Journal of Financial Risk Management
2012. Vol.1, No.2, 15-20
Published Online June 2012 in SciRes (http://www.SciRP.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2012.12003
The Threshold Effects of RMB Exchange Rate Fluctuations
on Imports and Exports
Chuanglian Chen
School of Economics and Management, South China Normal University, Guangzhou, China
Received March 10th, 2012; revised April 27th, 2012; accepted May 18th, 2012
Using threshold panel model, we estimate the effectiveness of exchange rate to imports and exports. We
conclude that there is a second threshold in both import and export regression models, and China’s trade
flows don’t accord with ML condition, when RMB exchange rate appreciation is less than 7.8%. Whereas,
when higher than 7.8%, the ML condition strongly holds, indicating that the RMB exchange rate appre-
ciation would deteriorate the China’s international revenue. As RMB exchange rate to US dollar has ex-
periences an appreciation of 22.2% from 2005Q3 to 2012Q1, thus China’s current account would be dete-
riorated. Therefore, some changes or policies should be made to deal with these problems.
Keywords: Threshold Effects, Exchange Rate, Imports, Marshall-Lener Condition
Introduction
On July 21, 2005, the People’s Bank of China makes a deci-
sion that the exchange rate regime was changed from a de facto
peg to the US dollar to a more flexible peg to a basket of for-
eign currencies. And on April 16, 2012, the PBC relaxes ex-
change rate fluctuations bands to 1%. As to this, the RMB ex-
change rate to US dollar has experiences an appreciation of
22.2% from 2005Q3 to 2012Q1. According to the traditional
elasticity theory, the exchange rate appreciation will lower
exports and increase imports. Moreover, if the Marshall-Lerner
condition holds, exchange rate (domestic currency) apprecia-
tion would deteriorate international revenue and devaluation
will improve the net trade flows.
The elasticity approach is still the most commonly used in
balance of trade flows analysis. Recently, a large body of lite-
ratures has reexamined the impact of exchange rate fluctuations
on the balance of trade through examining the ML condition
from a theoretical point of view. Oskooee-Bahmani (1998) ,
Bahmani-Oskooee and Kara (2003), De Silva and Zhu(2004) et
al. find that most countries’ trade elasticities are large enough
to support devaluation as a successful policy for improving the
balance of trade flows. Whereas, Wilson (2001) concludes that
there is no J-curve for Malaysia, Korea and Singapore, and the
ML conditions is not met. Luis Sastre (2012) also supports this
conclusion for other countries.
As to most domestic studies, the related empirical studies can
be classified into three categories. First, Li Yining (1991) ar-
gues that the demand elasticities of imports and exports are
insufficient. Second, the elasticities of exchange rate to trade
flows only reaches the critical value, thus the effect of ex-
change rate fluctuations to China’s trade is relatively small
(Chen, 1992). Third, most recently empirical literatures show
that ML condition holds in China (Dai, 1997; Feng, 2007; Liu,
Zhou, & Xu, 2010).
Although the conclusions are different in the above studies,
but all of them use linear model as an application. As the im-
pacts of exchange rate variations on imports and exports may
be non-linear, therefore, we employ the threshold panel model,
proposed by Hansen (1996, 1999), to estimate the threshold
effects. And then, analyze different threshold effects of ex-
change rate variations to imports and exports. From the empiri-
cal conclusions, we not only can test the effective of exchange
rate appreciation on trade, but also examine how large the ex-
change rate can appreciation, and wouldn’t deteriorate trade
flows.
Theoretical Model and Threshold Panel
Regression Model
Theoretical Model
Following the recent literature, we assume that the main de-
terminants of a country’s exports and imports are income, rela-
tive prices and trade cost. Thus, we assume that exports and
import demand function for each country take the form of


