Impacts of two-way foreign direct investment on carbon emissions: from the perspective of environmental regulation

China's foreign direct investment is an important driving force for economic growth, which also aggravates carbon emissions. Based on China's provincial panel data from 2003 to 2018, this paper uses the panel-fixed effect model and panel threshold model to explore the impacts of two-way foreign direct investment on carbon emissions and analyze the threshold effects of different environmental regulations. The empirical results show that inward foreign direct investment (IFDI) has a significant inhibitory effect on carbon emissions, while outward foreign direct investment (OFDI) leads to the aggravation of carbon emissions. Considering regional heterogeneity, environmental regulation in high-carbon areas mainly affects local OFDI, and environmental regulation in low-carbon areas mainly inhibits carbon emissions by affecting IFDI. In addition, high-carbon regions can achieve the inhibition of OFDI on carbon emissions by strengthening command-and-control regulation and reducing the promotion of OFDI on carbon emissions by strengthening market incentive regulation and voluntary regulation. Meanwhile, excessive command-and-control regulation and market incentive regulation in low-carbon areas bring unexpected regulatory effects, but the inhibitory effect of IFDI on carbon emissions can be increased by strengthening voluntary regulation.