Evaluation and optimization of ecological compensation fairness in prefecture-level cities of Anhui province

Scientific evaluation and continuous optimization of the fairness of ecological compensation are conducive to improving the effect of air pollution control. However, relevant research in this field is in its infancy. Based on the data on urban-scale PM2.5 concentration and ecological compensation from the third quarter of 2018 to the fourth quarter of 2020, this study takes 16 prefecture-level cities in Anhui Province as the research area and uses the Granger causality test to determine the PM2.5 overflow paths of each city. Moreover, using 2020 as an example, the PM2.5 spillover effect of each city is calculated, and the haze Gini coefficient of Anhui Province is obtained. According to the empirical results, the ecological compensation policy for PM2.5 control in Anhui Province is in a relatively equal fairness range (0.295). On this basis, combined with the scatter diagram of ecological compensation and spillover effect, it is suggested to reduce the ecological compensation of five cities, including Maanshan and Xuancheng, while the ecological compensation of the remaining 11 cities should be increased. Two feasible optimization schemes, i.e., annual adjustment and regular adjustment, are proposed for environmental regulators to choose.


Introduction
In recent years, haze pollution with PM 2.5 as the main component has been increasing in China. Haze pollution is harmful to public health and can lead to huge economic and social losses (Bui and Nguyen 2022). However, due to the complex formation mechanism of haze, vague emission boundary (Bland et al 2022), and significant spatial spillover (Zhou et al 2021), its governance involves the cost burden and benefit allocation among different administrative bodies, which easily leads to lack of fairness. Therefore, we need to pay special attention to the evaluation and optimization of ecological compensation fairness.
Environmental equity (or fairness) reflects a moral evaluation of people's rights, obligations, responsibilities, income, and investment in the process of using environmental resources (Gurney et al 2021). Among the research results of policy equity evaluation, the Gini coefficient is a relatively unique indicator. The Gini coefficient, also known as the Lorenz coefficient, was originally proposed to measure the income gap of residents in a country or region. Some scholars have introduced it into the field of environmental policy and constructed the carbon Gini coefficient (Xiao et al 2019). In the practice of ecological compensation for haze control, haze from one area overflows to another, thus polluting the latter. Therefore, the former should give ecological compensation to the latter. The policy fairness represented by the haze Gini coefficient mainly refers to the matching degree between the haze spillover effect of the emission source and the ecological compensation paid by it. The more proportional the two values are, the more fair the policy is, and vice versa. Hence, in addition to ecological compensation data, an important task is to measure the spillover effect of haze between cities. Currently, a large number of studies have focused on the haze spillover effect by mainly testing the regression Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. coefficient of several variables in one city to haze pollution in another, which does not represent the real haze spillover effect between cities.
Further, due to the lack of a scientific and reliable measurement basis for the haze spillover effect, the ecological compensation standard is difficult to be formulated accurately. Therefore, policymakers have to use the second-best method and implement the current mainstream compensation model. First, to determine the compensation standard according to the local status quo, calculate the amount of compensation based on the degree of pollution concentration exceeding the compensation standard. Second, cities that meet the secondary standard of the Ambient Air Quality Standard (GB3095-2012) in the previous year will be given a one-time reward of different scales, while non-compliant cities will be imposed certain penalties by provincial governments. Theoretically, the basis of ecological compensation is 'who protects, who benefits, who pollutes, who pays.' Although it is to encourage emission reduction, the policy design does not consider the haze spillover effect among cities. Therefore, how fair is the compensation policy ? Does it need to be adjusted and how ? These are two issues that this study focuses on.

