## Abstract

In this paper, we re-examine the relationship between trade flows, real effective exchange rates, and incomes by using the bilateral trade flows of 33 countries that form more than two-thirds of total world trade. For each country, we consider the bilateral trade flows of the country under consideration vis-à-vis all other countries. The analysis reveals the fact that for most of the countries, a real depreciation of the home currency has favorable effects on the home country’s trade balance in the long run. This long-run effect manifests itself in the short run for a small number of countries, indicating the fact that satisfying the Marshall-Lerner condition in the short run is more difficult. However, there is no evidence for the J-curve phenomenon, which suggests an initial deterioration in the trade balance in the short run following a depreciation.

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## Notes

- 1.
Hence, the J-curve is identified with the negative effect of depreciations on the trade balance in the short run, given that the ML condition is established. As emphasized in the literature (see, for example, Bahmani-Oskooee and Wang (2008) and Bahmani-Oskooee and Hegerty (2011) this definition of the J-curve, which is due to Rose and Yellen (1989), is somehow different from its traditional definition. When Magee (1973) first introduced the J-curve in the literature, he did not make a distinction between the short run and the long run. Hence, traditionally, the J-curve hypothesis is characterized as the negative effect(s) of devaluation on the trade balance, which is followed by positive effects.

- 2.
This empirical literature dates back to the pioneering study of Bahmani-Oskooee (1985).

- 3.
Bahmani-Oskooee and Wang (2008) have opened up a third line of empirical research in the J-curve literature. They argue that since the response of the trade balance of a country with respect to changes in the exchange rate between the country in question and one of its trading partners varies by commodity, using industry-level trade data and the real bilateral exchange rate would increase the benefits from employing disaggregate trade data. In a series of papers, although Bahmani-Oskooee and his co-authors (see Bahmani-Oskooee and Wang 2007; Bahmani-Oskooee and Hegerty 2011 among others) have shown that the use of industrial-level data provides more evidence in favor of the J-curve, the evidence still remains inconclusive. The more recent research in this area has focused on nonlinear reactions of trade balance to exchange rate changes. Bahmani-Oskooee and Fariditavana (2015), Bahmani-Oskooee and Fariditavana (2016), Bahmani-Oskooee et al. (2016), and Arize et al. (2017) among others, have shown that the effects of appreciation are different than those of depreciation, which supports the presence of asymmetric effects of real exchange rate changes on trade balance.

- 4.
See, for example, Boyd et al. (2001), for a derivation of a similar equation from aggregate import and export functions. The model defines the trade balance as the ratio of exports to imports instead of its traditional one: the difference of exports from imports. The purpose of this re-definition is purely empirical. It makes possible to use an full logarithmic model. We also have estimated a semi-logarithmic model, in which the trade balance variable is defined in its traditional way as the difference between exports and imports whereas all the other variables are expressed in logarithms. The results of this estimation is provided in the Appendix A.3.

- 5.
As a result, the analysis of panel data sets with large time series and cross-sectional dimensions has started to assume that the individual units of the data sets are interdependent, and advancements in this branch of the literature have recently been surveyed by Sarafidis and Wansbeek (2012) and Chudik and Pesaran (2013).

- 6.
They are assumed to be distributed independent of

*y*_{t}(country i’s income income),*y*_{jt}(country i’s trading partners incomes),*e*_{jt}, and**f**_{t}and allowed to be serially correlated over time. However, the common factors**f**_{t}can possibly be correlated with*y*_{t},*y*_{jt}, and*e*_{jt}. - 7.
We report the results associated with CCEMG estimators in Appendix A.2.

- 8.
Which implies that, in the case where

**f**_{t}contains unit root processes,*b*_{t},*y*_{jt},*e*_{jt}, observed factor and**f**_{t}must be cointegrated. However, as shown by Kapetanios et al. (2011), the results on the estimators of*β*_{j}and*γ*_{j}s hold even if the factor loading*λ*_{j}is zero (or weak in the sense of Chudik et al. (2011), and it is not necessary for*b*_{t},*y*_{jt},*e*_{jt}, observed factors and**f**_{t}to be cointegrated. What is required is that the idiosyncratic errors*u*_{jt}are stationary. - 9.
To capture the trend in real outputs, we run the CADF regressions with linear trends only. However, for the real exchange rate and trade balance, since the presence of the trend is not as apparent as it is for the real output, we prefer to run the CADF regressions, both with and without the linear trend, i.e., the intercept only.

- 10.
To save space, we do not report the results of the unit root tests for these 4 variables for all 33 countries in our sample. They are available upon request.

- 11.
To save space, the coefficient estimates of the observed factors and cross-sectional averages, which vary across trading partners of the country, are not reported. They are available upon request.

- 12.
Table II(b) in Pesaran (2007) of -2.08 CADF equations contain an intercept only.

