How does manufacturing haze pollution decrease in China: a decomposition study of structural model based on general equilibrium framework

Based on the annual mean PM2.5 concentration data of 30 provinces and cities in China from 2006 to 2020, this paper constructs a structural model of manufacturing haze pollution, expounds the main mechanisms affecting haze pollution, then statistically decomposes the main factors affecting the change of pollution emissions, and examines the direct and indirect impact paths of the change of haze pollution emissions in China. The study found that (1) the inhibitory effects of latent variables on manufacturing haze pollution is from strong to weak in order: industrial structure upgrading, environmental regulation, trade opening, productivity improvement, and economic scale expansion, while the optimal path for the indirect effect of exogenous latent variables on haze pollution is to rely on environmental regulation and opening up to achieve the improvement of productivity, so as to achieve the purpose of reducing haze pollution. (2) The analysis based on the PVAR model found that industrial structure adjustment is the key factor of haze decline in both the short and long term. Environmental regulation has an obvious effect on haze control in the short term, but in the long run, it still needs to rely on industrial structure adjustment, production efficiency improvement, and trade opening to achieve the goal of reducing haze. (3) There is an inverted U-shaped nonlinear relationship between output scale and environmental regulation. In addition, trade openness has a long-term effect on productivity. Technology spillovers from opening up can reduce haze pollution in the long run by improving productivity. (4) The environmental regulation policy in the central region is characterized by “race to the bottom,” while the eastern region shows the characteristic of “race to the top” in the policy game of improving productivity and optimizing the industrial structure. Therefore, haze control requires an appropriate intensity of environmental regulation to reduce the proportion of high pollution and high energy consumption industries. Make full use of the international cooperation platform of the “the Belt and Road Initiative” and the pilot free trade zone to promote substantive cooperation between Chinese enterprises and developed countries in the field of environmental protection technology, increase investment in research and development of clean equipment and cleaner production technology, improve productivity, help China’s green manufacturing, and contribute Chinese wisdom and Chinese solutions to global environmental governance and climate change.


Introduction
Over the past 40 years since China's reform and opening up, the rapid development of manufacturing industry has provided important material guarantee for China's rise, but also brought serious environmental problems. In particular, the full outbreak of haze has not only seriously affected public health, but also caused great social and economic losses. At present, the ecological environment problem is a prominent manifestation of China's unbalanced and uncoordinated development and has become an important constraint to meet the growing needs of the people for a better life. According to the "statistical bulletin of national economic and social development in 2021" issued by the National Bureau of statistics of China, among the 338 cities at and above the prefecture level monitored, 35.8% of the cities with urban air quality up to the standard and 64.2% of the cities without the standard. Haze is not only a phenomenon of environmental pollution, but also a phenomenon of industrial production. From an economic point of view, the composition of haze is actually the waste of industrial production. According to the calculation of the environmental protection department, 65% of the haze pollution comes from the extensive production of the manufacturing industry. "Made in China 2025," as the action plan for the first decade of China's implementation of the manufacturing power strategy, clearly points out that green manufacturing should be fully implemented. The Ministry of Industry and Information Technology of the People's Republic of China has successively issued the "industrial green development plan (2016-2020)" and the "guidelines for the implementation of green manufacturing projects (2016)(2017)(2018)(2019)(2020)," which put forward clear goals and tasks for the control and emission of air pollutants. However, haze pollution has the characteristics of complexity and protracted nature. There is interaction and coupling effect of haze pollution in different regions, which increases the difficulty of joint prevention and control of pollution control in haze regions. Therefore, China's air pollution problem is still serious and haze pollution control still shoulder heavy responsibilities. Based on this, it is of great practical significance to clarify the dynamic mechanism that affects haze pollution decrease. In order to better realize the "win-win" of environment and economy, this paper brings the exogenous factors and endogenous factors that affect haze pollution into a unified framework for discussion. Based on the general equilibrium model of haze pollution emissions, the main factors affecting the change of manufacturing pollution emissions are statistically decomposed, and the direct and indirect influence paths of each factor are clarified. Then, the panel vector autoregression model and spatial Durbin model are used to identify the mechanism of spatial competition under China's unique government behavior model. This paper provides proof and decision-making reference for accelerating the transformation of industrial development mode and realizing high-quality economic development while breaking through the constraints of resources and environment.

