Standard Errors for Variance Decomposition

[ateeb]

I want to report the point estimates and the corresponding standard errors because if the point estimate is twice the standard error than the point estimate is significant, any idea how can i extract the standard errors for each point estimate at each horizon?

[TomDoan]

For what do you want the standard errors? The variance decomposition? "Standard error bands" for those are just bad practice---they can't be non-negative and are highly skewed, so standard errors are a meaningless measure.

[ateeb]

Can you please refer to

Jin, J. C., & Mcmillin, W. D. (1993). The macroeconomic effects of government debt in Korea. Applied Economics, 25(1), 35–42. https://doi.org/10.1080/00036849300000109

and let me know what are they reporting in the parentheses in table 1 page 39?

Regards,

[TomDoan]

That's a 26 year old paper. Can that be computed? Yes. Is it bad practice? Yes.

[ateeb]

Anyways how we compute those would be a highly helpful thing. Can you please guide?

[TomDoan]

@MCFEVDTABLE can compute them. But don't do that. The percentiles are mildly interesting, the standard errors are simply a bad idea and don't mean what you think they mean.

[ateeb]

I read the reference manual also the link you provided for which i am thankful. I could not find what is the default percentiles in the program? like is it ||.16,.84|| or ||.05,.95|| ?
Regards,

[TomDoan]

The defaults are in brackets:

PERCENTILES=||percentiles for lower and upper bounds|| [||.16,.84||]

[ateeb]

for percentiles=||.05,.95|| it does not give numbers for the upper level. Can you please check if there is a bug or something? it does give answers for default.

[ateeb]

The vdcs also does not sum to 100 from this procedure using the default settings.

[ateeb]

It is not working with any other percentiles than the default. Please help. I want then at 5% and 95% and 10% and 90%.

Regards,

[TomDoan]

It actually needs to be ||.05,.50,.95||. However, if you're going to do this, I would really strongly suggest that you stick with the default. Again, these can't be interpreted the way IRF's are---they're very heavily skewed and are forcibly positive. The wide band is, in practice, with five variables, really really wide, and thus not really very interesting. The default is a narrower band (a robust "one-standard deviation" alternative) which is going to give more useful information.

[ateeb]

Thank you, so this program gives us only the confidence bands, we will still borrow the point estimates from Errors command? and these are only CI for those point estimates i.e. 5% and 95% confidence bands? Right?

Regards,

Ateeb

[TomDoan]

Not in any meaningful sense. Seriously. With five variables, you're going to get a bunch of nonsense numbers. Two variables as in the B-Q example, works OK because every simulated pair sums to 100, so the medians add to 100 and the lower bound of one shock plus the upper bound of the other add to 100, etc. With more than two, the medians won't sum, the lower and upper bounds tend to be very wide. This is what I wrote in a technical support question to someone who did this and was confused by the results:

Standard errors are a very poor measure of uncertainty regarding the FEVD precisely because of the asymmetry. Percentiles (like 16%-84%) are much better. However, note that the point estimate could easily fall outside even those. That's the nature of the FEVD calculation, since both positive and negative responses get squared, and are thus indistinguishable, a response which is close to zero in the point estimate [of the IRF], and statistically insignificant will likely lie outside its FEVD bounds since the randomness of the MC integration process will generally give a combination of larger positive and negative responses.

For that reason, these are not and should not be considered standard practice.

[ateeb]

So the basic question that i wanted to know answer to is that:

When we run the errors command, it computes the variance decompositions for each variable in the system?

The @MCFEVDTABLE procedure only computes the lower, median and upper bounds for the estimates?

e.g. if forecast error variance as per the Errors instruction is 4.5 for variable x1 due to shock in x2, then the error bands by @MCFEVDTABLE for x1 with a shock to x2 is what should be looked at? correct?

I know you have a different perspective of what is and what is not important and i respect that. But can you please explain this e.g. above? it that saying the right thing? these are only the bands right?