Initial allocation of SO2 emission rights based on the combination weighting method: evidence from China’s thermal power plants

Emission trading system is an effective market-oriented means to control pollutant emission, and reasonable initial allocation of emission rights is the premise of its smooth implementation. However, at present, the initial allocation of emission rights depends largely on the amount of emissions, which leads to weak positive guidance effect for enterprises. To explore the optimal initial allocation method of SO2 emission rights, this paper takes 8 thermal power plants in Dalian, China, as the research objects to calculate the initial allocation of SO2 emission rights, because SO2 is the main cause of acid rain, which is one of the most serious air pollution in China, and thermal power plants are among the main SO2 emitters. Firstly, an indicator system is established considering enterprise size, pollutant discharge, and social contributions, as well as pollution control capacity. Then, the combination weighting method is developed through integrating the subjective methods G1 and G2 with the objective ones, entropy and maximum deviation. The empirical results show that the enterprises with more desulfurization equipment or large heating supply are supposed to get more emission rights; the actual emission value of SO2 in half of the enterprises exceeds the theoretical ones; SO2 removal rate, desulfurization equipment quantity, and heating supply exert the most positive effects on the initial allocation of emission rights. The constructed model can be used as a reference for future research of initial allocation of other pollutants’ emission rights. Also, the implications have been proposed for the government, industry, and enterprises.


Introduction
The rapid development of China's economy consumed a large amount of energy, which significantly increased in emissions of CO 2 , SO 2 , and particulate matter (Zeng et al. 2019;Luo et al. 2019). Because of the aggravation of the greenhouse effect, most existing research focuses on CO 2 emission rights, while research on SO 2 emission rights is relatively underrepresented. However, compared with other atmospheric pollutants, SO 2 is an important cause of acid rain, which not only leads to air pollution, but also pollutes rivers, corrodes buildings, acidifies arable land, and even damages the human health (Li et al. 2015). China's SO 2 emission was 2.578 million tons in 2018, and the area affected by acid rain accounts for 30% of the total land area. According to the statistics released by China Economic Network in 2015, China had 624,000 industrial boilers, more than 80% of which are coal fired, with a resulting annual consumption of standard coal of 490 million tons. To resolve the detrimental environmental effects, many countries have adopted a variety of measures conducive to reducing SO 2 emissions. Prominent examples are, e.g., banning small thermal power plants, strengthening cleaner production audits, and promoting clean energy (Li et al. 2013;He et al. 2016). Among these measures, the emission trading system has become the favorite pollution control policy, since it realizes the pollution reduction at the lowest cost (Tang et al. 2020). The emission trading system has been first proposed by the USA in the 1970s, and China formally implemented it in 2007 (Jiao et al. 2017;Hou et al. 2020). In the process of the allocation of SO 2 emission rights, the first-level government determines the total amount of emissions according to the local economic and environmental Responsible Editor: Eyup Dogan * Ying Qu quying@dlut.edu.cn conditions; then, this amount is allocated to the second-level government, and from there to each enterprise according to its size and characteristics. The emission trading system is a type of market trading system based on environmental compensation, which can either indirectly or directly benefit enterprises. Compared with the means of publicity and education, it imposes a stronger guiding effect on enterprises. Data showed that China's SO 2 emissions have gradually decreased since 2007, from 36.6 million tons in 2007 to 2.57 million tons in 2018. The implementation of a SO 2 emission trading system exerts a significant effect on the SO 2 emission control; however, there is still a long way to go (Shin 2013). Thus, it is meaningful both for theory and praxis to develop a reasonable mechanism for the initial allocation of SO 2 emission rights (Ji et al. 2017a, b;Lee 2019).
In the 1990s, several researchers proposed that the initial allocation was the main barrier for emission rights trading (Van Egteren and Weber 1996), which was later corroborated by many other studies (Guo et al. 2012;Hang et al. 2019). However, there is currently not clear on the key factors affecting the initial allocation of SO 2 emission rights in thermal power plants. Therefore, this paper builds a multi-dimensional index system to evaluate the initial SO 2 emission rights allocation and explores the critical influencing factors. This will be of great significance to understand the gap between the theoretical and actual pollutant emissions. Dalian is an important city in the northeast old industrial base, where powers are mainly supplied by thermal power plants. In 2017, thermal power generation in Dalian was 19.77 billion kwh, accounting for 44.6% of the total. Despite the gradually increasing proportion of new energy power generation, the growth rate remains slow. Thermal power generation will still remain the main mode of power generation for Dalian in the foreseeable future. Currently in a carbon neutral context, Dalian is changing from a heavy industrial city to an ecological civilization one. Therefore, by selecting eight thermal power plants in Dalian as research samples, the results not only help to accelerate the green transformation process for this city, but also provide valuable experience for Chinese other industrial cities.
The contributions of this paper can be divided into two aspects. Theoretically, the optimal combination weighting method, including two subjective weighting methods and two objective weighting methods, is used to enhance the reliability of the research results. Furthermore, this study not only considers the status of enterprise emissions, but also takes the social benefits into account, which enriches the relevant research on the initial allocation of SO 2 emission rights. Practically, the model is applied to conduct an empirical study using the panel data of eight thermal power plants in Dalian, which is helpful to identify the main influencing factors of SO 2 emission right. Also, through the comparative analysis of the actual and theoretical emission value of each enterprise, this paper provides managerial and industrial implications accordingly, helping Dalian government to make relevant decisions and take corresponding measures.
The rest of paper is organized as follows. The "Literature review" section reviews and summarizes the related literature in this field. The "Methodology" section establishes the allocation model constructed in this paper. The "Empirical analysis" section is an empirical study of thermal power plants in Dalian. The results and discussion of the study are presented in the "Results and discussion" section. Finally, the "Conclusions and implications" section provides conclusions and implications.

