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In a normal VAR, we can orthogolize the errors via Cholesky decomposition and estimate OIRFs. Thus, transforming the structure of the errors so that they do not correlate.

In an SVAR, asumming we impose an orthogonal structure on the errors directly so that they do not correlate. And so if we estimate OIRFs from an SVAR instead of just IRFs, are we not orthogolizing the error structure twice? First, through a direct imposition of an uncorrelated error structure by specifying some matrix. And second, through Cholesky decomposition if we estimate OIRFs.

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Usually if you are estimating a SVAR model you would use structural impulse response functions (SIRF) not orthogonalized impulse response functions. SIRF are not exactly the same as just IRF or OIRFs. SIRF already takes the identification problem into account when the SVAR is estimated.

To learn more about this you can have look at this blog about impulse response functions in R - the blog is brief but explains difference between simple impulse response, orthogonalized impulse response, structural impulse response and generalized impulse response. More info can be found in sources cited therein.

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  • $\begingroup$ Thanks for your response. I really appreciate it. SVARs already take the identification problem into account (as the blog post says) by imposing a structure on the errors of the model (here, a diagonal matrix). Thus, SVARs already assume covariances of the errors/shocks are zero in this case. So why use OIRFs to identify the shocks/errors again after estimating an SVAR? That seems like identifying the shocks twice, first through SVAR and second through OIRF. $\endgroup$ – Emmanuel Ameyaw Nov 15 '20 at 21:09
  • $\begingroup$ @EmmanuelAmeyaw but as mentioned in my answer if you estimate SVAR you will use SIRF not OIRF $\endgroup$ – 1muflon1 Nov 15 '20 at 21:10
  • $\begingroup$ Yeah. I get that. I am reading this textbook (springer.com/gp/book/9783319982816). They use STATA's svar command to estimate the model by imposing a diagonal matrix on the errors of the model. After that, they plot OIRFs not IRFs. It seems like double identification to me. The book didn't say anything about it, why they did that. $\endgroup$ – Emmanuel Ameyaw Nov 15 '20 at 21:18
  • $\begingroup$ @EmmanuelAmeyaw well you did not mentioned the book in your question so I just assumed it was general not about that specific case. It is not normally appropriate to use OIRF with SVAR - maybe in that book they made a mistake - I would have check exactly their reasoning. Also problem with stata is that it is not programming language as let's say R and Stata's time series package offering is weak. Maybe they used it just because SIRF was not possible in stata at the time of the writing of the book. Maybe there is some reasoning in that specific case but generally you shouldn't use OIRF $\endgroup$ – 1muflon1 Nov 15 '20 at 21:43
  • $\begingroup$ Thanks!! Well, in STATA, you have to explicitly write down the diagonal matrix structure for the errors when using the svar command. So I think plotting IRFs after the estimation gives the SIRFs. And I guess we don't have anything like orthogonal SIRFs. $\endgroup$ – Emmanuel Ameyaw Nov 15 '20 at 21:59

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