## 4 Empirical Results
### Results of Classical and Spatial Panel Data Models  
Prior to estimating the spatial econometric model, we first provide below the results of the classical econometric models as our reference models. Included are the fixed effects model and the random effects model, with estimation results given in Table 1.  
To verify which is the better model, the fixed effects or the random effects, we performed a Hausman test. The null hypothesis can be strongly rejected, indicating that test results favor the fixed effects model (Model 1) against the random effects model (Model 2). From the second column in Table 1, estimation results show that all variables are significant at a 1% significance level. Specifically, we observed that the estimated coefficient of the _Aging_ variable is negative, indicating that population aging does inhibit GTFP; this finding is consistent with research by [PERSON] and [PERSON] (2017). The coefficient of the _FD_ variable is also negative, indicating that an increase in fiscal decentralization lowers GTFP growth. The impact of environmental regulation (_ER_) on GTFP is positive, indicating that increasing the stringency of environmental regulation contributes to GTFP growth. The _Energy_ variable has a negative impact on GTFP, showing that the coal-dominated energy structure is the main reason for low GTFP scores. The estimated coefficient of the _Med_ variable is also negative, implying that an increase in medical expenditure inhibits GTFP. Lastly, we observe that the _PerGPP_ variable has a positive estimated coefficient, confirming that income plays an important role in GTFP growth. From Figure 1, the spatial distribution of the GTFP of 30 provinces indicates strong spatial clustering. To ascertain if there is significant spatial autocorrelation, we carried out a [PERSON]'s I test to verify the hypothesis. [PERSON]'s I test results from 2002 to 2018 are set out in Table 2.  
Table 2 illustrates that [PERSON]'s I values of GTFP over the sample period are significant and positive, except for five years (e.g., 2002, 2003, 2006, 2007, and 2008), indicating spatial autocorrelation. In the early stage of the sample period, the GTFP scores in maps displayed \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{1}{c}{**Model (1)**} & \multicolumn{1}{c}{**Model (2)**} \\  & **Fixed Effects Model** & **Random Effects Model** \\ \hline \multirow{2}{*}{_Aging_} & \(-0.3952\) *** & \(-0.4798\) *** \\  & (0.1784) & (0.1723) \\ \multirow{2}{*}{_FD_} & \(-1.0921\) *** & \(-0.6750\) *** \\  & (0.1656) & (0.1308) \\ \multirow{2}{*}{_ER_} & 0.2064 *** & 0.1970 *** \\  & (0.0386) & (0.0399) \\ \multirow{2}{*}{_Energy_} & \(-1.5853\) *** & \(-1.4040\) *** \\  & (0.930) & (0.0846) \\ \multirow{2}{*}{_Med_} & \(-0.6968\) *** & \(-0.6205\) *** \\  & (0.1348) & (0.1195) \\ \multirow{2}{*}{_perGPP_} & 1.3445 *** & 0.9971 *** \\  & (0.1667) & (0.1346) \\ \multirow{2}{*}{_Constant_} & \(-4.8040\) *** & \(-3.5896\) *** \\  & (0.7421) & (0.6283) \\ \multirow{2}{*}{\(R^{2}\)} & 0.4985 & 0.4024 \\ \hline \hline \end{tabular} Note: standard errors in parentheses. **: \(p<0.05\), ***: \(p<0.01\).  
\end{table} 
Table 1: Results of classical panel data models. weak spatial clustering, while the spatial autocorrelation strengthened increasingly in the later stages. On the other hand, in the case of the _Aging_ variable, we observed that [PERSON]'s I values from 2002 to 2018 (except 2014) are positive at a 10% significance level at least, implying strong spatial clustering. Importantly, spatial interaction effects among the provinces should not be neglected when modeling the relationship between aging and GTFP. Next, we estimated the fixed effects and random effects of spatial lag models and spatial Durbin models incorporating spatial interaction effects. Similarly, the [PERSON] test results also prefer the fixed effects models.