Empirical Results and Discussion
Initially, the test for stochastic trends in the overaggressive representation of each
individual time series will be conducted prior concentration test. This study adopted
the Augmented Dickey-Fuller (ADF) unit root test proposed by Dickey and Fuller
(1981) as shown in Equation (3)
where
Yt
represents the first difference of the
Yt
, 1
and
0
refer to the coefficients
and intercept respectively, t denotes time, p is the number of lagged terms chosen
while
t
refers to white noise. The selection of optimal lag length of p is based on
Schwartz Information Criteria (SIC). The null hypothesis can be rejected when the statistic
value is negative and statistically significant. Table 6 depicts the results of the
ADF unit root test. The results indicate that the null hypothesis of a unit root cannot
be rejected at level, nevertheless, it can be rejected after first difference at 1% and
10% significance level respectively. This implies that all the time series variables are
non-stationary at level I(0), but stationary at first difference, I(1).
Since the variables are stationary at first difference, then we can proceed with the
congregation test as introduced by Johansen (1988) and Johansen and Juselius (1990).
The main purpose of this test is to investigate the existence of a long run association
among the variables which are integrated with same order. Table 7 indicates the
results of the congregation test. The null hypothesis of non-congregation (r=0) can be
rejected as both trace (λtrace) and max-Eigen (λmax) statistic values exceed the critical
values and significant at 1% level. Meanwhile, the null hypothesis of at most one
congregation vector cannot be rejected. This indicates that existence of a single
congregation vector in the model and implies a stable long run linear equilibrium
among the variables.