2.1. Study of the Initial Allocation Schemes of Carbon Emission Rights among Countries or Regions
The methods for distributing international carbon emission rights are mainly divided into two categories: one is developed according to the current status of carbon emissions and the long-term goals of global emissions reduction, based on an emissions per capita allocation; and the other is advocated for by developing countries, emphasizing the cumulative per capita emissions allocated based on historical responsibility [
9].
Currently, the EU Emissions Trading Scheme (EUETS) is the largest ETS in the world. The first stage (2005–2007) was conducted by auctioning 5% of carbon quotas and freely distributing the remainder. The second stage (2008–2012) increased the auction quota to 10%, after which large-scale public auctions were used to allocate quotas until the 2013 auction quota reached 50%; a 100% auction is expected in 2027 [
10]. In 2009, the Korean cabinet approved a 30% reduction in carbon dioxide emissions by 2020, compared to the general practice of a 5% decrease compared to 2005. Korea also devised a phased carbon trading market plan in 2013 that allocates the initial carbon emissions for free during the first five years and gradually increases the percentage of auctions over time, auctioning 100% of the quotas in the final stage in 2021 [
11]. Research by Goulder et al. [
12] showed that a considerable auction revenue would be produced only when sufficient free allocation of quotas compensated for the most vulnerable industries (but not excessive compensation), under the conditions of integrating U.S. industry and the overall economic form, and that some vulnerable industries would suffer enormous losses. In 2001, the Netherlands Energy Research Center and the Oslo International Center for Climate and Environmental Studies in Norway developed a more complex global multi-sectoral emissions reduction and sharing program based on the “three sector approach”. The program divides the world economy into seven sectors, namely, power generation, industrial, civil, transportation, services, agriculture and waste, and it determines each sectors’ carbon emission quotas according to the per capita emissions of countries [
13]. New South Wales’ initial allocation of carbon emissions to the state’s total population and its carbon emissions per capita were set in advance as the basis for calculating the total carbon emissions from the power industry. Second, electricity demand could be used to calculate the proportion of electricity demand and determine the available carbon emission rights [
14].
Given the enormous carbon emissions in China and the differences in carbon emissions between regions, the initial allocation of China’s regional carbon emission rights has long been a focus of both the government and academia [
15,
16,
17]. Currently, China has begun its carbon ETS. During the initial stage of carbon emissions trading in China, the implementation of the initial allocation has been coordinated by the relevant departments, and the mixed allocation method is mainly free distribution, with auctions as a supplement [
18]. Based on a large amount of foreign experience and many lessons, Lu Chunju and Zhang Ruixue [
19] noted that the method currently used, based on a grandfather system that allocates on the basis of historic emissions in China, can easily cause enterprises to exaggerate their declarations of carbon emissions, leading to excessive payments. Qiang et al. [
7] considered that China has currently only opened its carbon trading market in seven cities and proposed adopting the benchmarking method, which Beijing decided to implement in 2013. Based on the effectiveness of the market mechanism for the allocation of carbon rights, an increasing number of scholars believe that China should choose to gradually increase the proportion of auction quotas until the auction is completed [
20].
2.2. The Distribution Method for the Initial Distribution of Carbon Emissions Rights
The research on the initial distribution of carbon emission rights at home and abroad has mainly used the Zero-Sum Game Data Envelopment Analysis (ZSG-DEA) model, the Shapley model, the multi-region Computable General Equilibrium (CGE) model and the multi-factor comprehensive analysis. Based on a particle swarm optimization (PSO) algorithm, the fuzzy c-means (FCM) clustering algorithm and the Shapley decomposition method of total carbon emissions from 13 factors divided into four categories, Yu et al. [
21], divided the 30 provinces of China into four categories, studied the key factors of provincial carbon emissions growth, and identified the initial allocation of carbon emissions quotas. Feng et al. [
22] used the improved DEA-based centralized allocation model under the assumption of constant returns-to-scale (CRS) and variable returns-to-scale (VRS) returns to develop a plan for central allocation, citing the empirical applications of the OECD countries. Pang et al. [
23] allocated carbon emissions across countries based on the ZSG-DEA model and maximized allocation efficiency. Based on emissions and output allocation rules, Böhringer et al. [
24], provided an optimal scheme for carbon allowance under dynamic conditions and found that the grandfather distribution plan worked best in a closed system. However, among trading systems, the grandfather distribution plan is not the best. The drawback of the grandfather system is that it rewards companies that have done the least to reduce emissions in the past, which is not conducive to the goal of the carbon trading scheme. It would be unfair for companies with smaller space and higher energy efficiency to get fewer allocations than inefficient ones because of the early cuts. Additionally, the grandfather system applies only to facilities or capacities that were already operating at the start of a carbon trading transaction. Among open trading systems, this method cannot be corrected automatically for new entrants or additional capacity. In order to avoid carbon emission rights falling into the hands of rivals, some companies may not be willing to sell excess carbon emission rights, which will weaken the carbon emission rights market liquidity. The cost of obtaining carbon rights for new companies will increase, making it difficult for new companies to enter the market.
