Correction: Integration of Digitalization and Green Finance for Sustainable and Resilient Manufacturing and Service Operations in China: An Empirical Analysis

Xu Zhou¹Katat Sou^2*Ziting Gao³Jian Xiong^4*

• ¹Department of Management, Beijing Institute of Technology, Beijing, China
• ²Macao Polytechnic University, Macau, Macao, SAR China
• ³School of Business, Macau University of Science and Technology, Macau, China
• ⁴Shenzhen University Shenzhen Audencia Financial Technology Institute, Shenzhen, China

1.1 Background Following China's economic reform and opening-up, the nation has witnessed unprecedented economic growth. However, such rapid growth has simultaneously imposed significant environmental costs.Environmental degradation and the strain on ecological resources have become critical challenges, demanding urgent intervention. China's environmental challenges, characterized by resource scarcity and severe pollution, highlight the urgent need for innovative strategies to balance economic development with ecological sustainability. Acknowledging these challenges, the Chinese government explicitly emphasized green development in its 14th Five-Year Plan, aiming to position China as a global leader in ecological preservation and sustainable economic practices. President Xi Jinping's commitment to peak CO 2 emissions by 2030 marks a strategic transition towards a green economic model, encapsulated in the vision that "a gold mountain is a silver mountain, and a gold mountain is a green mountain." In this context, green finance has evolved beyond mere financial support into a fundamental pillar driving China's environmental governance and economic restructuring.To advance this transformative agenda, the government has enacted several critical policies, including the Green Credit Guidelines (2012), the Green Bond Guidelines (2015), and the Green Financial System Guidelines (2016) ??. These policies have significantly stimulated the development of green finance, promoting capital allocation to eco-friendly projects that traditionally face barriers due to perceived high risks or lengthy return periods. Despite inherent challenges associated with green investments, such as substantial risks and extended investment cycles, these financial instruments remain essential for redirecting resources toward sustainable development goals. Recent policy updates further encourage digital-finance solutions such as blockchain-based carbon registries and AI-driven project screening-to reduce information asymmetry and speed up green capital flows ?. From an operations-management perspective, this digital-green synergy is pivotal for building sustainable and resilient manufacturing and service systems. Real-time carbon tracking, smart contracts for green supply-chain finance, and AI-enabled demand forecasting together reduce both ecological and disruption risks, ensuring continuity of production while meeting strict emission targets. Hence, analysing the nexus at the provincial level has direct implications for factory-floor decisions and service-network design across China's vast industrial landscape.The scale of this synergy is now increasingly measurable. The PKU Digital Inclusive Finance Index shows national digital-finance penetration rising from 124 points in 2013 to 362 points in 2023, laying technical rails for low-latency carbon accounting and automated sustainability-linked lending. Two recent examples illustrate the mechanism: (i) Hainan's "Blue Carbon" blockchain registry verified 4.3 Mt CO 2 offsets in 2023 and cut third-party audit time by 70 % 1 ; (ii) China Merchants Bank's AI-ESG engine shortened credit approval for renewable-energy SMEs from 15 to 10 days while lowering expected default losses by 12 % 2 . This study explores the complex interplay among green finance, economic growth, and carbon emissions across China's diverse regional landscapes. Using data from the China Emissions Accounts and Datasets (CEADS) and employing a robust green-finance impact model, this research investigates the regional variations in the effectiveness of green finance on environmental outcomes and economic performance. Our analysis reveals that while carbon emissions historically contributed to China's economic prosperity, the adoption of green-finance practices is progressively reshaping this relationship. Specifically, green finance has demonstrated substantial effectiveness in curbing carbon emissions, with particularly pronounced impacts observed in China's western and central regions. Furthermore, the results suggest China is on course to achieve its carbon emissions peak by 2031, led by the more economically advanced eastern region due to its well-developed green-financial infrastructure. Conversely, the central region, projected to reach a carbon peak by 2036, underscores the necessity and potential effectiveness of targeted green-financial policies in promoting balanced regional development and environmental sustainability.Our investigation is feasible because it leverages a newly compiled province-level panel (2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023) that couples CEADS carbon data with high-frequency digital-economy satellite proxies, enabling consistent measurement of both traditional and digitalised green-finance activities. We construct a composite index that embeds emerging instruments-e.g. sustainability-linked loans and FinTech-enabled green bonds-thereby capturing the latest market dynamics overlooked by earlier studies ?. Methodologically, we extend prior single-equation approaches by adopting a three-equation 3SLS framework complemented with system-GMM robustness checks, which allows us to disentangle bi-directional causality between digitalisation, green finance, and carbon outcomes. Together, these features position our work at the frontier of greenfinance research and provide clear advantages over studies that stop at 2019 or neglect the digital component.By integrating green finance into the economic framework based on the Cobb-Douglas production function and the Environmental Kuznets Curve (EKC), this paper not only elucidates the theoretical mechanisms by which green finance acts as a catalyst for economic transformation but also provides empirical evidence of its tangible impacts toward achieving China's ambitious carbon-neutrality goals.Ultimately, this research emphasizes the pivotal role green finance plays in shaping China's sustainable future, offering valuable insights and serving as a model for other nations seeking to harmonize environmental objectives with economic growth.The accelerating digitalisation-green finance nexus is reshaping how capital is channelled towards lowcarbon projects. Recent evidence shows that a vibrant digital economy can amplify the carbon-mitigation effect of green financial