5.1.1.2 Mode
specification and series study
Let us proceed to the specification of a model, its estimation
and validation.
5.1.1.2.1 Model specification
The specification of an econometric model consists in
translating into mathematic form the theory or economic phenomena examined. The
specification requires the identification of variables and determining the form
of the equation that connects them.
5.1.1.2.1.1 The model variables
In the light of economic theory and empirical studies; the
variables selected for this study are:
·dependent variable or explained variable:
The weight of Togo's external debt will be approximated by the
ratio of outstanding debt at the period end in percentage of GDP
(DTPIB).
·independent variable or explanatory variables likely
to influence positively or negatively Togo's external debt
Import to GDP (MPIB) reflects the ratio of
imports relating to the income generating capacity of the economy as a whole.
They also express the level of output of foreign currencies relating to
resource base. The expected sign is positive. OJO (1989) and YAPO (2002)
achieved the same results.
The ratio between debt service and export
(DSEX) reflects the level of debt service relating to the
volume of income in foreign currencies available to the entire economy. The
expected sign is positive. AJAYI (1991) and YAPO (2002) achieved the same
results.
The population growth rate (POP) .Demographic pressure tends
to encourage debt. The expected sign is positive OJO (1989) and YAPO (2002)
came to same conclusions.
Either (GDPC), GDP per capita. Population
growth is an important variable in the grounds of debt. Demographic pressure
tends to encourage debt. Indeed, the population growth rate reduces the wealth
of the nation (GDP per capita). The expected sign is negative.
(TCH), the exchange rate of CFA/Dollar (the
exchange rate of the CFA franc against the dollar)
If the CFA franc is appreciated, the total external debt
converted into dollar decreases. It is important to note that Togo's external
debt is incurred in several currencies. The estimated sign is positive. KRUGMAN
(1988) and N'DIAYE (1993) achieved the same results.
The dummy variable (DUM93) will assess the
effect of the suspension of cooperation with key partners in the development of
Togo. It took the value zero (0) before 1993 and one (1) after. The expected
sign is negative.
The dummy variable (DUM94) that will capture
the effect of the devaluation of the CFA franc against the French franc
It takes the value zero (0) before 1994 and one (1) after. The
expected sign is positive.
5.1.1.2.1.2 Mathematical forms of the model
Our empirical model is based on that of OJO (1989) by the
introduction of other variables. Suppose Y the explanatory variables to the
dependent variable DTPIB.
The variable GDPH (GDP per capita) was expressed in
naperian/natural logarithm in order to avoid problems related to the effects of
magnitude and facilitate interpretations.
The shape of our model can be written as follows:
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
D(.) is the operator of the first difference defined by
D(Xt) = Xt - Xt-1
The coefficient C0 is the constant of the model
The coefficient C1 is the coefficient of error
correction (restoring force toward equilibrium / balance).
The coefficients C2, C4, C6,
C8, C10 represent the short-term dynamics.
The coefficients C1 C3, C5,
C7, C9 et C11 characterize the long-term
equilibrium.
· the short-term elasticity is : C2,
C4, C6, C8 et C10
· the long-term elasticity are: -
C3/C1, - C5/C1, -
C7/C1, - C9/C1 and -
C11/C1.
· Ut is the error term.
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