st: Hausman-Taylor model, general doubts

[<M.R.Sanchis-Guarner-Herrero@lse.ac.uk>]

I am a PhD student and I am currently working in a gravity-type model for migrations. My individuals are the different origin-destination pairs and I have 2208 individuals and 15 T. 

I initially estimated my model by POLS (with cluster-robust s.e.) and then by RE, because I did not want to lose the gravity variables like distances or borders. The BP-test (1980) was in favour of the second option.
But I don't think the assumptions of orthogonality between the individual effect and the regressors hold, so after some research I think it may be useful to estimate a Hausman-Taylor (1981) model. I have also skimmed some of the Peter Egger papers and he states that to estimate the gravity model from a PD approach, one should use HT.

I have read the Stata help on the web and I got kind of lost, so I wanted to ask you for some help, especially on two issues:
 
- I have both time variant (like wages or amenities) and time invariants (like distances and some dummies) as regressors for a share of migrations. All the regressors are lagged one year wrt the dependent vble. 
How do I decide which variables are correlated or uncorrelated to the individual effects? As I understand, in the HT model, the time-invariant variables correlated with the indiv effects are instrumented as they are treated as endogeneous and we can use the time-varying regressors to do so (in the original model). So, how do I identify which are strictly exogeneous?? 
 
- Then, I also read that the HT command in Stata does not control for heter/AC. Is it better to control for it to assure we have robust s.e.? Is there a way to control for this in Stata?

I am sorry if I am going over already asked questions. Thanks for your help

--------------
Rosa 

 "If we knew what it was we were doing, it would not be called research, would it?" - Albert Einstein 


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