## 3 Data and Method
### Research Method
#### 3.2.1 Three-Stage DEA Model  
The three-stage DEA model has three stages, as its name suggests. The environmental conditions of the samples are different, and the management level and technology are also different, which will lead to the deviation of the results. It is believed that the main environmental factors are energy efficiency, dependence on foreign trade, industrial structure and government intervention. Compared with the traditional DEA, the three-stage DEA model can effectively remove the influence of environmental variables and random errors, making the measurement results more accurate and objective [57]. The first stage: the slacks-based measure (SBM)-DEA model is as follows:  
\[ \begin{split}\rho=\min\frac{{}^{1-\frac{1}{\mathrm{N}}\sum\
olimits _{\mathrm{n}=1}^{\mathrm{N}}\frac{\mathrm{S}_{\mathrm{n}}^{\mathrm{S}}}{ \mathrm{N}+1}\frac{\mathrm{S}_{\mathrm{n}}^{\mathrm{S}}}{\mathrm{N}}}}{{}^{1+ \frac{1}{\mathrm{M}+1}\left(\sum\
olimits_{\mathrm{n}=1}^{\mathrm{M}}\frac{ \mathrm{S}_{\mathrm{n}}^{\mathrm{y}}}{\mathrm{N}+1}\right)\sum\
olimits_{ \mathrm{i}=1}^{\mathrm{L}}\frac{\mathrm{S}_{\mathrm{i}}^{\mathrm{b}}}{\mathrm{S }_{\mathrm{i}}^{\mathrm{b}}}}}\\ \mathrm{s.t.}\sum\limits_{\mathrm{k=1},\mathrm{k},\
eq\mathrm{j}}^ {\mathrm{k}}z_{\mathrm{k}}^{\mathrm{t}}x_{\mathrm{kn}}^{\mathrm{t}}+S_{\mathrm{ n}}^{\mathrm{x}}=x_{\mathrm{kn}^{\prime}}^{\mathrm{t}},\mathrm{n}=1\dots\dots\mathrm{N}\\ \sum\limits_{\mathrm{k=1},\mathrm{k},\
eq\mathrm{j}}^{\mathrm{k}} x_{\mathrm{kn}}^{\mathrm{t}}-S_{\mathrm{m}}^{\mathrm{y}}=y_{\mathrm{km}}^{ \mathrm{t}},\mathrm{m}=1\dots\dots\mathrm{M}\\ \sum\limits_{\mathrm{k=1},\
eq\mathrm{j}}^{\mathrm{k}}z_{\mathrm{ k}}^{\mathrm{t}}b_{\mathrm{ki}}^{\mathrm{t}}+S_{\mathrm{i}}^{\mathrm{b}}=b_{\mathrm{ ki}}^{\mathrm{t}},\mathrm{i}=1\dots\dots\mathrm{I}\\ z_{\mathrm{k}}^{\mathrm{t}}\geq 0,S_{\mathrm{n}}^{\mathrm{x}}\geq 0,S_{ \mathrm{m}}^{\mathrm{y}}\geq 0,S_{\mathrm{i}}^{\mathrm{y}}\geq 0,k=1\dots\dots\mathrm{K} \end{split}  \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline
**Target Layer** & **Criterion Layer** & **Index Layer** \\ \hline \multirow{6}{*}{Economic development} & \multicolumn{3}{c}{GDP per capita} \\  & \multicolumn{3}{c}{The per capita disposable income of urban residents} \\  & \multicolumn{3}{c}{Esconomic scale} \\  & \multicolumn{3}{c}{The per capita disposable income of rural residents} \\  & \multicolumn{3}{c}{The per capita investment in fixed assets} \\  & \multicolumn{3}{c}{The per capita retail sales of consumer goods} \\ \hline \multirow{6}{*}{Economic development} & \multicolumn{3}{c}{Engel coefficients of urban residents} \\  & \multicolumn{3}{c}{The added value of the tertiary industry as a proportion of GDP} \\  & \multicolumn{3}{c}{Fiscal expenditure per capita} \\ \hline \multirow{6}{*}{Environment protection} & \multicolumn{3}{c}{The amount of wastewater discharge} \\  & \multicolumn{3}{c}{The amount of exhaust emissions} \\  & \multicolumn{3}{c}{The average temperature} \\  & \multicolumn{3}{c}{The amount of solid waste discharge} \\ \cline{2-3}  & \multicolumn{3}{c}{Wastewater discharge compliance rate} \\  & \multicolumn{3}{c}{Comprehensive utilization rate of solid waste} \\  & \multicolumn{3}{c}{Exhaust emission compliance rate} \\  & \multicolumn{3}{c}{Environmental management} & \multicolumn{3}{c}{Environmental protection investment as a proportion of GDP} \\  & \multicolumn{3}{c}{Vegetation coverage} \\ \hline \multirow{6}{*}{Carbon emissions} & \multicolumn{3}{c}{Carbon emissions per capita} \\  & \multicolumn{3}{c}{Current status of carbon emissions} \\ \cline{1-1}  & \multicolumn{3}{c}{Carbon emission density} \\ \cline{1-1}  & \multicolumn{3}{c}{Carbon emission efficiency} \\ \cline{1-1}  & \multicolumn{3}{c}{Carbon emission efficiency} \\ \cline{1-1}  & \multicolumn{3}{c}{Pure technical efficiency} \\ \cline{1-1}  & \multicolumn{3}{c}{Scale efficiency} \\ \hline \end{tabular}
\end{table} 
Table 2: The assessment index system of the coordination degree in regard to carbon emissions, economic development, and environmental protection.