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Is There A J-Curve? A NewEstimation for JapanGupta-Kapoor Anju a & Ramakrishnan Uma aa Georgetown UniversityPublished online: 23 Aug 2006.

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INTERNATIONAL ECONOMIC JOURNAL Volume 13, Number 4, Winter 1999

IS THERE A J-CURVE? A NEW ESTIMATION FOR JAPAN

ANJU GUPTA-KAPOOR AND UMA RAMAKRISHNAN* Georgetown University

The controversial J-curve phenomenon is empirically tested using quarterly data for Japan between 1975:l and 1996:4. The effects of an appreciation of yen on the ratio of imports to exports (MIX) is analyzed using an error correction model. The impulse response function indicates that the J-curve holds for Japan during the flexible exchange rate regime. [F31, F32, F40]

1. INTRODUCTION

A change in the exchange rate has two effects on trade flows--price effect and volume effect. The price effect implies that a currency depreciation will cause imports to be more expensive and domestic exports to be cheaper for foreign buyers at least in the short run. Since the volume of goods imported and exported might not change drastically in the short run, the trade balance may initially deteriorate. However, the volume of trade changes eventually in response to the depreciation. In other words, the

I price effect is generally believed to dominate the volume effect in the short run. In the long run, however, if the Marshall-Lerner condition holds, the volume effect takes over and reverses the effect, and the trade balance improves. The total effect when plotted over time with trade balance on the y-axis will yield the J-curve.

This conventional wisdom on the J-curve has been called into question by Rose and Yellen (1989), who conclude that the J-curve phenomenon does not hold for the G-7 countries. Using a sample of 1960: 1 to 1985:4, they find no cointegration among the variables of interest and therefore use OLS and IV techniques to estimate the process. Rose (1990) performs the same exercise for a sample of developing countries and again finds that the J-curve phenomenon does not hold. Rose (1991) examines the empirical relationship between real effective exchange rate and aggregate trade balance for five major OECD countries for the post-Bretton Woods

I era. He shows some evidence of linear feedback from the exchange rate to the trade balance in the medium and long run only for Japan.

Backus (1993) examines the evolution of real trade balance for Japan using quarterly data from 1955:2 to 1993:2. Using vector autoregression (VAR) technique and the impulse response function, he reports the presence of a J-curve for Japan (the variables he considers are terms of trade and real balance of trade). He also forecasts

*The authors would like to thank Robert Cumby, Ivan Pastine, Tuvana Demirden, and two anonymous referees for their comments. All remaining errors are ours.

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72 A. GUPTA-KAPOOR AND U. RAMAKRISHNAN

that the trade surplus will fall from a high of 3.7 percent of GNP in 1992 to 2.6 percent in 1995. Demirden and Pastine (1995) indicate the presence of a J-curve for the United States using the VAR technique over the period 1975: 1 to 1990:4.

Bahmani-Oskooee and Alse (1994) examine the relationship between the ratio of imports to exports (MIX) and real effective exchange rate (REER) for many countries using the error correction method. For Japan, they find MIX to be stationary in levels, and therefore they drop the country from further analysis. The countries for which they estimate the J-curve, they find little evidence of a long run relationship between MIX and REER.

In this paper, we use an error correction model (ECM) to determine whether quarterly data on Japanese exports and imports exhibit a J-curve during the flexible exchange rate regime, between 1975:l to 1996:4. The impulse response function from the model is used to examine the J-curve phenomenon. Based on conventional wisdom, one would expect an equilibrium long-run relationship between trade balance and exchange rate. We also cany out robustness checks to verify the strength of this relationship.

The paper is organized as follows. Section 2 provides the basic model and explains the estimation technique of the study. Section 3 analyzes the results and provides robustness checks. Finally, the conclusions of the study are stated in section 4.

2. MODEL AND ESTIMATION

The J-curve is a nominal phenomenon.' The nominal merchandise trade balance, BN, is the difference between the value of merchandise exports (X) and imports (M). Following Bahmani-Oskooee and Alse (1994), we define the trade balance as the ratio of M to X. As explained in their study, this ratio is not sensitive to the units of measurement.

