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Short-run and Long-run Relationships Between Trade Balance and Real Exchange Rate for Bilateral Trade

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ABSTRACT                                                                    2

INTRODUCTION                                        3

  1. INTRODUCTION                                    3

LITERATURE REVIEW                                     6

2.1 MARSHALL LERNER CONDITION                         6

2.2 J-CURVE PHENOMENON                                     10

RESEARCH METHODOLOGY                                         13

3.1 TRADE BALANCE MODEL                                     13

3.2 DATA DESCRIPTIONS                                       15

3.3 DESCRIPTIVE ANALYSIS                                     16

3.4 AUTOREGRESSIVE DISTRIBUTEG LAG (ARDL)                         18

3.5 GENERAL ERROR CORRECTION MODEL (ECM)                        20

3.6 STABILITY TESTS                                        21

EMPIRICAL RESULTS AND DISCUSSIONS                                 22

SUMMARY AND CONCLUSION                                       31

REFERENCES                                                32


When the sum of trade elasticities is greater than one in absolute value, Marshall-Lerner condition exist indicating changes in exchange rate to have an impact on the country’s trade balance. Meanwhile, a continuing concept of Marshall-Lerner condition which is known as J-Curve effect states that at initial period, the impact on country’s trade balance deteriorate first, and will improve in the long-run. This paper empirically assess the short-run and long-run relationships between trade balance and real exchange rate for bilateral trade in the case of US with six trading partners using quarterly time series data from year 2000 to 2016. Using the bound testing approach known Autoregressive Distributed Lag (ARDL) model and general error correction models, this paper analyses whether both short and long-run association exists between trade balance and the variables. The empirical result reveals that there is no evidence of J-Curve effect in the short-run for any of the bilateral trade between US and six trading partners. However, the empirical findings indicate that movement of real exchange rate does have a positive impact in the long-run on the real bilateral trade balance between US and Canada while confirming that Marshall-Lerner condition holds for only one out of six pairs of bilateral trades. This paper also conducted stability tests on the long-run trade balance equations using CUSUM and CUSUMQ stability tests.



Economic theory suggests that exchange rate movement has great impacts to trade balance but the impact may vary, probably due to different level of economic development. One of the prominent impacts of exchange rate movement is that currency devaluation may improve a country’s trade balance in the long run only if the sum value of import and export demand elasticity is greater than one. This condition is known as the Marshall-Lerner condition. The existence of a long run association is significant to the elasticities approach to the determination of the trade balance. The elasticity approach is also known as the imperfect substitutes model. A fundamental point is the extent to which imports and exports are responsive to relative price changes, more specifically whether a currency devaluation improves the trade balance or otherwise. A country’s trade balance is computed as exports minus imports while the outcome of currency devaluation on the trade balance will be analysed by price and volume effects. Real currency devaluation improves the trade balance through two different outcomes. Firstly, the quantity of export will increase because devaluation will makes the domestic goods cheaper as compared to the foreign goods, thus making export more competitive. Secondly, the quantity of import will decrease because import is relatively more expensive. When both import and export respond to the currency devaluation, a country’s trade balance will improve. In contrary, if the amount of export and import is not responsive at the initial period of exchange rate depreciation, trade balance may be worsening in short-run due to decrease in export value and increase in import value but it will eventually improves in the long-run. This situation has been pointed out by Bahmani-Oskooee (1985) where in some cases under which the ML condition was satisfied but the trade balance continued to worsen instead of improving. This condition is known as J-curve effect. Magee (1973) pointed out that a situation where trade balance deteriorates instead of improving when currency devalues is due to the implications of currency-contracts signed prior to devaluation and newer currency-contracts signed after devaluation. When signing a currency-contract prior to devaluation, exporters prefer to receive payment in an expected stronger currency, while importers prefer to make payments in terms of currency which is expected to weaken. In a situation where both exporters and importers expectations to be similar, the currency denoted will depend on the relative market power of both exports and imports. Meanwhile, newer currency-contracts signed after devaluation is also known as the periods of pass through. The terminology of pass through means the behaviour of international prices on contracts signed after the devaluation occurs but before export and import quantities significantly responded to the exchange rate changes.  The expectation of currency devaluation is the increase of domestic price index of imports and decrease in the price index of exports. As the quantity of imports and exports will take a while to adjust after devaluation, Magee (1973) states that a successful pass through occurs when the trade balance of a country is worsening. The sluggishness or irresponsive quantities of exports and imports during ‘pass through period’ are due to supply being briefly perfectly inelastic because exporters cannot immediately adjust their output abroad. Likewise, demand is perfectly inelastic as importers require some time to substitute among goods and to alter the flow of orders. In a situation when both export and import supplies are inelastic in the short run, trade balance of a country will improve during the pass through period.

