This paper was presented in International Multidisciplinary Research Conference organised by INAAR and CVU and sponsored by Indo-Global Chamber of Commerce at MCCIA, Pune on 30th June,2015.
It is published in International Research Journal of Commerce ,Business and Social Sciences, Vol- IV,Issue-3(I),June 2015, pp-17-23
COINTEGRATION
BETWEEN WORLD TRADE AND GOLD AND SDR
Dr. Debesh Bhowmik (International Institute
for Development Studies, Kolkata)
Key
Words- Cointegration, World exports, World imports, SDR, Gold
JEL-C58,F33,P45
I.
Introduction
Prior to the inception of the Bretton Woods, the
economists had been searching for a single currency for the world economy where
metallic standard to key currency to multiple currency standard have been examined,
yet the imbalance and international liquidity problem could not be solved. Now,
IMF, some academicians and politicians
assume that if SDR be the world money for international transactions
then liquidity crisis ,global imbalance and financial crises may be solved.
In this respect, we try to verify the relation
between the world exports and imports with the world gold reserves and world
SDR reserves during 1968-2013.
II.Methodology
and Data
We used Johansen (1988) model for cointegration and
Johansen (1991, 1996) model for VAR Analysis. We have taken data on world
exports , imports , gold and SDR reserves from the International Financial
Statistics(IMF) for the period from 1968 to 2013.Assume , x1= world
export , x2= world import , y1= world gold reserve, y2=
world SDR reserve.
III.The
Main Econometric Observations
It is found from the double log regression model
that one percent increase in world gold reserves per annum led to 9.648%
decrease in world exports per year significantly during 1968-2013.But Johansen
cointegration test suggests that these two are not cointegrated during
1968-2013 which is verified by the Trace statistic and λ max statistic .
From the double log regression model ,the estimated
regression showed that one percent increase in world SDR reserves per year led to 1.658% increase in world exports per
year during 1968-2013.It is statistically significant . The Johansen
cointegration test showed that the Trace Statistic and λ Max Statistic have one
cointegrating equation with 5% significant level. Now if we use the double log
multiple regression model to relate world export, world gold reserves and world
SDR reserves during 1968-2013, we find that one percent increase in world gold
reserves per year leads to 1.2953% increase in world export per year which is
insignificant and one percent increase
in world SDR reserves per year leads to 1.663% decrease in world exports per
year which is significant statistically. Its R2 is high and F
statistic is significant.
Logx1= -16.70309+1.2953logy1-1.663logy2
(-0.6080) (0.3269) (8.728)*
R2=
0.656 , F= 38.162 , DW= 0.471,*=significant at 5% level.
In applying the Johansen cointegration test ,we got
the values of trace statistic and λ Max
statistic which showed one cointegrating equation. The values are given in
Table-1,
Table-1: Cointegration test of x1,y1
& y2
|
Hypothesized
no of CE(s)
|
Eigen
value
|
Trace
statistic
|
0.05
cv
|
prob
|
|
None*
|
0.4658
|
32.739*
|
29.797
|
0.0223
|
|
At
most 1
|
0.1512
|
7.0322
|
15.494
|
0.5739
|
|
At
most 2
|
0.00747
|
0.3077
|
3.84
|
0.5791
|
|
λ Max Statistic
|
||||
|
None*
|
0.4658
|
25.7071*
|
21.1316
|
0.0106
|
|
At
most 1
|
0.1512
|
6.7244
|
14.264
|
0.5222
|
|
At
most 2
|
0.00747
|
0.30776
|
3.841
|
0.5791
|
Source-Computed by Author
The estimated VAR model of X1 , Y1,
and Y2 is given below,
X1t=-72794.84+0.9916X1t-1+78.119Y1t-1+0.04809Y2t-1
(-1.008) (12.447)* (78.119) (0.5322)
R2=0.906 , F= 122.543*
Y1t=216.4743 – 2.33E-06X1t-1+0.7741Y1t-1+9.92E-05Y2t-1
(0.6382) (-0.022) (7.929)* (0.8359)
R2=
0.6382 , F= 22.347*
Y2t=52002.48+0.31648X1t-1-49.1302Y1t-1+0.7199Y2t-1
(0.527) (2.91)* (-0.484) (5.838)*
R2=0.793 , F=48.5848* , *= significant at 5% level.AIC=
55.299 , SC=55.796 , loglikelihood=-1149.295
The VAR model is a good fit with high R2
and F. But its Impulse Response Function showed that the VAR model is quite
unstable because of its divergence.
