reghdfe and different (non-nested) fixed effects

[Maria Ventura]

Hi,

I am running a model with reghdfe and different sets of fixed effects. For the purpose of the question, I will consider a set of cohort fixed effects (20 categories) and a set of household fixed effects (high dimensional). I notice that both the coefficient and standard errors change depending on whether I include only the second, high dimensional, set in the absorb() option or both sets of fixed effects. I assume it has to do with the dropped singletons (which, I think, are only dropped with respect to the fixed effects in absorb() ). Can anybody tell what should be the rationale to include or not fixed effects in absorb() vs, the main specification?

I am sorry I cannot include code but I am working on confidential data and could not find a dummy dataset that has enough observations to replicate.

[Andrew Musau]

reghdfe is from SSC, as you are asked to explain (FAQ Advice #12). Sergio's paper explains the rationale of dropping singletons: http://scorreia.com/research/singletons.pdf

I notice that both the coefficient and standard errors change depending on whether I include only the second, high dimensional, set in the absorb() option or both sets of fixed effects. I assume it has to do with the dropped singletons (which, I think, are only dropped with respect to the fixed effects in absorb() )

The coefficients should not change, only the standard errors. If they do, then that means that some of your variables are collinear with the fixed effects and you should rely on results obtained from the specification where all the fixed effects are absorbed.

Can anybody tell what should be the rationale to include or not fixed effects in absorb() vs, the main specification?

In fixed effects models, the fixed effects are nuisance parameters as we are only interested in controlling for them, therefore there should be no reason for leaving them in the main specification. Additionally, in wide panels with \(N>>T\), the fixed effects are not estimated consistently.

[Maria Ventura]

Thanks Andrew. Regarding the first part of the question, isn't the fact that coefficients also change consistent with greater number of observations dropped when I include everything in absorb()? I should say they do not change drastically (sign and order of magnitude are the same).

Also, I did look at Sergio's paper before asking the question, and it seems the problem with singletons should arise when fixed effects are nested with respect to clustering variable, which is not my case (hence why I was specifying this on the question). Would any of that still apply on this case?

[Andrew Musau]

Thanks Andrew. Regarding the first part of the question, isn't the fact that coefficients also change consistent with greater number of observations dropped when I include everything in absorb()?

No. If you disagree, provide a reproducible example that illustrates this. Whether included within absorb or as indicators in the command, the singletons do not affect estimates of the slope parameters.

Also, I did look at Sergio's paper before asking the question, and it seems the problem with singletons should arise when fixed effects are nested with respect to clustering variable, which is not my case (hence why I was specifying this on the question). Would any of that still apply on this case?

As far as I know, reghdfe drops singletons in case they exist for any variable specified within -absorb()-. If you do not want them dropped, specify the option -keepsingletons-. In any case, the default behavior for the Stata xt-commands is to keep singletons.

Undocumented
keepsingletons do not drop singleton groups