Unveiling the nonlinear impact: Green finance, carbon emission intensity, and digital economy integration

• Green finance has a nonlinear effect on carbon emission intensity, it can effectively reduce carbon emission intensity in the early stage, but the effectiveness decreases until it fails or even produces adverse effects. • The digital economy can effectively regulate the role of green finance in reducing carbon emission intensity and delay the arrival of failure points. • Green finance affects carbon emission intensity by non-linearly influencing green innovation and the level of marketization. • Reducing carbon emission intensity requires the synergy of multiple factors. Amid the global push for sustainable development, reducing carbon emission intensity is essential. Green finance serves as a crucial instrument, yet its effects at different stages of development remain underexplored. Using panel data from 30 Chinese provinces (2011–2020), this study employs quadratic, moderation, and mediation models to examine the nonlinear effects of green finance on carbon emission intensity, the moderating role of the digital economy, and the mediating effects of green innovation and marketization. Results show that green finance significantly reduces carbon emission intensity in the early stages but loses effectiveness beyond a certain threshold. The digital economy mitigates this diminishing effect, helping reduce carbon emission intensity at critical points. Additionally, the mechanism test results indicate that GF exerts a nonlinear influence on green innovation and marketization, initially promoting them but with diminishing effects over time, and indirectly impacting carbon emission intensity. The study highlights the importance of accounting for diminishing effectiveness when formulating green finance policies. To ensure long-term impact across different development stages, it is vital to integrate complementary factors, such as the digital economy. Future research should focus on dynamically evaluating green finance policies and examining the role of other economic and market factors, aiming to optimize environmental and economic outcomes at various stages of development.