## 3 Variables Description and Research Method
### Robustness Test  
The robustness test is mainly to ensure the stability of the model parameter estimates. The specific test methods mainly include changing the sample or increasing or reducing the sample observation, replacing with other variables and adopting different measurement methods. For the robustness of the results, this paper uses the panel space lag model and the panel space error model to test the robustness. The specific form of the model is  
\[Y_{it}=\rho\sum_{j=1}^{n}w_{ij}Y_{ji}+\mathbf{X}_{\mathbf{it}}^{{}^{\prime}} \mathbf{\beta}+a_{i}+\gamma_{t}+u_{it} \tag{7}\]  
\[\left\{ \begin{array}{l}Y_{it}=\mathbf{X}_{\mathbf{it}}^{{}^{\prime}}\mathbf{ \beta}+\varepsilon_{it}\\ e_{it}=\lambda w_{ij}\varepsilon_{jt}+v_{it}\end{array} \right. \tag{8}\]  
where \(i,j=1,2,3,\ldots,n\) represent regions, \(t=1,2,3,\ldots,T\) represents time; \(Y_{it}\) represents agricultural development; \(w_{ij}\) is an element in the spatial weight matrix \(\mathbf{W}\). When region \(i\) and region \(j\) are adjacent, \(w_{ij}=1\); when region \(i\) and region \(j\) are not adjacent, \(w_{ij}=0\); \(w_{ij}Y_{ji}\) represents the agricultural development of neighboring region; \(\mathbf{X}_{\mathbf{it}}=(X_{1 it},X_{2 it},\ldots,X_{kit})\) represents the amount of agricultural film usage and other influencing factors; \(\rho,\ \mathbf{\beta},\ \lambda\) represent the regression coefficient; \(\alpha_{i}\) represents the individual effect, \(\gamma_{t}\) represents the time effect; \(u_{it},e_{it},v_{it}\) represent the random error term. Through the spatial correlation test of Formulas (7) and (8), the results are shown in Table 3.  
It can be seen from Table 4 that [PERSON]'s I statistic is 13.733 and the corresponding \(p\) value is 0, which is less than 0.05. These show that the sample data have spatial correlation. The LM statistic and the robust LM statistic of the spatial panel error model are 179.751 and 145.714, respectively, and the corresponding \(p\) value is 0, which is less than the significance level of 0.05, indicating that the spatial panel error model can be used. The LM statistic of the spatial panel lag model is 34.066, and the corresponding \(p\) value is 0, which is less than the significance level of 0.05. The robust LM statistic of the spatial panel lag model is 0.05, and the corresponding \(p\) value is 0.865, which is greater than the significant level of 0.1. The spatial panel lag model passes the ordinary LM test, indicating that the spatial panel lag model can be used. Estimating the unknown parameters of Formulas (7) and (8), the regression results are shown in Table 4.  
It can be seen from Table 5 that in the panel space lag model and the panel space error model, the coefficients of agricultural film usage are 0.5840 and 0.4587, respectively, and the impact is significant. This is consistent with the sign of the influence coefficient of the agricultural film usage in the threshold regression model that crosses the threshold, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **Statistic** & **df** & \(p\)**-Value** \\ \hline Spatial error: & & & \\ Moran’s I & 13.733 & 1 & 0 \\ Lagrange multiplier & 179.751 & 1 & 0 \\ Robust Lagrange multiplier & 145.714 & 1 & 0 \\ Spatial lag: & & & \\ Lagrange multiplier & 34.066 & 1 & 0 \\ Robust Lagrange multiplier & 0.029 & 1 & 0.865 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Spatial correlation test results. but the value is smaller than the coefficient value. The coefficients of pesticide usage are \(0.0085\) and \(0.0254\), respectively, and the impact is significant. This is consistent with the sign of the influence coefficient of pesticide usage in the threshold regression model, and the value of the influence coefficient is very close. The coefficient of fertilizer input is \(-0.3549\) and \(-0.1976\), respectively, and the impact is significant.