How Does Carbon Emission Reduction Efficiency Affect Regional Income Inequality? The Mediator Effect of Interregional Labor Flow

Global income inequality is widening and carbon emissions remain high. So, reducing carbon emissions and income gap are urgent challenges. *e purpose of this paper is to analysis how carbon emission efficiency influences the region income inequality. *e improvement of carbon emission reduction efficiency has widened the regional income inequality with the flow of high-tech labor as an intermediary variable in China. Methods used in this article are mediating effect model and DEA method. *is paper constructs a disposable income model of income and health costs, where health costs are a function of carbon reduction. If income is fixed, then the expectations of disposable income will change as the level of carbon emission reduction changes. *is study finds that the disposable income expectations of high-income areas increases, while the disposable income expectations of lower-income areas decrease with the improvement of carbon emission reduction efficiency. High-income regions attract high-income labor from other regions, resulting in the widening of regional income inequality under the constraint of high cost of living. *is result is verified by the data of China from 2007 to 2017.*e regression model with Geordie coefficient as the dependent variable, carbon emission reduction efficiency as the core independent variable, gravitation of high-tech talent as the mediator variable, and urbanization rate, educational level, social security coverage, and highway and railway traffic mileage as control variables not only verifies the above results but also finds that high-tech talents’ flow is not the only intermediary between carbon emission reduction efficiency and regional income inequality.*is paper finds that when the carbon emission reduction efficiency increases by one unit, the income inequality gap of 25 provinces increases by 0.0202 units, provinces with high carbon emission reduction efficiency increases by 0.107 units, and provinces with medium carbon emission reduction efficiency increases by 0.026 units. However, the income inequality gap of provinces with low carbon emission reduction efficiency decreases by 0.0390 units. *e carbon emission reduction efficiency of the high and medium carbon emission reduction efficiency groups is proportional to the income inequality, while the low carbon emission reduction efficiency group is the opposite, when the carbon emission reduction efficiency is grouped into high efficiency group,medium efficiency group, and low efficiency group. *e reason for this result is that the high carbon emission reduction efficiency of the former attracts high-income high-tech talent, while the latter’s narrowing regional income inequality benefits from the reduction costs of health and the government’s ecological compensation.*e effectivemeasures to narrow the income inequality are to implement carbon emission reduction policy, industrial policy, education investment policy, and public service policy, according to the above findings.


Introduction
In 2018, China's income inequality, as measured by the Geordie coefficient, reached 0.48 (the data comes from China Statistical Yearbook), representing a significant income inequality and an increase of 0.01 compared with the preceding year.
is not only exceeds the international warning line of 0.4 but also reveals an increasing trend. In the same year, according to the Carbon Brief, China's carbon emission level remained the highest worldwide, amounting to 10 billion tons, having increased by 2.3 percent compared with 2017.
is is almost double that of the US, whose carbon emission level comes second to China's. Consequently, efforts to narrow income inequality and reduce carbon emissions are currently among China's top priorities. Extensive research has focused on the impact of income inequality on carbon emissions and suggested that the enlargement of income inequality leads to increased carbon emissions [1,2]. erefore, narrowing income inequality will not only improve the financial welfare of low-income groups but will also effectively reduce carbon emissions. Various indicators-China's high Geordie coefficient, the regional concentration of wealth brought about by the knowledge resources' agglomeration in the United States, and the report of Public service: benefiting the whole people or favoring private interests? (issued in 2019 by OXFAM, a British nonprofit organization) that the world's wealth is accumulating among a small number of wealthy, while the wealth of the poorest fifty percent of the population has been reduced by 11 percent-demonstrate that efforts aimed at narrowing income inequality are beset with difficulties, while carbon emission reduction goals are also difficult to achieve and that failure to mitigate income inequality may be a key contributor to high carbon emission levels.
Several papers have recommended that carbon emissions can be controlled through environmental regulation and carbon emission reduction technologies, which would not only reduce carbon emission levels but also narrow the income inequality gap [3]. However, since 2013, China's carbon emission increment is close to 0, and the intensity of carbon emission reduction has decreased significantly [4], but the income inequality gap is still increasing.
us, narrowing the income inequality gap merely relying on carbon emission reduction is not always true, but it also depends on carbon reduction path selection.
is paper demonstrates the reasons why China's current carbon emission reduction path is not conducive to narrowing the income inequality gap and puts forward improvement measures. And, the main contribution of this paper is to find that the improvement of carbon emission reduction efficiency is the reason to increasing the income inequality. e framework of the remaining part of this paper is mainly arranged as follows. Section 2 is literature review. Section 3 is the mechanism analysis of carbon emission reduction efficiency, increasing the income inequality. Section 4 is the construction of the econometric analysis model. Section 5 is the empirical results analysis. Section 6 is empirical analysis of subregions. Section 7 is the conclusion.