,, ,,
EXEX YPXPXTE

 and IM = IM(Y, PM, PD, T, E),
where EX and IM stand for exports and imports, respectively.
Yis China’s income, and Y

is trade partners’ income. PM
stands for import price, PD stands for domestic price, T denotes
trade cost, E denotes exchange rate, PX is export price, PX

is trade partners’ export price. Consider PD = PX = P, where P
is domestic price. PM= PX* = P*, where P
* is trade foreign
partners’ domestic price.
In order to estimate the effect of exchange rate to imports
and exports, as ESPP


αβ δ λ
texext itext
exy te

 
αβ δλ
timimt itim
imy te 
, where S denotes the bilateral
nominal exchange rate. Following the literature, we assume that
the rest of the trade partners’ demand for a country’s exports
(ex) and imports (im) take the following log-form:
(1)
t
(2)
where, the lowercase letters represent the logarithmic form of
the corresponding capital letters. As for the model, domestic
currency (exchange rate) appreciation would increase imports if

C. L. CHEN
λ0
0δ0
β0
0
β0
im , and exchange rate appreciation would reduce exports
if ex . denotes that trade cost would reduce both
imports and export. im indicates that the improvement of
the domestic income would increase imports, however, if the
domestic income is increased by imports substitution, then
im . indicates that the improvement of the for-
eign trade partners’ income would increase exports, however, if
income is increased by exports substitution, then ex
λ
β0βex

(Kara, 2002). Furthermore, the Marshall-Lener condition holds
if λλ
im ex
1

.
Threshold Panel Regression Model
In order to capture whether there is a structural change rela-
tionship between dependent variable and independent variables.
We use threshold panel regression model, proposed by Hansen
(1996, 1999), as an application. Consider a threshold panel
regression model based on Equations (1) and (2),


2
αβδ 1 λ
γ
λγ
texext it
ex tit
exy t
eIq

 
 ε
ext it
t
eIq

(
3)


2
αβδ 1 λ
γ
λγ
timim tit
im tit
imy t
eIq
 
 ε
im tit
t
eI q 

q

(4)
where, it is the threshold variable, representing the growth
ratio of exchange rate.

I

1Iq γq
denotes a Heaviside function,
indicating that it whenit , otherwise,

γ


γIq
1
λim

γS
0
2
λim

it . Equation (3) and (4) are estimated according to
Hansen (1999). When is known, we use ordinary fixed
effect regression model to estimate the values of ex and ex
or and , and the corresponding sum of squared errors
is 1. However, if is un-known, Chan (1993) and Han-
sen (1997) recommend estimation of by least-squares when
non-linear specification of Equation (3) and (4). This is easiest
to achieve by minimization of the concentrated sum of squared
errors. Hence the least-squares estimators of is
γ
γ
1
λ2 λ
γ

γ1
arg min γ S

1γS
γ
ˆ
γ ( 5)
The minimizing sum of squared errors from Equation (5) is
with variance estimate




2
1
ˆˆ σγ 1SnT

12
:λλH
2
(6)
Then, we have to test whether there is a threshold effect.
Hansen (1996, 1999) provides a hypothesis test, 0exex,
1exex or 0imim, 1imim. Thus an ap-
proximate likelihood ratio test of zero versus single threshold
can be based on the statistic
12
:λλH12 :λλH1 :λλH
2
101
ˆˆ
(λ)σS



S
FS (7)
where 0 denotes the sum of squared errors when null hy-
pothesis holds. The hypothesis of no threshold is rejected in
favor of single threshold if F1 is large. As is pointed by Hansen
(1999), since the null asymptotic distribution of the likelihood
ratio test is non-pivotal, we suggest using a bootstrap procedure
to approximate the sampling (empirical) distribution, and then
derive the bootstrap asymptotic and efficient p-value of the
according F-value under H0. The null of no threshold effect is
rejected if the p-value is smaller than the desired critical value.
Furthermore, Hansen (1996) proves that the statistic p-value
obeys uniform distribution in the large sample, and can be de-
rived through bootstrap.
Finally, we consider the construction of confidence intervals
for the threshold parameters, and then test whether the esti-
mated value of the threshold is a consistent estimator. Due to
the nuisance parameters, the traditional statistics would be non-
standard. In order to overcome this problem, Hansen (1999)
constructs a “no-rejection region” of asymptotic and efficient
confidence interval using the maximum likelihood ratio LR
statistics. Thus we can construct confidence interval to be