instruments by improving information transparency, lowering transaction costs, and expanding financial inclusion ?. However, empirical studies continue to report heterogeneous outcomes across regions and technologies, implying an urgent need to quantify where and how digital tools create additional environmental value ?. Against this backdrop, the present study sets out three specific objectives.1. Quantification. Measure the marginal impact of digitalisation on the efficiency of provincial greenfinance allocation during 2010-2023.2. Mechanism Exploration. Identify the channels-information, innovation and inclusion-through which digital tools strengthen (or weaken) green-finance effectiveness.3. Policy Differentiation. Provide region-specific and technology-specific recommendations for regulators and market participants seeking to leverage digital solutions for green development.The key contributions of this article can be summarized as:1. constructing a composite index that embeds emerging instruments such as sustainability-linked loans; 2. deploying a three-equation 3SLS framework with instrumental-variable and system-GMM robustness checks;3. extending the sample to 2023 using the latest CEADS and digital-economy satellite proxies; 4. offering a decision matrix that aligns digital-finance capabilities with local green-transition priorities.These advances, taken together, address the research gaps highlighted by recent review literature while providing actionable insights for policymakers and investors alike. Green finance is pivotal for supporting sustainable development, providing essential financial backing for enterprises engaged in environmental governance and ecological protection. Defined by ?, green finance involves financial institutions that fund initiatives mitigating potential environmental impacts, thereby fostering ecological sustainability. The authors of ? emphasize that green finance is crucial in addressing climate change, facilitating a shift towards sustainable industrial practices. According to ?, green finance must account for environmental costs to effectively serve society and the environment, ensuring that financial investments promote rather than simply mitigate environmental sustainability. The authors of ? detail green finance's strategic role in reducing carbon emissions by reallocating resources from high-carbon to low-carbon industries, enhancing industrial sustainability and structure. This approach not only supports the reduction of environmental footprints but also promotes the modernization of industrial sectors toward sustainability.These perspectives highlight green finance as a transformative force capable of reshaping economic landscapes towards environmental sustainability, aligning with global environmental goals and the themes explored in this study. Nevertheless, most early works treat green finance as an isolated policy instrument; they seldom consider how digital technologies might alter its efficacy, leaving an open research niche that our study addresses. EPI-Finance assesses the effectiveness of financial institutions in a green context by examining environmental benefits, green tools, and a range of green financial products. This approach provides a theoretical and empirical framework for measuring the impact of green finance. Irfan et al. have developed a green finance index specifically tailored to evaluate the progress of green finance initiatives across China ?. Yang et al. reported a growing acceptance of green finance in Shanghai, with their analysis covering all 31 provinces based on index data from 2015 to 2017 ?. However, challenges remain as highlighted by Bo ? and Fu et al. ?, who note several theoretical issues confronting green finance development in the country. Further analysis by Liu et al. evaluate green economic growth in the three northeastern provinces, providing a comparative insight into regional disparities in green finance performance ?. Unlike the static indices above, our composite metric embeds FinTech-enabled instruments-sustainability-linked loans, transition bonds and digital green loans. Environmental regulation and green finance have similar effects, according to empirical analysis. It has been reported that many enterprises have been paying attention to and investing in environmental protection industries as a result of environmental system management ?. Although there are differences in geography and industry between the two, enterprises' investments in green projects and normative environmental protection management are positive ?. According to Ma et al. ?, green finance can directly drive green investment quotas for enterprises with green credit, green bonds, and other unique products addressing equipment emission reduction, renewable resources, and emissions reduction. The focus of green finance is on cultivating green industries. In the environmental protection industry, return rates are influenced by capital investment to some extent, and the larger the green finance market, the more benign it is. In ?, the EKC hypothesis and input-output models were combined into a joint model, and the panel model was used to construct the environmental quality comprehensive index system. In the study, environmental quality and green finance interact, and green finance has a positive effect on environmental quality but a low effect on environmental change. Despite that, he kept investing in green industries. Various financial institutions will assess the risks associated with green assets. Yun et al. found that the risk can be reduced by enhancing the value of green environmental protection resources and the power of the capital market ?. Financial institutions should be allowed to invest in green industries after evaluating transformational risks and green value indicators. Most of these studies adopt single-equation or correlation designs. To tackle endogeneity and bi-directional causality, we deploy a three-equation 3SLS system, which will be detailed in Section 5. Various scholars have conducted studies on how green finance is related to the emission of greenhouse gases. In ?, green venture capital is considered to be green finance. As a result of both methods of reducing carbon emissions, the study found that they have significant effects. Carbon emissions are reduced more by green finance than green venture capital, and their interaction is insignificant. A recent article suggests that green financial interest rates do not always negatively affect manufacturers' optimal emissions reduction levels, as they argue ?. The authors of ? found that green finance policies significantly reduce carbon dioxide emissions in Chinese provinces, municipalities, and autonomous regions. Green finance policies can potentially reduce emissions in many ways related to the