How to obtain the matrix connecting reduced-form and structural residuals in a VAR

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p2021
Posts: 8
Joined: Thu Jul 01, 2021 3:35 pm

How to obtain the matrix connecting reduced-form and structural residuals in a VAR

Postby p2021 » Fri Jul 02, 2021 8:21 am

Suppose I estimate a VAR and then impose a Cholesky ordering assumption to conduct some structural analysis (IRFs, historical decompositions).

Eviews allows one to access both the reduced-form residuals (e) and the structural residuals (u).

But how can one access the corresponding matrix, as implied by the chosen Cholesky ordering, that connects the two, i.e. M such that e=Mu?

Peter

EViews Matt
EViews Developer
Posts: 560
Joined: Thu Apr 25, 2013 7:48 pm

Re: How to obtain the matrix connecting reduced-form and structural residuals in a VAR

Postby EViews Matt » Fri Jul 02, 2021 10:03 am

Hello,

After you perform either type of structural analysis, you can use the VAR object's @impfact data member to retrieve the underlying factorization matrix.

p2021
Posts: 8
Joined: Thu Jul 01, 2021 3:35 pm

Re: How to obtain the matrix connecting reduced-form and structural residuals in a VAR

Postby p2021 » Fri Jul 02, 2021 11:40 am

Got it, thank you. I also realized it's referred to as the S matrix in the structural-VAR part of the Eviews documentation, and thus that one can also get to it via performing Structural Factorization upon estimating a reduced-form VAR and then imposing identification restrictions that boil down to the Cholesky ordering.

EViews Matt
EViews Developer
Posts: 560
Joined: Thu Apr 25, 2013 7:48 pm

Re: How to obtain the matrix connecting reduced-form and structural residuals in a VAR

Postby EViews Matt » Fri Jul 02, 2021 12:20 pm

Quite right. Either of the first two SVAR restriction presets will produce an S matrix equivalent to a Cholesky decomposition.


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