## 3 Research Methodology
### Long- and Short-Run Effects Analysis  
Based on the results presented in Section 4.1, the application of the CS-ARDL approach in this study is both appropriate and well-founded due to its robust capability to address endogeneity, cross-sectional dependence, and slope heterogeneity among the constructs examined. The CS-ARDL method is particularly well-suited for analyzing panel data from OECD countries, as it effectively captures the dynamic relationships and interactions among CO2 emissions, renewable energy, environmental taxes, and other control variables. By accounting for the complexities and interdependencies inherent in the data, the CS-ARDL approach ensures a comprehensive and reliable analysis, thereby enhancing the validity and robustness of this study's findings. The detailed results are presented in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**CIPS Test**} & \multicolumn{2}{c}{**M-CIPS Test**} \\ \cline{2-5}  & **Level** & **1 st Level** & **Level** & **1 st Level** \\ \hline ca & \(-1.277\) & \(-2.968\) *** & \(-1.007\) & \(-3.813\) *** \\ re & \(-1.693\) & \(-4.117\) *** & \(-1.647\) & \(-5.093\) *** \\ en & \(-2.719\) *** & \(-3.515\) *** & \(-3.013\) *** & \(-4.453\) *** \\ gr & \(1.401\) & \(4.933\) *** & \(1.357\) & \(5.739\) *** \\ in & \(-1.329\) & \(-7.323\) *** & \(-1.442\) & \(-7.946\) *** \\ fdi & \(1.158\) & \(6.849\) *** & \(1.163\) & \(6.334\) *** \\ ur & \(-4.964\) *** & \(-7.425\) *** & \(-4.117\) *** & \(-7.082\) *** \\ ec & \(0.937\) & \(6.148\) *** & \(1.061\) & \(6.464\) *** \\ \hline \end{tabular} Note: *** 1% significance level.  
\end{table} 
Table 4: Results of unit root test. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Method** & **Without Break** & **Mean Shift** & **Regime Shift** \\ \hline \(Z_{\text{op}}\)(n) & \(-8.259\) *** & \(-7.973\) *** & \(-7.764\) *** \\ \(p\)-value & \(0.000\) & \(0.000\) & \(0.000\) \\ \(Z_{\text{tr}}\)(n) & \(-7.505\) *** & \(-7.106\) *** & \(-7.291\) *** \\ \(p\)-value & \(0.000\) & \(0.000\) & \(0.000\) \\ \hline \end{tabular} Note: *** 1% significance level. ca = f(re, en, gr, in, fdi, ur, ec).  
\end{table} 
Table 5: Results of cointegration test. Table 6 presents the findings of the long- and short-run effects analyses using the CS-ARDL approach, revealing the significant long-run negative impacts of renewable energy and environmental taxes on CO2 emissions, with coefficients of \(-\)0.258 and \(-\)0.175, respectively. These results are consistent with theoretical expectations and align with the existing literature, such as the studies by [PERSON] et al. (2018), [PERSON] et al. (2018), [PERSON] et al. (2018), and [PERSON] and [PERSON] (2018), which, similarly, demonstrate the efficacy of renewable energy adoption and environmental taxes in reducing carbon emissions. The negative coefficients indicate that increased consumption of renewable energy and higher revenues from environmental taxes contribute to substantial long-term reductions in CO2 emissions, emphasizing the importance of sustainable energy policies and fiscal measures in combating climate change. In the short run, renewable energy and environmental taxes continue to exhibit negative effects on CO2 emissions, with coefficients of \(-\)0.292 and \(-\)0.169, respectively. This consistency between the short- and long-term effects underscores the immediate and enduring impact of these variables on emission reductions. The immediate effect of renewable energy reflects its rapid potential to replace fossil fuels, while the effect of environmental taxes suggests a swift incentive for cleaner production practices and technological innovations. The analysis of the control variables shows diverse impacts on CO2 emissions. Both industrialization and urbanization exhibit positive coefficients in the long and short run, indicating that these factors contribute to increased emissions. These findings are consistent with previous studies by [PERSON] and [PERSON] (2018), [PERSON] and [PERSON] (2018), and [PERSON] et al.