Fig-1: The
Impulse Response Functions of VAR model of x1,y1 &y2
Source-Computed by author
The unit root circle test confirmed that one root
lies outside the circle and others lie inside the circle, and thus why VAR is
unstable which is shown in Table -2 and Fig-2
Table-2: Values of Roots
|
Roots
|
Modulus
|
|
1.058233
|
1.058233
|
|
0.713772
- 0.093269i
|
0.719840
|
|
0.713772
+ 0.093269i
|
0.719840
|
Source-
Computed by Author
Fig-
2: Unit root circle
Source- Computed by author
The residual test for normality assured that null
hypothesis of normality is rejected because the Skewness,Kurtosis and Jarque-Berra
which are distributed as Chi-square are significant.
Table-3: Normality test
|
component
|
Skewness
|
Chi-sq
|
df
|
prob
|
|
1
|
4.200634
|
42.54447
|
1
|
0.000
|
|
2
|
1.139789
|
8.678463
|
1
|
0.000
|
|
3
|
4.079677
|
41.41035
|
1
|
0.000
|
|
joint
|
92.63328
|
|
3
|
0.000
|
|
component
|
Kurtosis
|
Chi-sq
|
df
|
prob
|
|
1
|
24.82540
|
95.81405
|
1
|
0.0000
|
|
2
|
9.425477
|
22.91993
|
1
|
0.0032
|
|
3
|
25.78465
|
48.10460
|
1
|
0.0000
|
|
joint
|
166.8386
|
|
3
|
0.000
|
|
component
|
Jarque-Bera
|
|
|
|
|
1
|
138.3585
|
|
2
|
0.000
|
|
2
|
31.59839
|
|
2
|
0.000
|
|
3
|
89.51495
|
|
2
|
0.000
|
|
joint
|
259.4719
|
|
6
|
0.000
|
Source- Computed by author
The same econometric analysis can be applied in the
world import with world gold reserves and world SDR reserves during
1968-2013.The double log linear model
between world import and world gold reserves represents that one percent
increase in world reserves in gold per year induced to decrease world imports
by 1.027007% significantly per year during 1968-2013.The Johansen Cointegration
test suggests that Trace statistics confirmed two integrating equations but λ
Max statistics confirmed one cointegrating equation.
The relation between world import and world reserves
of SDR during 1968-2013 through double log regression model states that one
percent increase in world SDR reserves per year leads to 1.11348% increase in
world imports per year which showed statistically significant at 5% level. The
Johansen cointegration test also confirmed that there are two cointegrating
equations as observed by the Trace statistic and λ Max statistic.
Now the double log multiple regression among the
world import, world SDR and gold reserves during 1968-2013 signifies that one
percent increase in world SDR per annum leads to 1.10474 % increase in world
imports per annum which was found statistically significant but one percent
increase in world gold reserves per year leads to 2.30436% decrease in world
imports per annum during 1968-2013 which is statistically insignificant. The
estimated equation is given below.
logx2=13.2120-2.30436logy1+1.10474logy2
(0.7480) (-0.9046) (9.0174)*
R2=
0.6772 . F= 41.972* , DW= 0.646,*= significant at 5% level.
The Johansen cointegration test suggests that the
Trace statistic and λ Max statistic assured 3 cointegrating equations and they
are cointegrated in the order of I(1,1).The values are given below .
