MCFEVDTABLE—Confidence bands for FEVD

[TomDoan]

@MCFEVDTABLE is a procedure for generating error bands for the FEVD (forecast error variance decomposition) in a VAR using the output from a Monte Carlo procedure such as @MCVARDODRAWS.

Detailed description

[CRMS]

Thank you, now it works indeed.

Should I be worried if my variance decomposition by variable does not add up to 100.0 for most of the variables and time horizons? For some of the longer horizons I even get values below 90.0... Of course the error bands are large enough to still allow for the 100.0 to be included, but I feel somehow unsure about how to present these results.

[TomDoan]

Thank you, now it works indeed.

Should I be worried if my variance decomposition by variable does not add up to 100.0 for most of the variables and time horizons? For some of the longer horizons I even get values below 90.0... Of course the error bands are large enough to still allow for the 100.0 to be included, but I feel somehow unsure about how to present these results.

With two variables, you can't have that problem. Once you're beyond a two variable system, the results get increasingly difficult to interpret. It's not clear to me that these add any real value to IRF graphs.

[davidmacro]

Thank you, now it works indeed.

Should I be worried if my variance decomposition by variable does not add up to 100.0 for most of the variables and time horizons? For some of the longer horizons I even get values below 90.0... Of course the error bands are large enough to still allow for the 100.0 to be included, but I feel somehow unsure about how to present these results.

With two variables, you can't have that problem. Once you're beyond a two variable system, the results get increasingly difficult to interpret. It's not clear to me that these add any real value to IRF graphs.

If my FEVDs do not add up to 100 for most horizons and I have 4 variables, what is the best thing to do? Or how to I explain this phenomenon/limitation in my paper? Is there a way to normalize them to 100? Kindly help.

[TomDoan]

Percentiles don't linearize. If X+Y+Z==100, then mean(X)+mean(Y)+mean(Z)=100, but med(X)+med(Y)+med(Z) isn't necessarily 100. Because FEVD's are so highly asymmetric, using means rather than medians (and +/- standard deviation bands rather than percentiles) is misleading.

[TomDoan]

FEVD's have highly asymmetrical distributions which are pinned between 0 and 1 by construction. As a result, moment-based statistics such as means and standard errors provide poor measures of the center and spread of the distribution. Percentiles (such as a 16%-84% range) are much better. However, the point estimate (the FEVD at the least squares estimates) 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, an IRF which is close to zero in the point estimate, and statistically insignificant, will likely lie outside its FEVD bounds since the randomness of the Monte Carlo integration process will generally give a combination of larger positive and negative responses.

The "center" estimates are medians, not means. However, with more than two variables, they can add to a number well below 100%. (With two variables, if 50% of the draws have an FEVD below alpha, 50% of the draws for the other variable have to be above 1-alpha so by construction, their medians will have to sum to 1. While we provide this procedure, you will likely find that point estimates of the FEVD combined with error bands on the IRF's themselves provide better information.