Research on carbon emission quota allocation scheme under “Double Carbon” target: a case study of industrial sector in Henan Province

Abstract

To achieve China’s “Double Carbon” target, overall carbon emissions should be effectively controlled, and carbon emission quota (CEQ) allocation is an important tool. This study develops carbon emission prediction, CEQ allocation, and scheme feasibility evaluation models based on the principles of fairness, efficiency, and economy. The purpose is to propose a suitable CEQ allocation scheme for the Industrial Sector in Henan Province (ISHP). The results show that (1) the allocation model combining the technique for order preference by similarity to ideal solution (TOPSIS) and the zero-sum gains DEA (ZSG-DEA) can trade off the fairness and efficiency principles. (2) The reallocation scheme has an environmental Gini coefficient of 0.393 (< 0.4), which maximizes efficiency while lowering the abatement costs by 126.268 billion yuan, making it an ideal scheme that considers multiple principles. (3) CEQ should be reduced in 7 subsectors of ISHP while increasing in 33 others. Carbon emissions from these 7 subsectors are high, and CEQ should be reduced in accordance with the fairness principle. Even if their abatement costs are high and CEQ rises according to the efficiency principle, the increase is much smaller than the decrease. The findings are useful for optimizing the CEQ allocation under the “Double Carbon” target.

Appendices

Appendix 1. The TOPSIS-based initial allocation model

Determination of indicator weight

Analytic hierarchy process

AHP is a simple method to determine the weight of indicators at all levels proposed by Saaty (Saaty 1988). The AHP method is a subjective method of weighting. Based on the understanding of experts and scholars on the evaluation system, it creates a paired comparison matrix to obtain the feature vector. This feature vector represents the relative weight of each indicator and its importance in a specific category. Eigenvalues can be calculated by using eigenvectors. Therefore, this study invited six experts from the Development and Reform Commission of the Henan Provincial Government and the Bureau of Geology and Mineral Resources to grade and determine the comparative matrix. The following are the specific steps:

• Step 1: Build the comparison matrix. The indicators in Table 2 are ranked in order of importance based on expert opinions (Tan et al. 2020a). Construct the comparison matrix $\mathrm{A}={\left({\mathrm{a}}_{\mathrm{ij}}\right)}_{n\times n}$ as follows:

  $$A=\left[\begin{array}{cccc}{a}_{11}& {a}_{12}& \cdots & {a}_{1j}\\ {a}_{21}& {a}_{22}& \cdots & {a}_{2j}\\ \bullet & \bullet & \bullet & \bullet \\ \bullet & \bullet & \bullet & \bullet \\ {a}_{i1}& {a}_{i2}& \cdots & {a}_{ij}\end{array}\right]$$

  (1)

  where ${a}_{ij}$ denotes the importance of indicator i relative to indicator j.

• Step 2: Matrix consistency test. Calculate the eigenvalues and eigenvectors of the comparison matrix. We denote ${\lambda }_{max}$ as the largest eigenvalue and calculate the consistency ratio (CR):

  $$\mathrm{CR}=\mathrm{CI}/\mathrm{RI}=\left(\frac{{\uplambda }_{\mathrm{max}}-\mathrm{n}}{\mathrm{n}-1}\right)/\mathrm{RI}$$

  (2)

  where CI is consistency indicator, which is used to estimate the consistency of the comparison matrix. RI is the average random consistency index, which takes a value that increases with increasing order n (Zong et al. 2022). When CR ≤ 0.1, the consistency of this matrix is acceptable.

• Step 3: Determine indicator weights. The unit positive eigenvector corresponding to ${\lambda }_{max}$ is the weight of each indicator.

Entropy weight method

The entropy weight method is to calculate information entropy ${\mathrm{E}}_{j}$ according to the information of indicators, and determine the effective information in data and the weight of indicators by using the degree of difference between indicators. Therefore, the entropy weight method is an objective method to assign weights. If ${\mathrm{E}}_{j}$ is smaller, it means that the deviation of indicator data is larger, and the more information is provided, the greater its weight (Chen et al. 2021a). The following are the specific steps:

• Step 1: Normalize the matrix. Let ${x}_{ij}$ be the original data value of indicator j of subsector i, construct data matrix $\mathrm{X}={({x}_{ij})}_{m\times n} (i=1,2,\cdot \cdot \cdot ,m, j=1,2\cdot \cdot \cdot ,n)$. We normalize the matrix according to the properties of each indicator:

  $${\widetilde{\mathrm{x}}}_{\mathrm{ij}}=\left\{\begin{array}{c}\frac{{\mathrm{x}}_{\mathrm{ij}}-\mathrm{m}{\text{in}}({\mathrm{x}}_{\mathrm{i}})}{{\text{max}}({\mathrm{x}}_{\mathrm{i}})-{\text{min}}({\mathrm{x}}_{\mathrm{i}})}, when\, {\mathrm{x}}_{\mathrm{ij}}\, is\, positive\, indicator.\\ \frac{\mathrm{max}({\mathrm{x}}_{\mathrm{i}})-{\mathrm{x}}_{\mathrm{ij}}}{{\text{max}}({\mathrm{x}}_{\mathrm{i}})-{\text{min}}({\mathrm{x}}_{\mathrm{i}})},when\, {\mathrm{x}}_{\mathrm{ij}}\, is\, negative\, indicator.\end{array}\right.$$

