COINTEGRATION BETWEEN WORLD TRADE AND GOLD AND SDR

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,

X_1t=-72794.84+0.9916X_1t-1+78.119Y_1t-1+0.04809Y_2t-1

           (-1.008)    (12.447)*        (78.119)        (0.5322)

   R²=0.906  , F= 122.543*

Y_1t=216.4743 – 2.33E-06X_1t-1+0.7741Y_1t-1+9.92E-05Y_2t-1

           (0.6382)     (-0.022)            (7.929)*           (0.8359)

  R²= 0.6382   ,   F= 22.347*

Y_2t=52002.48+0.31648X_1t-1-49.1302Y_1t-1+0.7199Y_2t-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,

X_2t=-53592.38+1.0917X_2t-1+50.4505Y_1t-1+0.2843Y_2t-1

            (-0.663)     (1.177)       (0.608)          (2.963)*

 R²= 0.441    , F= 9.994

Y_1t=217.2006-7.83E-05X_2t-2+0.7737Y_1t-1+0.000103Y_2t-1

          (2.296)*     (-0.072)     (7.964)*        (2.296)*

          R²= 0.638   , F= 22.35*

Y_2t=6689.35+2.4565X_2t-1-9.9133Y_1t-1+0.806149Y_2t-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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