Literature review
Scholars have carried out a lot of research on environmental policy fairness, and their theoretical results mainly involve the following two dimensions.
First, most of the research recognized that environmental injustice is ubiquitous and analyzed the main sources of such injustice. In many cases, environmental injustice comes from the externality of pollution, and more specifically, from the inequality or mismatch between rights and responsibilities in environmental issues (Rayamajhee and Joshi 2018). For example, sometimes, it is not the one that produces the most pollution that makes the greatest effort to reduce pollution. Further, those who suffered losses due to environmental pollution did not receive corresponding ecological compensation from the polluter (Pan and Dong 2021). When considering the cross-regional spillover of pollution, environmental injustice in the treatment of haze pollution becomes particularly obvious.
Second, the existing research on policy fairness evaluation mainly focuses on three measurement perspectives. The first is to introduce fairness indicators, such as range, standard deviation, and Gini coefficient, or use relevant indicators to build an evaluation system such as TOPSIS multi-dimensional assessment (Zhang et al 2022a). The second is to impose fairness constraints such as total carbon emission control constraints (Chen et al 2021, Zhan 2022. The third is to construct an objective function based on fairness criteria, such as proportional fairness and max-min fairness, or further construct a multi-objective utility function (Hayes et al 2022) to reveal the impact of the individual utility gap on fairness. Among the above research methods, the Gini coefficient method is not only relatively simple in the calculation but also requires fewer data. Moreover, the Lorenz curve is used to present the measurement results, and the degree of policy fairness is clear. Therefore, the Gini coefficient has been widely used in the evaluation of policy equity in many fields (Sueyoshi et al 2021).
In addition, as an important basis for ecological compensation, the estimation of haze spillover effects has an important impact on the fairness of ecological compensation policies, thus attracting the attention of many scholars. According to the research scale of the haze spillover effect, the relevant achievements can be divided into two branches. On the one hand, some researchers investigate the global and local spatial correlation of PM 2.5 emissions among administrative subjects to determine whether there is a spatial spillover effect (He et al 2021) in the study area. On the other hand, some researchers explore the impact of core variables, such as energy consumption (Nan et al 2019) and urbanization rate (Du et al 2019), etc, on PM 2.5 emissions in local and neighboring cities. Due to the multiplicity, dynamics, and complexity of the influencing factors of the haze spillover effect and the lack of effective estimation methods, it is still difficult to accurately measure the haze spillover effect between regions.
In summary, although the Gini coefficient has been applied in fairness evaluation, there is no targeted research in the field of ecological compensation for haze control, which is closely related to the late start of domestic ecological compensation practice and the lack of data. Although many scholars have investigated the spatial spillover of haze pollution, currently, there is no recognized good method to estimate the haze spillover effect among cities.
This study aims to evaluate and optimize the fairness of haze ecological compensation in 16 prefecture-level cities in Anhui Province in China and contributes to the existing literature in two aspects. First, to the best of the authors' knowledge, it is the first attempt to calculate the haze spillover effect on the scale of prefecture-level cities with the help of the Granger causality test. In this way, the spillover path can be determined, and the spillover effect can be obtained after normalization combined with PM 2.5 emission concentration. Second, it calculates the Gini coefficient of haze in Anhui Province. The Lorenz curve is drawn using the data of the PM 2.5 spillover effect and ecological compensation in cities. Then, the fairness of the ecological compensation policy is determined, and the suggested adjustment amount of ecological compensation in each city is given with the help of the ecological compensation spillover effect scatter diagram. The results of this study can serve as the basis for the formulation of local government environmental supervision (especially ecological compensation) policies and are expected to effectively improve the effect of haze control. The remainder of this paper is organized as follows. Section 3 provides the materials and methods. Sections 4 and 5 present the results and discussion, respectively. The last section summarizes the study and offers policy implications.

Study area
The research area is Anhui Province. As an important part of the Yangtze River Delta, Anhui is located in East China, ranging from 114°54′ to 119°37′ E and 29°41′ to 34°38′ N. According to the Anhui Statistical Yearbook released in 2022, there are 16 prefecture-level cities in Anhui Province, namely Hefei, Huaibei, Bozhou, Suzhou, Bengbu, Fuyang, Huainan, Chuzhou, Luan, Maanshan, Wuhu, Xuancheng, Tongling, Chizhou, Anqing, and Huangshan. In 2021, this province achieved a total output of about $4,300 billion. In the past two years, its average economic growth rate reached 6%, higher than the national level (4.9%). Moreover, the local government has continuously strengthened environmental governance, implemented the Interim Measures for Ecological Compensation of Environmental Air Quality in Anhui Province in July 2018, and then carried out ecological compensation according to the year-on-year changes in environmental air quality in each city. From 2018 to 2020, the annual average concentration of haze emission for 16 prefecture-level cities in Anhui Province decreased from 45.9 μg m −3 to 39.1 μg m −3 , and the air quality improved significantly. As presented in table 1, the air pollutants (PM 2.5 and PM 10 with different weights) are assessed quarterly and liquidated at the end of each year. There are three important coefficients in table 1, namely the ecological compensation fund coefficient, quarterly coefficient, and target correction coefficient. Based on the information in table 1, the formula for the ecological compensation of cities in Anhui Province is as follows: ΔPM 2.5 and ΔPM 10 indicate the difference in average PM 2.5 and PM 10 concentrations of the current year and previous year, respectively. β c , β q , and β g refer to the ecological compensation fund coefficient, quarterly coefficient, and target correction coefficient, respectively (table 1).

