# Does Intensive Land Use Contribute to Energy Efficiency?--Evidence Based on a Spatial Durbin Model
## 3 Data and Methods
### Methods: Regression Model
#### 3.2.2 Spatial Regression  
This article adopts spatial econometric regression. The spatial measurement model is divided into three types: spatial lag model, spatial error model and spatial Durbin model [38]. The spatial lag model adds the spatial lag term of the explained variable to the general panel data model, indicating that the explanatory variable on a certain spatial unit is affected by the explanatory variable of the adjacent spatial unit; the spatial error model adds spatially related error terms, that is, the error term of a certain spatial unit model is considered to be affected by the adjacent spatial unit model error term; the spatial Durbin model integrates the characteristics of the spatial lag model and the spatial error model. This intensity of the influence of adjacent spatial units is represented by a spatial weight matrix. The spatial lag model, the spatial error model and the spatial Durbin model are as follows:  
\[y_{it}=\delta\sum_{j=1}^{N}W_{ij}y_{it}+\varphi+\beta x_{it}+C_{i}+\alpha_{t}+ \varepsilon_{it} \tag{6}\]  
\[y_{it}=\varphi+\beta x_{it}+C_{i}+\alpha_{t}+u_{it},u_{it}=\rho\sum_{j=1}^{N}W _{ij}u_{it}+\varepsilon_{it} \tag{7}\]  
\[y_{it}=\delta\sum_{j=1}^{N}W_{ij}y_{it}+\varphi+\beta x_{it}+\delta\sum_{j=1}^ {N}W_{ij}y_{ij}\theta+C_{i}+\alpha_{t}+\varepsilon_{it} \tag{8}\]  
where: \(\delta\) is the spatial regression coefficient, which represents the influence of the explained variable \(y\) of the adjacent spatial unit on the explained variable \(y\) of this spatial unit (\(y\) is the explained variable, which is energy efficiency \"_Ene_\"). If it is significantly positive, it means that the explained variable has obvious spatial overflow. That is, the increase in the variable by one spatial unit within the research scope corresponds to the increase in the variable in other spatial units; \(u_{it}\) is the spatial autoregressive error term; \(\rho\) is the spatial error coefficient, which represents the influence of the adjacent spatial unit error term \(u\) on the spatial unit error term \(u\); \(\theta\) is the spatial lag term coefficient of the explanatory variable, which indicates the influence of the explanatory variable \(x\) of the adjacent space unit on the explanatory variable \(y\) of this space unit; \(N\) is the number of spatial units, and W is the spatial weight matrix. First, use the LM test to determine whether the spatial lag effect and the spatial error effect are significant, then use Wald or LR test to judge whether the spatial Durbin model can be simplified into a spatial lag model or a spatial error model. Assumption 1: \(\theta=0\); assumption 2: \(\theta+\lambda\beta=0\). If assumption 1 passes the significance test, it is considered that the spatial Durbin model can be reduced to a spatial lag model. If assumption 2 passes the significance test, it is considered that the spatial Durbin model can be reduced to a spatial error model [34]. After testing, assumption 1 and assumption 2 are not true, so this article chooses the spatial Durbin model.