How does the urban–rural income gap affect regional environmental pollution?——Re-examination based on the experience of cities at prefecture level and above in China

Based on the traditional “EKC” theory, this paper examines the impact of urban–rural income disparity on environmental pollution in Chinese cities above the prefecture level from 2005 to 2015 using nonlinear models and spatial correlation models and tests the mechanism of action from two perspectives: demand scale and human capital. The results show that the urban–rural income gap has an obvious “inverted U-shaped” trend on environmental pollution. Both demand size and human capital are the main mechanisms affecting the environmental pollution effect of the urban–rural income gap, and the marginal pollution effects of both are “negative first and then positive” as the urban–rural income gap widens. The pollution effects of the urban–rural income gap are significantly spatially correlated at both the national and regional scales. The strength of environmental regulation is an important factor affecting the urban–rural income gap and has a significant “U-shaped” effect on regional pollution through the urban–rural income gap.


Introduction
Since the reform and opening up, China has adopted a development strategy of "biasing towards urban and nonagricultural sectors," which has enabled its economy to enter a period of sustained high-speed growth for more than 40 years. Therefore, China has become a major emerging industrialization country with the world's second-largest GDP and the world's largest industrial output for a long time. China's rapid economic growth has comprehensively improved the material living standards of residents. The per capita disposable income of urban residents and the per capita net income of rural residents increased from 1510.2 yuan and 686.3 yuan in 1990 to 42,000 yuan and 16,000 yuan in 2019, respectively. However, it should be noted that from 2000 to 2019, the per capita disposable income ratio of Chinese urban and rural residents dropped from 2.78 to 2.64, while the income gap between urban and rural residents widened from 4000 yuan to 26,000 yuan. 1 Based on typical facts, it can be found that although China's rapid economic growth has greatly improved the national income level, the problem of urban-rural income inequality is still very prominent. Income inequality not only directly hinders regional growth and industrial upgrading but also generates many social problems such as public security and law, which affect the daily life of residents. In response to the above challenges, the 13th Five-Year Plan issued by the Chinese central government in 2016 emphasized that "industry feeds agriculture, cities feed rural areas, and the integration of urban and rural development is improved." In other words, coordinating urban and rural development will become a key area of China's economic adjustment at this stage.
The development of industrialization drives the increase in energy consumption and rapidly drives economic development (Husnain et al. 2021), but it has also inevitably led to environmental problems. According to World Bank statistics, China's total carbon dioxide emissions in 2014 were about 10.29 billion tons, more than six times the 1.46 billion tons in 1978, with an average annual growth rate of over 5.5%. 2 Especially since 2013, large-scale haze weather has swept across China, and pollution problems derived from economic development have adversely affected the work and life of residents (Haider et al. 2020). The report of the 19th National Congress of the Communist Party of China pointed out: "the modernization that China wants to build is a modernization in which man and nature coexist in harmony. It is necessary to create more material wealth and spiritual wealth to meet the people's growing needs for a better life, and to provide more high-quality ecological products to meet the people's growing beautiful ecological environmental needs." 3 This requires China to transform its past extensive economic model, promote supply-side adjustment, further release the "bonus" of reforms, and strive to cultivate emerging growth points to cope with the "new economic normal" facing the country.
In recent years, scholars represented by Banerjee et al. (2021a) have incorporated the issue of "equity" into the research framework of environmental pollution. Given that the urban-rural income gap and environmental pollution are both key issues related to China's current economic growth and industrial transformation, a comprehensive and systematic discussion of the interaction between the urban-rural income gap and environmental pollution is important for improving the existing income gap and environmental pollution research system, as well as for the formulation of industrial policies. Regrettably, the existing research on the impact of the urban-rural income gap on environmental pollution is insufficient. First, Grossman and Kruegger (1991), Panayotou (1993), and Husnain et al. (2021) pointed out that there is an environmental Kuznets curve (EKC) between per capita income and environmental pollution. However, scholars such as Coondoo and Dinda (2008) believe that it is the income gap rather than the income level that affects environmental pollution. Second, many studies have discussed the impact of the regional Gini coefficient on local environmental pollution, but this is different from the urban-rural income gap. Then, some scholars believe that the income gap and environmental pollution are linearly related (Ghalwash 2008;Baek and Gweisah 2013), while others believe that the two should show a nonlinear relationship (Scruggs 1998;Yang and Liu 2012). Finally, although the mechanisms that affect environmental pollution are involved in income levels (Vona and Patriarca, 2011), human capital (Shen and Geng 2001), and environmental policies (Yu et al. 2019), they do not incorporate urban-rural income gap conditions into the research framework. Therefore, investigating the environmental pollution effect of the urban-rural income gap from a nonlinear perspective, and discussing its mechanism from the two dimensions of demand and supply, has strong theoretical and practical significance. Compared with the existing literature, the innovations of this paper are as follows. First, at the theoretical level and basic empirical level, this paper examines the impact of the urban-rural income gap on carbon emissions from a nonlinear perspective. The empirical results show that the impact of the urban-rural income gap on carbon emissions has the characteristics of an "inverted U." There is a clear difference between this result and the traditional linear view, and it is a supplement to the existing research system. In addition, different from the existing research that mostly discusses the impact of the regional economic development gap (that is, GDP inequality) on environmental pollution, this paper focuses on the pollution effect of residents' income inequality, which is more directional.
Second, at the level of mechanism inspection, the existing research is mainly based on the perspective of demand, with per capita income as the starting point to explore the impact of the income gap on environmental pollution. Based on the traditional perspective of demand, this paper further combines the perspective of supply to explore the mechanism of income disparity affecting environmental pollution from two aspects of consumption and production, which is an effective supplement to the mechanism research system in related fields.
Third, this paper is the first to use the urban and rural population data of prefecture level and above cities in China from 2005 to 2015, as well as the income and consumption data of urban and rural residents based on the author's manual search, to carry out empirical analysis, which not only greatly enriches the sample size of empirical research, but also makes the research horizon more detailed; it provides a more accurate basis for countries, especially developing countries, to carry out income distribution and environmental pollution control.
The rest of this article is arranged as follows: The second part is a literature review; the third part is model setting and data explanation; the fourth part is empirical regression and results in analysis; the fifth part is the impact mechanism test; the sixth part is the relationship between urban-rural income gap and environmental pollution introduced by spatial correlation; the seventh part is a further discussion of the urban-rural income gap and environmental pollution: the perspective of environmental regulation effects; the eighth part is the conclusion and policy enlightenment. Grossman and Kruegger (1991) and Panayotou (1993) per capita income and environmental pollution have an "inverted U-shaped" impact, and although the EKC theory has certain flaws, environmental pollution has been incorporated into the income distribution research framework earlier. This is a great enrichment of the theoretical system of income distribution. In subsequent studies, some scholars believe that the income gap, especially the widening of the urban-rural income gap, will often aggravate environmental pollution. Boyce (1994) established a power-weighted social decision-making model (PSDM) and pointed out that the poor tend to increase the development of natural resources to maintain basic survival, while the rich prefer to transfer assets to other regions when facing environmental pollution instead of investing locally to improve environmental quality, so the widening gap between the rich and the poor will significantly worsen the local environment. From the perspective of public expenditure, Magnani (2000) pointed out that the widening income gap will restrain the government's willingness to spend on the environment and lead to increased local pollution. Xiao and Li (2013) found through empirical research that the urban-rural income gap significantly increased the carbon emissions of provinces and municipalities in central and western China. Zhong and Zhao (2013) conducted an empirical study on China's inter-provincial panel data from 2003 to 2010 and concluded that the widening of the urban-rural income gap significantly increased local carbon emissions, while Zhang and Zhao (2014), Hao et al. (2016), and other studies also put forward similar views. Other studies believe that the widening of the urban-rural income gap will alleviate environmental pollution under certain conditions. Heerink et al. (2001) found through cross-country empirical results that the widening of the income gap does not necessarily directly lead to environmental degradation. Some scholars have pointed out that the urban-rural income gap and environmental pollution may have a nonlinear interactive relationship. Lv and Gao (2005) passed the empirical test of the inter-provincial panel secretary and pointed out that China's urban-rural income gap has a significant "inverted U-shaped impact" on regional carbon emissions. Liu et al. (2018) combined the income gap between urban and rural areas in China from 1996 to 2015, carbon emissions, and the per capita income gap in cities at the prefecture level and above. They empirically support the views of Lv and Gao, and Liu et al. point out that per capita income level determines the local EKC inflection point. It can be found that the academic circles still have disputes over the impact of the urban-rural income gap on environmental pollution.

