[Clyde Schechter]

Thanks for the reply, your comment was very helpful. In case that I didn't understand. In theory the predicted vaule for both models will be the "same". So if I do a ttest of the mean there will be no differences (neverless that graphically they didn't look the same)?

I'm not sure what you have in mind here. The output of the -predict, xb- command will be the same regardless of which variables get omitted. So if you do something like

xtreg ...., fe
predict yhat, xb
ttest yhat, by(whatever)

then, yes, the results will be the same regardless of which variables were automatically omitted in the original regression.

What do you refer about "These coefficients are only meaningful when looked at in terms of differences between them"? I understood the phrase but not how can I performi it in Stata.

For example, if you do

xtreg y x i.year, fe

the result for any particular year has no connection to reality. But the difference between, say, the coefficients for year = 2012 and year = 2015 is meaningful and is the same regardless of which variables Stata omitted to do the regression. You can get that difference with

lincom 2015.year - 2012.year

And, the same command will work even if 2015 or 2012 was omitted!