  (3)

• Step 2: Calculate the ratio for each indicator. The ratio of indicator j of subsector i refers to the change in size of the indicator.

  $${\mathrm{P}}_{\mathrm{ij}}=\frac{{\widetilde{\mathrm{x}}}_{\mathrm{ij}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{m}}{\widetilde{\mathrm{x}}}_{\mathrm{ij}}},\mathrm{i}=1,\cdots ,\mathrm{n}$$

  (4)

• Step 3: Calculate the entropy and weights of the indicators. If ${\mathrm{P}}_{ij}>$ 0, the entropy of the data is defined as ${\mathrm{E}}_{j}=-\frac{1}{{\text{ln}}\mathrm{m}}{\sum }_{i=1}^{\mathrm{m}}{\mathrm{P}}_{ij}{\text{ln}}\left({\mathrm{P}}_{ij}\right)$, and ${\mathrm{E}}_{j}$=0 otherwise. The calculation formula for indicator weight is as follows:

  $${\upomega }_{\mathrm{j}}=\frac{1-{\mathrm{E}}_{\mathrm{j}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\left(1-{\mathrm{E}}_{\mathrm{j}}\right)}\mathrm{j}=1,\cdots ,\mathrm{n}$$

  (5)

Combined weight of indicator

The weight of indicator j calculated by AHP and entropy weight method are ${\omega }_{1j}$ and ${\omega }_{2j}$, respectively. The comprehensive weight ${\omega }_{j}$ of indicator j can be calculated using Eq. (6):

$${\upomega }_{\mathrm{j}}=\frac{{\upomega }_{1\mathrm{j}}\bullet {\upomega }_{2\mathrm{j}}}{\sum_{\mathrm{j}=1}^{\mathrm{n}}{\upomega }_{1\mathrm{j}}\bullet {\upomega }_{2\mathrm{j}}}, \mathrm{j}=1,\cdots ,\mathrm{n}$$

(6)

The TOPSIS-based CEQ initial allocation model

The basic idea of TOPSIS is that the optimal solution should be closest to the positive-ideal solution and farthest from the negative-ideal solution (Zhu et al. 2020b). Based on the above indicator comprehensive weight ${\omega }_{j}$, this paper calculates the initial CEQ for each subsector using the TOPSIS method.

• Step 1: Normalize the matrix. We normalize the original data matrix $\mathrm{X}={({x}_{ij})}_{m\times n}$ and write the normalized matrix of X as Z.

• Step 2: Calculate the positive-ideal solution and negative-ideal solution. The optimal values of all indicators in the evaluation system constitute the positive-ideal solution, denoted as Z⁺. The definition of the negative-ideal solution Z⁻ is exactly opposite.

• Step 3: Calculate the distance from the positive-ideal solution and negative-ideal solution. The weight of each indicator is defined as ${\omega }_{j} (\mathrm{j}=1,\cdots ,\mathrm{n})$. Let ${{D}_{i}}^{+}$ be the distance between the indicator vector of subsector $i (i=1,\cdot \cdot \cdot ,m)$ and the positive-ideal solution. The definition of ${{D}_{i}}^{-}$ is exactly opposite.

  $${{\mathrm{D}}_{\mathrm{i}}}^{+}=\sqrt{\sum_{\mathrm{j}=1}^{\mathrm{n}}{{\upomega }_{\mathrm{j}}({{\mathrm{Z}}_{\mathrm{j}}}^{+}-{\mathrm{Z}}_{\mathrm{ij}})}^{2}}, {{\mathrm{D}}_{\mathrm{i}}}^{-}=\sqrt{\sum_{\mathrm{j}=1}^{\mathrm{n}}{{\upomega }_{\mathrm{j}}({{\mathrm{Z}}_{\mathrm{j}}}^{-}-{\mathrm{Z}}_{\mathrm{ij}})}^{2}}$$

  (7)

• Step 4: Determine the allocation ratio. The score for subsector i is recorded as ${S}_{i}=\frac{{{D}_{i}}^{-}}{{{D}_{i}}^{-}+{{D}_{i}}^{+}}$. The score ${S}_{i} (\mathrm{i }= 1, \cdots ,\mathrm{ m})$ is then normalized to obtain the initial allocation ratio for each subsector.

  $${{\mathrm{S}}_{\mathrm{i}}}^{*}=\frac{{\mathrm{S}}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{S}}_{\mathrm{i}}}$$

  (8)

• Step 5: Calculate the initial CEQ for subsectors. Multiply the allocation ratio ${{\mathrm{S}}_{\mathrm{i}}}^{*}$ with the total CEQ I to obtain the CEQ for subsector i:

  $${\mathrm{I}}_{\mathrm{i}}=\mathrm{I}\bullet {{\mathrm{S}}_{\mathrm{i}}}^{*}$$

  (9)

Appendix B

See Tables 7, 8, 9, and 10

Table 7 Indicator scenario design

Table 8 Variable regression coefficient

Table 9 AHP comparison matrix

Table 10 Weighting of CEQ allocation indicators