Many researchers work centres on the twin concepts of the Marshall-Lerner (ML) condition and the J-Curve phenomenon. While previous many previous studies analysed both Marshall-Lerner condition and J-Curve effect using aggregate data, this study will employ disaggregate data as proposed by Rose and Yellen (1989) to avoid aggregation bias. This is because application of aggregate data may prohibit the actual presentation of exchange rate movement at bilateral level.   The purpose of this paper, therefore, is to test the validity of Marshall-Lerner hypothesis empirically and to investigate whether the J-Curve phenomenon exists in the bilateral trade between the USA and the other six of the G-7 countries namely, Canada, France, Germany, Italy, Japan and the UK. This study aims to employ the most recent cointegration approach known as Autoregressive Distributed Lag (ARDL) model and error correction models (ECM) to identify the relationship between trade balance, domestic real income, trading partners’ real income and real exchange rate in the short-run and long-run, under elasticity approach.



Theoretically, the conventional perspective states that nominal currency devaluation improves trade balance of a country. The improvement of the trade balance in the long haul is crucial to the stabilization policies of the International Monetary Fund. Albeit multiple studies have been made, there is still no conclusive evidence to prove a general validity of Marshall-Lerner (ML) condition. As such, it is equally important to discuss the previous literatures that supported the existence of Marshall-Lerner condition.

In past literature, researchers have also discovered that currency devaluation effect varies markedly across the bilateral trade between the countries pairs and even between the industries within a country pair. This may be due to the trade affairs between the country pair and individual distinctiveness of each industry within that pair. For example, Bahmani-Oskooee (1985) proved that there are cases under which the ML condition was met but the trade balance continued to deteriorate. Hence, he recommended an alternative way by using short-term dynamics that detect the effect of currency devaluation on trade balance, i.e., the J-curve phenomenon.

Early studies of Marshall-Lerner condition often include additional variables such as expected depreciation by (Warner and Kreinin, 1986) and volatility by (Bahmani-Oskooee and Payesteh, 1993) besides the most basic variables such as income and relative prices. This is because the additional variables tend to contribute in finding evidence for Marshall-Lerner condition.

One of the earliest researches, Arize (1987) estimated import and export elasticities for eight African countries using additional variables or variations of the supply and demand models and reveals that M-L condition was met for seven countries. The research was explained further by Reinhart (1995) for 12 developing countries using dynamic ordinary least squares (DOLS). The result implies that African countries have large elasticities to meet the hypothesis of the Marshall-Lerner condition. Noland (1989) estimated export and import elasticities for Japan using ordinary leased square (OLS) and gamma distributed lag model and concluded that Marshall-Lerner condition was satisfied.

With the recent developments in econometrics literature, more recent researches of Marshall-Lerner condition have made use of cointegration technique. This is because many time series data are nonstationary; hence, standard statistical inferences are no longer valid because regression on nonstationary data may produce spurious relationship. An empirical study applying Engle-Granger two-step cointegration method to test Marshall-Lerner condition includes Andersen (1993). The result finds that most of the 16 OECD countries estimated exhibit an insignificant coefficient which relatively presents weak evidence of Marhsall-Lerner condition. Meanwhile, another research by Bahmani-Oskooee (2002) employed Engle Granger cointegration method for the case of Iran but the study was not on Marshall-Lerner condition but on test of volatility. However, the result reveals that Marshall-Lerner condition appears to be met.

The Johansen and Julius (1990) method, is a test for cointegration that allows more than one cointegrating relationship, unlike the Engle Granger technique. Bahmani-Oskooee and Niroomand (1998) used this method to estimate the trade elasticities for almost 30 countries. The result reveals that the evidence of Marshall-Lerner condition was satisfied; indicating that the long-run approach is indeed more effective.