2
1111
ˆˆ γγγσLRS S

 

1
(8)
Our asymptotic (1–α)% confidence interval for
γ
is the set



γ2log11αLR  
γ
such that of values of . One of
the convenient features of this confidence region is that it’s a
natural by-product of model estimation. The likelihood ratio
sequence LR is a simple re-normalization of these numbers, and
require no further computation. The above mode only considers
single threshold condition. In some applications there may be
multiple thresholds. In these cases we can use similar method to
search for the two or more threshold values, pointed out and
discussed by Hansen (1999).
Empirical Results and Analysis
Data Sources
This paper uses data from 1995Q1 to 2009Q3 for China export
to and import from 30 countries and regions1, and quarterly
data are seasonally adjusted by X-12ARIMA. The bilateral real
exchange rate is derived by
B
RERNRER CPI CPI


CPI
, where
NRER denotes bilateral nominal exchange rate, CPI is the
China’s consumer price index (with 2005 as the base year) and

is the trading partners’ consumer price index (with 2005
as the base year). The trade cost is derived by the following
equation according to Novy (2006),




12ρ2
2
,,,
1
ijij jiijji
TxxGDPxGDPxs


 

(9)
where, ,ij
x
denotes the exports of country i to country j.
i denotes the GDP of country i. i
GDP
x
denotes the exports
of country i. All the data, exports, imports, GDP, bilateral
nominal exchange rate, and consumer price index, are collected
from China’s Economic Internet Database and CEIC Global
Database. The descriptive statistics of the selected variables are
in Table 1.
Panel Unit Root Test and Panel Cointegration Test
The first step is to check for the stationary properties of the
variables involved. Table 2 represents the results of the panel
unit root tests. The level variables have been specified with
individual intercept and trend, and the first difference variables
are specified with individual intercept in the tests. A unit root is
detected for the level variables, while the first differences ap-
pear to be stationary. We conclude that each variable includes a
random walk component.
130 countries and regions include Argentina, Austria, Australia, Brazil,
Belgium, Denmark, German, Russia, French, Philippines, Finland, Kazakh-
stan, Korea, Holland, Canadian, Malaysia, USA, Japan, Swedish, Swiss,
Taiwan, Thailand, Spain, Hong Kong, New Zealand, Iran, Italy, Indonesia,
UK, and Chile.
16

