## 3 Method and Data  
### PSM-DID Model  
The DID method has been widely used to evaluate the ultimate effect of the implementation of a public policy. The principle is based on the counterfactual framework that evaluates the variability of the observations in both cases with and without the policy. The principle is based on the counterfactual framework that constructs a treatment group with policy interventions and a control group without policy interventions. If the common trend hypothesis is satisfied, that is, there is no significant difference between the treatment group and the control group before the policy's implementation, then the change of the treatment group before and after the experimental period can be considered to be the effect of the policy's implementation (counterfactual results). By comparing the differences of the treatment group and control group, we can get the actual effect of the policy shock [35; 36; 37; 38]. By introducing the PSM model, a random allocation can be achieved by checking the systematic differences between the samples before and after matching, thus eliminating the endogeneity problems that may exist in the model and ensuring the effectiveness of the PSM-DID model [39]. In this study, the pilot projects of ETS in Beijing, Tianjin, Shanghai, Chongqing, Guangdong, Hubei, and Shenzhen are regarded as a natural experiment. The treatment group is the provinces and cities that implement the ETS pilot policy, while the control group is the other provinces and cities that have not implemented the policy (excluding Tibet, Hong Kong, Macao, and Taiwan). To fully reflect the true implementation effect of the policy and consider the actual operating period of the ETS in Chongqing and Hubei, 2014 is regarded as the starting year of the pilot programs. After introducing the empirical dummy variables, the model is formulated as follows:  
\[\mathrm{C_{it}}=\alpha_{0}+\alpha_{1}\mathrm{prov_{i}}\times\mathrm{peri_{t}}+ \alpha_{2}\mathrm{Control_{it}}+\eta_{i}+\gamma_{t}+\mu_{it} \tag{1}\]  
\[\mathrm{Y_{it}}=\beta_{0}+\beta_{1}\mathrm{prov_{i}}\times\mathrm{peri_{t}}+ \beta_{2}\mathrm{Control_{it}}+\eta_{i}+\gamma_{t}+\mu_{it} \tag{2}\]  
here, \"prov\" represents the province dummy variable, the province i belong to pilot projects is set to 1, and the others are set to 0. \"peri\" represents the time dummy variable, the pre-pilot period is 2005-2013, and the post-pilot period is 2014-2017, the year t represents post-pilot is 1, while represents pre-pilot is 0. The interaction term defined as \"Z = prov \(\times\) peri.\" Cit represents the CO2 emissions of province i in year t, which measures the emissions reduction effect of the ETS pilot. Yit represents the GDP of province i in year t, which measuring the economic effect of the ETS pilot. Control represents the control variables affecting the emissions reduction effect and economic effect. \(\eta\) is the provincial fixed effect, \(\gamma\) is the time fixed effect, and \(\mu\) is the time disturbance term. Based on Equations (1) and (2), we are interested in the coefficient of the interaction term Z, which indicates the difference between the pilot provinces and cities and non-pilot provinces and cities during the experimental period, excluding the difference of the pilot provinces and cities and non-pilot provinces and citiesoutside the experimental period, so as to correctly evaluate the carbon reduction pilot's emission reduction and economic effects.