Literature review
In addition, environmental pollution is affected by many factors, and there is a lack of a unified understanding of how the urban-rural income gap through the mechanism path affects environmental pollution. Given the premise of other factors, environmental pollution is mainly closely related to market demand and manufacturer's supply. Because existing research usually only has a single perspective of "market demand" or "manufacturer supply," its research conclusions have obvious blind spots in explaining the dynamic law of China's environmental pollution evolution under the background of the continuous deepening of today's market economic system. Therefore, based on the dual perspectives of "demand side" and "supply side," this article summarizes the two major mechanism paths through which the urban-rural income gap affects environmental pollution from the theoretical level.

Scale of demand
In the research on the consumer side, all the conclusions are that the scale of demand has an important impact on environmental pollution, but the magnitude and direction of its impact are widely disputed. Some scholars believe that the widening income gap between urban and rural areas has aggravated environmental pollution. Through the 1986-2008 China time-series study, Pan and Ying (2010) found that the widening income gap has significantly increased environmental pollution, and the impact has a significant lag. Han and Han (2015) found that the widening income gap will not be conducive to the improvement of the environmental quality of the country after analyzing the experience of translational research. Zhan (2018) believes that the widening of the urban-rural income gap not only reduces the lowincome group's consumption preference for environmentally clean products, but may also stimulate the conspicuous consumption of high-income groups and ultimately lead to the deterioration of the regional environment. The research of Yang (2019) also found that the widening of the urban-rural income gap has increased regional environmental pollution by affecting the purchasing power of residents.
However, some studies believe that the appropriate expansion of the urban-rural income gap has alleviated environmental pollution. On the one hand, in the initial stage of economic development, an appropriate expansion of the income gap may be beneficial to fostering market demand for environmentally clean products, which in turn has formed the formation of frontier manufacturers to maintain production. It is beneficial to curb regional environmental pollution (Foellmi and Zweimüller 2006;Li 2012). Liu and Shen (2012) found through empirical research that the narrowing of the urban-rural income gap will increase the overall consumption scale of the market, while Zhu et al. (2012) calculated by using a sequence table of comparable input-outputs and found that the expansion of the consumption scale of Chinese residents will aggravate the environment pollution. Ma et al. (2019) also found through empirical tests that the widening of the urban-rural income gap in China's provinces and municipalities from 2000 to 2012 significantly suppressed consumer carbon emissions.

