The RATS Software Forum

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,

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?

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

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

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,

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.

Thank you Tom!