Hi,
I know that the question of how to understand the impulses in the OIRFs produced by Stata's irf command has come up occasionally, but I've never seen a clear authoritative answer, and it seems I've come across even contradictory or incorrect answers. So I'm hoping for some help, which will probably help others as well.
I am aware from online searches, including in this user formum, that the standard answer is that Stata's "simple" irf uses a unit impulse and oirf uses one standard deviation. And, indeed, I can see by a combination of visual inspection and relevant calculations from the e(Sigma) matrix after running a var command that the impulse of X on X itself is 1 for the irf and the relevant entry from the cholesky matrix for the oirf.
However, from this point I'm still confused on exactly how to interpret these magnitudes, and how to convert them to magnitudes that make sense to other people.
Becketti (2020) is reassuringly simple. He describes the interpretation of the OIRF as tracing out the response to a one unit increase in the impulse variable (e.g., "a random one-percentage-point increase in the inflation rate..."). However, others have pointed to equation 11.4.22 in Hamilton (1994), and this is where I get confused as the units appear to be standard deviations (e.g., "Expression 11.4.22 gives the consequences if y[j,t] were to increase by sqrt(var(u[j,t])) units").
Which is correct, or are they equivalent and I'm just not understanding? If it is a standard deviation increase, how do I interpret the standard deviations of these orthogonalized innovations and how would I translate them into units that normal people might understand?
To be more concrete: let's say I'm running a two variable var of Chinese and Vietnamese GDP growth (CHN, VNM), where the growth rates are annualized log quarterly growth rates [400*(ln(CHN) - ln(L.CHN)), etc]. The exact specification is immaterial to the question here. Let's say I want to examine the OIRFs of China on itself (CHN->CHN) and China on Vietnam (CHN->VNM). And let's further say I'd want to also make a statement to the effect that a "5 percentage point shock to CHN leads to a X% shock to VNM" after so many periods. Finally, let's assume that the standard deviation of the Chinese growth data is 5.
Given the Becketti (2020) description, this should be simple and in my example I'd just multiply my hypothetical CHN->VNM OIRF by 5. If its standard deviations, can I think of the standard deviations of the orthogonalized impulses as the standard deviation of the impulse variable? If so, would the interpretation of the CHN->VNM OIRF be the response of VNM to a 1SD CHN GDP shock? Since the standard deviation of my hypothetical CHN GDP data is already 5, I wouldn't need to make any adjustment to the OIRF at all.
Any help would be much appreciated!
Citations:
Becketti, S. (2020). Introduction to Time Series Using Stata, Revised Edition.
Hamilton, James D. (1994) Time Series Analysis
I know that the question of how to understand the impulses in the OIRFs produced by Stata's irf command has come up occasionally, but I've never seen a clear authoritative answer, and it seems I've come across even contradictory or incorrect answers. So I'm hoping for some help, which will probably help others as well.
I am aware from online searches, including in this user formum, that the standard answer is that Stata's "simple" irf uses a unit impulse and oirf uses one standard deviation. And, indeed, I can see by a combination of visual inspection and relevant calculations from the e(Sigma) matrix after running a var command that the impulse of X on X itself is 1 for the irf and the relevant entry from the cholesky matrix for the oirf.
However, from this point I'm still confused on exactly how to interpret these magnitudes, and how to convert them to magnitudes that make sense to other people.
Becketti (2020) is reassuringly simple. He describes the interpretation of the OIRF as tracing out the response to a one unit increase in the impulse variable (e.g., "a random one-percentage-point increase in the inflation rate..."). However, others have pointed to equation 11.4.22 in Hamilton (1994), and this is where I get confused as the units appear to be standard deviations (e.g., "Expression 11.4.22 gives the consequences if y[j,t] were to increase by sqrt(var(u[j,t])) units").
Which is correct, or are they equivalent and I'm just not understanding? If it is a standard deviation increase, how do I interpret the standard deviations of these orthogonalized innovations and how would I translate them into units that normal people might understand?
To be more concrete: let's say I'm running a two variable var of Chinese and Vietnamese GDP growth (CHN, VNM), where the growth rates are annualized log quarterly growth rates [400*(ln(CHN) - ln(L.CHN)), etc]. The exact specification is immaterial to the question here. Let's say I want to examine the OIRFs of China on itself (CHN->CHN) and China on Vietnam (CHN->VNM). And let's further say I'd want to also make a statement to the effect that a "5 percentage point shock to CHN leads to a X% shock to VNM" after so many periods. Finally, let's assume that the standard deviation of the Chinese growth data is 5.
Given the Becketti (2020) description, this should be simple and in my example I'd just multiply my hypothetical CHN->VNM OIRF by 5. If its standard deviations, can I think of the standard deviations of the orthogonalized impulses as the standard deviation of the impulse variable? If so, would the interpretation of the CHN->VNM OIRF be the response of VNM to a 1SD CHN GDP shock? Since the standard deviation of my hypothetical CHN GDP data is already 5, I wouldn't need to make any adjustment to the OIRF at all.
Any help would be much appreciated!
Citations:
Becketti, S. (2020). Introduction to Time Series Using Stata, Revised Edition.
Hamilton, James D. (1994) Time Series Analysis
