## 4 Results and Discussion
### Long- and Short-Run Effect Test Analysis  
To extend the analysis from the cointegration results to a more granular examination of the long- and short-run dynamics, it is critical to assess the implications of the FARDL model across different time horizons. The results of the cointegration tests have confirmed a robust long-term relationship between the key variables, indicating that despite temporary deviations, these variables converge towards a stable long-run equilibrium. In this context, the subsequent examination of short-run dynamics will provide valuable insights into the immediate, transient effects of trade policy, energy efficiency, and other influencing factors on CO\({}_{2}\) emissions. Conversely, the long-run estimates will capture the enduring, equilibrium adjustments that unfold over time. Table 4 offers a detailed presentation of these findings, facilitating a comprehensive understanding of how the determinants impact CO\({}_{2}\) emissions over both short and long durations. These results highlight not only the elasticity of CO\({}_{2}\) emissions in the short term but also the broader, sustained effects of the key variables in shaping South Korea's long-term environmental outcomes. As demonstrated in Table 4, short-term effects of South Korea's trade policy are marked by increased industrial activity, particularly in energy-intensive sectors such as manufacturing and petrochemicals, which leads to a rise in CO\({}_{2}\) emissions. This outcome is largely attributable to the rapid expansion of production capacities and heightened energy consumption facilitated by trade liberalization ([PERSON] et al. [65]; [PERSON] et al. [66]). The opening of markets and greater export activity, in the absence of strict environmental regulations, tends to elevate emissions, as highlighted by [PERSON] et al. [67] and [PERSON] et al. [68]. These studies observe that the initial phases of trade liberalization contribute significantly to CO\({}_{2}\) emissions as industries scale up to meet growing international demand. In contrast, over the long term, the relationship between trade policy and CO\({}_{2}\) emissions shifts as energy efficiency measures and technological advancements are gradually integrated. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Statistical Value** & **Lower Critical Value** & **Upper Critical Value** \\ \hline \(t\)-statistical test & \(-\)7.742 *** & \(-\)2.58 & \(-\)4.23 \\ F-statistical test & 21.218 *** & 3.07 & 4.44 \\ \hline \hline \end{tabular} Note: *** 1% significance level.  
\end{table} 
Table 3: Results of cointegration test. adoption of environmental standards within trade agreements, alongside innovations in green technologies, plays a critical role in reducing the carbon intensity of production. [PERSON] et al. [69] and [PERSON] et al. [70] provide evidence supporting this, demonstrating that trade policies, when aligned with environmental regulations, can reduce the energy intensity of exports and result in declining CO2 emissions over time. This aligns with the findings of the FARDL model in this study, which shows a negative long-term impact of trade policy on CO2 emissions. The primary distinction between this study and prior research lies in the treatment of the transitional phase. While earlier studies acknowledge the initial rise in emissions due to trade liberalization, this study offers a more detailed perspective by emphasizing the long-term mitigating effects of energy efficiency. Both studies converge on the conclusion that trade policies can have differing impacts across time horizons, with short-term increases in emissions ultimately offset by long-term reductions driven by technological progress and regulatory improvements. In the short term, energy efficiency has a negative effect on South Korea's CO2 emissions, primarily by reducing the energy intensity of production processes, particularly within energy-demanding industries such as manufacturing.