Studies on the sources of haze pollution
The existing literature on haze pollution mainly focuses on its hazards, regulations, causes, and other fields.
There have been a lot of theoretical research and empirical evidence on the harm caused by haze pollution, mainly including the following three aspects: (1) haze pollution has caused direct harm to human health (Xie et al. 2014), such as reducing life expectancy (Ebenstein et al. 2017), increasing the probability of obesity (Deschenes et al. 2020), and so on. (2) The haze pollution has produced many negative impacts on the economic and social development, such as affecting the decision of population migration and causing inequality in regional development (Chen et al. 2017; and is not conducive to the improvement of the industrial structure (Yu et al. 2021). (3) The haze pollution has produced various negative impacts on the production and operation of enterprises and other microeconomic entities, such as changing the earnings management system of enterprises (Liu and Liu 2015), causing enterprises to overstock their inventories (Li and Li 2017), increasing the labor cost of enterprises (Shen et al. 2019), and reducing the productivity of enterprises (Fu et al. 2021).
There is no unified conclusion on the effectiveness evaluation of haze regulation in the existing literature. Some scholars believe that government regulation will effectively reduce the spread of haze and promote the decoupling of haze. For example, Baksi and Bose (2010) analyzed the effectiveness of the haze regulation policy. Elgin and Mazhar (2013) also confirmed this view through empirical research and pointed out that there is a threshold for the intensity of haze regulation, which needs to reach a certain degree to effectively reduce haze pollution. Some scholars also believe that the smog regulation policy is ineffective. For example, Davis (2008) pointed out that the regulation measures cannot improve the air quality. Bagayev and Julie (2016) reached the conclusion that environmental regulation cannot alleviate pollution in the study of EU. Huang (2016) established a theoretical model based on the shadow economy. Through empirical research, it was found that environmental regulation had no significant impact on haze pollution, and the shadow economy would aggravate haze pollution.
Existing studies on the sources of haze pollution mainly focus on three explanations: structural adjustment, environmental regulation, and technological progress. Among them, structural adjustment includes two levels, one is the adjustment of industrial structure, and the other is the adjustment of energy structure. He (2015) and  found that the coal-dominated energy consumption structure is an important incentive for haze concentration, and significantly reducing the proportion of coal in energy consumption and optimizing the structural proportion of China's high energy consumption and high pollution industries can effectively alleviate haze pollution (Wei and Ma 2015). Some studies directly attribute changes in national air quality to environmental regulations. For example, Chay and Greenstone (2005) and Correia et al. (2013) found that a significant decrease in total suspended particulate pollutants in cities following the enactment of the Clean Air Act. Zhang and Wei (2014) believe that environmental regulation can not only directly affect pollution emissions, but also indirectly affect pollution emissions through structure, technology, and other ways. In view of haze, a special form of air pollution, Chen and Wu (2018) found that environmental protection tax is a powerful tool to control haze. There are also studies that suggest that if enterprises make technological progress, such as using less input to produce the same output every year or improving the level of clean technology, the air quality will be improved. The improvement of production efficiency caused by technological progress can alleviate the increase of pollution caused by the expansion of output scale to a certain extent, and the improvement of clean energy technology can effectively consolidate the policy effect of pollution control (Ehrlich and Holdren 1971;Yuan and Xie 2015;Wei et al. 2016). In addition, some scholars have decomposed the sources of air pollution and analyzed the factors affecting the change of pollution emissions from the perspectives of scale, structure, and technology (Grossman and Krueger 1991;Hamilton and Turton 2002;Cheng et al. 2008;Guo et al. 2013).
The above research provides us with profound insights into the impact of haze pollution in China's manufacturing industry. Based on the existing research, the innovation and marginal contribution of this paper are as follows: Firstly, this paper analyzes the influencing factors of pollution change based on the general equilibrium model of pollution emissions. On this basis, the cutting-edge structural model is used to explore the impact mechanism of haze pollution changes and provide reliable empirical evidence for a deep understanding and balance of haze control and the green transformation process of manufacturing industry. Secondly, this paper brings the exogenous factors (environmental regulation, trade and openness) and endogenous factors (economic scale, industrial structure) that affect haze pollution into a unified framework for discussion, decomposes the changes in pollution emissions, and comprehensively and systematically excavates the direct and indirect paths that affect pollution changes. Thirdly, local governments in China have deep and continuous intervention in the haze pollution and governance of manufacturing industry. Therefore, this paper uses panel vector autoregressive model and spatial Durbin model to identify the mechanism of spatial competition between local governments affecting haze pollution under China's unique government behavior mode, so as to provide a clear basis for formulating haze control policies.

Theoretical model
Based on Shapiro and Walker's method, this paper constructs a heterogeneous enterprise model to describe enterprise entry, production, trade, and pollution (Shapiro and Walker 2018). From this model, we can find the main factors that affect pollution emissions. This model assumes that there are only two countries in the world, and each country has an inelastic supply of production factors (labor). Due to the different productivity levels of enterprises, the investment and effect of these enterprises in reducing pollution emissions are heterogeneous.

Preference
Consumers in the destination country d have the following utility: Equation (1) describes the CES utility of different products within an industry and the Cobb-Douglas preferences of different industries. The distribution of spending by consumers in the destination country d among products depends on the measure Ω o,s for the s industry products produced in the origin country o. The parameter d,s is the expenditure share of the destination country d for industry s, where ∑ s d,s = 1 . The variable q od,s ( ) represents the quantity of various products in industry s shipped from the origin country o to the destination country d. Therefore, it can be understood that the consumption quantity of product depends on the production and trade costs in the origin country o, and a given product type is only produced in one country. The industry-specific parameter s > 1 represents the elasticity of substitution between different varieties. The CES utility hypothesis is a relatively common assumption, which means that consumers experience diminishing marginal utility from consuming a particular variety, while increasing utility in the total variety. (1)