Variable selection and data source
To ensure the availability of data and sufficiency of samples, this study uses the quarterly statistical caliber to obtain the PM 2.5 concentration and ecological compensation data of each city. The statistical range is from the third quarter of 2018 to the fourth quarter of 2020. Quarterly coefficient 100%, 60%, 60%, and 120% for the first, second, third, and fourth quarters, respectively. Target correction coefficient The target correction coefficient is determined according to the completion of air quality targets in each city. For cities that have achieved the quarterly target, the coefficient is 1. For cities that failed to meet the quarterly target, if the PM 2.5 concentration drop in the current quarter is higher than the provincial average level, the coefficient is 0.5. If the PM 2.5 concentration decreases year-on-year but the decline is lower than the average level of the whole province, the coefficient is 0.2. If the PM 2.5 concentration does not decrease but increases, the city shall turn in the ecological compensation to the provincial finance, and the coefficient is 1. For cities whose annual objectives have not been completed, the annual bonus and supplementary funds shall be multiplied by 0.9 or 1.1 for the turned-in funds at the end of the year. One-time reward A one-time reward of 5 million RMB will be given to cities (divided into districts) whose air quality in the previous year reached the class II standard of the ambient air quality standard (GB3095-2012). If the annual average PM 2.5 concentration of the city is further improved from the previous year, a one-time reward of 8 million RMB will be given at the end of the year.
3.2.1. PM 2.5 concentration for each city The data are sourced from PM 2.5 Historical Data Network 3 . As the website only provides monthly data, the average concentration of three months in the same quarter is used as the quarterly value.

Ecological compensation of each city
The data are from the Department of Science, Technology, Foreign Affairs and Finance of the Department of Ecology and Environment of Anhui Province.
3.3. Research ideas 3.3.1. Measure the spillover effect of urban PM 2.5 Referring to the study by Liu (2018), a Granger causality test was conducted to obtain the spillover path of PM 2.5 in Anhui Province. By multiplying the number of spill paths by the urban PM 2.5 emission concentration, we can obtain the initial spill o ; i then, it is normalized with Formula (3) to measure the spillover effect of PM 2.5 in each city Norm .
In Formula (2), overpath i and PM i 2.5 represent the number of PM 2.5 overflow paths and the emission concentration of PM 2.5 in each city, respectively. In Formula (3), o max and o min denote the maximum and minimum values of the initial overflow of all cities, respectively. Similarly, the normalized value of each city's ecological compensation (Norm ci ) can also be obtained using Formula (3).

Calculate the haze Gini coefficient
As mentioned earlier, the haze Gini coefficient reflects the matching degree between the haze spillover effect and the ecological compensation, so it can be used to measure the fairness of the haze ecological compensation policy. Therefore, using the internationally accepted formula that employs the Gini coefficient of income as a reference, the Gini coefficient of haze at the provincial level is calculated with slight changes, as presented in Formula (4). In Formula (4), Gini means the Gini coefficient of haze, and its value range is [0,1]. = Gini 0 implies absolute equality, which indicates that the ecological compensation paid by the assessed area is fully commensurate with its PM 2.5 spillover effect. As Gini increases, the degree of inequality also increases-a value of = Gini 1 means absolute inequality. In general, < Gini 0.2 can be regarded as absolute equality, -0.2 0.3 as relative equality, -0.3 0.4 as more reasonable, -0.4 0.5 indicates that the gap is large, and > Gini 0.5 denotes an extremely unfair distribution of ecological compensation spillover effect.
In addition, n represents the total number of cities evaluated. In this study, n = 16 (i.e., 16 prefecture-level cities in Anhui Province); p ci indicates the proportion of compensation for each group to the total compensation after grouping according to ecological compensation. p oi stands for the proportion of spillover for each group to the total spillover after grouping according to ecological compensation. p toi is the cumulative number of P oi .

