## 5 Empirical Results of Producer Services Agglomeration on Carbon Emission Reduction
### Analysis of Regional Heterogeneity  
Due to the obvious differences in the industrial structure, resource endowments, and economic foundations of different regions, the effect of the agglomeration of the producer service industry on carbon emissions may have regional heterogeneity [65]. The analysis is performed and the results are shown in Table 5.  
From the perspective of the difference between the east and the west, the effect of the agglomeration of producer service industry on carbon emissions is consistent with the results of the baseline regression, showing a significant negative effect. At the same time, this effect is more pronounced in the eastern region than in the central and western regions. The possible reason is that industrial manufacturing in the eastern region is more developed and carbon emissions are greater. The agglomeration of the producer service industry can reduce carbon emissions more significantly. From the perspective of the difference between the north and the south, the agglomeration of the producer service industry also shows the effect of carbon emission reduction, but it has not passed the significance test. It may be  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** \\ \hline  & **(OLS)** & **(SDM-IW)** & **(SDM-IW1)** & **(SDM-IW2)** & **(SDM-IW3)** \\ \hline lnser & \(-0.180\)**\({}^{**}\) & \(-0.248\)**\({}^{***}\) & \(-0.247\)**\({}^{***}\) & \(-0.190\)**\({}^{**}\) & \(-0.212\)**\({}^{***}\) \\  & (0.091) & (0.075) & (0.085) & (0.080) & (0.075) \\ _ecbz_ & \(0.432\)**\({}^{**}\) & \(0.757\)**\({}^{***}\) & \(0.483\) & \(0.539\)**\({}^{*}\) & \(0.501\)**\({}^{*}\) \\  & (0.184) & (0.263) & (0.308) & (0.280) & (0.289) \\ lnrkgm & \(1.472\)**\({}^{***}\) & \(2.742\)**\({}^{***}\) & \(1.930\)**\({}^{***}\) & \(1.975\)**\({}^{***}\) & \(1.365\)**\({}^{***}\) \\  & (0.378) & (0.398) & (0.357) & (0.400) & (0.337) \\ lnglmd & \(0.552\)**\({}^{***}\) & \(0.356\)**\({}^{***}\) & \(0.427\)**\({}^{***}\) & \(0.372\)**\({}^{***}\) & \(0.557\)**\({}^{***}\) \\  & (0.126) & (0.106) & (0.132) & (0.111) & (0.113) \\ lnrdry & \(-0.031\) & \(-0.047\)**\({}^{*}\) & \(-0.073\)**\({}^{**}\) & \(-0.043\) & \(-0.005\) \\  & (0.030) & (0.028) & (0.030) & (0.028) & (0.029) \\ lnpgdp & \(-0.006\) & \(-0.069\) & \(-0.140\) & \(-0.151\)**\({}^{*}\) & \(-0.109\) \\  & (0.054) & (0.086) & (0.090) & (0.084) & (0.093) \\ \hline W \(\times\) lnser & & \(-0.276\)**\({}^{**}\) & \(-1.122\)**\({}^{*}\) & \(-0.261\)**\({}^{**}\) & \(-0.294\)**\({}^{**}\) \\  & & (0.129) & (0.608) & (0.108) & (0.133) \\ W \(\times\) Y & & 0.258**\({}^{***}\) & \(-0.118\) & 0.227***\({}^{***}\) & \(0.307\)**\({}^{***}\) \\  & & (0.079) & (0.254) & (0.066) & (0.078) \\ \hline W \(\times\) X\({}^{\prime}\) & & Yes & Yes & Yes & Yes \\ _Ind-fixed effect_ & Yes & Yes & Yes & Yes & Yes \\ _Time-fixed effect_ & Yes & Yes & Yes & Yes & Yes \\ \hline \(N\) & 300 & 300 & 300 & 300 & 300 \\ r2\_a & 0.4148 & 0.5020 & 0.4710 & 0.4073 & 0.3212 \\ \hline \hline \end{tabular} Robust standard errors in parentheses. \({}^{*}p<0.1\), \({}^{**}p<0.05\), \({}^{***}p<0.01\). The following tables are the same.  
\end{table}
Table 4: The empirical results of the baseline model.  
that the difference between the north and the south is not enough to cause the difference in results, or it may be caused by sample selection. From both sides of the Heihe-Tengchong Line, the carbon emission reduction effect of the agglomeration of the producer service industry is more obvious on the southeast side than on the northwest side. This is mainly because the southeast side belongs to the economically developed area, and industrial production and manufacturing occupy a large proportion of the country. Increasing the level of agglomeration of the producer service industry will help to achieve carbon emission reduction in multiple ways [66].