Ecological Cost Factors.
According to environmental justice theory, scholars believe that environmental inequality is widespread [5,6], and it brings about the expansion of income inequality. erefore, the impact of environmental inequality of carbon emissions on income inequality cannot be neglected [7,8]. For microindividual units, different environmental conditions satisfy the demands of different income groups. Housing costs are often low in areas with low carbon emission reduction efficiencies, which are favored by low-income groups [9], and high pollution enterprises are not driven away as low-income groups lack the political negotiation ability [10], which lead to the formation of cluster districts of low-income groups [11]. Despite the government's implementation of measures aimed at improving the environment, this still primarily maintains the interests of high-income groups. Specifically, monetary penalties for smelters violating the Clean Air Act and the Clean Water Act are diverse across cluster districts of various income strata, but the punishment force in lowincome residential areas is far inferior to that in high-income residential areas [12]. Moreover, higher-income strata profit from the federal clean air standards in the US [13], while the lower-income strata are shocked by the negative impact of environmental protection acts on areas such as unemployment and rising oil prices [14]. e phenomenon of income inequality caused by environmental inequities in various countries or regions may also be explained by the "pollution haven hypothesis" [15]. Under open economic conditions, developed areas implement strict environmental protection policies, while underdeveloped areas pay greater attention to economic growth and ignore carbon emission reduction.
us, industries with low carbon emission reduction efficiency and low additional value continuously shift from developed areas to underdeveloped areas, resulting in the latter becoming the pollution haven of the former. Low-income areas attract more corporations with high pollution levels and low carbon emission reduction efficiency, leading to sustained environmental damage in these regions. By contrast, the environment in high-income areas is steadily ameliorated due to the attention paid to environmental quality and the establishment of high-quality environmental standards. Transnational corporations in developed countries transfer their industries with high pollution and low carbon emission reduction efficiency to less developed countries through joint ventures and sole proprietorship and even transfer their wastes. Because the added value of industries with low carbon emission reduction efficiency is relatively low; generally, the income inequality between low-income areas and high-income areas continues to widen.

Institutional Factors.
e current international economic order leads to environmental inequality and then expands the international inequality between the rich and poor countries and areas. e less developed countries export primary products with high environmental resource input, which is not only harmful to the local environment but also low-priced. By comparison, the developed countries import these goods, which not only protect their own environment but also encroach upon the environmental and economic interests of the less developed exporting countries [16]. Hence, most resources are transferred from underdeveloped areas to developed areas, and the deteriorated environment and increased carbon emissions in underdeveloped areas, owing to resource development, are not compensated for by the latter [17], resulting in widening inequality between the rich and the poor in the world.
Although the income level in high carbon emission areas is relatively low, low-income groups yearn for the lifestyle of high-income groups, which may contribute to the poor efficiency of carbon emission reduction and further exacerbate income inequality. If the consumption standard of the rich becomes the general consumption standard in a society with high-income inequality, all consumers will spend more in a bid to fulfill and sustain this standard [18], which perhaps explains the reason the income inequality gap is widening in the US with increased household bills and extended working hours of different income groups [19]. e same happened in China, whether the poor or the rich buy houses as much as possible, which also lead to carbon emission reduction difficulties [20]. A further comparison finds that income inequality increases per unit in relatively rich countries and the daily working time increased by 1.8 to 3.4 percent accordingly [21]. Longer working times are associated with larger ecological footprints produced by natural resources utilization based on consumption [22]. Moreover, a greater work burden weakens employees' awareness of environmental protection, for example, they may choose to drive private cars rather than cycle or take public transportation to save time or they may employ housekeeping service staffs whose commuting practices can generate more greenhouse gases [22,23]. Simultaneously, increased working time and working intensity could also raise the risk of disease in low-income groups. To insure their health or to treat diseases, low-income groups are likely to pay higher healthcare costs than the income received as a result of extended working time, which further contributes to widening income inequality.
Social elites are increasingly concentrated in specific communities and private schools [24], and high-quality resources are increasingly accumulating among a minority of rich people due to differences in the ecological environment, so the income of low-income groups will continue to decline. e isolation of the ecological environment is essential to fix the living and working places of different income strata, which results in the concentration of public resources and educational resources among high-income groups who have the ability to pay for these resources. By contrast, low-income groups have significantly fewer opportunities to acquire high-income jobs and high-quality education, which again contributes to widening the income inequality gap.