The most recent single-equation estimation method applied in multiple empirical studies is the autoregressive distributed lag (ARDL) approach introduced by Pesaran et al. (2001). This technique works for both stationary and non-stationary variables and it is employed by placing lagged levels of each variable separately into a short-run error-correction model (ECM). Razafimahefa and Hamori (2005) was one of the pioneer researchers that applied ARDL method for Madagascar and Mauritius on the import demand functions for the period of 1960 to 2000. The result indicates that all variables are cointegrated, but the price elasticities imply that Marshall-Lerner condition is only met for Mauritius. The finding of Bahmani-Oskooee and Kara (2003) which indicates that the summation of import and export elasticities was greater than one was developed further by Bahmani-Oskooee (2005) using the ARDL cointegration technique to evaluate import and export demand for 28 countries from 1973 to 1998. The result reveals that all equations are cointegrated, and that the sum of import and export demand elasticities exceeds one in absolute value indicating that Marshall-Lerner condition is met. However, the result only applies to most countries in the cases studied except for some developed European countries.

While many researchers start adopting new cointegration technique, Mahmud et al. (2004) applied a non-parametric technique to estimate Marshall-Lerner condition in six industrial countries using quarterly data from 1960 to 1998. Other than estimating export and import equations using ordinary least squares (OLS), the researcher also estimated with a nonparametric regression method called as local linear least squares (LLLS). This technique offers time-varying linear estimates of a variable within a window of certain length around it. The result of this empirical study was compared to the results of Bahmani-Oskooee Niroomand (1998) which Marshall-Lerner condition was met for almost all countries in the research. Meanwhile, this research reveals that Marshall-Lerner condition was satisfied for Norway only.

As the Marshall-Lerner condition is fundamentally an aggregate condition, currency devaluation might help to contribute in improving a country’s trade balance for one specific partner. Thus, the estimation of a country’s import and export price elasticities can be performed using bilateral data. However, Marquez (1990) argued that aggregate estimation might produce ambiguous results and excludes important bilateral effects. The researcher proceeds by estimating bilateral elasticities for five industrial countries with each other and the rest of the OECD countries with less developed countries using OLS. The result implies that Marshall-Lerner condition only holds for Canada, Japan, USA, OECD and OPEC countries. Bilateral analysis was developed further by Bahmani-Oskooee and Brooks (1999) to estimate price elasticities for USA with six trading partners using Johansen cointegration method. Marshall-Lerner condition holds for all countries except for Canada and Germany.








It appears that past empirical studies focused on two major streams of J-Curve phenomenon. The first category employs aggregate trade balance model involving two countries. For example, the case of home country and the rest of the world. The second category tested the J-Curve phenomenon by employing disaggregate trade balance model. This category was initially employed by Rose and Yellen (1989) which tested the validity of J-Curve phenomenon between US and six trading partners. However, the latter approach indicates that while a country’s trade balance is improving with one trading partner, it could be concurrently deteriorating with another.

J-Curve phenomenon is a twin concept of Marshall-Lerner condition and it has been explained by several researchers. Krueger (1983) stated that the existence of J-curve phenomenon is due to the fact that “at the time an exchange rate change occurs, goods already in transit and under contract have been purchased, and the completion of those transactions dominates the short-term change in the trade balance”. Thus, the trade balance deteriorates first, but after a period of time where elasticities have a chance to expand, it will start to improve.

The J-Curve phenomenon has captured the interest of researchers considerably in the past three decades. The following literature review will be based on relevant literature collected by Bahmani-Oskooee and Ratha (2004a) for the period of 1973-2003. One of the past researcher, Miles (1979) found that devaluations improved the balance of payments through capital account but do not improve the trade balance. However, using OLS method, Himarios (1985) employed similar framework to Miles’s research and found that devaluations do affect the trade balance in nine out of ten cases using traditional predicted direction. He critiques Miles’ results and pointing out that (i) the results are sensitive to the units of measurement; (ii) the impact of domestic and foreign variables may differ on the trade balance; (iii) compared to nominal exchange rate, the real exchange actually affects the trade balance and (iv) the lagged values of exchange rate is vital.

Meanwhile, Bahmani-Oskooee (1985) introduced a method of testing the J-Curve which is called Almon lag structure and employed the method for four countries with different currency exchange (Greece, India, Korea and Thailand) for the period of 1973-1980. Using the new method, he found evidence of a J-Curve for Greece, India and Korea; although the trade balance deteriorate at different pace for each case. In line with previous research, Bahmani-Oskooee and Malixi (1992) continue to emphasize the effective exchange rate, and applies an Almon lag structure on real exchange rate for the case of 14 countries for the period of 1973Q1-1985Q4. The evidence of J-Curve was found for Brazil, Greece, Korea and India and concluded that the short-run effects may not follow a standard pattern while long-run effects are favourable in most cases. It can be seen that these results are consistent with Bahmani-Oskooee (1985) but differ from the results of Himarios (1989) who also investigates J-Curve effect for the case of Egypt, Greece, India, Korea, Thailand, amongst others.

