Some follow up comments from a previous post on the Hausman test in the RE/FE context:
RE assumes that Cov(a[i],x[it])= 0. {The model here is: Y[it] = b*x[it] + e[it], where e[it] = a[i] + u[it]).} The coefficient estimates from using RE and FE have the following properties depending on whether that assumption is true:
b[RE] b[FE] Cov(a[i],x[it])=0 efficient, consistent inefficient, consistent Cov(a[i],xpit]!=0 inconsistent consistent
In words, if Cov(a[i],x[it])=0 is true, then since the coefficient estimates are both consistent, they are "likely" to be close and so the difference between b[RE] and b[FE] is small. If Cov(a[i],xpit]!=0, then since b[RE] is inconsistent, you would like that the difference is likely to be large.
The test statistics is (b[RE]-b[FE])' v^(-1) (b[RE]-b[FE]), where v is the estimated asymptotically variance of (b[RE]-b[FE]) with Chi square distribution.
Reference: Hausman test (fe vs. re), use robust SE or not? [Statalist],
Stata 12 help for hausman [Stata]