Time Series Analysis of China and Africa’s GDP: A Case of...

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Time Series Analysis of China and Africa’s GDP: A Case of Sudan
LIU Zhuang
Department of Economics, Lanzhou University, P.R.China, 730107
Abstract: Using 1985-2009 GDP data of both China and Sudan, the study investigate economic linkage
between the two countries. We find that: 1) there’s cointegration between China’s GDP and Sudan’s. 2)
Further analysis based on the construction of Vector Error Correction model has been employed,
Granger causality test based on VEC Model shows that the Granger causal relationship between the two
countries is insignificant. 3) Analysis using impulse response functions and variance decomposition
method has been conducted and reveals that part of variance in Sudan’s GDP can be explained by
China’s GDP, and 1 standard deviation of positive shock in GDP of China will give Sudan’s GDP a rise
of approximately 3 percent.
Keywords: China, Sudan, cointegration, VEC model, Granger causality test, generalized impulse
response functions, variance decomposition
1 Introduction
The emergence of Chinese economy has been observed in recent decades. As China speed up its
integration into the trade liberalization by joining the World Trade Organization, the connection of
China between the rest of the world has been strengthened by international trade. Also, rapid
development of trade between China and African countries has taken place during recent years, the
Sino-African trade has expanded from close to $10 billion in 2001 to nearly $130 billion in 2010,
What’s more, Chinese FDI has leaped from $100 million in 2000 to near $1 billion in 20061, the
increasing Sino-Africa trade has provided both side opportunities in globalization. Some researchers has
noticed the heated Sino-Africa relationship. According to Ali Zafar (2007), China effects Sub-Saharan
African economy mainly by its huge demand of resources particularly oil and metal, and its exports of
low-cost textile, the effect has been manifold, China’s strong demand of oil and metal has contributed to
the price and thereby benefiting those resources-export countries, but it also deteriorated the condition
of oil-import countries. The exports of textile has benefit African consumer while hurts local industry by
its low price. Joseph Onjala (2010) investigated the bilateral trade between China and Kenya, concluded
that the Sino-Kenyan trade relationship is manifold: China’s exports significantly impacted Kenya by
competition with local industry, on the other hand, the import from China is beneficial to Kenyan
economy and generally Kenyans are positive about the trade relationship with China. While the
emergence of China has stimulated extensive research, relatively little empirical analysis has been done
regarding the correlation between China and Africa economy in contemporary literature, In this paper
we’re engaged to apply time series method to examine the economic relationship using Sudan as an
example.
The economy of Sudan ranks the 8th among all African countries, its economy is dominated by
agriculture and mining. Oil is now the main driver of growth which contributed to 22% of the GDP,
while agriculture still accounts for more than one third of GDP and nearly two-thirds of employment2.
We think Sudan represent some similar properties exist among African economy, the investigation on
the GDP correspondence between Sudan and China should shed some light on analysis of Sino-African
economic relationship.
The paper is structured as follows: In Section 2, begins by general discussion of methodologies and data
employed in the paper. In Section 3, detailed empirical analysis is conducted to construct a Vector Error
1
2
Data is obtained from Chinese Ministry of Commerce.
Data obtained from African Outlook Review website.
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Correction model to estimate the Sino-Sudan economic relationship. Method of impulse response
