R2 of xtivreg2, fe and ivreg2 with dummies

[avmoliv]

I runned several models using xtivreg2, fe. For curiosity, I runned the same models using ivreg2 using dummies to control for the fixed effects. Not surprisingly, the results are the same. The R2 values of the panel estimator are systematically lower. The correlation between these two sets of R2 is almost perfect, however (at least for my problem). Is there any theoretical relation between the two? In other words: is it possible to calculate one using the value of the other?

Which one would you recommend to report? Both? None?

[Mark Schaffer]

The R-sq reported by xtivreg2,fe is the "within R-sq" and is the R-sq reported after the within transformation to remove the FEs. It's the same as the within R-sq reported by Stata's official xtreg, so you can get the formula for it from the xtreg help file entry. If you want ivreg2 to replicate this R-sq, you can use the partial(.) option to partial out the fixed effects. This works because ivreg2 reports the R-sq after any partialling out has been done.

[avmoliv]

Dear Mark,
Thank you for your reply to my message.

The thing I wanted to ask you is about the R2 of the fixed effects estimator. As it is the within estimator, I believe it will always be lower than the R2 from the equivalent LSDV model. The problem is: readers (and reviewers) may prefer an R-Squared of, say 0.80 (from an LSDV using ivreg2) than an R-Squared of 0.25 (from a FE using xtivreg2). The computational burden of running an LSDV may be a problem (if the dataset is large, with many dummies), specially because the FE routine is much quicker to run. But I usually prefer incurring in wasting more computational time to obtain the higher R2. In other words, I use xtivreg2 to experiment with the models and find the best one, but I report the equivalent model using LSDV from ivreg2.

Do you think my reasoning is wrong?

Best regards,

[Mark Schaffer]

Alessandro:

R-sq is just a goodness-of-fit measure. If you include your fixed effects as part of the "model fit", you will usually get a very high R-sq whether or not the model is very good. It's about as convincing as a high R-sq in a time-series regression (i.e., not very).

Whether or not you should include the contribution of FEs to the model fit probably depends on whether you think the FEs are parameters to be estimated (as in areg) or nuisance parameters that don't really count as part of the model (as in xtreg,fe). This approach is reflected in the R-sq reported with these commands. If you compare the R-sq using (1) LSDV using regress, (2) xtreg,fe, (3) areg, you'll find that (1) and (3) are the same.