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Encouraging enterprises to engage in green innovation is a potent strategy for reducing carbon emissions from production. As one of the largest carbon emitters, China has launched a series of policies to achieve carbon peaking and neutrality collectively referred to as China's dual carbon policy. However, existing research on the impact of China's dual carbon policy on green innovation by heavy-polluting enterprises is insufficient. To fill this gap, this study constructed a theoretical model to draw hypotheses about the impact of the dual carbon policy on enterprises' green innovation and verified this impact using a difference-in-differences model to conduct a quasi-natural experiment based on data from 2010 to 2022 from Chinese A-share-listed enterprises. The results indicate that the dual carbon policy had a significantly positive influence on green innovation in heavy-polluting enterprises. Moreover, environmental tax mediated this effect, while enterprises' total costs and subsidies positively moderated it. Additionally, the impact exhibited variations based on several key factors, including green patent type, carbon emissions, enterprise ownership structure, and Environmental, Social, and Governance ratings. This study supplements related research on the effects of environmental policy on green innovation and provides both theoretical and empirical support for adapting subsequent environmental policies. • This study explores the impact of China's dual carbon policies on green innovation by firms. • We create a theoretical model and validate it using data from listed Chinese firms. • The dual carbon policies significantly increase green innovation by firms. • This relationship is mediated by environmental tax and moderated by firm costs and subsidies. [ABSTRACT FROM AUTHOR]