## 2 Materials and Methods
### Data and Methodology
#### 2.2.4 The Spatial Dubin Model  
Based on the relevant literature, the maximum likelihood methods are further adopted to conduct relevant statistical tests on the selection of spatial econometric models. First, LM lag, LM Error, Robust robust-LM lag and robust-LM Error tests are adopted preliminarily to select the spatial model. The previous research shows that the spatial Dubin model (SDM) is more reasonable than the spatial lag model (SLM) and spatial error model (SEM) [26]. Second, if the Hausman test results show significance at a 1% level, then the fixed effect model should be preferred adopted. Moreover, by comprehensive analysis of individual fixed effect, time fixed effect and individual and time double fixed effect, it could be concluded that the spatial Dubin model with individual and time double fixed effect is more reasonable. Finally, the LR test is conducted to identify whether the spatial Dubin model has the possibility of degradation. The test results of the spatial lag model and the spatial error model all show insignificant at the level of 1%, indicating that the spatial Dubin model could fit the data better (Shown in Table 1). The SAR model considers the spatial correlation of the dependent variable. Furthermore, the SEM model considers the spatial influence of the random interference term. In contrast, the SDM model involves the spatial lag term of both the dependent variable and the independent variable, which could effectively identify the spatial spillover effect among regions. As Table 1 shows that SDM is the optimal model in this paper, which is set as follows:  
\[\text{Inagtfp}_{\text{it}}=\beta_{0}+\beta_{1}\text{Iner}_{\text{it}}+\beta_{ 2}\text{Infiscal}_{\text{it}}+\beta_{3}\text{Z}_{\text{it}}+\theta_{1}\text{ WIner}_{\text{it}}+\theta_{2}\text{WInfiscal}_{\text{it}}+\theta_{3}\text{WlnZ}_{ \text{it}}+\mu_{\text{i}}+\gamma_{\text{t}}+\varepsilon_{\text{it}} \tag{4}\]  
To further test whether there is a dual effect of environmental regulation (Iner) and financial support for agriculture (Infiscal) on agricultural green development, this paper added the interaction term of centralized environmental regulation and financial support for agriculture, and the model is set as follows:  
\[ \begin{array}{l}Inagtfp_{it}=\beta_{0}+\beta_{1}\text{Iner}_{it}+\beta_{2} \text{Infiscal}_{it}+\beta_{3}\overline{Iner_{it}}\times\overline{Infiscal} _{it}+\beta_{4}Z_{it}+\theta_{1}\text{WIner}_{it}+\theta_{2}\text{WInfiscal}_ {it}\\ \qquad\qquad+\theta_{3}\text{WIner}_{it}\times\overline{Infiscal}_{it}+\theta _{4}\text{Wln}Z_{it}+\mu_{i}+\gamma_{t}+\varepsilon_{it}\end{array}  \tag{5}\]  
The spatial dependence of variables is not only reflected in the mutual influence among regions in the current period but also has certain time inertia of variables. That means \(\ln agtfp\) in one lag period may have a dynamic effect on \(\ln agtfp\) in the current period. In this paper, \(\ln agtfp\) in one lag period is included in the spatial Dubin model. Then the model is constructed as follows:  
\[\text{Inagtfp}_{\text{it}}=\beta_{0}+\text{Ingtfp}_{\text{it}-1}+\beta_{1} \text{Iner}_{\text{it}}+\beta_{2}\text{Infiscal}_{\text{it}}+\beta_{3}Z_{ \text{it}}+\theta_{1}\text{WIner}_{\text{it}}+\theta_{2}\text{WInfiscal}_{ \text{it}}+\theta_{3}\text{WlnZ}_{\text{it}}+\mu_{\text{i}}+\gamma_{\text{t} }+\varepsilon_{\text{it}} \tag{6}\]  
Meanwhile, to further analyze whether the interaction of environmental regulation (Iner) and financial support for agriculture (Infiscal) has an impact on agricultural green development, the interaction relationships of the centralized environmental regulation and financial support for agriculture are introduced based on the above model.