Interpreting Stata's R^2 and rho in a fixed effects regression

[Carl Kier]

As i understand it, the rho indicates the percentage of the variance that is due to individual fixed effects (u_i). Is that correctly understood? In that case, is it correctly understood that the R^2 reported does not include the proportion of the variance that is due to individual fixed effects, only the proportion that is due to the variables that are "explicity" (i don't know how else to express it) a part of the model?

[Maxence Morlet]

Correct for your first question. That is the heterogeneity between units that is wiped out by the inclusion of the fixed-effects. You are left analysing the remaining variation (and that is usually a relatively small proportion).

The R squared, which is what I presume you're referring to, is the proportion of variation in the dependent variable explained by the model. Fixed-effects, or within analysis, solely analyses variation across time within one cluster, independent of other clusters (or units). The within R squared's interpretation must thus be adapted accordingly: it becomes the proportion of variation in the dependent variable, within one cluster, explained by regressors elicited in the model and their variation within one same cluster.

Hope this helps, please let me know if this was unclear.

[Fei Wang]

Other than the accurate interpretations in #2, a short answer to the second question is yes, too. Please refer to Stata's FAQ here.

[Carl Kier]

Correct for your first question. That is the heterogeneity between units that is wiped out by the inclusion of the fixed-effects. You are left analysing the remaining variation (and that is usually a relatively small proportion).

The R squared, which is what I presume you're referring to, is the proportion of variation in the dependent variable explained by the model. Fixed-effects, or within analysis, solely analyses variation across time within one cluster, independent of other clusters (or units). The within R squared's interpretation must thus be adapted accordingly: it becomes the proportion of variation in the dependent variable, within one cluster, explained by regressors elicited in the model and their variation within one same cluster.

Hope this helps, please let me know if this was unclear.

Thanks. I still have some questions.
There are three different R^2 reported, the within, between, and overall R^2. But in any case, based on the FAQ, it seems like this is the R^2 for the model after the variance that can attributed to individual fixed effects has been taken out. Is this correctly understood?