The Asymmetric Effects of Third-Country Exchange

This study examines the asymmetric effects of third-country exchange rate volatility on Turkish-German commodity trade. We analyzed annual time-series data spanning 1980-2022 for 79 (93) Turkish export (import) industries. The ARDL model found that third-country volatility, using the lira-dollar, had a significant short-term symmetric effect on 59 (67) Turkish export (import) industries. The NARDL model found that third-country volatility had a short-run asymmetric effect on trade volumes in more than half of the Turkish export and import industries. However, the short-run asymmetric effects turned into long-run asymmetric effects in about 50 percent of the industries. The results establish that nonlinear models lead to more significant short-run and long-run effects. The empirical evidence shows that the asymmetric assumption alone is insufficient, and third-country volatility should also be considered. The results suggest that all traders should consider how policy changes in a third-country may affect cross-country trade when designing their trade policies in a diversified trade environment.

rate volatility. When the exchange rate volatility increases, an x percent increase in volatility may decrease a country's exports by y percent. However, when the volatility decreases by x percent, that country's exports may increase by more than y percent, as traders may become more optimistic about the possibility of more stable exchange rates. Bahmani-Oskooee, Ridha Nouira, and Sami Saafi (2019) argued that the asymmetric response to increased volatility occurs because traders may assume that a decline in volatility is short-lived and do not respond to it. In particular, this "waitand-see" approach leads to an asymmetric response. The authors concluded that the asymmetric effects of exchange rate volatility are due to changes in traders' expectations, firms' pricing policies to hedge against uncertainty, and downward price rigidity. Moreover, empirical evidence also supports the notion that trade flows respond asymmetrically to exchange rate dynamics, and the same is expected of exchange rate volatility. Furthermore, Heba Ali (2019) argued that investors weight losses more heavily relative to economic gains (returns); they demand higher compensation for holding stocks with higher downside risk, leading to asymmetric behaviour. Following the same concept, Bahmani-Oskooee, Nouira, and Saafi (2019) argued that traders respond asymmetrically to exchange rate volatility when they weight losses higher than gains from holding foreign exchange to hedge against future transactions. Given this idea, this paper fills the existing research gap in the empirical international economics literature by examining the asymmetric impact of thirdcountry exchange rate volatility on Turkish-German commodity trade. To the best of the author's knowledge, this is the first empirical study to explore the asymmetric effects of third-country exchange rate volatility on Turkish-German commodity trade.

Methodology
The impact of exchange rate dynamics on commodity flows is often estimated using export and import demand models. Each model includes a scale variable (i.e., real income) and a relative price term (i.e., the real exchange rate). In addition, we have included a measure of exchange rate volatility that accounts for the so-called "third-country effect". We closely follow Cushman (1986), Bahmani-Oskooee, Hegerty, and Xi (2016), Bahmani-Oskooee, Iqbal, and Khan (2017), Bahmani-Oskooee and Aftab (2018), Abbasi and Iqbal (2020), and Usman, Apergis, and Anwar (2021), who all considered external volatility risks. In this study, we specify the following export and import demand equations: , = 0 + 1 + 2 + 3 + 4 + (2) The data are constructed from the perspective of Turkey; therefore, , and , in Equations (1) and (2) denote real export flows from Turkey to Germany and real import flows from Germany to Turkey for a given commodity i in a year t.
