Exchange rate depreciation and exports: The case of Singapore revisited

Exchange rate depreciation and exports:
The case of Singapore revisited


WenShwo Fang
Feng Chia University and the Overseas Chinese Institute of Technology
wsfang@fcu.edu.tw

Stephen M. Miller
University of Nevada, Las Vegas
stephen.miller@ccmail.nevada.edu

November 2004

This paper revisits the weak relationship between exchange rate depreciation and exports for
Singapore, using a bivariate GARCH-M model that simultaneously estimates time-varying risk.
The evidence shows that depreciation does not significantly improve exports, but that exchange
rate risk significantly impedes exports. In sum, Singaporean policy makers can better promote
export growth by stabilizing the exchange rate rather than generating its depreciation.

Keywords: depreciation, exchange rate risk, exports, bivariate GARCH-M model
JEL classification: F14, F31




*Corresponding author: Stephen M. Miller, Department of Economics, University of Nevada,
Las Vegas, 4505 Maryland Parkway, Box 456005, Las Vegas, NV 89154-6005.

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Exchange rate depreciation and exports:
The case of Singapore revisited
I. Introduction
A traditional view expects that exchange rate depreciation improves exports. For example, Junz
and Rhomberg (1973) and Wilson and Takacs (1979), employing data from a fixed exchange rate
period, and Bahmani-Oskooee and Kara (2003), using data from a flexible exchange rate period,
provide evidence that depreciation improves exports for developed countries. In an interesting
paper, Abeysinghe and Yeok (1998) find that exchange rate appreciation does not adversely
affect exports for Singapore because exports possess high import content. This paper argues that
exchange rate risk provides another channel the exchange rate to affect exports in Singapore.
That is, exchange rate risk adversely affects exports, although exchange rate depreciation does
not affect exports.
The probable effects of exchange rate risk received considerable attention, since the
collapse of fixed exchange rates in the early 1970s. Little consensus regarding its effect on
exports, however, exists. Ethier (1973) argues that exchange risk could lower exports due to
profit risk. De Grauwe (1988) suggests that exporters might increase volume to offset potential
losses. Broll and Eckwert (1999) note that the price of an option to export increases with risk.
Pozo (1992) uncovers a negative effect of exchange rate risk on UK real exports to the
US. Chowdhury (1993), Arize (1995, 1997), Weliwita et al. (1999), Arize et al. (2000), Arize et
al. (2003) and Fang and Thompson (2004) find negative effects of exchange risk on US, G7,
LDC, and NIC exports. Contrary evidence exists, however. Asseery and Peel (1991) find positive
relationships for multilateral exports, except for the UK. Kroner and Lastrapes (1993) uncover
positive effects of conditional variance on exports of France, Germany, and Japan, but negative
effects for the UK and US. McKenzie and Brooks (1997) discover positive risk relationship for

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Germany and the US. And Klaassen (2004) finds no effect on monthly bilateral US exports to the
other G7 countries.
The effects of the exchange rate or exchange rate risk on exports individually may
produce biased inference, if both affect exports and one is omitted. No research combines the
two effects of exchange rate changes together to analyze the relationship between exchange rates
and exports in the previous literature.
Generalized autoregressive conditional heteroscedasticity (GARCH) models specify the
relationships between means and variances as in Engle et al. (1987) and Bollerslev et al. (1992).
We apply the bivariate GARCH-M modeling approach to Singapore to provide evidence for the
effects exchange rate depreciation and its time varying variance on exports. Our methodology
differs from the study of Abeysinghe and Yeok (1998). They use OLS estimation with no risk
variable to explain the effect of exchange rate depreciation on exports. This specification may
overestimate the effect of depreciation if exports and exchange rate risk are negatively related as
shown in Arized et al. (2003). This paper estimates simultaneously the effects of exchange rate
depreciation and its risk and evaluates their joint effect on exports.
The rest of this paper is organized as follows. Section 2 describes the preliminary
statistics for exports and the exchange rates, focusing on properties of time varying variances of
the two variables. Section 3 briefly presents the main elements of the bivariate GARCH-M
model, reports the estimates of the model, and quantitatively analyzes the effects of exchange
rate risk on exports. Section 4 concludes.
II. Data and time-varying variances
To assess the net effect of exchange rate depreciation and its risk on exports, we employ a
nonstructural partial reduced-form approach of Rose (1990) and Klaassen (2004), where the real
exports (x) depend directly on real foreign income (y), the real exchange rate (q), and real