Literature review
With the increasing severity of environmental pollution, the awareness of the need for environmental protection has gradually enhanced. The concept of emission rights was first put forward by Dales, who believed that an emission right is the right of the obligee to discharge pollutants into the environment within the scope permitted by law (Dales 2002). However, the initial allocation of emission rights has not attracted much attention until the emission trading system has been implemented by the USA, where it achieved remarkable results (Zhu et al. 2012). Subsequently, this theory was used by the National Environmental Protection Agency for the management of atmospheric and river pollutant discharges; other countries have also carried out relevant practices and research. The theory of emission trading is mainly based on the Coase Theorem, the purpose of which is to encourage enterprises to improve technology, reduce the amount of pollution, and optimize the allocation of environmental resources (Gurianov 2015;Venmans 2016). Later, economists put forward the concept of "environmental capacity resources," whose property rights are emission rights, so it becomes necessary to define the ownership of emission rights (Wang and Wang 2016).
However, previous studies have hardly considered the impact of initial allocation on emission trading. With the accumulation of theories and practices associated with emission trading, economists and policy-makers gradually realized the importance of the allocation of initial emission right (Gurianov 2015). Among these, Lyon (1982) first studied the allocation of initial emission indicators in 1982. Later, Hahn (1984) showed that, in an incomplete competitive market, the efficiency of emission trading is, to some extent, affected by the initial allocation. Woerdman (2000) studied the impact of initial emission allocation and quantitative allocation on emissions trading. These studies revealed that the effect of the reduction of pollutant emissions not only depends on emissions trading, but also, to a large extent, on the initial allocation of emission rights. Therefore, it has become urgent to study the initial allocation of emission right and provide scientific suggestions for future emission reduction.
At present, there are two main types of research. On the one hand, the initial allocation of emission rights is determined by mathematical models. Shi et al. (2017) established a crossborder air pollution model based on game theory and studied the cost-effectiveness of emission reduction for three cities in Hunan Province, China. Huang (2018) considered the spatial dependence of SO 2 emissions and used the spatial Durbin model to study the impact of governmental expenditure for environmental protection on SO 2 emissions. On the other hand, the allocation of initial emission rights for specific pollutants is determined by establishing an index system, which involves the determination of influencing factors and the weight of each factor. For instance, Mackenzie et al. (2009) proposed a new initial allocation mechanism, i.e., the ranking of companies by assessing their external behaviors or characteristics independent of the emission trading market, to obtain the initial allocation. Chen et al. (2019) used a costbenefit analysis method to compare the economic costs and social benefits of desulfurization and emission reduction between China and the USA.
With regard to the choice of research objects, with the increasing rise of carbon emissions trading, most scholars currently study the initial allocation of CO 2 emissions (Duan et al. 2018;Han et al. 2018;Li et al. 2018). In addition, because of the serious haze phenomenon, the initial allocation of particulate matter emission rights has recently become the focus of scholars . The existing literature has mainly focused on the initial allocation of SO 2 emission rights in a specific region or province, between industries, or enterprises within an industry. Mostly, the distribution of SO 2 was considered from the perspective of regional integration, i.e., the total SO 2 emissions of a province as the whole allocating to each city, or one of a specific city distributing to each region (Guo et al. 2012;He et al. 2016). Only a few studies investigated the initial allocation of SO 2 emission on an industry or region. However, enterprise is the main body of pollutant discharge. Hence, it would be more effective to study SO 2 emissions reduction from the perspective of thermal power plants. Pollutant emission rights affect the allocation of enterprise resources to a certain extent, the key of the enterprise's benefits (Ji et al. 2017a, b;Wong et al. 2020). So what are critical factors impacting the initial allocation of SO 2 emission rights in thermal power industry, and how to make the initial allocation more reasonable for government departments have become the research problems of this paper. The initial allocation of emission rights in eight major thermal power enterprises in Dalian are studied based on establishing an indicator system and conducting empirical verification, and suggestions are presented for the government, industry, and enterprises to effectively reduce SO 2 emissions.

