5.1.2 Estimation and model validation
5.1.2.1 Model
estimation
We retain the estimation of Hendry's correction model as
follows (estimated in one step):
D(LDTPIB)t = C1*LDTPIB(t-1) +
C2*D(LTCH)t + C3*LTCH(t-1) +
C4*D(LMPIB)t + C5*LMPIB(t-1)
+C6*D(LPOP)t + C7*LPOP(t-1)
C8*D(LPIBH)t + C9*LPIBH(t-1) +
C10*D(LDSEX)t + C11*LDSEX(t-1) +
C12*DUM93 + C13*DUM94 + C0 + Ut
When estimating, the dummy variable DUM 93 was removed for
non-significance.
The results of the estimation of the ECM are given in the
table below.
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Dependent Variable: D(LDTPIB)
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Method: Least Squares
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Date: 11/12/09 Time: 08:28
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Sample (adjusted): 1981 2008
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Included observations: 28 after adjustments
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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LDTPIB(-1)
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- 0.978852
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0.197330
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- 4.960490
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0.0002
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D(LTCH)
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0.558390
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0.118836
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4.698839
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0.0003
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LTCH(-1)
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0.554834
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0.150469
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3.687379
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0.0022
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LMPIB(-1)
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0.177077
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0.073918
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2.395604
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0.0301
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D(LMPIB)
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0.297150
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0.079564
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3.734712
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0.0020
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D(LPOP)
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- 1.019847
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0.439043
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- 2.322887
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0.0347
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LPOP(-1)
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- 1.549542
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0.251331
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- 6.165357
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0.0000
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D(LPIBH)
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- 0.780145
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0.166637
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- 4.681709
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0.0003
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LPIBH(-1)
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- 0.591862
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0.134018
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- 4.416280
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0.0005
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D(LDSEX)
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0.146342
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0.031735
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4.611330
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0.0003
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LDSEX(-1)
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- 0.037082
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0.024915
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- 1.488334
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0.1574
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DUM94
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0.686178
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0.104388
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6.573314
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0.0000
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C
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9.373836
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1.778812
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5.269717
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0.0001
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R-squared
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0.938316
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Mean dependent var
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- 0.022853
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Adjusted R-squared
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0.888968
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S.D. dependent var
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0.143416
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S.E. of regression
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0.047788
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Akaike info criterion
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- 2.939651
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Sum squared resid
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0.034256
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Schwarz criterion
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- 2.321128
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Log likelihood
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54.15512
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F-statistic
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19.01445
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Durbin-Watson stat
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2.035061
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Prob(F-statistic)
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0.000001
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The coefficient associated with the resorting force is
negative (-0.978852) and significantly different from zero. So there is a
mechanism for error correction. The ECM is then valid.
Then we can perform all standard tests on this model. Then if
its predictive validity is good, it can possibly be used for forecasting.
5.1.2.2 Model
validation
To validate the results, we will proceed to the analysis of
the statistical and econometric validities of the model and then test the
predictive power of the model.
5.1.2.2.1 Statistical validity
5.1.2.2.1.1 Interpretation of the coefficient of
determination
The coefficient of determination R² is equal to 0.938316.
This means that 93.8316% of the fluctuations of the external
public debt of Togo are explained by the model.
5.1.2.2.1.1.1 Test
of significance
Fisher's exact test (overall model significance)
The model is globally significant because the value associated
with the probability of Fisher (f-Statistic = 0.000001) is less than 0.05. The
explanatory variables in this model generally have a significant effect on the
country's debt.
Testing student (test of individual significance of
coefficients)
The coefficients of the variables of the model are really
significant except that of LDSEX Long-term variable.
In view of the foregoing, the validity of the model is
accepted.
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