# Urbanization and Grain Production Pattern of China: Dynamic Effect and Mediating Mechanism
## 4 Results
### The Dynamic Effect of Urbanization on the GPP
As shown in Table 5, the results of the AR (2) test support the hypothesis of no second-order serial correlation in the regression equation, regardless of whether the panel is spatially dynamic or non-spatially dynamic, and regardless of whether control variables are included. The Sargan overidentification test also showed that the null hypothesis of instrumental variable validity could not be rejected, and the Wald tests all rejected the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{_LM Test_} & \multicolumn{2}{c}{**W1**} & \multicolumn{2}{c}{**W3**} \\ \cline{2-5}  & \(\chi^{2}\) & \(p\)**-Value** & \(\chi^{2}\) & \(p\)**-Value** \\ \hline LM-lag & 11.406 & 0.001 & 13.682 & 0.000 \\ Robust LM-lag & 13.519 & 0.000 & 8.789 & 0.003 \\ LM-error & 0.430 & 0.512 & 5.504 & 0.019 \\ Robust LM-error & 2.544 & 0.111 & 0.612 & 0.434 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: LM test for the spatial panel econometric model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Original Variables**} & \multicolumn{2}{c}{**LLC**} & \multicolumn{2}{c}{**IPS**} & \multicolumn{2}{c}{**ADF–Fisher**} & \multicolumn{2}{c}{**Harris–Tzavalis**} & \multirow{2}{*}{**VIF**} \\ \cline{2-2} \cline{5-9}  & **Value.** & \(p\) & **Value.** & \(p\) & **Value.** & \(p\) & **Value.** & \(p\) \\ \hline GPP & \(-1.882\) & 0.029 & \(-6.980\) & 0.000 & \(-5.734\) & 0.000 & 0.579 & 0.001 & \\ URBAN & \(-1.679\) & 0.046 & \(-1.631\) & 0.051 & 1.299 & 0.096 & 0.768 & 0.038 & 4.51 \\ MCI & \(-1.609\) & 0.054 & 0.387 & 0.065 & 0.915 & 0.018 & \(-4.501\) & 0.000 & 3.80 \\ PS & \(-4.015\) & 0.000 & \(-0.629\) & 1.000 & \(-3.088\) & 0.099 & 3.275 & 0.095 & 1.57 \\ ATECH & \(-2.067\) & 0.019 & \(-1.409\) & 0.079 & \(-2.500\) & 0.993 & 0.866 & 0.088 & 3.13 \\ lnPGDP & \(-4.011\) & 0.000 & 3.536 & 0.000 & \(-2.840\) & 0.997 & 0.924 & 0.070 & 6.10 \\ STRUC & \(-0.927\) & 0.023 & \(-0.169\) & 0.095 & \(-3.770\) & 0.059 & 4.617 & 0.000 & 1.67 \\ GAP & \(-4.162\) & 0.000 & \(-6.199\) & 0.000 & \(-7.179\) & 0.000 & \(-4.349\) & 0.000 & 2.19 \\ InEDU & \(-4.849\) & 0.000 & \(-9.347\) & 0.000 & 1.931 & 0.072 & \(-10.084\) & 0.000 & 5.04 \\ OPEN & \(-2.165\) & 0.015 & 1.655 & 0.951 & \(-2.267\) & 0.083 & 4.523 & 0.000 & 3.87 \\ FISCAL & \(-2.448\) & 0.007 & \(-6.747\) & 0.000 & 2.956 & 0.002 & \(-5.559\) & 0.000 & 3.04 \\ lnLAND & \(-2.453\) & 0.007 & \(-3.687\) & 0.001 & 3.306 & 0.001 & \(-0.889\) & 0.186 & 4.14 \\ lnTEM & \(-8.321\) & 0.000 & \(-11.903\) & 0.000 & \(-17.351\) & 0.000 & \(-21.153\) & 0.000 & 3.14 \\ lnPRE & \(-5.506\) & 0.000 & \(-12.622\) & 0.000 & \(-18.140\) & 0.000 & \(-18.467\) & 0.000 & 4.25 \\ lnSUN & \(-7.357\) & 0.000 & \(-12.619\) & 0.000 & \(-18.578\) & 0.000 & \(-17.894\) & 0.000 & 3.50 \\ \hline \hline \end{tabular} Note: The different unit root tests all include time trend and subtract the cross-sectional mean.  
\end{table} 
Table 3: Unit root test results of variables. original hypothesis at the 1% significance level. Overall, the established dynamic panel model was reasonable and effective. According to the test results, the statistical characteristics of the dynamic spatial panel econometric were better than those of the dynamic panel model when not considering spatial correlation, and the differences in the significance of the estimated coefficients under different spatial weight matrices were also significant. Since the significance and sign of the coefficients under the grain distance weight matrix W3 were improved considerably, the focus was set on the estimation results of the dynamic spatial panel model based on the W3. Under W3, the time lag coefficients and spatial lag coefficients were significantly greater than 0 regardless of whether the control variables were included, indicating a significant spatial spillover effect and path dependency of GPP between regions.