INTERNATIONAL JOURNAL OF BUSINESS,MANAGEMENT AND SOCIAL SCIENCES
VOL-IV,ISSUE-I(II),APRIL 2015,45-49
(This paper was presented on 24th April,2015, at Sadguru Gadage Maharaj College,Karad Vidyanagar,Karad.Maharastra.)
Is there any relation of Euro Area’s trade
with foreign exchange and SDR reserves?
Dr.Debesh Bhowmik
Key words- SDR, foreign exchange reserves, cointegration,
VAR
Introduction
It is noted that Euro Area has not shown the
identical behavior like USA and the world in describing the relation of export
and import with foreign exchange and SDR from the survey period during
1999-2013.
It may be that Euro Area depends on Euro for its
intra-trade and has utilised foreign exchange and SDR for international trade. Therefore,
the role of foreign exchange and SDR in analyzing foreign trade is rather
different that other big blocs and nations.
In this paper, we will verify this notion through
the econometric model from 1999 to 2013.
Methodology
and data
We have used the Johansen model (1988,) for
cointegration and also used Johansen model (1991,1996) for applying VAR model.
We collected data of exports, imports, foreign exchange reserves and SDR from
International Financial Statistics (IMF) for Euro area.
Assume x1= exports of Euro Area, X2=
imports of Euro Area.X3= foreign exchange reserves of Euro Area,X4=
SDR reserves of Euro Area.
We also used the semi log and double log linear
model for trend values.
The
major findings of the Econometric model
There is inverse relation between exports of Euro
Area with the total reserves of foreign exchange (excluding gold) in which the
double log regression model observed that one percent increase in total
reserves per year would lead to a decrease of 1.3636% export per year of Euro
Area during 1999 to 2013.This is statistically significant. On the other hand,
the Johansen co-integration test proved that both are not co-integrated because
the Trace and λ Max statistic are insignificant and have no cointegrating
vectors.
The export of Euro Area has the positive relation
with the SDR reserves of Euro Area from the period of 1999-2013 which is shown
by the double log linear model where it is observed that one percent rise in
SDR reserves of Euro Area per year leads to 0.40258% increase in export of Euro
Area per year. This estimation is statistically significant.
The Johansen co-integration test suggests that Trace
and λ Max statistics showed one cointegrating equation in relating export and
reserves of SDR of Euro Area during 1999-2013.
The double log multiple regression model tells us
that one percent rise in total foreign and SDR reserves per year leads to
decrease in 1.1988% in export and 0.3060 percent increase exports respectively
in Euro Area during 1999-2013.The t are significant for all coefficients, high
value of F and R2.
The regression equation is given below,
Logx1=13.288-1.1988logx3+0.3060logx4
(10.156)* (-5.15)* (3.312)*
R2=
0.789 , F= 22.497* , DW=1.893
,
The Johansen co-integration test suggest that the
Trace and λ Max statistics confirmed only one cointegrating equation .
Table-1: Cointegration test
No.
of hypothesized (CEs)
|
Eigen
value
|
Trace
statistic
|
0.05
c.v.
|
Prob.
|
None*
|
0.93937
|
47.778*
|
29.797
|
0.0002
|
At
most 1
|
0.4999
|
11.338
|
15.494
|
0.1915
|
At
most2
|
0.16398
|
2.3284
|
3.841
|
0.1217
|
λ
Max Statistic
|
||||
None*
|
0.93937
|
36.440*
|
21.131
|
0.0002
|
At
most1
|
0.4999
|
9.0096
|
14.264
|
0.2854
|
Atmost
2
|
0.16398
|
2.328
|
3.841
|
0.1270
|
Source- Calculated by author
The import of
Euro Area has inverse relation with the total reserves of foreign exchange
during 1999-2013 where double log regression equation states that one percent
rise in foreign exchange reserves of Euro Area per year leads to 1.388261% fall
in imports of Euro Area per year during the survey period. This is
statistically significant .
The Johansen cointegration test suggests that the
Trace and λ Max statistics confirmed no cointegrating vector.But the imports of
Euro Area has the positive correlation with the reserves of SDR during the
period of 1999-2013 in which the double log regression model suggest that one
percent increase in SDR reserves of Euro Area per year would lead to 0.40897%
increase in imports of Euro Area per year during the specified period. This
result is statistically significant .The Johansen cointegration test suggests
that there is one cointegrating vector as observed by the Trace Statistics and
λ Max statistics.
The double log multiple regression model confirms
that one percent increase in SDR reserves would leads to 0.3107 % increase in
imports of EU and one percent increase in total foreign exchange would lead to
1.22088% decrease in import of EU during 1999-2013 respectively where both are
statistically significant with high R2 and F values.