Eco-Innovation Factors.
e increase in carbon emission reduction efficiency can narrow income inequality, but it might also lead to growing income inequality because the differences in the ecological environment among various regions restrict the diffusion of carbon emission reduction innovation technology. e income of high-income groups mastering innovation technology will further increase, while that of low-income groups in adverse living conditions will decrease owing to the lack of innovation technology [25], which is obvious in developed countries [7]. While lowincome groups typically lack the educational background to master these technologies, innovation technology is mastered by well-educated high-income groups because of the separation of working and living areas and the significant difference in the quality of education is enjoyed by the two income strata. Carbon emission reduction efficiency is high in high-income areas but is poor in low-income areas. erefore, from a broad perspective, the carbon emission reduction efficiency has not reached the optimal level. Lowincome groups are unable to grasp the innovation technology associated with carbon emission reduction; thus, it cannot be used to reduce the carbon emissions of high carbon industries within a short period. Moreover, these high carbon industries are not located in the living and production areas of high-income groups, and carbon emission reduction also entails certain costs, so high-income groups lack the motivation to help low-income groups reduce carbon emissions. However, the mobility of carbon dioxide obliges the high-income groups to engage in political discourse aimed at closing down the high carbon emission industries where low-income groups work in directly. As a result, this leads to unemployment among low-income groups, intensifying income inequality between the two groups. erefore, when carbon emission reduction efficiency increases, income inequality may switch from decreasing to increasing. e reason income inequality switches from decreasing to increasing may also be that the efficiency of carbon emission reduction does not correspond to the level of economic development because excessive carbon emissions result in widening income inequality. Different levels of economic development align with different industrial structures that release carbon emissions to varying degrees [26]. If pursuing the reduction of carbon emissions and improvement in the efficiency of carbon emission reduction is beyond the ability of current carbon emission reduction technologies, a key means of reducing carbon emissions would be to cease the production of high carbon emission enterprises, that is, reducing carbon emissions by decimating the economy. e result of economic recession is unemployment, and unemployed groups are mainly the lowincome employees of high carbon emission enterprises, so income inequality will also increase.
Furthermore, income inequality and carbon emission reduction are both mutually causal with technological innovation, and technology, as an intermediary, is one of the paths of correlation between the two. Technological innovation is the main factor in widening income inequality [3]. In turn, the expansion of the income inequality gap will also impede the progress of technological innovation; as such, the expansion is not conducive to enhanced research and development (R&D) investment and the introduction of new technology [27]. However, several scholars have advanced contrasting perspectives [28]. Moreover, some studies have suggested that ecological innovation technology is an effective means of carbon emission reduction [16,26,29]. In turn, regulations aimed at promoting carbon emission reduction could drive technological innovation [30].
Technological innovation may be an intermediary variable in the interaction between income inequality and carbon emissions, but numerous studies have focused on the Mathematical Problems in Engineering impact that income inequality has on carbon emission reduction. Wang et al. [31] alone argued that carbon emission reduction is the one-way cause of income inequality. Lin et al. [32] pointed out further that China's carbon trading market promotes technological progress by increasing R&D investment and altering income inequality [3]. Yet, few studies have thoroughly examined the impact of carbon emission reduction on income inequality. e uncertain relationship between technological innovation, income inequality, and carbon emission reduction may be caused by the level of economic development. Most studies have indicated that the relationship between income inequality and carbon emission reduction is in inverse proportion in developed regions, while it is in direct proportion in underdeveloped regions [8]. Hence, when studying the impact of carbon emission reduction on income inequality, we should take into account the level of economic development and the influence of technological innovation.
Existing research focuses on the analysis of the correlation between carbon emission reduction and income inequality, as well as the reasons why the former affects the latter, but does not pay attention to the impact of the improvement of carbon emission reduction efficiency on income inequality. However, improving carbon emission reduction efficiency, which is the most commonly used method in carbon emission reduction, is one of the most effective ways to reduce carbon emissions. However, if we only focus on the improvement of carbon emission reduction efficiency and do not pay attention to the impact on the income inequality, it may lead to an increase in social unfairness. erefore, it is necessary to analyze the impact of carbon emission reduction efficiency on income inequality.
Overall, the correlation between income inequality and carbon emission reduction is affected by economic development level and technological innovation. However, the two factors remain underexplored, leading to ambiguity regarding the precise correlation between income inequality and carbon emission reduction, that is, the effects of reducing income inequality and carbon emissions are not obvious. Existing studies have five main defects. First, although numerous studies have consistently concluded that the relationship between income inequality and carbon emissions are related to the degree of economic development, the degree of economic development has been subjectively established, that is, it has no quantitative basis and the denotation is ambiguous. Moreover, the degree of economic development is simply divided into two classes-developed and underdeveloped-which mask the differences between individuals who are in the same class but at different developmental levels. Second, technological innovation is considered a direct factor in income inequality; however, it actually plays an indirect role by changing the material capital productivity or human capital productivity.
ird, carbon emission reduction does not simply entail the reduction of carbon emissions. e maximum reduction of carbon emissions should be pursued on the condition that it will not result in an economic recession. However, most studies have overlooked this requirement. Fourth, there are endogeneity problems due to the causal relationship between carbon emission reduction and income inequality. Fifth, the current research has proposed that carbon emission reduction can narrow the income inequality gap, but the carbon emission reduces significantly and the income inequality gap widens simultaneously in China. And, the path of carbon emission reduction affecting income inequality is not clear.
In view of the above, aiming at the first four research deficiencies, this paper uses environmental Data Envelopment Analysis (DEA) to calculate carbon emission reduction. is includes economic development level and technological progress and defines them as the efficiency of carbon emission reduction. Carbon emissions can be expressed as carbon reduction efficiency to solve endogeneity problems. en, based on this, the period random effects model is used to analyze the impact of carbon emission reduction efficiency on income inequality. Aiming at the last research flaw, this paper proves that labor mobility is one of the ways through which the efficiency of carbon emission reduction widens the income inequality.

