3.2 Unit root Test
Most macroeconomics data are nonstationary; hence it was
primordial to test for stationarity before the regression in order to avoid
misleading results. Therefore, a formal test is applied in order to check the
stationarity of the series. Series which are stationary at level is said to be
integrated of order zero, I (0). The ones which attained
stationarity after differencing is said to be integrated of order
one, I (1).
3.2.1 ADF test
Augmented Ducky Fuller (ADF) test was used to test for the
stationarity. It consists of running a regression of the first differences of
the series against the series lagged once, lagged difference terms and
optionally, a constant and time trend. This can be expressed as follows:
(1)
Where is the dependent variable, is constant term, trend
variable, is
stochastic disturbance term.
The test for unit root was carried out on the coefficient of ().
If the coefficient
is significant from zero, then the hypothesis that has a unit
root is rejected. The
fact that the null hypothesis is rejected indicates stationarity.
The null hypothesis is
that the variable is a non-stationary series (H0: )
and it is rejected when
is significantly negative ( ).
If the computed value of the ADF statistic is more negative
than the critical values, then the null hypothesis (H0) is rejected and the
series considered to be stationary or integrated of order zero, I(0). Contrary,
failure to reject the null hypothesis implied that the series is non-stationary
leading to another test on the first difference of the series. If the series
attained stationarity after the first difference, they are considered
integrated of the order one, I (1). If not, further difference was conducted
until stationarity was reached.
Table 3.3 Unit root test of level
|
variable
|
Constant
|
Trend
|
|
ADF
statistic
|
1%
|
5%
|
10%
|
ADF
statistic
|
1%
|
5%
|
10%
|
|
GDP
|
0.581
|
-3.605
|
-2.937
|
-2.607
|
-1.766
|
-4.205
|
-3.526
|
-3.195
|
|
FD
|
-2.035
|
-3.605
|
-2.936
|
-2.606
|
-1.883
|
-4.205
|
-3.526
|
-3.194
|
|
CP
|
-1.948
|
-3.615
|
-2.941
|
-2.609
|
-2.207
|
-4.219
|
-3.533
|
-3.198
|
Table 3.4 Unit root test of first difference
|
variable
|
Constant
|
Trend
|
|
ADF
statistic
|
1%
|
5%
|
10%
|
ADF
statistic
|
1%
|
5%
|
10%
|
|
D(GDP)
|
-6.250
|
-4.211
|
-3.529
|
-3.196
|
-6.250
|
-4.212
|
-3.529
|
-3.197
|
|
D(FD)
|
-4.663
|
-3.610
|
-2.938
|
-2.607
|
-4.585
|
-4.211
|
-3.529
|
-3.196
|
|
D(CP)
|
-2.818
|
-3.621
|
-2.943
|
-2.610
|
-3.769
|
-4.226
|
-3.536
|
-3.200
|
3.2.2 Test Results
Results of the unit root test showed that all the series were
nonstationary. The ADF test statistics were lesser than the critical values
indicating that the series were nonstationary at level (Table 3.3).
Furthermore, all the variables attained stationarity at first difference at 10%
significance level. The calculated values of the ADF statistics were more
negative than the critical values implying that the series were integrated of
order one I (1) (Table 3.4).
| 
