Testing the J-curve hypothesis between South Africa and its five major trading

partners

Prepared by Kgalalelo Setou, Eliphas Ndou and Thabo M Mokoena *

South African Reserve Bank

Research Department

October 2011

Abstract

This paper investigates empirical evidence of a J-curve between South Africa and

five major1 trading partners, namely: the euro area, the United States (US), the

United Kingdom (UK), Japan and Switzerland. The paper expresses the bilateral

trade balances between South Africa and each foreign trading partner as a function

of real output in South Africa, and real outputs of trading partner countries using a

vector error correction model. The generalised impulse response functions confirm

evidence of a J-curve between the South African bilateral trade balance with the US

and the UK. The speed of adjustments suggests that 33,6 per cent of South Africa’s

trade balance with the US is achieved within a quarter but full adjustment takes

nearly three quarters. It takes about 2,75 quarters in the UK for the trade balance to

return to equilibrium at a speed of 36,3 per cent per quarter.

JEL classification: C12; C22 Keywords: Trade balance; J-curve; exchange rate depreciation; VECM Corresponding authors’ e-mail addresses: Kgalalelo.Setou@resbank.co.za Eliphas.Ndou@resbank.co.za Thabo.Mokoena@resbank.co.za *The views expressed are those of the author(s) and do not necessarily represent those of the South African Reserve Bank or

Reserve Bank policy. While every precaution is taken to ensure the accuracy of information, the South African Reserve Bank shall not be liable to any person for inaccurate information or opinions contained herein. This paper was prepared for the International conference on International Trade and Investment, held in December 2011 in Mauritius, Le Meridien Hotel. 1China has been excluded from the study due to unavailability of data.

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Table of Contents

1 Introduction ............................................................................................................ 2

2 Theory .................................................................................................................... 2

3 Literature survey.................................................................................................... 6

4 The model............................................................................................................... 8

5 Methodology .........................................................................................................12 5.1 Vector error correction model ..................................................................... 8

6 Data and empirical results ...................................................................................12 6.1 Dynamic impulse responses ...................................................................... 1 6.2 Variance decompositions ........................................................................... 3

7 Conclusion and policy implications ..................................................................... 5

List of Figures Figure 1 Supply and demand of foreign exchange ......................................................... 5 Figure 2 The j-curve ....................................................................................................... 5 Figure 3 Generalised impulse responses ....................................................................... 2 List of Tables Table 1 Unit Root Tests ...............................................................................................12 Table 2 Test for cointegration.......................................................................................14 Table 3 VECM results ................................................................................................... 0 Table 4 Forecast error variance decompositions ........................................................... 4

2

1 Introduction

The role of exchange rate depreciation on the trade balance has been examined

extensively in some economies and mixed evidence was reported. The level of South

Africa’s nominal exchange rate has been a concern raised in policy-related

discussions, which suggests that economic growth could potentially be stimulated

through the net exports channel. However, these discussions are often not backed by

any empirical evidence and tend to over-emphasise the role of rand–dollar

depreciation and not even a basket of currencies. This paper investigates evidence

and identifies South Africa’s five big trading partners: The euro area, the United

States (US), the United Kingdom (UK), Japan and Switzerland’s real exchange rate

depreciation that could lead to improvements in the trade balance or persistent

worsening in the trade balance, or could lead to a J-curve phenomenon in which

trade balance deterioration in the short run is offset by an improvement in the long

run.

Rose and Yellen (1989) suggest that a change in the exchange rate has price and

volume effects on trade flows. The price effect means currency depreciation causes

export goods to be cheaper to foreign buyers. The volume effect is such that in the

medium to long term, the volume of exports to a foreign country ought to increase as

the real income and purchasing power of the trading partner rise. However, if the rise

in real income is due to an increase in the production of import-substitute goods, then

imports may decline even as income increases. The impact of exchange rate

changes on the trade balance is therefore ambiguous.

Magee (1973) argued that after currency depreciation, the contracts that have been

concluded at an old exchange rate dominate the short-run response of the trade

balance. Over time new trade contracts at relatively competitive prices begin to exert

their favourable impact on trade volumes and boost elasticities, thus improving the

trade, leading to a J-curve effect. The impact of currency depreciation/devaluation on

the trade balance was initially analysed by estimating the Marshall-Lerner condition,

a mathematical condition stating that if the absolute values of the export and import

3

demand elasticities sum up to more than unity, then currency depreciation improves

the trade balance in the long run.