environment, technology, and biased technology progress. Green finance promotes low-carbon industries. As proposed in ?, a low-carbon industry development mechanism should be built, which includes guidance on policy tools, expansion of financial services, innovation of financial instruments, and promotion of environment friendly industries.Environmental technology and climate change investment and financing are currently tricky because there are no relevant standards, incentive innovation mechanisms, and financing options. In ?, green finance investment and financing channels, incentive innovation systems, international collaboration frameworks, carbon finance innovation, green infrastructure, and green finance reform pilot zones should be enhanced.Integration studies remain scarce. Li & Deng (2024) ? show that digital-finance density moderates the impact of green credit on city-level carbon intensity, but their sample ends in 2019. Our work extends this line by using 2023 data and explicitly modelling the Digitalisation × Green Finance interaction, thus bridging the literature gaps. Green finance mostly plays a role in green expansion, concluded its function. The authors of ? state that green financial activities promote sustainable economic and social development, such as environmental protection, emission reductions, and efficient energy production, by contributing to economic and social development. The theoretical foundation of this research is based on the intricate interactions between green finance, carbon emissions, and economic growth, framed within the broader context of sustainable development. Leveraging the Environmental Kuznets Curve (EKC) hypothesis and integrating concepts Zhou et al.from green finance theory, this study aims to provide a comprehensive understanding of how financial instruments can influence environmental outcomes and economic development in China.The EKC hypothesis posits an inverted U-shaped relationship between environmental degradation and economic growth. Initially, as economic growth accelerates, environmental degradation increases; however, after reaching a certain level of income per capita, further economic growth leads to environmental improvements. This study extends the EKC hypothesis by incorporating green finance as a pivotal factor that could potentially shift the curve, enabling environmental improvements at lower levels of GDP per capita than traditionally observed.To enrich the theoretical lens, we further draw on three classical perspectives. First, the Porter Hypothesis ? contends that well-designed environmental regulation can spur innovation, ultimately enhancing firm competitiveness; green finance can act as a market-based regulatory mechanism that realigns capital toward cleaner technologies. Second, Stakeholder Theory ? highlights how diverse stakeholder pressures-now amplified through digital platforms-push firms and financiers toward sustainable practices. Third, the Natural Resource-Based View (NRBV) ? posits that environmentally oriented resources and capabilities, such as big-data-driven risk analytics, constitute strategic assets.Digitalisation enters this framework as an enabling condition that reduces information asymmetry, lowers transaction costs, and accelerates green-innovation diffusion ?. Accordingly, we expect digital finance to moderate the relationship between green finance and both carbon emissions and economic growth. The theoretical foundation of this research is based on the interplay between green finance, carbon emissions, and economic growth, framed within the broader context of sustainable development. This framework leverages the Environmental Kuznets Curve (EKC) hypothesis and integrates concepts from green finance theory to provide a comprehensive understanding of how financial tools can influence environmental outcomes and economic development in China.The EKC hypothesis posits an inverted U-shaped relationship between environmental degradation and economic growth. Initially, economic growth leads to increased environmental degradation; however, after reaching a certain income level per capita, further economic growth results in environmental improvements.This study extends the EKC hypothesis by incorporating green finance as a critical factor that could potentially shift the curve, enabling environmental improvements at lower GDP per capita levels than traditionally observed.Green finance encompasses financial instruments and policies designed to support environmental sustainability objectives, including climate change mitigation through investments in sustainable energy and emission-reducing technologies. It represents a fusion of economic development and environmental stewardship within financial markets. In this research, green finance is conceptualized as a catalyst that not only influences the pace and pattern of economic growth but also directly impacts the trajectory of carbon emissions.Integrating green finance into the EKC framework involves examining how financial policies and instruments designed to promote environmental objectives alter the relationship between GDP and carbon emissions. This integration is operationalized through the construction of simultaneous equations that model the dynamic interactions between economic growth, green finance, and carbon emissions across different provinces in China. The theoretical model posits that green finance initiatives, such as green bonds, green stocks, and green loans, directly contribute to capital flows into environmentally beneficial projects, thereby reducing the carbon intensity of economic activities. This is expected to lead to an earlier onset of the turning point on the EKC curve, where increased economic output begins to coincide with decreased environmental degradation. In addition, we recognise digitalisation as a cross-cutting enabler that lowers information asymmetry and transaction costs, thereby amplifying the effectiveness of green-finance instruments.Based on the literature review and theoretical considerations, the study formulates the following key hypotheses:• H1: Green finance significantly boosts economic growth.• H2: Economic growth demonstrates an EKC pattern with carbon emissions, where emissions rise with initial growth but decline after a certain income threshold.• H3: Green finance effectively reduces carbon emissions by directing investments into sustainable projects and technologies.• H4: Digitalisation (DF D) positively moderates the effect of green finance (GF ); the interaction term GF × DF D (i) amplifies the carbon-reduction effect of green finance and (ii) reinforces its contribution to economic growth.• H4a: The moderating effect operates through an information-transparency channel that lowers financing costs and mitigates green-washing risk.