## 4 Results and Discussion
### Robustness Test Analysis  
To validate the robustness of the empirical findings, this analysis applies three econometric techniques: fully modified ordinary least squares (FMOLS), dynamic ordinary least squares (DOLS), and canonical cointegration regression (CCR). These methods are designed to address potential econometric issues such as endogeneity and serial correlation, thereby ensuring the reliability and accuracy of the long-run coefficient estimates. FMOLS is particularly effective in adjusting for serial correlation and endogeneity, making it well-suited for dealing with small sample sizes and time series that are integrated. DOLS further enhances the robustness by incorporating leads and lags of differenced variables, which corrects for potential biases in ordinary least squares (OLS) and yields consistent estimates in the context of cointegrated relationships. Similarly, CCR transforms the original data before estimation to tackle endogeneity and serial correlation, providing additional robustness to the long-term estimates. By employing these three methods, the study ensures that the estimated long-run relationships, particularly those involving trade policy, energy efficiency, and CO2 emissions, are rigorously tested and validated. The results obtained from the FMOLS, DOLS, and CCR estimations, as presented in Table 5, confirm the consistency and robustness of the key findings, offering further assurance in the credibility and reliability of the conclusions drawn from the analysis.  
As evidenced in Table 5, all estimated coefficients are statistically significant at the 1% level, underscoring the robustness of the results across the FMOLS, DOLS, and CCR models. Notably, the negative coefficients for trade policy and energy efficiency across all models indicate that enhancements in both areas contribute to a reduction in CO2 emissions, thus improving environmental quality and promoting sustainability in South Korea. These findings are consistent with the baseline results and further confirm that policies designed to liberalize trade, when coupled with improvements in energy efficiency, have a substantial positive impact on reducing emissions. In the case of trade policy, these results suggest that the strategic integration of environmental regulations within trade agreements can play a pivotal role in mitigating the environmental footprint of industrial activities, particularly in sectors that are energy-intensive. Similarly, improvements in energy efficiency contribute directly to emissions reduction by lowering the energy consumption per unit of output across industries. This is particularly relevant for South Korea, where economic growth has traditionally been tied to energy-intensive manufacturing sectors. These findings resonate with previous studies that highlight the dual benefits of trade liberalization and energy efficiency in reducing environmental degradation ([PERSON] et al. [87]; [PERSON] [88]; [PERSON] and [PERSON] [89]). The consistency of the results across FMOLS, DOLS, and CCR further enhances the credibility of the conclusions, as these methodologies are specifically designed to correct for issues such as endogeneity and serial correlation, ensuring that the estimated relationships reflect true long-term effects. Consequently, the negative coefficients not only corroborate the baseline findings but also provide additional evidence that policies aimed at improving energy efficiency and trade regulation can be key drivers of long-term environmental sustainability in South Korea. Thus, the results offer robust support for policy frameworks that emphasize sustainable trade practices and technological innovation in energy efficiency as essential components of national and global efforts to reduce CO\({}_{2}\) emissions.