4.7 JOHANSEN COINTEGRATION MODEL SELECTION
Table 6 shows the results of the Johansen Cointegration test
used to investigate whether there exists long-run relationship among the
cointegrating variables
TABLE 6: Cointegration Rank Test (Trace)
|
Unrestricted Cointegration Rank Test (Trace)
|
|
|
|
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value
|
Prob.**
|
|
None * 0.593373 63.0262
|
47.85613
|
0.001
|
|
At most 1 0.254132 25.2321
|
29.79707
|
0.1533
|
|
At most 2 0.198491 12.91741
|
15.49471
|
0.1179
|
|
At most 3 0.08268 3.624537
|
3.841466
|
0.0569
|
|
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
|
|
|
|
* denotes rejection of the hypothesis at the 0.05 level
|
|
|
|
**MacKinnon-Haug-Michelis (1999) p-values
|
|
|
Source: Eviews 8,2019
Table 6 revealed that Trace test indicates 1 cointegrating
equation at the 0.05 level of significant
Table 7: Cointegration Rank Test (Maximum
Eigenvalue)
|
Unrestricted Cointegration Rank Test (Maximum
Eigenvalue)
|
|
|
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value
|
Prob.**
|
|
None * 0.593373 37.79411 27.58434
At most 1 0.254132 12.31469 21.13162
At most 2 0.198491 9.292868 14.2646
|
0.0017
0.5169
0.2626
|
|
At most 3 0.08268 3.624537 3.841466
|
0.0569
|
|
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05
level * denotes rejection of the hypothesis at the 0.05 level
|
|
Source: Eviews 8,2019
Table 7 revealed that Maximum Eigenvalue test indicates 1
cointegrating equation at the 0.05 level of significant.
Since both tests reveal that the variables under study are
cointegrating. therefore, these results reveal the existence of a long-run
equilibrium relationship between the variables.
4.8 ESTIMATED LONG-RUN MODEL
The estimation of the Long-run model helps in discussing some
classical tests like t-Test and
F-test, discussing about Adjusted R-squared (coefficient of
determination), but also in making a deeper analysis.
P a g e 35 | 48
Table 8: Long run relationship between dependent and
independent variables
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
C
|
3.748438
|
0.05855
|
64.02121
|
0.0000
|
|
LDT
|
0.163171
|
0.052121
|
3.130639
|
0.0033
|
|
LTGS
|
0.603103
|
0.061307
|
9.837459
|
0.0000
|
|
LTITT
|
-0.005913
|
0.034365
|
-0.172055
|
0.8643
|
|
R-squared
|
0.991228
|
Mean dependent var
|
6.975523
|
|
Adjusted R- squared
|
0.99057
|
S.D. dependent var
|
0.388659
|
|
S.E. of regression
|
0.037741
|
Akaike info criterion
|
-3.629615
|
|
Sum squared resid
|
0.056976
|
Schwarz criterion
|
-3.467416
|
|
Log
likelihood
|
83.85154
|
Hannan-Quinn criter.
|
-3.569464
|
|
F-statistic
|
1506.693
|
Durbin-Watson stat
|
1.333763
|
|
Prob(F- statistic)
|
0.00000
|
|
|
|
Source: Eviews 8,2019
Table 8 Shows the results of long run
relationship between dependent variable and the independent variables and it is
interpreted as follows:
The DT and TGS are two variables which were statistically
significant to influence GDP in Rwanda during the period of study.
The DT has been significant at 5% level of significance and
possesses expected positive sign in long run model, however the positive
cointegrating coefficient of 0.163171 shows a positive relationship between GDP
and the DT in that a 1% increase in DT would increase GDP to 0.163171 %. The
results confirm the expected sign, and this positive sign may mean that in the
long run, the biggest of host's country market is likely to encourage GDP. DT
is statistically significant in explaining changes in GDP, suggesting that DT
is an important factor in influencing Rwandan GDP.
The effects of TGS on GDP: TGS has a positive effect on GDP
and significant relationship with GDP in Rwanda at 5% level of significance.
the results show that increase in TGS by 1% leads to 0.603103% increase to GDP
in Rwanda.
P a g e 36 | 48
P a g e 37 | 48
TITT has a negative effect on GDP and not significant
relationship with GDP in Rwanda. TITT is statistically insignificant in
explaining changes in GDP during the period of Q12007 to Q42017.
The coefficient of determination: the coefficient of
determination (R2) is 0.99057. This means that 99.06% of variations in the
dependent variable GDP are explained by the independent variables considered in
the model.
The P-value of the F-statistic is 0.000000, which means the
overall model is statistically significant at 5% level of significance.
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