Human capital
In the research on the supply side, human capital accumulation can effectively improve local environmental pollution that has become a basic consensus (Goetz et al. 1997;Lan and Munro 2013), but there is still some controversy about how the urban-rural income gap affects regional labor costs. Many opinions believe that the widening of the urban-rural income gap will inhibit the accumulation of human capital. Chao and Shen (2014), from the perspective of China's inter-provincial level, found that the expansion of the urban-rural income gap in provincial administrative regions from 1995 to 2012 will strengthen rural residents' education investment financing constraints, which will not be conducive to the accumulation of human capital in the region. Lv et al. (2015) also believe that the widening of the urban-rural income gap will lead to educational inequality, which is not conducive to human capital accumulation in the long run. Based on China's current national conditions, Zhang and Li (2016) pointed out that the expansion of urban and rural income is not conducive to the equalization of labor quality, and the limited investment in the human capital of rural residents will significantly hinder the expansion of human capital in China.
However, there are opinions that the supply of highskilled labor not only significantly increases the productivity of high-skilled labor, but also produces significant positive externalities to other residents (Liang and Lu 2015). The possible reason is that environmentally clean products are technology-intensive products, and their R&D and production may require key breakthroughs by top talents at certain stages. The moderately widening urban-rural income gap leads to the differentiation of human capital and may have a positive effect on the cultivation of top talents (Zweimuller 2000). In other words, in the period when the overall human capital is insufficient, the expansion of urban and rural income can promote the accumulation and agglomeration of high-skilled human capital in certain periods and is conducive to the production of technology-intensive products including environmentally clean products. Gao and Wang (2016) also believe that the structural agglomeration of human capital caused by the expansion of the urban-rural income gap may promote innovation. Sun et al. (2017) found that the accumulation of human capital reaches a certain threshold before it can play a significant upgrade and innovation effect. Therefore, it can be found that in some cases, although the expansion of the urban-rural income gap has led to a slowdown in the accumulation of human capital, the innovative effect of the spatial accumulation of high human capital may help alleviate regional environmental pollution.
Most of the existing studies examine the impact of the income gap on environmental pollution from a linear perspective, for example, Boyce (1994), Magnani (2000), Xiao and Li (2013), Zhong and Zhao (2013), Zhang and Zhao (2014), and Hao et al. (2016). However, with the development of the income distribution research system in recent years, more and more researchers have begun to focus on the nonlinear research of income disparity on economic growth, total factor productivity, and environmental pollution. Relevant studies have shown that the impact of income disparity on environmental pollution does have strong nonlinear characteristics (Lv and Gao 2005;Liu et al. 2018). The reason is that, on the one hand, changes in income gaps will directly affect the overall scale of demand and supply of environmental protection products in the region; on the other hand, it will also lead to the differentiation of demand and supply among different groups within the region, which in turn will lead to structural changes in local demand and supply. Given the important role of local demand and human capital in environmental pollution, we believe that income disparity forms scale and structure effects, both of them play a role on the demand side and the supply side at the same time, which is an important reason for the nonlinear impact of income gap on environmental pollution. On the demand side, due to the small size of the local market in the initial stage of economic development, moderately widening the income gap is conducive to guiding consumption to a small number of high-income groups and forming a structural effect of demand (Gao and Wang 2016;He et al. 2020). Thus, this is conducive to fostering relatively high-priced demand for environmentally friendly products, which has positive significance for reducing pollution. With the improvement of the economic level and the increase of the overall income level of the society, affected by the diminishing marginal propensity to consume, the continuous decline of the marginal consumption of high-income groups will inhibit the total scale of social demand, which is not conducive to further expanding the social demand for environmentally friendly products. In other words, in the initial stage of the economy, the structural effect of the income gap on the demand side is stronger than the scale effect, and a moderate increase in the income gap will help reduce pollution. When economic development reaches a certain level, the scale effect of the income gap on the demand side exceeds the structural effect, and the widening of the income gap will be detrimental to reducing pollution. It can be found that the income gap has a potential nonlinear impact on environmental pollution from the perspective of the demand side.
On the supply side, the R&D and production of environmentally friendly products often rely on key breakthroughs in cutting-edge technologies by cutting-edge technicians. Due to the relatively small stock of social resources in the initial stage of economic development, appropriate expansion of the income gap can guide social resources to agglomerate to a small number of people and form a structural effect of human capital, which is conducive to concentrating resources to accelerate the cultivation of cutting-edge technical personnel (Gao and Wang 2016;He et al. 2020), and then accelerate the research and development and production of environmentally friendly products, which will promote emission reduction to a certain extent. When the economy develops to a certain stage, the further widening of the income gap will exacerbate the unfair distribution of social resources and hinder the overall accumulation of local human capital, which will, in turn, hinder the expansion of production of environmentally friendly products and increase environmental pollution. That is to say, in the initial stage of the economy, the structural effect of the income gap on the supply side is stronger than the scale effect, and a moderate expansion of the income gap will reduce pollution. With economic development, the scale effect of the income gap on the supply side is stronger than the structural effect, and the widening of the income gap is not conducive to reducing pollution. It can be found that similar to the demand side, the income gap also has a potential nonlinear impact on environmental pollution from the perspective of the supply side.
Based on the above-mentioned theoretical induction and logical deduction, as well as current China's national conditions, this article puts forward the following hypotheses: Hypothesis 1: The urban-rural income gap significantly affects China's environmental pollution, and the impact may exhibit EKC-type nonlinear characteristics. China has a vast territory, and many conditions such as historical development, geographical location, factor endowments, and institutional policies have significant differences between regions, which also makes China's economic development also show obvious differences. Based on the consumption scale theories such as Zhan (2016), Li (2017), and Liu et al. (2018) and the human capital theories sorted out in the previous article, this article further proposes: Hypothesis 2: The impact of the urban-rural income gap on environmental pollution has not only the threshold effect of the consumption scale but also the threshold effect of human capital. This phenomenon also has a significant geographic location.

Model assumptions
Given the complexity of the impact of China's urban-rural income gap on environmental pollution, this article intends to design the following empirical model based on existing research: In the formula, PI represents the pollution intensity, i represents the city at the prefecture level and above, t represents the year, G represents the urban-rural income gap, D is the set of control variables, and are the fixed effect of cities at the prefecture level and above (hereinafter referred to as the city effect), the year effect, and ξ stands for residual. To further test the real impact of the urban-rural income gap on China's environmental pollution, this paper introduces the quadratic term of the urban-rural income gap to investigate its possible nonlinear impact on environmental pollution.

The explained variable
Environmental pollution (PI). At the municipal level, this paper selects the annual carbon emissions of prefecture level and above cities in China as a measure of environmental pollution. The main reasons are as follows: first of all, with the emergence of events such as "global warming and sea-level rise," the bleak future of the "Kyoto Protocol," "the escalation of disputes in the Paris Climate Agreement" and other events in recent years, countries and regions have become more concerned about the issue of carbon emissions. Secondly, China has grown into a newly industrialized country in the world, and carbon emissions, as an important indicator of the degree of industrialization, are closely related to industrial growth and transformation and upgrading; Finally, compared to factors such as sulfur dioxide emissions, wastewater emissions, smoke, and dust emissions, China's carbon emission-related data are more complete and more credible. Therefore, in the empirical stage, this article chooses carbon emissions as a measure of urban pollution: (1) Total carbon emissions (CO2). This article studies the environmental pollution of production and life in prefecture level and above areas. Since the carbon emissions of industrial power generation mainly come from thermal power generation, China's factor endowment has long been "rich in coal and poor in oil," which has led to a high degree of dependence on coal for domestic power production. Therefore, this article refers to the method of Han and Xie (2017), selecting the carbon emissions of coal, natural gas, and liquefied petroleum gas consumption in the region to estimate the carbon emissions of the entire region. The specific estimation methods are as follows: Among them, I represents the total carbon emissions of cities at the prefecture level and above. C coal , C natural , and C liquid are the carbon emissions of coal, natural gas, and LPG, respectively; E electricity , E natural , and E liquid are the local power generation, natural gas power generation, and LPG power generation, respectively; σ is the carbon dioxide emission coefficient of coal, the equivalent value is 1.3023 kg/kWh (Ma et al. 1999); and ω is the proportion of coal power generation in the total power generation. Because coal power generation statistics are gradually released after 2012, and coal power generation has long been the total thermal power generation in China, this paper selects thermal power generation as a substitute variable for coal power generation for conversion, θ is the carbon dioxide emission coefficient of natural gas, and μ is the carbon dioxide emission coefficient of liquefied petroleum gas.
(2) This article uses per capita carbon emissions (total carbon emissions/GDP, PI_P, kg/person) to reflect the carbon emissions of cities at the prefecture level and above in China and adopts carbon emission intensity (total carbon emissions/GDP, PI_G, kg/yuan) as a substitute variable for robustness discussion.

