Panel regression: what to do when Hausman test fails and want to keep time invariant regressors?

Question

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!

Answer 1

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.

Answer 2

Did you check for cross sectional independence?If you reject the cross sectional independence, you need to use the robust hausman test, not the usual hausman. See, here