st: Hausman Test when the RE OLS model includes time-constant variables

["Pavlos C. Symeou" <p.symeou@jbs.cam.ac.uk>]

Dear Statalisters,

I have a question regarding the Hausman specification test. I want to include in my OLS model 7 time-constant variables which depict the industry classification 
of a firm. In order to use the Hausman test, I first estimate the FE model, I store the estimation results, then run the RE model and finally ask Stata for the 
estimation of the Hausman test. As it is expected, the time-constant variables are dropped from the FE model but not from the RE. This implies that the Hausman 
test compares two different models; one with time-constant variables and one without. The Hausman test rejects the RE model. If I omit the time-constant 
variables from the two models, then the Hausman test compares comparable models and still rejects the RE model. Yet, inclusion of the time-constant variables in 
the OLS model is important for its correct specification so I interact these variables with year dummies and include the interaction variables (and exclude the 
original time-constant variables) in both FE and RE models. I rerun the Hausman test which now rejects the FE in favor of the RE model. I am confronted here 
with a dilemma where I can only perform the Hausman test if I interact my time-constant variables with year dummies, but what I actually need from my final 
model is the inclusion of the original time-constant variables, which however leads to the wrong estimation of the Hausman test.

I would appreciate if you could advise on this. Should I arbitrarily choose the RE model that can involve the time-constant variables in its estimation? Otherwise?

Yours,

Pavlos
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