## how to specify a "non-fundamental" shock in SVAR

Questions and discussions on Vector Autoregressions

### how to specify a "non-fundamental" shock in SVAR

I saw this structure in Lee (1998) JFQA paper.“Permanent, Temporary, and Nonfundamental Components of Stock Prices,”
In his three-variable (say x, y ,z) var model, he specifies three shocks e1, e2, and e3. e1 he calls permanent shock, e2- transitory shock, and e3- non-fundamental shock.
Three restrictions to just-identify the SVAR are:
e2 has no long-run effect on x (Blanchard and Quah)
e3 does not have impact on both x and y, since x and y are all fundamental variables and they should not have the non-fundamental shock.

My question is how to do the two e3-restrictions? I have thought of this problem for a long time, and I still cannot thing out the explicit conditions.
So could anyone help me?
Thanks a lot!
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

Is the non-fundamental shock equivalent to short-run restriction?
But I cannot see this equivalence and convince myself?
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

It sounds as if this is a combination of short and long-run restrictions with the long-run restriction shape being

. 0 .
. . .
. . .

and the short-run

. . 0
. . 0
. . .
TomDoan

Posts: 2724
Joined: Wed Nov 01, 2006 5:36 pm

### Re: how to specify a "non-fundamental" shock in SVAR

Thanks, Tom.
I got this solution too. But
Can this restriction make sure all past and current non-fundamental shock e3 have no impact on x and y?
I will try to do it on real data shortly and see the result.

TomDoan wrote:It sounds as if this is a combination of short and long-run restrictions with the long-run restriction shape being

. 0 .
. . .
. . .

and the short-run

. . 0
. . 0
. . .
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

No. That's impossible with an unrestricted VAR. You could only do that with a near-VAR with the x and y equations restricted to have no "Z" variables.
TomDoan

Posts: 2724
Joined: Wed Nov 01, 2006 5:36 pm

### Re: how to specify a "non-fundamental" shock in SVAR

right, that problem puzzles me a lot.
I do not know how it is realized in that paper, and i guessed it may use near-VAR, but the author does not mention it at all.
If you have time, could you see that paper. I just make sure my understanding is right.
Attachments
Bong-Soo-Lee-1998.pdf
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

another question?
if I use new-VAR, can we perform the similar structure decomposition as SVAR?
How to realize it in RATS?
Thanks a lot!
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

zxlstoner wrote:right, that problem puzzles me a lot.
I do not know how it is realized in that paper, and i guessed it may use near-VAR, but the author does not mention it at all.
If you have time, could you see that paper. I just make sure my understanding is right.

So far as I can tell, the paper is just wrong. He refers to (10) as the source of "at least" 3 additional restrictions, but (10) has an infinite number of restrictions. Picking the three long and short run restrictions just identifies the model but doesn't force the full polynomials to behave as required. You can only do that with a block recursive VAR structure combined with the long and short restrictions.

The Peersman 2004 OBES thread is about a near-VAR done using Gibbs sampling.

http://www.estima.com/forum/viewtopic.php?f=4&t=522

Since the short and long-run restrictions just identify the structural model, they impose a restriction on the coefficients so you can draw the coefficients and covariance matrix using the Gibbs sampling, and then factor the covariance matrix.
TomDoan

Posts: 2724
Joined: Wed Nov 01, 2006 5:36 pm

### Re: how to specify a "non-fundamental" shock in SVAR

Thanks a lot, Tom.
you confirm my understanding and puzzle about that paper.
I shall use near-VAR.
I just read Peersman 2004 OBES, but it is a little different from a model in my mind, such that

say, variables x, y ,z, i want to identify three shocks or innovations e1 e2 e3. my restrictions are: e2 does not have long-run effect on both x and z, and additionally e3 should not have effect on x (so called non-fundamental, no past and current effects on x). How should I construct the near-VAR? I have thought about it for a while, but still do not have some clues. Actually, I am new to near-VAR and related techniques.

TomDoan wrote:
zxlstoner wrote:right, that problem puzzles me a lot.
I do not know how it is realized in that paper, and i guessed it may use near-VAR, but the author does not mention it at all.
If you have time, could you see that paper. I just make sure my understanding is right.

So far as I can tell, the paper is just wrong. He refers to (10) as the source of "at least" 3 additional restrictions, but (10) has an infinite number of restrictions. Picking the three long and short run restrictions just identifies the model but doesn't force the full polynomials to behave as required. You can only do that with a block recursive VAR structure combined with the long and short restrictions.

The Peersman 2004 OBES thread is about a near-VAR done using Gibbs sampling.

http://www.estima.com/forum/viewtopic.php?f=4&t=522

Since the short and long-run restrictions just identify the structural model, they impose a restriction on the coefficients so you can draw the coefficients and covariance matrix using the Gibbs sampling, and then factor the covariance matrix.
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

### Re: how to specify a "non-fundamental" shock in SVAR

zxlstoner wrote:Thanks a lot, Tom.
you confirm my understanding and puzzle about that paper.
I shall use near-VAR.
I just read Peersman 2004 OBES, but it is a little different from a model in my mind, such that

say, variables x, y ,z, i want to identify three shocks or innovations e1 e2 e3. my restrictions are: e2 does not have long-run effect on both x and z, and additionally e3 should not have effect on x (so called non-fundamental, no past and current effects on x). How should I construct the near-VAR? I have thought about it for a while, but still do not have some clues. Actually, I am new to near-VAR and related techniques.

That doesn't sound like it's feasible. In a three variable system, you can make one shock have no effect on two variables (at any horizon) by imposing a block structure in the VAR of

x x 0
x x 0
x x x

or you can have two shocks have no effect on one variable with

x 0 0
x x x
x x x

You can't impose one shock having no effect on one variable. (There's no invertible finite lag VAR which will accomplish that).
TomDoan

Posts: 2724
Joined: Wed Nov 01, 2006 5:36 pm

### Re: how to specify a "non-fundamental" shock in SVAR

Thanks a lot.
You explain so clearly.
zxlstoner

Posts: 7
Joined: Wed Mar 17, 2010 9:42 pm

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