Mechanism to Widen the Income Inequality by Improving Carbon Emission Reduction Efficiency: Labor Migration Path
e mechanism to widen the income inequality gap by improving carbon emission reduction efficiency is that the improvement of carbon emission reduction efficiency in high-income areas may attract high-income groups in low carbon emission reduction efficiency areas, which will further expand the income inequality. It means that labor migration is a mediator variable in the carbon emission reduction efficiency, widening the income inequality. How to move the labor is decided by the judgment of expected utility, including expected wage and living costs [33]. One of the main living costs is health costs, which are reduced by improving the ecological environment [26,34]. Suppose the health cost of a province is m h . e carbon reduction level is e h ∈ [0, 1]. e closer to 1 e h is, the more the carbon emission reduces. e average wage levels in high-income and low-income regions are ω I and ω J , respectively, ω I > ω J , so the disposable income in these two areas are erefore, the disposable incomes are, respectively, in the high-income and low-income areas, and σ 2 is a constant. If people are risk-averse, the risk aversion coefficient is α � − d 2 U/dy 2 /dU/dy. According to the risk aversion coefficient, the utility function is U(y) � − C 1 /α exp(αy) + c 2 , which is simplified as U(y) � − C exp(− αy). Other regional information Z is fixed.
e conditional expectation functions of utility, respectively, are formulas (1) and (2) in high-income and low-income areas: Suppose ω I is a constant in high-income areas: Suppose ω J is a constant in low-income areas: e first derivatives of the carbon emission reduction of equations (3) and (4) are equations (5) and (6), respectively: and us, the utility of high-income area increases, and the utility of low-income area decreases with the improvement of carbon emission reduction efficiency. Specifically, the carbon emission reduction efficiency has improved in high-income areas, and the gravitation of high-income areas to the labor of low-income areas has increased. However, when labor migrates to highincome areas from low-income areas, it is necessary to estimate costs, such as wage level, flow distance, and price level. In China, the main cost is house price [35]. erefore, most of the labors settled down in high-income areas; from low-income areas are higher-income groups, such as hightech talent, while low-income labor cannot afford the high living costs in high-income areas. is leads to the laborer agglomeration with the same income level and expands the income inequality gap.

Base Panel Model.
According to the above analysis, a panel data model is used to analyze the impact of carbon emission reduction on income inequality. According to a study by Grunewald et al. [8], the dependent variable is the Geordie coefficient (G) for measuring income inequality, the core independent variable is carbon emission (C), and the mediator variable is the labor gravitation (Labor_grav). Furthermore, the control variables include the level of economic development (Y), technological innovation (T), the level of urbanization (Urb), education level (Edu) [36], basic pension insurance (Pen) [37], unemployment insurance (Unempl) [38], health insurance (Heal) [39], highway density (Hwd), and railway density (Rwd) [40]. All control variables are represented by c ij . e specific models are equations (7)- (9): Labor It is divided into three steps to judge the mediator variable. e first step is to check whether the carbon emission reduction efficiency has a significant impact on the Geordie coefficient, as shown in equation (7). If it is significant, then the second step is to test whether the carbon emission reduction efficiency significantly affects the labor gravitation, as shown in equation (8). If it is significant, then the third step is to examine the significance of the impact of carbon emission reduction efficiency and labor gravitation on the Geordie coefficient. If the impact of labor gravitation is significant, the labor gravitation is the mediator variable of the carbon reduction efficiency impacting on the Geordie coefficient.