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exchange rate risk ( h ). Real foreign income positively affects the demand for exports. An
q
increase in the real exchange rate, a depreciation, implies cheaper exports abroad and improves
real exports. The effect of real exchange rate risk proves theoretically ambiguous.
To provide evidence, we use bilateral exports between Singapore and the U.S. on a
monthly basis over the sample period from January 1979 to October 2002. Seasonally adjusted
real export revenue equals nominal export revenue in domestic currency deflated by the
consumer price index (CPI). We convert the bilateral nominal exchange rate, defined as the
domestic currency price of the U.S. dollar, into a real exchange rate by multiplying the nominal
rate by the ratio of the U.S. CPI to the domestic CPI. Foreign income equals the industrial
production index of the US, with base year 1995. All data come from the International Financial
Statistics and Direction of Trade of the IMF.
Two reasons suggest the adoption of the bilateral approach. First, the ratio of bilateral
exports between Singapore and the US to Singapore’s total exports is 15.3% over the sample
period. The US accounts for a substantial proportion of exports from Singapore. Second, using
bilateral exports avoids the asymmetric response of trade flows to exchange rate depreciation and
its risk across countries. We, then, can focus on the simple relationship between exchange rate
changes and exports. In addition, Klaassen (2004) finds that the exchange risk in developed
countries does not exhibit enough variability to uncover its effect on exports, and suggests
studying the risk effect, using data on developing countries, for which volatile exchange rate risk
may exist.
Statistical analysis of variables identifies appropriate GARCH models for further
analyses. In our sample, Singapore experienced exchange rate depreciation and export growth.
The average rate of export growth equals 0.530% while the average depreciation rate equals

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0.093%. Both the mean and the standard deviation of export growth greatly exceed those of the
rate of depreciation. Skewness statistics for the growth rate of real exports ( lx
? ) and the growth
t
rate of the real exchange rate ( lq
? ) cannot reject symmetry, but Kurtosis statistics significantly
t
exceed 3 at the 5-percent level, implying leptokurtic series with fat tails. The Jarque-Bera test
rejects normality. Non-normality and the fat-tailed nature suggest estimating GARCH models
under the Student-t distribution.
After selecting lag length by the AIC criterion, the Augmented Dickey-Fuller (ADF) test
shows that lx
? and lq
? prove individually stationary [i.e., I(0)] series at the 5-percent level.
t
t
Valid inference in GARCH models requires stationarity in variables. The Ljung-Box Q-statistic
tests for autocorrelation. The number of lags ( k ) affects the power of the test. Tsay (2002)
suggests choosing k = ln(T ) . The number of observations, T , in our sample equals 285,
accordingly, we set k =5.65. We test for autocorrelations up to 6 lags. Ljung-Box Q-statistics
indicate autocorrelations in lx
? , but no autocorrelation in lq
? . Ljung-Box Q-statistics for
t
t
squared lx
? and squared lq
? suggest the possible presence of time-varying variance for the
t
t
two series. To adequately capture the dynamic structure of the data, we employ an ARMA
process for both the mean and variance equations of the two variables.
We estimate univariate GARCH(1,1) models first to identify properties of the changing
variances for lx
? and lq
? . The Ljung-Box Q( k ) statistics for the standardized residuals of
t
t
lx
? show no autocorrelations up to 6 lags, suggesting that the AR(2) process achieves white
t
noise. Since the exchange rate does not possess autocorrelation, we specify the mean equation of
lq
?
as a constant. No evidence of autocorrelation emerges, given the low Ljung-Box Q( k )
t
statistics for the standardized residuals of lq
?
. The estimates in the two variance equations are
t
significantly positive. Moreover, ? + ? = 0.933 < 1 and ? + ? = 0.807 < 1 show that each
1
2
1
2

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time-varying variance process is stable for lx
? and lq
? . The higher coefficient of volatility
t
t
persistence of lx
? relative to that of lq
? is consistent with the higher standard deviation of
t
t
lx
? . The low Ljung-Box Q-statistics for the squared standardized residuals up to 6 lags show no
t
remaining heteroscedasticity. The estimated coefficients of the degree of freedom v are
significant at the 5-percent level, implying the appropriateness of employing the GARCH(1,1)
for both lx
? and lq
? under the t-distribution.
t
t
The two variables, lx
? and lq
? , possess time-varying variances, suggesting the use
t
t
of the bivariate GARCH model to examine the relationship between exports and exchange rate
changes.
III. The empirical bivariate GARCH-M model and estimation
The following eclectic GARCH-M model provides the framework for assessing the net effect of
exchange rate depreciation and its risk on exports.