X and M are functions of domestic income, foreign income and exchange rate. The reduced form equation for J-curve estimation in log-linear form is thus:

where, YN and YN are nominal domestic and foreign incomes, NEER is the nominal effective exchange rate, and v is the error term. NEER is defined as the weighted average of the indexed bilateral exchange rates: NEER = FIi[(e{e)* 100/(e{e)'990~2]wr,

where i refers to the domestic country's (i.e., Japan) main trading partners (namely, US, Canada, Germany, France, UK, Italy, and Korea), and wi are their respective trade

'All the studies in the literature so far have used real data to analyze the J-curve. The distinction between the real and nominal frameworks is highlighted by Meade (1988), but she does not provide any empirical analysis.

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IS THERE A J-CURVE? 73

weights. ei is the number of units of each trading partner's currency per dollar, and e is the number of units of domestic currency (yen) per unit of foreign currency (US dollar). (ei / e) has been indexed to 1990:2. Based on the above equation, an appreciation is given by a rise in NEER. However, since we use the ratio of imports to exports to define trade balance, a currency appreciation should lead to a decline in MIX in the domestic country in the short-run (due to price effect), and to an increase in MIX in the long-run (due to volume effect).

In most of the studies done so far on the J-curve, attention is paid only to the direct effect and not to the feedback effect. The effect of a depreciation of the exchange rate on the balance of trade, given by the partial derivative aB/aE, shows the direct effect of the depreciation. However, feedback effects arise from a one-time change in exchange rate which will have an impact not only on the balance of trade, but also on the future exchange rate, which will in turn affect the balance of trade and so on. Further, there are additional feedback effects from other endogenous variables, such as domestic income and foreign income. These feedback effects (which could be linear or non-linear), represented by the total derivative dB/de, have to be captured to analyze the dynamics of the J-curve. A vector autoregression and the impulse response function will take these feedback effects of the exchange rate fluctuations into account.

Before estimating a VAR, we first carry out diagnostic tests for unit roots. If the series have unit roots in levels, then first differencing usually makes them stationary. If the variables are individually I(1), then the existence of a stationary relationship among the variables implies that they are cointegrated. If a VAR in first difference is estimated, the model would still be misspecified because variables in levels contain useful information for forecasting beyond what is contained in a finite set of lagged changes in the variables alone (Hamilton, 1994: 573). On the other hand, a vector error correction (VEC) model which introduces the restrictions implied by the long run relationship would be appropriate.

Accordingly, this paper uses the following specification of the VEC model for estimation.'

where 2, = vector of endogenous variables, viz., [MIX, NEER, YN, yN] p, = deterministic component

3;. = matrix of coefficients

n=apJ, where a is the speed of adjustment parameter, and P' is the cointegrating vector, and

u, = residual matrix.

ZSee Hamilton (1994: Ch. 19) for a detailed analysis of the Vector Error Correction model.

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74 A. GUPTA-KAPOOR AND U. RAMAKRISHNAN

The impulse response function and the variance decomposition effectively capture the dynamic properties of the system. We focus on the impulse response function along with the corresponding standard errors to capture the J-curve phenomenon.

3. RESULTS

Data

Quarterly data ranging from 1975: 1 to 1996:4 are used for the analysis. Logarithms of all variables are used to estimate the VEC model given by equation (2). The model is estimated with three lags of each variable. GDP in current dollars is used as a proxy for income of Japan. Rest of the world income is estimated by taking the weighted average of the purchasing power parity (PPP) adjusted GDP of the seven trading partners of Japan. The weights are based on the share of exports and imports of the country with Japan in 1990. The share of these seven countries accounts for about 65 percent of Japan's trade.

All the variables except PPP that are used in the construction of nominal and foreign GDP are drawn directly from the International Financial Statistics data tapes. PPP is drawn from the Penn World Tables, version 5.0, and the OECD Main Economic Indicators. The trade share of the other seven countries, that constitute the rest of the world, with Japan are drawn from the Direction of Trade Statistics (1992). NEER is constructed as noted earlier.

Time Series Properties and Cointegration Analysis

Unit root tests were conducted on each variable to test for stationarity with three lags. Non-stationarity in levels characterizes NEER, MIX, and domestic i n ~ o m e . ~ These variables become 1(0) upon first differencing. However, foreign income is 1(0) at the 1% level of significance. As Hansen and Juselius (1995: 1) have noted, "not all individual variables included in Z, need be I(1), as is often incorrectly assumed. To

find cointegration, between non-stationary variables, only two of the variables have to be I(1)". The system of variables should be chosen because of their economic relevance, and not merely for their time series properties.

