Missed Wald Chi2 due to dummy variables and variables which are only available for one time period

[Eva Lan]

Dear Statalist community,

As part of my thesis I am doing Random-Effects Models (I have tested it with Breusch and Pagan Lagrange-Multiplier and it says the REM is okay) and DiD Estimations.
Unfortunately, I am running out of time and got some unexpected new output from my data since I created a new dummyvariable (x1, x2, x3).

I use:
by se, sort: xtreg success age sex happy children pets per x1 x2 x3 dis aim sum car hours loan, re

Variables:
x3 always gets omitted due to collinearity and I have no idea why.
(Would it make sense to delete it? But actually I don't have any reason for that except of the collinearity which I can't explain. Or can I solve the problem otherwise so it doesn't get omitted?)
Moreover I have two variables which are only relevant for se = 2!
Moreover, I want to use the REM, because in the Fixed-effects model more than half of my variables get omitted due tu collinearity (most of them are time invariant).

Wald chi2 / Prob > chi2 = . :
You can see the problem in the two pictures. I receive dots/missing values for Wald chi2 and consequently for Prob > chi2.
I have read that the Prob > chi2 value had to be < 0.05 for the model to be okay. Otherwise, I won't be allowed to use the models and its output. [due to https://www.princeton.edu/~otorres/Panel101.pdf] (Please correct me, if there is something wrong.)
So I have no idea how to evaluate this models output.
Do you know and can you help me how I am able to either receive values for the Wald chi2 and for the Prob > chi2 to analyze my results or how I am able to continue my work?

Thank you very much in advance!!

[Carlo Lazzaro]

Eva:
- I would assume that your problem rests on the dummy you created;
- going -re- because -fe- (as expected) wipes out all your time-invariant parameters might be hazardous if you have not investigated (via -hausman-) whether -fe- specification fits your data better that -re- specification:
- collinearity is a matter of fact and there's nothing you can do but change your regression model;
- the omitted Wald test may be explained by singletons in your dataset (see -help j_robustsingular-).

[Eva Lan]

Thank you very much for your helpful answer, Carlo Lazzaro!

I have checked the hausmantest. If I keep those variables it tells me to use the -re-. If I drop all of the omitted variables it would change into the -fe-.
So I will try to find another way.

[Carlo Lazzaro]

Eva:
in order to avoid re-inventing the wheel and propose a regression model than may give an improper representation of the data generating process, I would also take a look at the literature in your research field and see what others did in the past when presented with the same research goal.