# Does Intensive Land Use Contribute to Energy Efficiency?--Evidence Based on a Spatial Durbin Model
## 3 Data and Methods  
### Data  
#### 3.1.1 Data Selection  
To figure out the relationship between intensive land use and energy efficiency, the following variables are selected in this paper:  
(1) Explained variable (energy efficiency, _Ene_): Referring to [PERSON] (1996) and [PERSON] et al. (2020) [25], the input variables selected in this article are labor (unit is thousands, measured by the number of employees), capital (unit is RMB million, estimated according to the method of [PERSON] et al. [26] and energy (unit is thousand tons of standard coal); the output variable is GDP (unit is one hundred million yuan). This study uses the chain network DEA to quantify energy efficiency [27; 28], so each city above the prefecture level is a decision-making unit \(DMU_{i}\), assuming that there are s (\(s\) = 1, 2,..., \(S\)) stages in the whole process, the input variables and output variables of each stage are \(I_{i}^{s}\) and \(O_{i}^{s}\), respectively, and satisfy \(I_{i}^{s}\)\(\in\)\(R_{+}^{as}\) and \(O_{i}^{s}\)\(\in\)\(R_{+}^{\beta s}\); the intermediate variable of the \(s\) stage and the \(s+1\) stage is set to \(P_{i}^{(s,s+1)}\), and it satisfies \(P_{i}^{(s,s+1)}\)\(\in\)\(R_{+}^{\gamma(s,s+1)}\), where \(\alpha\), \(\beta\) and \(\gamma\) represent the number of input variables, output variables and intermediate variables, respectively, \(\alpha\) = 1, 2,..., \(x\), \(\beta\) = 1, 2,..., \(y\), \(\gamma\) = 1, 2,..., \(\Delta^{S}\) is the model weight, \(w^{S}\) is the weight variable of the \(s_{th}\) order in the whole process, and \(\lambda^{S}\)\(\in\)\(R_{+}^{n}\), \(\mu^{s}\) and \(\mu^{s+}\) are the slack variables of the input variable and the output variable [29; 30], respectively; the goal of the network envelope analysis model can be expressed as \(\theta\):  
\[\theta=min\frac{\sum_{s=1}^{S}\omega^{s}[1-\frac{1}{\alpha}(\sum_{x=1}^{\alpha }\frac{I_{i}^{s-}}{I_{0}})]}{\sum_{s=1}^{S}\omega^{s}[1+\frac{1}{\beta}(\frac {\sum_{y=1}^{\beta}}{O_{\gamma_{0}}^{s}})]} \tag{1}\]  
The constraints are:  
\[ \begin{array}{l}I_{0}^{s}=\sum\limits_{i=1}^{n}\lambda_{i}^{s}I_{i}^{s}+\mu ^{s-}\\ O_{0}^{s}=\sum\limits_{i=1}^{n}\lambda_{i}^{s}O_{i}^{s}+\mu^{s+}\\ P^{(s,s+1)}\lambda^{s+1}=P^{(s,s+1)}\lambda^{s}\\ \sum\limits_{i=1}^{N}\lambda_{i}^{s}=\frac{S}{\alpha}\omega^{s}=1\\ \lambda^{S},\mu^{S-},\mu^{S+},w^{S}\geq~{}0\end{array} \]  
The efficiency of stage \(s\) can be expressed as:  
\[\theta_{s}=\frac{1-\frac{1}{\alpha}(\sum_{x=1}^{\alpha}\frac{\mu_{x}^{s-*}}{I _{0}})}{1+\frac{1}{\beta}(\sum_{y=1}^{\beta}\frac{\mu_{y}^{s+*}}{O_{\gamma_{0} }^{s}})} \tag{2}\]  
(2) Explanatory variable (intensive land utilization, _Liu_): China currently divides regional land into construction land and non-construction land. The former can be understood as the land that serves productive labor and capital factors and where various factors of production can play a role; the latter refers to other land, which does not have the nature of production. Because (positive) intensive land use refers to the investment of more production factors per unit area of land and the agglomeration of urban internal space, this article selects GDP density, population density, electricity consumption density, employment density, local fiscal expenditure density, and the inverse numbers of urban patch density (the inverse number of indicators that measure the degree of urban decentralization). The calculation method of density is the ratio of the total amount of economic indicators to the area of construction land. The ratio of the total amount to the total urban area is not adopted because many cities have large tracts of land without economic activities, and only the area of construction land is engaged in economic activities. The weighting is divided into subjective and objective methods.