4.1.2. Innovation Agglomeration

Figure 4 shows that, Overall, innovation agglomeration is more extreme across China's provinces—there are fewer regions of high agglomeration and more regions of medium and low agglomeration. Analysing the spatial distribution pattern, it is clear that innovation agglomeration is high in the eastern region and low in the western region, with Sichuan Province standing out as the core province in western China. Combined with the time evolution pattern, it can be found that the divisional pattern has not changed significantly during the 13 years, indicating that the spatial distribution pattern has further solidified and behaved with obvious high and high agglomeration characteristics.

#### *4.2. Spatial Regression Results*

Table 2 presents the regression results for the direct and indirect effects of the five regression in this study. Model I test Hypotheses H1 and H2. Models II, III, IV, and IV test hypotheses H3 and H4.

**Figure 4.** Innovation agglomeration distribution. (**a**) Innovation agglomeration in 2006. (**b**) InnovaTable 2010. (**c**) Innovation agglomeration in 2014. (**d**) Innovation agglomeration in 2018.

From Model I, the direct effect coefficient of innovation agglomeration is −0.2315 (significant), while its indirect effect coefficient is 0.2287 (insignificant). Therefore, hypothesis H1 holds, but Hypotheses H2 does not, i.e., innovation agglomeration helps to reduce industrial pollution emissions on the region, but it does not have a spillover effect.

In Models II–V, Hypotheses H3 and H4 can be tested by the direct and indirect effect coefficients of the interaction terms of innovation agglomeration and the explanatory variables (Human, Material, Urban and Government). The direct effect coefficients of the four models are −0.0627, −0.0152, −0.0018 and −0.0104, respectively, and all of them pass the 10% significance level test, indicating that Hypotheses H3 (H3a, H3b, H3c and H3d) holds, but the indirect effects are not significant, indicating that Hypotheses H4 (H4a, H4b, H4c and H4d) does not.

### *4.3. Robustness Tests*

#### 4.3.1. Spatial Autocorrelation Test

Spatial autocorrelation is the basis for spatial econometric model. Although industrial pollution is inherently spillover in nature, it is logical to use a spatial econometric model for the study. However, in order to be rigorous, this study still measured the spatial autocorrelation of industrial pollution between 2006 and 2018, and visualised the results using global Moran's I statistics and Moran scatter. Table 3 shows the global Moran's I statistics in 2006–2018, which shows that the majority of *p*-values are less than 0.10, indicating that industrial pollution in China has spatial autocorrelation at the provincial level. Figure 5 shows that there are obvious agglomeration characteristics in the distribution of industrial pollution in China, among which, low-low agglomeration is predominant. In summary, it is reasonable to use spatial econometric models in this study.


**Table 2.** Regression results.

\*\*\*, \*\*, and \* respectively indicate statistical significance at the 1%, 5%, and 10% levels.

**Table 3.** Global Moran's I value.


#### 4.3.2. Model Applicability Test

To test the superiority of SDM over SAR, we made the hypothesis that the spatial lag of the explanatory variables in the model, WX = 0. It was found that all regression models rejected the null hypothesis, i.e., SDM should be used for research rather than SAR.

To test the superiority of SDM over SEM, we made the hypothesis that the spatial lag of the explanatory variable in the model, WX = −rho \* X. It was found that all regression models rejected the null hypothesis, i.e., SDM should be used for research rather than SEM.

**Figure 5.** Moran scatters. (**a**) Local Moran's I in 2006. (**b**) Local Moran's I in 2010. (**c**) Local Moran's I in 2014. (**d**) Local Moran's I in 2018.

In order to verify that the S&T fixed effect model outperforms the time-period fixed effect model and the spatial fixed effect model in this study, all regression models were tested using the F-test and the null hypothesis was rejected. (Table 4).

**Table 4.** F statistic value.