represents a structural dummy variable that captures the effect of the trade liberalization reforms on bilateral trade flows (i.e., = 0 for years from 1980-1983 and = 1 for years from 1984-2022). Theoretically, we expect 1 > 0 and 1 > 0, showing that trade liberalization reforms in Turkey can positively affect commodity trading between the two countries. We also introduced other country-specific dummy variables that were not statistically significant. The export volume ( , ) in Equation (1) is determined by three explanatory variables: Germany's real income ( ), the real lira-euro exchange rate ( ), and the real lira-dollar exchange rate volatility ( ). Similarly, import volume ( , ) in Equation (2) is determined by three explanatory variables: Turkey's real income ( ), the real lira-euro exchange rate ( ), and the real lira-dollar exchange rate volatility ( ). We theoretically expect 2 > 0 and 2 > 0, showing that an increase in real income within Germany and Turkey will stimulate commodity trade between the two countries. As outlined in Appendix A.2., the construction of the variable ensures that an increase in value implies a real depreciation of the lira against the euro. Given this definition, we anticipate that Turkish exports will increase in response to lira depreciation, thus lowering the price of Turkish commodities in euros. Hence, we theoretically expect 3 > 0. In contrast, we expect 3 < 0 as lira depreciation reduces imports. To account for the third-country effect, Equations (1) and (2) feature the inclusion of a real exchange rate volatility measure, represented by , which denotes the volatility of the Turkish lira against the U.S. dollar. This volatility measure could positively or negatively impact Turkish commodity trade with Germany, reflecting the associated risks traders face and the degree of substitution for cross-border traded products. The present study follows the approach of Bahmani-Oskooee and Aftab (2017,2018) to derive the measure of thirdcountry exchange rate volatility employing the generalized autoregressive conditional heteroskedasticity (GARCH 1, 1) approach. The variable of interest, REX, is assumed to be random and follow an AR(1) process as follows: = 0 + 1 −1 + (3) In equation (3), is white noise with ( ) = 0 and 2 ( ) = ℎ 2 . To predict the variance of , the conditional variance of (ℎ 2 ) can be estimated using the following specification: ℎ 2 = 0 + 1 −1 2 + 2 −2 2 + 3 −3 2 + ⋯ + − 2 + 1 ℎ −1 2 + 2 ℎ −2 2 + 3 ℎ −3 2 + ⋯ + ℎ − 2 (4) To determine the forecast values of the conditional variance (ℎ 2 ), we used the GARCH (p,q) model according to Equation (4) as a measure to capture the time-varying volatility of the real exchange rate. Both Equations (3) and (4) are estimated simultaneously after an autoregressive conditional heteroscedasticity (ARCH) effect is detected. In Equation (4), the order of the GARCH model is determined by the significance of the parameters βs and s. As in most cases, a GARCH (1,1) specification is appropriate as in our case. The estimation results of the parsimonious GARCH (1,1) model are presented below, where their respective p-values indicate the significance of the parameters in parentheses: = 0.6646 + 0.7595 −1 + (0.0150) (0.0000) ĥ 2 = 0.016015 + 0.103758 ̂− 1 2 + 1.036535 ĥ −1 2 (0.0189) (0.0442) (0.0000) The real exchange rate volatility measure is illustrated in Figure 1 to provide further insights into the analysis. In the context of evaluating the short-run effects of the explanatory variables on commodity trade, traditional Autoregressive Distributed Lag (ARDL) models (1) and (2) are not suitable as they are long-run equations. Therefore, a widely adopted approach is to specify Equations (1) and (2) as error-correction representations, enabling the estimation of the explanatory variables' short-run impacts on trade volumes. Consistent with this approach, we follow Hashem, M. Pesaran, Yongcheol Shin, and Richard J. Smith (2001) and use the error-correction models (5) and (6)  −1 + 2 −1 + 3 −1 + 4 −1 + ′ (6) In the above error-correction specifications, the short-term effects are captured by the first-differenced variables, while the normalized coefficients capture the long-term effects ( . . , 2 − 4 on 1 in (5) and 2 − 4 on 1 in (6)). For instance, the short-run effect of real lira-dollar volatility on export volumes is reflected in the estimate of 5 in (5) and on import volumes by 5 in (6). The models presented in Equations (5) and (6) are known as symmetric or linear ARDL models developed by Pesaran, Shin, and Smith (2001), which offer several advantages over alternative estimation methods. For example, they enable unbiased estimation for small samples and simultaneous estimation of short and longrun coefficients. In addition, mixed orders of integration can be considered, provided that none of the variables has an I(2) order. However, cointegration must be present for the long-run coefficients to be meaningful. Pesaran, Shin, and Smith (2001) proposed the F-test to test for cointegration, which employs new critical values. This test involves upper and lower critical bounds for a given significance level and several exogenous variables (k). The null hypothesis of no cointegration is rejected if the calculated value of the F-statistic exceeds the critical upper bound and vice versa. Bahmani-Oskooee and Aftab (2017) criticized previous empirical studies that assumed that exchange rate uncertainty affects trade flows symmetrically. They showed that exchange rate dynamics violate this strict assumption and can have asymmetric effects on trade flows. In this study, our primary objective is to examine whether the effect of third-country exchange rate volatility on Turkish-German commodity trade is symmetric or asymmetric. To achieve this, we follow Yongcheol Shin, Byungchul Yu, and Matthew G. Nimmo (2014) by decomposing an increase from a decrease in volatility. We begin by constructing ∆ , which includes both positive and negative fluctuations. Subsequently, we apply the concept of partial sums to generate two new series, namely the partial sum of positive variations (POS) and the partial sum of negative variations (NEG).
