## 4 Results and Analysis
### Results of Simultaneous Equations Model  
Specifically, the simultaneous equation model in this part consists of equations (1) and (2). This paper selects the three-stage least squares estimation method (3 SLS). Tables 4 and 5 are the results of the simultaneous equation model estimated using the 3 SLS method. Consistent with expectations, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **OLS** & **FE** & **RE** & **OLS** & **FE** & **RE** \\ \hline
**2S** & & & & **PM2.5** & & & \\ _PM2.5_ & 0.205 *** & 0.088 *** & 0.111 *** & _2S_ & 0.877 *** & 0.434 *** & 0.478 *** \\  & (11.09) & (2.87) & (4.00) & & (6.37) & (2.94) & (3.29) \\ _FA (In)_ & 3.712 *** & 1.668 *** & 1.714 *** & _Pop (In)_ & 5.336 *** & \(-\)0.530 & \(-\)0.226 \\  & (7.27) & (3.98) & (4.18) & & (4.11) & (\(-\)0.42) & (\(-\)0.18) \\ _Imnovation (In)_ & \(-\)5.873 *** & \(-\)3.394 *** & \(-\)3.573 *** & _FDI (In)_ & 2.951 *** & 1.035 & 1.192 \\  & (\(-\)12.64) & (\(-\)7.57) & (\(-\)8.27) & & (2.04) & (1.01) & (1.15) \\ _Open_ & 0.680 *** & 0.291 & 0.289 * & _Trans (In)_ & 18.799 *** & 5.317 *** & 6.194 *** \\  & (3.81) & (1.58) & (1.64) & & (6.97) & (2.50) & (2.90) \\  & & & & _Enviro_ & \(-\)0.432 *** & 0.056 & 0.039 \\  & & & & (\(-\)2.96) & (0.54) & (0.37) \\  & & & & _Open_ & \(-\)1.639 *** & \(-\)1.162 * & \(-\)1.214 *** \\  & & & & & (\(-\)2.91) & (\(-\)2.51) & (\(-\)2.64) \\  & & & & _UL_ & \(-\)0.968 *** & \(-\)0.060 & \(-\)0.154 \\  & & & & (\(-\)5.96) & (\(-\)0.36) & (\(-\)0.93) \\  & & & & _CEI_ & \(-\)2.692 *** & \(-\)1.009 & \(-\)1.255 \\  & & & & & (\(-\)3.84) & (\(-\)1.27) & (\(-\)1.62) \\ _\_cons_ & 15.187 *** & 38.564 *** & 37.688 *** & \(-\)50.046 *** & 18.698 & 15.137 \\  & (2.61) & (9.60) & (8.92) & & (\(-\)2.80) & (0.96) & (0.78) \\ _R-sq_ & 0.556 & 0.507 & 0.525 & & 0.595 & 0.384 & 0.449 \\  & 234 & 234 & 234 & & 234 & 234 & 234 \\  & & & 0.0000 & & & 0.000 \\ _Prob \(>\) Ethur2_ & & & & & & 0.0000 \\ _Hussman test_ & & \(-\)4.27 & & & & 304.65 *** & \\ \hline \hline \end{tabular} Note: The numbers in brackets are t statistics; ***, **, and * represent their significance at 1%, 5%, and 10% levels, respectively.  
\end{table} 
Table 2: Single equation estimation results of secondary industry and air pollution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **OLS** & **FE** & **RE** & **OLS** & **FE** & **RE** \\ \hline
**3S** & & & & **PM2.5** & & \\ _PM2.5_ & \(-\)0.217 *** & \(-\)0.078 * & \(-\)0.117 *** & _3S_ & \(-\)0.700 *** & \(-\)0.176 & \(-\)0.213 * \\  & (\(-\)10.00) & (\(-\)1.84) & (\(-\)3.18) & & (\(-\)5.52) & (\(-\)1.56) & (\(-\)1.89) \\ _FA (In)_ & \(-\)2.958 *** & \(-\)0.899 & \(-\)1.076 * & _Pop (In)_ & 5.314 *** & \(-\)0.226 & 0.132 \\  & (\(-\)4.94) & (\(-\)1.55) & (\(-\)1.92) & & (4.01) & (\(-\)0.18) & (0.10) \\ _Imnovation (In)_ & \(-\)7.493 *** & \(4.377 ***\) & \(4.922 **\) & _FDI (In)_ & 3.136 *** & 0.550 & 0.720 \\  & (13.74) & (7.04) & (8.42) & (2.13) & (0.54) & (0.69) \\ _Open_ & \(-\)0.036 & \(-\)0.210 & \(-\)0.060 & _Trans (In)_ & 21.148 *** & 6.669 *** & 7.726 *** \\  & (\(-\)0.17) & (\(-\)0.83) & (\(-\)0.25)  
the estimation results of the simultaneous equation model are more accurate than the estimation results of the single equation model in terms of statistical significance and rationality of the estimated coefficients. In order to ensure the robustness of the estimation results, six different specifications are used in this paper, and the corresponding results are labeled as models (1)-(6). Specifically, the model (6) is a benchmark estimation model, including all control variables in the two equations. (1)-(5) include some control variables in the model. For equation (1) in the simultaneous equation model, in models (1) to (6) the positive and negative coefficients of the PM2.5 concentration remain stable and in models (3) to (6) are significant at 1% since.