Impulse response functions (irf/oirf) - size of impulse?

[Lars Jensen]

Hi,

I have a question on the interpretation of STATA's impulse/response magnitudes using the oirf option.I think STATA by default uses a 1 unit (as opposed to for instance a 1 std.dev) increase in the impulse variable, is that correct?

I have attached a graphical example from a VECM I estimated. Since both my variables are in natural logs my interpretation of the graph would be the following: a 100 percent increase in variable x (impulse variable) leads to an almost 30 percent increase in variable y (my response variable) 10 periods ahead. Would that be a correct reading/interpretation of the oirf results?

Sincerely,
Lars

[Lars Jensen]

[Update]

Since I had little luck getting replies in this fora I contacted STATA for some clarification. In case useful for others I'm posting my understanding and an attempt to answer my own question, and for others to comment on.

First of all, I should mention that I did find a couple of threads asking about the oirf and irf and the magnitude of impulses. The typical response is that the oirf uses a one standard deviation (sd) whereas the irf is a one unit increase. However, what confused me was that the sd in the oirf is not the standard deviation of the impulse variable. More precisely it is a one unit sd of the orthogonalized innovation in the equation for the impulse variable. Alternatively the root mean squared error (rmse). If anyone would like to know more I was referred to James D. Hamilton (Time series analysis, 1994). More specifically equation 11.4.19 is for a one unit impulse function and 11.4.22 for the one unit sd in the orthogonalized innovation.

Second, I will attempt to answer my own question on the interpretation of the oirf graph. I have included the oirf table below for 'impulse=x response=y' in column A and 'impulse=x response=x' in column B. Period 0 in column B is exactly the one unit sd of the orthogonalized shock in the equation for x (or the rmse of the estimated x). Now if I for instance wanted to know 'How much will y change for a one-unit permanent increase in x?'. My intuition would be to divide column A by column B as I have done in column C. In that case a one unit increase in x would immediately raise y by 0.185 and in the long run 0.761 which is exactly my estimated long run beta (in the cointegration equation for x and y).

Best,
Lars

Period	A. oirf (x --> y)	B. oirf (x --> x)	C. (A/B)
0	0.059	0.317	0.185
1	0.161	0.337	0.477
2	0.215	0.348	0.617
3	0.243	0.354	0.687
4	0.258	0.357	0.723
5	0.266	0.359	0.742
6	0.270	0.359	0.751
7	0.272	0.360	0.757
8	0.273	0.360	0.759
9	0.274	0.360	0.761
10	0.274	0.360	0.761

[Luis Pecht]

Lars, thanks for your effort to clarify this. Very useful !!

[Elvio Carsughi]

Dear Lars, I am writing my thesis at the moment and I am encountering some problems with the IRFs both from the SVAR and VAR. For me is still not clear the difference between IRF and OIRF, however, most of the papers I cite use OIRF so for now I am going with this as well. Secondly, and this gets really specific, I don't have clear in mind what to do when using a Proxy-SVAR. Because in a Proxy-SVAR the shocks are in theory not the innovations (error terms) but they are one of the variables in the vector, usually considered exogenous hence placed first in the ordering.
I hope I was clear and I even more hope that you can help me with these issues since I have not progressed since days.