R2 -xtreg, fe- vs R2 -areg, absorb(id)

[Anna Jongma]

Dear all,

I am running a panel regression with individual fixed effects. When using the -xtreg, fe- command, I get very low R2 (both for within, between and overall, all ranging from 0.000 to 0.10)

However, on the much quoted page https://www.princeton.edu/~otorres/Panel101.pdf that when reporting the R2 for fixed effects models, the R2 from - areg, absorb(id) - is preferred to the R2 obtained from -xtreg, fe-. Is this indeed the case, and if so, why? Indeed, with -areg, absorb(id)- I get an adjusted R2 that is much more sensible (0.63). However, since my standard errors have change between the two specification, I am a bit confused as to whether it is appropriate to report the R2 from this regression when using the standard errors from the xtreg,fe specification.

Many thanks in advance.

Edit: I should have mentioned that I am clustering standard errors that the geographical level, hence why I think the standard errors from xtreg,fe are more appropriate as explained in this post https://www.stata.com/statalist/arch.../msg00596.html

[FernandoRios]

Hi Anna
I think it all depends on what do you want to show with the R2. If you look into the Stata manual (help xtreg, the pdf>methods and formulas>r2) you will see what exactly is used to estimate the reported R2. The bottom line is that this do not account for fixed effects.
When you use areg, the R2 actually accounts for the fixed effects as part of the explained variance.
Both statistics are corrects, but the one for areg may be deceivingly high. Perhaps your best option is to provide both R2 in your paper. The within R2 is what the model is really explaining with the variables you usually report in the paper. The "areg-r2" will be the overall fitness when fixed effects, which you do not report anyways, are taken into account.
HTH
Fernando

[Anna Jongma]

Hi FernandoRios

Thank you for your very quick and clarifying response!

Now that I am reading a bit more about the difference between xtreg and areg, I am wondering whether xtreg is in fact right in my case. As said, I have 2 years of panel data and want to include individual fixed effects, but cluster standard errors at the geographical residence level.

Is xtreg, fe vce(cluster district) or areg, absorb(id) vce(cluster district) more appropriate in this case?

Kind regards!

[FernandoRios]

I think they should both give you the same results. But im not sure if xtreg would cluster by district or by id in this case.
I would still report the within R2.
Fernando

[Anna Jongma]

Hello,

whilst my coefficients are the same, the Standard errors are not unfortunately. Hence I was wondering which approach is more appropriate.

kind regards!

[FernandoRios]

Since youhave panel data, i would use the xtreg, fe results.