## 2 Index System Construction, Research Methods and Data Sources
### \(\beta\) Convergence Test of the Coupling Coordination
#### 3.2.1 Spatial Correlation Test
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Variable** & **The Whole Nation** & **The Eastern Region** & **The Central Region** & **The Western Region** & **The Northeastern Region** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Absolute \(\beta\) \\ Convergence test \\ test \\ \end{tabular} } & D & \(-0.401\)*** & \(-0.461\)*** & \(-0.70\)*** & \(-0.39\)*** & \(-0.56\)*** \\  & W \(\times\) D & 0.11 & 0.060 & 0.57 ** & \(-0.05\) & \(-0.06\) \\  & \(p\) & 0.082 & \(-0.170\) & \(-0.23\) & 0.02 & \(0.15\)* \\  & \(v\) & 0.039 & 0.047 & 0.093 & 0.038 & \(0.063\) \\  & R\({}^{2}\) & 0.79 & 0.95 & 0.71 & 0.50 & 0.64 \\  & LogL & 833.71 & 311.58 & 202.73 & 287.97 & 316.73 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Conditional \(\beta\) \\ Convergence test \\ test \\ \end{tabular} } & D & \(-0.16\)*** & \(-0.26\)*** & \(-0.48\)*** & \(-0.27\)*** & \(-0.33\)*** \\  & \(d(\text{P}\text{C}\text{D})\) & \(0.01\)* & 0.03 & 0.05 & \(0.012\)* & \(0.015\) \\  & \(d(\text{T}\text{C}\text{D})\) & \(0.01\)* & 0.06 * & 0.04* & \(0.02\)* & \(0.01\)** \\  & \(Open\) & 0.05 & 0.08 * & 0.03 & \(-0.2\) & \(-0.1\) \\  & \(GE\) & \(0.001\)*** & 0.001 ** & 0.01 & 0.001 & 0.001 \\  & \(Fin\) & \(0.02\)** & 0.05 ** & 0.06 & 0.01 ** & 0.01 \\  & test & \(v\) & 0.013 & 0.026 & 0.050 & 0.024 & 0.031 \\  & Space lag & & & & & \\  & term of & & & & & \\  & control & & & & & \\  & variable & & & & & \\  & \(p\) & 0.14 & 0.03 & 0.38 & 0.25 & 0.14 \\  & R\({}^{2}\) & 0.43 & 0.47 & 0.59 & 0.2 & 0.37 \\  & LogL & 693.83 & 288.64 & 173.79 & 252.11 & 126.73 \\ \hline \hline \end{tabular} Note: ***, ***, * are Significant at 1%, 5% and 10% Levels Respectively.  
\end{table} 
Table 5: \(\beta\) Convergence Test of Coupling. different in different regions. (3) The openness significantly promotes the coupling coordination degree in the eastern region to convergence at a high level, and the impact on the western and northeast regions is negative. This indicates that openness helps improve the coupling coordination level in the eastern region, and there is a need to further expand the opening degree of other regions. (4) Lastly, finance significantly supports the coupling coordination degree of the whole country, The convergence speed of the coupling coordination degree of the whole country, the eastern region and the western region has accelerated by the financial development. Additionally, the impact coefficient on the central and northeast region is positive but insignificant. This infers that the utilization efficiency and reasonable allocation of the financial resources affect the level of coupling coordination. Thus, sufficient attention should be paid to the imbalance of excessive and low utilization of financial resources in the eastern region and the lack of financial resources in the western underdeveloped provinces. In addition to this, the local fiscal expenditure significantly enhances the coupling coordination degree to high intensity in eastern China. However, the proposed effect is positive but insignificant in the western, central, and northeast regions. This reflects that the local fiscal expenditure could partly improve the coupling coordination between the digital economy and industrial green high-quality development, owing to the possible crowding-out effect of local fiscal expenditure on private credit, which hinders the effective flow of capital elements across different regions and industries, thus impeding industrial green high-quality development.