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

TL;DR

This paper analyzes how green finance influences carbon emission intensity (CEI) across 30 Chinese provinces from 2000 to 2022, incorporating climate risk via the Climate Physical Risk Index (CPRI). Using Bayesian Additive Regression Trees (BART) with SHAP and PDP for interpretability, it uncovers a nonlinear inverted-U relationship between the Green Finance Index (GFI) and CEI, with a threshold around 0.3 after which green finance begins to meaningfully reduce emissions. The study finds regional heterogeneity—stronger emission reductions in the eastern regions and weaker effects in central/western provinces—and identifies a significant GFI×TEC interaction, where green finance dampens the marginal effect of energy consumption on CEI. Contrary to expectations, CPRI does not show a significant direct impact on CEI in this provincial, annual panel setting. The results underscore the need for region-specific green finance policies and suggest that advanced green financial systems can enhance energy efficiency and low-carbon transitions, particularly in energy-intensive contexts.

Abstract

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.

Figures (6)

• Figure 1: Test of normality of errors using QQ-plot and the Shapiro-Wilk test (left), residual plot to assess heteroskedasticity (right).
• Figure 2: The average inclusion proportions of explanatory variables in the tuned BART model, reflecting how frequently each variable appears in the model's decision paths. The y-axis represents the average inclusion proportions calculated over 100 model constructions. The segments atop the bars indicate the 95% confidence intervals.
• Figure 3: In the tuned BART model, this figure displays the top 10 variable pairs ranked by average interaction counts, based on 25 model constructions. The vertical axis represents the average number of interactions, and the segments atop the bars indicate 95% confidence intervals.
• Figure 4: PDP of GFI on CEI. The black line represents the average marginal effect of GFI on CEI when all other variables are held constant. The shaded gray area and blue lines indicate the 95% credible interval, reflecting model uncertainty. The narrowing of the credible interval suggests increasing model certainty. The x-axis shows GFI values, while the y-axis represents the average predicted CEI at each GFI level, conditional on other variables being fixed.
• Figure 5: SHAP PDP of GFI on CEI, color-coded by region (red for Eastern, purple for Central, yellow for Western). Each point represents an observation, with the x-axis showing the value of GFI and the y-axis showing the corresponding SHAP value, which reflects the marginal contribution of GFI to the model prediction of CEI. SHAP values represent the marginal contribution of a given feature (GFI) to the model's prediction of CEI. A positive SHAP value indicates that GFI increases predicted CEI (i.e., contributes positively), while a negative value suggests a suppressing effect (i.e., contributes negatively).