Logx2=13.3835-1.220889logx3+0.3107logx4
(10.845)* (-5.415)* (3.565)*
R2=
0.8135 , F= 26.172* , DW=1.839
Moreover, the Johansen cointegration test suggests
that there is only one cointegrating vector as observed by the Trace and λ Max
statistics which are given below in Table-2.
Table-2:
Cointegration test of imports, foreign exchange and SDR of Euro Area
No.
of hypothesized (CEs)
|
Eigen
value
|
Trace
statistic
|
0.05
c.v.
|
Prob.
|
None
|
0.93335
|
45.9238*
|
29.797
|
0.0003
|
At
most 1
|
0.48233
|
10.7150
|
15.494
|
0.2296
|
At
most2
|
0.15279
|
2.1555
|
3.8414
|
0.1420
|
λMax
Statistic
|
||||
None
|
0.93335
|
35.2088*
|
21.131
|
0.0003
|
At
most1
|
0.48233
|
10.7150
|
14.264
|
0.9246
|
At
most2
|
0.15279
|
2.1555
|
3.841
|
0.1420
|
Source- Calculated by author
Thus, it is proved that Euro Area export and import
have no cointegration with total foreign reserves but have cointegration with
the reserves of SDR during the period of 1999-2013.
Let us have a VAR model of x1, x3,
x4 respectively in one period lag to show the relationship
explicitly. The estimated equations are given below,
X1t=2290.512+0.4665X1t-1 -6.093X3t-1+35.4603X4t-1
(1.167) (1.332) (-0.963) (1.359)
R2=
0.769 ,
F= 11.137
X3t= 207.936 -0.02692X1t-1 +0.2094X3t-1+0.8222X4t-1
(1.744) (-1.265) (0.529) (0.518)
R2=
0.514 F= 3.53
X4t=10.692+0.00142X1t-1 -0.04409X3t-1
+ 0.71303X4t-1
(0.818) (0.610) (-1.017) (4.104)*
R2=
0.858 , F= 20.152*
Loglikelihood
= -219.77 , SC= 33.65 , AIC=33.110,*=
significant at 5% level.
Thus, the VAR model of Euro Area export with foreign
exchanges and SDR is a good fit with high R2 but the t values of the
coefficients are not significant. Moreover, the Impulse Response Functions in
all cases do not converge to zero which
concludes instability that are shown below in Fig-1.
Fig-1: Impulse Response Function of export, foreign
exchange and SDR
Source-
Calculated by author
Yet the unit root circle test showed that all the
roots of Characteristic Polynomial are less than zero and lie inside the unit
circle which means VAR satisfies the stability condition. The values of the
roots are shown in the table and their positions are shown in the unit root
circle in Fig-2.
Table-3:Roots of Characteristic polynomial
roots
|
Modulus
|
0.967855
|
0.967855
|
0.435367
|
0.435367
|
-0.01265
|
0.014265
|
Source- Calculated by author
Fig-2
Source- Calculated by author
Doornik-Hansen VAR residual normality test confirms
that only joint kurtosis is significant at Chi square distribution but
skewness, kurtosis and Jarque-Bera showed insignificant , that’s why the normality
is rejected.
Table-4:Doornik-Hansen normality test
component
|
Skewness
|
Chi-sq
|
df
|
prob
|
1
|
0.228856
|
0.205167
|
1
|
0.6506
|
2
|
-0.458241
|
0.805338
|
1
|
0.3695
|
3
|
0.071878
|
0.020371
|
1
|
0.8865
|
joint
|
1.030877
|
3
|
0.7938
|
|
component
|
Kurtosis
|
Chi-sq
|
df
|
prob
|
1
|
2.960292
|
1.611232
|
1
|
0.2043
|
2
|
3.068134
|
1.212961
|
1
|
0.2707
|
3
|
3.669513
|
5.310471
|
1
|
0.0212
|
joint
|
8.134664
|
3
|
0.0433
|
|
component
|
Jarque-Bera
|
|||
1
|
1.816399
|
2
|
0.4032
|
|
2
|
2.018300
|
2
|
0.3645
|
|
3
|
5.330842
|
2
|
0.0696
|
|
joint
|
Source- Calculated by author
The VAR model of Euro Area imports with foreign
exchange reserves and SDR is shown below by estimating the equations were found
as before.
X2t=2045.064+0.5089X2t-1 –
5.4219X3t-1+35.880X4t-1
(1.06) (1.449) (-0.846) (1.383)
R2=0.794
, F= 12.606
X3t=214.455 -0.0286X2t-1+0.1857X3t-1+0.959X4t-1
(1.77) (-1.298) (0.4608) (0.587)
R2=0.518
, F= 3.58
X4t=10.852+0.00141X2t-1-0.0443X3t-1+0.7107X4t-1
(0.812) (0.580) (-0.998) (3.950)*
R2=
0.857 , F= 20.07*
AIC=32.95 ,
SC= 33.501 , loglikelihood=-218.673,*=
significant at 5% level.
