Rescale the SVAR IRFs to 1 unit shock

[BinhPham]

Hi Tom,

I estimate an AB-type SVAR model in full-, first-half, and second-half samples.

I want to compare the IRFs of a specific variable between the three samples. Obviously, each sample gives a different standard deviation (diagonal elements of B-matrix).

Is it correct if I multiply the IRF and its error-bands of each estimation (sample) by 1/SD(shock) so that all IRFs have the same a unit shock? I think the linear structure gives it but not very sure because the error-bands are obtained from MC or bootstrap.

Thank you and best regards,

[TomDoan]

It is true that shocks and error bands (whether done as standard errors or percentiles) scale. However, I'm not entirely sure what you are trying to do. In an A-B model, the shocks don't correspond 1-1 to variables. Are you trying to standardize on one particular shock having a unit impact on one particular target variable? What method are you using to do the error bands?

[BinhPham]

Hi Tom,

I am comparing the AB-SVAR model IRFs, say, a shock to var X -> var Y. So, I have 3 samples, full, first 1/2, and half 1/2.

Now I have 3 IRFs set (only X -> Y). I want to standardize them because I want to see how different is a unit shock to X impact Y in each period?

I have MC integration IRFs. Could I rescale each IRF and error-bands with its StdDev? How about Delta Methods for the error bands?

Many thanks to your support

[TomDoan]

What is your structural model? As I said, in an SVAR the shocks don't correspond 1-1 to variables.

[BinhPham]

Hi Tom,

My SVAR is perhaps an A-model as, for example,

A = lower triangular matrix with 1's on main diagonal and other zero restrictions so that it is over-identifying.

B = diagonal matrix (*,0,0,0; 0,*,0,0; 0,0,*,0; 0,0,0,*)

So, parameters on B are size of shocks loaded.

I estimates the model in three episodes and want to compare, say, response of var 2 to a shock to var 3.
To make them comparable, I rescale the IRFs and error-bands by their B(i,i).

As you say there is no 1-1 relationship between shock and variable, what is a valid way to rescale the IRFs to a such 1 unit impulse?

I think if we pre-multiply inv(B)*A*u = e

Because B is diagonal so that we can rescale to a unit impulse. Is it correct?

Many thanks for your help,

[TomDoan]

Your model is a restricted Cholesky factor, which is a much more accurate description of what you're doing than A-B SVAR. Because of the recursive definition, you can, indeed, associate the shocks 1-1 with the variables. You can transform a factor (f) to unit impacts with something like:

compute f=%ddivide(f,%xdiag(f))

Note that you can use the Waggoner-Zha sampler for a restricted Cholesky factor.

[BinhPham]

Thank you Tom!