Explaining variables
The income gap between urban and rural areas (G). Referring to the measurement method of the Gini coefficient in Chen Gang's (2011) research, this paper intends to adopt the urban Gini index (Gini Index) to reflect the urban-rural income gap in cities at the prefecture level and above. The specific calculation formula is: (2) Among them, p r and p u are the proportions of the urban-rural population and urban population at the prefecture level and above; w r and w u are the proportions of the rural population's total income in gross local revenue and the proportion of the urban population's total income in gross local revenue. The value range of the urban-rural Gini coefficient is [0,1]. The larger the value, the larger the urban-rural income gap, and vice versa, the smaller. Since China's urban population data of prefecture level and above cities have been published relatively and completely in various statistical yearbooks and statistical bulletins since 2005, and the relevant data has been seriously missing again after 2015, the period of this paper is 2005-2015, and the urban-rural Gini coefficient of 270 cities at prefecture level and above in China from 2005 to 2015 was calculated based on the above method.

Control variables
(1) Industrial structure (structure). Ma and Stern (2008) believe that the upgrading of the industrial structure reduces carbon emissions, and Shao et al. (2019) also pointed out that the upgrading of the industrial structure will increase the level of local carbon emissions. This article refers to the research of Yuan et al. (2016) and uses the logarithm of the per capita added value of the secondary industry (10,000 yuan/person).
(2) Economic openness (FDI). Given the serious lack of urban trade data within the research span, this article intends to use foreign direct investment to reflect the degree of local economic openness. Xu and Deng (2012) found that technological improvements brought about by foreign direct investment have significantly improved China's environmental pollution; however, the "pollution paradise" hypothesis argues that foreign direct investment often brings environmental pollution to the host country's lowend industries (Markusen And Venables 1999;Keller and Arik 2002). And this article selects the logarithm of the local per capita foreign direct investment (USD/person) as an indicator reflecting the degree of capital freedom. (3) Degree of urbanization (urban).  pointed out that the expansion of urbanization has increased local carbon emissions, and Liddle (2004) also believes that urbanization may help alleviate carbon emissions. Therefore, this paper selects the proportion of the urban population in the total population to reflect the degree of urbanization in the region. (4) Infrastructure. He et al. (2019) found that improved infrastructure will increase residents' public transportation utilization rate and reduce carbon emissions. Indicators such as highway mileage and railway mileage within the jurisdiction can reflect the level of local infrastructure construction to a certain extent. This paper selects the number of buses per capita (vehicles/10,000 people) in cities at and above the local level to measure the level of infrastructure. (5) Finance. Lu et al. (2015a) believe that the current fiscal expansion has regulated local pollution to a certain extent. However, Feng and Fang (2014) found that the negative effects of the expansion of public fiscal expenditures on China's environmental pollution control have gradually emerged. This paper selects the proportion of local annual fiscal expenditures in GDP and takes the logarithm to measure the intensity of local public fiscal expenditures. (6) Leverage. Tamazian et al. (2009) found that financial development has a significant inhibitory effect on per capita carbon emissions, but Boutabba (2014) believes that financial expansion has increased the total carbon emissions. Therefore, this article selects the local financial leverage ratio as a measure of the degree of local financial development. The specific calculation method is: the leverage ratio = of the balance of various loans of financial institutions at the end of the year/GDP.

Data sources and statistical analysis of variables
The period of the sample data in this article is selected from 2005 to 2015. The selected relevant data mainly come from the "China Statistical Yearbook," "China City Statistical Yearbook," "China Regional Statistical Yearbook," "China Electric Power Yearbook," statistical yearbooks of various provinces and cities, and annual statistical bulletins of cities at the prefecture level and above. To avoid the heteroscedasticity problem that may appear in the empirical process, this paper has carried out logarithmic processing on some variables. In particular, this article is restricted by the statistical results of urban and rural permanent residents in various yearbooks and statistical bulletins and excludes the urban and rural Gini coefficients of all cities in Jilin Province. In addition, to obtain balanced panel data, this paper further excluded some data from prefecture level and above cities with a serious lack of relevant data. The statistical description of the variables is shown in Table 1.