From an economic policy perspective, the motivation for the analysis appearing

below is as follows: The fundamental question of whether the exchange rate

depreciation can improve the trade balance needs to be quantified to determine

whether there exists a stable long-run relationship between the exchange rate and

the trade balance. The non-existence of a stable long-run relationship implies that

exchange rate depreciation may not improve the trade balance in the long run. As

Stučka (2004) points out, if a stable long-run relationship exits, it is beneficial to

quantify the degree of trade balance improvements in order to weigh the trade

balance benefits against the costs of permanent depreciation, such as higher

exchange rate pass-through to domestic prices, leading to a permanent rise in

inflation.

To the best of our knowledge, Kamoto (2006) and Moodley (2010) are the only

studies that have analysed the J-curve hypothesis with regard to South Africa.

Kamoto (2006) focused on the bilateral trade relations between the US and Malawi.

The study found that in the short run the South African trade balanced declined by

around 5 per cent due to a 1 per cent real depreciation. This is due to the price effect,

implying that a unit value of import increase resulted in a larger increase in total

imports relative to total exports. By contrast, Moodley (2010) focused on the J-curve

effect of South Africa and BRIC countries and used the long-term trade balance

model and autoregressive distributed lag (ARDL) model to search for the existence of

the J-curve effect. The author found that currency depreciation would not lead to a

long-term improvement in the trade balance. This is because the exchange rate is

one of many variables that influence both the exports and imports.

This paper’s focus is broader in that it explores the J-curve hypothesis for bilateral

relations between South Africa and its five major trading partners using the vector

error correction model combined with generalised impulse response functions. These

generalised impulse response functions introduced by Pesaran and Shin (1998)

suggest that the order in which the variables are arranged does not matter.

4

Based on generalised impulse response functions, we found support for the J-curve

in South African bilateral trade balances with the US and UK only. Thus, a real

depreciation of the rand against the US dollar and British pound leads to immediate

deterioration in the trade balance before improving it in long run, thereby supporting

the J-curve hypothesis.

The rest of the paper is organised such that section 2 briefly discusses the trade

balance theory, Section 3 discusses literature survey, Section 4 the model, Section 5

methodology, section 6 data and emperical results and section 7 concludes and

provides some policy implications.

2 Theory

According to Appleyard, Field and Cobb (2008), changes in the exchange rate bring

about appropriate switches in expenditures between domestic and foreign goods.

Assuming a current-account deficit, an increase in the exchange rate (depreciation of

the home currency) causes foreign goods to become more expensive, leading

consumers to reduce the consumption of imports and increase the consumption of

domestic alternatives. At the same time, home exports become relatively cheaper to

foreign buyers, causing them to switch expenditures from their own products to the

cheaper imports. Short-run elasticities of supply and demand, however, tend to be

smaller (in absolute terms) than long-run elasticities.

On the demand side, consumers do not often adjust immediately to changes in

relative prices due to the time it may take to change consumption plans or product

commitments. As such, they may be slow to react to changes in the exchange rate.

In general, contracts may already exist that commit importers to a certain volume of

imports at the previous exchange rate. In some instances, the volume of imports may

even rise if importers view the initial rise in the exchange rate as the first of several

rises to come, and purchase more in the present period to avoid higher domestic

prices in the future. It is therefore not surprising for the quantity of imports demanded

and hence the foreign exchange needed to remain relatively constant in the short run

even though the domestic currency is depreciating, making the short-run demand

5

curve for foreign exchange vertical as depicted by D’ in Figure 1 below. In the long

run, the demand curve for foreign exchange will approximate the long-run demand

curve D, as more normal quantity responses occur.

Figure 1 Supply and demand of foreign exchange

On the supply side of foreign exchange, the supply of exports may not increase

immediately in response to depreciation of the exchange rate (e) if producers choose

to raise the domestic price in response to increased foreign demand, thus increasing

short-term profit margins at the expense of increased sales. In addition, binding

contracts may already exist based on certain quantities at the old exchange rate. If

the quantity of exports does not rise in the short run with the depreciation of the

currency, then the short-run supply curve of foreign exchange will be backward-

sloping as depicted by S’ in Figure 1 above. With the passage of time, however, the

supply curve will take on characteristics of long-run supply curve S. Therefore, if

consumers and producers are unresponsive in the short run as depicted by Figure 1,

a depreciation of a home currency actually leads to short-run worsening in the trade

account before it ultimately gets better; a resultant response curve is often referred to

as the J-curve as depicted in Figure 2. In figure 2, X represents exports, M

represents imports, and X-M is the trade balance, which is a function of exchange

e

0

Foreign exchange

S’ D'

D

S

6

rate (e) over time. The longer both groups (consumers and producers) remain

unresponsive to the change in the exchange rate, the deeper the J-curve response.

Figure 2 The J-curve

Such an adjustment is crucial to policy-makers in that it adds to the uncertainty in the

currency market, and if the short-run market conditions are not stable, the exchange

rate can overshoot the new long-run equilibrium rate and adjust back down as long-

run responses become more evident.

