## 3 Method and Data
### DDD Model  
In the estimation of the above mentioned DID model, for the purpose of further analyzing the mechanism of the effects of the economic development differences and industrial development differences on the ETS pilot policy, this study introduces dummy variables for the economic development differences and industrial development differences to construct a DDD model as follows:  
\[\mathrm{C_{it}}=\alpha_{0}+\alpha_{1}\mathrm{prov_{i}}\times\mathrm{peri_{t}} \times\mathrm{if\_econ_{j}}+\alpha_{2}\mathrm{prov_{i}}\times\mathrm{peri_{t}} +\alpha_{3}\mathrm{prov_{i}}\times\mathrm{if\_econ_{j}} \tag{3}\]  
\[\mathrm{C_{it}}=\alpha_{0}+\alpha_{1}\mathrm{prov_{i}}\times\mathrm{peri_{t}} \times\mathrm{if\_indu_{j}}+\alpha_{2}\mathrm{prov_{i}}\times\mathrm{peri_{t}} +\alpha_{3}\mathrm{prov_{i}}\times\mathrm{if\_indu_{j}} \tag{4a}\] \[+\alpha_{4}\mathrm{peri_{t}}\times\mathrm{if\_indu_{j}}+\alpha_{5} \mathrm{controlu_{j}}+\eta_{1i}+\gamma_{t}+\mu_{it}\] \[\mathrm{C_{it}}=\alpha_{0}+\alpha_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_cons_{j}}+\alpha_{2}\mathrm{prov_{i}} \times\mathrm{peri_{t}}+\alpha_{3}\mathrm{prov_{i}}\times\mathrm{if\_cons_{j}}\] (4b) \[\mathrm{C_{it}}=\alpha_{0}+\alpha_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_serv_{j}}+\alpha_{2}\mathrm{prov_{i}} \times\mathrm{peri_{t}}+\alpha_{3}\mathrm{prov_{i}}\times\mathrm{if\_serv_{j}}\] (4c) \[+\alpha_{4}\mathrm{peri_{t}}\times\mathrm{if\_serv_{j}}+\alpha_{5} \mathrm{controlu_{j}}+\eta_{1i}+\gamma_{t}+\mu_{it}\] \[\mathrm{Y_{it}}=\beta_{0}+\beta_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_econ_{j}}+\beta_{2}\mathrm{prov_{i}}\times \mathrm{peri_{t}}+\beta_{3}\mathrm{prov_{i}}\times\mathrm{if\_econ_{j}}\] (5) \[\mathrm{+}\beta_{4}\mathrm{peri_{t}}\times\mathrm{if\_econ_{j}}+ \beta_{5}\mathrm{controlu_{t}}+\eta_{1i}+\gamma_{t}+\mu_{it}\] \[\mathrm{Y_{it}}=\beta_{0}+\beta_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_indu_{j}}+\beta_{2}\mathrm{prov_{i}}\times \mathrm{peri_{t}}+\beta_{3}\mathrm{prov_{i}}\times\mathrm{if\_indu_{j}}\] (6a) \[\mathrm{Y_{it}}=\beta_{0}+\beta_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_cons_{j}}+\beta_{2}\mathrm{prov_{i}}\times \mathrm{peri_{t}}+\beta_{3}\mathrm{prov_{i}}\times\mathrm{if\_cons_{j}}\] (6b) \[\mathrm{Y_{it}}=\beta_{0}+\beta_{1}\mathrm{prov_{i}}\times \mathrm{peri_{t}}\times\mathrm{if\_serv_{j}}+\beta_{2}\mathrm{prov_{i}}\times \mathrm{peri_{t}}+\beta_{3}\mathrm{prov_{i}}\times\mathrm{if\_serv_{i}}\] \[\mathrm{+}\beta_{4}\mathrm{peri_{t}}\times\mathrm{if\_serv_{j}}+ \beta_{5}\mathrm{controlu_{j}}+\eta_{1i}+\gamma_{t}+\mu_{it} \tag{6c}\]  
here, if_econ is the dummy variable of the economic development differences, and if_indu, if_cons, and if_serv are the dummy variables of the industrial, construction, and service development differences, respectively (classified according to the categories of the industries that are involved in carbon trading in the pilot provinces and cities, as shown in Appendix A). The economic growth level and industry development levels are characterized by per capita GDP, per capita industrial added value, per capita construction added value, and per capita service added value, respectively. If above indicators of the province j ranks at the top 50% of the China, corresponding dummy variables if_econ, if_indu, if_cons, and if_serv are set to 1, the other provinces are set to 0. The remaining variables are defined as in Equations (1) and (2). In the above equations, we are also concerned with the coefficient of the triple cross term. In this paper, the DDD model is based on the DID model and adds the dummy variables of economic development level difference and industrial development level difference, in order to further analyze whether the development level difference will affect the impact of ETS. Through the significance of the double cross term Z, we can initially determine whether the DID satisfies the common trend hypothesis and the necessity of DDD analysis.