C. L. CHEN
Table 1.
Summary statistics.
V. Obs. Mean Std. Dev. Min. Max.
ex 1740 2.281 1.610 –3.083 6.115
im 1740 2.054 1.509 –2.834 5.769
y 1740 8.096 0.506 7.252 9.180
y* 1740 6.949 1.517 3.885 11.603
e 1740 0.101 2.726 –2.953 7.816
t 1740 0.405 0.073 0.048 0.521
Table 2.
Panel unit root test results.
LLC Breitung IPS ADF-Choi PP-Choi
ex 1.14 [0.87] 1.57 [0.94] –0.32 [0.37] –0.18 [0.43] –0.32 [0.37]
im 1.01 [0.84] –3.50 [0.00] 6.13 [1.00] 6.25 [1.00] 5.99 [1.00]
y –0.45 [0.33] 5.34 [1.00] –1.32 [0.09] –0.89 [0.19] 2.64 [1.00]
y* –8.01 [0.21] 1.18 [0.88] 0.60 [0.73] 0.52 [0.70] 2.43 [0.99]
e 0.06 [0.52] –0.99 [0.16] –2.55 [0.01] –2.62 [0.00] –2.06 [0.02]
t –0.61 [0.27] –2.82 [0.00] 1.65 [0.95] 2.20 [0.99] 2.59 [1.00]
Δex –34.3 [0.00] –14.36 [0.00] –38.7 [0.00] –28.80 [0.00] –28.37 [0.00]
Δim –45.3 [0.00] –19.30 [0.00] –46.55 [0.00] –32.83 [0.00] –33.71 [0.00]
Δy –4.33 [0.00] –25.71 [0.00] –2.56 [0.01] –2.37 [0.01] –20.37 [0.00]
Δy* –22.4 [0.00] –13.64 [0.00] –25.1 [0.00] –22.02 [0.00] –22.71 [0.00]
Δe –32.2 [0.00] –18.25 [0.00] –28.5 [0.00] –24.27 [0.00] –23.84 [0.00]
Δt –23.52 [0.00] –3.20 [0.00] –22.0 [0.00] –19.27 [0.00] –33.12 [0.00]
Note: Numbers in square brackets stand for p-values.
For the panel cointegration tests results presents in Table 3.
The null of no cointegration is rejected by all of the Pedroni
(1999, 2004) tests at the 1% level. The panel cointegration tests
point to the existence of long run relationships between exports,
foreign trade partners’ income, exchange rate and trade cost,
and between imports, domestic income, exchange rate and trade
cost.
Threshold Effect Test
In the second step, we use the growth ratio of nominal ex-
change rate as a threshold variable to estimate the model. To
determine the numbers of thresholds, the model (3) was esti-
mated by least squares, allowing for (sequentially) zero, one,
two and three thresholds. The test statistics F1, F2 and F3,
along with their bootstrap p-value, are shown in Table 4.
As for the export equation, we find that the test for single
threshold F1 (6.009) is strongly significant with a bootstrap
p-value of 0.013, and the test for a double threshold F2 (3.495)
is significant, with a bootstrap p-value of 0.066. On the other
hand, the test for a third threshold F3 (2.958) is not close to
being statistically significant, with a bootstrap p-value of 0.109.
We can conclude that there is strong evidence that there are two
thresholds in the regression relationship. For the analysis of
import equation, we also can find high evidence that there are
two thresholds in the regression relationship. Therefore, the
remainder of this paper, we work with these double threshold
models.
Threshold Estimated Value
The point estimates of the two thresholds and their asymp-
totic 95% confidence intervals are reported in Table 5. The
estimates are 0.0179 and 0.0449 for export equation, –0.0071
and 0.0776 for import equation, which are very small or very
values in empirical distribution of the growth ratio of the
nominal exchange rate threshold variable. Thus the three cla-
sses of bilateral nominal exchange rate indicated by the point
estimates are those with “very low exchange rate fluctuation”,
“very high exchange rate fluctuation” and “other”. The asymp-
totic confidence intervals for the threshold are tight, indicating
little uncertainty about the nature of this division.
More information can be learned about the threshold esti-
mates from plots of the likelihood ratio function LR in Figures
1 and 2. The point estimates are the value of at which the
likelihood ratio hits the zero axis. It’s interesting to examine the
unrefined first-step LR, the point where the LR1 equals zero for
the export equation, which occursat 1. There is a
second major dip in the LR around the second-step estimate
2. For the analysis of import equation, we can also
find the similar evidences in the Figure 2. Therefore, the single
threshold likelihood conveys information suggests that there is
γ
ˆ γ0.0179
ˆ
γ0.0449