This is good fit with high R2 and F
The Impulse Response Functions of the VAR model showed
that they are diverging and the VAR model is unstable. It is shown in Fig-3.
Fig-3: Impulse Response Function
Source-
Calculated by author
The unit root circle test assured that the roots of characteristic
polynomial lie inside the unit circle and are less than one and satisfies the
stability condition.
Table-5:
Roots of characteristic polynomial
Root
|
modulus
|
0.978754
|
0.978
|
0.407833
|
0.407833
|
0.017995
|
0.017995
|
Source- Calculated by author.
The unit circle is given below
Fig-4
Source- Calculated by author
The Doornik-Hansen VAR residual normality test
confirmed that the normality is rejected since the component values of
skewness, kurtosis and Jarque-Bera are not significant.
Table-6: Doornik-Hansen normality test
Component
|
Skewness
|
Chi-sq
|
df
|
prob
|
1
|
0.352922
|
0.483147
|
1
|
0.4870
|
2
|
-0.441389
|
0.748688
|
1
|
0.3869
|
3
|
0.085350
|
0.028714
|
1
|
0.8654
|
joint
|
1.260549
|
3
|
0.7385
|
|
component
|
Kurtosis
|
Chi-sq
|
df
|
prob
|
1
|
3.018876
|
1.455512
|
1
|
0.2276
|
2
|
3.015199
|
1.106527
|
1
|
0.2928
|
3
|
3.644780
|
5.157678
|
1
|
0.0231
|
joint
|
7.719717
|
3
|
0.0522
|
|
component
|
Jarque-Bera
|
df
|
prob
|
|
1
|
1.938659
|
2
|
0.3793
|
|
2
|
1.855215
|
2
|
0.3955
|
|
3
|
5.186392
|
2
|
0.0748
|
|
joint
|
8.980266
|
6
|
0.1747
|
Source- Calculated by author
Conclusion
The paper concludes that the exports and imports of
Euro Area have no cointegration with total foreign exchanges reserves showing
unstable VAR but these have cointegration with SDR having unstable VAR during
the study period of 1999-2013 and SDR have positive impact on international
trade.
The shortcoming of the model is that the paper has
taken only 15 years for analyzing VAR and cointegration which are too short but
we were bound to take such data because the Euro Area and its currency Euro
have been started since 1999.
References
[1]Bhowmik,Debesh, 2003, Essays on International Money, Deep and Deep, New Delhi
[2]……………, 2014, The
Euro crisis and international liquidity problems, Synergy publications, New
Delhi
[3]……………,2014,
A new track of reform in international monetary system, D.N.Konar and
A.K.Karmakar ed(2014)-Post reforms
:Indian Economy, Regal Publications, New Delhi.
[4]
Boorman,Jack T. and A.I.Card.,2011, Reform
of the international monetary system,Sage Publications,NewDelhi
[5]Enders,Walter.,2011,Applied Econometric Time Series.Wiley
Student Edition.
[6]Engle R.F. and Granger C.W.J.,
1987, Cointegration and error correction: Representation, estimation and
testing. Econometrica, 55:251-276.
[7]Johansen,S.,
1988,Statistical Analysis of Cointegrating Vectors. Journal of Economic
Dynamics and Control, Vol.
12,231-254.
[8]……………….,1991,Estimation
of Hypothesis Testing of Cointegration Vectors in Gaussian Vector
Autoregressive Models, Econometrica 59,Nov,1551-80
[9]……………..,1994, The
role of the constant and linear terms in cointegration analysis of
nonstationary variables. Econometric
Reviews,13, 205-229
[10] Johansen S., 1995, Likelihood-Based Inference in Cointegrated
Vector Autoregressive Models. Oxford University Press.
[11]………….,1996, Likelihood-Based Inference in Cointegrated
Vector Autoregressive Models,2nd edition, Oxford University
Press.
[12]……….. and
K.Juselius.,1990,Maximum likelihood estimation and cointegration with
application to the demand of money. Oxford
Bulletin of Economics and Statistics,52(2),169-210.
[13]Johnson.A.,2006,The
effects of FDI inflows on Host Country Economic growth. CESIS Electronic working paper series no-58.
[14]I.M.F.-
International Financial Statistics-Various
Years.
[15]
Ocampo,Jose Antonio.,2010,Building an SDR based Global Reserve system,Journal of Globalisation and Development,No-2.
[16] Williamson,John.,2005, Revamping the International Monetary System.Institute for
International Economics.