Many previous research employed OLS technique such as Junz and Rhomberg (1973), Himarios (1985), Rose and Yellen (1989) and Marwah and Klein (1996). Demirden and Pastine (1995) states that estimating J-Curve effect using OLS estimation is suitable only in a fixed exchange rate environment. But not suitable for a flexible exchange rate regime because any changes in the exchange rate will affect other variables which are likely to influence the result of trade balance. As feedback effects cannot be captured in the OLS regression, it is impossible to directly interpret the OLS coefficients on the lagged exchange rates because of the delayed effect of the exchange rate on the trade balance. Then, Demirden and Pastine (1995) introduced new cointegration technique called Vector Autoregression (VAR) approach by Sims (1980). This technique is suitable for a flexible exchange rate regime because it endogenizes all variables involved and provides highly flexible estimation environment. By using this method, the result demonstrates that the feedback effect is economically significant.

Similar to researches for Marshall-Lerner condition, the recent development in econometric literatures emphasize that adopting the Autoregressive Distriuted Lag (ARDL) cointegration would be beneficial to estimate J-Curve more accurately. Some recent empirical studies employing ARDL method includes Bahmani-Oskooee and Kanitpong (2001) for a bilateral analysis between Thailand and five countries. The result indicates that J-Curve effect was found between Thailand and the USA in one relation and between Thailand and Japan in another relation.

This summary has shown that previous researchers employed various type of technique to test on Marshall-Lerner condition and J-Curve phenomenon.




The trade balance model in this study will be adopted from Rose and Yellen (1989).  However, instead of taking the difference of imports and exports, the trade balance is measured as the ratio of US nominal imports from trading partner over her nominal exports to the same trading partner. The model takes the following long-run (contegrating) form:

ln⁡TBj,t= a0+a1 ln Yt,t+a2 lnYj,t+ a3ln⁡RERj,t+ ut  (1)

Where the measure of the trade balance, TB is the ratio of imports to exports;

Yt,tis the real income of US which is the industrial production index of US;

Yj,tis the real income of the industrial countries which is the industrial production index of the trading partner and

RERj,tis bilateral real exchange rate in which a decrease reflects a real devaluation of the US dollar against the currency of trading partner j. According to the normal phenomenon, we expect that

a1would be positive because of the assumption that when US’s national income increases, the consumption of imported goods from US’s trading partner will increase too. However, if the increase in US income is because of the increase in the production of import substitute goods, imports may actually decline yielding a negative estimate for

a1. Thus,

a1could be positive or negative depending on the situation. Similar to

a1, estimated value of

a2could either be positive or negative.  Meanwhile, if real currency devaluation is to increase exports while lowering imports which satisfies the Marshall-Lerner condition, we expects that

a3> 0. However, under J-Curve phenomenon, we expects

a3< 0 because an increase in real exchange rate indicates a real depreciation of the US dollar relative to j’s currency.  initially reduces the demand for export but increases the demand for imports. Hence, the trade balance worsens at first but will eventually improve as export and import volumes adjust to the price changes. To test the J-Curve effect, the short-run dynamics must be incorporated into the long run.


The empirical investigation will be carried out with quarterly data on bilateral aggregate real imports and exports from each external source, over the period between 2000Q1 and 2016Q4. With the USA as the home country in a bilateral trade setting with the other G-7 countries are Canada, France, Germany, Italy, Japan and the UK.


TBjwhich is the trade balance of US with her trading partners, the data were collected from Direction of Trade Statistics of IMF, while for

Yt,twhich the real income of US, the data were collected from the Central Bank of the United States called The Federal Reserve System. As for

Yj,t, which is the real income of country j, data were collected from International Financial Statistics of IMF. The

RERj,tvariable is constructed as (

PT× NER) / 


Pjis country j’s Consumer Price Index (CPI),

PTis US’s CPI.

NERjis the nominal bilateral exchange rate defined as number of US Dollar per unit of country j’s currency. All CPI data were obtained from International Financial Statistics of IMF while all exchange rate data were collected from the Federal Reserve System. All real values are measured in base of year 2010.



