Re: st: structural var

[Michael Hanson <mshanson@mac.com>]

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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