## 5 Empirical Results and Discussion
### Regression Results  
Random effects are used as a benchmark for measuring the accuracy of the spatial econometric models (SLM, SEM, and SDM). When comparing these three models, it is evident that they all produce coefficients with the same directional signs. However, if the focus is solely on direct effects, the SEM can be examined, as its statistically significant variables show minimal differences with those of the SLM. On the other hand, if the indirect effect is of interest, the SDM is the most appropriate choice. This is supported by the model \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Obs** & \multicolumn{2}{c}{**2012**} & \multicolumn{2}{c}{**2017**} & \multicolumn{2}{c}{**2022**} \\  & **Mean** & & **Min/Max** & **Mean** & & **Min/Max** & **Mean** & **Min/Max** \\ \hline PM\({}_{25}\) & 231 & 19.357 & Min & 11.948 & 15.615 & Min & 11.435 & 15.704 & Min & 11.323 \\  & & (3.771) & Max & 27.001 & (2.083) & Max & 19.352 & (2.085) & Max & 19.187 \\ \hline Population & 231 & 279.789 & Min & 16.174 & 300.575 & Min & 18.320 & 312.403 & Min & 19.027 \\ density & (686.090) & Max & 538.2581 & (741.628) & Max & 562.951 & (775.694) & Max & 577.6456 \\ \hline GTP per & 231 & 139.956.948 & Min & 41,074.000 & 162.737.849 & Min & 558.614.466 & 172.189.788 & Min & 60.876.433 \\ capita & & (135,805.876) & Max & 970.0200 & (152,620.342) & Max & 1,017.023.244 & (152,306.472) & Max & 1,003,496.913 \\ \hline Industrial & 231 & 50,637,499.189 & Min & 13,988.457 & 272.587.788.251 & Min & 14,381.052 & 82,125.296.321 & Min & 10,525.159 \\ density & & (159,485,243.579) & Max & 1,065.949.279.061 & (228,455.012.632) & Max & 1,565,100.976.437 & (230,089.098.661) & Max & 1,426,639.278.506 \\ \hline Energy consumption per capita & 231 & 1971,688 & Min & 475.806 & 2142.882 & Min & 534.198 & 2250.422 & Min & 617.313 \\  & & (1969/084) & Max & 10,377.009 & (1968.598) & Max & 11,335.862 & (1869.915) & Max & 10,141.995 \\ \hline \hline \end{tabular} Note: standard deviation in parentheses.  
\end{table} 
Table 6: Descriptive statistics. Figure 5: LISA cluster maps of bivariate analyses: PM\({}_{2.5}\) and energy consumption per capita during 2012–2022. fit indicators, including the AIC, BIC, and likelihood ratio test, where the SDM exhibits the lowest AIC and BIC values and the highest likelihood ratio test value. Table 7 summarizes the results of the random effects, spatial lag (SLM), and spatial error models (SEM). In the table, the non-spatial regression results are divided into three models: M1, M2, and M3. M1 and M2 are estimated separately by including _LnGPPp_ and _LnGPPpc_2 separately to avoid multicollinearity issues. Although these estimations are divided into two models, their results remain consistent with those of M3, which includes all variables. The estimation results from M3 indicate that provinces with a high population density (_LnPop_dens_) tend to have higher PM\({}_{2.5}\) concentrations because these provinces are major pollution sources. According to [54], the household sector ranks first among the top three sources of PM\({}_{2.5}\) emissions, surpassing other sources. In other words, an increase in population density within a province leads to a rise in PM\({}_{2.5}\) concentrations in that area. Additionally, M3 reveals the relationship between PM\({}_{2.5}\) concentration and economic growth (_LnGPPp_ and _LnGPPp_c2), which follows a U-shaped pattern, which is in contrast to the Environmental Kuznets Curve (EKC) theory. This suggests that economic development initially reduces environmental degradation, but at a certain point, when the economy reaches a large scale, it begins to negatively impact the environment, leading to rapid degradation. In other words, during the early stages of economic development, its impact on environmental degradation is relatively minor. However, as the economy expands significantly, further economic growth exacerbates environmental deterioration.