Re: [Gretl-users] Restrictions in VECM model...
On Wed, 7 Jan 2009, Sven Schreiber wrote:
Am 06.01.2009 18:34, Mariusz Doszyn schrieb:
> Hello...
> I've got VECM model with [3x3] matrix Pi=alpha*beta' that looks as
> follows: [-1, a1*b, a2*d; 0, b-1, 0; 0, 0, d-1]. a1, b, a2 and d are
> parameters. I was thinking about imposing restrictions for elements that
> equals 0. As I'm aware it's not possible to put such restrictions on
> matrix Pi (or am I wrong?). It's better to find sensible 'alpha' and
> 'beta' in this case (but I don't have any ideas yet )?
> With regard,
> Mariusz
>
AFAICS this is a very strange Pi-matrix because it's triangular with
non-zero diagonal elements. In general that would mean that it has full
rank, so there is no cointegration, therefore it's not really a VECM
model but "just" a reparameterized levels-VAR.
Sven is right. To be exceedingly picky, one shouldn't say that there is no
cointegration: in fact, there's "too much" cointegration, since all the
variables are stationary (hence, each possible linear combination is
stationary too).
It is true, however, that the particular form of the \Pi matrix implies
some restrictions on the VAR. The way I would estimate such a system is
via SUR on the VECM formulation.
Maybe it would be helpful if you could explain why you are using a
VECM
model here and why you have this structure of the Pi matrix. Normally
the interpretation is in terms of the alpha and beta matrices.
I agree.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti