Development of carbon finance in China based on the hybrid MCDM method

The study addresses how to accurately evaluate and rank the level of carbon finance development across Chinese regions amid rapid policy changes and the evolving carbon market. Prior research often overlooked provincial environmental heterogeneity and used outdated or narrow indicator sets. The paper aims to innovate the evaluation framework by integrating environmental, regulatory, market, financial, and innovation dimensions, and by introducing a hybrid MCDM approach (combining TOPSIS and VIKOR) complemented with AISM to produce robust regional rankings and investment guidance for carbon finance.

Comparative studies indicate that TOPSIS and VIKOR often yield different rankings; TOPSIS may align more closely with certain external assessments (e.g., Hezer et al., 2021 for COVID-19 security), while both methods have been applied in environmental, economic, and medical contexts (e.g., Sari et al., 2020). However, most works apply them separately rather than in an integrated manner, leading to disparate results. The importance of regulation and policy for low-carbon development is underscored (Yang et al., 2023), with the PITI index recognized as a reputable measure of environmental information disclosure (Ding et al., 2022) and the CRAES/IPE Carbon Neutral Composite Index evaluating local climate ambition and capacity. ETS systems are widely recognized market-based tools with significant economic impacts (Ritz, 2022; Jin et al., 2020). Financial sector effectiveness (green credit, stock markets) affects sustainability (Sharma et al., 2023) and bank efficiency relates negatively to nonperforming loan ratios (Phung et al., 2022). Innovation and the tertiary sector influence carbon efficiency and low-carbon innovation (Zhou et al., 2022; Pan et al., 2022). The AISM approach (Ni, 2020; Su et al., 2023) offers advantages over ISM by resolving clutter in complex hierarchical evaluations and has been extended to business strategy and supply chains; here it is applied to regional environment–economy analysis.

Indicator system: The study reconstructs a carbon finance evaluation index tailored to Chinese regions, drawing on Chen et al. (2020). Five primary dimensions are used: (A) Carbon environment (CO2 emission intensity; civilian vehicle ownership; forest coverage); (B) Carbon regulation (PITI; industrial pollution control investment; environmental protection tax for listed companies; industrial waste gas treatment investment; Carbon Neutral Composite Index); (C) ETS market (total carbon emission allowances in 2022; total volume share in 2022; average carbon transaction price in 2022); (D) Carbon finance/products and financial sector (carbon bond issuance; daily individual stock returns of carbon-neutral concept stocks excluding cash dividends; growth rate of green loans in 2022; nonperforming loan ratio; share of financial industry value added in the tertiary sector); (E) Carbon innovation (R&D intensity; value added of the tertiary industry as % of GDP). Data sources include China Environmental Statistics Yearbook, China Statistical Yearbook, IPE, WIND, CSMAR, CRAES, EPS, and the national ETS annual report. Weighting: Indicators are standardized and weighted using the entropy weight method to reflect dispersion and information content. Higher dispersion yields higher weight. Hybrid TOPSIS–VIKOR: The method links distance-based solutions from both models. Steps: (1) Determine positive/negative ideal solutions (PIS/NIS). (2) Compute Euclidean distances to PIS (D+) and NIS (D−) as in TOPSIS. (3) Apply VIKOR to compute group utility and regret using normalized gaps to best/worst: classical S+ (maximize group utility, negative toward PIS) and R− (minimize individual regret, negative toward PIS); extend to S− and R+ (distances toward NIS, positive indicators). (4) Summarize three columns of positive and negative ideal distances (Table 2) and average to obtain SDR+ (toward PIS) and SDR− (toward NIS). (5) Compute a compromise solution Q per a mixing parameter K in [0,1], where ranking changes can occur at inflection points of K. Cluster analysis identifies K-intervals with stable rankings. AISM: Using the decision matrix of SDR+ and SDR− (Table 5) for eight evaluation subjects (Guangdong, Beijing, Shenzhen, Shanghai, Hubei, Fujian, Tianjin, Chongqing), construct relationship matrix A, then derive UP (result-priority) and DOWN (effect-priority) hierarchical levels. Compute the general skeleton matrix S to infer directionality and produce UP/DOWN topology, revealing hierarchical structure and stability. Robustness: A mental-accounting-based sensitivity test varies decision intervals (e.g., shrinking [0,1] to [0.1,0.9] and focusing on subintervals [0,0.1866] and [0.8099,1]) and re-runs clustering to check stability of rankings and topology. Outputs: Entropy weights (Table 4), SDR+ and SDR− (Table 5), Q rankings across K-intervals (Tables 6–7), AISM hierarchy (Tables 8–9), and robustness verification.