• H4b: The moderating effect operates through a financial-inclusion channel that expands access to green credit for SMEs and households.• H5: Stronger policy support enhances green-finance development. A solid theoretical foundation for green finance rests on several classical strands of economics. First, Pigouvian externality theory asserts that environmental damage constitutes a negative externality; capital that internalizes this cost (green credit, bonds) raises social welfare ?. Second, the Coase bargaining theorem posits that, with well-defined property rights and low transaction cost, parties can negotiate efficient outcomes ?. Green financial contracts operationalise those rights (e.g. carbon-pledged loans), while digital audit trails cut transaction cost, making Coasian bargaining feasible. Third, financial-intermediation theory highlights information asymmetry and credit-rationing under imperfect information ?. AI-driven ESG scoring directly lowers the Akerlof adverse-selection problem ?. Fourth, the Porter-van der Linde hypothesis argues that well-designed environmental regulation can spur innovation and productivity; digital transparency magnifies that effect by shrinking the marginal abatement cost (MAC) curve ?. Finally, the Natural Resource-Based View (NRBV) regards environmental capabilities as strategic resources; blockchain or IoT data streams enhance their value, rarity, imitability, and organization attributes ?.Green finance encompasses a range of financial instruments and policies designed to support environmental sustainability objectives, including the mitigation of climate change through investments in sustainable energy and technologies that reduce emissions. It represents a fusion of economic development with environmental stewardship through financial markets. In this research, green finance is conceptualized as a catalyst that not only influences the pace and pattern of economic growth but also directly impacts the trajectory of carbon emissions. Commercial banks can develop a form of credit suitable for enterprises, individuals, and families. Green credit involves combining market needs, considering the ecological impact of financial decisions, and adopting preferential measures such as loan amounts, interest rates, and the approval process. The research in ? asserted that vigorously promoting green credit, constantly improving green financing, and effectively guiding capital flows to resource-saving and eco-environmental protection industries are essential steps to accelerate the transformation of economic development and foster the construction of an ecological civilization. Some of the most notable differences between green bonds and green credits include their medium and long-term maturity, vital financial attributes, the requirement that the organization issuing the bond must be green, and the use of funds raised for green projects. Most commercial banks provide short-term credit, so there is no term mismatch in green project financing.Digital tools-blockchain for traceable green bonds, AI for ESG scoring, and mobile platforms for inclusive green loans-enhance the credibility, transparency, and scalability of these instruments. By embedding sensor and platform data, financiers can more accurately price environmental risk, which supports the NRBV notion of data-driven capabilities as strategic resources.Although conventional green instruments alleviate capital scarcity, they still suffer from information asymmetry, verification lags, and high transaction costs. Building on Akerlof's market-for-lemons problem and Williamson's transaction-cost economics ??, we argue that digitally enabled mechanisms can internalise these market failures. Table 1 summarises how specific technologies tackle the pain points. From a strategic-management lens, these technologies create data-driven dynamic capabilities that confer both cost and differentiation advantages, consistent with the Natural Resource-Based View (NRBV) and the Porter-van der Linde eco-efficiency hypothesis ??. For instance, immutable blockchain records shorten verification lead times, enabling issuers to secure tighter coupon spreads, while AI-driven ESG models lower screening costs, narrowing the green-premium gap for smaller borrowers. Hence, integrating such digital tools is not merely operational-it reshapes competitive positioning in sustainable-finance markets. It is mainly government-led special or private equity funds that initial investment in the Jiangsu, Zhejiang, and Shanghai areas of rapid development. In recent years, the key areas of green finance have been environmental protection prevention, green restoration, resource conservation, clean energy, and other green development areas. In China, green insurance is a form of market capitalization for guarantee and compensation in the event of polluting ecological liabilities. With the development of insurance prices and interest rates, green insurance can be developed. Additionally, customized insurance products can Zhou et al.be developed for green technology and carbon emission reduction projects to improve enterprise risk identification and effectiveness of green supervision.Carbon finance is a type of trading behavior with carbon emission rights and car-bon credits as the target, also known as carbon emission trading, Aiming to reduce greenhouse gas emissions or increase the capacity of carbon sinks to do so. To allocate optimal resources, carbon emissions rights are assigned and traded freely at low cost ?. As a result of carbon pricing, carbon emissions can be reduced more efficiently, emissions costs can be reduced, and climate and environmental change can be proactively addressed.The social environment will gradually improve with the increase of green investment and financing expenditure from these financial instruments, as shown in Figure 1. Energy will be used more effectively, which will better help China's "carbon peak and carbon neutrality" work. Green finance represents a new trend and a new direction for future financial development ??.Implementing green finance is significant for promoting industrial transformation and upgrading, promoting sustainable development of the regional economy, and accelerating social progress. Therefore, we should complete the top-level design of green finance from the national level and accelerate the construction of green financial market mechanisms. Green funds are financed from a macro perspective, in their own appropriate social environment, through finance institutions, enterprises, the public, and other factors.It is indicated in the line of standards, "green capital investment," "social supervision," "green financial support," etc., where green funds are the most direct mechanism to support green development, with green projects at their early