Environmental DEA Methodology and Panel Model
Improvement. Equations (7) and (9) analyze carbon emissions rather than carbon emissions' reduction. To overcome this defect, this study uses the environmental DEA methodology to calculate the efficiency of carbon emission reduction, as shown in formula (10), which is an output set of production technology of production function P(x) � (y, u) : (x, y, u) ∈ T producing GDP and CO 2 [41]. x represents the input elements including capital, labor, and energy. T is the technological innovation in the production process. e outputs of the various optimal decision-making units form the production frontier, which is determined by the hypersurface composed of all effective production activity points (x, y, u) in P(x). P(x) has the characteristics of closedness, boundness, and convexity. e reason this paper chooses the model of constant scale is that the survey period is 10 years, which belongs to the shortterm study: is paper replaces the variable C in equations (7)-(9) with the results δ of equation (10), δ ∈ [0, 1]. δ calculates the relative value of carbon emission reduction from each decision-making unit relative to the production frontier, that is, the efficiency of carbon emission reduction, which means the undesirable output CO 2 remains as low as possible. Figure 1 describes the calculating process of δ based on the production function P(x). If the two output types-GDP and CO 2 -both have strong disposability, the production frontier is OGC, which assumes that no CO 2 is generated in production. If the undesirable output of GDP has strong disposability and the undesirable output of CO 2 has weak disposability, the production frontier is OABC, at which the point of origin exists only when the CO 2 output is equal to zero, which is consistent with the reality. e sample points B, G, M, and N in the figure correspond to the outputs of the optimal decision-making unit, which consists of the frontier of the production function P(x) at which the efficiency of the decision-making unit is the highest and its value is equal to 1. Point D of the inner frontier represents the position of a decision-making unit, the efficiency of which can be improved because its value is less than 1.
Under the condition of unchanged factor input from D to F, the carbon emission reduction is improved up to the maximum under the condition of unchanged desirable output of GDP.

Index Selection, Data Sources, and Descriptive Statistics.
is paper studies the impact of carbon emission reduction on income inequality based on labor gravitation as a mediator variable in China. e dependent variable G is the Geordie coefficient measuring income inequality in each province. e mediator variable Labor_grav is the labor gravitation measured by gravitation in the high-tech workforce, and its calculation method refers to the research of Witt and Witt [42]. e independent variable δ is carbon emission reduction efficiency based on the environmental DEA methodology measuring carbon emission reduction. e control variables include urb, which is measured by the proportion of urban population in each province; Edu is measured by the average education years using the concrete calculation method of (6 + Edu)/28 because most Chinese citizens begin attending elementary school at the age of 6 and graduate with a doctoral degree at the age of 28; Pen, Unempl, and Heal are pension, unemployment insurance, and health insurance, respectively, measured by the ratio of each type of insurance participants to the total population in each province; Hwd and Rwd are, respectively, measured by the ratio of highway and railway mileage to the total population in each province. e data selection, data sources, and data calculation methods are as follows. e data regarding G come from the China Statistical Yearbook, referring to Sundrum [43]. e data pertaining to population, capital, labor, and GDP are also from the China Statistical Yearbook. e perpetual inventory method is used to calculate capital, taking 2000 as the basic period. Similarly, we calculate the actual GDP taking 2000 as the basic period. e data regarding energy consumption come from the China Energy Statistical Yearbook. CO 2 data are from the "Energy" section in the "2006 IPCC Guidelines for National Greenhouse Gas Inventories" designated by the Intergovernmental Panel on Climate Change, which can be specifically calculated using the final consumption of industrial energy data from the China Energy Statistical Yearbook. e Urb, Edu, Pen, Unempl, and Heal data are all from the China Urban Statistical Yearbook. e data regarding highway and railway mileage are from the China Transportation Statistical Yearbook. In the absence of data from individual indices in some provinces, we use a balanced dataset with annual measurements from 2007 to 2017, covering 25 provinces. e summary statistics of these data are shown in Table 1.

