3.3 Empirical results
In this section, an optimal lag length is chosen and results of
the Cointegration test as well as the Vector error correction model (VECM)
estimates are presented.
3.3.1. Vector Autoregression (VAR) Lag Length
Since all the variables are integrated of order one, application
of Johansen Cointegration test is more appropriate; Johansen (1991, 1995). Yet,
Johansen Cointegration test is sensitive to the lag length. Therefore an
optimal lag length (p) must be chosen. Also, before estimation of the VECM
model with associated cointegrating vector, it is necessary to select optimal
lag length of initial VAR. Different information criteria were computed for
different time lags; each at 5% level of Likelihood Ratio (LR), Final Predict
Error (FPE), Akaike Information Criteria (AIC), Schwarz Information Criteria
(SC), and Hannan-Quinn information criteria (HQ). Result showed that the
appropriate lag for all the criteria was one. Hence, the number of lags
required in the Cointegration test was set to one (p=1).
Table 3.5 VAR lag order selection criteria
|
Lag
|
LogL
|
LR
|
FPE
|
AIC
|
SC
|
HQ
|
|
0
|
-16.792
|
NA
|
0.006
|
1.099
|
1.231
|
1.145
|
|
1
|
99.058
|
205.957*
|
1.60e-06*
|
-4.836*
|
-4.308*
|
-4.652*
|
|
2
|
105.206
|
9.905
|
1.89e-06
|
-4.678
|
-3.754
|
-4.356
|
|
3
|
110.411
|
7.517
|
2.41e-06
|
-4.467
|
-3.147
|
-4.007
|
|
4
|
119.311
|
11.373
|
2.57e-06
|
-4.462
|
-2.746
|
-3.863
|
|
5
|
128.401
|
10.099
|
2.82e-06
|
-4.467
|
-2.355
|
-3.729
|
* indicates lag order selected by the criterion , LR:
sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error, AIC: Akaike information criterion,
SC: Schwarz information criterion, HQ: Hannan-Quinn information criterion
3.3.2. Cointegration Test
As Engle and Granger (1987) pointed out, it is possible that a
linear combination of nonstationary series may be stationary. If such
stationary combination exists, the non-stationary time series are said to be
co-integrated and it is then possible to interpret it as a long-run equilibrium
relationship among the variables. Johansen (1995) suggested two test statistics
based on Likelihood ratio (LR); the trace statistics and the Maximum Eigenvalue
statistic. The first statistic tests the null hypothesis that the number of
Cointegration vector is less than or equal to r against the
alternative that
the number of Cointegration vector is equal to r. The
second statistic tests the null hypotheses that the number of Cointegration
vector is equal to r against the alternative that it is equal to
r+1.
Table 3.6 Johansen Cointegration test
|
Unrestricted Cointegration Rank Test (Trace)
|
|
|
Hypothesized
No. of CE(s)
|
Eigenvalue
|
Trace
Statistic
|
0.05
Critical Value
|
Prob.**
|
|
None
|
0.441
|
26.032
|
29.797
|
0.127
|
|
At most 1
|
0.061
|
2.763
|
15.494
|
0.976
|
|
At most 2
|
0.006
|
0.227
|
3.841
|
0.633
|
|
Trace test indicates no cointegration at the 0.05 level *
denotes rejection of the hypothesis at the 0.05
level **MacKinnon-Haug-Michelis (1999) p-values
|
|
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
|
|
Hypothesized
No. of CE(s)
|
Eigenvalue
|
Max-Eigen
Statistic
|
0.05
Critical Value
|
Prob.**
|
|
None *
|
0.441
|
23.268
|
21.131
|
0.024
|
|
At most 1
|
0.061
|
2.535
|
14.264
|
0.972
|
|
At most 2
|
0.005
|
0.227
|
3.841
|
0.633
|
|
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05
level * denotes rejection of the
hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999)
p-values
|
| 