3 Literature survey

In a recent study, Hsing and Sergi (2010) apply the vector error correction model and

generalised impulse response function to establish that in the case of the US and six

of its western European trading-partner countries, there is support for the J-curve

hypothesis with regard to Germany, but find no evidence in the case of Belgium,

France, Italy, Spain and the Netherlands.

Point of depreciation

(X – M) = f (e, time)

X –M (+)

Time

(-) )

0 )

7

In examining the relationship between the exchange rate and bilateral trade balance,

a common method of testing the J-curve, while controlling for other determinants,

Sun and Chiu (2010) found a stable long-run relationship for Taiwan and several of

its trading partners: China, Hong Kong, the US, Japan, South Korea and Malaysia.

The authors used the ARDL model and found that apart from the US, there is no

specific pattern supporting the J-curve phenomenon for these trading partners.

Contrary to J-curve studies on Malaysia, which were carried out using aggregate

trade data and found no support for the relation between the real value of the ringgit

and the Malaysia trade balance, Bahmani-Oskooee and Harvey (2010) used bilateral

trade data for Malaysia and its 14 largest trading partners, and provide some support

for the J-curve hypothesis. They used cointegration and error-correction modelling to

distinguish the short-run effects of currency depreciation from its long-run effects.

Gupta-Kapoor and Ramakrishnan (1999) tested the J-curve phenomenon for Japan

using an error correction model. The resultant impulse response function indicates

that the J-curve holds for Japan during periods of flexible exchange rate.

In investigating the macro-determinants of Korea’s persistent bilateral trade deficit

with Japan and its trade surplus with the US, Kim (2009) used Johansen’s

cointegration error-correction model on variables such as the trade balance, real

exchange rate, domestic and foreign incomes and relative money supply. Kim (2009)

found that all these variables affected bilateral trade balances and found the

existence of a long-run equilibrium among them. The J-curve effect was found to

exist between Korea and Japan.

In the case of Eastern European emerging economies, Bahmani-Oskooee and Kutan

(2009) analyse several new European Union (EU) members – Cyprus, the Czech

Republic, Hungary, Poland – and EU candidate members Bulgaria, Croatia, Romania

and Turkey. The method of testing the J-curve they use is to establish a direct

relation between the trade balance or the terms of trade and the real exchange rate

in addition to other determinants of the trade balance using the bounds-testing

approach. In the context of bounds testing, it at times becomes necessary to impose

a lag structure on the exchange rate to determine the existence of the J-curve effect,

8

which is supported if the exchange rate carries negative coefficients for short-horizon

lags followed by positive coefficients for longer-horizon lags. Using a bounds-testing

form of cointegration, the authors found support for the J-curve in 3 out of 11 cases:

Bulgaria, Croatia and Russia.

One major conclusion from the above analysis is that empirical support for the J-

curve effect exists but tends to be limited.

4 The model

The paper adopts the model in Hsing and Sergi (2010) to express the trade balance

as a function of real exchange rate and real foreign output. Imports are a function of

the real exchange rate and home real output. The bilateral trade balance between

South Africa and individual trading foreign partners is then expressed as a function of

the real exchange rate, real output in South Africa and the foreign trading partner

country, respectively.

),,( ,,,,

Foreign

tj

SA

titijtij YYEfTB [1]

tjiTB,

= trade balance in South African expressed in rands defined as the ratio of

exports (X) to imports (M),

tjiR, = SA

i

Foreign

jtji PPE, is real exchange rate. An increase in tjiR

, means real

depreciation of South African exchange rate per foreign currency

tijE ,= the nominal South African exchange rate (rand) per foreign currency unit

Foreign

jP = price level in the foreign trading-partner country

SA

iP = price level in South Africa (home)

Foreign

jY = the trading-partner country’s real GDP expressed in South African rand

SA

iY = the South African real GDP in rand

i = South Africa (home) country

j = the foreign trading-partner country.

9

This paper estimates equation [1] using the vector error correction model (VECM) to

derive the short-run relationship and the long-run cointegrating equations. We note

that each variable can affect the trade balance, either in a negative or positive way.

These possibilities are shown in equations [2], [3],[ 4] and, consequently, interpreted

accordingly.

00loglog orYTB SA [2]

00loglog orYTB Foreign [3]

00loglog orETB [4]

The first two equations show the impact of a change in real GDP in South Africa and

foreign trading-partner country respectively. The positive sign in equation [2]

indicates that higher real GDP in South Africa may reduce imports from a trading

partner due to growth in import-substitution production. The negative sign suggests

that higher real GDP in South Africa would increase imports from a foreign trading-

partner country and deteriorate the trade balance. The effects of foreign income are

shown in equation [3]. The positive sign indicates that higher real GDP in a foreign

trading-partner country leads to more exports from South Africa, whereas a negative

sign suggests that higher real GDP in the foreign trading partner may stimulate

growth in import-substitution production and reduce imports from South Africa.

