Shortrun and Longrun Relationships Between Trade Balance and Real Exchange Rate for Bilateral Trade
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TABLE OF CONTENTS
ABSTRACT 2
INTRODUCTION 3
 INTRODUCTION 3
LITERATURE REVIEW 6
2.1 MARSHALL LERNER CONDITION 6
2.2 JCURVE 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
ABSTRACT
When the sum of trade elasticities is greater than one in absolute value, MarshallLerner condition exist indicating changes in exchange rate to have an impact on the country’s trade balance. Meanwhile, a continuing concept of MarshallLerner condition which is known as JCurve effect states that at initial period, the impact on country’s trade balance deteriorate first, and will improve in the longrun. This paper empirically assess the shortrun and longrun 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 longrun association exists between trade balance and the variables. The empirical result reveals that there is no evidence of JCurve effect in the shortrun 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 longrun on the real bilateral trade balance between US and Canada while confirming that MarshallLerner condition holds for only one out of six pairs of bilateral trades. This paper also conducted stability tests on the longrun trade balance equations using CUSUM and CUSUMQ stability tests.
 INTRODUCTION
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 MarshallLerner 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 shortrun due to decrease in export value and increase in import value but it will eventually improves in the longrun. This situation has been pointed out by BahmaniOskooee (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 Jcurve effect. Magee (1973) pointed out that a situation where trade balance deteriorates instead of improving when currency devalues is due to the implications of currencycontracts signed prior to devaluation and newer currencycontracts signed after devaluation. When signing a currencycontract 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 currencycontracts 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 MarshallLerner (ML) condition and the JCurve phenomenon. While previous many previous studies analysed both MarshallLerner condition and JCurve 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 MarshallLerner hypothesis empirically and to investigate whether the JCurve phenomenon exists in the bilateral trade between the USA and the other six of the G7 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 shortrun and longrun, under elasticity approach.
2. LITERATURE REVIEW
2.1 MARSHALL LERNER CONDITION
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 MarshallLerner (ML) condition. As such, it is equally important to discuss the previous literatures that supported the existence of MarshallLerner 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, BahmaniOskooee (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 shortterm dynamics that detect the effect of currency devaluation on trade balance, i.e., the Jcurve phenomenon.
Early studies of MarshallLerner condition often include additional variables such as expected depreciation by (Warner and Kreinin, 1986) and volatility by (BahmaniOskooee 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 MarshallLerner 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 ML 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 MarshallLerner condition. Noland (1989) estimated export and import elasticities for Japan using ordinary leased square (OLS) and gamma distributed lag model and concluded that MarshallLerner condition was satisfied.
With the recent developments in econometrics literature, more recent researches of MarshallLerner 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 EngleGranger twostep cointegration method to test MarshallLerner 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 MarhsallLerner condition. Meanwhile, another research by BahmaniOskooee (2002) employed Engle Granger cointegration method for the case of Iran but the study was not on MarshallLerner condition but on test of volatility. However, the result reveals that MarshallLerner 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. BahmaniOskooee and Niroomand (1998) used this method to estimate the trade elasticities for almost 30 countries. The result reveals that the evidence of MarshallLerner condition was satisfied; indicating that the longrun approach is indeed more effective.
The most recent singleequation 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 nonstationary variables and it is employed by placing lagged levels of each variable separately into a shortrun errorcorrection 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 MarshallLerner condition is only met for Mauritius. The finding of BahmaniOskooee and Kara (2003) which indicates that the summation of import and export elasticities was greater than one was developed further by BahmaniOskooee (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 MarshallLerner 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 nonparametric technique to estimate MarshallLerner 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 timevarying 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 BahmaniOskooee Niroomand (1998) which MarshallLerner condition was met for almost all countries in the research. Meanwhile, this research reveals that MarshallLerner condition was satisfied for Norway only.
As the MarshallLerner 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 MarshallLerner condition only holds for Canada, Japan, USA, OECD and OPEC countries. Bilateral analysis was developed further by BahmaniOskooee and Brooks (1999) to estimate price elasticities for USA with six trading partners using Johansen cointegration method. MarshallLerner condition holds for all countries except for Canada and Germany.
2.2 JCURVE PHENOMENON
It appears that past empirical studies focused on two major streams of JCurve 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 JCurve phenomenon by employing disaggregate trade balance model. This category was initially employed by Rose and Yellen (1989) which tested the validity of JCurve 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.
