Substantive response or strategic response? The induced green innovation effects of carbon prices

China has established carbon emission trading markets to mitigate increasingly severe environmental issues and promote carbon emission reduction. So far, several studies have examined the impact of establishing pilot carbon markets on green innovation by firms in pilot regions or the implications of being covered by a carbon market on firms' green innovation. In contrast, few studies have focused on the relationship between carbon prices and corporate green innovation. Accordingly, our study analyzes the impact of changes in carbon price on green innovation by firms. We use panel data from listed firms in key emission industries in seven pilot regions from 2015 to 2021. Our results indicate that (1) the increase in carbon prices has a significantly positive influence on the green innovation of sample firms, which mainly promotes their substantive green innovation. However, its impact on their strategic green innovation is not significant. (2) Rising carbon prices can affect corporate green innovation through signaling and cost-saving mechanisms, thus more strongly promoting green innovation of regulated firms and firms in regions with a carbon market having better liquidity. (3) Higher carbon prices can lead to green innovation by nonstate-owned firms, particularly in terms of substantive green innovation. (4) Firms with poor ability to pass on cost tend to be more active in enhancing total and substantive green innovation when faced with higher carbon prices. Finally, we propose policy suggestions based on these results. Our study confirms the positive role of increasing carbon prices and provides reference value for further improving carbon market design and promoting sustainable growth of firms.