Enterprise and market structure
Enterprises on the fringes of competition can choose to pay sunk costs f e o,s and enter the market and compete with productivity .When an enterprise decides to produce, a separate fixed cost must be paid, and the enterprises engages in monopolistic competition, which can maximize profits by choosing the price p od,s and reducing the investment proportion a.
In Eq. 2, od,s ( ) = p od,s ( )q od,s ( ) − o l od,s ( ) od,s − t o,s z od,s ( ) od,s − d f od,s . p od,s ( ) is the product price paid by consumers in destination country d to enterprise , then the sales revenue of each enterprise is p od,s ( )q od,s ( ) , while requiring l od,s ( ) units of labor to produce products for the destination country d at the wage level o . Part of this labor 1 − a is used for production, and the remaining part a is used to reduce pollution. Each enterprise pays a pollution tax t o,s per ton based on the number of tons of pollution z od,s ( ) emitted by the production of goods destined for the destination country d. Enterprises face the iceberg trade costs, so parameters are required od,s ≥ 1 . Enterprises that choose to enter the market of the destination country must pay a fixed cost f od,s (for domestic trade, oo,s = f oo,s = 1 ). In addition, it is assumed here that the productivity distribution is Pareto distribution, and its cumulative distribution function is: where b o,s is the productivity of industry s in the origin country o, and the parameter s describes the degree of dispersion of productivity within an industry s. For the sake of simplicity, this paper no longer considers the product category , and measures an enterprise with enterprise productivity . The enterprise's sales volume is as follows: It can be found in Eq. (4) that the unit output of the enterprise depends on the intensity of environmental regulation, that is, q od,s ( )∕l od,s ( ) = (1 − a( )) , when the intensity of environmental regulation is greater, enterprises allocate more investment to reducing pollution emissions a rather than production 1 − a . Therefore, it can be understood that environmental regulation can reduce the production scale of enterprises.

Pollution
Enterprises generate pollution emissions through the following equation: It is assumed here that environmental regulations are sufficiently stringent that all enterprises are reducing emissions to some extent. It is also assumed that s > s − 1 (1 − s ) , that is, the entrant has a finite expected profit. Then, Eq. (5) shows that pollution is an increasing function of output (production scale) and a decreasing function of emission reduction (environmental regulation). The pollution level of an industry here depends on the original attributes of each industry, which can reflect the production technology, inputs, or other characteristics of the industry. Polluting emissions in this model can also be described as another production factor in the Cobb-Douglas production technology. Solving for a and then substituting into Eq. (4), the Cobb-Douglas production function of total output with respect to pollution emissions and production factors is obtained: where represents the Cobb-Douglas share of polluting emissions. If it is assumed that industry s is the polluting industry in the country; then from Eq. (6), it can be known that the smaller the output of the polluting industry, the smaller the pollution emission. Therefore, the proportion of polluting industries (industrial structure) in the country also determines the pollution intensity of the country.

Competitive equilibrium
In the competitive equilibrium, the utility of consumers is maximized, the profits of enterprises are maximized, and the labor supply of each country is equal to the labor demand: Equation (7) shows that a country's labor supply L o has five distributional uses: paying fixed costs to gain productivity L e o , engaging in production and reducing pollution L

Comparative static analysis
In the above model, the effects of three shocks on pollution intensity are mainly considered: environmental regulation, productivity, and trade. Here, let i i o,s ( ) ≡ ∑ j z oj,s ( )∕ ∑ j q oj,s ( ) denote the pollution intensity of an enterprise with productivity , defined as pollutants emitted per unit of output. I o,s ≡ Z o,s P o,s ∕R o,s represents the pollution intensity of an industry, which is defined as the pollutants emitted per unit of actual output of the industry. P o,s represents the industry price index, Z o,s is the total emission (5) z od,s ( ) = (1 − a( )) 1∕ s l od,s ( ) Finally, let od,s denote the share of country d's spending on products of industry s purchased from country o. This indicator can also measure the degree of trade openness; that is, the larger the index value, the higher the degree of openness. Therefore, for an enterprise with productivity , its pollution intensity and its derivative with respect to productivity is: Due to s ∈ (0, 1) , it can be judged that as the productivity of the enterprise increases, the pollution intensity of the enterprise will decrease. The pollution intensity of the industry and its first-order conditions are as follows: SinceI o,s , do,s , do,s > 0 , for any country with non-zero trade cost, I o,s ∕ do,s > 0 . Therefore, it can be judged that industry pollution intensity is inversely proportional to environmental protection tax (environmental regulation) and industry productivity, and inversely proportional to trade iceberg cost (trade openness). To sum up, this paper finds that there are five main factors affecting the pollution intensity: environmental regulation, productivity, production scale, industrial structure, and trade openness.
This paper further draws on the method of Grossman and Krueger (1995) to decompose the sources of changes in industrial air pollution and conducts statistical decomposition of the internal sources of pollution changes. The composition of the total pollution intensity Z is as follows: In Eq. (14), Y is the total output. I s is the proportion of industry s pollution emissions in the total output. E s is the output proportion of industry s. I s can be further transformed into: where P s ∕C s is the proportion of the industry s pollution emission P to the industry's total input C. This indicator can be understood as the pollution emission per unit input; that is, the more advanced the clean technology, the smaller the pollution emission. C s ∕Y s is the input-output ratio of industry s, which can be understood as the productivity of the industry; that is, the higher the productivity, the smaller the pollution emissions. Combined with Eq. (15), the total pollution intensity Z can be expressed as: According to Eq. (16), the intrinsic sources of pollution emissions can be summarized into the following three pathways: (1) economic scale Y ; (2) technology I s , including total factor productivity and green productivity; (3) industrial structure E s . Based on this, this paper divides the main factors affecting pollution emissions into two categories: external factors and internal factors. Among them, external factors include environmental regulation and trade openness; internal factors include economic scale, productivity, and industrial structure (Fig. 1). Based on this classification, we will conduct a SEM analysis of the factors influencing the decline in pollution emissions in China.