Standardization of Indexes
An indicator system usually contains different dimensions and orders of magnitude among indexes based on their meanings and properties. When the order of magnitude of indicators varies strongly, and if the original index value is directly analyzed, an index with larger value will play a stronger role for calculations, while an index with smaller value will appear to have less effect. Therefore, to weaken the impact of different dimensions on the evaluation results, while ensuring reliability, it is necessary to standardize the data of the original indexes under each criterion level. The calculation equation is as follows (Zhao et al. 2018): where Yij represents the normalized value of data; Xij represents the value of index j of the enterprise i; m represents the number of evaluated enterprises; n represents the number of indexes in the evaluation system; i=1, 2, …,m; and j=1, 2, …,n.

Index weight calculation
In the existing research, the integration of subjective and objective weighting methods is almost adopted (Feng et al. 2018;Han et al. 2018;Li et al. 2018). This paper combines four weighting methods including two subjective and two objective ones, which can minimize the information display and yield more scientific index weights (Guo 2002). The principle underlying this method is simple, its operability is strong, and the results of comprehensive evaluation are comparable. In view of the fact that the initial allocation of emission rights is a complex decision-making system, it is necessary to consider a variety of factors comprehensively, and the differences between emission subjects, as well as the relationship between emission subjects and the total amount. Hence, this paper adopts G1 method and G2 method for getting subjective judgment and entropy method and deviation maximization method for objectively reflecting the differences of indicators. Compared with the single subjective or objective weighting method, the combined one is more scientific, and its results are more reliable.

G1 method
The G1 method is a subjective method without consistency test, which was proposed by Guo (Guo 2002). Compared with analytic hierarchy process (AHP), the G1 method does not need to construct a judgment matrix, which clearly reduces the computational complexity (Qian et al. 2014). It is simple, intuitive, and does not restrict the number of elements in the same level: a) Determine the order relation among evaluation indexes.
b) The ratio rj of the importance of adjacent evaluation indexes Yj − 1 and Yj is given by experts. c) The weight of the index k (k = 1, 2,… ,n) is calculated as follows: d) With the weight ωk, the values of other indexes can be obtained.

G2 method
The G2 method is an interval mapping weighting method for practical application, which can directly express the subjective views and risk awareness of experts and offers the advantages of less calculation and easy promotion (Zhao et al. 2018): a) Experts identify the least important indicator Yk. b) Determine the ratio rj of the importance of other indicators to Yk. c) Calculate the weight of the index jto the criterion layer.