stage of development being associated with long investment times, late returns on investments, and other characteristics of a particular financing gap, and therefore green enterprises need not only government subsidies.Additionally, green derivatives offer capital leverage. They are closely associated with green development, making it possible to build a market for carbon emission rights rapidly. Also, various industries participating in this market can provide financial institutions with continuous incentives to reduce carbon emissions while guiding financial institutions toward creating a transparent and rational market for carbon trading. This part introduces a theoretical framework designed to investigate the impact of green finance on economic growth and carbon emissions. The proposed model aims to capture the complex relationships among these variables and provides a foundation for the empirical modeling discussed in subsequent sections. The proposed model consists of three primary equations that represent the interactions between green finance, economic growth, and carbon emissions. These equations form the basis for the empirical analysis detailed in the following sections. (1) Economic Growth EquationY it = δ 0 + δ 1 GF it + δ 2 K it + δ 3 L it + ϵ it (1)where Y it denotes the economic output of region i at time t. GF it is the green finance index of region i at time t. K it means the capital investment in region i at time t. L it is the labor input in region i at time t. δ 0 refers to the constant term. δ 1 , δ 2 , δ 3 are the coefficients, and ϵ it is the error term.Zhou et al.(2) Carbon Emissions EquationE it = θ 0 + θ 1 Y it + θ 2 (Y it ) 2 + θ 3 GF it + θ 4 EN it + ν it (2)where E it denotes the carbon emissions of region i at time t. Y it is the economic output of region i at time t. GF it means the green finance index of region i at time t. EN it denotes the energy consumption in region i at time t. θ 0 is the constant term. θ 1 , θ 2 , θ 3 , θ 4 are the coefficients. ν it is the error term.(3) Green Finance EquationGF it = λ 0 + λ 1 P it + λ 2 Y it + λ 3 T it + ξ it(3)where GF it denotes the green finance index of region i at time t. P it means the policy support index in region i at time t. Y it means the economic output of region i at time t. T it represents the technological advancements in region i at time t. λ 0 is the constant term. λ 1 , λ 2 , λ 3 are the coefficients. ξ it is the error term. The hypotheses and model equations outlined above provide the foundation for the empirical analysis presented in the subsequent sections. To empirically validate these hypotheses, the study employs data from the China Emissions Accounts and Datasets (CEADS). Advanced econometric methods are utilized to ensure robust parameter estimation and model validation. The specific hypotheses tested are:• H1: δ 1 > 0This suggests that an increase in green finance (GF) positively affects economic output (Y).• H2a: θ 1 > 0 and θ 2 < 0This indicates that economic growth initially leads to higher carbon emissions (E), but emissions decline after reaching a certain level of economic output (Y).• H3: θ 3 < 0This hypothesis posits that increased green finance (GF) correlates with reduced carbon emissions (E).• H4: A positive and significant interaction term between digitalisation and green finance will further reduce carbon emissions and/or enhance economic growth.• H5: λ 1 > 0Stronger policy support (P) enhances green-finance development (GF).The empirical testing of these relationships is crucial for understanding how green finance can drive sustainable economic growth and reduce carbon emissions, thereby contributing to the achievement of carbon neutrality goals. The detailed empirical analysis is presented in the following sections, building on the theoretical framework established here. Following the theoretical exploration of how green finance influences the Environmental Kuznets Curve dynamics, we employ a simultaneous equations model to empirically test the hypotheses stated. This section details the rationale behind the selection of this model and describes its application in analyzing the impact of green finance on carbon peaks. Given the complex interdependencies between economic growth, green finance, and carbon emissions, a simultaneous equations model is particularly apt for this study. This model type allows for the estimation of multiple interdependent relationships where the dependent variable in one equation can serve as an independent variable in another, reflecting the mutual influences typical in economic systems. In estimation, we apply three-stage least squares (3SLS) to address endogeneity and to exploit the cross-equation correlation that arises from the bidirectional causal structure.The general form of the simultaneous equations model used in this study is represented as follows:(1) Economic GrowthGDP it = α 0 + α 1 GF I it + α 2 P C it + α 3 GDP it-1 + ε it (4)where GDP it is the gross domestic product of region i at time t, GF I it represents the green finance index, P C it is the per capita carbon emissions. Moreover, α 0 represents the baseline level of GDP when all other variables are zero. α 1 denotes the coefficient of the Green Finance Index, measuring how changes in green finance affect GDP. α 2 is the coefficient of per capita carbon emissions, indicating the impact of emissions on GDP. α 3 means the coefficient for the GDP of the previous time period, capturing the effect of past economic performance on current GDP.(2) Green FinanceGF I it = β 0 + β 1 GDP it + β 2 P C it + β 3 REG it + µ it(5)where REG it includes regulatory and policy variables influencing green finance activities in region i at time t, and µ it is the error term. β 0 represents the baseline level of the Green Finance Index when all other variables are zero. β 1 denotes the coefficient of GDP, assessing the influence of economic growth on green finance. β 2 is the coefficient of per capita carbon emissions, examining how emissions levels impact green finance. β 3 means the coefficient for regulatory and policy variables, showing how changes in policy and regulation affect green finance.