## 5 Empirical Results of Producer Services Agglomeration on Carbon Emission Reduction
### Robustness and Endogeneity Test  
For the robustness tests, this paper adopts two methods to approach it. One is to replace the variables, and the other is to replace the model [67; 68]. The results are shown in Table 6.  
First, this paper calculated the carbon emissions of coal (cc), oil (oc), and natural gas (gc) separately, and incorporated them into the model for estimation. Columns (1)-(3) show that the agglomeration of the producer service industry has a significant effect on reducing carbon emissions from coal and natural gas, indicating that the above baseline estimation results have a certain degree of robustness. In addition, the estimated coefficients are \(-0.289\) and \(-0.576\), respectively, indicating that the agglomeration of the producer service industry has differences in the reduction of carbon emissions from different energy sources, and the effect on natural gas is more obvious. The possible reason for this conclusion is that natural gas is an environmentally friendly fuel, and the total amount of carbon dioxide \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** & **(6)** & **(7)** \\ \hline \multirow{2}{*}{Inser} & \(\mathbf{ln}cc\) & \(\mathbf{ln}cc\) & \(\mathbf{ln}cc\) & **(SEM-IW)** & **(SEM-IW2)** & **(SEM-IW3)** \\ \hline \multirow{2}{*}{Inser} & \(-0.289\)\({}^{*}\) & \(-0.180\) & \(-0.576\)\({}^{***}\) & \(-0.170\)\({}^{**}\) & \(-0.237\)\({}^{***}\) & \(-0.178\)\({}^{**}\) & \(-0.151\)\({}^{**}\) \\  & (0.153) & (0.117) & (0.196) & (0.076) & (0.082) & (0.082) & (0.077) \\ \hline \multirow{2}{*}{\(X^{\prime}\)} & Yes & Yes & Yes & Yes & Yes & Yes & Yes \\  & Yes & Yes & Yes & Yes & Yes & Yes & Yes \\ \(W\times Y\) & Yes & Yes & Yes & Yes & Yes & Yes & Yes \\ \hline \multirow{2}{*}{\(W\)} & 300 & 300 & 300 & 300 & 300 & 300 & 300 \\  & r2\_a & 0.3211 & 0.4275 & 0.3301 & 0.4590 & 0.4153 & 0.4296 & 0.4177 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The empirical results of the robust test of the effects. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** \\ \hline \multirow{2}{*}{\(W\times X^{\prime}\)} & \(\mathbf{ln}cc\) & \(\mathbf{ln}cc\) & \(\mathbf{ln}cc\) \\  & & (0.114) & & \\ \multirow{2}{*}{\(W\times X^{\prime}\)} & & \(-0.157\) & & \\  & & (0.111) & & \\ \multirow{2}{*}{\(W\times Y\)} & & & & \(-0.293\)\({}^{***}\) \\  & & & & (0.082) \\ \multirow{2}{*}{\(W\times Y\)} & & 0.252 \({}^{***}\) & 0.224 \({}^{***}\) & 0.274 \({}^{***}\) \\  & & (0.080) & (0.081) & (0.078) \\ \hline \multirow{2}{*}{\(X^{\prime}\)} & Yes & Yes & Yes \\  & Yes & Yes & Yes \\ \multirow{2}{*}{\(W\times X^{\prime}\)} & Yes & Yes & Yes \\ \multirow{2}{*}{\(Ind\)-fixed effect} & Yes & Yes & Yes \\  & & & & Yes \\ \multirow{2}{*}{\(Time\)-fixed effect} & Yes & Yes & Yes \\ \multirow{2}{*}{\(N\)} & 300 & 300 & 300 \\  & r2\_a & 0.4986 & 0.5076 & 0.5009 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The empirical results of regional heterogeneity. released by the combustion of coal and oil far exceeds that of natural gas. With the same standard amount of energy, natural gas has the least carbon emissions. In addition, the agglomeration of the producer service industry also has a negative impact on oil carbon emissions, but it has not yet passed the significance test. Then, according to the model selection and test results, compared with the spatial lag model, the spatial error model also shows good adaptability to this research. Therefore, the spatial error model is used to re-regress. Columns (4)-(6) show that under different spatial weight matrices, the spatial error model can still get basically the same conclusions, confirming the robustness of the results. This paper deals with the possible endogenous problems caused by missing variables and measurement errors, etc., by lagging the core explanatory variables and control variables.