JCurve phenomenon is a twin concept of MarshallLerner condition and it has been explained by several researchers. Krueger (1983) stated that the existence of Jcurve 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 shortterm 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 JCurve 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 BahmaniOskooee and Ratha (2004a) for the period of 19732003. 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, BahmaniOskooee (1985) introduced a method of testing the JCurve 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 19731980. Using the new method, he found evidence of a JCurve for Greece, India and Korea; although the trade balance deteriorate at different pace for each case. In line with previous research, BahmaniOskooee 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 1973Q11985Q4. The evidence of JCurve was found for Brazil, Greece, Korea and India and concluded that the shortrun effects may not follow a standard pattern while longrun effects are favourable in most cases. It can be seen that these results are consistent with BahmaniOskooee (1985) but differ from the results of Himarios (1989) who also investigates JCurve 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 JCurve 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 MarshallLerner condition, the recent development in econometric literatures emphasize that adopting the Autoregressive Distriuted Lag (ARDL) cointegration would be beneficial to estimate JCurve more accurately. Some recent empirical studies employing ARDL method includes BahmaniOskooee and Kanitpong (2001) for a bilateral analysis between Thailand and five countries. The result indicates that JCurve 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 MarshallLerner condition and JCurve phenomenon.
3.0 RESEARCH METHODOLOGY
3.1 TRADE BALANCE MODEL
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 j over her nominal exports to the same trading partner. The model takes the following longrun (contegrating) form:
lnTBj,t= a0+a1 ln Yt,t+a2 lnYj,t+ a3lnRERj,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 j 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 j 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 MarshallLerner condition, we expects that
a3> 0. However, under JCurve 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 JCurve effect, the shortrun dynamics must be incorporated into the long run.
3.2 DATA DESCRIPTIONS
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 G7 countries are Canada, France, Germany, Italy, Japan and the UK.
For
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) /
Pj, where
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.
3.3 DESCRIPTIVE ANALYSIS
To estimate the cointegrating trade balance model with a view of testing the MarshallLerner condition and JCurve phenomenon, several econometric techniques were adopted in the past two decades. According to BahmaniOskooee and Kara (2005), many researchers providing evidence of trade elasticities such as Wilson and Takacs (1979), Warner and Kreinin (1983), BahmaniOskooee (1986), Marquez and McNeilly (1988) and Marquez (1990) employed common econometric approaches such as ordinary least square (OLS) or twostage 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 shortrun as well as the longrun response of the bilateral trade balance to real bilateral exchange rate adjustment, the convenient technique is to adopt errorcorrection 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 longrun relationships. Compared to Johansen approach where longrun 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 pretesting 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 longrun and shortrun 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).
3.4 AUTOREGRESSIVE DISTRIBUTED LAG (ARDL) BOUND TESTING APPROACH
An ARDL representation of equation is formulated as follows:
∆lnTBj,t
=
b0+
∑i=1m b1i ∆lnTBj,ti+
∑i=0m b2i ∆lnYt,ti+
∑i=0m b3i ∆lnYj,ti+
∑i=0m b4i ∆lnRERj,ti+
b5 lnTBj,t1+
b6 lnYt,t1+
b7 lnYj, t1+
b8 lnRERj,t1+
vt (2)
where m 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 Waldstatistics. Ftest is employed to test the existence of the longrun relationship. The longrun 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 nonexistence of the longrun relationship is
H0: b1= b2=b3= b4=0against the alternative hypothesis
H1: b1≠ b2≠b3≠b4≠0. The Ftest involves asymptotic critical value bounds which is nonstandard 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 Ftest estimation exceeds the respective upper critical values, then
H0is rejected indicating there is evidence of a longrun relationship between the variables regardless of the order of integration of the variables. Meanwhile, if the Ftest estimation is below the upper critical value, we fail to reject the null hypothesis; supporting lack of cointegration. On the other hand, if the Ftest falls into the bounds, then the result is inconclusive. According to Kremers et al. (1992), we can remedy an inconclusive case, by employing the errorcorrection term to establish the cointegration. Since this paper utilizes quarterly data, we impose four lags on each firstdifferenced variable in eq. (2) and provide the result of Ftest for cointegration in Table 1.
3.5 GENERAL ERROR CORRECTION MODEL (ECM)
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 shortrun dynamics with the longrun equilibrium without losing long run information. A general error correction model (ECM) of Equation (3) is formulated as follows:
∆lnTBt= b0+ ∑i=0m b1i∆ lnTBti
+
∑i=0m b2i∆lnYt,ti+ ∑i=0m b3i∆lnYj,ti +
∑i=0m b4i∆lnRERti+ λECt1+
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).
3.6 STABILITY TESTS OF BROWN ET AL. (1975)
The result of cointegration estimated from Equation (2) may not necessarily demonstrate that the estimated coefficients are stable as argued by BahmaniOskooee 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 shortrun dynamics to the longrun 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.
4.0 EMPIRICAL RESULTS AND DISCUSSION
Quarterly data from 2000Q1 to 2016Q4 period were used to estimate Equation (2) for six trading partners of US. The standard Augmented DickeyFuller (ADF) and PhillipsPerron 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 preroot testing involved in this paper. To estimate the shortrun and longrun relationship between variables, the number of length on the first difference variables must be identified first. According to BahmaniOskooee and Brooks (1999), this step is usually sensitive to laglength on each first differenced variable. Therefore, to validate this, the Fstatistic 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 laglength. 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 longrun 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 longrun. If the estimated Fstatistics 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 longrun relationship between the variables. However, at this stage, the results are still considered preliminary.
Table 1. The results of Ftest for cointegration (null hypothesis, WALD TEST)
Trading partner  Calculated Fstatistic 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 Fstatistics falls above the 1%, 5% and 10% upper bond respectively. 
After determining the longrun 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 BahmaniOskooee and Brooks (1999), if cointegration were found on each variables, the lagged order of the variables which jointly together form the lagged errorcorrection 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 longrun 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
REXti) in Panel A of Table 2 while the errorcorrection term based on different lag orders which is denoted by
ECt1in 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
Errorcorrection terms 
Diagnostic test  
i=0  i=1  i=2  i=3  i=4  ECt1  R2  LM test  
Canada  0.0487
(0.2198) 
0.5051
(1.8465) *** 
0.1882
(0.6475) 
0.48271
(1.6928) 
0.1338
(0.4732) 
0.2202
(0.6111) 
0.7065  1.5909
0.2280 

