Structual impulse responses generated by the DSGE-VAR model

[Jesse]

Dear Johannes,
Are impulse response functions generated by the DSGE-VAR model called structural impulse responses?
Given that the number of structural shocks equal the number of observable variables, does each observable variable in the DSGE-VAR model function identifying one structural shock (the structural shocks in the underlying DSGE model)
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

[jpfeifer]

See

Question regarding intuition behind DSGE-VARs

Let me try to answer: Yes, it’s a structural VAR. See section 4.3 of Del Negro/Schorfheide (2004). My understanding is that you are estimating the DSGE model parameters by combining a prior on the DSGE model with combined DSGE model and VAR estimated on actual data. That way you get a posterior on the model parameters. Again, see Del Negro/Schorfheide (2004). If you now change the weight of the DSGE model fit relative to the VAR fit on the data, of course the posterior will change.

[Jesse]

Dear Johannes,
Thank you very much and sorry about asking redundant questions.
But I am confused about the order of the structural shocks appear in the DSGE-VAR model, are the order of the structural shocks coincide with the order of observable variables appearing in the VAR model? Assuming the number of observable variables equal the number of structural shocks and the DSGE-VAR model is identifiable. Is there a one-for-one relationship between observable variables and structural shocks in the DSGE-VAR model?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse

[jpfeifer]

Again, the answer is right there in Section 4.3 of Negro/Schorfheide (2004). The DSGE model has a unique impact matrix for the shocks. That information can be used for identification in the VAR. See their equation (40). There is no Cholesky factorization going on, so the order will not matter.