*3.5. Model Design*

This study takes the form of the Cobb-Douglas production function and considers industrial pollution emissions as an "output". By taking the logarithm of both sides of the C-D production function, we transform the equation into a linear function and at the same time mitigate the heteroskedasticity generated by the panel data. εit is the random perturbation term.

$$
\ln \Upsilon\_{\rm it} = \Theta\_{\rm it} + \beta \ln \lambda\_{\rm it} + \gamma \ln \text{Control}\_{\rm it} + \varepsilon\_{\rm it} \tag{15}
$$

Since the spatial Durbin model has the widest range of applicability, we transform Formula (15) into the form of SDM.

$$
\ln \Upsilon\_{\rm ft} = \beta \ln \Upsilon\_{\rm ft} + \delta\_1 \mathbf{W} \ln \Upsilon\_{\rm ft} + \gamma \ln \mathbf{C} \mathbf{control}\_{\rm ft} + \delta \varepsilon\_2 \mathbf{W} \ln \mathbf{C} \mathbf{control}\_{\rm ft} + \varepsilon\_{\rm if} \tag{16}
$$

Panel models usually use either fixed effects or random effects. Random effects assume that all regression variables containing individual random effects are exogenous and are often used to "see the big picture". Fixed effects, on the other hand, assume that the variables containing the effects of individuals are endogenous. [53] Therefore, as the study is for 30 provinces in China, fixed effects are used in this paper. There are three forms of fixed effects in the spatial panel model: spatial fixed effect, time-period fixed effect and spatial and time-period (S&T) fixed effect. The spatial fixed effect reflects characteristics that do not vary with time but vary with individuals (σi), while the time-period fixed effect reflects characteristics that do not vary with individuals but vary with time (τt). Since industrial pollution emissions have distinct regional characteristics and Yu et al. found that smog pollution has a time-varying trend and diffusivity [34], the S&T fixed effect model was used in this study and the spatial lag term of the explanatory variable (Ind\_pol) was added to control for this (see Formula (17)).

ln Yit = αW ln Yit + β ln Xit + δW ln Xit + γ ln Controlit + ωW ln Controlit + σi + τt + εit (17)

> Finally, substituting the variables mentioned in the article into Formula (17), ge<sup>t</sup> Formula (18). In which, Explanatoryv,it represents the explanatory variables for period t of province i in dimension v, that is, human capital dimension, material capital dimension, urban function dimension and governmen<sup>t</sup> dimension.

$$\begin{array}{ll} \text{In Ind.}\, \text{pol.}\, -\text{pol.} & \text{aW } \ln \text{Ind.}\, \text{pol.}\, +\beta\_{1} \text{W } \ln \text{Innno\\_agg}\_{\text{it}}\\ & & + \beta\_{2} \ln \left(\text{Explanatory}\_{\text{v,it}} \ast \ln \text{Inno\\_agg}\_{\text{it}}\right) \\ & & + \delta\_{1} \text{W } \ln \text{Inno\\_agg}\_{\text{it}} \\ & & + \delta\_{2} \text{W } \ln \left(\text{Explanatory}\_{\text{v,it}} \ast \ln \text{Inno\\_agg}\_{\text{it}}\right) \\ & & + \gamma\_{1} \ln \text{Per\\_GDP}\_{\text{it}} + \gamma\_{2} \ln \text{FDI}\_{\text{it}} + \gamma\_{3} \ln \text{Enner\\_stru}\_{\text{it}} \\ & + \omega\_{1} \text{W} \ln \text{Per\\_GDP}\_{\text{it}} + \omega\_{2} \text{W} \ln \text{FDI}\_{\text{it}} + \omega\_{3} \text{W} \ln \text{Enner\\_stru}\_{\text{it}} \\ & + \sigma\_{1} + \tau\_{\text{t}} + \varepsilon\_{\text{it}} \end{array} \tag{18}$$

**4. Results**

*4.1. Analysis of Spatial-Temporal Evolution* 4.1.1. Industrial Pollution

Figure 3 shows that the regions of medium and low industrial pollution are mostly the more economically developed regions, and there is a clear distribution characteristic—the eastern coastal region have less industrial pollution, while some parts of central and western China have more. However, over time, the eastern region solidified its low industrial pollution levels, while the central region generally maintained medium industrial pollution levels and northern China clearly behaved in a high industrial pollution trend.

**Figure 3.** Industrial pollution distribution. (**a**) Industrial pollution in 2006. (**b**) Industrial pollution in 2010. (**c**) Industrial pollution in 2014. (**d**) Industrial pollution in 2018.