Econometric model
SEM integrates traditional path analysis, multiple regression, and factor analysis, and the model is able to handle multiple dependent variables while accounting for measurement error. Therefore, through SEM analysis, the above theoretical analysis can be more rigorously verified. SEM includes two parts: measurement model and structural model. Where the measurement model is expressed as: The structural model is represented as: where x and y are the observed variables of the exogenous latent variable and the endogenous latent variable , respectively. Λ x and Λ y are factor loading matrices. B represents the relationship between endogenous latent variables, Γ represents the relationship between exogenous latent variables and endogenous latent variables; , , and are residual terms. The above two models are based on the following basic assumptions: (1) the mean of the residual terms , , and is 0; (2) the residual terms and are not related to the latent variables and ; (3) the residual term is not related to , the residual term is not related to , , and .

Variables and data description
According to the analysis of the theoretical model, this paper regards economic scale (scale), productivity (tfp), and industrial structure (compo) as endogenous latent variables affecting haze pollution (pm), and considers environmental regulation (er) and trade openness (trade) as exogenous latent variables. The observed variables corresponding to each latent variable are shown in Table 1.

Haze pollution variable (pm)
Different from most literatures using indicators such as "waste gas, waste water, waste residue" to measure haze pollution, this paper uses the concentration of PM2.5 as an important indicator to measure haze pollution, which can more accurately and objectively measure the atmospheric environment of a region pollution situation. Based on the annual World PM2.5 density map from 2006 to 2020 released by the social and economic data and Application Center (SEDAC) affiliated to the international geoscience information network center (CIESIN) of Columbia University, this paper calculates the annual mean value of China's provincial PM2.5 concentration by masking the map of China in ArcGIS.

Exogenous latent variables
Environmental regulation (er) is expressed by the proportion of industrial pollution control investment in GDP. At the same time, this paper also draws on the method of Chen et al. to use the ratio of the frequency of words related to "environmental protection" in the local government work report to the total number of words in the local government work report to express environmental regulation . Words related to "environmental protection" include: environmental protection, pollution, energy consumption, emission reduction, ecology, green, low carbon, air, chemical oxygen demand, sulfur dioxide, carbon dioxide, PM 10 , and PM 2.5 . Trade openness (trade) is expressed by the proportion of total imports and exports in GDP. In order to distinguish the difference between import and export trade and processing trade, this paper also expresses trade openness by deducting the proportion of total imports and exports in GDP after processing trade.

Endogenous latent variables
Economic scale is represented by industrial added value, industrial output, and GDP, respectively. Productivity (tfp) is represented by regional productivity and energy utilization, respectively, where regional productivity takes industrial added value as expected output, capital stock, and employment as main inputs, and is estimated by data envelopment analysis (DEA). Energy utilization refers to the industrial output per unit of energy input. The industrial structure (compo) is represented by the proportion of the six highenergy-consuming industries in the total industrial output value, the ratio of service industry to industry, and the proportion of natural gas in energy consumption. The six high energy-consuming industries refer to the manufacturing of chemical raw materials and chemicals, non-metallic mineral products, ferrous metal smelting, and calendaring, nonferrous metal smelting and calendaring, petroleum coking and nuclear fuel processing, and the production and supply of electric power and heat. Since the proportion of the six high energy-consuming industries in industrial output has an opposite impact on pollution than the other two observed variables, the reciprocal is used here to represent it.

Data quality analysis
Firstly, we need to test the reliability of the data, refers to the stability and reliability of variables. It is usually expressed by the reliability coefficient Cronbach α. Generally speaking, if the reliability coefficient reaches above 0.9, it indicates that the reliability is good; if it reaches above 0.8, it indicates that it is acceptable; if it does not reach 0.7, it indicates that the variable needs to be corrected. According to the calculation, the overall Cronbach α of the latent variables in this paper is 0.836, and the single Cronbach α all exceed 0.8, indicating that the reliability of the sample is high.
Secondly, we need to test the validity of the data. Validity test mainly refers to structural validity test, which generally tests the validity of the data through kmo test and Bartlett sphericity of the original data. According to the calculation, the KMO value is 0.736, which exceeds the critical value of 0.5. The statistical significance probability of Bartlett sphericity test is 0.000 < 0.005, indicating that the sample has good validity and is very suitable for factor analysis.

Direct influence mechanism of latent variables
In this paper, Mplus software is used to establish the SEM model of haze pollution, and the initial model is calculated. The model is adjusted according to the evaluation of model fitting to obtain the final impact path map (Fig. 2).
The direct effects of exogenous latent variables (environmental regulation (er) and trade openness (trade)) on haze pollution (pm) are negative, and their coefficients are − 5.784 and − 3.467 respectively; that is, the stronger the environmental regulation and the more open the trade environment, the lower the haze pollution. The direct influence coefficients of endogenous latent variables (economic scale (scale), productivity (tfp), and industrial structure (compo)) on haze pollution are 1.898, − 2.563, and − 5.996, respectively; that is, the less output, the higher productivity and the more optimized structure, the lower haze pollution. This is consistent with the previous theoretical analysis. From the perspective of standardized regression coefficient, industrial structure optimization can produce better haze control effects. The industrial structure adjustment here includes three dimensions: reducing the proportion of high pollution and high energy consumption industries, vigorously developing the service industry, and increasing the proportion of clean energy consumption.