Entropy method
The entropy method is a widely used method for objectively calculating weights, suitable for continuous variables, and its calculation process is clear. It considers that the information entropy value is a measure of information uncertainty (Zhang et al. 2019). The smaller the value, the larger the influence of the index on the decision result, and the greater the weight that should be assigned; the larger the information entropy value, the smaller the difference between the indicators, and the smaller the weight that should be assigned. The size of the information entropy value represents the degree of differences between different indicators, and objective weights are calculated according to the size of the value. The main steps are as follows: a) The equation for calculating the index proportion fij is as follows.
fij ¼ xij where x ij represents the initial value of the index j in enterprise i; i = 1, 2, …, m; and j = 1, 2, …, n.
b) Calculate the entropy of indexes.
where ej represents the entropy of the index j; suppose that when fij = 0, fij ln(fij) = 0.
c) ωj is set as the weight of the index j, and its calculation equation is shown below: Maximum deviation method The maximum deviation method assumes that if the index is more discrete, the impact of the index on the evaluation results will be larger, and consequently, the weight of the index should be higher. This method can automatically determine the weighted coefficients among the evaluation indexes. The obtained ranking results are accurate and reliable and have no subjective randomness (Qian and Luan 2017;Yi et al. 2019).
a) Suppose that tij is the normalized value of index j in enterprise i; ωj is the weight of the index j. For index j, the equation to calculate the deviation Fij(ω) between enterprise i and other enterprises is (k = 1, 2, …, m): b) For index j, the total deviation F between all enterprises and other enterprises is: c) According to the principle of maximum deviation, the following optimization model is constructed: d) The optimization model is solved and normalized to obtain the index weight.

Combination weighting method
The weight obtained by the G1 method, the G2 method, the entropy method, and the deviation method is calculated, respectively, and then, the combination weight c is: In Eq. (12), αc represents the combination coefficient; and ∑ 4 c¼1 αc = 1, and c = 1, 2, 3, 4.
With regard to the combination coefficient, the following two factors should be considered.
a) The minimum generalized distance between the weighted score of each evaluation object and the ideal point should be guaranteed.
In Eq. (13), di represents the generalized distance between weighted score and the ideal point of each evaluation object; ω c j represents the weight of index j under the method c; Yij represents the normalized value of index j in enterprise i.
b) The Jaynes maximum entropy principle is introduced to reflect the consistency of the weight allocation results for each index. The following objective functions are established based on minimizing the difference of the weight allocation results.
c) The Lagrange function is constructed to solve the combined weight coefficient A.
Compared with other methods, the coefficient obtained by Eq. (16) minimizes the generalized distance between the weighted score of each evaluation object and the ideal point; furthermore, it can better reflect the consistency of the weighting results (Zhao et al. 2018).

Construction of index system
The initial allocation of emission permits needs to comprehensively consider factors in the decision-making process. Chen et al. (2013) studied the initial allocation of CO 2 emissions by establishing an index system, which incorporates economy, technology, policy, carbon emissions, and energy efficiency. He et al. (2016) explored the influencing factors of regional SO 2 emission. The results showed that the scale is the main factor causing the increase of SO 2 emission, while the progress of technology and the treatment improvement are the main ones for its reduction. On establishing the index system of emission right allocation (Guo et al. 2012;Feng et al. 2018;Hang et al. 2019), scholars mainly focused on the economic development of regions, industries, or enterprises, and seldom took into account the social contribution of enterprises.
Therefore, this paper sets up three criteria layers that affect the initial allocation of emission right: enterprise size, pollutant discharge and social contributions, and pollution control capacity. It reflects the overall strength and development of enterprises through size and examines the effects of the behavior of enterprises through the pollutant discharge and social contributions. Furthermore, it reflects the scientific and technological capabilities and developmental prospects of enterprises through their emission reduction and pollution control capability. In summary, this paper not only focuses on the pollutant emissions of enterprises, but also pays attention to their social contributions and performances, making the allocation more equitable. Under criterion layers, 10 tertiary indicators are set up. The constructed indicator system is shown in Table 1.
In the criterion layer of enterprise scale, registered capital reflects economic scale, installation supply and boiler tonnage represent production scale, and staff number indicates size of the workforce. On the pollutant discharge and social contributions, SO 2 emission reveals the pollutant discharge level, coal consumption denotes the energy input, and generation supply and heating supply show the social contributions. These parts are negative and positive outputs of thermal power enterprises. About the pollution control capacity, it is displayed by the variables of SO 2 removal rate and desulfurization equipment quantity.

