## 4 Empirical Results
### Heterogeneity Impact on Policy Effect
#### 4.5.2 Industrial Development Differences  
By introducing the dummy variables of the industrial development differences, we study whether there is heterogeneity in the policy effect of the ETS pilot project in provinces with different industries. These industries are divided into industry, service and construction according to the seven ETS pilots (see Appendix A for the details). According to Equations (4a-4c), as shown in Table 8, the DID and DDD interaction term coefficients of models m1, m3, and m5 without the control variables are not significant. The interaction coefficients of models m2, m4, and m6 with the control variables are significant, and the R-squared significantly increases to 95%. Due to the length limitations of this paper, in the following, we mainly focus on the results of models m2, m4, and m6. From a statistical perspective, the coefficients of the control variables for these three models are significant with better statistical significance. The economic significance analysis is as follows. (1) The Z value and the DID interaction coefficients of models m2, m4, and m6 all pass the t-test at the 10% level or better, thus indicating that there may exist time trend differences between the control group and the treatment group. Therefore, the DDD estimation provides more robust results than the DID estimation. (2) The coefficients of Z*if_ are 0.058, -0.488, and 0.081, respectively, which indicate that the policy has a weaker inhibitory effect on the carbon emissions of provinces with higher levels of industrial and construction development compared with the provinces with lower levels of industrial and construction development. Furthermore, the policy has a stronger inhibitory effect on the carbon emissions in the provinces with higher levels of service development compared with the provinces with lower levels of service development. (3) From the perspective of the mechanism's effect, the population size, emissions intensity, and per capita GDP factors have major positive effects on carbon emissions; the environmental pollution control intensity, research structure, and research intensity have negative effects on carbon emissions (the urbanization rate, industrialization, and proportion of coal consumption proportion have positive economic effects). \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Inc**} & \multicolumn{2}{c}{**Ingdp**} \\ \cline{2-5}  & **m1** & **m2** & **m3** & **m4** \\ \hline Z*if\_econ & \(-0.209\) (\(-0.71\)) & \(-0.370\)***(\(-3.96\)) & \(0.001\) (\(0.59\)) & \(0.007\) (\(0.87\)) \\ Z & \(-0.044\) (\(-0.20\)) & \(0.089\)* (\(1.85\)) & \(0.013\) (\(1.03\)) & \(-0.052\)* (\(-1.77\)) \\ lnp & & \(2.248\)*** (\(4.37\)) & & \\ us & & \(0.010\)*** (\(4.41\)) & & \\ a & & \(0.176\)*** (\(10.55\)) & & \\ is & & \(0.012\)*** (\(7.77\)) & & \\ ci & & \(0.167\)*** (\(9.90\)) & & \\ energs & & \(0.008\)*** (\(8.01\)) & & \\ environs & & \(-0.053\)**(\(-2.34\)) & & \\ rs & & \(-0.048\)(\(-0.78\)) & & \\ ri & & \(-0.032\)*(\(-1.84\)) & & \\ lnk & & & \(0.565\)*** (\(23.03\)) \\ lnl & & & & \(0.523\)*** (\(30.57\)) \\ lne & & & & \(-0.023\)(\(-1.53\)) \\ control & no & yes & no & yes \\ province & yes & yes & yes & yes \\ time & yes & yes & yes & yes \\ R-square & 0.520 & 0.957 & 0.568 & 0.981 \\ \hline  & & & \\ \multicolumn{4}{c}{\({}^{*}p<0.05\), **\(p<0.01\), ***\(p<0.001\).} \\ \end{tabular}
\end{table} 
Table 7: Policy effect of economic development differences. From Table 9 (Equations (6a)-(6c)), we can see that although the coefficients of Ink, Inl, and Ine are significant, the interaction coefficients in the DDD estimation of Z*if_ are not significant, showing that the level of industrial development has no significant impact on the economic effect of the policy.