Indirect influence mechanism of exogenous latent variables
The exogenous latent variables may have an impact on the endogenous latent variables, and then affect the haze pollution. Therefore, this paper takes three endogenous latent Observing the path coefficient of the indirect influence mechanism, it can be found that the "innovative compensation" effect of environmental regulation has a more significant effect on haze governance (the influence coefficient is − 1.182), while the "scale effect" of environmental regulation and trade opening will have an adverse effect on haze governance (the impact coefficients are 1.579 and 1.515, respectively). The results of other paths except path 2 are consistent with the research results of existing literature. In path 2, strengthening environmental regulation will lead to an increase in output scale. The explanation for this conclusion is that although lower environmental regulation will not change the behavioral choices of enterprises, it will still increase the operating costs of enterprises. Then, enterprises can choose to raise the selling price to make up for the rise in costs, and the increase in output scale may be caused by the rise in selling price. In the long run, with the increasing intensity of environmental regulation, enterprises may choose to reduce the production of such non clean goods, thereby reducing pollution emissions. To test this hypothesis, this paper adds the squared term of environmental regulation (er2) to the model and analyzes the model again (Fig. 3). Figure 3 shows that the relationship between environmental regulation and output scale is a nonlinear "inverted U-shaped" relationship; that is, with the increase of environmental regulation intensity, the output scale first increases and then decreases. This result confirmed the above conclusion. At the same time, after adding er2 to the model, the influence direction of other paths does not change.  Holtz-Eakin et al. (1998) believed that the vector autoregression method can combine panel data and time series well, and proposed the panel vector autoregression (PVAR) model for the first time to analyze the dynamic characteristics between variables. PVAR model combines the advantages of time series and panel data and can describe the impact of various latent variables on haze pollution at multiple levels and from multiple perspectives. In order to examine the relationship between latent variables and haze pollution within a system framework, this paper further analyzes the dynamic influence between latent variables and haze pollution by constructing a PVAR model. The PVAR model in this paper is constructed as follows:

PVAR model construction
where PM it is the explained variable, that is, haze pollution; Π is the parameter matrix to be estimated; p is the lag order selected by the PVAR model; and X it−p is the latent variable of the model. Since both exogenous and endogenous latent variables are represented by multiple observation variables, the entropy method is used to determine the weight of each (20) observation variable, so as to determine the comprehensive latent variable index, which is expressed as environmental regulation (er), trade openness (trade), productivity (tfp), industrial structure (compo) and economic scale (scale).

GMM estimation of PVAR model parameters
Because panel data has a time trend, the data is often unstable, which can lead to "false regression" of the model. Therefore, before using GMM to estimate the model, it is necessary to test the stationarity of each variable. This paper mainly uses LLC test and HT test to test each variable. Both test results reject the null hypothesis of panel unit root; that is, the data is stationary. In addition, this paper selects the optimal lag phase of the model according to the AIC, BIC, and HQIC statistics as lag 3. In order to better control individual effects and endogenous problems, this paper uses GMM to effectively estimate model parameters. The specific estimation results are shown in Table 3. As shown in column 1 of Table 3, the increase of environmental regulation (er) with lag 1 and the economic scale (scale) with lag 2 will lead to an increase in haze pollution, while environmental regulation (er) with lag 2 and industrial structure (compo) with lag 3 can inhibit haze. As shown in columns 1 and 5 of Table 3, the increment of haze pollution (pm) and economic scale (scale) have strong dynamic explanations for themselves. The relationship among the other latent variables can be summarized as follows: the influence of environmental regulation (er) on trade (trade) presents the characteristics of first inhibition and then promotion. In the long term, trade openness (trade) is conducive to the improvement of productivity (tfp). The above results are consistent with the usual theoretical explanation: the production cost of enterprises is significantly increased due to the impact of environmental regulations, leading to a significant decline in the competitiveness of enterprises, which has a negative impact on short-term exports. The "innovation compensation" effect of environmental regulation has begun to highlight, which will continuously encourage enterprises to optimize production and improve efficiency, which is beneficial to enterprises' export. The higher the level of opening up, the larger the scale of its international trade in products and services. This means that economic development can give full play to comparative advantages and improve the level of specialization, and can also accumulate experience through "learning by doing" to further improve total factor productivity.
The above conclusions can only reflect the dynamic evolution process of various latent variables in a macroscopic manner, and cannot specifically explain the dynamic transmission mechanism and the contribution of shock variables. Therefore, it is necessary to further analyze the dynamic relationship between the latent variables and haze pollution.

