predict after xtreg, fe is NOT predicting the fixed effect

[Alan Brito]

Dear users,

if you read xtreg postestimation's help file, it says:

" u calculates the prediction of u_i, the estimated fixed or random effect."

However, if you then read the "Methods and Formulas" under xtreg, fe (more precisely, page 23 here: http://www.stata.com/manuals13/xtxtreg.pdf), you can see that what Stata's xtreg is actually calculating is the whole time-invariant component. This component includes the fixed effect (unobserved heterogeneity) and all time-invariant variables and their respective coefficients. So, things like e.g. gender, race, etc will get lumped all together into the prediction. I confirmed this by running a second stage between those predicted values and the time-invariant factors, getting quite similar (!) values compared with those from the RE.

Notice however that the random effect is precisely that, the unobserved heterogeneity component. This means that predicted "effects" under both methods are not comprable.

I believe the help file should be very explicit on what the command is actually calculating. Otherwise, people like me get mislead about how easy is to do FE, and forget what is really going on.

[Jesse Wursten]

That's exactly what the fixed effect is though, no? There are no estimates for gender, race, etc if you include fixed effects, because they all get demeaned out (or are collinear with the panel dummies).

[Alan Brito]

Yes, but it is misleading to put the FE and RE in the same bundle, under the same variable u_i (as in the help file... se my quote above). For the FE, it should be u_i+x_i*b. That is different from u_i alone, which is what RE is predicting.

[Jesse Wursten]

But x_i * b doesn't exist in a fixed effect setting? (assuming x_i is a time invariant regressor) You literally cannot produce an estimate for b in a FE regression. Because x_it - xi_bar will be zero everywhere. Meaning you can multiply it by any coefficient you want without changing anything.

[Clyde Schechter]

Yes, but it is misleading to put the FE and RE in the same bundle, under the same variable u_i

Well, FE and RE are very different models if you look at them deeply enough. Even in terms of the predictor variables that are not colinear with the fixed effects, the meaning (not just the value) of a FE coefficient is different from the meaning of an RE coefficient. The former estimates within-panel effects, whereas the latter is an average of within- and between- panel effects. Those are conceptually very distinct (and in terms of results, it is not hard to find data sets where they even have opposite signs.

I think that u_i and b, and so on, are just generic regression terminology and have to be interpreted in light of the particular regression model. Otherwise we would have to invent distinct terminology for every single regression model.

[Alan Brito]

The problem is that the word "effect", used in both cases, under the same notation, seem to indicate the same thing. Surely, it is responsibility of everyone to know exactly what is going on, but a little help from Stata's help files would come in handy.

[Clyde Schechter]

But then why don't you object to the use of b and the word "coefficient" used indifferently in FE and RE? They are at least as different as u_i. Or perhaps you do object to that as well?