Johansen's likelihood ratio cointegration test was performed to analyze the cointegrating relationship among the variables. The results are reported in Table 1. There are 2 cointegrating equations at the 5% level of significance. Note that, generally, for every I(0) variable in the model, the cointegration rank increases

3The regressions were run with an intercept but no time trend. The Augmented Dickey Fuller test statistics at the 5% level of significance are -1.95, -1.5, -2.7, and -3.7 for MIX, NEER, Y,,,, and pN, respectively. The unit roots were not found to be sensitive to a time trend for the variables considered.

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IS THERE A J-CURVE? 75

accordingly (Hansen and Juselius, 1995:l). In our model, foreign income is I(O), and therefore we get two cointegrating vectors.

Table 1. Johansen's Cointegration Test for Nominal Variables - -

Eigenvalue Likelihood 5 Percent 1 Percent Hypothesized Ratio Crltlcal Value Crit~cal Value No. of CE(s)

- - - -- -- - - - - - --

0.44 98.03 53.12 60.16 None **

0.30 48.08 34.91 41.07 At most 1 **

0.12 17 61 19.96 24.60 At most 2

0.07 6.56 9.24 12.97 At most 3 - - - - - -

Note: ** denotes rejection of null at 1% level Series: M/X NEER FN YN

The cointegrating relation, given by the 0 matrix, can often be interpreted as a long-run relationship among the variables in levels. Our P matrix indicates that when the yen appreciates by I percent, the long run increase in the ratio of MIX is 4.1 p e r ~ e n t . ~ However, this long-run relationship between MIX and exchange rate is not unique since there are two cointegrating equations. Therefore, the interpretation of the cointegrating equations is no longer straight forward. Since any linear combination of variables will preserve the stationarity of the residual in a cointegrating equation, there is an identification problem.

We consider the response of the ratio of M to X to an impulse (innovation) in exchange rate. The impulse response function indicates that the nominal data used for the analysis follow the J-curve pattern. The period of the short-run deterioration in MIX follows the conventional wisdom that it will last for about one year.5 Figure 1 plots the responses of MIX to a one-time appreciation of yen.

Figure 1 indicates that the initial deterioration in the ratio MIX is 1.1 percent for a one standard deviation shock in exchange rate of about 4.6 percent. The percentage change in the ratio MIX that is obtained through the impulse response function is converted to MIX values by normalizing the first period response to 100. Thus, the ratio of MIX deteriorates to around 99 in the first quarter, and declines to a maximum of 97.8 by the fourth quarter which is equivalent to a 2.2 percent fall from the initial level. The short-run price effect lasts for four quarters, beyond which the volume effect sets in. By the sixth quarter, the initial deterioration in MIX caused by the price effect has been fully recovered, and the ratio MIX continues to

'Test results available upon request. 'Krugman and Obstfeld (1 991 : 45 1).

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76 A. GUPTA-KAPOOR AND U. RAMAKRISHNAN

rise at a decreasing rate. The dotted lines are the 95% confidence intervals. They show that the short-run deterioration is somewhat significant and the long-run rise is highly significant.

Figure 1. Response of MIX to a 4.6 Percent Appreciation in Nominal Effective Exchange Rate

Robustness Checks

All previous studies have used real variables for the J-curve analysis. To check the robustness of our results, we performed the same analysis using three lags with all real variables. We use GNP at 1990 prices for real income of Japan, Y,. Y*R is the weighted average of GDP at 1990 prices for the same group of countries as in the nominal analysis. The real effective exchange rate (REER) is computed as follows:

1990:2 W l

R = REER = n. ( 5.x , loo/ ( 5.L ) 1 . where i refers to Japan's major

trading partners. R E ~ R is defined as the weihted average of the indexed bilateral real exchange rates. ei is the number of units of each trading partner's currency per US dollar, p is Japan's wholesale price index, and pi is the consumer price index of the trading countries. Based on the above calculations, an increase in REER implies that the currency has appreciated. The estimation of an error correction model with three lags of the above variables indicates that a J-curve prevails with the real variables also.' A 4.1 percent shock to REER results in a decline in MIX for four quarters as in the nominal analysis. By the fifth quarter, the decline in

6All variables except REER are I(1).