Results
. We calculate the carbon emission reduction efficiency of 25 provinces in China using formula (10), as shown in Table 2. e closer the geographical location is, the greater the similarity of regional carbon emissions is and the closer the personnel exchanges are, according to the spatial economy theory. erefore, the regions with similar carbon emission reduction efficiency are more likely to be geographically close, and personnel flow more frequently. erefore, the law of the impact of carbon emission reduction efficiency on income inequality in regions with similar carbon emission reduction efficiency levels is worthy of in-depth analyses. We use the variance analysis method to divide 25 provinces into three groups according to low, medium, and high carbon emission reduction efficiency. e grouping results are shown in Figure 2. It is worth noting that most provinces in the low carbon emission reduction efficiency group are located in western China, including Inner Mongolia, Guangxi, Sichuan, Chongqing, Guizhou, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang, which are the country's least developed regions; most provinces in the medium carbon emission reduction efficiency group are located in central China, including Shanxi, Heilongjiang, Anhui, Jiangxi, Henan, and Hubei, which are moderately developed regions; most of the provinces in the high carbon emission reduction efficiency group are located in the east of China, including Beijing, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Guangdong, and Hainan, which are developed regions.
We use the period random effect model based on equations (7)-(9) to analyze the data from 25 provinces. e regression results of the 25 provinces and the three groups corresponding to the low, middle, and high carbon emission reduction efficiency levels are shown in Tables 3-6, respectively.      Table 3 verifies that the higher the carbon emission reduction efficiency is, the wider the income inequality is based on the labor gravitation as a mediator variable. If the 25 provinces are divided into 3 groups according to carbon reduction efficiency level, the carbon emission efficiency and income inequality are in a positive correlation in high and medium carbon emission reduction efficiency groups, while the relationship is opposite in low carbon emission reduction efficiency group. e impact path of carbon emission reduction on the income inequality of different groups is shown in Figures 3-6. e carbon emission reduction efficiency increases per unit, and income inequality will be increased by 0.0202 of a unit of 25 provinces accordingly. It includes direct effects and indirect effects. On the one hand, the carbon emission reduction efficiency increases per one unit, and the income inequality will be increased by 0.0167 of a unit in the direct effect. On the other hand, the carbon emission reduction efficiency increases per one unit, and the gravitation of high-tech talent will be increased by 0.0014 of a unit; then, the income inequality will be increased by 2.4477 of a unit in the direct effect. erefore, the sum of direct and indirect effects is the effect of 0.0202 of a unit. e improvement of carbon emission reduction efficiency in high and medium carbon emission reduction efficiency groups also widens the income inequality. e specific impact path is shown in Figures 4 and 5. However, the low carbon emission reduction efficiency provinces are contrary to the other provinces with a significance level of 10% in Figure 6, and the income inequality is narrow.

Regional Research
Regardless of whether it is 25 provinces or 3 groups, the impact of carbon emission reduction efficiency on income inequality is not completely mediated through the gravitation toward high-tech talent. is shows that the gravitation to high-tech talent is only one of the paths through which the carbon emission reduction efficiency affects the income inequality.
e more efficient the carbon emission reduction is, the higher the regional income is in Figure 2. Most provinces with high carbon emission reduction efficiency are situated in eastern China, which is a developed region with the highest income level and higher living costs, such as high housing prices and health costs, and the high income in this region attracts a high-quality labor force. By contrast, lowincome workers choose to leave such areas because they cannot afford the high cost of living in the region. With the continuous assembly of a high-quality labor force, the demands for high-quality ecology also increase. erefore, a high-quality ecological environment can hold on to a highquality labor force with high income and squeeze out the low-quality labor force with low income, leading to increased income inequality.
ere is a negative correlation between carbon emission reduction efficiency and the Geordie Coefficient in Figure 6. e carbon emission reduction efficiency increases per unit, and the income inequality will be increased by 0.0065 of a unit because of gathering talent; meanwhile, health costs 0.3507 * * * − 0.0011 0.5520 * * * * is the significance under the level of 10%; * * is the significance under the level of 5%; * * * is the significance under the level of 1%. Data source: calculation.  have fallen to increase the disposable income of low-income groups and the income inequality is narrowed by 0.0455 of a unit. As a result, the income inequality is narrowed by 0.0390 of a unit. is also shows that the cost of living may be the main factor affecting the income inequality in the low carbon emission reduction efficiency group. Nevertheless, the Chinese government has implemented various subsidy policies aimed at environmental protection, such as subsidizing the afforestation of farmers in these two regions, because the government attaches great importance to the protection and restoration of the ecological environment. As afforestation can effectively improve carbon emission reduction efficiency and farmers receive plantation subsidies from the government, the carbon emissions and income inequality both decrease. It is worth noting that the mean carbon emission reduction efficiency across the country is 0.3841, which is lower than the 0.7240 of the high carbon emission reduction efficiency group, higher than 0.3587 of the medium carbon emission reduction efficiency level group, and higher than 0.1642 of the low carbon emission reduction efficiency level group. However, it has the weakest effect on increasing income inequality, that is, as the carbon emission reduction efficiency increases by one unit, income inequality will be increased by 0.020 of a unit. e effect is less than the impact of carbon emission reduction on income inequality in high and medium carbon emission reduction efficiency groups. e reason may be that one of the chief ways of improving carbon emission reduction efficiency is to optimize resource allocation and generalize carbon emission reduction technology, while their effects are both related to regional coverage. e wider the region is, the more involved the provinces are and the larger the geographical distance will be, resulting in higher resource allocation costs and greater coordination difficulties. Administrative barriers also impede technology generalization, influencing the effect of carbon emission reduction efficiency in increasing income inequality. By comparison, there are fewer provinces in many of the high and medium carbon emission reduction efficiency groups than there are across the nation, and many provinces are geographically adjacent and cooperate closely with one another internally, which is convenient for resource allocation and exchange of carbon abatement technology.
Urban-rural income inequality is one of the main sources of income inequality in China. Agricultural income is used to subsidize industrial production over long periods of time, leading to farmers' income levels being lower than those of urban residents; therefore, urbanization is a key factor in narrowing the income inequality gap. However, in the grouping models, the coefficient of Urb is significant in medium and low carbon emission reduction efficiency but is Gravitation to high-tech talent Regional income inequality Carbon emission reduction efficiency 0.0167 * 0.0014 * * * 2.4477 * * * Figure 3: Influence path of 25 provinces.
Regional income inequality Carbon emission reduction efficiency 0.0980 * * 0.0043 * * * 2.0796 * * * Gravitation to high-tech talent Figure 4: Influence path of the high carbon emission reduction efficiency provinces.

