## 4 Measurement Estimation and Analysis
### Robustness Test  
Following the practice of [PERSON] et al. (2020) [24], this paper replaces the explained variable atmospheric environmental pollution comprehensive index and adopts PM2.5 to measure the degree of atmospheric environmental pollution and conduct a robustness test. Akin to the atmospheric environmental pollution comprehensive index, higher concentration of PM2.5 signifies worse air quality and more serious atmospheric environmental pollution, and vice versa. As Table 6 suggests, the total effect, direct effect and indirect effect of atmospheric self-purification capacity (wlnAPI) on PM2.5 annual average concentration (InPM) prove significantly negative. In terms of spatial spillover, after replacing the explained variables, atmospheric self-purification capacity has a significant negative correlation with the environmental pollution in one region and its neighboring regions. There are differences between PM2.5 and other pollutants. PM2.5 mostly contains fine particulate matters and possesses strong regional transmissibility. Therefore, the deterioration of PM2.5 pollution in one region has a negative impact on the PM2.5 concentration in neighboring regions and even farther regions. PM2.5 concentration is jointly determined by natural (external) factors and human (internal) factors. The intensity of pollutant emission forms the fundamental internal cause of high incidence of environmental pollution weather. Natural conditions, such as precipitation, wind speed, temperature, vegetation, and mountain barrier, constitute external factors that affect the rise of environmental pollution weather. When PM2.5 concentration exceeds atmospheric self-purification capacity, the hazard of environmental pollution intensifies, which undermines the ecosystem. In terms of the threshold effect of the robustness test (as shown in Tables 7 and 8), this paper first analyzes the threshold values of the single threshold and double threshold of environmental regulation, as well as the 95% confidence intervals. In terms of environmental regulation, its single threshold value is 9.387, and double threshold values are 9.387 and 3.2189. Table 7 shows 95% confidence intervals in a detailed way. \begin{table}
\begin{tabular}{c c c} \hline  & **(1)** & **(2)** \\ \hline  & **InAEP** & **InAEP** \\ \hline  & \(-1.310\) ** & \(-1.331\) ** \\  & \((-2.114)\) & \((-2.154)\) \\  & \(-0.069\) ** & \(-0.078\) * \\  & \((-1.672)\) & \((-1.903)\) \\  & \(-0.773\) ** & \(-0.766\) ** \\  & \((-8.235)\) & \((-8.183)\) \\  & Iner & \(-2.204\) ** & \(-2.150\) ** \\  & \((-38.391)\) & \((-36.858)\) \\  & \(0.611\) ** & \(0.606\) ** \\  & \((3.621)\) & \((3.593)\) \\  & \(-0.046\) ** & \(0.001\) \\  & \((-2.530)\) & \((0.070)\) \\  & \(-0.080\) *** & \(-0.032\) * \\  & \((-4.547)\) & \((-1.747)\) \\  & & \(-0.065\) *** \\  & & \((-3.632)\) \\  & \(3.521\) *** & \(2.762\) ** \\  & \((4.507)\) & \((3.464)\) \\ \hline  & \(3990\) & \(3990\) \\  & \(R^{2}\) & \(0.580\) & \(0.582\) \\  & adj. \(R^{2}\) & \(0.547\) & \(0.549\) \\ \hline \end{tabular} \(t\) statistics in parentheses. * \(p\) < 0.1, **_p_ < 0.05, *** \(p\) < 0.01.  
\end{table} 
Table 5: The Estimation of Threshold Effect. in the Beijing-Tianjin-Hebei region and an insignificant inhibitory effect in the Chengdu-Chongqing Economic Circle, where the coefficient of the total effect reaches \(-19.533\). In the Beijing-Tianjin-Hebei region, both the direct effect and the indirect effect prove significantly negative, indicating that atmospheric self-purification capacity weakens environmental pollution in local and neighboring regions. The Beijing-Tianjin-Hebei region suffers from serious environmental pollution because of the high emission intensity of pollutants. In the region, there is unreasonable industrial structure, with a large proportion of heavy industry. Particularly, in Tangshan, Xingtai, and other cities, industrial structure mainly covers iron and steel and coal.