## 4 Measurement Estimation and Analysis
### The Estimation Result and Analysis of Threshold Effect  
To determine the specific form of the threshold model, this paper tests whether environmental regulation has a threshold effect, as well as a specific number of thresholds, as shown in Table 3. Besides, this paper analyzes the threshold values of the single threshold and double threshold of environmental regulation (Iner), as well as the 95% confidence intervals. In terms of environmental regulation, its single threshold value is 11.6349, and double threshold values are 11.800 and 10.274. Table 3 shows 95% confidence intervals in a detailed way. Then, this paper presents the threshold effects of variables. As the results of the self-sampling test suggest, the single threshold effect of environmental regulation passes the significance test of 5%, and its double threshold effect passes the significance test of 5% (Table 4). Therefore, the variable environmental regulation has a single threshold and double threshold effects. Table 5 shows the regression results of the single threshold effect (1) and double threshold effect (2) of environmental regulation (Iner). This paper will analyze the difference in the impact of atmospheric self-purification capacity on environmental pollution under the single threshold effect of environmental regulation. According to the statistical results in Table 5, when environmental regulation (Iner) reaches less than 11.6349, the regression coefficient of environmental regulation to environmental pollution (InAEP) proves significant and reaches \(-0.080\); when environmental regulation reaches higher than 11.6349, the regression coefficient of environmental regulation to environmental pollution proves significant and reaches \(-0.065\). As evinced, with the increase in the natural logarithm of environmental regulation (the removal of industrial sulfur dioxide), its inhibitory effect on environmental pollution weakens, which basically accords with Hypothesis 3. The reason is that in general, environmental regulation in China largely depends on a command-control approach, with the aid of economic incentive. Economic-incentive-oriented environmental regulation besris people's behavior motivation with market signals. For example, in the control of air pollution, emission taxes are levied on sulfur dioxide, nitrogen oxides, and smoke and dust emissions. Some countries start to execute carbon taxes and other policies. The cost of pollution expands with the increase in pollution, forcing enterprises to save production costs by supplementing investment, promoting technological innovation, adopting cleaner production technology, and introducing more advanced production equipment. If enterprises cannot upgrade pollution-control equipment or technology in a short term, they will depress production scale, decrease the production of polluting products, or turn to the production of green products in a bid to ease environmental pollution. This demonstrates that under the threshold effect of environmental regulation, atmospheric self-purification capacity can significantly reduce environmental pollution. The command-control approach regulates various activities of pollution emission. To meet the requirements of environmental regulation, enterprises necessarily increase their production costs, and to maximize their profits, enterprises expand their production scale. These multiply the emission of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Threshold** & **F** & _p-Value_ & **BS-Reps** & **10\%** & **5\%** & **1\%** \\ \hline Single Threshold & Single & 27.340 & 0.040 & 300 & 22.772 & 25.6212 & 32.5621 \\ Double Threshold & Single & 27.590 & 0.030 & 300 & 21.877 & 26.3749 & 31.5228 \\ Double & Double & 23.990 & 0.043 & 300 & 17.258 & 23.6188 & 28.9096 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The Results of the Self-Sampling Test of the Threshold Effect of Variables.