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Re: st: structural var


From   Michael Hanson <mshanson@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: structural var
Date   Wed, 03 Mar 2010 21:12:09 -0500


On Mar 3, 2010, at 7:47 AM, anna steccati wrote:

I need to estimate a structural VAR with 2 equations as follows:

x(t)=x(t-1)+…+x(t-5)+y(t)+…+y(t-5)

y(t)=y(t-1)+…+y(t-5)+x(t-1)+…+x(t-5)


The presence of the contemporaneous term y in the first equation makes it
impossible to estimate it with the var command.

Is there a way to estimate the model with the SVAR command? Should I add
more identification restrictions?

Anna,

If you need to estimate a structural VAR (as you state), then you need to use -svar-. What you have proposed for your model is a simple two- equation recursive VAR -- it can be identified via a Choleski decomposition. In the [TS] manual, look at the first example of a "short-run just-identified SVAR model." Your model is even simpler, as you have only two equations. The identifying assumptions that A is lower triangular (i.e., the A(1,2) element is zero) and the two structural error terms are uncorrelated (using the identity for the variance matrix is only a normalization) gives enough restrictions to recover all the remaining structural parameters. Note that is your case, the restriction is imposed on the y(t) equation (that is, x(t) has a coefficient of zero in the y(t) equation), which means it should be listed first in your -svar- command, given that A is lower triangular.

In other words,

matrix A = (1,0\.,1)
matrix B = (.,0\0,.)
svar y x, aeq(A) beq(B)

ought to do the trick.

Hope this helps,
Mike


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