Re: [Gretl-users] Gretl-users Digest, Vol 92, Issue 9
I doubt that you can restrict the two equations to have the same
variance. They will simply be based on the fit of the estimated a1 and
a2 coefficients. The reason is that VAR coefficients do not depend on
the system's var-cov matrix when maximizing the likelihood function
(unless for some reason the restrictions create a dependence -- but I
fairly sure they do not). This is generally the consequence of having
the same right hand side variables in each equation.
In the end, your 'restrict model1' method is probably the easiest
way to accomplish what you really want.
Alternatively, you could estimate one equation where you stack the
observations so the y1 observations have y1(-1) in the first column
and the y2 observations have y2(-1) in the same column. Then reverse
the case for the second column such that y2(-1) is stacked above
y1(-1).
It is not clear whether you are using restricted or unrestricted
constant terms, but stacked vectors of ones and zeros will accomplish
whatever you desire.
Then the 'one' equation will have a single estimated standard error,
but it will not be 'restricted' in any way.
From: Dominik Menno <menno(a)vwl.uni-mannheim.de>
Subject: [Gretl-users] estimate restricted VAR
I would like to estimate a symmetric VAR(1) process
y = A y(-1) + u
where u is random variable with variance covariance matrix S.
Symmetric in the sense that the diagonal elements of A are equal and the
off-diagonals are equal, i.e. a11 = a22 and a12=a21. But now the
problem: I also want to restrict the variance covariance matrix to be
symmetric, that is, the variances should be the same.
Therefore my question: How can I impose restrictions on the estimated
variance covariance matrix? Any ideas?