Regional income inequality
Carbon emission reduction efficiency 0.0233 * 0.0007 * * 4.7558 * * * Gravitation to high-tech talent Figure 5: Influence path of the medium carbon emission reduction efficiency provinces.

Regional income inequality
Carbon emission reduction efficiency -0.0455 * * 0.00068 * * 9.5194 * * * Gravitation to high-tech talent is is because the former two correspond to central and western China, which have low levels of urbanization, while the latter corresponds to eastern China, which has the highest urbanization level. erefore, we can effectively narrow income inequality only by improving the low level of urbanization. Education increases human capital accumulation, raises the market price of workers, and is also a means of increasing income for low-income groups and narrowing the income inequality gap; therefore, the coefficient of this variable is significant in all models. Pensions mainly provide life security for retirees, which are helpful in satisfying basic living needs among older people, who lose the ability to form part of the labor force and prevent further expansion of the income inequality gap between the employed and retirees. Health insurance protects the ill from poverty ensuing from high medical expenditure and, thus, it is also an important factor in mitigating income inequality.
However, the coefficients of unemployment insurance, highway density, and railway density have no obvious effect on narrowing income inequality in most models.
is is because the strict regulations surround the receipt of unemployment insurance in China; for example, unemployment insurance may be received for no longer than two years, and the amount of unemployment insurance is low, so its impact on income inequality is largely insignificant. However, unemployment insurance is significant in the low carbon emission reduction efficiency group because the income is low and its source is in western China alone, where unemployment insurance is likely to be a key source of income. Consequently, it is the only region with a negative proportion between income inequality and unemployment insurance. Simultaneously, it is the only region in which the impact of health insurance on income inequality is insignificant, which may be related to the region's low health insurance coverage. In the other two groups, health insurance coverage exceeds thirty-five percent. Coverage is more than fifty percent in Hebei and Xinjiang, while that in other provinces is less than twenty-five percent in this group, resulting in the limited impact of health insurance on income inequality in this region. Highways and railways promote economic development as infrastructure but have no obvious effect on income inequality. Only the railway of the high carbon emission reduction efficiency group, which lies in eastern China, has a significant effect on narrowing the income inequality gap. is region has China's highestdensity railway lines, which significantly promotes the flow of production factors that help low-income groups find higher-income jobs at lower cost and faster speed.

