Public debt of Togo: an attempt to identify the explanatory factors

5.1.2.2.2 Econometric validity

5.1.2.2.2.1 Test of multicollinearity

This test is to compare the coefficient of determination of the model estimated to the coefficient of simple correlation of the explanatory variables taken two by two. The simple correlation matrix of explanatory variables (see Table 3, Appendix 7) shows that all correlation coefficients between the explanatory variables of the model are actually lower than R². So the variables of the model used are not collinear.

5.1.2.2.2.2 Test of errors homoscedasticity

5.1.2.2.2.2.1 White testing

Hypothesis testing is a follows:

H1: homoscedastic model

H2: heteroscedastic model

The model is homoscedastic if the two probabilities are all greater than 5%.

Probability values are all greater than 5% (Table n°4, Appendix 7) in this case the errors of the model are homoscedastic.

5.1.2.2.2.2.2 ARCH Test

Hypothesis testing is as follows:

H1: homoscedastic errors

H2: heteroscedastic errors

The errors of the model are homoscedastic if the probabilities are greater than 5%.

In this case, the two possibilities are greater than 5%. The errors of the model are homoscedastic (table 5, Appendix 7);

5.1.2.2.2.2.3 Breusch - Godfirey Correlation test of errors

Hypothesis test is a follows:

H1: uncorrelated errors

H2: Correlated errors

We accept Ho if the probabilities are all greater than 5%.

Both probabilities being greater than 5 % (Table 6, appendix 8), ECM errors are uncorrelated. Estimates obtained by OLS are optimal.

5.1.2.2.2.2.4 Ramsey specification test

ECM has lagged variables, instead of the Durbin - Watson test, it is rather that of Ramsey that will tell us if the model is well specified or not.

Hypothesis test is as follows:

H1: the model is well specified

H2: the model is not well specified.

We accept HO if the probability is greater than 5⁰/₀. The values of the two probabilities are greater than 5⁰/₀ (Table7, Appendix 8); we accept HO; the model is well specified.

5.1.2.2.2.2.5 Jarque - Bera test

The assumption of normality of the errors terms is essential because it will classify the statistical distribution of the estimators. The assumptions of the normality test are:

Hypothesis testing is as follows:

H1: the variables follow normal distribution N (m, ó)

H2: the variables do not follow a normal distribution N (m, ó)

In the threshold of 5%, we accept the hypothesis of normality as soon as the value of probability is greater than 0.05%.

The value of probability is 0.606636 (Figure 9, Appendix 4). The errors of the errors correction model thus follow a normal distribution.

In view of the foregoing, the model can be validated econometrically.

5.1.2.2.2.2.6 Analysis of the Model's stability

5.1.2.2.2.2.6.1 Cusum stability test (Brown, Durbin, Ewans)

The Cusum stability test can detect structural instabilities

In this case, the curve is not outside the corridor (Figure 11, Appendix 5). Then, the model coefficients are stable. The estimated ECM is then structurally stable.