## 4 Empirical Analysis
### Analysis of Co-Integration  
In this research, only indicators that are stationary at the first difference level (I(1)) were selected for the co-integration test based on [PERSON] theory. Under the established hypothesis, if the analysis results in a rejection, this indicates that there is  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Tau Test** & & & **MacKinnon Critical Value** \\ \hline
**Variables** & **Level I(0) Value** & **Variables** & **First Difference I(1) Value** & **1\%** & **5\%** & **10\%** \\ \hline \(\ln(Y)\) & \(-3.01\) & \(\Delta\ln(Y)\) & \(-4.73\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Itr)\) & \(-3.11\) & \(\Delta\ln(Itr)\) & \(-5.01\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(In)\) & \(-3.55\) & \(\Delta\ln(In)\) & \(-6.40\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(E-M)\) & \(-3.00\) & \(\Delta\ln(E-M)\) & \(-4.55\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(If)\) & \(-2.75\) & \(\Delta\ln(If)\) & \(-4.59\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Ft)\) & \(-2.39\) & \(\Delta\ln(Ft)\) & \(-4.60\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Ge)\) & \(-2.55\) & \(\Delta\ln(Ge)\) & \(-4.35\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Es)\) & \(-3.05\) & \(\Delta\ln(Es)\) & \(-4.77\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Hr)\) & \(-3.77\) & \(\Delta\ln(Hr)\) & \(-4.79\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Se)\) & \(-3.01\) & \(\Delta\ln(Se)\) & \(-4.66\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Sc)\) & \(-2.50\) & \(\Delta\ln(Sc)\) & \(-4.79\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Ee)\) & \(-3.15\) & \(\Delta\ln(Ee)\) & \(-5.05\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(EI)\) & \(-3.05\) & \(\Delta\ln(EI)\) & \(-5.11\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(Eg)\) & \(-3.79\) & \(\Delta\ln(Eg)\) & \(-5.73\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \(\ln(CO_{2})\) & \(-3.55\) & \(\Delta\ln(CO_{2})\) & \(-5.09\) *** & \(-3.85\) & \(-3.15\) & \(-2.70\) \\ \hline \end{tabular} Note: *** denotes a significance, \(\alpha=0.01\), \(\Delta\) is the first difference, and \(\ln\) is the natural logarithm.  
\end{table}
Table 1: Unit Root Test at Level I(0) and First Difference I (1).  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Variables** & **Hypothesized No of CE(S)** & **Trace Statistic Test** & **Max-Eigen Statistic Test** &
\begin{tabular}{c} **MacKinnon Critical Value** \\ \hline \(\Delta\ln(Y)\), \(\Delta\ln(Utr)\), & & & **1\%** & **5\%** \\ \(\Delta\ln(In)\), & & & & & \\ \(\Delta\ln(E-M)\), & & None *** & 255.01 *** & 201.05 *** & 15.05 & 10.25 \\ \(\Delta\ln(If)\), \(\Delta\ln(Ft)\), & & & & & \\ \(\Delta\ln(Ge)\), \(\Delta\ln(Es)\), & & & & & \\ \(\Delta\ln(Hr)\), \(\Delta\ln(Se)\), & & & & & \\ \(\Delta\ln(Sc)\), \(\Delta\ln(Ee)\), & & At Most 1 *** & 85.00 *** & 81.01 *** & 11.25 & 7.45 \\ \(\Delta\ln(Ei)\), \(\Delta\ln(Eg)\), & & & & & \\ \(\Delta\ln(CO_{2})\) & & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: Co-integration test by [PERSON] and [PERSON].  
statistical significance, which makes it suitable for further application. The results of the analysis are presented in Table 2.  
From Table 2, it was found that all indicator variables exhibit co-integration. At the None point, the trace test value was 255.01, and the Max-Eigen Statistic Test value was 201.05, both of which are higher than the MacKinnon critical values, indicating statistical significance at the level of \(\alpha\) = 0.01. At Most 1, the trace test value was 85.00, and the Max-Eigen Statistic Test value was 81.01, both of which are higher than the MacKinnon critical values, indicating statistical significance at the level of \(\alpha\) = 0.01. The results of the analysis show that all the indicators tested for co-integration have long-term relationships. Based on these properties, it is appropriate to use them to construct the SEM-VAL model to analyze the long-term magnitude of influence.