Data source and processing
Thermal power generation is the main source of SO 2 in China (Liu and Wen 2012;Bai et al. 2018). This study selects 8 thermal power enterprises of Dalian as the research sample, and the indicator data were provided by Dalian Eco-Environmental Affairs Services Center due to the difficulty of obtaining the relevant data directly. For data confidentiality and convenient analysis, these enterprises are listed as enterprises 1-8, and the value of each indicator are brought into Eq.
(1) for standardized calculation according to their attributes.

Determination of the combination weights
The process of determining index weight by the G1 method is as follows.
Firstly, the importance of the criterion layer is ranked based on the experts' opinions: X3 > X2 > X1.
Secondly, the relative importance ratio of adjacent indexes is determined: r2 = X3/X2 = 1.6, r3 = X2/X1 = 1.2. Then, by substituting r2 and r3 into Eqs. (2) and (3), the weights of the criteria layers are 0.2427, 0.2913, and 0.4660, respectively. Similarly, the weight of each index can be obtained, as shown in the third column of Table 2.
The process of determining index weight by the G2 method is as follows.
Firstly, the least important index X1 is given by experts. Secondly, the importance ratios of other indicators to X1 are determined: r1 = X2/X1 = 1.2; r2 = X3/X1 = 1.6. By introducing r1 and r2 into Eq. (4), the weights of the criteria layers are 0.4211, 0.3158. and 0.2632, respectively. Similarly, the weight of each index can be calculated, as presented in the fourth column of Table 2.
Next, the normalized data are brought into Eqs. (5) and (6), and the entropy value of each index is obtained. Then, the weight of the entropy value of each index is calculated according to Eq. (7), as shown in the fifth column of Table 2. Then, the normalized data are brought into Eq. (11) to get the weight of each index under the maximum deviation method, as shown in the sixth column of Table 2.
Finally, the standardized data and the index weights from each method are substituted into Eq. (16). The weight coefficients of methods got are α1 = 0.2605, α2 = 0.20825, α3 = 0.1567, and α4 = 0.3003. Then, the index weights under the optimal combination are obtained from Eq. (12), as shown in the seventh column of Table 2.

Calculation of initial allocation ratio of enterprises
When calculating the initial allocation ratio of each enterprise, the original data is normalized firstly and then multiplied with the comprehensive weight to obtain the initial allocation ratio of each enterprise. The results are shown in Table 3 and Fig. 1.

Analysis of the initial allocation results
As seen in Fig. 1, the initial allocation proportion of emission right obtained by enterprise 3 is the largest, accounting for 24.69% of the total. According to Table 3, the desulfurization equipment quantity of enterprise 3 is the largest, and its SO 2 emission is also at a high level. Therefore, it is reasonable for enterprise 3 to get the largest proportion of emission rights. And enterprise 6 and enterprise 1 is only next to enterprise 3, which is 17.28% and 16.81% respectively. The heating supply of these two enterprises is obviously higher than that of others, so the allocation proportions of these are larger. Enterprise 6 is the only coal-fired power plant in the Dalian Development Zone, which mainly focuses on heating and cogeneration. Its social contribution is particularly significant.
Enterprise 7, enterprise 4, and enterprise 2 have the least allocation of emission rights, accounting for 3.13%, 6.79%, and 6.93%, respectively. Their scales are comparatively small, which is an important factor that affects the allocation of emission rights. Based on the optimal combination of weights, the initial allocation model of SO 2 emission right considers all characteristics of thermal power enterprises. Subjective and objective methods are combined, thus making the results more scientific.