Researchers have widely used the decomposition of exchange rate volatility using the partial sum approach. Notable recent studies that have employed this method include Bahmani-Oskooee andAftab (2017, 2018), Usman, Apergis, and Anwar (2021), and Iqbal, Aziz, and Nosheen (2022), among others. Following the same procedure, we utilize the method above to construct POS and NEG series for the lira-dollar volatility, denoted as and , respectively.
, 0) (8) Following the decomposition of the lira-dollar exchange rate volatility measure ( ) into its positive and negative components, we proceed by incorporating the decomposed components into Equations (5) and (6), resulting in Equations (9) and (10): The utilization of partial sum variables in Equations (9) and (10) renders them nonlinear error-correction specifications, commonly referred to as Nonlinear Autoregressive Distributed Lag (NARDL) models, whereas Equations (5) and (6) are linear or symmetric ARDL models. The linear ARDL framework developed by Pesaran, Shin, and Smith (2001) can be extended to NARDL models. In a nonlinear ARDL approach, the F-test critical values proposed by Pesaran, Shin, and Smith (2001) can still be applied to determine the joint significance of the lagged-level variables.
To investigate whether there is an asymmetry between the positive and negative effects of volatility, we apply the Ordinary Least Squares (OLS) technique to estimate Equations (9) and (10) and perform asymmetry tests. The purpose of these tests is to determine whether the effects of volatility increases and decreases are the same or whether they are asymmetric. Specifically, we conduct short-run and long-run Wald tests to examine whether the effects of an increase in uncertainty are equal to those of a decrease in uncertainty or whether they are asymmetric (Bahmani-Oskooee and Aftab, 2017). In particular, (1) Short-run adjustment asymmetry occurs when POS has a different number of lags than NEG.
(2) Short-run asymmetric effects occur when the sign/size of the estimates associated with POS and NEG differ for each lag order j.
(3) Short-run cumulative/joint/impact asymmetry can be detected when the sum of estimates associated with POS is statistically different from the sum of estimates associated with NEG (∑̂5 ≠ ∑̂6 in Equation (9) and ∑̂5 ≠ ∑̂6 in Equation (10)). (4) The long-term asymmetric effect is confirmed when the normalized estimate associated with POS and NEG is statistically different. The Wald test is applied to test the hypothesis of long-run asymmetry for model (9), i.e., (̂4 −̂1 ⁄ ≠̂5 −̂1 ⁄ ). In addition, the long-run asymmetry hypothesis is tested using the Wald test for model (10), i.e., (̂4 −̂1 ⁄ ≠̂5 −̂1 ⁄ ).

Empirical results
Usman, Apergis, and Anwar (2021) demonstrated the suitability of Equations (9) and (10) for estimating NARDL export and import models, respectively. In addition, we estimate linear ARDL models [(5) & (6)] to compare linear and nonlinear ARDL models. The estimation uses annual time-series data spanning 1980-2022 for 79 exporting and 93 importing industries. The exporting industries account for 86.73% of Turkey's total exports to Germany, while the importing industries account for 94.91% of Turkey's total imports from Germany. Although the ARDL approach does not require pretesting of variables for stationarity, we perform the Augmented Dickey-Fuller (ADF) test to confirm that no variables are I(2). The ADF unit root test revealed that our variables are mixed: I(0) and I(1). This result necessitates the use of the ARDL bounds test for empirical analysis. A maximum of three lags are applied to each first-differenced variable, as annual data are used, while Akaike's Information Criterion (AIC) is applied to determine the proper lag orders. In the analysis of annual time-series data, it is possible to include a maximum of 4 lags. However, prior studies, such as Bahmani-Oskooee and Yongqing Wang (2007Wang ( , 2008 and Bahmani-Oskooee, Harvey, and Hegerty (2013), employed only 2 lags. It is worth noting that cointegration analysis tends to be more effective with longer time-series data rather than with many observations (Craig Hakkio and Mark Rush, 1991). Moreover, each industry's reported coefficient estimates and associated diagnostic tests are among the optimal models. 4.1 Linear export model Table 1 contains estimated coefficients of the linear export model (5), and Table 2 shows its associated diagnostic tests. According to Bahmani-Oskooee and Marzieh Bolhassani (2014), if an exogenous variable has at least one significant lagged effect at the 10% (5%) significance level in the short-run, we refer to this as "Yes" in Table 1. Conversely, a "No" indicates no significant short-run lagged coefficient. The short-run estimates show that Germany's income ( ) has at least one significant short-run effect in 67 industries, reflecting the significance of the income effect on export volumes. The short-run estimates also demonstrate that the real bilateral exchange rate ( ) has a significant shortrun impact on the exports of 65 Turkish industries. The diagnostics show that most export industries are small in terms of their export share, but some large export industries are also included, e.g., industries coded 711, 719, 732, and 841.
