Page 32 - Contributed Paper Session (CPS) - Volume 1

CPS658 Sagaren P.
With unrestricted parameters the model is consistent with linear trends in the
differenced series Ayt and thus quadratic trends in y t . In this case, estimation
and inference may be unreliable (Doornik, Hendry, and Nielson, 1998).

Table 7
Co-integration Rank Test Using Trace
H0: H1:
Rank=r Rank>r Eigenvalue Trace Pr > Drift in Drift in
Trace ECM Process
0 0 0,4135 21,899 0,0156 Linear Quadratic
1 1 0,1987 0
6,4257 0,0114

From Table 7 above, it is clear that for a linear drift in the VECM there
is a quadratic drift in the Co-integration space.Further the series is not co-
integrated implying that the model is inappropriate.

6. Conclusions
It is important to give considerable attention to the deterministic
components of the models when modelling long run relationships. The
estimation results for each of the five cases show theimportance of the choice
of the deterministic components in the cointegration model. For each of the
five cases, based on the choice of the deterministic components, the results
are significantly different.
When the model excludes all deterministic components in the data (case
1), implying no growth and zero intercepts in every cointegrating relation,
favourable cointegration results are obtained. However,from the given data it
is evident that an intercept is needed to account for the initial level of
measurements Y0 . Consequently, this option with the long run relationship
given by y1 t = 1.101548 y2 t cannot be justified. On the other hand, when the
model does not allow for a separate drift (constant) but allows for a constant
in the cointegration space (case 2) we obtain favourable cointegration results
with a restriction on the intercept term. This option is with the long
relationship, y1 t = 0.779868 y2 t + 3.34869 is clearly approriate. For cases 3 ,4
and 5, the eviedence in favour of cointegration is extremely weak.
Given the different results for each of the cases for this empirical
application, we recommend that extreme care should be taken when specifying
deteministic components during cointegration modelling.

References

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