(3) Carbon EmissionsP C it = γ 0 + γ 1 GDP it + γ 2 GF I it + γ 3 EC it + ξ it(6)where EC it denotes energy consumption metrics, and ξ it is the error term. γ 0 indicates the baseline level of emissions when all other variables are zero. γ 1 is the coefficient of GDP, indicating how economic growth impacts carbon emissions. γ 2 denotes the coefficient of the Green Finance Index, measuring the effect of green finance on carbon emissions. γ 3 denotes the coefficient of energy consumption, assessing the impact of energy use on emissions.These simultaneous equations approach is suitable for this analysis due to the bidirectional causality between the variables. For instance, while green finance can influence economic growth and carbon emissions, the level of economic development and the regulatory environment can also impact the volume and effectiveness of green finance initiatives. Additionally, as economic activities expand, they may lead to increased emissions unless mitigated by effective green finance policies.By employing this model, we can robustly capture the dynamics of green finance as both an outcome of certain economic conditions and a driver of environmental and economic changes. This allows us to delineate the contribution of green finance to achieving carbon peaks and adapting economic structures towards sustainability in a more granular and accurate manner. Green finance can promote economic development. There are several ways in which funds are channelled from high-energy, high-polluting industries into green energy-saving fields through green finance ?. This regulates energy use and is linked to economic growth but also impacts environmental adjustment. Economic growth influences green finance. Green finance will be positively influenced by financial development as finance itself expands. On the other hand, if economic growth worsens environmental pollution, green finance will also grow. The theoretical transmission mechanism combines ecological quality, green finance, and economic growth. In addition, we posit that digitalisation enhances these channels by lowering information costs and expanding financial inclusion. The Digital Finance Density (DFD) index therefore enters the model via an interaction term GF × DF D.By including energy consumption in the Cobb-Douglas function ? as a limiting and essential factor in capital and labor contributing to economic growth, the relationship function between environmental pollution and economic growth is constructed:GDP = A • K α • L β • E χ (7)Among them, A is the total factor productivity, K is the capital stock, L is the working population, E is the energy consumption, and α, β, χ are the elastic coefficients of the corresponding variables. Considering that green finance can affect the size of carbon-emission factors through environmental-protection technology progress, carbon emissions are correlated with energy consumption and green finance, E = GF I • P CCE.Substituting into (1) yieldsGDP = A • K α • L β • GF I χ • P CCE χ . (8)Then, we introduce foreign direct investment:GDP = a • P CF I • K α • L β • GF I χ • P CCE χ ,(9)where P CF I denotes foreign direct investment. Assuming constant returns to scale (α + β + χ = 1), dividing both sides by L and log-linearising gives the measurable formgdp it = ϕ 0 + ϕ 1 pcf i it + ϕ 2 k it + ϕ 3 gf i it + ϕ 4 pcce it +ϕ 5 (gf i it × df d it ) + ε it . (10)The EKC curve mainly explains the relationship between income and environmental quality through an inverted-U shape ?. As well as inverted-U relationships, EKC may take on N-type or inverted-N shapes.Green-finance variables are therefore included in the equation linking income and carbon emissions:ln pcce it = γ 1 + γ 2 gdp it + γ 3 gdp 2 it + γ 4 gdp 3 it + γ 5 gf i it +γ 6 (gf i it × df d it ) + ε it . (11)To capture regional heterogeneity we add three control variables: (i) Because green-industry loans are long-term and staged, early investment may spur later investment, implying endogeneity:gf i it = η 1 + η 2 gdp it + η 3 pcce it + η 4 gf i it-1 + ε it . (13)To probe the information-transparency mechanism (H4a), we introduce a fourth equation in which the dependent variable is the financing cost of green bonds (f in cost it ):f in cost it = δ 0 + δ 1 gf i it + δ 2 df d it + δ 3 (gf i it × df d it ) + δ 4 U R it + ν it . (14)Equations ( 4), ( 6), ( 7) and ( 11) are estimated simultaneously via three-stage least squares (3SLS) to address endogenous feedbacks among green finance, digitalisation and carbon outcomes, with robustness checks using system-GMM. To establish a comprehensive green-finance assessment system, this study expands beyond traditional green-credit and green-bond indicators. We construct a composite index GF Index consisting of three sub-dimensions, as shown in Table 2:• Banking Sub-index: outstanding stock of green credit, sustainability-linked loans, and carbonemission-right-pledged loans;• Capital-Market Sub-index: issuance volume of labelled green bonds, sustainability-linked/transition bonds, and green asset-backed securities;• FinTech & Insurance Sub-index: mobile-platform green loans, digital-inclusive green loans, and green-insurance premiums. Pre-2018 banking series from the former CBRC are back-cast using chain growth rates to ensure temporal consistency. To eliminate scale differences among indicators, the extreme-value method is applied in ( 15)-( 16) to rescale raw data to the interval (0, 1). Objective weights are then derived via the entropy method ( 18)-( 20).The resulting provincial composite score and the three sub-scores are later employed in §5.3 to test regional heterogeneity. In line with H4, we introduce a provincial-level Digital Finance Density (DFD) index (df d it )Zhou et al.from the PKU Digital Inclusive Finance Index. The indicator is normalised with the same procedure below and enters the interaction term GF × DF D in Section 4.3.To eliminate the impact of the difference in the order of magnitude between different indicator units, the extreme-value method is used in ( 15) and ( 16) to process the raw data. Since indicators differ in units and magnitudes, the extreme-value method rescales them to the interval 0-1. A weight coefficient between each index is then obtained using the entropy method, which avoids subjective weighting error.When B ita is a positive indicator,B * ita = B ita -min(B ita ) max(B ita ) -min(B ita ) ,(15)and when B ita is an inverse indicator,B * ita = max(B ita ) -B ita max(B ita ) -min(B ita ) .(16)Normalisation yieldsC ita = B * ita n i=1 T t=2005 B * ita .(17)Entropy of indicator a isD a = -ln(nT ) n i=1 T t=2005 C ita ln C ita ,(18)and its variance coefficientE a = 1 -D a .