## 3 Variables and Model  
### Variables  
Independent variable: Carbon dioxide emissions serve as a critical indicator of South Korea's environmental sustainability, closely linked to the country's industrial composition, energy consumption patterns, and policy frameworks. As a highly industrialized nation with significant reliance on fossil fuels, South Korea has experienced elevated levels of greenhouse gas emissions, positioning CO2 emissions as a prominent measure of its environmental impact. Studies by [PERSON] [34], [PERSON] and [PERSON] [35], and [PERSON] et al. [36] emphasize the strong relationship between CO2 emissions, energy use, and economic growth in South Korea. The nation's rapid urbanization and industrial expansion have driven emissions upward, although recent investments in green technologies and energy-efficient practices have begun to temper this trajectory. Despite these advancements, South Korea remains among the world's leading CO2 emitters, highlighting the urgency of transitioning to a low-carbon economy to meet international climate objectives. The government's commitment to reducing CO2 emissions by 40% by 2030, relative to 2018 levels, underscores the centrality of CO2 as a metric for both environmental performance and policy direction. Initiatives such as the Korean Emissions Trading System reinforce the pivotal role of CO2 emissions in guiding South Korea's sustainable development strategy ([PERSON] et al. [37]). Consequently, CO2 emissions are not only a key indicator of environmental sustainability but also serve as a fundamental variable in assessing the broader economic-environmental nexus in academic research. Their inclusion in this analysis reflects the country's ongoing efforts to balance robust economic growth with stringent environmental responsibilities. Core variable: Trade policy and energy efficiency are key determinants of South Korea's carbon dioxide emissions, particularly due to the country's position as a heavily industrialized and export-driven economy. Recent authoritative studies highlight that South Korea's liberal trade policies, while driving economic growth, have also led to elevated CO2 emissions. This is largely due to the energy-intensive nature of key industries such as steel and petrochemicals ([PERSON] and [PERSON] [38]; [PERSON] et al. [39]; [PERSON] [40]). The expansion of exports, facilitated by trade liberalization, has resulted in increased energy consumption and, consequently, higher emissions. However, evidence also suggests that the incorporation of energy efficiency measures within trade policies can counteract this upward trend in emissions. For example, [PERSON] and [PERSON] [41] and [PERSON] and [PERSON] [42] demonstrate that advancements in energy efficiency, spurred by domestic regulations and international environmental agreements, have reduced the energy intensity of South Korea's exports. This shift has facilitated a partial decoupling of economic growth from CO2 emissions, marking an important step towards sustainability. Further, the adoption of cutting-edge technologies and the implementation of stringent energy efficiency standards--promoted through various trade agreements--have enabled South Korean industries to lower CO2 emissions per unit of output ([PERSON] [43]; [PERSON] [44]; [PERSON] et al. [45]). Thus, while trade expansion has traditionally been linked to higher emissions, these findings underscore the positive impact of integrating energy efficiency into trade frameworks. Moving forward, the alignment of trade policies with robust energy efficiency standards will be crucial to South Korea's pursuit of long-term carbon reduction goals and sustainable economic growth. Control variable: Economic growth, urbanization, industrialization, foreign direct investment, and green technology innovation are pivotal drivers of South Korea's CO2 emissions.