France  0.1078
(0.4374) 
0.4480
(2.9810)* 
0.6564  0.6654
0.7186 

Germany  0.0853
(0.3270) 
0.2371
(2.7322)* 
0.6708  0.6452
0.6666 

Italy  0.4509
(1.148) 
0.3048
(2.3677)** 
0.7018  4.5938
0.0010** 

Japan  0.003891
(1.001) 
0.0608
(0.5089) 
0.1898  0.9640
0.3302 

UK  0.1929
1.1296 
0.21506
(1.5107) 
0.5202  0.4390
0.8191 

*, ** and *** indicate statistical significance at 1%, 5% and 10% level.
Parenthesis for Panel A and Panel B indicate tratios. Parenthesis for LM test indicates the PValues. 
Panel A of Table 2 reflects the shortrun coefficient estimates of the lagged firstdifferenced real exchange rate to ascertain the JCurve phenomenon in this paper. Based on panel A of Table 2, there is no evidence of JCurve 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 JCurve 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 (
ECt1) 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 BreuschGodfrey 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 pvalue is more than 5% significance level indicating that this study fails to reject the null hypothesis. Meanwhile, most countries equations have a high Rsquared value which shows strong positive correlation between dependent and independent variables.
To explore the longrun 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
Income 
Foreign Income  Exchange Rate 
Canada  ARDL (3,1,4,4)  1.7796
(2.0932)*** 
0.49204
(2.0899)*** 
0.0418
(3.0121)* 
0.0075
(1.9702)*** 
0.4903
(2.3206)** 
France  ARDL (1,0,6,0)  0.1057
(0.2555) 
0.2687
(2.0902)** 
0.0049
(1.5032) 
0.011159
(2.1788)** 
0.152121
(1.8110)*** 
Germany  ARDL (5,3,5,0)  0.7309
(1.4312) 
0.3939
(3.1222)** 
0.0487
(1.9487)*** 
0.0104
(1.9336)*** 
0.2389
(2.2653)** 
Italy  ARDL (4,1,2,0)  0.3352
(0.7681) 
0.4207
(4.4801)* 
0.0301
(2.0139)** 
0.0117
(3.4005)* 
0.5337
(4.3571)* 
Japan  ARDL (1,0,1,0)  0.6062
(1.8814)*** 
0.7118
(7.7931)* 
0.0073
(1.5230) 
0.0117
(3.2335)* 
0.0012
(0.7325) 
UK  ARDL (3,1,2,0)  0.0723
(0.1907) 
0.3198
(2.4503)** 
0.0160
(1.7021)*** 
0.0173
(3.9901)* 
0.0164
(0.2175) 
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 tratios 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 MarshallLerner 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 shortrun 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 MarshallLerner 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 BahmaniOskooee and Brooks (1999) found that there is no specific pattern supporting the JCurve phenomenon. However, a real dollar devaluation has a favourable effect on the US trade balance. Meanwhile, in another study testing MarshallLerner condition between US and the six trading partners, BahmaniOskooee and Brooks (1999) found evidence of MarshallLerner 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 MarshallLerner condition only holds for Canada only.
Finally, the parameter stability tests were employed on Equation (3), which captures the shortrun dynamics of Equation (2) and the longrun effect of Equation (1). The stability of the shortrun and longrun 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
Figure 2. Plot of CUSUMQ for France
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 shortrun and longrun 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 
5.0 SUMMARY AND CONCLUSION
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 MarshallLerner condition. This paper has estimated the MarshallLerner condition and JCurve 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 shortrun and longrun 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 shortrun pattern supporting the evidence of JCurve effect in any of US’s bilateral trade. Nevertheless, the longrun results indicate that a real dollar devaluation has a favourable longrun effect on the US trade balance. This provide support that MarshallLerner 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 BahmaniOskooee and Brooks (1999) in terms of JCurve estimation only.
The limitation of this study is that the results could be spurious because no preroot testing was performed on each variable and all together. Although Autogregressive Distributed Lag (ARDL) framework does not require preroot 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 preroot 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 heteroscedasticityconsistent estimation model introduced by Newey and West (1987).
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