Error bands for over identified SVAR

[AdamElderfield]

Hi,

In an effort to learn the RATS language I am trying to recreate (and update for more recent data) the model in Dungey Pagan (2000) "A Structural VAR Model of the Australian Economy" a link to the paper can be found here for those interested:

Working Paper

Thanks to help on near var estimation, I have estimated the reduced form using SUR and saved the VCV matrix to pass to CVMODEL command, all works fine. I've managed to generate IRFs using the @VARIRF command, which also works fine. However, I'd like to generate error bands for the IRFs. As I understand it, the structural model is over identified, there are 29 free parameters to be estimated from an 11 variable VAR - which a just identified model would require n*(n+1)/2 = 66 parameters to be estimated.

When trying the procedure @MONTVAR I get the error:

Code: Select all

# MAT2. Matrices with Dimensions 30 x 11 and 29 x 11 Involved in + Operation
The Error Occurred At Location 645, Line 66 of MONTEVAR

Which from looking at the forum is due to the fact this procedure seems to work on just identified systems:

https://estima.com/forum/viewtopic.php?f=4&t=3322

So I was hoping that someone could please direct me to some documentation / examples that illustrate the procedures to generate error bands for IRFs for an over identified system? In the user guide there is an example to generate errors, but that isn't followed through to IRF's or plotting the IRF's with error bands. I also have a the ecourse on VARS and SVARS, but a (very) quick scan didn't reveal what I was after.

Happy to do the required reading and coding, just want a point in the correct direction.

Thanks

Adam

[TomDoan]

Am I missing something, or is there effectively no discussion of how this was done technically (other than a reference to using Kilian's bootstrap, which is for VAR's, not near-VAR's)? The near-VAR and overidentified SVAR don't play together very well. The usual two-step method of handling an SVAR is to estimate the VAR, then estimate the SVAR using the covariance matrix from the VAR. That works, whether the SVAR is just identified or overidentified, because for a full VAR, the maximum likelihood estimates of the lag coefficients are the same regardless of the covariance matrix. You can do the same thing with a just identified SVAR and a near-VAR because, even though the ML estimates of the lag coefficients in a near VAR depend upon the covariance matrix, the just identified SVAR doesn't restrict that. The problem comes with the combination of the restricted lag coefficients AND the restricted covariance matrix. The likelihood maximizer requires a full system estimate including both the lag coefficients and the structural model. This model is small enough that that would be feasible, but the fact that they never mention doing that would seem to indicate that they must have done something not 100% correct.

[AdamElderfield]

Thanks for the reply Tom, no I don't think you're missing anything. I checked the final published version of the paper (the one I linked to is a working paper) and there's nothing more mentioned beyond the comment regarding the Killian approach.

There is some GAUSS code provided by the authors, but from what I can tell it doesn't produce the confidence intervals. Looking through the code, the authors estimate each equation via OLS. That is, each contemporaneous relationship along with its lags. One of the reasons for trying to do this estimation from the more standard reduced form / structral VAR approach was that I wanted to understand the differences between what the authors had done and what text books would suggest (although, I didn't quite appreciate the issues with a near VAR and an over-identified model).

Would there be a way forward here, or is the best I can do is analyse the IRFs without error bands (which to me isn't all that interesting), perhaps the FEVD might be a better tool for analysis here?

At least this has been an educational experience! And hey, slowly but surely getting across the language!

Thanks

Adam