# The Impact of Polycentric Structure on CO\({}_{2}\) Emissions: Evidence from China
## 2 Materials and Methods
### Methodology
The first stage of two-stage least squares (2 SLS) was as follows:  
\[Q_{i,t}=\beta_{0}+\beta_{1}Hllh_{i,t}+\beta_{2}Unemploy_{i,t}+\sum\tau_{\bar{ \tau}}*X_{\bar{\mu},t}+\mu_{i}+\varphi_{t}+\varepsilon_{i,t} \tag{3}\]  
where \(Hllh_{i,t}\) and \(Unemploy_{i,t}\) represent the ratio of river density to the exchange rate and the proportion of unemployment, respectively. The second stage of 2 SLS was as follows:  
\[Carbon_{i,t}=\delta_{0}+\delta_{1}\widehat{Q_{i,t}}+\sum\tau_{\bar{\tau}}*X_{ \bar{\mu},t}+\mu_{i}+\varphi_{t}+\varepsilon_{i,t} \tag{4}\]  
where \(\widehat{Q_{i,t}}\) is the first-stage predicted value for the polycentricity (i.e., \(Q_{i,t}\)). Previous studies have verified the mediating role of transportation, household carbon emissions, and industrial emissions in the relationship between polycentric structures and CO\({}_{2}\) emissions [6; 11]. We proposed two innovative pathways to examine how polycentric structures affect CO\({}_{2}\) emissions. We hypothesized that green technology and energy consumption might serve as potential mechanisms through which polycentric structures influence CO\({}_{2}\) emissions. To test these hypotheses, we measured green technology as the logarithm of the annual number of green patent applications plus one assessing its mediating effect on the relationship. For energy consumption, we used the logarithm of electricity consumption to evaluate its potential mediating role in the relationship between polycentricity and CO\({}_{2}\) emissions. With these variables in place, we constructed the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variables** & **Obs.** & **Mean** & **S.D.** & **Min** & **Max** \\ \hline Carbon & 5278 & 2.743 & 0.858 & 0.0881 & 5.441 \\ Q & 5269 & 0.924 & 0.540 & 0.252 & 5.498 \\ lngy & 5226 & 3.868 & 0.282 & 2.086 & 4.525 \\ lnFDI & 4672 & \(-\)6.201 & 1.386 & \(-\)15.250 & \(-\)1.816 \\ lnpeople & 5295 & \(-\)2.717 & 0.973 & \(-\)7.624 & 0.340 \\ lnfs & 5290 & \(-\)2.094 & 0.504 & \(-\)4.221 & 0.994 \\ lnsci & 5279 & 11.370 & 1.270 & 5.727 & 15.430 \\ lnurba & 5240 & \(-\)1.809 & 0.665 & \(-\)3.358 & 1.249 \\ Hllh & 5330 & 0.291 & 0.209 & 0.00577 & 2.278 \\ Unemploy & 5278 & 3.884 & 0.697 & \(-\)0.486 & 7.051 \\ LCC & 5330 & 0.139 & 0.346 & 0 & 1 \\ ETS & 5330 & 0.0356 & 0.185 & 0 & 1 \\ Rep.carbon & 5071 & 7.841 & 0.569 & 6.047 & 11.51 \\ PCE & 5275 & \(-\)3.104 & 0.765 & \(-\)5.931 & \(-\)0.270 \\ Win\_carbon & 5278 & 2.742 & 0.844 & 0.739 & 4.652 \\ Gti & 4968 & 3.225 & 1.683 & 0.693 & 8.897 \\ Energy & 2789 & 13.070 & 1.221 & 4.625 & 16.54 \\ Lngreencov & 5243 & 3.488 & 0.459 & \(-\)1.715 & 5.957 \\ Lnplg & 5125 & 8.820 & 1.510 & 1.386 & 13.809 \\ Lnws & 5330 & 0.735 & 0.266 & \(-\)0.302 & 1.582 \\ Lnhum & 5330 & 4.227 & 0.143 & 3.590 & 4.481 \\ Lntem & 5323 & 2.588 & 0.482 & \(-\)2.036 & 3.274 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of variables. following model to analyze the impact of polycentric structures on CO\({}_{2}\) emissions through these proposed pathways:  
\[M_{i,t}=\gamma_{0}+\gamma_{1}Q_{i,t}+\sum\tau_{j}*X_{j,j,t}+\mu_{i}+\varphi_{t}+ \varepsilon_{i,t} \tag{5}\]  
where \(M_{i,t}\) represents mediators (i.e., green technology and energy consumption).