Drawing a scatter diagram of ecological compensation-spillover effect
Combined with the scatter chart, the normalized adjustment value of the ecological compensation for each city, Norm , ai can be calculated using Formula (5). Further, the final ecological compensation adjustment amount, a , i is obtained using Formula (6).

Variable descriptive statistics
In this study, the fairness of the air quality ecological compensation policy was evaluated and optimized by taking the quarterly haze concentration (PM 2.5 ) and ecological compensation (COMP) as samples from the third quarter of 2018 to the fourth quarter of 2020 in Anhui Province (a total of 10 periods). The descriptive statistics of the variables are presented in table 2.

Unit root test
As presented in table 3, the results obtained using the five-unit root test methods all reject the null hypothesis at the 1% significance level, indicating that the data series are stationary and meet the requirements of the Granger causality test.

Granger causality test
Using a Granger causality test, the causal paths are obtained and presented in table 4. The table reveals that all the 16 cities can be both 'cause' and 'effect'. In other words, haze overflow is common, which is consistent with the research conclusion of Mao et al (2022).

Haze spillover effect
Using Formulas (2) and (3), the haze spillover effect is calculated based on the PM 2.5 concentration of 16 cities in 2020 (taking the average value of four quarters in 2020) (see table 5). The number of overflow paths in column 2 of table 5 is consistent with the data in column 4 of table 4. Only the haze spillover is considered here, ignoring the haze input from adjacent cities. This is done to focus more on the impact of haze emissions in each city on other cities and determine the responsibility of haze control compensation.

Gini coefficient of haze
Next, using Formula (4), the Gini coefficient of the ecological compensation policy for haze control in Anhui Province is calculated, with the result of 0.295 indicating the relative fairness of the policy (see figure 1). This reveals some room for optimization of the compensation policy. However, it is undeniable that the ecological compensation policy for environmental air quality in Anhui Province has not only effectively promoted the emission reduction of haze but also achieved a relatively acceptable degree of policy fairness.

Ecological compensation optimization
The scatter diagram is drawn using the data of ecological compensation and spillover effect in Anhui Province in 2020. As depicted in figure 2, Hefei and other five cities are located at the lower right of the 45-degree line, indicating that the ecological compensation (normalized value) of these cities is relatively lower than the spillover effect (normalized value); the situation in 11 cities such as Huaibei is just the opposite. This reflects the Note: ① The variables PM 2.5 and COMP in the table respectively represent the average value of haze emission concentration for each city by quarter (unit: μg/m 3 ) and ecological compensation (unit: 10,000 RMB). In order to obtain stable time series data, the natural logarithm of the original data of the above two variables is taken. 'imbalance' between ecological compensation and spillover effects in these 16 cities. However, the specific intensity and direction of the adjustment of ecological compensation in each city need to be further calculated using Formulas (5) and (6). As presented in the third and fourth columns of table 6, the ecological compensation of Maanshan, Xuancheng, Tongling, Anqing, and Huangshan in 2020 (highlighted in italic font in table 6) should be reduced. On the contrary, the remaining 11 cities were suggested to make different ranges of increase in ecological compensation. Based on the same idea, the adjustment of ecological compensation in subsequent years can be obtained. As the Granger causality test needs to meet requirements of sufficient sample size, at least the latest three years should be taken as the investigation period. The adjustment program can be roughly divided into two schemes. The first type is adjusted yearly. For example, in 2021, the spillover effect is estimated based on the haze emission data from 2019 to 2021. Combined with the ecological compensation in 2021, the Gini coefficient of haze can be calculated, and the adjustment scheme of ecological compensation can be finally determined. The second type is periodic adjustment such as every three years. After calculating the adjustment amount for 2018-2020, the total adjustment amount can be obtained by adding up the value of three years and applying it in 2021. By 2023, the total adjustment of three years will be calculated by using the data for 2021-2023. The new adjustment will be realized again in 2024 and so on. The basic principles of the two schemes are the same, but there are differences in the calculation basis and interval period. Table 5. Estimation of haze spillover effect of cities in Anhui Province (taking 2020 as a calculating example).

