Thread by @jmwooldridge

Based on questions I get, it seems there's confusion about choosing between RE and FE in panel data applications. I'm afraid I've contributed. The impression seems to be that if RE "passes" a suitable Hausman test then it should be used. This is false.

I'm trying to emphasize in my teaching that using RE (unless CRE = FE) is an act of desperation. If the FE estimates and the clustered standard errors are "good" (intentionally vague), there's no need to consider RE.

RE is considered when the FE estimates are too imprecise to do much with. With good controls -- say, industry dummies in a firm-level equation -- one might get by with RE. And then choosing between RE and FE makes some sense.

Unfortunately, it is still somewhat common to see a nonrobust Hausman test used. And this makes no logical sense when every other statistic has been made robust to serial correlation and heteroskedasticity. So either the traditional Hausman test should be adjusted, or use CRE.

In Stata, the following is common, and correct:

xtreg y i.year x1 ... xK, fe vce(cluster id)
xtreg y i.year x1 ... xK z1 ... zJ, re vce(cluster id)

But often it is followed by this:

xtreg y i.year x1 ... xK, fe
estimates store b_fe
xtreg y i.year x1 ... xK z1 ... zJ, re
estimates store b_re
hausman b_fe b_re

In addition to being nonrobust, the df in the test will be wrong: It should be K, not (T - 1) + K. The latter is easy to fix, the former is tricky ....