function and variance decomposition is performed and the results are presented. Conclusion is finally
presented in Section 4.
2 Data and Methodologies
2.1 Data
In this study, we use the 1985-2009 GDP data of China and Sudan, for analytical simplicity and the
reason that Sino-Sudan connection becomes observable after the 1980s. The data is retrieved from Penn
World Table, collected by Center for International Comparisons of Production, Income and Prices,
University of Pennsylvania. Purchasing Power Parity converted GDP per capita is used and transformed
using Chain Fisher index at 2005 constant price. Then log transformation is applied on the data.
2.2 Methodologies
The main objective of this paper is to investigate the relationship between China and Sudan using GDP
data and time series methods. Unit root test and cointegration test is first employed to examine time
series properties of the data. According to results of the unit root test and cointegration test, using
framework developed by Davidson et al., (1978), a VEC Model is constructed, and Granger causality
test, variance decomposition and impulse response functions analysis is employed in turn to capture
their dynamic causal relationship. Statistical software Eviews 5.0 is used for analysis in this paper.
3 Empirical Analysis and Results
3.1 Unit root test
To carry out cointegration analysis and further analysis on VEC Model, time series must be stationary,
Philips (1987) points out that ‘spurious regression’ may happen using non-stationary time series for
direct analysis, Unit root test is thus needed, here we use Augmented Dickey-Fuller Test, the result is
shown in Table 1: (C, T, P) indicates the inclusion of constant term, linear trend and lag length,
respectively. Lag length is determined by Schwarz Information Criteria. Here the null hypothesis is that
the series have unit root, which indicates non-stationarity and vice versa. The t-statistics and p-value for
each variable at both level and first-difference is given in the table, from the table we can conclude that
both lnCHN and lnSUD are integrated of order 1.
Table 1 Result of Augmented Dickey-Fuller Test
Critical
Variable
(C, T, P)
t-statistics
p-value*
values(5%)
lnCHN
(C, 0, 4)
1.2621
-3.0207
0.9973
lnSUD
(C, 0, 0)
-0.7940
-2.9919
0.8028
D(lnCHN)
(C, 0, 3)
-4.5752
-3.0207
0.0019
D(lnSUD)
(C, 0, 1)
-4.7117
-3.0049
0.0012
*MacKinnon (1996) one-sided p-values.
conclusion
Accept
Accept
Reject
Reject
3.2 Cointegration test
The existence of cointegration which indicates long-run relationship between the two variables is the
prerequisite for the further analysis. Based on the result of unit root test, the two series lnCHN and
lnSUD are all I(1), this enable us to use the approach pioneered by Johansen (1988) to examine their
cointegration, Johansen test is thus conducted using Eviews 5.0, Both Johansen (trace) test and Johansen
( max eigenvalue) test have reap the same results shown in Table 2. From the result, both trace test and
maximum eigenvalue test indicate 1 cointegration equations at the 0.05 level.
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Table 2 Result of Johansen cointegration test
Maximum
Hypothesized
Trace
Critical
Conclusion
eigenvalue
number of CE(s)
statistics
value(5%)
statistics
None*
17.0127
15.4947
16.5356
1 CE
At most 1
0.4771
3.8415
0.4771
* denotes rejection of the hypothesis at the 0.05 level
Critical
value(5%)
Conclusion
14.2646
3.8415
1 CE
3.3 Vector Error Correction Model
Vector Error Correction Model is developed by Davidson et al., (1987). The main idea of VEC Model is
to include an error correction term which adjusts short-run fluctuation, thus enabling the model to
capture both long-run and short-run properties. Engle and Granger (1987) pointed out that if
non-stationary variables are cointegrated, VAR model would be misspecified, and cointegrated
non-stationary variables can always be expressed by VEC Model. Given that cointegration relationship
exists between the two variables, we can then construct the VEC model. The VEC Model can be
expressed as follows:
k

