Errors SD in a BVAR model

[AhmedSahlool]

Hi Tom,

I hope this finds you well,

In order to interpret the IRF results that I obtain with a BVAR model estimated with Gibbs sampling, I would like to know how to get the Standard deviation of different shocks?

To explain better, The impulse responses that I obtain with the @MCGraphIRF procedure are linear in the sizes of the shocks; the one SD shocks are used to put the whole set of responses into a proper context.

In order to understand better the results, we need to know what "one SD" measures for each variable. For instance: The magnitude of standard deviation shocks is 0.28 percentage point for world growth, 27 basis points for U.S. T-bill rates, etc.

In the case of a BVAR estimated with Gibbs sampling, should I sum the errors variance covariance matrix in each draw and average it, as we do with other results?

Thank you for your time,

Ahmed

[TomDoan]

The range of the impact responses usually gives you the information that you need. But if you want to, then yes, you can get them by averaging across draws.

[AhmedSahlool]

Would you kindly elaborate more, as I'm trying to average and it is taking a lot of time and effort.

I started by declaring the matrix "Struc_sigmad", to store the structural residuals, and this outside the loop,

DEC Rec[real] Struc_sigmad(nvar,nvar)

Then I fill it with zeros to sum inside the loop,

compute Struc_sigmad=%zeros(nvar,nvar)

Inside the loop, I transform the reduced form errors' variance covariance matrix to structural one by:

compute Struc_sigmaddraw=(INV(%decomp(sigmad)))*sigmad*TR(INV(%decomp(sigmad)))

Then I sum the output "Struc_sigmaddraw" inside the matrix "Struc_sigmad"

compute Struc_sigmad(i,j) = Struc_sigmad(i,j) + Struc_sigmaddraw(i,j)

I got the message ## MAT13. Store into Out-of-Range Matrix or Series Element

Would you kindly give me some help

[AhmedSahlool]

Sorry for bothering,

I think that I succeeded to average following the same way as to get the record for model coefficients:

I started by declaring the matrix "Struc_sigmad", to store the structural residuals, and this outside the loop,

DEC Series[Rect] Struc_sigmad

Then I fill it with zeros,

gset Struc_sigmad 1 ndraws = %zeros(nvar,nvar)

Inside the loop, I transform the reduced form errors' variance covariance matrix to structural one by "I don't know if this transformation is correct":

compute Struc_sigmaddraw=(INV(%decomp(sigmad)))*sigmad*TR(INV(%decomp(sigmad)))

I keep the whole record of matrices

compute Struc_sigmad(draw)=Struc_sigmaddraw

Then outside the loop i average by:

dec rect StrucMatrix(nvar,nvar)
do i=1,nvar
do j=1,nvar
sstats(mean) 1 ndraws Struc_sigmad(t)(i,j)>>StrucMatrix(i,j)
end do j
end do i

The final output is a diagonal matrix with ones on the diagonal, I was expecting to have the variance of each structural shock on the diagonal; some thing different from one!! Is it the transformation equation above?

What do you think, could you kindly give me some guidance.

[TomDoan]

This

compute Struc_sigmaddraw=(INV(%decomp(sigmad)))*sigmad*TR(INV(%decomp(sigmad)))

creates the identify matrix by construction.

The information that you want (so far as I can tell) is already incorporated into the graphs in the "own" impact responses. If you want to compute this, what you want is just

compute Struc_sigmaddraw=%decomp(sigmad)

The diagonals of that will be the loadings onto the own Cholesky-factored shocks.