# The Impact of Polycentric Structure on CO\({}_{2}\) Emissions: Evidence from China
## 2 Materials and Methods
### Methodology  
Accounting for unit-variant and time-variant variables, we adopted a two-way fixed effects model to control for both unit- and time-fixed effects. We constructed the following model:  
\[Carbon_{i,t}=\alpha_{0}+\ \alpha_{1}Q_{i,t}+\sum\tau_{j}*X_{j,t}+\mu_{i}+\varphi_{t}+ \varepsilon_{i,t} \tag{2}\]  
where the subscript \(i\) represents different cities, \(t\) represents time variables, \(Carbon_{i,t}\) represents the natural logarithm of regional CO\({}_{2}\) emissions, \(Q_{i,t}\) represents the polycentricity of \(i\), \(X_{j,t}\) is the matrix-vector of the control variables, \(\mu_{i}\) represents a city-specific effect to control for unobserved heterogeneity, \(\varphi_{t}\) represents the control for the year-fixed effect, and \(\varepsilon_{i,t}\) is the stochastic disturbance term. To mitigate concerns about endogeneity and figure out the causality between polycentric spatial structures and CO\({}_{2}\) emissions, we constructed two IVs that were correlated with polycentric spatial structures but met the exogeneity condition of CO\({}_{2}\). Specifically, we followed [PERSON] et al. (2010) and used the river density/exchange rate (i.e., Hlhl) as the first instrument for polycentricity (2010). Proximity to water sources could affect the spatial structure of cities ([PERSON] et al., 2011). In the meantime, it is not related to CO\({}_{2}\) emissions. Thus, river density is a proper IV for polycentricity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Definition** \\ \hline Dependent variable & \\ Carbon & The logarithm of regional CO\({}_{2}\) emissions. \\ \hline Independent variables & \\ Q & The Pareto exponent. \\ \hline Mediating variable & \\ Gti & The logarithm of the annual number of green patent \\  & applications plus one. \\ Energy & The logarithm of electricity consumption. \\ \hline Control variables & \\ lngy & The share of the secondary sector in GDP. \\ lnFDI & The logarithm of the ratio of the region’s actual use of \\  & foreign capital to GDP in that year. \\ Inpeople & The logarithm of the ratio of the total population to the \\  & local land area at the end of the year. \\ lnfis & The logarithm of the ratio of regional general budget \\  & fiscal expenditure to GDP. \\ lnsci & The logarithm of the ratio of regional science and \\  & technology expenditure to GDP. \\ lnurba & The logarithm of the ratio of the urban employed \\  & population to the year-end household population. \\ Other variables & \\ Hlhl & The ratio of the river density to the exchange rate. \\ Unemploy & The ratio of unemployment to the population. \\ LCC & If it is the pilot city of Low-carbon city policy, this \\  & variable = 1, 0 otherwise. \\ ETS & If it is the pilot city of the emissions trading scheme, this \\  & variable = 1, 0 otherwise. \\ Rep\_carbon & The CO\({}_{2}\) emissions proposed by [PERSON] et al. (2017) \\ PCE & CO\({}_{2}\) emissions per capita. \\ Lngrecnov & The logarithm of canopy coverage. \\  & The logarithm of household consumption of liquefied \\  & petroleum gas. \\ Lnps & The logarithm of average wind speed. \\ Lnhum & The logarithm of average relative humidity. \\  & Lntem & The logarithm of average temperature. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions and operations of variables. We then proposed an innovative instrument, namely, the proportion of unemployment (i.e., unemployment as a percentage of the population). It has been proven that there are interdependencies between labor market behavior and the spatial structure of cities [19]. A large proportion of unemployed people indicates that the city has developed excessively or poorly, which leads to a lack of impetus for further expansion of the city, which has a negative impact on polycentricity. Meanwhile, the proportion of unemployment cannot affect CO\({}_{2}\). Finally, the ratio of river density to exchange rate and the proportion of unemployment were IVs for polycentric spatial structure.