2
lx
?
= a + ?a ? lx
?
+ b ? ly
?
+ c ? lq
?
+ d ? h
+ ? (1)
t
0
i
t ?i
t 1
?
t 1
?
q,t 1
?
x,t
i 1
=
lq
?
= e + ? (2)
t
0
q,t
?
(? ,? ?
=
? | ?
~ Student ? t( ) (3)
t
x,t
q,t )
t
t 1
v
?
? h
h
?
x,t
xq,t
H = ?
? (4)
t
h
h
? xq,t
q,t ?
2
h
= ? +? ??
+ ? ? h
(5)
x,t
0
1
x,t 1
?
2
x,t 1
?
2
h
= ? + ? ??
+ ? ? h
(6)
q,t
0
1
q,t 1
?
2
q,t 1
?
h
= ? ? h ? h (7)
xq,t
xq
x,t
q,t
where lx
? ? 100×( ln x - ln x ), lq
? ? 100×( ln q ln
ln
ln
? ,
t -
qt 1
? ),
ly
? ? 100×( yt - yt 1? );
t
t
t 1
?
t
t
t

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conditional on the information set ? available at time t ?1, follows a bivariate Student-t
t 1
?
distribution with degrees of freedom, v . h and h equal conditional variances while h
x,t
q,t
xq,t
equals the covariance. Now, ? equals the correlation coefficient of lx
? and lq
? . The
xq
t
t
presence of h in equation (1) means that equations (1) to (7) constitute a bivariate
q,t
GARCH(1,1)-M model. The conditions that ? > 0 , and ? > 0 ensure positive conditional
i
i
variance. The conditions that ? +? < 1 and ? + ? <
1
2
1 imply stable variances. The constant
1
2
correlation specification (Bollerslev 1990) is modeled through (7). This specification reduces the
number of parameters and increases the degrees of freedom of model estimation. All parameters
in equations (1) to (7) are estimated by maximizing the following log-likelihood function of
bivariate Student-t distribution:
1
? v + 2 ?
? v ?
? v + 2 ?
?
?
?
?
? ?

ln
H
L = ln ?
? ln
?
?
(v ? 2)? ln?
? 0.5ln H ?
?ln
? ?
?
?
?1
t
t
t
+
? (8)
t
? 2 ?
? 2
t
?
? 2 ?
?
v ? 2
?
where ? (•) equals the Gamma function.
The model explains changes in exports. The reduced-form equation includes the
depreciation rate and its risk as well as the rate of change of foreign income as explanatory
variables. The statistical significance and sign of the estimated c and d coefficients in equation (1)
provide a simple and straightforward test of the relationship between real export growth and
exchange rate depreciation and its volatility. If the estimate of c exceeds zero, then exchange rate
depreciation improves exports. Exchange rate volatility affects exports through exporters’
responses to perceived risk. When exchange rate uncertainty leads to profit risk, then, ceteris
paribus, the demand for exports falls (i.e. d < 0). The net effect on exports includes the
exchange rate depreciation and its volatility.

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The estimation results are as follows:1

?lx =
485
.
1
? 621
.
0
?lx
? 266
.
0
?lx
+ 880
.
0
?ly
+ 229
.
0
?lq
? 254
.
0
h
t
t 1
?
t ?2
t 1
?
t 1
?
q,t 1
?
(
)
431
.
0
*
(
)
051
.
0
*
(
)
050
.
0
*
(
)
711
.
0
( 277
.
0
)
(
)
150
.
0
*
?lq =
032
.
0
t

(
)
082
.
0
h
=
692
.
2
+ 104
.
0
2
?
+ 864
.
0
h
x,t
x,t 1
?
R,t 1
?

(
)
666
.
0
*
(
)
014
.
0
*
(
)
011
.
0
*
h
=
362
.
0
+ 154
.
0
2
?
+ 700
.
0
h
q,t
q,t 1
?
q,t 1
?

