## 2 Index System Construction, Research Methods and Data Sources
### \(\beta\) Convergence Test of the Coupling Coordination  
#### 3.2.1 Spatial Correlation Test  
Stata12.0 software is used in this study to conduct the Moran's I test on the coupling coordination degree between the digital economy and industrial green high-quality development. The coupling coordination degree is significantly positive for the period ranging from 2008 to 2020, indicating that the neighboring regions affect the level of coupling coordination in a region (see Table 4). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Year** & **Moran’s I** & **z** & \(\mathbf{p}\) \\ \hline
2008 & 0.137 & 2.881 & 0.004 \\
2009 & 0.176 & 3.53 & 0 \\
2010 & 0.135 & 2.859 & 0.004 \\
2011 & 0.206 & 4.033 & 0 \\
2012 & 0.201 & 3.953 & 0 \\
2013 & 0.192 & 3.812 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Moran’s I Index of Coupling coordination. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & **Intra-Regional Differences** & \multicolumn{2}{c}{**Inter-Regional Differences**} & \multicolumn{2}{c}{**Hypervariable Density**} \\ \cline{2-5}  & **Value** & **Contribution Rate** & **Value** & **Contribution Rate** & **Value** & **Contribution Rate** \\ \hline
2008 & 0.0295 & 22.77\% & 0.0264 & 20.42\% & 0.0735 & 56.81\% \\
2009 & 0.0337 & 22.79\% & 0.0304 & 20.52\% & 0.0839 & 56.69\% \\
2010 & 0.0269 & 22.55\% & 0.0324 & 27.18\% & 0.0599  
(2) Convergence test of conditional \(\beta\): The Hausman test result \(p>0.05\), supports the null hypothesis of the random effect model. Therefore, this study performs the conditional \(\delta\) convergence test using a random effect. Table 4 contains the influence of conditional \(\beta\) convergence of economic development, finance, technological innovation, local fiscal expenditure, and openness. The estimated regression results are as follows: firstly, the coefficients of conditional \(\beta\) in the whole nation and the four regions are all significantly negative. This reflects that there exists a convergence trend of conditional \(\beta\) in these regions. The central region displays the fastest convergence speed, with a value of 0.05, while the western region demonstrates the slowest convergence speed. Furthermore, the speed of all regions is higher than that of the nation. The control variables in the central region have the most significant coordination benefits. that the central region has the most obvious coupling coordination effect of the control variables. Secondly, the factors of regions are not only quite different, but the influence degree of the \(\beta\) convergence process is also different. (1) Consequently, economic development exerts a positive impact on the coupling coordination between the digital economy and industrial green high-quality development. This means that economic development provides material support to improve coupling coordination. However, there is only significant convergence of the coupling coordination between the country and the western region. Therefore, it is essential to focus on supporting the economic development of the western region while adopting the digital economy as a driving force of development and exploring the turning point of industrial green and high-quality development. (2) Technological innovation shows a significant positive influence on the coupling coordination degree. In addition, it promotes the coupling coordination level to converge at a high intensity, but the steady-state values are different, thereby indicating that the technological innovation promotes the coupling coordination degree between the digital economy and industrial green high-quality development, but the impact degree is \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Year** & **Moran’s I** & **z** & \(p\) \\ \hline
2014 & 0.197 & 3.891 & 0 \\
2015 & 0.185 & 3.671 & 0 \\
2016 & 0.186 & 3.691 & 0 \\
2017 & 0.171 & 3.448 & 0.001 \\
2018 & 0.153 & 3.139 & 0.002 \\
2019 & 0.186 & 3.673 & 0 \\
2020 & 0.195 & 3.743 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._