Empirical results of the basic model
To eliminate the potential unit root problem of the model, this paper selects ADF to test the unit root of the variables.
The relevant results are shown in Table 2. It can be found that the P value of each variable is less than 0.1%, so the null hypothesis of the existence of a unit root is rejected, that is to say, the variable data selected in this paper is stable and can be used for empirical testing.
Models 1-3 in Table 3 show the empirical results of the impact of urban and rural Gini coefficients on per capita carbon emissions under the basic model. Model 1 tested the relationship between the urban and rural Gini coefficient and per capita carbon emissions without the inclusion of control variables. The results found that the primary parameter of the urban and rural Gini coefficient was significantly positive, and the quadratic parameter was significantly positive, that is, the impact of urban and rural Gini coefficient on per capita carbon emissions does have nonlinear characteristics. Model 2 introduces control variables at the prefecture level and above, but does not control the city effect and year effect. Model 3 further controls the city effect and year effect while introducing control variables. It can be found that the primary parameter of the urban-rural Gini coefficient is significantly positive, and the quadratic parameter is significantly negative, indicating that the urban-rural income gap has an "inverted U-shaped" impact on environmental pollution in the process of expanding. The first-order partial derivative concerning G can be obtained from the results of model 3: PI G = 5.5079 − 19.8224G , if it is equal to 0, then there is: G = 0.2779 , that is, when the urban-rural income gap is lower than 0.2779, the widening of the urban-rural income gap increases the per capita carbon emissions of the land, and when it is higher than 0.2779, the widening urban-rural income gap reduces per capita carbon emissions.
In addition, the parameters of industrial structure and urbanization rate in each control variable of model 3 are significantly positive, indicating that the increase of the added value of the secondary industry in the GDP will increase the per capita carbon emissions. In other words, the current economic growth model characterized by the expansion of the secondary industry has significantly increased regional environmental pollution. The parameters of FDI are significantly negative, which indicates that in China, FDI has significantly improved China's environmental pollution through technological diffusion effects, while its "pollution paradise" effect is relatively limited in China. The parameter of the urbanization rate is significantly positive, indicating that China's long-term rapid industrialization and urbanization have exacerbated environmental pollution. The infrastructure parameters are not significant, indicating that they have no significant relationship with the environmental pollution in China. The coefficient of fiscal spending is significantly negative, indicating that increased government spending will increase per capita carbon emissions. The leverage ratio parameter is significantly negative, indicating that regional financial development may help to weaken the constraints of production financing, encourage enterprise R&D and upgrade, and alleviate local pollution. In terms of the parameter symbols and significance of comprehensive control variables, industrial structure, FDI, urbanization rate, fiscal expenditure, and leverage ratio will have a stronger impact on local environmental pollution. Therefore, the current energy conservation and emission reduction targets can be mainly carried out around the optimization of industrial structure, economic opening, urbanization, government finance, and regional financial development.
Heteroskedasticity and autocorrelation of model variable indicators may bias the model results. To examine whether there are heteroskedasticity and autocorrelation in the basic model, this paper carried out the heteroscedasticity and autocorrelation test, and the results are shown in Table 4. It can be found that the P value of the heteroskedasticity test is 0.0000, indicating that the null hypothesis that the model does not exist in heteroscedasticity is rejected. The P value of the autocorrelation test is also 0.0000, that is, rejects the null hypothesis that the model does not have autocorrelation. To overcome the influence of heteroskedasticity and autocorrelation on the results of the basic model, this paper uses the robust standard error to correct model 4. The results show that the firstorder parameter of the urban and rural Gini coefficient is significantly positive, and the quadratic parameter is significantly positive. In other words, after eliminating the interference of heteroskedasticity and autocorrelation on the basic model, the impact of the urban-rural income gap on carbon emissions is still promoted first and then suppressed.
Model 5 is the empirical result of the fixed-effects panel model (IV-FE) under the condition that the explained variable lags one period as the instrumental variable. The results show that the linear and quadratic parameters of the urban and rural Gini coefficient are significant, and the signs are consistent with expectations. Therefore, combined with models 1-5 in Table 3, it can be found that the urban-rural income gap between prefecture level and above cities in China from 2005 to 2015 has a significant "inverted U"-shaped impact on urban pollution.

Robustness and endogeneity test
(1) Robustness test. Models 1-2 performed bilateral tailing of 1% and bilateral tailing of 1% on the explained variables, respectively (Table 5) . Among them, the primary parameter of the urban and rural Gini coefficient was significantly positive, and the quadratic parameter was significantly negative, which was con-sistent with the regression results of the basic model; the inflection points of models 1-2 are 0.2727 and 0.2953, which are still close to the results of the basic model. Model 3 uses carbon emission intensity to replace the original indicator as to the explained variance of the model. The primary term of the urban and rural Gini coefficient is significantly positive, and the second term is significantly negative. The inflection point is about 0.3070, which is also basically consistent with the original model. Model 4 replaces the original control variables with the one-period lagging term of the control variables to conduct an empirical test on the original model. The urban-rural Gini coefficient is still significantly positive for the primary term and significantly negative for the quadratic term, and the inflection point is at about 0.2546 which is still consistent with the original model. (2) Endogenous testing. Given the serious endogeneity between the variables may have a significant impact on the empirical regression results, this article must fully consider the potential endogeneity of the model. On the one hand, the setting of the empirical model in this paper cannot include all the factors that affect environmental pollution, such as environmental protection expenditures and R&D personnel in cities at and above the level; on the other hand, there is a two-way cause and effect between the explained variables and explanatory variables of the empirical model in this paper. The relationship is that the urban-rural income gap affects environmental pollution, and environmental pollution, in turn, affects the urban-rural income gap. Therefore, this article refers to the research of Gao and Wang (2016) and selects the explanatory variable to lag one period as an instrumental variable to test the model's endogeneity. The results are shown in model 5; the Hansen test value is within a reasonable interval, indicating that the selection of the instrumental variables in this paper is reasonable and effective; after the system GMM model is used to deal with the endogenous problem, the primary parameter of the urban and rural Gini coefficient is significantly positive, and the quadratic parameter is significant. It is negative, which is consistent with the empirical results of the basic model; in model 5, the inflection point of the urbanrural income gap on China's environmental pollution is located at about 0.2615, which is not much different from the inflection point of the basic model.
Therefore, combining the two-sided shrinking test, the two-sided censoring test, the explanatory variable/explanatory variable index replacement method, and the systematic

