On Wed, 2 Jul 2014, Deborah Sy wrote:
Hi all,
Yes, I'll be reading onto that. Another question I have is that I've been
using a 9x9 matrix with a lot of constraints (here, it is 36) which is not
random (i.e. they were backed up by theoretical assumptions). In such case,
given any possible combinations of the 0's, the determinant will most
likely be zero and therefore, no solution will exist (unless it is a
Cholesky-decomposition or if there really exists a combination that
provides a solution in this relatively large matrix). Does it follow that I
will not be able to estimate the SVAR because no such solution exists? This
has been bugging me for days already. Any ideas?
The problem is unlikely to be the rank of your contraint matrix. If
you fill a 9x9 matrix with 36 zeros at random, the probability if it being
singular is zero (it shouldn't be difficult to prove this formally)
although of course the event is not impossible (nice example of an event
with 0 Lebesgue measure).
Assuming your matrix is nonsingular, the requirement of having 36
constrained elements is necessary, but not sufficient: it's an order
condition. If you look at my 2006 ET article I mentioned earlier, you'll
see that there is another condition that needs to be satisfied (I call it
the "structure" condition). Automtic checking of both is part of the code
I'm working on now. When I'm done, I'll post a message to the list.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
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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