(
)
054
.
0
*
(
)
028
.
0
*
(
)
026
.
0
*
h
=
0.104
? h ? h
xq,t
x,t
q,t

(0.072)
v =
955
.
7

(
)
261
.
2
*
Q
)
3
( = 173
.
4
Q
)
6
( = 153
.
11
2
Q
)
3
( = 995
.
8
2
Q
)
6
( =
145
.
22

2
2
2
2
Estimated coefficients in the two variance equations are positive and significant.
Volatility persistence equals 0.968 for lx
?
and 0.854 for lq
?
. The two variance processes
t
t
converge. The estimated correlation coefficient between lx
?
and lq
?
equal 0.104 that
t
t
nearly equals the coefficient of 0.102 calculated from the two series. The degree of freedom of
the t-distribution, estimated jointly with other parameters, is significant. That is, the hypothesis
of using a standardized student-t distribution is not rejected at the 5-percent level. The bivariate
Ljung-Box Q ( ) statistics (Hosking, 1980) for the standardized and squared standardized
2 k
residuals of lx
?
and lq
?
do not detect any remaining autocorrelation or conditional
t
t
heteroscedasticity at the 5-percent level. The bivariate GARCH-M model in equations (1) to (7)

1
2
Q ( ) and Q ( ) are the bivariate Ljung-Box statistics (Hosking, 1980) for standardized and squared
2 k
2 k
standardize residuals for autocorrelations up to k lags; v is degree of freedom. * denotes significance at
the 5% level.

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is adequate for further inferences.
The marginal effect of real US income (industrial production) on exports exhibits the
expected positive sign, which is not significant at the 5% level. Thus, bilateral exports from
Singapore to the US do not respond to US economic activity.
Exchange rate depreciation exhibits the expected positive effect, which is also not
significant. Exchange rate risk possesses a significantly negative effect on exports, however.
Regarding the magnitude of the effect, the mean value of conditional variance h in the
q,t
bivariate GARCH-M model is 2.55. The ceteris paribus average monthly effect of the risk on
export revenue (mean value of h × d ) equals -0.65 percent. The standard deviation of h of
q,t
q,t
1.75 implies that the range of potential monthly influences on export revenue calculated by
(mean of h ± standard deviation)× d covers the range [-0.20%, 1.09%], a rather substantial
q,t
effect, since the mean growth rate of real exports equals just over 0.5 percent, as noted above.
The mean value (=0.093) and the estimated coefficient (=0.229) of the depreciation rate
implies the average monthly impact of 0.02 percent. When the net effect of the exchange rate
movement is gauged by the sum of the two average effects, the significant risk effect dominates,
leading to a negative net effect.
IV. Conclusion
Previous research that investigated the responsiveness of exports to exchange rate depreciation
generally concluded that exports react increasingly to exchange rate depreciation. This paper has
revisited the weak relationship between exchange rate depreciation and exports in Singapore by
using monthly data over the period of 1979-2002. Unlike Abeysinghe and Yeok’s (1998) OLS
estimates based on annual data of 1975-1992, we account for the time varying variance of the
data, employ bivariate GARCH-M modeling technique to estimate the effects of exchange rate

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depreciation and its risk on exports.
In sum, the effect of exchange rate depreciation on exports is positive but insignificant,
supporting the findings of Abeysinghe and Yeok’s (1998). Second, time-varying real exchange
rate risk exhibits a significant negative effect on exports of substantial magnitude. Third, the
exchange risk effect dominates the depreciation effect, leading to a negative net effect of
exchange rate changes on export revenue.
The policy implications suggest that Singaporean authorities can elicit stronger export
growth by ensuring a more stable exchange rate rather than by engineering its depreciation.

References
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Competitiveness. The Case of Singapore,” Applied Economics 30, 51-55.
Arize, A. C. (1995) “The Effects of Exchange-Rate Volatility on U.S. Exports: An Empirical
Investigation,” Southern Economic Journal 62, 34-43.
Arize, A. C. (1997) “Foreign Trade and Exchange-Rate Risk in the G-7 Countries: Cointegration
and Error-Correction Models,” Review of financial Economics 6, 95-112.
Arize, A. C, Osang, T. and Slottje, D. J. (2000) “Exchange-Rate Volatility and Foreign Trade:
Evidence From Thirteen LDC’s,” Journal of Business and Economic Statistics 18, 10-17.
Arize, A. C., Malindretos, J. and Kasibhatla, K. M. (2003) “Does Exchange-Rate Volatility
Depress Export Flows: The Case of LDCs,” International Advances in Economics
Research 9, 7-19.
Asseery, A. and Peel, D. A. (1991) “The Effects of Exchange Rate Volatility on
Exports:
Some New Estimates,” Economics Letters 37, 173-177.
Bahmani-Oskooee, M. and Kara, O. (2003) “Relative Responsiveness of Trade Flows to a
Change in Prices and Exchange Rate,” International Review of Applied Economics 17,
293-308.

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Document Outline

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