Heterogeneity analysis
Given China's vast territory, factors such as geographic location, factor endowments, and historical conditions have significant heterogeneity among regions, and the above heterogeneity may lead to differences in the impact of the urban-rural income gap on urban environmental pollution. Therefore, it is very important to discuss the heterogeneity of urban environmental pollution caused by the urban-rural income gap. This article refers to existing research and uses three classification standards to discuss consistency: First, according to the practice of most traditional documents, the sample cities are divided into eastern, central, and western regions according to their geographic location; the second is to draw on the research of Li (2017), divide the median of the sample capital-labor ratio in 2013 as the dividing line, and divide the cities into high and low according to the capital-labor ratio of each city in 2013; the third is to refer to the method of city size division by Sun et al. (2018) and classify cities with an urban population of more than 3 million in 2013 as large cities and classify them as small and mediumsized cities with an urban population of less than 3 million. The results of heterogeneity analysis are shown in Table 6. Models 1-3 respectively give the empirical results of the impact of the urban-rural income gap on urban pollution in the eastern, central, and western regions of China. Among them, the "inverted U-shaped" impact of the urban and rural Gini coefficient on per capita carbon emissions is more significant in the eastern, central, and western regions of China. From the perspective of the inflection point of environmental pollution, the inflection points in the eastern, central, and western regions are 0.2276, 0.2574, and 0.2860, respectively, which are all within the value range of [0,1], indicating that the income gap between urban and rural areas in China from 2005 to 2015 has a significant "inverted U-shaped" impact on environmental pollution in the eastern, central, and western regions. In addition, the inflection point of China's environmental pollution has been increasing from the east, middle, and west, indicating that from the east to the west, the pollution incentive range of the widening urban-rural income gap in China has shown a continuous expansion. Among the control variables, industrial structure, urbanization, and fiscal intensity have significantly expanded environmental pollution in the eastern region, while FDI and infrastructure have significantly suppressed environmental pollution, and the environmental pollution effect of the leverage ratio is not significant; for the central region, the urbanization rate, fiscal intensity, and increased environmental pollution have no significant impacts on other factors; for the western region, the industrial structure and urbanization rate are the main factors affecting local environmental pollution, and the effects of other factors are less obvious. Models 4-5 give the empirical results of capital-labor endowment heterogeneity. The first-order parameter of the urban-rural Gini coefficient in areas with a high capitallabor ratio and the low-capital-labor ratio is significantly positive, and the quadratic parameter is significantly negative. Moreover, the environmental inflection point of areas with a high capital-labor ratio is located at 0.2797, while the environmental inflection point of areas with a low capitallabor ratio is located at 0.2784. The inflection points of the two types of areas are similar. Therefore, the income gap between urban and rural areas in China is either in areas with high capital-labor ratios or areas with high capital-labor ratios. Areas with low capital-labor ratios all have a significant "increase" and then "decrease" influence on environmental pollution, and there is no significant difference in the locations of the environmental pollution peak points of the urban-rural income gap between the two types of areas. Among the control variables, the industrial structure of cities with high capital-labor ratio, urbanization rate, and fiscal strength are the main factors that increase environmental pollution, while FDI plays a major role in reducing pollution; for cities with low capital-labor ratios, the industrial structure and urbanization rate are the main factors that exacerbate urban pollution, while FDI and leverage have significantly suppressed local pollution.
In addition, this article draws on the research of Sun et al. (2018), classifies cities at prefecture level and above with urban populations of more than 3 million in 2015 as large cities, and classifies the remaining samples as small-and medium-sized cities, trying to discuss the heterogeneous impact of urban-rural income gap on environmental pollution from the perspective of city scale, and the results are shown in models 6-7. The results show that the urban-rural Gini coefficient of large cities and per capita carbon emissions show a "rising first and then suppressing," with an inflection point at 0.2039; while the urban-rural Gini coefficient of small and medium-sized cities also shows a trend of "rising first and then suppressing" per capita carbon emissions, its inflection point is at 0.2903, which is much larger than that of large cities. Therefore, the urban-rural income gap between the two cities has the same impact on environmental pollution. The scope of pollution incentives for the income gap between urban and rural areas is much higher than that in large cities. Among the control variables, the industrial structure, urbanization rate, and fiscal intensity in large cities have increased environmental pollution, while FDI and infrastructure have played a good environmental cleaning effect; for small and medium-sized cities, the industrial structure and urbanization rate have increased environmental pollution. The main factors of pollution and FDI and leverage ratio have a significant positive effect on reducing local pollution. In summary, the "inverted U-shaped" impact of the urban-rural income gap on environmental pollution is significant in the eastern and central regions, but not in the western region. In addition, the environmental inflection point of the urban-rural Gini coefficient in the central region, high-capitallabor regions, and small and medium-sized cities is far away. Therefore, the urban-rural income gap has only an increased effect on local environmental pollution in reality, while the environmental inflection points of the eastern region, low-capital labor regions, and urban-rural Gini coefficients of large cities are located at a lower position. Therefore, the urban-rural income gap in the above-mentioned regions has a significant "inverted U-shaped" impact on environmental pollution.

Mechanism test
The previous article empirically tested the impact of China's urban-rural income gap on environmental pollution and discussed its robustness and heterogeneity. As mentioned above, the urban-rural income gap has an impact on the environment from both the demand and supply sides. Therefore, from the demand side, this article uses the logarithm of the local per capita consumption (yuan/person) as an intermediary index to test the changes in the urban-rural income gap. The impact of changes in the scale of demand, which in turn leads to changes in local environmental pollution, is specifically measured as follows: Among them, consumption it represents the per capita consumption expenditure of cities at the I prefecture level and above in year t (thousand yuan/person), and consumption iut and consumption irt are the urban per capita consumption expenditures and rural per capita consumption expenditures, respectively. Among them, consumption iut and consumption irt are the per capita nominal consumption expenditure of urban residents and the per capita nominal consumption expenditure of rural residents, respectively, obtained by deflation according to the urban consumer price index of the province (city) where the city is located and above and the consumer price index consumption it = consumption iut • p iut + consumption irt • p irt of rural residents in China (base period: 2005). In addition, this article uses the human capital index as an intermediary indicator to test from the perspective of the supply side that the urban-rural income gap causes changes in human capital and then affects the impact of environmental pollution. The calculation method of the human capital index is as follows: Among them, h is the human capital index, edu is the number of students in school, and p, j, and c are elementary school, junior high school, and university, respectively.
In addition, to effectively test the mediation effect, this paper sets the empirical model as: Among them, consumption and HC represent the local per capita consumption and human capital index, respectively. Equations 1-2 test the mediating effect of per capita consumption and human capital index on the urban-rural income gap. Equations 3-4 test the mediating effects of per capita consumption and human capital in the process of the urban-rural income gap affecting environmental pollution. Equation 5 adds the interaction terms of the urban-rural income gap and per capita consumption, and human capital index to the original model, and comprehensively examines the changes in market demand and human capital caused by changes in the urban-rural income gap, and thus the impact on urban pollution. The test results are shown in Table 7.
The results of models 1-2 show that the expansion of the urban-rural income gap in cities at the prefecture level and above in China from 2005 to 2015 has generally restrained consumption and human capital. And through the test results of model 3, it can be found that the expansion of the consumption scale can not only increase the consumption of environmentally friendly products and reduce pollution but also may increase environmental pollution due to the restriction of the urban-rural income gap. The results of model 4 show that although the accumulation of human capital helps directly reduce urban environmental pollution, the urban-rural income gap can also increase environmental pollution through the indirect effects of human capital.
From the results of model 5, it can be seen that after incorporating per capita consumption, human capital, and their respective interactions with urban and rural Gini coefficients into the model, at the end of the demand scale, the parameter of per capita consumption is significantly negative, and the parameter of the interaction term with the urban-rural income gap is significantly positive, which means that the expansion of demand directly reduces urban pollution on the one hand. This may be caused by the upgrade of demand caused by consumption expansion and then promote the consumption of environmentally friendly products; on the other hand, the urban-rural income gap may indirectly and significantly restrain the overall consumption scale of environmentally friendly products through the income distribution effect, while the scale of demand is expending. On the human capital side, the human capital index parameter is significantly negative, and the interaction term with the urban-rural income gap is positive. This shows that the expansion of human capital also directly reduces urban pollution. This is obviously because the expansion of human capital has expanded the accumulation of skilled labor. "Pool" actively promotes the production of environmentally friendly products by enterprises; however, the urban-rural income gap induces the formation of a small amount of highend human capital through the income distribution effect and indirectly hinders the improvement of the environment by inhibiting the accumulation of local human capital. The test results of model 5 are further obtained after the first derivative of the demand scale and human capital are obtained: When PI consumption = 0 , it can be found that the environmental pollution inflection point of the urban and rural Gini coefficient to per capita consumption is at 0.1307, that is, when the urban and rural Gini coefficient is less than 0.1307, the expansion of per capita consumption alleviates environmental pollution; when the urban and rural Gini coefficient is greater than  0.1307, the expansion of per capita consumption aggravates environmental pollution. And when PI∕ HC = 0 , it was found that the environmental pollution inflection point of the urban-rural Gini coefficient on the human capital index was at 0.3047, that is, when the urban-rural Gini coefficient was less than 0.3047, the human capital index had a depressing effect on per capita carbon emissions; when the urban-rural Gini coefficient was greater than 0.3047, the human capital index promotes per capita carbon emissions. Based on the above results, it can be concluded that the scale of demand and human capital have significantly affected environmental pollution and the impact has a "positive U-shaped" trend, and the urban-rural income gap has played a key control role in the above-mentioned impact process.

