**3. Model Setting and Data Description**

*3.1. Model Construction*

3.1.1. Superefficient EBM Model

The hybrid distance function model (EBM) can be compatible with the radial ratio of input frontier values to actual values and realize the effective combination of radial and nonradial methods in data envelopment analysis. The model makes up for the deficiencies of DEA and SBM, giving more consideration to the efficiency level [24–28]. The following superefficient EBM model with undesired outputs and nondirectional and constant payoffs of scale is used to measure the green economic efficiency of 280 cities across China, and the obtained combined efficiency value (GEE) is used as the core explanatory variable of the spatial econometric model.

$$\begin{array}{lcl} \mathbf{r}^\* = & \min \frac{\boldsymbol{\Phi} - \boldsymbol{\varepsilon}\_\mathbf{x} \sum\_{\mathbf{i}=1}^m \mathbf{w}\_i^- - \mathbf{s}\_\mathbf{i}^- / \mathbf{x}\_{i0}}{\boldsymbol{\Phi} + \boldsymbol{\varepsilon}\_\mathbf{y} \sum\_{\mathbf{i}=1}^n \mathbf{w}\_\mathbf{r}^+ + \mathbf{y}\_\mathbf{r}^- / \mathbf{y}\_{i0} + \boldsymbol{\varepsilon}\_\mathbf{z} \sum\_{\mathbf{p}=1}^n \mathbf{w}\_\mathbf{p}^- \mathbf{x}^- - \mathbf{y}\_\mathbf{p}^- / \mathbf{z}\_\mathbf{p}}} \\ \text{s.t.} & \begin{cases} \sum\_{\mathbf{i}=1}^n \mathbf{x}\_{i\mathbf{j}} \lambda\_\mathbf{j} + \mathbf{s}\_\mathbf{i}^- = \boldsymbol{\Phi} \mathbf{x}\_{i0} \ (\mathbf{i} = 1, 2, \cdots, \mathbf{m}) \\ \sum\_{\mathbf{j}=1}^n \mathbf{y}\_\mathbf{r} \lambda\_\mathbf{j} - \mathbf{s}\_\mathbf{r}^+ = \boldsymbol{\Phi} \mathbf{y}\_\mathbf{r} \mathbf{0} \ (\mathbf{r} = 1, 2, \cdots, \mathbf{s}) \\ \sum\_{\mathbf{i}=1}^n \mathbf{z}\_\mathbf{p} \lambda\_\mathbf{j} + \mathbf{s}\_\mathbf{p}^- = \boldsymbol{\Phi} \mathbf{z}\_\mathbf{p} \mathbf{0} \ (\mathbf{p} = 1, 2, \cdots, \mathbf{q}) \\ \lambda\_\mathbf{j} \geqslant 0, \mathbf{s}\_\mathbf{i}^-, \mathbf{S} \mathbf{r}^+, \mathbf{s}\_\mathbf{p}^- \ge 0 \end{array} \tag{1} \\ \end{array} \tag{1}$$

Regarding the specific meaning of these variables, r\* denotes the combined efficiency value, and x, y and z denote the input, desired output and undesired output elements, respectively. m, s and q denote their quantities. λ denotes the relative importance of the reference unit, ε is the core parameter representing the importance of the nonradial component, and θ is the efficiency value in the radial condition. wi, wr and wp denote the i-th input, r-th desired output and p-th nonweights of the expected output indicators.