Similar exchange rate depreciation may affect the trade balance in two ways as

indicated in equation [4]. The positive sign in equation [4] indicates that real

depreciation may lead to improvements in the bilateral trade balance when the

volume effect dominates the value effect. By contrast, a negative sign indicates that a

depreciation due to value-effect dominance over the volume effect results in a

deterioration in the bilateral trade balance.

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5 Methodology

5.1 Vector error corection Model This section explains briefly the cointegrating-VECM technique used in this empirical

investigation. We assume the reduced form VAR(p) model is given by equation [5].

p

i

titit eZZ1

. [5]

where tZ for nt ,...,2,1 is a 4x1 time series containing bilateral trade balance,

bilateral real exchange rate, as well as both domestic and foreign incomes. The i

is a 4x4 parameter matrix, p is the lag length, te is a 4x1 vector of white noise

series. A linear combination of cointegrated variables can be expressed in a vector

error correction mechanism of order p as in equation [6] where is difference

operator.

1

1

1 .p

i

tititt ZectZ [6]

1

1

1 .p

i

tititt ZectZ [7]

Equation [6] can be expressed in the form that includes both the first differences and

levels of time series in the model as in equation [7]. Equating equations 6 and 7

implies = where and represent the vector of speed of adjustment and

long run cointegration relationships respectively. The speed of adjustment ( ) shows

how the system converges to the long run equilibrium from the cointegration

regression. Alternatively, it is a measure of the average speed at which the

dependent variable adjusts to a change in an equilibrium condition. The lagged one

period error correction terms )(ect represents a deviation from the equilibrium in the

period 1t .

As defined in equation [1] under the model section, the cointegration equations for

South Africa’s trading partners are normalised around the trade balance variables.

11

However, will also report the speed of adjustment coefficients which show how these

trade balance variables converge to their long run equilibrium. The convergence

towards equilibrium requires the speed of adjustment value to be between 0 and -1.

Finding a negative error correction term which is statistically significant is a robust

evidence of the cointegrating relationship amongst the variables. Lastly the

coefficients in matrices i on itZ captures the short run causal dynamics of the

models.

Before proceeding with the above analysis we perform to test whether the variables

in the VAR have unit roots and whether cointegrating relationships exist. This should

provide valid statistical inferences on the estimated result. We test for unit roots using

the Augmented Dickey Fuller test, Phillips Perron and KPSS tests. Finding that

variables are nonstationary, we then proceed to perform lag length selection using

Akaike Information Criteria (AIC). Finally, we apply the Johansen Maximum

Likelihood (ML) cointegration test to establish whether there exists a linear

combination of variables that are integrated to order of one. There are two test

statistics produced by the Johansen ML procedure. Both can be used to determine

the number of cointegrating vectors present, sometimes they may not always indicate

the same number of cointegrating vectors. As an illustration, suppose that there are

r cointegrated relationships, the null hypothesis of the Trace test suggests the

number of cointegrating vectors is less than or equal to r , whereas the alternative

hypothesis suggests more than r . However, the null hypothesis of the Maximal

Eigenvalue suggest r cointegrating vectors against the alternative of )1( r vectors.

It is possible for these tests to indicate more than one cointegrating relationship. In

such a case we use economic theory to choose the relationship.

We conclude by testing for a possibility of J-curve effect, from the generalised

impulse responses functions from the estimated VECM. In particular, the impulse

responses functions will show the bilateral trade balances’ response to a one

standard deviation denoting a depreciation in the bilateral exchange rate. The

preceding statement implies that we should for look evidence similar to trade balance

path shown in figure 2.

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6 Data and empirical results

This paper uses quarterly data from the first quarter of 1998 to the fourth quarter of

2010. However, the data for the euro area starts from the first quarter of 1999, which

coincides with the adoption of the euro-area currency. We collected data from the

direction of trade statistics published in the International Financial Statistics (IFS) for

the bilateral trade and imports for South Africa and five trading partners, namely the

US, UK, Japan, Switzerland and the euro area.