Response of haze pollution to latent variable impact
According to the estimation results of the PVAR model, this paper further analyzes the long-term dynamic interaction between haze pollution and latent variables through the impulse response function. The impulse response function was simulated by Monte Carlo for 200 times, and the impulse response diagram of each latent variable shock lag of 6 periods was obtained. The impulse response function can well simulate the dynamic impact trajectory of haze pollution on the impulse response from another latent variable under the condition that the values of other latent variables remain unchanged in the current and previous periods, and it can better reflect the dynamic transmission path among variables.
As shown in Fig. 4, the impact of haze pollution on itself tends to be flat from the third period of lag, and the value is relatively large, indicating that the impact on haze pollution mainly comes from itself; that is, the increment of haze pollution has a certain economic inertia. This conclusion is consistent with the GMM estimation results above. The influence of latent variables on the impact of haze pollution from strong to weak is: industrial structure (compo), economic scale (scale), productivity (tfp), trade opening (trade), and environmental regulation (er). Specifically, the impact from the upgrading of the industrial structure has a significant inhibitory effect on haze pollution. This inhibitory effect is strongest with lag 3, and then maintains a relatively stable state of inhibition. This shows that the adjustment of industrial structure is the key factor to reduce haze pollution. The impact from the expansion of economic scale has a relatively significant promoting effect on the increment of haze pollution for a long time, but the impact of economic scale expansion is lower than the impact of industrial structure impact; that is, economic expansion will not hedge the positive effect of industrial structure upgrade. The impact from productivity improvement and trade opening has a Fig. 4 Response of haze pollution to latent variable impact significant and stable inhibitory effect on haze pollution in the long run, and this inhibitory effect is the strongest with lag 2. The impact from environmental regulation will lead to the increment of haze pollution in the short term and will inhibit haze pollution in the medium and long term. This conclusion is consistent with the conclusion of the SEM model above.

Response of endogenous latent variable to exogenous latent variable impact
Combined with the above analysis results, this paper further analyzes the mediating ways of exogenous latent variables affecting haze pollution. As shown in Fig. 5, the impact of environmental regulation and trade openness on economic scale is small and insignificant numerically, but the two exogenous latent variables have a more significant effect on productivity. Among them, the promotion effect of environmental regulation on productivity fluctuated greatly, and its influence began to weaken and stabilized with lag 2, while trade opening had a long-term promotion effect on productivity, indicating that the technology spillover generated by opening to the outside world can reduce haze pollution in the long term by improving productivity. Although the influence of two exogenous latent variables on industrial structure also has a long-term positive effect, it is not significant. According to the above conclusions, the upgrading of industrial structure is the most effective way to restrain haze pollution. Therefore, it can be considered that there is still much room for reducing haze pollution through trade opening.

Variance decomposition
In order to verify the analysis results of the impulse response function, this paper further uses variance decomposition to test the contribution of structural shock to the impact of haze pollution. The model has also been simulated by Monte Carlo for 200 times, and the variance decomposition results of each variable are shown in Table 4. As shown in Table 4, in the next 10 years, haze pollution will have the greatest impact on itself. Although the impact of the Fig. 5 Response of endogenous latent variable to exogenous latent variable impact shock has weakened year by year, the proportion is still as high as 71.45% with lag 10. In the medium and long term, the upgrading of industrial structure and productivity have the highest impact on haze pollution, and the impact has increased year by year. In addition, environmental regulation has the least impact on haze pollution, accounting for less than 1%. In terms of indirect effects, environmental regulation has less effect on the three endogenous latent variables, while trade opening has a greater effect on the three latent variables. In the medium and long term, the productivity improvement effect caused by the technological spillover of trade openness is the most significant, with a contribution of more than 20%, but the impact of trade openness on the industrial structure is relatively small, and its highest contribution is 1.93% with lag 10.