To estimate the cointegrating trade balance model with a view of testing the Marshall-Lerner condition and J-Curve phenomenon, several econometric techniques were adopted in the past two decades. According to Bahmani-Oskooee and Kara (2005), many researchers providing evidence of trade elasticities such as Wilson and Takacs (1979), Warner and Kreinin (1983), Bahmani-Oskooee (1986), Marquez and McNeilly (1988) and Marquez (1990) employed common econometric approaches such as ordinary least square (OLS) or two-stage least square (2SLS) and concluding mixed result. Therefore, the solution to this problem is to employ the multivariate cointegration analysis such as Johansen (1988) andJohansen and Juselius (1990) which provide full information and maximum likelihood procedure.

As the objective of this paper is to identify the short-run as well as the long-run response of the bilateral trade balance to real bilateral exchange rate adjustment, the convenient technique is to adopt error-correction modelling and cointegration approach. With recent development in econometric literature, this paper will employ the Autoregressive Distributed Lag (ARDL) model which was introduced by Pesaran and Shin (1998) and Pesaran et al. (2001) to establish the direction of causation between variables. Compared to the conventional Johansen (1998) and Johansen and Juselius (1990) method, there are benefits of using this approach to estimate the long-run relationships. Compared to Johansen approach where long-run relationships were estimated within a context of a system of equations, ARDL analysis utilizes only a single reduced form equation (Pesaran & Shin, 1998). While Johansen approach requires unit root testing to identify the order of integration, ARDL approach avoids conventional unit root pre-testing on variables, which indicates that the estimation on the existing relationship between variables is applicable irrespective of whether the underlying regressors are purely stationary I(0), purely I(1) or a mixture of both. In addition, the ARDL technique does not require the larger number of specification to be made in the estimation of standard cointegration test. Irrespective of the exogeneity of explanatory variables (if any), the long-run and short-run parameters, can be acquired by employing OLS with applicable asymptotic inferences to the ARDL model with appropriate lag length (Duarte and Holden, 2001). Also, ARDL does not specify the optimal number of lags to be employed in the estimation whereby it is possible to employ different optimal lags on different variables. Most importantly, ARDL allows the usage of limited sample data (30 to 80 observations) to estimate the bound testing in which the set of critical values were developed by Narayan (2004).


An ARDL representation of equation is formulated as follows:




∑i=1m b1i ∆lnTBj,t-i+

∑i=0m b2i ∆lnYt,t-i+

∑i=0m b3i ∆lnYj,t-i+

∑i=0m b4i ∆lnRERj,t-i+

b5 lnTBj,t-1+

b6 lnYt,t-1+

b7 lnYj, t-1+

b8 lnRERj,t-1+

vt            (2)

where stands for the optimal lag length. Equation (2) differs from a standard distributed lag model in Equation (1) where it includes a linear combination of the lagged level variables. The ARDL procedure involves two stages. The first stage of conducting ARDL cointegration method is the bound testing which is based on F or Wald-statistics. F-test is employed to test the existence of the long-run relationship.  The long-run effect of real depreciation is implied based on the size and significance of

b8which is normalized by

b5. The null of no cointegration hypothesis, in other words, null hypothesis of non-existence of the long-run relationship is

H0: b1= b2=b3= b4=0against the alternative hypothesis

H1: b1≠ b2≠b3≠b4≠0. The F-test involves asymptotic critical value bounds which is non-standard regardless of whether the variables are I(0) and I(1) or even fractionally integrated. Therefore, Pesaran et al. have calculated two sets of appropriate critical values for a given significance level. One set assumes all variables are I(0) while another assumes all variables are I(1). If the F-test estimation exceeds the respective upper critical values, then

H0is rejected indicating there is evidence of a long-run relationship between the variables regardless of the order of integration of the variables. Meanwhile, if the F-test estimation is below the upper critical value, we fail to reject the null hypothesis; supporting lack of cointegration. On the other hand, if the F-test falls into the bounds, then the result is inconclusive. According to Kremers et al. (1992), we can remedy an inconclusive case, by employing the error-correction term to establish the cointegration. Since this paper utilizes quarterly data, we impose four lags on each first-differenced variable in eq. (2) and provide the result of F-test for cointegration in Table 1.


