< PreviousMin-Joon Kim •384• (2013) reported symmetric and significant effects of oil price shocks on trade in Malaysia, Singapore, and Japan during 1999–2011, in both the short and long run. Using a Global VAR (GVAR) model, Allegret et al. (2015) analyzed the impact of oil price shocks on the trade balances of 30 major economies over the period 1980–2011. The results showed that trade balances responded differently depending on the type of oil shock. Likewise, Algaeed (2020) found that oil price shocks had a symmetric effect on the Saudi Arabian economy from 1970 to 2018, with particularly strong effects in the long run. In fact, since the effects of oil price fluctuations on the trade balance varied in both sign and magnitude, many studies emphasized their asymmetric nature (e.g., Rafiq et al., 2016; Vatsa and Baek, 2024; Baek and Nam, 2025). Baek and Kwon (2019) found asymmetric effects of oil price shocks on the trade balance in six major African economies, particularly in the long run. Moshiri and Kheirandish (2024) concluded that the asymmetric nature of oil price shocks led to varied trade responses across regions, with short-term effects being more volatile and long-term impacts depending on trade structure. In addition, some studies have found that oil price shocks do not significantly affect trade flows in either the short or long run. For instance, Korhonen and Ledyaeva (2010) found no strong link between oil price fluctuations and trade balances in oil-exporting countries of Eastern Europe and the former Soviet Union. Similarly, Berument et al. (2010) reported weak or insignificant effects of oil prices on trade balances in Middle Eastern countries. These results suggest that trade flows may be insensitive to oil shocks due to factors like macroeconomic policies, long-term contracts, or flexible exchange rates, highlighting the role of country-specific structures in shaping these effects. Ⅲ. Methodology According to Bahmani-Oskooee and Goswami (2004) and Bahmani-Oskooee and Ardalani (2006), the traditional export-import demand function—is typically associated Energy Prices and Export–Import Behavior: The Vietnam–Korea Perspective •385• with relative income and price measures. However, estimating price elasticity using this traditional approach is no longer appropriate, as export and import prices cannot be accurately determined based on bilateral trade. This is because a country often exports different goods to different trading partners. Therefore, a more suitable approach is to assess the sensitivity of exports and imports to exchange rate fluctuations. In contrast, Baek and Nam (2025) argued that conventional export-import or trade balance models, which consider only two macroeconomic variables—exchange rate and income—may produce weaker empirical results by omitting the oil price variable, which is closely linked to trade. Based on the work of Bahmani-Oskooee and Goswami (2004), Bahmani- Oskooee and Ardalani (2006), and Baek and Nam (2025) incorporated the oil price variable into their model. In this section, we follow Baek and Nam (2025) to examine how oil price shocks and other macroeconomic variables affect export and import functions. Additionally, global events such as the 2008 financial crisis and the more recent COVID-19 pandemic may also influence the structure of the data (Kim, 2024; Zaghdoudi et al., 2023). We have incorporated these two events into our model. The export and import functions are represented by Equations (1) and (2). log log log log (1) log log log log (2) Where ( ) represents the real export (import) value of Vietnam to (from) Korea. Similarly, ( ) represents the real income of Korea (Vietnam). is defined as the bilateral real exchange rate between Vietnam Dong (VND) and Korean Won (KWR). Accordingly, an increase in means a decrease in VND. represents the world crude oil price. We include dummy variables, representing the global financial crisis in 2008 and representing the COVID-19 pandemic, to control for the impact of global events Min-Joon Kim •386• on trade. 1) Econometrically, we first interpret the short-run and long-run effects of the explanatory variables on the dependent variable by following the ARDL model proposed by Pesaran et al. (2001). It is well recognized that time series data are often associated with many unknown structural breaks, which may not be fully captured by the traditional ARDL framework. Furthermore, structural breaks in the data may also be influenced by global events such as the 2008 Asian financial crisis and the COVID-19 pandemic (Kim et al., 2024). To address this limitation, this study applies the Fourier ARDL (FARDL) model introduced by Yilanci et al. (2020). The Fourier function does not require prior information about the nature, frequency, or timing of structural breaks, nor does it require multiple parameters, thereby offering adequate size and power properties (Kirikkaleli et al., 2023; Syed et al., 2023). The incorporation of the Fourier trigonometric function allows the model to effectively capture smooth structural changes in the data, resulting in more efficient estimates compared to the standard ARDL model. In the context of bilateral trade between Vietnam and Korea during the period 2008–2024, structural changes may arise from events such as the Vietnam–Korea Free Trade Agreement (VKFTA) signed in 2015, fluctuations in global oil prices, the 2008 financial crisis, the US–China