C. L. CHEN
Table 3.
Panel cointegration test results.
Panel V Panel Rho Panel PP Panel ADF Group Rho Group PP Group ADF
Statistics 1.32 (4.82) –4.53 (–8.24) –5.94 (–9.30) –1.82 (–3.75) –5.16 (–8.15) –7.77 (–10.8) –2.90 (–4.28)
p-value 0.09 (0.00) 0.00 (0.00) 0.00 (0.00) 0.03 (0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00)
Note: Numbers in and out brackets stand for imports and export equations.
Table 4.
Threshold effect test results.
Model Threshold effect test Single threshold Double threshold Triple threshold
F-statistics 6.009 3.495 2.958
Export equation
p-value 0.013 0.066 0.109
F-statistics 13.692 20.540 1.341
Import equation
p-value 0.000 0.000 0.260
1% 6.386 6.252 8.343
5% 4.174 3.923 4.220 Critical value
10% 2.840 3.037 3.170
Note: The p-values of F-statistics are calculated by 10000 numbers of bootstrap based on empirical distribution.
Table 5.
The threshold estimated value.
Double threshold effects
Threshold value estimator 95% conf. int. Threshold value estimator 95% conf. int.
Export equation 0.0179 [–0.0018, 0.0308] 0.0449 [–0.1017, 0.0648]
Import equation –0.0071 [–0.0308, 0.0002] 0.0776 [0.0757, 0.0813]
0
1
2
3
4
5
6
-0.10 -0.06 -0.04 -0.02 -0.01 0.00 0
7
.01 0.02 0.04
LR
10% Critical Value
Figure 1.
LR test of export equation.
0
2
4
6
8
10
12
14
-0.07 -0.04 -0.02 -0.01 0.00 0.01 0.02
16
0.03 0.04 0.06
LR
10% Critical Value
Figure 2.
The LR test of import equation.
a second threshold in the regression.
Empirical Results
Tables 6 and 7 give the double threshold regression empiri-
cal results of the exports and import equation, respectively. We
use ordinary fixed effect regression and double threshold re-
gression to estimate the model (3) and (4). In order to overcome
the heteroskedasticity of the model, the standard errors are
White-corrected.
As is shown in Table 6 for the ordinary fixed effect regres-
sion model, the export flexibility of exchange rate is –0.566%,
indicating that the exports decline 0.566%, when the exchange
rate appreciation 1%. As for the estimated results of double
threshold regression, we can find that the export flexibility of
exchange rate would be –0.563%, when exchange rate appre-
ciation is less than 1.8%. However, when the exchange rate
appreciation is between 1.8% and 4.5%, the export flexibility of
exchange rate would be –0.591%. Furthermore, when the ex-
change rate appreciation is higher than 4.5%, the export flexi-
bility of exchange rate would be –0.569%.
As is shown in Table 7 for the ordinary fixed effect regres-
sion model, the import flexibility of exchange rate is 0.382%,
indicating that the imports increase 0.382%, when the exchange
rate appreciation 1%. As for the estimated results of double
threshold regression, we can find that the import flexibility of
exchange rate would be 0.328%, when exchange rate deprecia-
tionis less than 1.8%. However, when the exchange rate appre-
ciationis between –1.8% and 7.8%, the import flexibility of ex-
change rate would be 0.401%. Furthermore, when the exchange
18

C. L. CHEN
Table 6.
Export equation: double threshold regression.
Ordinary fixed effect Double threshold
Variable Beta Rob-std t Beta Rob-std t
yit 1.29 0.047 27.32 1.30 0.047 27.47
tit –24.12 0.771 –31.29 –24.11 0.769 –31.36
eit –0.57 0.0348 –16.25
eit·I (qit ≤ 1.8%) –0.56 0.035 –16.21
eit·I (1.8% ≤ qit ≤ 4.5%) –0.59 0.036 –16.66
eit·I (qit ≥ 4.5%) –0.57 0.035 –16.10
Table 7.
Import equation:double threshold regression.
Ordinary fixed effect Double threshold
Variable Beta Rob-std t Beta Rob-std t
yit 0.59 0.023 25.29 0.59 0.023 25.50
tit –19.35 0.658 –29.43 –19.32 0.651 –29.69
eit 0.38 0.026 14.69
eit·I (qit ≤ –1.8%) 0.33 0.024 13.67
eit·I (–1.8% ≤ qit ≤ 7.8%) 0.40 0.025 16.04
eit·I (qit ≥ 7.8%) 0.45 0.026 17.39
Table 8.
Marshall-Lener condition results.
Threshold model Linear model ML condition
λex λim
λim λex λλ
im ex