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IS THERE A J-CURVE? 77

MIX is fully reversed.' To check robustness further, we introduced ln(PdPx) also as an endogenous

variable in order to check whether the movement in the price ratio is as predicted by theory, i.e. a rise in Px in the short-run following an appreciation. An error

correction model was analyzed using five endogenous variables, namely, NEER, M E , PM/PX, Yw YN ."

Figure 2. Relative Price Change With a 4.5 Percent Appreciation in Nominal Effective Exchange Rate

'To conserve space, the figure is not reproduced here. It is available from the authors upon request.

8 P d P x is non-stationary in levels and stationary in first difference.

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78 A. GUPTA-KAPOOR AND U. RAMAKRISHNAN I

Figure 2 presents the impulse responses of MIX and P d P x due to an appreciation in yen. In the short run, the price ratio clearly deteriorates (due to the rise in P,) until the fourth quarter, capturing the price effect caused by an appreciation of the yen. This results in the fall in MIX (as shown by the upper panel of the figure) which also lasts till the fourth quarter. Beyond the fourth quarter, the percentage change in price ratio stabilizes. The long-run improvement in the trade balance is due to the volume effect (as explained earlier). This analysis is consistent with Meade's (1988) "textbook J-curve" description.

1

4. CONCLUSIONS

The focus of the paper was to use an error correction model, and the impulse response function to determine whether a J-curve exists with Japanese data. The results of the analysis imply that the J-curve phenomenon holds for Japan. In fact, the results generally follow the pattern predicted by theory. The presence of cointegration implies that there is a long-run equilibrium relationship between MIX and the exchange rate.

As for the J-curve itself, several reasons may be responsible for the lag in volume adjustment in response to a change in exchange rate. Firstly, finding alternative supply sources are costly for the buyers of goods. Therefore, the volume will not adjust unless the impact of the change in price outweighs the adjustment costs. Secondly, there may be lags in finding new investment opportunities to take advantage of the exchange rate. Thirdly, contractual obligations force trade to occur at the volumes set prior to the depreciation. It is difficult to test some of these reasons - they serve more as plausible explanations rather than testable hypotheses.

REFERENCES

Backus, David K., "The Japanese Trade Balance: Recent History and Future Prospects," Paper prepared for "Trade Policy and Competition," Tokyo, Japan, 1993.

Bahmani-Oskooee, Mohsen and Alse, Janardhanan, "Short-Run Versus Long-Run Effects of Devaluation: Error Correction Modeling and Cointegration," Eastern Econoinic Journal, Fall 1994,453-64.

Demirden, Tuvana and Pastine, Ivan, "Flexible Exchange Rates and the J-Curve," Economic Letters, 1995, 373-77.

Direction of Trade Statistics, Washington: International Monetary Fund. 1992. Hamilton, James D., Time Series Analysis, Princeton: Princeton University Press,

1994. Hansen, Henrik and Juselius, Katarina, CATS in RATS: Cointegration Analysis of

Time Series, Evanston: Estima, 1995.

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IS THERE A J-CURVE? 79

Krugman, Paul and Obstfeld, Maurice, International Economics, 2nd edition, New York: Harper Collins, 199 1.

Meade, Ellen E., "Exchange Rates, Adjustment, and the J-Curve," Federal Reserve Bulletin, October 1988, 633-44.

Organization for Economic Cooperation and Development, Main Economic Indicators, various issues.

Rose, Andrew K., "Exchange Rates and the Trade Balance: Some Evidence from Developing Countries," Economic Letters, 1990, 271-75.

Rose, Andrew K., "The Role of Exchange Rates in a Popular Model of International Trade: Does the Marshall-Lerner Condition Hold?," Journal of International Economics, 1991, 301-316.

Rose, Andrew K. and Yellen, Janet L., "Is There a J-Curve," Journal of Monetary Economics, 1989,53-68.

Mailing Address: Dr. Uma Ramakrislznan, 6252 Musefield Court, Alexandria, VA 22304, U.S.A. Tel: (202) 623-5413, E-mail: urarnakrishnan@imf:org Mailing Address: Professor Anju Gupta-Kapoor, Department of Economics, Georgetown University, Washington, DC 20057, U.S.A. Tel: (202) 687-5563, E-mail: guptaal @gusun.georgetown.edu

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