Discussion
Compared with previous studies, this study is relatively special in terms of research perspective and ideas. The existing research on ecological compensation mainly centers on the fields of watershed, forestry, and soil (Guan et al 2021, Sun and Li 2021, Zhang et al 2022b; only a few scholars pay attention to ecological compensation due to air pollution. Liu (2021) established a value evaluation system for compensation for ecological environmental damage caused by air pollution, but the spillover effect was not involved in the evaluation method. Considering the spatial spillover, some studies have analyzed the indirect effects of various variables in one region on atmospheric pollution in another region (Feng et al 2020, Avilés-Polanco 2022. However, these effects are not additive, so the total spillover effect between regions cannot be obtained. As traditional panel regression cannot deal with this problem well, we creatively use a Granger causality test to obtain the number of spillover paths and  to approximately calculate the haze spillover effect. This method may not be optimal but is meaningful. Furthermore, some studies have evaluated the fairness of ecological compensation (Huang and Zhou 2022), and the optimization of unfairness in compensation was not discussed in depth. This paper optimizes the ecological compensation based on the haze Gini coefficient and the scatter diagram of ecological compensation -haze spillover effect, which provides an important theoretical basis for the development of urban-scale haze ecological compensation.
To ensure the best applicability of the conclusions of this study, attention should be paid to the scope of ecological compensation when applying them in practice. Specifically, we estimate the haze spillover effect using a Granger causality test. This method is mainly applicable to ecological compensation between multiple cities under the jurisdiction of the same province. The main reason is that the natural environmental factors, economic and social factors, and resource endowments of these cities are sufficiently similar, and the number of haze spillover routes can reflect the relative size of haze spillover effects between cities to a certain extent. However, if the decision-makers intend to apply these findings to cross-provincial and even nationwide ecological compensation for haze, they should be more cautious. We believe that with the continuous improvement of research methods and the progress of haze monitoring technology, there will be more equitable ecological compensation for haze in the future.
In addition, this study can be extended to a finer scale, for example, from cities to counties or key industries. This extension would not only reveal the uniqueness of ecological compensation for haze on different scales but also better reflect the concept of 'polluters pay and the injured get compensation' on a smaller scale, which is more conducive to realizing the internalization of pollution costs, thus encouraging the emission reduction of the major polluters. This needs further systematic research.

Conclusions and policy implications
The evaluation of environmental policy is one of the hot topics in environmental economics. Based on the background of the implementation of ecological compensation for environmental air quality in China and using the haze emission and ecological compensation data of 16 prefecture-level cities in Anhui Province, the research samples from the third quarter of 2018 to the fourth quarter of 2020 were constructed. Further, the spillover effect of haze in prefecture-level cities was estimated using a Granger causality test. The Gini coefficient of haze in Anhui Province was further calculated to determine the fairness of the ecological compensation policy within the whole province. This study reveals that the ecological compensation policy of Anhui Province in 2020 has achieved relative fairness (0.295). Considering the spillover effect of haze, it is suggested to reduce the ecological compensation in five cities (Maanshan, Xuancheng, Tongling, Anqing, and Huangshan) while increasing that in the other 11 cities. The adjustment plan can be implemented yearly or periodically. This study provides the following important policy implications. First, the ecological compensation policy promotes the reduction of haze emissions in cities but weakens the fairness of the compensation policy to a certain extent as it ignores the spillover effect of haze between cities. Therefore, it is necessary to incorporate spillover effects in policy design (ex-ante control) or to adjust ecological compensation in policy implementation (ex-post control). In addition, with the progress of compensation practice, provinces are revising the standards of ecological compensation, which requires continuous studies on the fairness of compensation policies and the regular optimization adjustment, to make the compensation standards transparent and the main bodies of compensation clear. It truly practices the concept of environmental equity of 'the protector benefits and the polluter pays.' The relevant conclusions of this study are only used as a policy reference to improve the ecological compensation mechanism and cannot be simply and directly applied to the adjustment of ecological compensation in practice. This is mainly because the endowment of environmental resources and the level of economic-social development varies greatly among regions. Hence, in addition to the haze spillover effect, other relevant variables (such as economic growth, urban population, and industrial structure) may also affect the results. Due to the limitation of space, the authors did not discuss how to rationally allocate ecological compensation between emission reduction performance incentives and cross-regional compensation for haze pollution. All the above topics need to be further studied systematically and deeply.