3.1.2. Spatial Durbin Model

This study adopts the spatial Durbin model (SDM) to test the spatial spillover effect of the tourism development level on urban green economic efficiency and carbon emission intensity and explores the nonlinear characteristic relationship on this basis. The acceleration of regional economic integration makes it possible for green economic efficiency to interact spatially among different cities. The spatial econometric model makes up for the deficiency that traditional measurement cannot introduce spatial factors, the spatial Durbin model contains the spatial dependence of both dependent and independent variables [14,20,21], and models (1)–(4) are as follows:

```
lnGEEit = ρWlnGEE + β1lnTCit + β2lnCONit + θ1WlnTCit + θ2WlnCONit + δi + μt + εit
lnGEEit = ρWlnGEEit + β1lnTCit + β2 ln2 TCit + β3lnCONit + θ1WlnTCit + θ2Wln2TCit + θ3WlnCONit + δi + μt + εit
               lnCIit = ρWlnCIit + β1lnTCit + β2lnCONit + θ1WlnTCit + θ2WlnCONit + δi + μt + εit
  lnCIit = ρWlnCIit + β1lnTCit + β2 ln2 TCit + β3lnCONit + θ1WlnTC + θ2Wln2TCit + θ3WlnCONit + δi + μt + εit
                                                                                                                    (2)
```
where i and t denote region and time, respectively, W represents the spatial weight matrix, and β<sup>i</sup> and θ<sup>i</sup> are the parameter vectors to be estimated and the spatial regression coefficients of the tourism development level. "Green economic efficiency" is GEE, CI is "carbon emission intensity", TC is "tourism development", CON is the control variable, and ρ is the spatial regression coefficient. "Tourism development" is TC, CON is the control variable, and ρ is the spatial regression coefficient. δ<sup>i</sup> is the individual fixed effect, μ<sup>t</sup> is the time fixed effect, and εit is the random error term.

3.1.3. Semiparametric Panel Spatial Lag Model

The semiparametric panel spatial lag model not only analyzes the influence of spatial factors but can also test the spatial nonlinear relationship between variables. To further analyze the spatial nonlinear effects of tourism development on urban green economic efficiency and carbon emission intensity, this paper draws on the related research [55] to further construct a semiparametric panel spatial lag model.

$$\begin{array}{l} \text{lnCEE}\_{\text{it}} = \alpha\_{\text{i}} + \rho \text{WlnCEE}\_{\text{it}} + \beta\_{1} \text{lnCON}\_{\text{it}} + \theta\_{1} \text{WlnCON}\_{\text{it}} + \text{G} (\text{lnTC}\_{\text{it}}) + \varepsilon\_{\text{it}}\\ \text{lnCI}\_{\text{it}} = \alpha\_{\text{i}} + \rho \text{WlnCI}\_{\text{it}} + \beta\_{1} \text{lnCON}\_{\text{it}} + \theta\_{1} \text{WlnCON}\_{\text{it}} + \text{G} (\text{lnTC}\_{\text{it}}) + \text{u}\_{\text{it}} \end{array} \tag{3}$$

where G(lnTCit) represents the nonparametric part of the unknown function, α<sup>i</sup> represents the individual effect, εit and uit represent the random perturbation term.