Analysis of the difference between the actual and theoretical SO 2 emission
In 2017, the industrial SO 2 emission of Dalian was 50628.2 t. According to the statistical data of recent years, the SO 2   Fig. 2, while the actual SO 2 emissions of enterprises are shown in Fig. 2. As shown, the actual SO 2 emissions of enterprise 1, enterprise 4, enterprise 5, and enterprise 8 all exceed the theoretical value, especially enterprise 5. It can be seen from Table 3 that the boiler tonnage and SO 2 emission of enterprise 5 both rank first among these eight enterprises; however, its generation supply and heating supply fall behind seriously. We conducted a further communication with enterprise 5 and learned that there may be two reasons why the actual SO 2 emission value of it is much higher than the theoretical value. First, the number of desulfurization equipment in the enterprise is very small; second, in addition to power generation and heating, enterprise 5 is also engaged in a number of businesses that need coal consumption. The main purpose of these businesses is not heating or power generation, so there is no statistics on values of heating supply and generation supply, thus causing a situation that the coal consumption and SO 2 emissions are large, but the heating supply and generation supply are small. According to the index weight in this study, the proportion of generation supply and heating supply is greater than coal consumption and SO 2 emissions, so the theoretical value is far lower than the actual value.
While the emission value of enterprise 3 is the far lower than the theoretical value, in Table 2 and Table 3, the number of desulfurization equipment in enterprise 3 is large, which indicates that the technology level or the ability to control pollutants are strong, so the enterprise 3 can reduce the emission of SO 2 through treatment equipment and means. During the 12th Five-Year Plan period, enterprise 3 reformed the electrostatic bag dust removal system, optimized the original sulfur removal system, and greatly improved the effect of pollutant treatment. This material and the results of this study have achieved mutual confirmation. Also, this enterprise is of medium scale; however, the power generation is at a high level, the production efficiency is high, and the contribution to society is high. Such enterprises should be encouraged and supported. The common characteristic of enterprises whose actual emissions exceed the theoretical ones is that although the scale of the enterprise is large, the quantity of desulfurization equipment is small. This leads to low removal rate, thus causing more severe environmental pollution. Such enterprises should increase their investment in environmental protection equipment and should improve the applied treatment technology. Moreover, the government should strengthen the monitoring and control of these enterprises.
A significant difference exists between the actual and theoretical SO 2 emission values for each enterprise. This indicates that the government's current regulations on the pollutant emissions not fully consider the original differences of enterprises. In this case, strict initial allocation of SO 2 emission rights plays an important role for reducing the generation of pollutants and regulating production behavior. For enterprises with high generation supply (e.g., enterprise 3), heating supply (e.g., enterprise 1), and SO 2 removal rate (e.g., enterprise 6), the government should grant more initial SO 2 emission rights to encourage them to expand production scale and create more value for the society. In contrast, for ones with low SO 2 removal rates (e.g., enterprise 7), they should receive less initial emission rights. In this way, if enterprises want to discharge more pollutants, they need to buy additional emission rights from the market, which will add their production costs. Hence, in the long run, it is a more feasible way for enterprises to enhance environmental investments and upgrade technology level to reduce SO 2 emissions.

Analysis of the main influencing factors
According to the above research, the indicators in the first and second criterion layer are twice that in the third one. Therefore, based on the principle of fair, average index score of criterion layers are 0.0854, 0.1001, and 0.1291. So these three criterion layers are ranked by the importance from large to small, namely pollution control capability, pollutant discharge and social contribution, and enterprise scale. The result indicates that the relevant management departments should pay more attention to these enterprises' social contribution and pollution control capability. This is helpful for thermal power enterprises to actively undertake social responsibility and environmental protection responsibility.
Besides, SO 2 removal rate and desulfurization equipment quantity have the largest weight, indicating that under the condition of a certain total amount of allocation rights (although the economic contribution of enterprises needs to be considered), the level of sewage treatment of enterprises also occupies a certain proportion. This means that the importance of the pollution control level of enterprises has been affirmed, which induces the enthusiasm of enterprises to conduct pollution control from their side and embody certain fairness. Independent of which kind of policies the government formulates, these need to improve the efficiency and enthusiasm of enterprises toward pollution control. The result affirms that enterprises with high level of discharge treatment provide an incentive for other enterprises.
Moreover, the weight of staff number is the smallest since modern enterprises gradually adopt intelligent production and detection; therefore, the number of employees does not reflect the size of an enterprise anymore. Although the number of employees in specific enterprises is small, which may be because of their high level of modernization and intelligence, their production level and pollution control capacity may be stronger. The second smallest weight is the weight of SO 2 emissions. More SO 2 emissions do not represent the economic or social contribution of enterprises, which is possibly due to the use of outdated equipment or the high sulfur content of raw materials. If more emission rights are obtained because of its large emissions, this will lower the enthusiasm of enterprises to conduct pollution control and reduce emissions. This is not conducive to environmental protection and violates the original purpose of the allocation of emission rights.
In order to verify the reliability of the results, we consult 10 experts for their views on this study through field visits. Among them, there are 5 thermal power enterprise practitioners including 2 senior managers and 3 middle managers; 3 professors in research fields of ecological governance, air pollution control, and environmental management; and 2 government officials from local environmental protection department. They all believe that the allocation of SO 2 emission rights in this paper is reasonable, which is the consideration direction of the initial allocation.