More importantly, the third-country volatility effect (lnVOL TRUS ) was observed in 70 cases, where at least one short-run estimate was significant. According to these results, the short-term third-country effect dominates Turkish exports to Germany. Do these short-run estimates hold in the long-run? To answer this question, we turn to the normalized longrun coefficients in Table 1. Our long-run estimates demonstrate that the real bilateral exchange rate significantly impacts 37 industries. This estimate has a positive sign for 30 export industries and a negative sign for seven exporting industries. A negative sign means that a lira depreciation will lead to fewer exports to Germany. Similarly, Germany's income (lnY GR ) has a significant estimate in 51 cases. The long-run coefficient has an expected positive sign in 39 industries, suggesting that Germany imports more goods from Turkey as its economy grows. In the remaining 12 cases, however, the coefficient has a negative sign. This could be because Germany produces more substitute products at home and imports fewer products from Turkey (Bahmani-Oskooee, 1986). In addition, the effect of the trade liberalization reforms is significant in 55 industries, negative in 9 industries, and positive in 46 industries. As for the third-economy effect, the long-run findings show that the real lira-dollar volatility (lnVOL TRUS ) has a significantly negative estimate in nine small industries. As the lira-dollar exchange rate becomes more volatile in these export industries, Turkish importers shift from Germany to the U.S. This must be a risk-averse community of traders who benefit from increasing their revenues today to compensate for losses in the future. Nevertheless, there are 61 cases where lira-dollar volatility has a significant positive coefficient, suggesting that Turkish importers of these goods substitute U.S. products with German products when the lira-dollar exchange rate is highly volatile; this confirms the long-run substitution effect. Since the long-run results depend on the presence of cointegration, we turn to Table 2. We compare the upper critical bounds of the F-statistic of Paresh K. Narayan (2005) with the calculated values of the F-statistic listed in the first column of the diagnostics in Table 2. The F-test confirms cointegration for all models at the 5% (10%) significance levels. Based on ECMt-1, cointegration is also detected for all specifications using the critical values of Anindya Banerjee, Juan Dolado, and Ricardo Mestre (1998). Additionally, the adjusted R 2 shows that all models are well-fitted. The Lagrange Multiplier test (LM) is applied to check for serial correlation. The associated diagnostic is significant in only seven cases, meaning that only seven functions are affected by serial correlation. The Ramsey RESET test detects model misspecification, and the associated diagnostic is significant in only six cases. Hence, this confirms that our model is appropriately specified in most industries. In addition, CUSUM and CUSUMSQ tests are utilized to establish each function's short-run and longrun stability. Due to the large estimates, we report stable cases as "S" and unstable cases as "US". Based on the CUSUM or CUSUMSQ diagrams, the proposed specification is stable in almost all cases. Thus, we conclude that the results of the linear export specification are meaningful. Table 3 presents the empirical estimates of the linear import model (6), and Table 4 displays its associated diagnostics. The findings indicate that the third-country effect ( ) has at least one significant short-run lag estimate in 73 cases. Are the short-run estimates consistent in the long-run? The long-run coefficients reveal that the third-economy effect ( ) has a significant impact on 50 Turkish import industries. This volatility effect has a positive (negative) sign in 15 (35) industries. The positively affected industries include the two largest Turkish import industries, coded 541 and 581, which import about 12.57% of their products from Germany. In contrast, the three largest import industries, coded 711, 719, and 732, which import approximately 34.21% of goods from Germany, are negatively affected by third-country risk. Intuitively, the analysis suggests that Turkey continues to grow and relies more on imports from the United States to meet its increasing local demand. Hence, there is a strong indication that the U.S. dollar (external currency risk) should be included in the analysis to better understand Turkey's actual import patterns from Germany. As for the other explanatory variables in the linear import specification, the 1984 trade liberalization reforms (DM) impacted Turkish import industries in 62 cases. Moreover, improved Turkish economic activity ( ) favours German products in Turkey in 49 significant cases. Finally, the long-run impact of the real bilateral exchange rate (lnREX) is positive (negative) in 13 (60) cases. The expected negative estimate suggests that the depreciation of the lira against the euro hampers Turkish imports from Germany for most industries. Once again, the validity of the linear import model estimates depends on the associated diagnostic tests being passed. The F or ECMt-1 test detects cointegration in those industries whose exogenous variables have significant normalized long-run coefficients. Due to the high adjusted R 2 , almost every specification has a good fit. In most cases, the LM and RESET diagnostics confirm autocorrelation-free residuals and appropriate optimum econometric specifications. Finally, the CUSUM and CUSUMSQ tests indicate stable model estimates.