Tan and Junfei [
25] used the ZSG-DEA model to evaluate the efficiency of the quotas for the initial allocation of carbon emissions rights in EU countries in 2009. Based on the total amount of control, Jiekun et al. [
26] used the income NDV-DEA optimization model to improve allocation efficiency, considering the grandfather system, the principle of equality and the principle of the ability to pay for the initial carbon emissions allocation in China’s provinces. Pan et al. [
27] found that the allocation of the original DEA model was less efficient and used the ZSG-DEA model to calculate the carbon emission rights allocation results of six major industries in China. Yong and Shushu [
28] considered 14 factors of fairness, efficiency and sustainable development, using the Criteria Importance Though Intercreria Correlation (CRITIC) method and fuzzy optimization to calculate the initial distribution of carbon emission rights in East China. Both Ning [
29] and Sufeng [
30] adopted the information entropy multi-attribute decision-making model to construct evaluation systems and to estimate the initial allocation quota of carbon emissions rights in the industry and the Chinese provinces. Kai et al. [
9] used China’s 2030 emission reduction target as the breakthrough point and built an allocation model for carbon emissions rights in China’s 31 provinces and municipalities over 15 years a comprehensive use of factor analysis, regression analysis, correlation analysis, cluster analysis and other quantitative methods. Based on the Gini coefficient optimization model, Huihui et al. [
31] devised a fair distribution of carbon emission rights in 132 countries worldwide and discussed the remaining carbon emissions in each country. Xiao [
32] conducted a carbon emission quota analysis based on forward looking, population, GDP, per capita GDP, and disbursement capacity, finding that forward-looking principles are more suitable for the coordinated development of all provinces in China. Jingjing and Xiangsheng [
33] considered the problem of interest games in the construction of carbon emissions trading markets and used the Analytic Network Process (ANP) method and the Shapley model based on weight improvement to allocate carbon emission rights in China.
In summary, scholars at home and abroad have conducted research into the initial allocation of carbon emission rights, laying the foundation for follow-up development in this field.
Table 1 provides a summary of the research into the allocation of carbon emission rights. On the whole, there are still some shortcomings in the current research.
(1) The indicators of the influencing factors in the initial allocation of carbon emission rights must be improved. Currently, scholars have mainly considered factors such as population, carbon intensity, GDP, and energy consumption when studying the initial allocation of carbon rights [
31,
32,
34] without considering other factors that reflect sustainable development. The lack of sustainable development factors will result in the unequal distribution of carbon emissions rights, which will lead to an excess of carbon emissions in provinces that have a better environmental infrastructure and a higher technology capacity; this is not conducive to the coordinated development of all the country’s regions. In the selection of indicators, some studies have adopted a combination of subjective and objective factors [
35,
36,
37]. Subjective factors are the individual subjective evaluation scores, which incur the bias of human intention and affect the allocation of carbon rights.
(2) The fairness of the allocation of carbon emission rights must be improved. Most studies only allocated the carbon emission rights regionally and did not further evaluate the fairness of the distribution results [
5,
25,
38]. At the same time, some research used the Gini coefficient to evaluate the overall fairness but did not further explore the reasons for the unfair distribution results.
Considering the existing research, this paper applies the improved TOPSIS method (technique for order preference by similarity to an ideal solution) to China’s initial carbon emissions allocation to provinces and the theoretical distribution of carbon emission rights and actual carbon emissions comparative analysis. On this basis, this paper fairly evaluates the initial provincial allocation scheme for carbon emissions. Compared with existing research, the main innovative points of this paper are as follows:
(1) It uses the improved TOPSIS method to conduct the initial provincial allocation of carbon emission rights in China. TOPSIS is a commonly used and effective method for multi-objective decision-making analysis that is also known as the superior-inferior solution distance method. This paper is the first to apply the TOPSIS method to the study of the regional decomposition of carbon emission rights. At the same time, the traditional TOPSIS method mainly relies on subjective judgment when determining the weights of various influencing factors. To eliminate the influence of subjectivity, this paper uses the TOPSIS model improved by the entropy method, with a matrix of evaluation indicators to determine the indicator weight. This method allows it to more objectively reflect the order of information, rendering the evaluation results more practical.
(2) It enriches the carbon emissions impact of the indicator system. In light of the shortcomings of past studies on carbon rights allocation that used a small number of factors, such as population, carbon emission intensity, GDP, and energy consumption, this paper adds forest cover, the proportion of secondary industries and the market turnover of technology as emissions factors; these three indicators respectively symbolize the accommodation environment, industrial structure and technology innovation ability. The indicator system of the factors influencing carbon emissions, constructed in this paper, better reflects the sustainability of the future development of carbon emissions in all provinces, resulting in research results with more practical significance.
(3) In the context of this research, we evaluate the initial allocation of carbon emission rights fairly and explore the deep-seated reasons for the unfair carbon emissions between regions. After the initial provincial allocation of carbon emissions rights, this paper also uses the Gini coefficient to fairly evaluate the distribution results in a fair manner. At the same time, because the Gini coefficient does not explore unfair factors, this paper further uses the subgroup decomposition of the Gini coefficient to analyze the contributions of carbon emissions to the five major economic regions within and between regions, exploring the underlying causes of the unfair distribution of carbon emissions.
The remainder of this paper is arranged as follows: the third part is the model construction, the fourth part is the calculation of the carbon emissions of China’s provinces, the fifth part is the results of the analysis, the sixth part is a comparison and discussion, and the seventh part is the conclusion and suggestions.