Table 1 Unit root tests

Null hypothesis: Non-stationarity Non-stationarity Stationarity

Test ADF

PP KPSS

Variable Test statistic Test statistic Test statistic

USA

Log TB -3.467224* -3.447282* 0.495142*

Logrealexch -1.712113*** -1.702923*** 0.274563***

Logsay -0.885505*** -0.437266*** 0.940722

Logsausay -2.212150*** -2.581788*** 0.919465

UK

Log TB -2.574293** -4.092813 0.479377*

Logrealexch -1.475681*** -1.508342*** 0.284445***

Logsay -0.885505*** -0.437266*** 0.940722

Logsauky -1.915899*** -2.330399*** 0.871886

Euro area

Log TB -2.951321* -5.197292 0.150131***

Logrealexch -2.806981** -2.495853*** 0.206143***

Logsay -0.885505*** -0.437266*** 0.940722

Logsaeuroy -1.885994*** -1.982829*** 0.882377

Japan

Log TB -2.583276*** -2.436340*** 0.705406*

Logrealexch -1.609573*** -1.713846*** 0.407929**

Logsay -0.885505*** -0.437266*** 0.940722

Logsajapy -1.183473*** -1.309440*** 0.762613

Switzerland

Log TB -1.448562*** -2.632801** 0.822259

Logrealexch -3.006116* -2.623398** 0.086801***

Logsay -0.885505*** -0.437266*** 0.940722

Logsajapy -1.658390*** -1.684428*** 0.789179

1. Kwiatkowski-Phillips-Schmidt-Shin (1992, Table1)

* denotes acceptance of the hypothesis at the 0.01 critical level ** denotes acceptance of the hypothesis at the 0.01 and 0.05 critical levels *** denotes acceptance of the hypothesis at the 0.01, 0.05, and 0.10 critical levels

13

We begin by testing for stationarity of the variables to identify the order of integration

and proceed to test for cointegrating relationships in subsequent sections. Table 1

shows the unit-root test results based on three tests: Augmented Dickey-Fuller

(ADF), Phillips-Perron (PP) and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests.

The ADF test confirms the existence of unit roots in all variables. The PP rejects that

the UK trade balance is nonstationary. However, the KPSS test finds stationarity in

other variables and rejects it in other variables. Thus evidence on the stationarity is

mixed from the three tests. According to the ADF and PP tests, we proceed to test

whether there are any cointegrating relationships among these variables.

Table 2 shows the cointegration tests based on Trace eigen-value-statistics and

Maxi-eigen-value statistics. Both Trace-statistics and Maxi-statistics confirm the

existence of more than one cointegrating relationship between South Africa’s bilateral

trade balances with the US. In most cases the trace-statistics and maxi-statistics

indicate different numbers of cointegrating relationships. The Trace-statistics indicate

one cointegrating relationship under the UK. In the case of Japan the trace-statistic

indicates two cointegrating vectors whereas the maximum statistics indicates no

cointegration. The Maxi-statistics indicate one cointegrating relation with regard to

Switzerland. In general, the statistics confirm the existence of at least one

cointegrating relationship. However, where the statistics indicate more than one

cointegerating relationship, we rely on theory to decide on the specification of

cointegration equation.

The result in Table 2 suggests that there is a long-run equilibrium relationship among

bilateral trade balances between South Africa and the trading partners’ real GDP, the

real exchange rate and South African real output. Hence, we estimate a vector error

correction model, which is a restricted VAR estimated using nonstationary variables

in levels. The VAR lagged lengths vary from one to three lags is determined by AIC.

The results are presented in Table 3 and the graphs of the cointegrating relations are

in Appendix A.

Table 2 Test for cointegration

NB. Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level; * denotes rejection of the hypothesis at the 0.05 level. ** denotes rejection of the

hypothesis at the 0.10 level; ProbM: MacKinnon-Haug-Michelis (1999) p-values

Trace-eigenvalue test Max-eigenvalue test

Number of

cointegrating

equations

Eigenvalue Statistic Critical

Value

Prob M

Statistic Critical

Value

ProbM

USA None 0.453906 58.14987 47.85613 0.0040* 28.43331 27.58434 0.0389*

At most 1 0.267637 29.71656 29.79707 0.0511** 14.63948 21.13162 0.3150

At most 2 0.248897 15.07708 15.49471 0.0577** 13.45201 14.26460 0.0669**

UK None 0.395132 46.68948 47.85613 0.0641** 24.13179 27.58434 0.1302

At most 1 0.233418 22.55770 29.79707 0.2685 12.75905 21.13162 0.4746

At most 2 0.169550 9.798646 15.49471 0.2965 8.917824 14.26460 0.2931

Japan None 0.351922 48.04850 47.85613 0.0480* 20.81974 27.58434 0.2873

At most 1 0.316453 27.22877 29.79707 0.0962** 18.26207 21.13162 0.1203

At most 2 0.160746 8.966700 15.49471 0.3685 8.411606 14.26460 0.3384

Switzerland None 0.426647 42.84867 47.85613 0.1363 27.25640 27.58434 0.0550**

At most 1 0.199055 15.59227 29.79707 0.7406 10.87618 21.13162 0.6597

At most 2 0.090335 4.716085 15.49471 0.8382 4.639242 14.26460 0.7865

Euro area None 0.675727 69.53263 47.85613 0.0001* 52.92990 27.58434 0.0000*

At most 1 0.205876 16.60273 29.79707 0.6692 10.83423 21.13162 0.6638

At most 2 0.107422 5.768506 15.49471 0.7227 5.341164 14.26460 0.6983

Table 3 VECM results:

Dependent variable is log trade balance

US UK Japan Switzerland

Euro Area

Long-run equation c -0,904 -13,91 20,84 -103,75 2,2702

logR -1,59(1,40) 2,24(1,95)*** -3,3 (2,38)** 1,399 -0,34(1,14)****

Log Ysa

-1,10(0.84) 2,55 (1,92)*** -3,5(1,6) 10,3(3,56)** -0,1028

LogYforeign

1,83(-1,74)*** -1,84(1,94)*** 1,95(1,5) -3,4(1,9)*** -0,006

Speed of adjustment

ECT -0,336(-1,9)*** -0,363(-2,2)** -0,456(-3,4)* -0,500(-3,1)* -0,802(5,3)*

Adjustment per quarter 33,6% 36,3% 45,6% 50% 80,2%

Quarters to full adjustment

2,98 2,75 2,19 2 1,24

ECT is error correction term. * denotes significant at the 0.01 critical level, ** denotes significant at 5 per

cent, *** denotes significant at 10 per cent, ****denotes significant at 20 per cent. t-values are inside

the brackets.

We begin by interpreting the long-run equation in Table 3. We provide an economic

interpretation of the effects of the bilateral exchange rates, as well as domestic and

foreign income effects on the bilateral trade balances. We find that rand depreciation

against the Japanese yen, the US dollar and the euro leads to deterioration in the

South African trade balance relative to a particular partner country, suggesting that

the price effect dominates the volume effect. By contrast, the real depreciation

against the UK pound and Swiss franc has a positive impact on the bilateral trade

balances, indicating the dominance of the volume effect over the price effect in the

long run.

As stated in equation [3] there are two possibilities related to the domestic income

effects on the bilateral trade balances. We find that an increase in the South African

income (GDP) leads to deteriorations in bilateral trade balance with the US, Japan

and the euro area. This suggests that income is spent on imports, which worsens the

bilateral trade balances. However, a positive sign of the South African income on UK

and Switzerland bilateral trade balances suggests that growth in import-substitution

production reduces imports from these countries.

1

Lastly, we find a positive impact of both US and Japan incomes (GDP) on respective

bilateral trade balances. This suggests an improvement in bilateral trade balances

through foreigners buying more South Africa exports. Moreover, we find a negative

income effect in the UK, Switzerland and euro area on the bilateral South African

trade balances. This suggests that higher GDP growth in these countries leads to

growth in import-substitution production, thereby reducing imports from South Africa.

It is also important to quantify the percentage of the trade balance eliminated in each

quarter and the time taken towards full adjustment. Hence, we analyse the error-

correction terms reported in Table 3. The speeds of adjustments have the expected

signs and are statistically significant at all conventional levels. About 33,6 per cent of

South Africa’s trade balance with the US is significantly eliminated within a quarter

but full adjustment takes nearly three quarters. In addition, the percentage of the

trade balance eliminated towards equilibrium is 36,4 per cent for the UK, 45,6 per

cent for Japan, 50 per cent for Switzerland and 80,2 per cent with the euro area. This

means it takes about 2,75 quarters in the UK, 2,19 quarters in Japan, 2 quarters in

Switzerland and 1,24 quarters in the euro area for these bilateral trade balances to

go back to equilibrium.

6.1 Dynamic impulse responses

This section examines the reactions of South African bilateral trade balances to the

bilateral real exchange rate depreciation shocks using generalised impulse

responses. We look for a J-curve similar to the one displayed in Figure 2. The

generalised impulse responses functions of the real exchange rate depreciation

effects on respective bilateral trade balances are shown in Figure 3.

We find three patterns regarding the response of the bilateral trade balance in

response to bilateral real exchange depreciation shocks. Firstly, a real depreciation

of the rand against the US dollar and the real depreciation of the rand against the

British pound show a J-curve in the trade balance. It is seen that the initial worsening

of the trade balance is followed by an improvement over time. Secondly, we find

persistent worsening in the bilateral trade balances in response to the rand’s real

depreciation against both the Japanese Yen and Swiss franc shocks. Thirdly, the

2

South African bilateral trade balance with the euro area shows a J-curve followed by

deterioration in longer horizons in response to real depreciation of the rand against

the euro.