trade war, and the COVID-19 pandemic. These events can introduce smooth and cyclical structural changes in the trade data between the two countries. Therefore, the FARDL model is an appropriate and meaningful approach for examining the impact of oil prices on this trade flow. The FARDL model is represented by Equations (3) and (4). ∆ log Δ log Δ log Δ log Δ log (3) log log log log ρ ρ 1)Several empirical studies have also examined the impact of the global financial crisis and COVID-19, such as Baek (2014), Baek and Nam (2021), and Kim (2024).Energy Prices and Export–Import Behavior: The Vietnam–Korea Perspective •387• ∆ log Δ log Δ log Δ log Δ log (4) log log log log In Equations (3) and (4), represents the Fourier function. Yilanci et al. (2020) applied a single frequency for , as proposed by Ludlow and Enders (2000), where Θ sin Θ cos . Accordingly, the FARDL model is detailed in Equations (5) and (6) as follows: ∆ log Δ log Δ log Δ log Δ log (5) log log log log ρ ρ Θ sin Θ cos ∆ log Δ log Δ log Δ log Δ log (6) log log log log Θ sin Θ cos Here, the short-run estimated coefficients are denoted by for Equation (5) and for Equation (6). Similarly, the long-run coefficients for Equations (5) and (6) are given by to and to , respectively. and to represent the optimal lags of the models. 2) The amplitude and phase shift of the frequency component are denoted by Θ and Θ , respectively. , , and represent the Fourier frequency, trend, 2)The optimal lag length is selected based on the Akaike Information Criterion (AIC).Min-Joon Kim •388• and sample size, respectively. The Fourier frequency ( ), which ranges from 0.1 to 4.0 in increments of 0.01, helps identify an unknown number of structural changes occurring at unspecified points in the data. According to Christopoulos and Leon-Ledesma (2011), fractional frequencies are effective in detecting permanent breaks, while integer frequen- cies are associated with identifying temporary structural breaks. Meanwhile, is assigned the value 3.14. To establish cointegration in Equations (5) and (6), we apply two tests: the F-statistic and the t-statistic, as suggested by Pesaran et al. (2001) and Shin et al. (2014). 3) Ⅳ. Estimation Findings 1. Preliminary analysis We perform several preliminary tests to ensure the necessary conditions for applying the ARDL framework are met. First, the ARDL model requires that the variables be either stationary at level, (0), or at first difference, (1). To verify this, we apply the Dickey-Fuller GLS (DF-GLS) unit root test, with the results presented in Table 1. The findings confirm that all variables in the empirical model are either (0) or (1), indicating their suitability for ARDL estimation. Next, we employ the F-test and t-test to examine cointegration between the variables (Panel A of Table 2). At the 1% level, both the F-statistic and t-statistic for the export and import functions are statistically significant, confirming cointegration among the variables. Finally, an essential condition for applying the ARDL model is the absence of serial correlation in the residuals. We determine lag five as the optimal lag for equations (5) and (6) and conduct the Lagrange Multiplier (LM) test. The LM test results (Panel D, Tables 2 and 3) show no evidence of 3)The F-statistic tests the null hypothesis for Equation (5), and for Equation (6). Meanwhile, the t-statistic tests the hypotheses hypothesis and in the respective equations. When the values of the F- and t-statistics exceed the upper critical value, cointegration is confirmed.Energy Prices and Export–Import Behavior: The Vietnam–Korea Perspective •389• serial correlation at the 5% level. This confirms that the ARDL framework employed in this study is appropriate. 2. Export model results We begin our discussion with the long-run estimates presented in Panel B of Table 2. The result is quite surprising, as we find no significant long-run impact of crude oil price shocks on Vietnam’s export activities to Korea. Although the estimated coefficient of log , is negative, it is not significant at the 10% level. Regarding the real exchange rate, the positive estimated coefficient of log is statistically significant at the 10% level. This indicates that, in the long run, VND depreciation (appreciation) leads to an increase (decrease) in Vietnam’s export volume to Korea through a decrease (increase) in export prices—fully consistent with conventional economic theory. As for Korea’s real income, the positive coefficient of log is highly significant (1% level), indicating that Korea’s economic growth tends to promote Vietnam’s exports. The short-run results are presented in Panel C of Table 2. We find that oil price shocks affect Vietnam’s exports to Korea in the short run. However, this effect is positive—a result that appears counterintuitive. When crude oil prices rise, export costs also increase. <Table 1> Dickey-Fuller GLS unit root test results VariableLevelFirst differenceI (d) Real exports log 0.657 (13)–5.505 (0)***I (1) Real imports log –0.411 (1)–8.704 (0)***I (1) Vietnam’s real income log –4.769 (0)***I (0) Korea’s real income log 1.108 (13)–3.428 (2)***I (1) Real exchange rate log 0.355 (2)–1.871 (5)*I (1) Crude oil prices log –2.670 (1)***I (0) Note: Lag lengths in the DF-GLS test are selected using the Schwert Information Criterion (shown in parentheses). Critical values at the 1%, 5%, and 10% levels are –2.58, –1.94, and –1.62, respectively. Symbols ***, **, and * indicate significance at the 1%, 5%, and 10% levels.Min-Joon Kim •390• <Table 2> Results of FARDL model for Vietnam’s export to Korea CoefficientStd. ErrorProb. Panel A: Cointegration tests F-statistic 5.779*** –0.452 (–4.848)*** Panel B: Long-run results log –0.0270.0880.764 log 0.803*0.4170.056 log 2.020***0.7150.005 Constant–4.364***0.9000.000 Panel C: Short-run results ∆ log 0.0130.0910.889 ∆ log 0.174**0.0880.049 ∆ log ∆ log 0.1130.3260.730 ∆ log ∆ log ∆ log 0.685***0.1720.000 ∆ log –0.0350.1860.851 ∆ log –0.765***0.1810.000 0.0180.0220.397 –0.277***0.0580.000 –0.0100.0360.784 –0.0190.0230.425 Panel D: Diagnostic tests LMRESETCUSUMCUSUMSQ 0.233 0.255StableStable Note: t-values are in parentheses. The upper critical values for the F-statistic at the 1%, 5%, and 10% levels are 5.61, 4.35, and 3.77, respectively; for the t-statistic of , they are –4.37, –3.78, and –3.46. LM is the Lagrange Multiplier test for autocorrelation ( χ distribution). RESET tests for model specification. CUSUM and CUSUMSQ assess parameter stability. Symbols ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.Energy Prices and Export–Import Behavior: The Vietnam–Korea Perspective •391• Nevertheless, in the Korean market, Vietnamese goods may still maintain a competitive advantage over products from other countries. Furthermore, higher oil prices may lead to increased transportation costs and overall commodity prices, thereby raising the value of Vietnamese exports. Additionally, rising oil prices could signal an economic recovery in Korea, as they may reflect increased energy demand. This could increase demand for imports of consumer goods, components, and raw materials from Vietnam to support Korea’s manufacturing activities. In addition, Vietnamese export enterprises may not be immediately affected by the rise in oil prices due to existing inventories or trade contracts signed prior to the increase. As a result, export revenues may grow due to higher export prices, creating a temporary positive effect. Regarding the real exchange rate, even at the 10% level, the estimated coefficient of ∆ log is not significant, suggesting that it does not influence Vietnam’s exports in the short run—unlike the effect observed in the long run. This implies that Vietnam’s exports to Korea are relatively insensitive to short-term changes in the bilateral real exchange rate. Meanwhile, Korea’s real income has a significant short-run impact on Vietnam’s exports, although the nature of the effect differs. Several diagnostic tests are performed, including tests for serial correlation (LM tests), regression specification (RESET tests), and parameter stability (CUSUM and CUSUMSQ tests) (Panel D of Table 2 and Figure 1). These results strongly support the stability and optimality of the FARDL model. 3. Import model results We now turn to the import function, focusing on the long-run results (Panel B of Table 3). Surprisingly, although the estimated coefficients for , , and are positive, they are not statistically significant. This suggests that Vietnam’s import activities from Korea are not affected by shocks to crude oil prices, bilateral real exchange rates, or domestic real income in the long run. Thus, Vietnam’s imports are relatively insensitive to exchange rate fluctuations, and domestic income is not a major determinant of imports from Korea over the long term. Min-Joon Kim •392• <Table 3> Results of FARDL model for Vietnam’s import from Korea CoefficientStd. ErrorProb. Panel A: Cointegration tests F-statistic 7.278*** –0.249 (–5.439)*** Panel B: Long-run results log 0.0310.1070.776 log 0.0980.5510.859 log 0.1710.1940.380 Constant0.187***0.0650.005 Panel C: Short-run results ∆ log –0.0580.0690.398 ∆ log 0.306***0.0720.000 ∆ log 0.0970.0700.171 ∆ log 0.2070.2420.394 ∆ log ∆ log ∆ log 0.726***0.0580.000 ∆ log ∆ log 0.443***0.0870.000 –0.043*0.0260.093 0.054*0.0290.068 –0.0110.0170.508 Panel D: Diagnostic tests LMRESETCUSUMCUSUMSQ 1.774 0.124StableStable Note: t-values are in parentheses. The upper critical values for the F-statistic at the 1%, 5%, and 10% levels are 5.61, 4.35, and 3.77, respectively; for the t-statistic of , they are –4.37, –3.78, and –3.46. LM is the Lagrange Multiplier test for autocorrelation ( χ distribution). RESET tests for model specification. CUSUM and CUSUMSQ assess parameter stability. Symbols ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively.Energy Prices and Export–Import Behavior: The Vietnam–Korea Perspective •393• Regarding the short-run results (Panel C of Table 3), a positive impact of oil price shocks on Vietnam’s imports is observed. Although production and transportation costs often increase due to rising oil prices, Vietnam’s imports from Korea continue to grow to meet the increasing demand for domestic production and consumption. Moreover, key high-tech goods—such as machinery, equipment, and electronic components—which account for a large proportion of imports from Korea, have low price elasticity and are therefore not significantly affected by rising transportation costs in the short term. Therefore, despite higher oil prices, Vietnam’s imports from Korea tend to increase. We again observe that changes in the real exchange rate do not have a significant short-run <Figure 1> Results of CUSUM and CUSUMSQ tests Note: The figure displays stability test results for FARDL model parameters in export (a) and import (b) functions.Next >