–0.57 0.38 0.95
qit ≤ –1.8% –0.56 0.33 0.89
–1.8% ≤ qit ≤ 1.8% –0.56 0.40 0.96
1.8% ≤ qit ≤ 4.5% –0.59 0.40 0.99
4.5% ≤ qit ≤ 7.8% –0.57 0.40 0.97
qit ≥ 7.8% –0.57 0.45 1.02
rate appreciation is higher than 7.8%, the import flexibility of
exchange rate would be 0.452%.
Analysis of Nonlinear Marshall-Lener Condition
Based on the estimated results of Tables 6 and 7, we can de-
rive the Marshall-Lener condition in Table 8.
From the Table 8, we can see that Marshall-Lener condition
would be λλ0.95
im ex for the linear model. As for the
threshold regression model, the λλ0.89
im ex when ex-
change rate depreciation is less than 1.8%, when exchange rate
appreciation is between –1.8% and 1.8%, λλ0.96
im ex,
when exchange rate appreciation is between 1.8% and 4.5%,
λλ0.99
im ex, when exchange rate appreciation is between
4.5% and 7.8%, λλ0.97
im ex, and when exchange rate
appreciation is higher than 7.8%, λλ1. 0 2
im ex. We can
conclude that λλ
imex to be different, along with the fluc-
tuations of the exchange rate. Furthermore, from the estimated
results, we conclude that China’s trade to thirty trade partners
don’t accord with Marshall-Lener condition, when the bilateral
RMB exchange rate appreciation is less than 7.8% for the “very
low exchange rate fluctuation” regime. However, when the
bilateral RMB exchange rate appreciation is higher than 7.8%
for the “very high exchange rate fluctuation” regime, the Mar-
shall-Lener condition strongly holds, indicating that the domes-
tic currency (RMB exchange rate) appreciation would reduce
the China’s current account surplus.
Conclusion
This paper examines the effectiveness of exchange rate fluc-
tuations to imports and exports. Traditional studies use linear
model as an application to analyze the elasticities of exchange
rate on imports and exports. However, the impacts of exchange
rate variations on imports and exports may be non-linear, there-
fore, we employ the threshold panel model, proposed by Han-
sen (1996, 1999), to estimate the threshold effects.
Firstly, we find that there is a second threshold in both im-

C. L. CHEN
port and export regression models. Exchange rate appreciation
will lower exports, and devaluation will improve import, whe-
reas both have threshold effects.
Secondly, the estimated results show that China’s trade flows
don’t accord with Marshall-Lener condition, when the bilateral
RMB exchange rate appreciation is less than 7.8%. Whereas,
when the bilateral RMB exchange rate appreciation is higher
than 7.8%, the Marshall-Lener condition strongly holds, indi-
cating that the RMB exchange rate appreciation would deterio-
rate the China’s international revenue.
Finally, this paper illustrates that the exchange rate variations
on trade flows has threshold effect. As the RMB exchange rate
to US dollar has experiences an appreciation of 22.2% from
2005Q3 to 2012Q1, which is higher than 7.8%, therefore, the
RMB appreciation will deteriorate China’s current account by
now. We must pay more attention to it, and make some changes
or policies to deal with these problems.
Acknowledgements
This research is supported by Humanities and Social Sci-
ences Youth Project of Chinese Ministry of Education (12YJC-
790006), National Social Sciences Foundation (12BJL057),
Guangdong Planning Youth Project of Philosophy and Social
Sciences (GD11YYJ01), and South China Normal University
Youth Teachers’ Research Fund
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