Nonlinear export model
We will now examine whether the effects of real exchange rate volatility on trade flows exhibit asymmetric effects. To this end, we tested the short-run and long-run asymmetry hypotheses using the Wald-SR TRUS and Wald-LR TRUS tests. We found that the short-run adjustment is asymmetric in most cases due to the lag order (j) associated with increased (∆ ) and decreased (∆ ) volatility not matching. In all cases, we observed short-run asymmetric effects of third-country volatility using the magnitude or sign difference between ∆ and ∆ . Furthermore, we also identified third-country short-run joint asymmetry, which is observed when the sum of coefficients attached to ∆ differs from the sum of coefficients attached to ∆ . Asymmetric effects of lira-dollar volatility can be observed using the Wald-SR TRUS test estimates for 63 industries (see Table 6). However, these significant estimates are notable for small and large Turkish export industries. These major export industries include 684 (aluminium), 711 (power generation machinery), 719 (machinery and appliances), 732 (road motor vehicles), and 841 (clothing except fur clothing), which together account for about 49.1% of exports. Regarding the third-country volatility effects, the thirdeconomy effect is notable in 41 Turkish export industries where POS TRUS or NEG TRUS is statistically significant at 5% (10%) significance levels. Based on the difference in magnitude or sign between the POS TRUS and NEG TRUS estimates, we observe long-run asymmetric effects for all small and large export industries for the third-economy. However, the significant effects associated with the third-economy that depends on Wald-LR TRUS are noticeable in 49 industries (see Table 6). For the nonlinear export specification (9), we first consider the short-run effects of real exchange rate uncertainty and the third-economy effect. According to the NARDL empirical estimates in Table 5, the short-run effect of the thirdeconomy was found either by ∆ and ∆ in 61 cases. However, the short-run third-economy effect was found in 70 industries in the earlier linear modelling framework. The analysis suggests that the decrease in significant cases is due to the gradual nonlinear adjustment of the third-economy effect. Furthermore, the volatility effect for the third-economy reveals remarkable asymmetric effects on export flows. The long-run estimates of the NARDL export model show that the real bilateral exchange rate (lnREX) significantly impacts 35 industries. This estimate has a positive sign for 24 and a negative sign for 11 export industries in Turkey. Specifically, the positive coefficient of the real exchange rate shows that the depreciation of the Turkish lira against the euro favours more exports from Turkey to Germany. In contrast, the negative estimate of the real exchange rate means that the lira's depreciation leads to fewer goods exports from Turkey to Germany. The long-run estimates also show that German income (lnY GR ) has a significant positive estimate in 45 cases, suggesting that Germany imports more products from Turkey as its economy grows. Conversely, the income coefficient has a negative sign in 8 industries. This could be because Germany produces more substitute products domestically and imports fewer products from Turkey (Bahmani-Oskooee, 1986). Moreover, trade liberalization reforms (DM) are significant in 55 cases, negative in 53 small and large industries and positive in 2 small industries. As for the third-economy effect, the long-run estimates of negative volatility (NEG TRUS ) demonstrate that real lira-dollar volatility has a significantly negative coefficient in 37 small and large industries. As the lira-dollar exchange rate becomes more volatile in these export industries, Turkish importers are shifting their activities from Germany to the U.S. There must be a risk-averse group of traders who benefit from increasing their revenues today to compensate for futur losses in the future. In contrast, the long-run estimates of positive volatility (POS TRUS ) show that there are 33 cases where lira-dollar volatility has a significant positive coefficient, suggesting that Turkish importers of these goods turn away from U.S. products and prefer German products when the lira-dollar exchange rate is highly volatile; this confirms the long-run substitution effect in export industries. Once again, diagnostic tests are necessary to support the validity of the long-run coefficient estimates. The asymmetry of cointegration is crucial in this regard. Table 6 presents significant F-test results in 69 cases that support cointegration. Additionally, all functions provide cointegration based on ECMt−1. The high value of the adjusted R 2 implies that the proposed model is a good fit for each industry. The Ramsey RESET test also indicates that the nonlinear export specification is correctly specified in most industries. Serial correlation is not a significant problem in all cases, as shown by the LM test. Finally, the CUSUM or CUSUMSQ tests demonstrate that the short and long-run coefficients of all industries are stable.

