Dr.DEBESH BHOWMIK

Dr.DEBESH BHOWMIK

Saturday 1 August 2015

Is there any relation of Euro Area's trade with foreign exchange and SDR reserves?



 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.
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