## 4 The Analytical Methods
### Econometric Models  
The [PERSON]'s CD Test and Breusch and Pagan LM Test exhibited cross-sectional dependence (see Table 1 in Appendix A), indicating that the random effects model is more appropriate than the pooled-OLS model. The random effects model allows for the inclusion of time-invariant variables (e.g., geographic location), which are critical for spatial modeling and not considered in the fixed effects model. In this study, a non-spatial and \begin{table}
\begin{tabular}{c c c c c} \hline
**Type** & **Variables** & **Description** & **Years** & **Sources** & **Expected Sign** \\ \hline \multirow{7}{*}{Dependent Variable} & \multirow{7}{*}{PM\({}_{2.5}\)} & \multirow{7}{*}{The PM\({}_{2.5}\) concentration} & \multirow{7}{*}{2012} & \multirow{7}{*}{Applications, Version 2} \\  & & in each province & 2017 & & (MERRA-2) bands \\  & & (ug/m\({}^{3}\)) & 2022 & & DUSMASS52 + \\  & & & & OCSMASS\(\times\) & \\  & & & & SSMSMS\(\times\) & \\  & & & & SQMASS\(\times\) & \\  & & & & (132.14/96.06) & \\ \hline \multirow{7}{*}{Population density (Pop\_dens)} & \multicolumn{2}{c}{A variable that represents the province’s population density relative to its size. (Unit/km\({}^{2}\))} & \multirow{7}{*}{2012} & \multirow{7}{*}{Office of the National Economic and Social Development Council (NESDC)} & \\  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \hline \multirow{7}{*}{Independent Variables} & \multirow{7}{*}{Industrial density (Indus\_dens)} & \multirow{7}{*}{2012} & \multirow{7}{*}{2017} & \multirow{7}{*}{Thailand Industrial} & \multirow{7}{*}{+/-} \\  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \hline \multirow{7}{*}{Energy consumption per capita (Energy\_cons\_pc)} & \multicolumn{2}{c}{A variable that shows the province’s economic activities, using energy consumption per capita consumption per capita as an indicator (KWh/person)} & \multicolumn{2}{c}{Metropolitan Electricity} & \multirow{7}{*}{+} \\  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \cline{3-5}  & & & & & \\ \hline \end{tabular}
\end{table} 
Table 4: Description of the data. three spatial random effects models are used: the Spatial Lag Random Effects Model (SLM), the Spatial Error Random Effects Model (SEM), and the Spatial Durbin Random Effects Model (SDM). The non-spatial random effects model is used to provide a benchmark for the other models and is expressed as follows:  
\[ \begin{array}{l}LnPM_{2.5 it}=a+\beta_{1}LnPop\_dens_{it}+\beta_{2}LnGPPpc_{ it}+\beta_{3}LnGPPpc_{it}^{2}\\ \hskip 14.226378 pt+\beta_{4}LnIndus\_dens_{it}+\beta_{5}LnEnergy\_cons\_pc_{it}+ \mu_{i}+\lambda_{i}+\varepsilon_{it}\end{array}  \tag{4}\]  
Here, \(i\) denotes the province; \(t\) denotes the time periods (2012, 2017, and 2022); \(\mu_{i}\) is the spatial fixed effects, indicating the city-specific and time-invariant variables that are not included in the model. \(\lambda_{i}\) is the time-fixed effects, indicating time-specific and city-invariant variables that are not included in the model and must be controlled for; and \(\varepsilon_{it}\) is the random error. The first spatial random effects model applied in this study is the SLM, which captures the spatial effects of neighboring regions, known as the spatial spillover effect. This model is denoted in Equation (5). \[