As the existence of cointegration has been established, the second stage of conducting ARDL method is estimating the error correction model (ECM). The benefit of adopting ECM is that it simultaneously estimates the short-run dynamics with the long-run equilibrium without losing long run information. A general error correction model (ECM) of Equation (3) is formulated as follows:

∆lnTBt= b0+ ∑i=0m b1i∆ lnTBt-i


∑i=0m b2i∆lnYt,t-i+ ∑i=0m b3i∆lnYj,t-i  +

∑i=0m b4i∆lnRERt-i+ λECt-1+

ut      (3)

where is the speed of adjustment parameter while EC is the residuals obtained from the estimation of cointegration model in Equation (1). The error correction model result implies the speed of adjustment of the long run relationship after a short run shock. The optimum lag number in the ARDL model for this paper is selected using model selection criteria such as Akaike’s Information Criteria (AIC). However, this paper also considers the lag number suggested by another criteria which is Schwarz Information Criterion (SIC).


The result of cointegration estimated from Equation (2) may not necessarily demonstrate that the estimated coefficients are stable as argued by Bahmani-Oskooee and Brooks (1999). Thus, to ascertain the stability or instability in the trade balance model, this paper will implement stability test which is introduced by Brown et al. (1975) on Equation (3). Stability test includes cumulative sum (CUSUM) and cumulative sum of squares (CUSUMSQ) tests based on the recursive regression residuals. These tests also integrate the short-run dynamics to the long-run through residuals. The CUSUM and CUSUMSQ are plotted against the break points of the model and restructured recursively. If the plot of CUSUM and CUSUMSQ statistics fall inside the critical bounds of 5% significance, this paper will conclude that the coefficients of the regression are stable. The results of these tests are displayed as a graphical representation.


Quarterly data from 2000Q1 to 2016Q4 period were used to estimate Equation (2) for six trading partners of US. The standard Augmented Dickey-Fuller (ADF) and Phillips-Perron unit root tests are employed to identify the integration order of the variables tested. However, the ARDL model does not require unit root testing. Hence, there is no pre-root testing involved in this paper. To estimate the short-run and long-run relationship between variables, the number of length on the first difference variables must be identified first. According to Bahmani-Oskooee and Brooks (1999), this step is usually sensitive to lag-length on each first differenced variable. Therefore, to validate this, the F-statistic was tested by changing the lags order on each first differenced variable from 4 to 8. The procedure to obtain the lag number was by employing unrestricted VAR by means of Akaike Information Criterion (AIC). The results are presented in Table 1 along with the critical values at the bottom of the table.

The result of the test indicates varies significance levels across six trading countries with the choice of lag-length. On imposing 8 lags, the test illustrates the existence of a cointegration in the case of 5 out of 6 trading countries which are France, Germany, Italy, Japan and UK at 1%, 5% and 10% significance level. By applying 6 lags, only the UK shows bilateral relationships reflecting cointegration at 1% significance level.  On the other hand, when implementing 4 lags, the existence of cointegration relationships was found only in Canada out of 6 bilateral cases. The results suggest that long-run relationship between trade balance and other variables such as domestic income, foreign income and exchange rate exist in all six countries (Canada, France, Germany, Italy, Japan and UK). This relationship indicates that these variables have a tendency to move together in the long-run. If the estimated F-statistics value is larger than the critical upper bound limit at 90%, 95% and 99% when referred to Pesaran et al. table, then the hypothesis is rejected indicating that there is evidence of a long-run relationship between the variables. However, at this stage, the results are still considered preliminary.

Table 1. The results of F-test for cointegration (null hypothesis, WALD TEST)

Trading partner Calculated F-statistic for different lag lengths
Lag 4 Lag 6 Lag 8
Canada 4.105568** 1.250710
France 1.870703 1.955426 3.876924**
Germany 2.603180 3.180250 3.260894*** 

Italy 2.062794 1.637890 4.468459* 

Japan 1.154317 1.077934 4.434947* 

UK 1.325902 6.579918* 3.690921** 

Note: The relevant critical value bonds are taken form Pesaran, Shin & Smith (2001) [Case III with an unrestricted intercept and no trend and number of regressors = 4 from]. They are 3.74 – 5.06 at the 1%, 2.86 – 4.01 at the 5% and 2.45 – 3.52 at the 10% significance levels respectively. 

*, ** and *** denote that F-statistics falls above the 1%, 5% and 10% upper bond respectively.

After determining the long-run relationship between US’s trade balance and its variables, the next stage is to identify short run causality hypothesis using error correction model (ECM). According to Bahmani-Oskooee and Brooks (1999), if cointegration were found on each variables, the lagged order of the variables which jointly together form the lagged error-correction term must be hold. However, although there is no cointegration found, the lagged error term must still be retained to identify its significance and thus, the long-run association.