(19)Finally, the entropy weight isβ a = E a A a=1 E a . (20)Each province's overall green-finance score is computed as the weighted sum of the normalised indicators, with sub-scores retained for robustness tests. Using CO 2 = n i=1 E i • CEF i • N CV i(21)Energy fuels are represented by I, CEF by carbon dioxide emission factor, and NCV by low calorific value, i.e., heat generated by the unit of fuel energy. In each province, the Bureau of Statistics publishes how much energy fuel is converted into standard coal:CO 2 = E * • 29.27 • CEF *(22)where E * represents the amount of all energy converted into standard coal, CEF * stands for the CO2 emission factor of standard coal, considering that the calculation of 2018-2019 data should be maintained with the caliber of CEADS data before 2017, so CEF * calculation uses historical CEADS carbon emission data and the number of standard coal to calculate the standard coal carbon dioxide emission factor of each province. Before the empirical analysis of the model, it is necessary to judge the identifiability and stationarity of the above simultaneous equations, which have three endogenous variables (GDP, GFI, and PCCE)and four exogenous variables (PCFI, K, UR, and IAV). Equation ( 7) excludes two exogenous variables (PCFI and K), Equation ( 9) excludes UR and IAV, and Equation ( 10) retains all four. Each satisfies the simultaneous-equation identification rule:A -A i ≥ B i -1,(23)All the exogenous variables are represented by A, Ai represents all the exogenous variables, and Bi represents all the endogenous variables. ( 7) and ( 9) are just identified, while ( 10) is recognized overly when the left formula is greater than the right formula.A stationarity test of the unit root test data is performed after the identification test to ensure that the model does not result in pseudo-regression or pseudo-correlation phenomena. According to previous literature, the panel data is tested for stationariness using LLC and Fisher-ADF. The panel data is considered stationary only when both are significant at the 5% level. A unit root test result is shown in Table 3, and there is no unit root in the panel data if Fisher-ADF and LLC tests have P values less than 5%.Identification and estimation rely on four assumptions, i.e., linearity in parameters, valid external instruments, (one-period lags of the endogenous regressors and region-specific policy dummies), no perfect collinearity, and homoscedastic idiosyncratic disturbances. Instrument relevance is confirmed by first-stage F -statistics exceeding 24 for every endogenous regressor. Over-identifying restrictions are not rejected by the Hansen J-test (p > 0.10), supporting instrument validity. Different regions develop economically, environmentally, and financially at unequal paces; thus separate 3SLS regressions are run on 30 provincial units and on eastern, central, and western sub-samples (Table 4).Hansen J-tests (full sample p = 0.23) and Kleibergen-Paap rk-F statistics (F = 27.4) confirm instrument validity and strength.The financial development contributes to the reduction of carbon dioxide emissions over the long term.This aligns with the observations from Table 4, which demonstrate that carbon emissions significantly drive economic growth at a national level. However, while economic growth often leads to increased energy consumption and carbon emissions, green finance can mitigate these effects by directing investments towards low-carbon industries. Despite challenges like high capital requirements and lengthy return periods, green finance remains crucial for steering China's economy towards sustainable development.In terms of regional impacts, carbon emissions from the eastern and western regions significantly influence economic development. The effect is more pronounced in the eastern regions due to their advanced technological development and higher efficiency in energy combustion. In contrast, the central region experiences a slight inhibition in economic growth due to less efficient carbon emission management.This discrepancy highlights the varying levels of technological advancement and dependency on industrial development across regions. The western regions, with their lower energy combustion efficiency and reliance on outdated technologies, face urgent needs for transformation and technological innovation.Interestingly, green finance has a dual role; it inhibits economic development in the western regions while promoting it in the eastern and central regions. The impact of foreign direct investment (FDI) on promoting energy technology innovation is limited, particularly in the central region, where the focus on reducing carbon emissions is weak. Nevertheless, polluting and energy-intensive industries continue to drive eco-nomic growth, especially in areas with low green financial efficiency from FDI.The distribution of foreign funds and the dynamics of capital stocks further illustrate regional disparities.Foreign investments are more likely to flow into the eastern regions, which have transitioned from capital-intensive to technology-intensive industries. In contrast, the central region remains more reliant on traditional industrial development, characterized by higher capital intensity.A significant inhibitory effect of green finance on carbon emissions is shown in Table 5. However, the coefficient is small, the effect is weak, and efficiency still needs improvement. A parabolic plot between national economic development and carbon emissions shows both positive and negative coefficients for pcgdp1 and pcgdp2. In the case of poor economic development, carbon emissions increase gradually with the rise of per capita GDP and when the rise of per capita GDP exceeds a certain threshold. A carbon emissions peak as a whole can effectively reduce carbon emissions, so a carbon emissions peak can effectively reduce carbon emissions as a whole. Energy sources with high carbon emissions, such From the perspective of each region, green finance reduces carbon emissions significantly. Western and central regions have more significant effects, while eastern regions have more minor effects. The inverted U-shaped graph displays growth and carbon emissions in the east and west. In contrast, an inverted N-shaped graph shows growth and emissions in the center, at the apex of the three regions, carbon emissions peak. Urbanization significantly reduces carbon emissions in central and western regions. While the eastern region has a higher urbanization rate than the western region, the effect on carbon emissions is insignificant due to the slight change, probably be-cause most eastern regions have had over 70% urbanization since 2005-emissions in all three regions.From the perspective of the entire nation, as shown in Table 6, it is evident that increasing carbon emissions has a significant "backward" effect on green finance from the perspective of the whole country.As carbon emissions gradually rise, green environmental protection policies will also become more robust as green finance increases. The financial sector has become more active as a result of economic development.As analyzed above, economic development has accelerated the flow of funds. This indicates that green finance has characteristics of self-scale expansion, as the lagging phase of the green finance industry is associated with significant positive changes in green finance investment.Carbon emissions have a significant "backward force" effect that can be seen in the central and western regions but not in the eastern regions, where environmental protection technology is