- Indicator importance: Entropy weights show financial industry development (D) as the most influential primary category; among secondary indicators, R&D intensity (E1) has the highest weight (0.09243). Other relatively high weights include C1 (0.08874), D1 (0.08622), E2 (0.06869), and C3 (0.06833). The overall weight sums to 1. - Joint distances: Combined TOPSIS–VIKOR distances (Table 5) indicate, for example, Beijing (SDR+ = 0.186826; SDR− = 0.316085) and Guangdong (SDR+ = 0.183775; SDR− = 0.299926) are closest to PIS and farthest from NIS among the eight subjects, signaling superior performance. - Compromise rankings by K-interval (Table 7): • For 0 ≤ K < 0.186638 and 0.186638 ≤ K < 0.809853: Beijing > Guangdong > Shenzhen > Shanghai > Hubei > (Fujian vs Tianjin interchange) > Chongqing. • For 0.809853 ≤ K < 1: Guangdong > Beijing > Shenzhen > Shanghai > Hubei > Tianjin > Fujian > Chongqing. - Example Q-values (Table 6): For K = 1, Guangdong Q = 0.000000 (best), Beijing Q ≈ 0.019544, Chongqing Q = 1.000000 (worst). For K = 0, Beijing Q = 0.000000 (best), Guangdong Q ≈ 0.085172, Chongqing Q = 1.000000. - AISM hierarchy (Table 9): First echelon/top level: Guangdong and Beijing; followed by Shenzhen (Level 1), Shanghai (Level 2), Hubei (Level 3), Fujian and Tianjin (Level 4/5), and Chongqing last (Level 5). The topology indicates a rigid, stable structure. - Drivers of carbon finance: Technological innovation, financial sector development, and an active ETS market are key positive drivers. - Robustness: Rankings and hierarchical topology remain consistent under alternative decision intervals, indicating robustness of the hybrid method’s results.

The integrated TOPSIS–VIKOR approach effectively addresses the research goal of producing a robust, interpretable ranking of regional carbon finance development. By fusing distance-to-ideal concepts (PIS/NIS) from both methods and averaging distances (SDR+ and SDR−), the method captures both group utility and individual regret while preserving comprehensive ranking capability. The AISM hierarchy further elucidates structural relationships among regions, revealing a stable, rigid ranking system. Empirically, Beijing and Guangdong consistently emerge as the best investment choices for carbon finance, with Shenzhen and Shanghai forming the next tier. Entropy weighting highlights that financial sector depth and innovation capacity (notably R&D intensity) are pivotal, while ETS market activity significantly contributes. These findings underscore policy and strategic implications: strengthening financial sector development, accelerating R&D and innovation, and deepening participation in the ETS can bolster regional carbon finance competitiveness.

The paper contributes a hybrid MCDM framework that integrates TOPSIS and VIKOR distance measures and augments interpretation with AISM-based hierarchical analysis. Applying this framework to Chinese pilot provinces and cities yields a robust investment ranking, consistently placing Beijing and Guangdong at the top, followed by Shenzhen and Shanghai. The study identifies financial development, R&D intensity, and ETS market activity as key levers for advancing carbon finance. The methodology offers a generalizable approach for environmental and economic development assessment and decision support. Future work can extend the indicator system as new data and policies emerge, expand the set of evaluated regions, and further explore sensitivity to alternative weighting schemes or additional market/innovation metrics.