Nonlinear import model
Before interpreting the results of the NARDL import model, we tested the short-run and long-run asymmetry hypotheses using the Wald-SR TRUS and Wald-LR TRUS tests. We observed short-run nonlinear effects for exchange rate uncertainty and the third-economy effect in all cases, based on the difference in sign or size between the ∆ and ∆ estimates. The lag orders of the estimates for ∆ and ∆ were different in most cases, thus confirming the shortrun adjustment asymmetry concerning the influences of appreciation and depreciation on volatility. The asymmetry of third-country effects is detectable for 79 industries based on the significant Wald-SR TRUS test. Therefore, based on the short-run modelling, where exchange rate uncertainty and external volatility are decomposed into POS and NEG components using nonlinear adjustment, we conclude that most import industries exhibit asymmetric effects. Similarly, the Wald-LR TRUS test shows that the long-run asymmetry of lira-dollar volatility exists in 70 cases (see Table 8).
We will now discuss the short-run and long-run estimates of the NARDL import specification (10) in Table 7, and the associated diagnostics are shown in Table 8. The short-run asymmetric results for the third-economy effect show that ∆ or ∆ has at least one significant lagged effect in 68 cases. However, the earlier symmetric ARDL import model showed 69 significant cases. From the non-linear framework, we can conclude that the number of import industries affected by the volatility of the lira-dollar exchange rate remains roughly the same. The long-run estimates of the NARDL import model in Table 7 show 67 industries where the third-economy effect captured by POS TRUS or NEG TRUS is significant. This volatility effect has a significant positive value in 49 import industries and a significant negative value in 43 import industries. The positively affected industries include the four largest Turkish import industries with codes 541, 581, 711, and 729, which import about 20.6% of their products from Germany. In contrast, the two largest industries with codes 719 and 722, which together import about 17.6% of goods from Germany, are negatively affected by third-country risk in the long-run. In addition, the measure of third-country volatility mainly affected the small import industries in the long-run. However, the significant impact of third-country volatility was observed in 49 import industries for the linear modelling approach. We further explain the results of the third-country effect of volatility. For example, in the previous symmetric model, the estimated coefficient of the thirdcountry effect was positive for the import industry coded 581 (plastic materials, regenerated cellulose & resins with an import share of 8.33%). However, our asymmetric analysis shows this result is primarily due to increased exchange rate uncertainty (POS TRUS ). Similarly, in the previous symmetric analysis, the coefficient of the third-country effect was positive for one of the largest import industries with code 541 (medical and pharmaceutical products with an import share of 4.24%). However, the asymmetric analysis shows that this result is primarily due to increased exchange rate volatility (POS TRUS ). The same results can be confirmed for other small import industries. Hence, we conclude that the effect of third-country volatility improves the estimation results of the import specification and affirms that it is a significant predictor of Turkey's import flows. As for the other explanatory variables in the nonlinear import specification, we conclude that the dummy variable (DM) used to capture the impact of the 1984 trade liberalization reforms in Turkey has a significant negative effect in 70 cases. Moreover, improved Turkish economic activity ( ) favours German products in Turkey in 67 out of 93 significant cases, suggesting that Turkey will import more from Germany as its economy grows. In contrast, a significant negative estimated coefficient is associated with Turkish real income in 5 cases, indicating that as Turkey's economy grows, more import-substituting products are produced domestically, and imports decline over time. Finally, the long-run impact of the real bilateral exchange rate (lnREX) is positive (negative) in 40 (26) cases. The negative estimate of the real exchange rate confirms that the continuous depreciation of the Turkish lira against the euro hinders Turkish imports from Germany. Once again, cointegration is required to demonstrate the validity of the obtained long-run coefficient estimates. Table 8 shows that the ECMt−1 test is significant in all cases. In contrast, the F-test is not significant in 14 cases. Other diagnostic tests also support the long-run results. For example, the adjusted R 2 demonstrates the model's goodness in all functions. The LM test confirms that there is no autocorrelation in most cases. The Ramsey RESET test indicates that the proposed model is appropriately specified. Finally, the CUSUM and CUSUMSQ tests for all models support the short-run and long-run stability of the coefficients.

