Negative Innovations using IRF functions

[Maali Alburaies]

Hello, I want to create an IRF for a negative innovation. I read that the standard innovation is a positive one-unit shock and I was wondering whether/ how it
is possible to change the type of the innovation to be negative? For a linear IRF, or impulse response function (which will be forthcoming from a linear VAR) the effect of (k x \sigma) is k times the effect of 1 \sigma, where k is any real number (including -1). Thus one can calculate the effect of any scaling of the standard +1 \sigma shock from the reported IRF.

[Joan Stein]

Hello Maali,

unfortunately I cannot provide a fully satisfying solution for your problem. I am also very interested in negative shock IRFs. So if you are finding a solution, i would be very thankful, if you can share it afterwards.
What I can mention is, that I found this working paper, where the authors assume negative shocks to be mirrored versions of the positive shocks:
https://ideas.repec.org/p/unu/wpaper/wp-2012-025.html

Even though they also mention, that such an assumption stands in contradiction to multiple empirical findings of papers that are focused on such mechanisms and found a asymmetric relation between positive and negative shocks.

[Morad Bali]

Hello !

Well, to my best knowledge, it is basically supposed to be symetric. What you read in one way is similar the other way around.

Let's assume your OIRF result in step 0 is +0.05, for an impulse of x and response of y. Interpretation could be both 1) and 2) :
1) A one unit positive variation of x increases y by 0.05
2) A one unit negative variation of x decreases y by 0.05

If you really want to specify a negative shock, I doubt that you can do it with STATA without changing the used algorithm.
If you manage to do it (with STATA or something else), please, update this post. It would be interesting to know if results differ from those out of the "symetric logic".

[Maali Alburaies]

Dear all

Thanks for your response. I'm trying my best to solve this with STATA because other software can give you the response of negative shocks.
Mr.Morad you can see the Prof.Kilian's paper on the American Economic Review website .He did the analysis using MATLAB and he calculates the negative response shock of oil supply on the
real oil prices:

you can find the coding in following website:

https://www.aeaweb.org/articles?id=1.../aer.99.3.1053

[Morad Bali]

Thank you for the reference.

Regarding other softwares, except if someone has coded a specific function, I am almost certain that this "negative shock" option is only a mirror of the positive one.

I don't have time for it right now, but you can check it by simply comparing results between these softwares and what you obtain in STATA.

Let us know, it's interesting!