text: Q:
  
  Panel regression: what to do when Hausman test fails and want to keep time invariant regressors?
  
  I am running a panel data regression.  First, I did a pooled OLS regression.  Then I did a random effects (re) one.  I carried out the Hausman test, and it refuted the null hypothesis (ie. I am discouraged to use random effects over fixed effects).  So, I did the following:
  (1) I carried out a Hausman-Taylor regression (in Stata, xthtaylor).  Using xtoverid, I got that this model is OK when compared with the fixed effects one.  However, this model displays no $\text{R}^2$ value.  Furthermore, I was told that Hausman-Taylor is not a good model to use when you goal is to use the model to estimate outcomes.
  I am trying to find out about the minimum distance estimator.  It should be a procedure that allows me to combine fixed effects with time invariant regressors.  Is there a Stata command for that?  Do you know any reference on this topic?
  Any suggestion on how to deal with my current problem is very welcome!  
  
  A:
  
  The following not-yet-published paper is, in my opinion, an excellent introduction and answer to the problem you bring up:
  http://polmeth.wustl.edu/media/Paper/FixedversusRandom_1_2.pdf
  To summarize, you can still proceed with the random effects approach, but you must first modify the model to account for the fact that the within-cluster and between-cluster effects differ (i.e., what the Hausman test indicates). You can do this by adding the cluster means of your predictor as a separate predictor in the model, and then optionally also applying within-cluster centering to the original predictor. The details of this procedure and the resulting interpretations are discussed at some length in the paper linked above.
  
  