Green Finance and Carbon Emissions: A Nonlinear and Interaction Analysis Using Bayesian Additive Regression Trees

As a core policy tool for China in addressing climate risks, green finance plays a strategically important role in shaping carbon mitigation outcomes. This study investigates the nonlinear and interaction effects of green finance on carbon emission intensity (CEI) using Chinese provincial panel data from 2000 to 2022. The Climate Physical Risk Index (CPRI) is incorporated into the analytical framework to assess its potential role in shaping carbon outcomes. We employ Bayesian Additive Regression Trees (BART) to capture complex nonlinear relationships and interaction pathways, and use SHapley Additive exPlanations values to enhance model interpretability. Results show that the Green Finance Index (GFI) has a statistically significant inverted U-shaped effect on CEI, with notable regional heterogeneity. Contrary to expectations, CPRI does not show a significant impact on carbon emissions. Further analysis reveals that in high energy consumption scenarios, stronger green finance development contributes to lower CEI. These findings highlight the potential of green finance as an effective instrument for carbon intensity reduction, especially in energy-intensive contexts, and underscore the importance of accounting for nonlinear effects and regional disparities when designing and implementing green financial policies.

💡 Research Summary

This paper investigates how green finance influences carbon emission intensity (CEI) across Chinese provinces by employing Bayesian Additive Regression Trees (BART) and SHapley Additive exPlanations (SHAP) to capture and interpret complex nonlinearities and high‑order interactions. Using a balanced panel of 30 provinces from 2000 to 2022, the authors construct a composite Green Finance Index (GFI) from seven sub‑indicators (green bonds, funds, credit, insurance, equity, support, and investment) weighted by the entropy method. The dependent variable is the logarithm of CO₂ emissions per unit of GDP, i.e., CEI. Additional covariates include total energy consumption (TEC), a Climate Physical Risk Index (CPRI) built from extreme temperature, rainfall, and drought metrics, and a suite of socioeconomic controls (GDP, industrial structure, R&D intensity, urbanization, population density, FDI, government intervention, environmental regulation). Variables with high skewness are log‑transformed, and multicollinearity is checked via GVIF/aGSIF.

Methodologically, the study first fits a BART model, which assembles many shallow regression trees under a Bayesian prior, allowing flexible function approximation while quantifying posterior uncertainty. Five‑fold cross‑validation demonstrates superior predictive performance relative to traditional fixed‑effects linear regressions. In the second stage, SHAP values are computed to decompose each prediction into additive contributions from every predictor, facilitating both global importance ranking and local effect visualization.

Key empirical findings are: (1) GFI exhibits an inverted‑U (concave) relationship with CEI. At low levels of green finance, CEI rises—likely reflecting administrative and coordination costs—whereas beyond a certain threshold, further green finance reduces CEI, indicating that mature green‑finance ecosystems generate efficiency gains and technology diffusion. (2) This relationship is heterogeneous across regions. The western provinces show the strongest negative slope after the turning point, while the eastern provinces display a flatter curve, suggesting that institutional capacity and industrial composition modulate the effectiveness of green finance. (3) CPRI does not have a statistically significant direct effect on CEI; SHAP contributions are near zero, implying that physical climate risk, as measured, does not directly drive provincial carbon intensity during the sample period, perhaps acting through intermediate channels not captured in the model. (4) Interaction analysis reveals that in high‑energy‑consumption scenarios, the marginal effect of GFI on CEI becomes more negative, highlighting that green finance is especially potent in energy‑intensive contexts.

The authors interpret these results as evidence that green finance is not a uniformly linear policy lever; its impact depends on scale, regional characteristics, and the energy intensity of the local economy. They argue that policymakers should (i) support the scaling up of green‑finance instruments beyond the initial development phase to surpass the identified turning point, (ii) tailor green‑finance incentives to regions with high energy consumption or lower institutional readiness, and (iii) consider separate mechanisms for climate‑risk mitigation, as direct risk exposure appears to have limited explanatory power for carbon intensity.

Methodologically, the paper contributes by (a) demonstrating the feasibility of BART for environmental‑policy analysis, (b) integrating SHAP to overcome the “black‑box” criticism of machine‑learning models, and (c) providing a systematic framework that jointly assesses nonlinear main effects and interaction pathways. Limitations include the exclusion of Taiwan, Hong Kong, Macau, and Tibet due to data gaps, and the reliance on aggregate provincial indices that may mask intra‑provincial heterogeneity. Future research directions suggested are: incorporating spatial econometric structures to capture spillovers, using higher‑frequency climate‑risk metrics, and extending the approach to other emerging economies.

In sum, the study offers robust empirical evidence that green finance can substantially reduce carbon emission intensity when sufficiently developed, especially in energy‑intensive provinces, while also underscoring the need for region‑specific policy design and the value of advanced machine‑learning tools for nuanced environmental analysis.