## 5 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Model (3)**} & \multicolumn{2}{c}{**Model (4)**} & \multicolumn{2}{c}{**Model (5)**} & \multicolumn{2}{c}{**Model (6)**} \\  & **Fixed Effects Spatial** & **Random Effects Spatial** & **Fixed Effects Spatial** & **Random Effects Spatial** \\  & **Lag Model** & **Lag Model** & **Durbin Model** & **Durbin Model** \\ \hline \multirow{2}{*}{_Aging_} & \(-0.3920\) ** & \(-0.4300\)** & \(-0.6164\)** & \(-0.8139\)** \\  & (0.1721) & (0.1726) & (0.2439) & (0.2428) \\ \multirow{2}{*}{_FD_} & \(-1.1051\)** *** & \(-0.9254\)** *** & \(-1.3479\)** *** & \(-1.0545\)** \\  & (0.1618) & (0.1556) & (0.2123) & (0.2078) \\ \multirow{2}{*}{_ER_} & \(0.2080\)** *** & \(0.2032\)** *** & \(0.2016\)** *** & \(0.2064\)** \\  & (0.0373) & (0.0382) & (0.0471) & (0.0478) \\ \multirow{2}{*}{_Energy_} & \(-1.5918\)** *** & \(-1.5328\)** & \(-1.7742\)** *** & \(-1.6787\)** \\  & (0.0906) & (0.0904) & (0.0963) & (0.0980) \\ \multirow{2}{*}{_Med_} & \(-0.7016\)** & \(-0.6601\)** & \(-0.5614\)** & \(-0.5380\)** \\  & (0.1303) & (0.1266) & (0.1548) & (0.1568) \\ \multirow{2}{*}{_perGPP_} & \(1.3545\)** *** & \(1.1982\)** *** & \(2.2313\)** *** & \(1.7354\)** \\  & (0.1620) & (0.1553) & (0.2524) & (0.2537) \\ \multirow{2}{*}{\(\rho\)} & \(0.7590\)** & \(-0.0169\) & \(0.1091\)** & \(0.0949\) \\  & (0.0542) & (0.0549) & (0.0618) & (0.0626) \\ \multirow{2}{*}{\(W\times Aging\)} & & & \(0.7455\)** & \(1.0065\)** \\  & & & & (0.3437) & (0.3465) \\ \multirow{2}{*}{\(W\times FD\)} & & & \(0.7380\)** & \(0.5056\)** \\  & & & & (0.2864) & (0.2746) \\ \multirow{2}{*}{\(W\times ER\)} & & & \(-0.0540\) & \(-0.0572\) \\  & & & & (0.0614) & (0.0623) \\ \multirow{2}{*}{\(W\times Energy\)} & & & \(0.6632\)** & \(0.5848\) \\  & & & & (0.2123) & (0.2080) \\ \multirow{2}{*}{\(W\times Med\)} & & & & \(0.0251\) & 0.0280 \\  & & & & (0.2220) & (0.2248) \\ \multirow{2}{*}{\(W\times perGPP\)} & & & \(-1.4574\)** & \(-1.0371\) \\  & & & & (0.3167) & (0.3112) \\ \multirow{2}{*}{_Corr \(R^{2}\)_} & \(0.4985\) & \(0.3795\) & \(0.5238\) & \(0.3935\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of spatial lag models and spatial Durbin models. of a given province. The main reason is the competition caused by population mobility between adjacent provinces. Specifically, as a province is aging rapidly, it provides limited job opportunities for young people. Due to large differences in economic level and salaries, young people in aged provinces tend to migrate to economically developed neighboring provinces. These younger migrants not only improve the demographic structure of the region, but they also enhance economic growth and GTFP improvements. The direct effect of fiscal decentralization (_FD_) is significant and negative, implying that it has a negative impact on GTFP in a given province. In other words, the higher fiscal decentralization, the lower GTFP. One possible interpretation is that after the tax-sharing reform, the central government adopted a GDP-oriented appraisal mechanism. In response, local governments took active measures to stimulate rapid economic growth at the expense of environmental quality. High fiscal decentralization implies that local governments have more autonomy, so they tend to prioritize economic growth at the expense of environmental protection. As a result, the environment worsened and GTFP was thus impaired. In contrast, the indirect effect of fiscal decentralization is positive, implying that the increased fiscal decentralization of neighboring provinces improves local GTFP growth. We found that the direct effect of environmental regulations (_ER_) is significant and positive, indicating that environmental regulation improves GTFP growth in a given province. This finding supports the [PERSON] hypothesis. One reasonable explanation is that intensified environmental regulation pushes the regulated enterprises in the local region to innovate production technologies and introduce advanced equipment which can improve GTFP.