# Urbanization and Grain Production Pattern of China: Dynamic Effect and Mediating Mechanism
## 4 Results
### The Dynamic Effect of Urbanization on the GPP  
Since the time dimension is considered, to avoid pseudo-regression problems, unit root tests on the panel data are required to ensure the stationarity of variables. We used four test methods--LLC (Levine-Lin-Chu), IPS (Im-Pesaran-Skin), ADF-Fisher, Harris-Tzavalis--to conduct the tests of the variables (Table 3). The results show that most of the variables passed the significance test under different methods, and they were stationary. Although individual variables did not pass the significance test under a certain method, when considered together, it can be concluded that the null hypothesis of the existence of a unit root was rejected for that variable; i.e., this variable was also stationary. In addition, the variance inflation factors (VIF) of the independent variables were all significantly less than 10, with an average VIF of 3.57, indicating that there was no significant multicollinearity problem among the variables. According to common practice, the spatial correlation of GPCI was tested with the global Moran's I. The test results under the three different spatial weight matrices showed that the Moran's I scores for GPCI under W1 and W3 were significantly greater than 0, at [0.145, 0.303] and [0.469, 0.532], respectively. Therefore, grain production in each region had \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Year** & **COG Coordinates** & **Direction** & **Distance/km** & **Semi-Major Axis/km** & **Semi-Minor Axis/km** & **Azimuth/\({}^{c}\)** \\ \hline
1996 & 114.289\({}^{\circ}\) E, 33.978\({}^{\circ}\) N & - & - & 1244.192 & 737.020 & 55.477 \\
2000 & 113.686\({}^{\circ}\) E, 33.469\({}^{\circ}\) N & southwestward & 78.932 & 1229.486 & 738.227 & 56.712 \\
2018 & 115.091\({}^{\circ}\) E, 35.770\({}^{\circ}\) N & northeastward & 196.337 & 1384.636 & 736.314 & 55.936 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of COG and SDE of the GPP in China. Figure 2: COG transfer and SDE of grain production in China. relatively significant positive spatial autocorrelation and dependence, and the index and significance were higher under W3; that is, the demonstration effect in one region affected grain production in neighboring regions, thus exhibiting spatial agglomeration characteristics, which also showed certain discontinuity in time variation. With the distance between regions and the scale of production taken into consideration, the spatial agglomeration strengthened and became more pronounced. However, the [PERSON]'s I under W2 was insignificantly negative, indicating difficulties in reflecting the agglomeration characteristics of grain production spatial correlation among regions by considering geographic distance alone. Then, two Lagrange multipliers (LM-lag and LM-error) and their robust forms (Robust LM-lag and Robust LM-error) were used to discriminate the spatial lag form and the spatial error form of the dynamic spatial panel model. The principle was to first compare the significance of the Lagrange multipliers and select the significant one to build the empirical model. If both Lagrange multipliers were significant, the significance of their robust forms was further compared, and the significant one was selected to build the spatial econometric model. Since the Moran's I under W2 was not significant, only the LM tests under W1 and W3 were performed (Table 4). Only LM-lag passed the significance test under W1, while LM-lag and LM-error passed the significance test under W3, yet Robust LM-error did not pass the significance test. Taken together, the spatial lag form under both matrices was significantly better than the spatial error form. For comparison, this paper also includes the test results of non-spatial ordinary dynamic panel regressions based on GMM (Table 4).