RJF,
The Cholesky decomposition approach to identifying structural shocks is usually justified
on the basis of information lags or some other timing issue. For example, in a system with
inflation and the federal funds rate, inflation could be ordered first if one thinks (as
most do) that changes in the funds rate can't affect inflation in the same period.
Your point is exactly right though; such a timing (recursive) arrangement may be hard to
justify, especially if there are more than a few variables. That's why people look for
alternatives such as those outlined in Jack's SVAR package.
PS
-----Original Message-----
From: gretl-users-bounces(a)lists.wfu.edu [mailto:gretl-users-bounces@lists.wfu.edu] On
Behalf Of Dr RJF Hudson
Sent: Saturday, June 09, 2012 5:50 AM
To: r.lucchetti(a)univpm.it; Gretl list
Subject: Re: [Gretl-users] difference between SVAR and VAR IRFs
Hello, Dr Lucchetti
I'm hoping for a leg up on your Cholesky comment please, because I'm a bit
confused.....
Let's think of the expression X^T * A* X > 0 where A= LL^T
( A is symetric and positive definite) and X is real and non-zero ie all is as commonly
known (eg, ' T ' = transpose, etc) The question is how do we find L One way is to
use Cholesky's procedure.
Now this is merely a mathematical procedure.
Obviously if a different matrix A is formed by re-arranging the variables then a different
solution lower triangular matrix L will be obtained.
My query is simple...what does a mathematical procedure ( Cholesky) know about cultural
shocks ?
Am I missing something ?
RJF Hudson
----- Original Message -----
From: "Riccardo (Jack) Lucchetti" <r.lucchetti(a)univpm.it>
To: "Gretl list" <gretl-users(a)lists.wfu.edu>
Sent: Saturday, June 09, 2012 6:28 PM
Subject: Re: [Gretl-users] difference between SVAR and VAR IRFs
On Sat, 9 Jun 2012, Muheed Jamaldeen wrote:
Hello!
Also, the Cholesky is just one way of retrieving the structural shocks by
overcoming the identification problem. results from the cholesky
decomposition (which is basically a lower triangular matrix of the
variables) varies with the ordering of the variables. So an SVAR can use
either a cholesky or some other form of (usually based on theory)
restrictions preventing contemporaneous impacts of other variables.
Hope that helps?
Here's a non-technical paper that might help:
http://www.econstor.eu/dspace/bitstream/10419/17887/1/kap1072.pdf
Cheers mate.
You may also want to take a look at the pdf file documenting gretl's
implementation of SVAR: go to the "Model" menu, choose "Time Series"
and
then "Structural VAR". Click on the "Help" button and the pdf file
should
open. It's mainly oriented to help the user set up his model in gretl, but
it also contains a few theory bits and some literature pointers you may
find useful.
--------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
--------------------------------------------------
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