and technological innovation. Specifically, FDI, energy consumption, and technological innovation help to reduce carbon emissions under the constraint of environmental regulation. However, the cross term of environmental regulation and industrial structure on carbon emissions is not significant.
Based on the results of this study, the following recommendations are provided. First, based on the space spillover characteristics of carbon emissions, the government should firstly identify the spatial agglomeration characteristics of China's carbon emissions in carbon emission management and adopt different governance strategies for different agglomeration areas. At the same time, because the level of carbon emissions in the region will impact the carbon emissions of surrounding areas, the government should seek cross-regional cooperation in the process of carbon emissions governance. Second, while strengthening environmental regulation, the government should intensify the management on hidden economies, so as to prevent and control highly polluting industries from shifting to hidden economies for the sake of circumventing environmental regulation. ird, full consideration should be given to the differential impact of FDI, energy consumption, and technological innovation when formulating environmental regulatory policies. It is necessary to formulate different policies for the full play of environmental regulation in reducing carbon emissions by affecting regional FDI, energy consumption, and technological innovation.
is paper systematically analyzes the direct and indirect effects of environmental regulation on carbon emissions, but it still has the following limitations. First, environmental regulation could affect carbon emissions through many factors, from which this paper only considers the four key elements of FDI, energy consumption, industrial structure, and technological innovation, and other factors such as fiscal decentralization would be studied in future research. Second, in the selection of the spatial econometric model, although the classic spatial lag model is selected in this paper, future research would choose different spatial models, such as the spatial error model and the spatial Durbin model.

Data Availability
e data used to support the findings of this study have been deposited in [https://pan.baidu.com/s/ 1iQf4fH2Eqe75BbA5GWfLXg].

Conflicts of Interest
e authors declare that they have no conflicts of interest.