Why does stata omit because of collinearity in some models but not others?

[Ella Ki]

In a wage regression I am running, Stata omits the "nonwhite" variable because of collinearity for the fixed effects model but not for pooled OLS or random effects.

Is this only because collinearity is a problem in the FE model?

Or, should the other models be re-estimated with that variable omitted?

There isn't really a particular reason why this variable should be collinear with the others so I'm not sure why Stata has removed it.

[daniel klein]

Not much information here, but note that any variable that does not vary within panel units will be collinear with the fixed-effects. Such variables cannot be included in a within-variance estimator.

Best
Daniel

[Ella Ki]

Not much information here, but note that any variable that does not vary within panel units will be collinear with the fixed-effects. Such variables cannot be included in a within-variance estimator.

Best
Daniel

That makes lot of sense, as values for a race variable never change.

Might that also explain why some "highest qualification" dummies become insignificant - because they are unlikely to change too?

I am using highest qualification attained instead of years of education.

What does this mean if you have to control for things like race and education, and you wanted to compared pooled OLS models with fixed effects?

Update: I have learnt that even though FE cannot produce coefficients for these variables, they do control for them - should one still include them in the regression then?

[daniel klein]

If the variation within panel units is small, then the standard errors for the coefficients of such variables will tend to be large.

Best
Daniel