- 13.
In all cases, 1 lag has appeared to be sufficient to capture all short-run effects. In other words, allowing more lags does not alter the results presented here.

- 14.
The half-lives are computed according to the following formula: \(-\frac {ln(2)}{ln(1+\phi )}\)

- 15.
It can be argued that not allowing more lags prevents the appearance of such effects. However, in all cases, 1 lag has appeared to be sufficient to capture all short-run effects. In other words, allowing more lags does not alter the results presented here.

- 16.
Note that only in 5 of these 8 countries the sign of the coefficient is correct (a positive sign is correct unlike the trade balance equation in Table 5).

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## Acknowledgements

The authors would like to thank the Editor and two anonymous referees for their helpful comments and suggestions. The usual disclaimer applies.

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## Appendices

### Appendix

### A.1 Results with CCEMG estimators

In this appendix we provide the estimation results when CCEMG is also preferred in the long-run estimation.

Table 6 provides the long-run coefficient estimates. In 22 countries, the real depreciation of the domestic currency leads to an improvement in the trade balance in the long run, supporting the validity of Marshall-Lerner condition. For most of these countries, the results indicate an improvement in the trade balance of more than 1 percent as a result of 1 percent real depreciation.

Table 7 presents the estimation results of panel error correction equations. We find evidence in favor of a significant positive relationship between exchange rate depreciation and the trade balance for only 3 countries in the short run. On the other hand, we could not find any support in favor of the J-curve hypothesis other than South Africa where a negative exchange rate coefficient appears to be significant. For all countries, the error correction coefficient estimates have the correct sign and are significant.

### A. 2 Long-run Causality

In this paper, following the related literature we have assumed that the causality runs from real exchange rate to trade balance not vice versa. In this appendix we question this assumption and to what extend the data supports the possibility of an reverse causality running from trade balance to real exchange rate as in Zhang and Macdonald (2014). To accomplish this task we also estimate the below panel error correction equation with real exchange rate being the dependent variable.

Together with Eq. (5), the above equation defines a panel vector error correction model with exogenous variables (PVECMX). Since all the *ϕ*_{j} in the trade balance equation (Table 5) are already found to be significant, testing the significance of the error correction coefficients \(\phi ^{\prime }_{j}\) in the real exchange rate equation provides a test for the long-run non-causality from trade balance to real exchange rate versus bi-directional causality. Table 8 provides the estimation results of the above equation. As can be followed from the table, in only 8 of the 33 countries error correction coefficients appear to be significant.^{Footnote 16} This evidence supports the long-run non-causality from trade balance to real exchange rate.

Additionally we calculate the cointegration tests for the “reverse” equation of real exchange rate. Table 9 presents the results. As can be seen from the table, the results are in favor of cointegration only for a few countries and only for some test statistics. This result constitutes a sharp contrast with those that are presented in Table 5, where, cointegration is supported by the data for almost all countries. This provides a further evidence on the uni-directional long-run causality running from real exchange rate to trade balance.

### A. 3. Results with semi-logarithmic model

In this appendix we provide all the estimation results with trade the trade balance is defined as the difference between exports and imports, without taking its logarithm where all the other variables are expressed in logarithms.

Table 10 provides the long-run coefficient estimates. In 18 countries the real exchange rate appear to have significant long run effects on the trade balance. In 14 of them, the real depreciation of the domestic currency leads to an improvement in the trade balance in the long run, supporting the validity of Marshall-Lerner condition. The coefficients estimates indicate the response of trade balance in billion US dollars as a response to 1 percent change in the real exchage rate. The magnitudes vary across countries from 150 billion to 3.5 trillion (Japan).

Table 11 illustrates the CIPS panel unit root test statistics for the estimated residuals \(\hat {u}_{jt}\). We conclude in favor of the stationarity for the majority of the countries up to lag 2, whereas the majority of these countries’ tests statistics indicate the presence of unit roots at higher orders.

Table 12 shows the result of panel cointegration tests. Overall the results indicate the presence of cointegration for the majority of the countries.

Table 13 presents the estimation results of panel error correction equations. We find evidence in favor of a significant positive relationship between exchange rate depreciation and the trade balance for 10 countries in the short run. On the other hand, we could not find any support in favor of the J-curve hypothesis other than Malaysia, Switzerland and the UK, where a negative exchange rate coefficients appear to be significant. For all countries, the error correction coefficient estimates have the correct sign and are significant.

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Yazgan, M.E., Ozturk, S.S. Real Exchange Rates and the Balance of Trade: Does the J-curve Effect Really Hold?.
*Open Econ Rev* **30, **343–373 (2019). https://doi.org/10.1007/s11079-018-9510-3

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### Keywords

- Competitive devaluation
- Marshall-Lerner condition
- J-Curve
- Panel data
- Panel data cointegration
- CCE estimator

### JEL Classification

- C23
- F10
- F30