Figure 3 Generalised impulse responses

USA UK

-.07

-.06

-.05

-.04

-.03

-.02

-.01

.00

.01

.02

1 2 3 4 5 6 7 8 9 10

Response of LOGTB to Generalized OneS.D. LOGREALEXCH Innovation

-.012

-.008

-.004

.000

.004

.008

.012

.016

1 2 3 4 5 6 7 8 9 10

Response of LOGTB to Generalized OneS.D. LOGREALEXCH Innovation

Japan Switzerland

-.09

-.08

-.07

-.06

-.05

-.04

-.03

-.02

-.01

.00

1 2 3 4 5 6 7 8 9 10

Response of LOGTB to Generalized OneS.D. LOGREALEXCH Innovation

-.13

-.12

-.11

-.10

-.09

-.08

-.07

1 2 3 4 5 6 7 8 9 10

Response of LOGTB to Generalized OneS.D. LOGREALEXCH Innovation

Euro Area

-.04

-.03

-.02

-.01

.00

.01

1 2 3 4 5 6 7 8 9 10

Response of LOGTB to Generalized OneS.D. LOGREALEXCH Innovation

3

6.2 Variance decompositions

This section examines the quantitative significance of the variables that explain

bilateral trade balance movements. The results are presented in Table 4 below. The

bilateral trade balances are largely exogenously determined in the first eight quarters

as more than 60 per cent of volatilities are explained by own movements in bilateral

trade balance across the five countries. The percentages of variances explained by

own bilateral trade balance movements are often persistent between South Africa

and US, UK and Switzerland as they are explained 100 per cent in the first quarter

and 71 per cent in 24 quarters.

We find that real exchange rate depreciation against the US dollar and UK pound

explains less variability in the respective bilateral trade compared to the proportion

explained by domestic income. However, we find that the exchange rate becomes

significantly important for bilateral trade movements against the euro area, Japan

and Switzerland, with the euro, Japanese yen and Swiss franc, accounting for 63 per

cent, 34 per cent and 21 per cent in 24 quarters respectively. Moreover, among

foreign incomes we find that the Japanese income explains the highest variability in

bilateral trade movements, accounting for 23 per cent in 24 quarters.

4

Table 4 Forecast error variance decompositions of the trade balance

Period S.E. LOGTB LOGREALEXCH LOGY

SA LOGY

Foreign

USA

1 0.159095 100.0000 0.000000 0.000000 0.000000 4 0.237100 84.00575 1.602873 11.21705 3.174328 8 0.244466 81.59085 2.024944 11.32065 5.063550 12 0.249393 78.46898 3.129241 11.41589 6.985882 16 0.255178 75.62661 4.237788 11.50526 8.630335 20 0.260996 73.35299 5.163305 11.43095 10.05275 24 0.266627 71.33147 5.985820 11.32148 11.36123 UK

1 0.164588 100.0000 0.000000 0.000000 0.000000 4 0.201472 91.69722 0.520492 5.824139 1.958145 8 0.233723 85.24531 1.868445 9.111977 3.774273 12 0.256234 80.96029 3.718670 10.51525 4.805794 16 0.276114 77.32130 5.532754 11.62147 5.524482 20 0.294477 74.39903 7.052647 12.47788 6.070447 24 0.311699 72.06624 8.282832 13.15199 6.498939 Euro Area

1 0.067400 100.0000 0.000000 0.000000 0.000000 4 0.076797 84.89490 4.900210 2.210362 7.994527 8 0.092026 60.32935 31.47954 2.590638 5.600470 12 0.116904 39.84927 51.35047 5.290902 3.509362 16 0.134706 33.10005 57.60789 6.438071 2.853989 20 0.148203 29.66853 61.04209 6.749036 2.540345 24 0.160704 27.00925 63.77321 6.944472 2.273059 Japan

1 0.154375 100.0000 0.000000 0.000000 0.000000 4 0.219689 78.49750 9.288273 3.206935 9.007293 8 0.303924 51.63060 29.18440 4.126368 15.05864 12 0.374528 42.35161 32.48115 6.048515 19.11872 16 0.432521 38.36046 33.15638 7.019619 21.46354 20 0.483278 35.93547 33.69019 7.546356 22.82799 24 0.529251 34.29544 34.07357 7.900259 23.73073 Switzerland

1 0.395250 100.0000 0.000000 0.000000 0.000000 4 0.505173 82.09259 6.309890 6.191439 5.406082 8 0.600529 76.06544 14.07982 4.786591 5.068141 12 0.690442 73.89668 17.33159 3.632877 5.138857 16 0.771151 72.73856 19.11384 2.918950 5.228646 20 0.843965 71.95149 20.32195 2.440468 5.286091 24 0.910929 71.38292 21.19330 2.097764 5.326016

5

7 Conclusion and policy implications

We found support for the J-curve effect from the generalised impulse response

functions in South African bilateral trade balances with the US and the UK only.

