Good Morning,
I have recently began experimenting with VAR modelling on EViews for my Undergraduate Research Project. My intention is to derive orthogonal impulse response functions so as to interpret both IRF and VEDC's in my analysis. My initial intention was to opt for a the Recursive SVAR with a unit triangular A matrix and diagonal B matrix (option 1), however I found that in the presence of cointegration, when using a VECM I was unable to select any structural factorisations and as such opted to select Cholesky df adjusted shocks to my system instead.
My query is that, when assessing the IRF's for my noncointegrated stationary VAR models, I found that they were identical whether I used the recursive SVAR with structurally decomposed shocks or a nonstructural VAR with Cholesky shocks. My question therefore is whether this is simply a coincidence or are the two methodologies identical?
The implications are that, while I might use the recursive factorisation on the VAR models, in the case of my VECM models, this would not necessarily be an option in EViews, as far as I am aware.
I would be most grateful for any advice on the matter,
Andrew Slaven
( Undergraduate Student  Aberystwyth University )
Recursive SVAR vs VAR model with Orthogonal IRFs
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Recursive SVAR vs VAR model with Orthogonal IRFs
Last edited by Andrew Slaven on Mon Sep 12, 2022 2:10 am, edited 1 time in total.

 Posts: 3
 Joined: Fri Aug 19, 2022 1:28 am
Re: Recursive SVAR vs VAR model with Orthogonal IRFs
I am using EViews Version 12.

 EViews Developer
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 Joined: Thu Apr 25, 2013 7:48 pm
Re: Recursive SVAR vs VAR model with Orthogonal IRFs
Hello,
Your observation is not a coincidence. Both approaches examine the residual covariance matrix to produce a triangular factorization matrix that represents a new orthogonal basis for the endogenous variables. While we may think about those resulting basis vectors differently depending on usage, e.g., calling them shocks versus structural variables, what's important is that this particular type of triangular factorization most likely has a unique solution (derived from the covariance matrix most likely being positive definite). Consequently, both approaches are likely to produce the same IRFs.
Your observation is not a coincidence. Both approaches examine the residual covariance matrix to produce a triangular factorization matrix that represents a new orthogonal basis for the endogenous variables. While we may think about those resulting basis vectors differently depending on usage, e.g., calling them shocks versus structural variables, what's important is that this particular type of triangular factorization most likely has a unique solution (derived from the covariance matrix most likely being positive definite). Consequently, both approaches are likely to produce the same IRFs.

 Posts: 3
 Joined: Fri Aug 19, 2022 1:28 am
Re: Recursive SVAR vs VAR model with Orthogonal IRFs
Thank you very much for your response. I have done some more reading on the Cholesky Decomposition and matrix algebra and with your answer things are certainly clearer now.
All the best,
Andrew
All the best,
Andrew
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