Conclusions and implications
Conclusions By focusing on the initial SO 2 emission right allocation in thermal power industry, this paper establishes the index system including enterprise scale, environmental pollution, social contribution, and emission reduction capacity and develops an initial allocation model by combining the two subjective weighting methods of G1 and G2 with the two objective ones of entropy method and maximum deviation method. Then an empirical analysis is conducted to evaluate the initial right of SO 2 emission through taking 8 thermal power plants in Dalian as research objects. The findings of this study are as follows.
Firstly, SO 2 emission rights of 8 thermal power plants in Dalian are redistributed. The results show that the enterprises with more desulfurization equipment or large heating supply are allocated more emission rights.
Secondly, according to the evaluation results, the actual emission values of four thermal power enterprises of Dalian in 2017 exceeded the theoretical allocation ones. Generally, these enterprises have less desulfurization equipment and weaker abilities to control pollutants.
Thirdly, according to the weight calculation results, the main influencing factors including SO 2 removal rate, desulfurization equipment quantity, and heating supply are identified. The first two factors indicate the enthusiasm of enterprises in pollution control and emission reduction, and heating supply reflects the social contribution of enterprises.

Implications
The findings of this paper are conducive to the initial allocation of emission permits being more equitable while providing some references for government departments to make decisions on thermal power plants. Some suggestions are put forward for the government, industry, and enterprises.
For government departments, first of all, it is urgent to improve the legal system of SO 2 emissions trading. By promulgating regulations and trading rules related to SO 2 emissions trading, the responsibilities and rights of the main pollutant discharging body and the distribution body are clearly defined. This provides strong legal support for SO 2 emissions trading. Moreover, the government should start from the sources of pollution, strengthen the control over the source discharge, strictly verify the data reported by enterprises, and establish a real-time monitoring management and supervision system. These measures will ensure the smooth progress of emissions trading.
For the thermal power industry, as the focus of the development of the power industry, 70% of the total annual electricity consumption in China is a contribution of the thermal power industry. The thermal power industry needs to sum up the experience and lessons learnt of their extensive development in the past. Moreover, they should constantly improve and innovate and vigorously promote energy saving and emission reduction. These measures can realize the coordination of high-speed economic development and the protection of the ecological environment. At the same time, the industry should also improve the index system of the initial SO 2 emission rights allocation to ensure the efficiency and fairness of the initial allocation results.
For enterprises, it is time to improve production and management modes and promote energy saving and emission reduction to the strategic level of enterprises. Also, the market will inevitably be dominated by green high-tech industries; therefore, enterprises are facing serious pressures and challenges, and consequently, they must increase investment in scientific research, engage in technological innovation, and decrease costs while protecting the ecological environment. This can not only meet the requirements of environmental protection policies, but also reduce energy consumption and enhance the competitiveness of enterprises.
The limitations of this paper are as follows: On the one hand, this paper uses eight thermal power plants in Dalian as the research object, and therefore, the results may mainly be applicable to Dalian, but not to other areas. In the future, more cities should be selected, and regional research should be conducted to thus improve the applicability and universality of the index system. On the other hand, while the key factors that affect the initial allocation of SO 2 emission rights in thermal power plants were identified, the impact path of these key factors on the results of the allocation of emission rights is also valuable and should be deeply studied to provide a theoretical reference for the decision-making of relevant governmental departments at a deeper level.
Availability of data and materials The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.