better, carbon emissions are nearing their peak, and green fi-nance is not being stimulated due to the lack of environmental protection technologies. Central and western areas of the country also benefit from economic development, while eastern regions do not appear to be affected. It is also important to note that the eastern region has solid environmental protection technologies, carbon emissions are nearing their peak, and economic development won't bring more capital to green fi-nance. The lagging phase significantly influences green finance investments in the three regions. For robustness and endogeneity checks, we re-estimate the system via two-step system-GMM (Blundell-Bond). Key coefficients-α 1 (GF→GDP) and γ 2 (GF→PCCE)-retain sign and remain significant at the 1% level. The Hansen test of over-identifying restrictions (p = 0.18) fails to reject instrument validity; Arellano-Bond AR(2) test shows no second-order serial correlation (p = 0.27). A Durbin-Wu-Hausman test rejects the exogeneity of GF at the 1% level, confirming the need for instrumental methods. The model in ( 9) estimates show that the EKC curves in each region show a particular parabolic shape, and according to the parabolic vertex theory, both the in-verted N-type and the inverted U-shape have vertices above the parabola. The coefficients of GDP, gdp2, and gdp3 in the estimated results can calculate the per capita GDP corresponding to the parabolic vertices by the optimal fit model. When the estimation model is inverted Ushaped, the estimation model is a quadratic equation, ac-cording to the parabolic nature of the quadratic function, when the carbon emissions reach the apex, GDP = -γ2/2γ3. When the estimation model is inverted N type, the estimation model is a cubic equation, according to the three-dimensional function of the parabolic nature. When carbon emissions reach the second peakgdp = -γ 3 - (γ 3 ) 2 -3 • γ 2 • γ 4 / (3 • γ 4 )(24)Through the above parabolic properties, it is possible to calculate the per capita GDP level corresponding to the carbon peak of the whole country and each region and then calculate the years required to reach the corresponding per capita GDP according to the trend so that the time required for the carbon peak of each region can be calculated. This is shown in the following Table 7.It is clear from Table 7 that there is a great deal of heterogeneity among regions in terms of economic development and carbon emissions and that there is also a great deal of variation in the timing of carbon peak. Under the existing level of green financial growth, the time for the country to achieve a carbon peak is 2031, slightly later than the 2030 carbon peak target required by the state; the eastern region will take the lead in achieving carbon peaking, corresponding to 2029, one year ahead of schedule to complete the carbon peak target, while the western region will achieve carbon peak in 2031, which is consistent with the national time. The central region will achieve a carbon peak at the latest, corresponding to 2036, as pointed out in the previous empirical analysis. The central region's industrial-based economic structure and backward environmental protection technology urgently need green financial support because carbon emissions have a slight inhibitory effect on economic development, even though the effect is not significant.Figure 2 presents the evolution of green finance, carbon emissions, and GDP from 2005 to 2030, illustrating significant trends that underscore the interplay between economic growth and environmental impact within China. This graph is crucial for establishing a foundational understanding of how these three In Figure 3, the boxplot categorizes the green finance indices by region, revealing the variability and median levels of financial engagement towards environmental sustainability across China. This visual comparison highlights which regions are leading in green finance and which are lagging, offering a critical regional perspective that complements the macro-level insights from the time series analysis. This figure is instrumental in identifying regional disparities, guiding policymakers where targeted interventions are needed most.Figure 4 explores the direct relationship between green finance and carbon emissions through a scatter plot enhanced with a regression line. This analysis is pivotal as it quantitatively assesses the impact of green financial initiatives on carbon output, providing empirical evidence to support the hypothesis that increased green financing correlates with reduced carbon emissions. The regression line serves to clarify the strength and direction of this relationship, emphasizing the potential of green finance as a lever for environmental change within economic frameworks.The heatmap in Figure 5 offers a detailed correlation matrix analyzing how green fi-nance, carbon emissions, and GDP interact across different regions. By showcasing the correlation coefficients, this figure provides insights into the dynamics at play between economic growth, environmental degradation, and the infusion of green capital. The heatmap is particularly useful for visualizing complex interdependencies and for sup-porting arguments regarding the need for integrated financial and environmental strategies that vary by region. To assess whether the impact of green finance differs across provinces and across sub-dimensions of green finance, we conduct two complementary exercises as follows. The coefficients indicate that the FinTech & Insurance channel yields the strongest marginal carbonreduction effect when combined with digitalisation (-0.024), followed by Banking, whereas the Capital-Market sub-index shows a weaker-statistically insignificant-interaction. This suggests that digitally delivered retail and SME products are critical for deep decarbonisation in less-developed regions. We group the 31 provinces into Eastern (11), Central (10), and Western (10) blocks and compute group means of the three sub-scores over 2019-2023. A simple difference-in-means test (not tabulated) confirms that the Eastern-Western gap is significant at the 1 % level for all three dimensions. These findings reinforce our policy recommendation to prioritise digital-infrastructure investment and inclusive green credit programmes in lagging Central and Western provinces. Overall, the heterogeneity analysis corroborates the main conclusion: digitalisation amplifies the carbonmitigation effect of green finance, but the strength of this amplification varies by product type and regional digital maturity. Let u t = (u 1t , . . . , u N t ) ′ denote the N -vector of structural residuals from the carbon-emission equation (Eq. ( 7)) in year t (t = 1, . . . , T ). Cross-section dependence (CSD) arises when Cov(u it , u jt ) = σ ij ̸ = 0 (i ̸ = j),