The relationship between the urban-rural income gap and environmental pollution introduced by spatial correlation
With the strengthening of China's regional integration trend, the correlation between production and consumption in various regions continues to deepen. Given the possible spatial correlation of environmental pollution, the concept of "spatial correlation" needs to be introduced when examining the environmental pollution effects on the urban-rural income gap. In other words, the environmental pollution among cities above the prefecture level in China may be geographically related. To characterize the spatial correlation of environmental pollution between regions, it is required to select an appropriate spatial weight matrix to modify the original model. This article uses Moran's I index to reflect the relevance of regional environmental pollution, and its basic expression is as follows: In the above formula, PI = 1 � 2 n is the number of cities at the prefecture level and above (the value is 270 in this paper), and d ij is the spatial weight matrix. Considering that the spatial correlation of environmental pollution is mainly manifested in the degree of geographical distance, this paper selects the geographical distance matrix as the space weight matrix, and the geographical distance matrix is defined where d is the distance between the urban areas of two prefecture level and above cities. Concerning existing research, this paper sets the environmental pollution model of the urban-rural income gap including spatial correlation as: The test results of the relationship between the urban-rural income gap and environmental pollution with the introduction of spatial correlation are shown in Table 8. The results of model 1 show that, after considering the spatial correlation, the primary parameters of the urban and rural Gini coefficients in the full sample and the eastern, central, and western samples are still significantly positive, and the quadratic parameters are significantly negative, and the size and sign of the parameter are similar to the regression results of the basic model, indicating that from 2005 to 2015, the impact of urban-rural income gaps on environmental pollution in all prefecture level and above cities in China or eastern, central, and western cities showed a steady "inverted U-shaped" trend. The environmental inflection points of the country, the east, the central, and the west are located at 0.2510, 0.2205, 0.2505, and 0.2672, respectively, which have not changed much from the basic model. In addition, the sign, size, and significance of the control variables are not much different from the regression results of the basic model. Therefore, it can be considered that it is reasonable to incorporate spatial correlation into the basic model. In addition, after incorporating spatial correlation into the basic model, the ρ parameter is positive across the country and in the eastern, central, and western regions, and both have passed the 1% significance test, indicating that whether it is in the country or the eastern, central, and western regions internally, there is a significant positive spatial correlation between environmental pollution in cities at prefecture level and above. In other words, the increase in environmental pollution in a specific area will significantly drive environmental pollution in surrounding areas.