Table-4: Cointegration test of x2,y1 & y2
|
Hypothesized
no of CE(s)
|
Eigen
value
|
Trace
statistic
|
0.05
cv
|
prob
|
|
None*
|
0.909594
|
120.1075
|
29.797
|
0.000
|
|
At
most 1*
|
0.338847
|
21.566
|
15.494
|
0.005
|
|
At
most 2*
|
0.106163
|
4.60149
|
3.84
|
0.0319
|
|
λ Max Statistic
|
||||
|
None*
|
0.909594
|
98.54142
|
21.1316
|
0.000
|
|
At
most 1*
|
0.338847
|
16.96459
|
14.264
|
0.018
|
|
At
most 2*
|
0.106163
|
4.601498
|
3.841
|
0.0319
|
Source- Computed by author
The estimated VAR model of X2, Y1,
and Y2 are given below,
X2t=-53592.38+1.0917X2t-1+50.4505Y1t-1+0.2843Y2t-1
(-0.663) (1.177) (0.608) (2.963)*
R2=
0.441 , F= 9.994
Y1t=217.2006-7.83E-05X2t-2+0.7737Y1t-1+0.000103Y2t-1
(2.296)* (-0.072) (7.964)* (2.296)*
R2=
0.638 , F= 22.35*
Y2t=6689.35+2.4565X2t-1-9.9133Y1t-1+0.806149Y2t-1
(0.0649) (2.076)* (-0.093)
(6.586)*
R2=0.772 , F=
43.095* , AIC=55.676 , SC= 56.172 , loglikelihood=-1157.197,*= significant at
5% level.
Again, the values of two roots lie inside the unit
circle and one root which is greater than one ,lies outside the unit circle
which showed that the VAR model is unstable.
Table-5
: Values of Roots
|
Roots
|
Modulus
|
|
1.801502
|
1.801502
|
|
0.753849
|
0.753849
|
|
0.116222
|
0.116222
|
Source- Computed by author
Fig- 3: Unit root circle
Source-
Computed by author
The VAR model is found good fit but the Impulse
Response Functions are diverging which means the VAR model is unstable. It is
shown in Fig-4
Fig- 4: Impulse response functions of VAR model of x2,y1
& y2
Source- Computed by author
The residual test for normality showed that the Chi
Square distribution of Skewness,Kurtosis and Jarque-Berra are significant which
confirmed that null hypothesis of no normality is rejected. It is given in the
Table-6.
Table-6:
Normality Test
|
component
|
Skewness
|
Chi-sq
|
df
|
prob
|
|
1
|
2.630436
|
26.46427
|
1
|
0.000
|
|
2
|
1.166359
|
8.993752
|
1
|
0.0027
|
|
3
|
5.084170
|
50.37757
|
1
|
0.000
|
|
joint
|
|
85.8356
|
3
|
0.000
|
|
component
|
Kurtosis
|
Chi-sq
|
df
|
prob
|
|
1
|
20.72866
|
14.09559
|
1
|
0.0002
|
|
2
|
9.470174
|
22.10563
|
1
|
0.0000
|
|
3
|
31.35488
|
294.9126
|
1
|
0.0000
|
|
joint
|
|
331.1139
|
3
|
0.000
|
|
component
|
Jarque-Bera
|
|
|
|
|
1
|
40.55987
|
|
2
|
0.000
|
|
2
|
31.09938
|
|
2
|
0.000
|
|
3
|
345.2902
|
|
2
|
0.000
|
|
joint
|
416.9495
|
|
6
|
0.000
|
Source- Calculated by Author.
IV.Conclusion
Thus, it was verified that world exports and imports
are positively related with world SDR reserves
but world exports and imports are not always positively/negatively
related with world gold reserves during the period of 1968-2013.World export is
cointegrated with SDR but not with gold, on the other hand, world import is
cointegrated with both gold and SDR. The
multivariate Johansen model showed that both world export and import are
significantly cointegrated with gold and SDR.
Their VAR models were found good fit but did not satisfy the stability
conditions.
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