Summary and conclusion
Since all countries are interdependent in today's globalized world, trade flows between two trading partners can be affected by other countries' economic and trade policies. To capture the impact of the third-country effect, we followed Bahmani-Oskooee and Aftab (2018) and included the real lira-dollar exchange rate volatility. Thus, in addition to the real lira-euro exchange rate dynamics, we sought to capture the impact of lira-dollar exchange rate volatility on trade volumes between Turkey and Germany using commodity-level trade data. Previous empirical studies have shown that exchange rate volatility can positively and negatively affect trade, with higher volatility potentially impeding trade and lower volatility expanding it. However, recent research has shown that the impact of exchange rate volatility on trade can be asymmetric, i.e., an increase in volatility can affect trade flows differently than a decrease in volatility due to changes in traders' expectations, firms' pricing policies, and downward price rigidity. This paper empirically examines the asymmetric effects of exchange rate uncertainty and the third-country effect on bilateral trade between Turkey and Germany. Based on annual time-series data spanning 1980-2022, we examined 79 export and 93 import industries trading between Turkey and Germany. Following the linear ARDL model developed by Pesaran, Shin, and Smith (2001), we observed significant short-run effects of the real lira-dollar volatility (third-country effect) in 70 Turkish industries exporting to Germany; however, the long-run effects persisted in 71 industries. In contrast, when we employed the linear ARDL import specification, we observed that real lira-dollar volatility had significant short-run effects in 69 cases, while these effects persisted in the long-run in 49 cases. The linear analysis of the third-country volatility effect showed that the short-run effects were short-lived, as they vanished over time in most industries. As traders in these industries hedge to escape exchange rate volatility over time (Bahmani-Oskooee, Usman, and Ullah, 2020), the hedging costs earned by exporters are passed on to importers in the form of higher commodity prices, which hurts commodity trade (Augustine C. Arize, Thomas Osang, and Daniel J. Slottje, 2000). In most industries, empirical research examining bilateral and third-country volatility (Bahmani-Oskooee and Kanitpong, 2019; Usman, Apergis, and Anwar, 2021) has found more significant effects in the short-run than in the long-run. In contrast, when we applied the NARDL specification developed by Shin, Yu, and Nimmo (2014), the number of industries affected by exports and imports changed. Based on empirical evidence, Cushman (1986) argued that exchange rate volatility might be overstated if the third-country effect is ignored. According to our analysis, the weak impact of exchange rate volatility after including external volatility risk could be due to the neglect of the asymmetry assumption. Based on shortrun nonlinear analysis, the third-country effect of lira-dollar volatility was significant in most cases (i.e., for 61 Turkish exporting and 68 Turkish importing industries). These short-run asymmetric third-country volatility effects are even more substantial regarding significant long-term asymmetry effects.