In this stage, the optimum number of length was selected as eight for the estimation of equation (2) and equation (3) to avoid over or under parameterization in equation (2).  To determine the optimum number of lag to be included in ECM estimation, this paper employed Akaike Information Criterion (AIC). As the objective of this paper is to determine the dynamics of currency devaluation on the trade balance, the results of equation (2) and (3) are presented in Table 2 down below. For brevity of presentation, this paper will only report the coefficient estimates of the real exchange rate (∆ln

REXt-i) in Panel A of Table 2 while the error-correction term based on different lag orders which is denoted by

ECt-1in Panel B of Table 2.

Table 2. Coefficient estimates of ∆ln Real Exchange Rate and Error Correction Term based on AIC

Trading Partner Panel A 

Number of lags on ∆ln RER

Panel B 

Error-correction terms

Diagnostic test
i=0 i=1 i=2 i=3 i=4 ECt-1 R2 LM test
Canada 0.0487 



(-1.8465) ***









0.7065 1.5909 


France -0.1078 




0.6564 0.6654 


Germany -0.0853 




0.6708 0.6452 


Italy -0.4509 




0.7018 4.5938 


Japan -0.003891 




0.1898 0.9640 


UK 0.1929 




0.5202 0.4390 


*, ** and *** indicate statistical significance at 1%, 5% and 10% level. 

Parenthesis for Panel A and Panel B indicate t-ratios.

Parenthesis for LM test indicates the P-Values.

Panel A of Table 2 reflects the short-run coefficient estimates of the lagged first-differenced real exchange rate to ascertain the J-Curve phenomenon in this paper. Based on panel A of Table 2, there is no evidence of J-Curve phenomenon in any bilateral relationship as the real exchange rates does not alter from negative to positive in any cases in this study. For example, while the case of Canada, there are positive as well as negative coefficients with no specific pattern, while as for France, Germany, Italy and Japan, they are all negative coefficients. Finally, for UK, the coefficient is positive. None of the cases meet the qualification to be considered as an evidence of J-Curve phenomenon. However, considering the objective of this paper is to identify the dynamics of currency devaluation, the impact of the lags of the real exchange rates on the trade balance from error correction model of the AIC model was estimated. The results are reported in panel B of Table 2 which reflects that there is cointegration relationship in France, Germany and Italy as the error correction terms (

ECt-1) are statistically significant at 1% for France and Germany and 5% for Italy. Therefore, the temporary cointegration results in Table 2 are now confirmed for France, Germany and Italy. However, the speed of adjustment coefficient for France (-0.45), Germany (-0.24) and Italy (-0.30) are considered low indicating a slow rate of convergence to equilibrium in any case of a shock to the cointegrating association. The pattern of coefficients altering from negative to positive implies that an initial deterioration occurs followed by an improvement in the trade balance.

Diagnostic test for all six bilateral cases were employed to the ECM model using Breusch-Godfrey Serial Correlation LM test for autocorrelation among the residuals. The results indicate that serial correlation in the residuals exist for two out of six bilateral cases which include Canada and Italy. Meanwhile for the remaining cases, the p-value is more than 5% significance level indicating that this study fails to reject the null hypothesis. Meanwhile, most countries equations have a high R-squared value which shows strong positive correlation between dependent and independent variables.

To explore the long-run effect of the exchange rate on bilateral trade balance, the normalized coefficients of Equation (2) is reported in Table 3.

Table 3. The Long run ARDL model estimates based on AIC

Countries Order of ARDL Constant Trade Balance Domestic 


Foreign Income Exchange Rate
Canada ARDL (3,1,4,4) 1.7796 










France ARDL (1,0,6,0) -0.1057 










Germany ARDL (5,3,5,0) 0.7309 










Italy ARDL (4,1,2,0) -0.3352 










Japan ARDL (1,0,1,0) 0.6062 










UK ARDL (3,1,2,0) -0.0723 










AIC is criteria are utilized appropriately to select the order of ARDL. The order of optimum lags is based on the specified ARDL model. For example, AIC (3, 1, 4, 4) for Canada suggests that 3 lags are imposed on ∆ln TB, 1 lags on ∆ln Domestic Income, 4 lags on ∆ln Foreign Income and 4 lags on ∆ln Exchange Rate in equation (2). Absolute t-ratios are in parentheses. *,** and *** denote that significant at 1%, 5% and 10% level respectively.

