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As a major carbon dioxide-emitting country, China set carbon trading market to reduce enterprise carbon emissions through the rational allocation of carbon quotas among different enterprises and regions. The market has also conducted a preliminary exploration for the country to achieve carbon dioxide emissions peak in 2030 and carbon neutrality in 2060 while actively addressing the challenges of global climate change. This study analysed the emission reduction effect of China's carbon trading pilot policy, especially the role of carbon quota and carbon trading price. The analysis used county-level panel data from 1997 to 2017, regarded the implementation of the carbon trading pilot policy as a quasi-natural experiment, and used the difference-in-differences method. The results showed that, first, the policy implementation not only reduced regional carbon emissions but also inhibited carbon dioxide emissions per capita, with long-term effects. Second, the carbon emission reduction effect brought by the carbon pilot policy showed significant heterogeneous results with the different degrees of regional carbon emissions and environmental supervision. The effect was greater in areas with higher carbon emission density and stronger legal supervision. Third, the difference in carbon quota allocations resulted in different emission reduction effects, among which the historical method had the strongest effect. The carbon quota price and number of enterprises participating carbon trading market were the key factors affecting carbon emission reduction. • This paper investigates the impact of carbon emission trading market on the carbon reduction. • China provides an excellent "Quasi-natural Experiment" for assessing the role of carbon emission trading market in environmental management. • It is found that policy implementation has significantly reduced various types of carbon emissions, and this reduction effect is long-term. • Stimulating the vitality of the carbon market and expanding the supply and demand of carbon quotas are the main ways to achieve carbon emission reduction. [ABSTRACT FROM AUTHOR]