Further discussion on the urban-rural income gap and environmental pollution: the perspective of environmental regulation effects
From the foregoing, it can be seen that the urban-rural income gap has a significant "inverted U-shaped" impact on urban pollution, and this impact is realized through its nonlinear impact on the scale of demand and human capital. So in the context of China's increasingly strict environmental system in recent years, what is the impact of the urban-rural income gap on urban pollution? Based on the above perspective, examining the impact of urban-rural income disparity on urban pollution may help to better understand the (12) inherent relationship between China's urban-rural income disparity and environmental pollution. Zhan (2018) and Banerjee et al. (2021b) pointed out that the intensity of environmental regulations and the urban-rural income gap have had a significant impact on the regional environment. Therefore, this paper re-examines the urban-rural income gap and environmental pollution in cities at the prefecture level and above in China from the perspective of the intensity of environmental regulations. Environmental regulation intensity (regulation). Existing studies have adopted three main types of environmental regulation indicators: one is the proportion of pollution investment and pollution charges in each region in the added value of the secondary industry; the other is the laws, regulations, policies, rules, and regulations related to the environment formulated and promulgated for the region organizing documents, using the number of results to reflect the intensity of regional environmental regulations; third, constructing the intensity of local pollution emissions and the intensity of environmental regulations with the help of regional industrial smoke, industrial wastewater, and sulfur dioxide emissions as a proportion of the added value of the secondary industry. As this article selects China's prefecture level and above cities from 2005 to 2015 as the research object, this article refers to the research of Ye et al. (2018) that uses industrial smoke, industrial wastewater, and sulfur dioxide emissions to account for the proportion of the secondary industry's added value in 2005-2015 China's prefecture level and above cities' environmental regulation intensity index; the specific calculation method is as follows: In the above formula, p ijt represents the emissions of the jth pollutant from prefecture level and above cities in year t, GDP sec represents the added value of the secondary industry, and pd represents the pollution emission intensity per unit of the added value of the secondary industry. On this basis, the above calculation results are further standardized: In the above formula, pd s ijt is the normalized value of p ijt . Based on the above results, the intensity of environmental regulations can be calculated: To investigate how the urban-rural income gap affects urban pollution from the perspective of environmental regulation, this paper introduces environmental policies based on the original model, to explore the effect of environmental regulation in the impact of the urban-rural income gap on environmental pollution; the model is as follows: Appropriate smoothing of the original data is very important for model checking. In this system of equations, this paper takes the logarithm of the environmental regulation intensity index, abbreviated as lnreg. The results are shown in Table 9. The results of model 1 show that the lnreg parameter is significantly negative, indicating that environmental regulations have significantly suppressed the urban-rural income gap. From the results of model 2, it can be found that the primary parameter of environmental regulation is significantly negative, and the second parameter is significantly positive. This indicates that theoretically, the impact of environmental regulation on environmental pollution is "inhibiting" and then (16) "promoting" positive. The possible reason for the "U-shaped" trend is that appropriate environmental regulations can help eliminate high-polluting enterprises and effectively regulate residents' consumption behavior. Industrial transformation and consumption upgrades can effectively reduce environmental pollution; however, as the intensity of regulation continues to increase, the excessive environmental threshold may not only inhibit the daily needs of ordinary residents but also force companies to "steal discharge" of pollutants, which will increase environmental pollution. According to model 3, it can be seen that the urban and rural Gini coefficient parameter is significantly positive, that is, the expansion of the urban and rural Gini coefficient in China at this stage has increased the local per capita carbon emissions as a whole. Model 4 adds the urban-rural Gini coefficient based on model 2. As a result, the primary term of environmental regulation is significantly negative, the second term is significantly positive, and the parameter of the urban-rural income gap is significantly negative. Therefore, it can be considered that the urban-rural Gini coefficient has played a significant intermediary role in the process of environmental regulation and in the process of "suppressing" and then "promoting" carbon emissions per capita. That is, appropriate environmental regulations can help improve the urban-rural income gap and thus reduce environmental pollution; in turn, excessively stringent environmental regulations may increase the income gap between urban and rural areas and worsen the local environment.

Conclusions and policy implications
Environmental protection and the income gap between urban and rural areas are hot issues that China's economy and society are concerned about at this stage. To investigate the potential nonlinear relationship between urban and rural income gap and environmental pollution, this paper explores the impact and mechanism of urban and rural income gap on environmental pollution in China's prefecture level and above cities from 2005 to 2015; the results show that the impact of urban-rural income gap on environmental pollution does have significant nonlinear characteristics. Different from the existing research mostly based on income level, this paper first points out at the theoretical and logical level: that the urban-rural income gap has an impact on environmental pollution mainly through the scale of demand and human capital, and the above mechanisms are important reasons for the "inverted U-shaped" trend effect of the urban-rural income gap on environmental pollution, which increases first and then decreases. Based on the above logical deduction, this paper uses the panel data of 270 prefecture level and above cities in China from 2005 to 2015 for empirical testing. The results show that the income gap between urban and rural areas in China has indeed caused the local environmental pollution to show an "inverted U-shaped" trend, and the inflection point of environmental pollution appears at 0.2779. The "inverted U-shaped" trend of environmental pollution in the urban-rural income gap is evident in the eastern, central, and western regions, regions with high capital-labor ratios, low capital-labor ratios, and large and small cities. The urban-rural income gap significantly affects environmental pollution through the scale of demand and human capital. The inflection points of urban and rural income environmental pollution between the scale of demand and human capital are located at 0.1307 and 0.3047, which is also the main cause of the "inverted U-shaped" trend of environmental pollution in the urban-rural income gap. Given the potential spatial correlation of environmental pollution, the empirical results of the spatial correlation model in this paper show that after the introduction of spatial correlation, the "inverted U-shaped" impact trend of China's urban-rural income gap on environmental pollution is still significant, with the inflection point at 0.2501, and the impact of geographical proximity on environmental pollution is also significant. Although environmental regulation has a "positive U-shaped" impact on environmental pollution through the income gap between urban and rural areas, in other words, reasonable environmental regulation helps to improve the environment, but too strict environmental regulation will not help energy conservation and emission reduction but may aggravate environmental pollution.
Therefore, this article has the following policy enlightenments to deal with China's environmental pollution at this stage: First, each region should choose the macro-control measures for the urban-rural income gap that is appropriate to the region's characteristics and that can maximize the local potential to ensure stable economic growth and steady improvement of residents' lives while maximizing energy conservation and emission reduction. The eastern region, regions with high capital-labor ratios, and large cities' urbanrural income gaps are already at a low overall position, but proactively adopting urban-rural economic integration and promoting urban-rural integration can still effectively alleviate environmental pollution; for the central and western regions, low-capital-labor regions as for small-and mediumsized cities, the integration of urban and rural income may increase local pollution in the short term, and it is particularly important to establish a governance system that coordinates industrial growth and environmental protection. Second, relying on urban and rural income governance policies and scientifically combining market mechanisms to manage the local environment. In areas with low urban-rural income gaps, market consumption and basic education should be actively expanded, especially support and tilt for inclusive people's livelihood expenditures; in areas with high urban-rural income gaps, local industry status, resource endowments, etc. should be combined objective reality and reasonable promotion of consumption upgrades and human capital accumulation, to avoid excessive consumption and waste of resources. Third, build and improve a comprehensive environmental protection management system. In the process of urbanrural dualization and environmental pollution control, it is particularly critical to construct and improve the pollution control system from the perspective of local characteristics. Therefore, effectively explore the pollution control effects of industry, urbanization, and environmental regulations; increase market-oriented construction; actively participate in and integrate the global production system; comprehensively promote infrastructure construction; and encourage and guide financial development, technological innovation, and other means that will pollute the region governance that is of great significance. Fourth, focus on the coordination of local governance and regional cooperation. The spatial relevance of environmental pollution requires that regions need to gradually get rid of the previous single local governance model and transform it into regional cooperative governance. Therefore, it is necessary to encourage the transition from regional competition to regional cooperation, eliminate regional administrative barriers and local protectionism, and promote regional inter-industry collaboration and integration and integration of regional factor markets to improve resource efficiency.