Spatial competition analysis of haze pollution
Due to the impact of natural environment and weather, there is no clear boundary for pollution emissions and there is a strong space spillover. Space spillover itself is an economic phenomenon, and it is the embodiment of the economic externality of the impact of the economic decisions or behaviors of one region on another region. With the continuous promotion of regional economic integration, the economic exchange between regions has also determined that spatial correlation must be considered when conducting regional economic research. Therefore, due to the spatial spillover of pollution and the externalities of economic behavior, the spatial factors of haze pollution should be considered. First of all, this paper uses Moran's I to test whether the spatial correlation of air quality exists between different regions. Table 5 shows the test results of Global Moran's I under three spatial weight matrices (W1, W2, and W3 represent economic distance matrix, 0-1 adjacency matrix and geographical distance matrix respectively). As shown in Table 5, Moran's I are all positive numbers, and have passed the Z(I) significance test, indicating that there is indeed a positive spatial correlation between haze pollution and it is characterized by spatial agglomeration. Therefore, it is feasible and necessary to use spatial econometric model to analyze the spillover of haze pollution. Pang et al. (2019) proposed that when the economy develops to a certain level, the governance preference of local governments will be triggered to shift from economic growth to environmental protection. When the level of economic development is relatively backward, under the pressure of official promotion and fiscal decentralization, the marginal cost of environmental protection of local governments will be much higher than the marginal benefit. Even if the central government has issued unified environmental regulations, the preference of local governments for economic growth will also make environmental protection policies greatly discounted in the actual implementation and supervision, so as   to fail to achieve the expected results, which is also reflected in the policy competition on haze control among regions. Based on this, this paper further uses the spatial econometric model to analyze the spatial competition of haze pollution, and to estimate the strategic interaction among factors affecting haze pollution. In order to determine the optimal spatial regression model suitable for the sample data in this paper for empirical analysis, this paper uses maximum likelihood estimation method to estimate SDM, SEM, and SAR. Table 6 shows the estimated results of relevant parameters. As shown in Table 6, the maximum R 2 of SDM estimation results is 0.886, the minimum value of the sum of squares of residuals 2 is 0.033, and the maximum value of the log likelihood function is 883.966. At the same time, the 2 test result is 0.249, which is close to 0. The spatial Hausman test result is 481.473, which is significant at the level of 1%. To sum up, SDM with spatiotemporal double fixed effects is the best empirical analysis model in this paper. The specific estimation results are shown in column 1 of Tables 6 and 7. As shown in column 1 of Table 6, the estimated coefficients of b1 and w_b1 under the full sample are both positive, indicating that the increase of local environmental regulation intensity will expand the haze pollution, and the increase of the neighboring environmental regulation intensity will have a negative spillover effect on local haze pollution. Therefore, for the local area, if the neighboring areas strengthen environmental regulation, the local area should reduce the intensity of environmental regulation for the purpose of reducing pollution, so as to form a "race to the bottom" spatial competition of environmental regulation policy. The above analysis results show that environmental regulation will have an "inverted U-shaped" nonlinear effect on haze pollution. The estimation results of adding the square term of environmental regulation are shown in column 1 of Table 7. It can be found that when the intensity of environmental regulation exceeds the critical value of 1.6825, the strategic interaction of "race to the top" will be formed between regions. However, 98.79% of the observations are still in the game state of " race to the bottom." As shown in column 2 of Table 7, the estimated coefficients of d1 , e1 , w_d1, and w_e1 under the sample in the eastern regions are all negative, indicating that local productivity improvement and industrial structure upgrade are conducive to reducing haze pollution. At the same time, the environmental policies of neighboring areas have a positive spillover effect on the local. Therefore, the optimal strategy for the local area is to make the same policy choice when improving productivity and optimizing industrial structure in neighboring areas, that is, to form a "race to the top" strategic interaction. As shown in column 3 of Table 7, the estimated coefficients of b1 and w_b1 under the sample in the central regions are both positive, indicating that when the environmental intensity is low, a game state of "race to the bottom" will be formed between regions.
According to column 4 of Table 7, the spatial competition of haze pollution in the western regions is not significant.

Discussion
The above empirical analysis results answer the impact mechanism of haze pollution emission change in China. The results show that in the short term, environmental regulation can play a role in reducing haze pollution, but in the long term, it still needs to rely on industrial structure adjustment and productivity improvement to achieve the goal of reducing haze pollution. There is usually a "U"-type nonlinear relationship between environmental regulation and haze pollution, because the game state between "following the cost theory" and "innovation compensation theory" affects the environmental governance effect (Kumar and Managi  Ranocchia and Lambertini 2021). In the short term, polluting enterprises are under the pressure of environmental costs and have the motivation to move to areas with low environmental regulation intensity, which is also the realistic basis of the "Pollution Paradise Hypothesis" (Lenonard 1984;Bakhsh et al. 2017). Under the influence of China's fiscal decentralization system, environmental regulation has exerted a significant inhibitory impact on firms' eco-innovation as well as on firms' eco-investment and eco-planning innovation. The underlying cause of this situation is mainly that, during the observation period, China's environmental policies were mainly command-and-control policies and pollutant drainage fee policies, which tended to focus on the terminal treatment of pollutant emissions, resulting in limited innovative incentive effect (Chen and Wu 2018).
In the long term, with the improvement of the intensity of environmental regulation, especially after environmental protection has been included in the government's performance appraisal system, an invisible "environmental barrier" often forms in the region. When the pollution cannot be transferred, the sunk costs and operational risks of polluting enterprises will become larger. On the contrary, high-tech industries and clean industries are more favored by the local government. At this time, enterprises will be forced to carry out technological innovation and start transformation and upgrading (Becker 2005). As a result, the local innovation efficiency has been greatly improved, the overall industrial structure in the region has also been upgraded, and the goal of reducing haze pollution has also been achieved.
According to the results of the spatial econometric model, we find that there is competition in environmental governance policies among local governments in China, and the feature of "race to the bottom" is more significant. Similar evidence can be found in Wang and Lei (2021). Under the current pressure of economic competition in China, local governments usually ignore the pressure of resources and the environment and change the structure of their fiscal expenditures to develop the economy (Pan et al. 2020). On the one hand, to increase total GDP in the short term, local governments will not hesitate to increase the development and utilization of natural resources or even predatory exploitation, resulting in problems such as increased environmental pollution and reduced resource utilization efficiency (Fredriksson and Millimet 2002). On the other hand, after the reform of the taxsharing system in China, local governments' financial power has increased, while administrative power has decreased, which has caused a serious imbalance in local fiscal revenue and expenditure. In this context, local governments usually increase fiscal revenue through disorderly competition for capital and other flow factors, and public products such as environmental governance are selectively ignored to relieve fiscal pressure. In the context of the Chinese government's selection criteria for officials based on economic performance, the promotion competition in which local governments compete for GDP was launched, which further stimulated local governments to compete for flow factor resources such as capital and labor, even at the expense of other public resources (Sigman 2009). In this process, environmental public goods, as typical non-economic public goods, were the first victims of local government competition and become a tool of local government resource competition. From the analysis of regional heterogeneity, the central regions has a more significant "race to the bottom" game state, while the eastern region shows a "race to the top" feature in the policy game of improving productivity and optimizing industrial structure. With China's increasing efforts towards ecological and environmental protection and under the pressure of tight environmental protection, the eastern regions have become more focused on high-quality economic development, so the development mode has shifted from quantity to quality . By contrast, local governments in the eastern regions have the conditions and ability to restrain resource mismatch. They can establish cooperation with some institutions and enterprises to actively maintain the order of the factor market and promote the healthy development of the factor market (Naughton and Byrd 1995). In addition, the financial and legal system in the eastern regions is mature, and property rights are clearly defined so that the distorting effect of local government incentives on the factor market can be avoided to a certain extent. For the central regions, local governments often adopted a "scale competition" strategy, resulting in local economic development remaining in the stage of "quantity competition." As a result, environmental governance was relaxed, and investment projects were aggressively attracted to develop the local economy. Eventually, these areas fell into a vicious "race to bottom," which not only damaged the factor market structure of the jurisdiction but also further exacerbated environmental pollution.

