How to deal with Omitted Variables in School Fixed Effects Model

Hi everyone,

I'm running a School Fixed Effects Model and I'm facing a particular problem with one omitted variable at class level.

This is my command for the first attached file:

xtreg puts_mat puss clss pu_fem pu_whi pu_housi , fe i(id_sc)robust cluster(id_sc)

Where:

puts-mat is pupils test scores in math
puss is pupils socioeconomic status
clss is the mean of pupil's socioeconomic status aggregate at class level
pu_fem is pupil's sex
pu_whi is pupil's skin colour
pu_housi is pupil's number of household members
id_sc is the school's unique ID number (that I use to fix school effects)

My problem is particularly with the variable clss of pupil's characteristics aggregated at class level. As you can see, it's omitted in the Stata outputs attached below. However, this variable is only omitted when I run school fixed-effects model considering only schools with one classroom in my sample (to avoid self-selection into classroom). Previously, when I first run the same fixed-effects model with schools with more than one classroom the clss variable had was NOT omitted.

What puzzles me is the fact that in the second Stata output uploaded below, when I add another class-level variable cl_tedu (educational level of the teacher's classroom), this variable is NOT omitted, even in the school fixed-effect model with only one classroom per school considered.

Therefore, it looks like the clss is only omitted in my school fixed-effects model because it's aggregate, and not because it's class-level.

Any tips about that?

Thanks.