# The Impact of Polycentric Structure on CO\({}_{2}\) Emissions: Evidence from China
## 3 Results
### Robustness Checks
#### 3.2.5 Psm  
One might argue that the CO\({}_{2}\) abatement was not achieved by polycentric spatial structure but by the selection bias between polycentric structure and monocentric structure. To mitigate such selection bias, we adopted propensity scores to match cities in the polycentric structure with those in the monocentric structure and make them comparable. The propensity score is estimated using a logit regression model. Columns (1)-(3) in Table 5 reported the results using nearest neighbor matching (1:4), caliper matching, and kernel matching, respectively. The results of balance tests were reported in Appendix A Table A Table A1 and Figure A1, Table A2 and Figure A2, and Table A3 and Figure A3, respectively. The results of balance tests demonstrated that after matching, there was no significant bias between cities with polycentric and monocentric structures, indicating that PSM helped mitigate selection bias. After matching, the impact of polycentric spatial structures on CO\({}_{2}\) emissions was still significantly negative, implying a positive role for polycentricity in CO\({}_{2}\) reduction.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** \\
**Variables** & **Carbon** & **Carbon** & **Rep.Carbon** & **PCE** & **Win.Carbon** \\ Q & \(-\)0.045 *** & \(-\)0.045 *** & \(-\)0.018 *** & \(-\)0.128 *** & \(-\)0.055 *** \\  & (\(-\)2.33) & (\(-\)2.42) & (\(-\)2.52) & (\(-\)2.67) & (\(-\)2.92) \\ LCC & \(-\)0.067 *** & & & & \\  & (\(-\)4.26) & & & & \\ ETS & & \(-\)0.119 *** & & & \\  & & (\(-\)5.83) & & & \\ Control & YES & YES & YES & YES & YES \\ City FE & YES & YES & YES & YES & YES \\ Year FE & YES & YES & YES & YES & YES \\ Observations & 4513 & 4513 & 4313 & 4513 & 4513 \\ R-squared & 0.948 & 0.949 & 0.850 & 0.915 & 0.941 \\ \hline \end{tabular} Notes: t-values are in parentheses; ***, and *** represent the 5%, and 1% significance levels, respectively; the coefficients of the control variables (i.e., the secondary industry as a percentage of GDP, foreign direct investment, population density, the percentage of budget fiscal expenditure and technology expenditure on GDP, and the ratio of the employed population), year and time dummies are not reported to save space.  
\end{table}
Table 4: Robustness check: the impact of polycentric spatial structures on CO\({}_{2}\) emissions.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **(1)** & **(2)** & **(3)** \\
**Variables** & **Carbon** & **Carbon** & **Carbon** \\ Q & \(-\)0.0558 *** & \(-\)0.0508 *** & \(-\)0.0508 *** \\  & (\(-\)3.15) & (\(-\)2.64) & (\(-\)2.64) \\ Control & YES & YES & YES \\ City FE & YES & YES & YES \\ Year FE & YES & YES & YES \\ Observations & 3771 & 4508 & 4508 \\ R-squared & 0.947 & 0.947 & 0.947 \\ \hline \end{tabular} Notes: t-values are in parentheses; *** represent the 1% significance levels, respectively; the percentage of budget fiscal expenditure and technology expenditure on GDP, and the ratio of the employed population are adopted to match cities in the polycentric structure with those in the monocentric structure; the coefficients of the control variables (i.e., the secondary industry as a percentage of GDP, foreign direct investment, population density, the percentage of budget fiscal expenditure and technology expenditure on GDP, and the ratio of the employed population), year and time dummies are not reported to save space.  
\end{table}
Table 5: Robustness check: the impact of polycentric spatial structures on CO\({}_{2}\) emissions using PSM.