Conclusion
Firstly, this paper uses the heterogeneous enterprise model to decompose the factors that affect pollution emissions and summarizes the sources and ways of pollution emissions. Then, taking the panel data of 30 provincial-level areas (except Tibet, Hong Kong, Macao, and Taiwan) from 2006 to 2020 as the research object, the SEM model and the PVAR model were used to test the internal logical relationship between each variable and haze pollution, and systematically explore the impact mechanism of haze pollution emission changes in China. The main conclusions from the current study are: • The inhibitory effects of latent variables on haze pollution from strong to weak are: industrial structure upgrade (− 5.996), environmental regulation (− 5.784), trade opening (− 3.467), productivity improvement (− 2.563), and economic scale expansion (1.898). The optimal path for exogenous latent variables to indirectly affect haze pollution is to rely on environmental regulation and opening-up to increase productivity and reduce haze pollution (the impact effects are − 1.182 and − 0.597, respectively). • According to the analysis results of the PVAR model, it can be found that in the medium and long term, the impact of potential variables on the impact of haze pollution from strong to weak are: industrial structure, economic scale, productivity, trade openness, and environmental regulation. This shows that no matter in the short or long term, the adjustment of industrial structure is the key factor for the reduction of haze. The short-term effect of environmental regulation is obvious, but in the long-term, the goal of reducing haze pollution must be achieved by relying on industrial structure upgrading, productivity improvement and trade opening. • In addition, trade opening has a long-term promoting effect on productivity, indicating that technological spillovers from opening up can reduce haze pollution in the long run by increasing productivity. According to the spatial competition analysis of haze pollution, it can be found that there is still "race to the bottom" in environmental regulation policies between regions, which is particularly prominent in the central regions. Meanwhile, the eastern regions show the characteristics of "race to the top" in the policy game of improving productivity and optimizing industrial structure.
Based on the above research conclusions, we put forward the corresponding policy recommendations: Firstly, the adjustment and upgrading of industrial structure should be accelerated. Economic development should implement the concept of green development, focus on optimizing the industrial structure, reduce the proportion of high pollution and high energy consumption industries, vigorously develop the service industry, accelerate the green transformation of "Made in China," promote the deep integration of consumer goods industry and service industry, so as to get rid of the dependence on resource consuming industries.
Secondly, further opening up to the outside world. Against the background of rising global trade protectionism, we should make full use of the international cooperation platform of the "the Belt and Road Initiative" and the free trade zone to promote substantive cooperation between Chinese enterprises and developed countries in the field of environmental protection technology, draw on the successful experience of pollution control, and gradually improve environmental protection standards to match with international high standards. At the same time, we will raise the entry threshold for pollution intensive enterprises, give play to the technology spillover effect of high-quality foreign-funded enterprises, and help China's green manufacturing.
Thirdly, pay attention to the control effect of technical efficiency on haze. Enterprises should increase investment in research and development of clean equipment and clean production technology, vigorously explore and use clean energy, strive to improve resource utilization efficiency, implement ISO14000 environmental management series standards, and reduce pollution emissions in the production process, thereby reducing operating costs and improving productivity.
Fourthly, improve the mechanism for joint prevention and treatment of air pollution. We should further break down regional barriers, achieve policy consistency or policy coordination within the region, constantly improve the level of regional cooperation, and strengthen the unity of the concept and action framework of joint defense and governance within the region. On the basis of existing relevant laws, regulations and policies, strengthen the "hard constraint" of specific punishment measures for violations of laws and regulations, so as to implement relevant laws, regulations, and policies. At the same time, a regional horizontal ecological compensation mechanism should be established to achieve the balance of regional interests.
Author contribution Luxin Yang was responsible for the design of the present study, reviewed the manuscript, and assisted with manuscript revision. Yucheng Liu conducted data collection, performed the statistical analyzes, drafted, and revised the manuscript.
Funding This study was funded by the General Program of the National Natural Science Foundation of China (grant number: 7207030935).

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics approval and consent to participate All the authors approved the final manuscript and agreed to its publication in the Environmental Science and Pollution Research.

Competing interests
The authors declare no competing interests.