Re: [Gretl-devel] $vcv in vecm
Allin Cottrell schrieb:
On Sat, 2 Jan 2010, Sven Schreiber wrote:
> Allin Cottrell schrieb:
>> Accessing $vcv has never been implemented for VECMs, and I
>> wouldn't know how to do it. You can use $jvbeta to get the
>> covariance of the \beta estimates.
> Ok, then what about adding $vcv to the following statement in chapter 12
> of the user guide:
>
> " VARs and VECMs: $stderr and $yhat are not available"
OK, that statement is now changed. It was out of date: $stderr
and $yhat are in fact available for VARs and VECMs. The only
"missing" accessor is $vcv for VECMs. That's because I don't know
what to do about the covariance block for \beta and the other
coefficients.
Well what one *could* do is to treat the error-correction terms as given
due to the super-consistency (T-convergence) of the cointegration
coefficients, and then the remaining system is just multi-equation OLS.
This would be justified asymptotically. So for the stacked system the
covariance of the coefficients estimates would be:
\hat{\Omega} \otimes (X'X)^{-1},
where X holds all regressors (identical across equations, lagged
differences plus the EC terms) and \Omega is the covariance matrix of
the system residuals ($sigma I guess).
Defined like this, $vcv would also include the standard errors of the
alphas, although within the Johansen procedure those are calculated
differently I think (not sure right now, would need to check). But
asymptotically the difference shouldn't matter anyway. (BTW, if there is
a difference, i.e. if standard errors of alpha can also be gotten in
another way from Johansen, it may be worthwhile to think about adding an
accessor $jvalpha.)
So altogether you would have $jvbeta for the cointegration relations,
and $vcv for the coefficients of the rest (transitory terms).
cheers,
sven