∆
=
ln
CHN
[α1i ∆ lnCHNt−i + β1i∆ ln SUDt−i ] + λ1ECMt−1 +ε1t
∑


i=1
(1)

k
∆ ln SUD = [α ∆ ln SUD + β ∆ln CHN ] + λ ECM +ε
∑
2i
t −i
2i
t −i
2
t −1
2t

i =1
In the model, the ECM is the error correction term, εis white noise error, k denotes the lag length and t
denotes time.
After we get the estimation of the model using Eviews5.03, an AR Roots test is used to test the stability
of the model, the AR Roots Graph is shown in Figure 1, from the graph, we can see except the 1 unit
root imposed by the model, all the roots lies within the unit circle, indicating that the model is stable, so
further analysis can be carried on.
Inverse Roots of AR Characteristic Polynomial
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Figure 1 AR Roots Graph
3.3.1 Granger Causality Test based on VEC Model
Since the normal Granger causality test only apply to the stationary series, according to Gao (2006) test
on cointegrated non-stationary series have to be carried out based on the VEC Model, we employ an
alternative using Granger Causality/Block Exogeneity Wald test to examine the long-run causal
relationship. The result of Granger Causality test is shown in Table 3. The test result shows neither the
3
Estimation parameters are not reported in the paper but will be given upon request.
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null hypothesis that D(lnCHN) does not Granger cause D(lnSUD) nor that D(lnSUD) does not Granger
cause D(lnCHN) is accepted at 0.05 significant level.
Table 3 VEC Granger Causality/Block Exogeneity Wald Tests Result
Dependent variable: D(lnCHN)
Excluded
D(lnSUD)
All
Dependent variable: D(lnSUD)
Chi-sq
0.4873
0.4873
Df
2
2
Prob
0.7838
0.7838
Excluded
D(lnCHN)
All
Chi-sq
1.9253
1.9253
df
2
2
Prob
0.3819
0.3819
3.3.2 Variance Decomposition
Variance decomposition indicates how much of the predict error variance can be explained by
exogenous shock of other variable. Result is shown in Figure 2 for a 10 year period using Cholesky
Decomposition. From the graph, for all the periods, almost all of the variance of lnCHN is exclusively
explained by itself, for lnSUD, at the 4th period, most of the variance is explained by itself, only 10%
can be explained by lnCHN, in the following period, explaining power of lnCHN increase and account
for approximately 40% of the variability and the remaining 60% is explained by lnSUD itself in the 10th
period.
Variance Decomposition of LNCHN
Variance Decomposition of LNSUD
100
100
80
80
60
60
40
40
20
20
0
0
1
2
3
4
5
LNCHN
6
7
8
9
10
1
LNS UD
2
3
4
5
LNCHN
6
7
8
9
10
LNSUD
Figure 2 Variance Decomposition Results
3.3.3 Impulse Response Functions
Variance decomposition explained the proportion of variance in one variable that is explained by the
other variables, but the more specific effect is remained unknown. Impulse response function is thus
employed to further analyze the effect. Here we use the generalized impulse response function whose
framework is developed by Pesaran and Shin (1998), it will examine the dynamic behavior of one
variable after exogenous change in one of the other variable. The results is shown is Figure 3, as
illustrated in the graph, in response to a positive standard deviation shock in itself, lnCHN will increase
by approximately 6 percent and then become stable after the 3rd period, as to a positive standard
deviation shock in lnSUD, it will decrease a little bit and recover at about the 6th period. The impact is
less than 1 percent, so lnCHN is relatively insensitive to lnSUD. For the variable lnSUD, the shock in
itself will cause strong vibration at beginning and die down to original level at the end of the 10th period,
regarding to shock from lnCHN, it will at first decrease and then display upward trend in the following
period and eventually become stable after the 8th period, increasing by approximately 3 percent. The
GDP of Sudan is relatively sensitive to China’s GDP.
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Response of LNCHN to Cholesky
One S.D. Innovations
Response of LNSUD to Cholesky
One S.D. Innovations
.07
.08
.06
.06
.05
.04
.04
.03
.02
.02
.00
.01
-.02
.00
-.01
-.04
1
2
3
4
5
LNCHN
6
7
8
9
10
1
2
LNSUD
3
4
5
LNCHN
6
7
8
9
10
LNSUD
Figure 3 Impulse Response Functions Results
4 Conclusion
The findings in this paper indicate the existence long-run equilibrium relationship between GDP of
China and Sudan, supported by Johansen cointegration test. However, Granger causality test based on
VEC Model indicating no significant causal relationship between China and Sudan. Using variance
decomposition and impulse response function analysis, we find evidence that China’s GDP growth can
exert an upward impact on Sudan’s GDP and part of Sudan’s variance in its GDP can be explained by
China’s GDP performance.
Apart from the result, the limitation in this paper should be noted as well. First, the analysis only
investigate the relationship statistically, doesn’t provide insight into the underlying reason for their
relationship. The study can be enriched when time series data such as trade volume is acquired in the
future. Second, our research only limit to the GDP data of the two countries, using Sudan as an example
to capture the economic linkage between China and Africa, further analysis can be conducted to extend
the results to other African countries.
References
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