# Does Intensive Land Use Contribute to Energy Efficiency?--Evidence Based on a Spatial Durbin Model
## 3 Data and Methods
### Methods: Regression Model  
#### 3.2.1 Benchmark Regression  
This paper establishes a panel least squares regression model:  
\[y_{tt}=\beta_{1}x_{it}+\beta Control_{it}+I+t+\varepsilon_{it} \tag{5}\]  
Among them, \(y\) is the explained variable, which is energy efficiency (\(Ene\)) in this article, \(x\) is the explanatory variable (\(Liu\)), which is the level of intensive land use in this article, and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Name** & **Explanation** & **Data Source** \\ \hline \multirow{2}{*}{dependent variable} & energy efficiency (\(Ene\)) & this study uses the chain network DEA to quantify energy efficiency. & Yearbooks of various provincial administrative units, and “China Energy Statistical Yearbook” \\ \hline \multirow{3}{*}{independent variable} & intensive land utilization (\(Liu\)) & we select GDP density, population density, electricity consumption density, employment density, local fiscal expenditure density, and the inverse numbers of urban patch density, using EVM method to give weights. & “China Statistical Yearbook”, “China City Statistical Yearbook”, Chinese Basic GIS data. \\ \hline \multirow{3}{*}{threshold variable} & \multirow{3}{*}{spatial integration (\(Spa\))} & the specific method is to use night light data to connect the geometric center of a certain city with the geometric centers of all neighboring cities. The night light brightness of all county-level administrative units & Visible Light Imaging Linear Scanning Service System (DMSP/OLS) in the U.S. Defense Weather Satellite and Visible Near Infrared Imaging Radiometer (NPP/VIIRS) from the National Polar \\ \hline \multirow{3}{*}{control variables} & GDP (\(Gdp\)) & gross domestic product & \\ \hline \multirow{3}{*}{\begin{tabular}{c} GDP per capita (\(Gpp\)) \\ \end{tabular} } & GDP per capita & gross domestic product per capita & \\ \hline \multirow{3}{*}{\begin{tabular}{c} secondary industry \\ ratio (\(Ssr\)) \\ \end{tabular} } & the proportion of secondary industry in total GDP. & “China Statistical Yearbook”, “China City Statistical Yearbook” \\ \hline \multirow{3}{*}{\begin{tabular}{c} tertiary industry \\ ratio (\(Tsr\)) \\ \end{tabular} } & the proportion of tertiary industry in total GDP. & “China Statistical Yearbook”, “China City Statistical Yearbook” \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} opening up (\(Fdi\)) \\ \end{tabular} } & the proportion of actual utilization of foreign capital in total GDP. & \\ \cline{2-2} \cline{3-3}  & patent applications & logarithm of the number of \\ \cline{1-1} \cline{2-2} \cline{3-3}  & (\(Pat\)) & patent applications & infrastructure \\ \hline \multirow{3}{*}{
\begin{tabular}{c} innovation \\ efficiency (\(In\)e) \\ \end{tabular} } & \multirow{3}{*}{quantitative method o refers to [PERSON] et al. (2021)} & China national knowledge infrastructure, “China Statistical Yearbook”, “China City Statistical Yearbook” \\ \cline{1-1} \cline{2-2} \cline{3-3}  & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Variables explanation.  
_Control_ is the control variable. After [PERSON]'s test, this article adopts a two-way fixed effects model. Therefore, this article adds dummy variables for year t and individual \(i\).