5:34 p.m.
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
11:20 a.m.
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.
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.
cheers,
sven
11:38 a.m.
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
3:45 p.m.
> 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.
Thanks Sven and Jack...
You're right that it could be just VAR model. I was thinking mostly about
ways of making restrictions on matrix 'Pi', sorry:). According to my model
I'm trying to do something like this:
ct=s+a1*yt+a2*rt+ut, yt=a+bY[t-1]+u1t, rt=c+dr[t-1]+u2t where yt (GNP) and
rt (interest rate) could be I(1). I'm trying to put this into VAR model with
restrictions...
With regard,
Mariusz
1:05 p.m.
Mariusz Doszyń schrieb:
Thanks Sven and Jack...
You're right that it could be just VAR model. I was thinking mostly about
ways of making restrictions on matrix 'Pi', sorry:). According to my model
I'm trying to do something like this:
ct=s+a1*yt+a2*rt+ut, yt=a+bY[t-1]+u1t, rt=c+dr[t-1]+u2t where yt (GNP) and
rt (interest rate) could be I(1). I'm trying to put this into VAR model with
restrictions...
With regard,
Mariusz
Ok, so what you want to do is: (a) check whether or not the variables
are actually I(1), (b) in case they are, estimate the cointegrating
relationship(s) between them. IMHO there is no need to prespecify any
particular form of dynamics or lag structure like you seem to be doing
(eg., AR(1) models for r_t and y_t).
For (a) you could either apply conventional unit root tests to the
variables, or you could do the Johansen test straight away and infer the
integration status of the variables from the estimated/tested
cointegration rank. (E.g., like jack said, if you find full rank 3 then
all variables would be I(0).)
What you probably have in mind is a cointegration rank of 1 with the
cointegration relationship involving all three variables. That would
give you the long-run relation c_t = a1 y_t + a_2 r_t, and all variables
would be I(1). In terms of your previously stated Pi matrix you would of
course also have a rank of only 1, since the diagonal elements b-1 and
d-1 would actually be zero.
good luck,
sven
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4 comments
4 participants
participants (4)
-
Mariusz Doszyn -
Mariusz Doszyń
-
Riccardo (Jack) Lucchetti -
Sven Schreiber