Comparison Empirical IRF from SVAR with Theoretical IRF

Hi everyone,

Firstly, thank you all for the support, I have been reading for a while and it is incredible the effort you put on it.

I would like to ask something that I have already seen in the forum but it is still quite not clear to me.

Let us suppose that I obtain the IRF from a model, let us say a simple baseline NK model, without trend or permanent shocks.
Let us now suppose that I want to compare the IRF of the model with those obtained by a SVAR (with identification coming from the restrictions implied from the model). The original data are not stationary and in order to get the IRF from the data, I apply either a log-difference or a difference of levels (depending on the variable). Of course, once I have the empirical IRF in difference I also can obtain the ones in levels (it is enough to cumulate the IRF).
Now, which of the two do I have to compare with those obtained from the theoretical model?
Intuitively I would say that I have to compare those in difference. However, in this case, it seems to me that I would compare the IRF showing the response of, let us take a variable, “output” (for the model) with the IRF showing the response of “output growth” (for the SVAR), given that the transformation of the log-difference data “output” delivers me the “output growth”. From this perspective, I should then compare the model IRF of output coming from the model with the “levels” IRF of output coming from SVAR.

Thank you in advance

Ideally, your DSGE model and the VAR model match in terms of specification. If you estimate your VAR in first differences, i.e. impose a unit root, then your DSGE model should also allow for permanent shocks. Then you can match the IRFs of output growth.
Otherwise, you would be comparing apples and oranges, as you correctly note.

Thank you for the answer.

Ok, so one should compare the IRF “output” of the DSGE with the IRF (in levels) “output” of the SVAR in order to compare apple with apple, but doing so may be somewhat misleading if the model itself does not allow for a permanent shock.

So, going back to the case presented in the first message, there is no way to compare the twos? I was also thinking about cumulating the IRF of the model, but it looked to me that it is basically the same thing I said before, so it may be wrong as well.

Why are you estimating the sVAR in first differences then?

Well, the original data are not stationary, the alternative would be doing a VECM.
Anyway, my answer was more related to the “nature” of the variable coming out of the DSGE, related to the possible mistake in comparing “apples and orange”, and I think I understood.
Thank you very much!

Your DSGE model implies cointegration between variables. If you could estimate a VECM, then your sVAR also features cointegration, so you could estimate it in levels (or alternatively, you could use a trend in the VAR)