Thus, a real depreciation of the rand against the dollar and British pound leads to

immediate deterioration in the trade balance before it improves in the long run. It was

found that the depreciation of the South African rand against the Japanese yen, the

Swiss franc and the euro led to deterioration in the trade balance, suggesting that the

price effect dominated the volume effect.

There are some policy implications related to long-run equation findings. However,

these results should be treated with caution as some variables in the cointegrating

relationships are marginally significant and the sample period is short in some cases.

The long-run negative relationship between bilateral real exchange rate and bilateral

trade balance between South Africa and US, Japan and the euro area suggests that,

over the long term, the price effect of goods from these countries exceeds the

volume of goods exported by these countries. Hence, in the long term, after

accounting for inflation effects, South Africa spends more resources on goods bought

abroad than what it actually receives. South Africa, in long term, is better off through

receipts of its exports than imports from the US and Switzerland.

We find that an increase in South African income leads to deteriorations in the

bilateral trade balance with the US, Japan and euro area. This suggests that South

African income is spent on imports, which worsens the bilateral trade balances.

However, a positive sign of South African income on the UK and Switzerland bilateral

trade balances suggests that growth in import-substitution production reduces

imports from these countries. A negative effect of an increase in incomes in the UK,

Switzerland and the euro area on South African bilateral trade balances suggests

that higher GDP in these countries may lead to growth in import-substituting

production which reduces imports from South Africa. In policy terms this suggests

6

that it is important to identify where the substitution of the production of importable

goods rises faster to enable economic growth.

We also found evidence that trade movements, depending on the trading partner,

can be explained by foreign income, as in the case of Japan, and the real exchange

rate depreciation, especially for the euro area, Japan and Switzerland. Domestic

incomes become better explanatory variables, particularly in the bilateral trade

balance movement with the UK and the US. These findings imply that any emphasis

on real exchange depreciation should be directed to particular trading partners and

cannot be generalised to all trading partners. The possibilities of growth in import-

substitutions linked with foreign income should not be under-estimated during policy

discussions.

7

References

Bahmani-Oskooee, M and Ratha, A. 2004. The J-curve: A literature review. Applied

Economics, 36, 1377–1398.

Freeman, R. 1982. J-curves and stability of the foreign exchange market.

International Finance Discussion Papers, Number 198.

Hsing, Y and Sergi B S. 2010. Test of the J-curve hypothesis between the US and

six European countries and policy implications. Journal of Transnational

Management, 15:2, 176–185.

Kamoto, E B. 2006. The J-curve effect on the trade balance in Malawi and South Africa. Master of Arts in economics thesis, The University of Texas at Arlington. Kim, A. 2009. An empirical analysis of Korea’s trade imbalances with the US and Japan. Journal of the Asia Pacific Economy, Vol.14, No.3, 211–226.

Juselius, K. 2006. The cointegrated VAR model, methodology and applications.

Oxford University Press.

Magee, S P. 1973. Currency contracts, pass through and devaluation, Brooking Paperson Economic Activity’, 1, 303–25. Moodley, S. 2010. An estimation of the J-curve effect between South Africa and the BRIC countries. Master of Business Administration thesis, Gordon Institute of Business Science, University of Pretoria. Pesaran, M H and Shin Y. 1998. Generalized impulse response analysis in linear multivariate model. Economic Letters, 58, 17–29.

8

Rose, A, and Yellen, J L. 1989. Is There a J-curve? Journal of Monetary Economics, 24, pp. 53–68. Stučka, T. 2004. The effects of exchange rate change on the trade balance in Croatia. IMF Working Paper Series, No. WP/04/65. Sun, C and Chiu, Y. 2008. Taiwan’s trade imbalance and exchange rate revisited.

Applied Economics, 42:7, 917–922.

Appendix A: Cointegrating relations graphs

USA UK

-.6

-.4

-.2

.0

.2

.4

.6

99 00 01 02 03 04 05 06 07 08 09 10

Cointegrating relation 1

-.8

-.6

-.4

-.2

.0

.2

.4

.6

98 99 00 01 02 03 04 05 06 07 08 09 10

Cointegrating relation 1

Japan Switzerland

-.6

-.4

-.2

.0

.2

.4

.6

.8

98 99 00 01 02 03 04 05 06 07 08 09 10

Cointegrating relation 1

-0.8

-0.4

0.0

0.4

0.8

1.2

98 99 00 01 02 03 04 05 06 07 08 09 10

Cointegrating relation 1

Euro area

9

-.3

-.2

-.1

.0

.1

.2

.3

99 00 01 02 03 04 05 06 07 08 09 10

Cointegrating relation 1