## 4 Empirical Analysis
### Results Analysis and Discussion
#### 4.2.3 Convergence Analysis  
(1) The absolute \(\beta\)-convergence model selection and result analysis  
The aforementioned [PERSON]'s I index test demonstrated that there exist clear spatial correlation characteristics in China's _ITE_. It is now necessary to consider whether an econometric model combining spatial effects can reveal the convergence characteristics of China's regional _ITE_. Since the space panel model is divided into a fixed effect space panel model and a random effect space panel model, the first test was to determine which type of space panel model should be built in a general study. The results of the Hausman test are generally used to determine whether to use a fixed effect model, to estimate a random effect first, and to test whether to reject the original hypothesis. Then, if a fixed-effect model is decided upon, the time, space or dual fixed effects model need to be established using the likelihood ratio test (LR test). Finally, Lagrange Multiplier tests (LM_Error and LM_Lag) were performed to determine whether the Spatial Lag Model (SLM) or Spatial Error Model (SEM) should be used. The entire process of analysis is shown in Figure 8.  
Figure 8: The process of convergence analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Year** & **2009** & **2011** & **2014** & **2016** \\ \hline L-L & Jilin, Guangdong, Guangxi, Tibet, & Jilin, Fujian, Guangdong, Guangxi, Tibet, & Jilin, Hunan, Heilongjiang, Fujian, Qinghai, Xinjiang. & Jilin, Yunnan, Tibet, \\ aggregation & Shaanxi, Gansu, Ningxia, Qinghai, & Yunnan, Qingha, Xinjiang. & Xinjiang. \\ \hline H-L & Inner Mongolia, Jiangxi, Guizhou, Chongqing, & Inner Mongolia, Jiangxi, Guizhou, Chongqing, & Inner Mongolia, Shanghai, Gansu, Sichuan, Yunnan. & Shanghai, Gansu, Sichuan \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._In the current study, the panel data model was tested using Matlab software. The results show the outcome of the Hausman test (29.175, 0.0000), the LR test (514.37, 0.0001), and that p values are significant at the 5% level. Thus, a double fixed effect model needed to be established. By conducting the LM_Error and LM_Lag tests, the absolute \(\beta\)-convergence model of China's regional _ITE_ was then constructed. The test results are shown in Table 6.  
In Table 6, it is evident that neither the LM_Error nor the LM_Lag passed the significance test, but that the Robust LM_Error and the Robust LM_Lag passed the significance test. However, by undertaking a numerical comparison, it emerged that the spatial error autocorrelation was more significant than the spatial hysteresis autocorrelation, i.e., the space where the absolute \(\beta\)-convergence. Since the SEM was found to be better than the SLM, Formula (6) was chosen. The estimated results are shown in Table 7.  
The maximum likelihood test method was used to estimate the spatial autocorrelation model, as shown in Table 6. The obtained \(\beta\) coefficient was \(-0.1057\), which is less than zero and passed the 1% significance test, indicating that there existed a significant, absolute \(\beta\)-convergence among the regions' _ITE_ during 2009-2016. We could, therefore, further calculate the convergence rate of 1.39%. The goodness-of-fit value indicates that the reliability of the estimation results is high. The spatial residuals passed the 1% significance test, indicating that there was a positive correlation between the _ITE_ of one province and its neighboring provinces during 2009-2016. Through the empirical analysis, the introduction of the factor of spatial effect was found to have a significant impact on the absolute \(\beta\)-convergence of regional _ITE_, indicating that inter-regional connections and cooperation play a crucial role in narrowing the gaps between different regions' _ITE_. According to the \(\beta\)-convergence result, the half-life cycle of regional _ITE_ convergence was 49.8 years.