Comparing the linear ARDL with the NARDL estimates, we found that they are industry-specific. For instance, the linear export model showed that the real lira-dollar volatility does not significantly affect Turkish exports to Germany for the largest Turkish export industry coded 841 (clothing except fur clothing with an 18.35% export share). If we had solely used the symmetric ARDL model, we would have concluded that real lira-dollar volatility has no long-run effect on Tukish exports to Germany in this industry. In contrast, the NARDL export specification showed that while an increase in volatility has a significant positive effect in this industry, a decrease in volatility has no long-term effect. This result is due to the nonlinear adjustment of the real lira-dollar volatility. Concerning Turkey's imports from Germany, the negative insignificant long-run estimate of the traditional ARDL model appeared to be linked solely to an increase in real lira-dollar volatility, not to the decrease in this volatility, as suggested by the nonlinear model estimates. Ultimately, we observed that an increase in real lira-dollar volatility appeared to increase Turkey's exports to and imports from Germany. The empirical findings of the present study have important policy implications, particularly for traders who seek to manage their downside risks and capitalize on the return opportunities associated with trading activities. Specifically, the study results can aid potential investors and traders in export-oriented and import-substituting industries to make informed investments in sectors of the economy that benefit from exchange rate fluctuations when an economy chooses to float its exchange rate. Furthermore, including a third-country effect highlights the need for all market participants and stakeholders to recognize that changes in trade policy instruments in a third-country can significantly affect crossborder trade. Finally, incorporating asymmetric effects in the analysis yields more realistic results and provides policymakers clear evidence of traders' behaviour when volatility increases or decreases. The study recommends that policymakers prioritize export-oriented trade policies to boost foreign trade with other countries rather than engaging in short-term domestic currency manipulation. The main focus of economic policy should be on value addition to the existing production process to increase exports and meet the growing local demand for domestically produced goods. Similarly, import-substituting policies should prioritize the production of capital goods and luxury items. In addition, increased emphasis should be placed on improving the quality of domestically produced goods to enhance the competitiveness of local industries in the global market and contribute significantly to world trade, ultimately increasing citizens' economic well-being and long-term prosperity. Grauwe, De Paul. 1988. "Exchange rate variability and the slowdown in growth of international trade." Staff Papers, 35 (1) A.2. Variables = Volume of exports of commodity i by Turkey to Germany. The nominal export value (in USD) for each exporting industry is obtained from Source A. In the absence of commodity prices, we followed Usman et al. (2021) and deflated nominal export values using the Turkish export unit value index (2015=100). We compiled data on the Turkish export unit value index from Source C.
= Volume of imports of commodity i by Turkey from Germany. The nominal import value (in USD) for each importing industry is obtained from Source A. In the absence of commodity prices, we followed Usman et al. (2021) and deflated the nominal import values using the Turkish import unit value index (2015=100). We compiled data on the Turkish import unit value index from Source C.
= Measure of Turkey's real income. It is represented by Turkey's real GDP (constant 2015 US$). Data on Turkey's real GDP is obtained from Source C.
= Measure of Germany's real income. It is represented by Germany's real GDP (constant 2015 US$). Data on Germany's real GDP is obtained from Source C.
= The real exchange rate between the Turkish lira and the euro. In the absence of readily available data for the lira-euro exchange rate, we calculated it using a cross-exchange rate against the USD using the following formula: ( ℎ * ). The results of the cross-exchange rate show the nominal exchange rate (NEX) between the lira and the euro, which is then converted into the real exchange rate using the expression: = ( × ). Here, NEX = the nominal exchange rate (i.e., the number of lira per euro), = the price level in Germany (measured by CPI), and = the price level in Turkey (measured by CPI). Thus, the depreciation of the Turkish lira can be attributed to an increase in the exchange rate. The euro/dollar exchange rate was calculated before 1999 by applying the conversion rate of 1.95583 Deutsche Mark = 1 euro. Data for all nominal exchange rates are taken from Source B, except for the nominal euro/dollar exchange rate, which is taken from Source D. Similarly, data on consumer price indices are collected from Source B.
= Volatility measure of the real bilateral exchange rate between the Turkish lira and the USD (REX), which is constructed as = ( × ). In this expression, = the nominal exchange rate (i.e., the number of lira/USD), = the price level in the United States (measured by CPI), and = the price level in Turkey (measured by CPI). Following Bahmani-Oskooee and Aftab (2017), the measure of volatility is obtained using the GARCH (1, 1) approach.  . LM is the Langrange Multiplier test of residual serial correlation, and RESET is Ramsey's test for functional misspecification. LM and RESET tests are distributed as χ 2 with one degree of freedom. The critical values of these diagnostics are 2.70 (3.84) at the 10% (5%) significance level, respectively. CUSUM and CUSUMSQ are recursive estimates used to test the stability of all estimated coefficients. Each industry export share is calculated as a percentage of Turkey's total exports to Germany over the sample period. This export share value is based on 2022. n.e.s refers to not elsewhere defined.   table as under Table 2. (ii) Each industry import share is calculated as a percentage of Turkey's total imports from Germany over the sample period. This import share value is based on 2022.    Notes: (i) The same notes apply to this table as under Table 6. (ii) Each industry import share is calculated as a percentage of Turkey's total imports from Germany over the sample period. This import share value is based on 2022.