Based on Table 3, only the case of bilateral trade of Canada provides evidence of Marshall-Lerner condition. This is because, the real exchange rate coefficient for Canada presents positive and statistically significant at 5% level, i.e. depreciation in real exchange rate (RER) leads to improvement in trade balance. This implies that although the short-run effects were mixed for Canada, the long run impacts of a real dollar devaluation against Canada seems to have a favourable outcome on its bilateral trade balance. The real exchange rate coefficient for Japan appears to be positive too, but it is not statistically significant at any level. As for other bilateral cases, the results fail to detect the validity of Marshall-Lerner condition which suggests that the exchange rate does not influence the bilateral trade balance of the countries.

The result of this paper seems to be similar to the previous study involving bilateral trade between US and six trading partners (Canada, France, Germany, Italy and Japan), where Bahmani-Oskooee and Brooks (1999) found that there is no specific pattern supporting the J-Curve phenomenon. However, a real dollar devaluation has a favourable effect on the US trade balance. Meanwhile, in another study testing Marshall-Lerner condition between US and the six trading partners, Bahmani-Oskooee and Brooks (1999) found evidence of Marshall-Lerner condition in four out of six cases which include Japan, UK, France and Italy. However, the result of this paper is not similar to the previous study as Marshall-Lerner condition only holds for Canada only.

Finally, the parameter stability tests were employed on Equation (3), which captures the short-run dynamics of Equation (2) and the long-run effect of Equation (1). The stability of the short-run and long-run coefficients are tested using the CUSUM and CUSUMSQ tests. Figure 1 and 2 shows the graphical representation of these two tests for France.

Figure 1. Plot of CUSUM for France

C:UsersFakhira MusaPicturesScreenshotsScreenshot (878).png

Figure 2. Plot of CUSUMQ for France

C:UsersFakhira MusaPicturesScreenshotsScreenshot (879).png

Figure 1 indicates a stable bilateral trade relationship between US and France. It is clear from Figure 1 that none of the CUSUM statistic graph cross the critical bounds, implying that indeed all short-run and long-run elasticities are stable. The graphical results for the other countries are not displayed here for brevity. However, both CUSUM and CUSUMQ tests indicate stable relationships in four of six countries including France, Germany, Japan and the UK. As for Italy, it is slightly unstable as the CUSUM statistic falls slightly outside the critical bounds of 5% significance. The summary results of these tests are presented in Table 4 below.

Table 4. Stability test results based on CUSUM and CUSUMQ

Trading partner CUSUM CUSUMQ
Canada Stable Unstable
France Stable Stable
Germany Stable Stable
Italy Unstable Stable
Japan Stable Stable
UK Stable Stable


While devaluations are theoretically assumes to unconditionally improve the trade balance of a country, the sum of the price elasticities of both export and import demands must equal to more than unity then only the trade balance will improve, a condition known as the Marshall-Lerner condition. This paper has estimated the Marshall-Lerner condition and J-Curve phenomenon through a reduced form of trade balance model in the case of US data with six trading partners (Canada, France, Germany, Italy, Japan and UK) over the period of 2000 to 2016. This study estimated the short-run and long-run effects of real currency devaluation of the US Dollar on trading partners using a recent cointegration approach by Pesaran et al. (2001) known as Autoregressive Distributed Lag (ARDL). To determine the relative speed of adjustment of trade balance to a change in real exchange rates, a distributed lag length was introduced on the variables of equation 2 and 3 using Akaike Information Criterion. The empirical result indicates that there is no specific short-run pattern supporting the evidence of J-Curve effect in any of US’s bilateral trade. Nevertheless, the long-run results indicate that a real dollar devaluation has a favourable long-run effect on the US trade balance. This provide support that Marshall-Lerner condition holds in one out of six cases which is Canada. Finally, to identify the stability of bilateral trade association, CUSUM and CUSUMQ tests were employed and found the conclusion that 4 out of 6 cases were stable in both tests which include France, Germany, Japan and UK. The results of this study are consistent with Bahmani-Oskooee and Brooks (1999) in terms of J-Curve estimation only.

The limitation of this study is that the results could be spurious because no pre-root testing was performed on each variable and all together. Although Autogregressive Distributed Lag (ARDL) framework does not require pre-root testing to identify the integration order of the variables, the unit root test could determine the presence of I(1) and I(0) properties of underlying regressors. Therefore, I recommend future study to employ pre-root testing to detect unit roots when using time series data.  Lastly, more additional test to ensure the robustness of the findings should be carried out by future researchers such as heteroscedasticity-consistent estimation model introduced by Newey and West (1987).



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