Conclusion
is paper's vital contribution is its identification of China's improvement of carbon emission reduction efficiency has widened the income inequality through gravitation to highincome talent. e data analyses results with respect to 25 provinces in the period of 2007 to 2017 show that China improves the efficiency of carbon emission reduction and increases income inequality. High-skilled labor moves to high-income areas to increase disposable income. ese regions are concentrated in eastern China, which not only have high carbon emission reduction efficiency but also have lower health costs than other regions. e low-income labor cannot afford the high cost of living in areas with high carbon emission reduction efficiency and shift to low carbon emission reduction efficiency areas with low cost of living. ese areas are concentrated in central and western China. erefore, the agglomeration of labor with the same income has led to increased income inequality. Particularly, in eastern China, which is the most developed region, the average efficiency of carbon emission reduction is the highest and the range of increasing income inequality is the widest. Although the effects of carbon emission reduction efficiency on income inequality in central and western China are lower than those in eastern China, they are still significant, benefiting from the Chinese government's carbon abatement subsidies to these two regions. Moreover, there are large distances between some provinces that have vast territories, or there are administrative and market barriers between certain provinces, hindering the effective circulation of resources and leading to the impact of carbon emission reduction efficiency on income inequality being lower than that of any of the three regions.
In addition to carbon emission reduction efficiency, urbanization, education, pensions, health insurance, unemployment insurance, highway density, and railway density all have different degrees of impact on income inequality. Raising the urbanization rate in low urbanization areas, elevating education levels, expanding the coverage of basic pension insurance and health insurance, and increasing the construction of highways and railways will be beneficial in improving the effect of the efficiency of carbon emission reduction with respect to narrowing the income inequality gap.
China's eastern region gives full play to the advantages of high-quality human resources, promoting the technological progress of carbon emission reduction. e government continues to subsidize ecological protection measures, such as afforestation and conversion of cropland to forest in the central and western regions with the aim of improving the ecological income of local farmers, further mitigating the income inequality in the eastern region in particular. e government should also continue to optimize government organization and strengthen cooperation among discrete provinces by, for example, improving efficiency within a provincial group, by establishing urban agglomerations and creating better links between different urban agglomerations and by gradually reducing administrative and technical barriers. e main conclusions include the following: (i) Carbon tax should be reasonably levied and carbon trading market mechanisms should be established.
Intensive use of resources in China's central and western regions has resulted in low efficiency of carbon emission reduction. To reverse this trend, carbon tax should be properly levied to maintain the speed of economic development and reduce carbon emissions. A carbon trading market should also be Mathematical Problems in Engineering established and each region should be encouraged to reduce carbon emissions through the market mechanism. In the eastern region, although the efficiency of carbon emission reduction is high, the carbon emissions are also relatively high. In the central and western regions, after the efficiency of carbon emission reduction has been improved, a significant reduction in carbon emissions may ensue. If a carbon trading market is established, the excess carbon emission index in the central and western regions could be sold to the eastern region, as a means of reducing the regional income inequality. (ii) Access to education should be equally feasible for all. One reason for the low efficiency of carbon emission reduction in China's central and western regions is the scarcity of R&D personnel working on low carbon technology, which may be solved through the provision of education and training. Different education levels in different regions give rise to various human capital values. e higher the value is, the more advanced the carbon emission reduction technology is and the greater the wealth accumulation will be. Wealth shows the characteristic of intergenerational transmission due to the absence of inheritance tax in China which leads to not only the transmission of income inequality but also the possibility of expanded income inequality. Additionally, the higher the wealth, the higher the quality of regional education and the more advanced the carbon emission reduction technology, which further widens the income inequality gap to form a vicious circle. erefore, the improvement of education levels in the central and western regions might reverse the trend of regional income inequality expansion. (iii) e equalization of regional basic public services should be promoted, and the possibility of attracting and retaining high-quality talented workers from the central and western regions should be developed. e central and western regions should not only cultivate talent but also attract and retain it. In addition to income, providing the same basic public services as developed regions is the key to retaining talent. ese public services include medical services, education and training services, and humanities and arts leisure services.
(iv) e industrial structure should be continuously upgraded, and the rate of return on labor input should be gradually increased. e proportion of China's three industries has not reached the optimal level, and there is still increasing room for tertiary industry. With the increase in the proportion of the tertiary industry, the demand for a labor force is increasing. Due to the decrease in the proportion of secondary industry, the demand for capital has declined correspondingly. Consequently, labor income increases with the decrease of the rate of return on capital input. Because production input consists primarily of capital in the eastern region and labor in the central and western regions, the continuous upgrading of industrial structure is one means of reducing the capital income of the eastern region and improving the labor income of the central and western regions. In the process of this transformation, although the proportion of secondary industry decreases, the production efficiency, including the efficiency of carbon emission reduction and labor efficiency will be significantly improved by optimizing the allocation of resources. e improvement of the efficiency of carbon emission reduction reduces the CO 2 emission per unit of output, and the promotion of labor productivity will result in surplus labor that must be transferred to the tertiary industry. e tertiary industry in the eastern region has been relatively well developed, with limited absorption of labor forces. By contrast, the demand for labor in the developing tertiary industry is large in the central and western regions, together with the demand for talent to implement strategies for the rise of the central region and the development of the western region, causing the income of the labor force to increase accordingly and reducing the income inequality gap across China's different regions.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

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