Hausman test in presence of heteroskedasticity

[Clara Weber]

Hi everyone,

I did a hausman test to check wether a FE or RE model would be more appropiate. However, there is presence of heteroskedasticity, thus, I would add "robust" to my regression. My question now is how reliable the result from the hausman test is as you can not perform it with robust SEs. According to the result of the hausman test, a RE model would be more appropiate, but I am pretty sure FE would be better in this case (I am using a pandel data set and look at countries). Is the result of the hausman test even valid?
I also performed the xttest0 command and concluded that there is no presence of random effects, which would confirm my suspicion of using a FE model.
Can anyone help me regarding the meaning/validation of a hausman test in presence of heteroskedasticity? Is the result valid?

Thanks!!

[George Ford]

ssc install rhausman

[Carlo Lazzaro]

Clara:
as an aside to George's helpful reply, you may want to consider the community-contributed module -xtoverid- that supports cluster-robust standard errors.
Tha said, the lack of a panel-wise effect detected by -xttest0- may mean that you should switch to pooled OLS.

[Jeff Wooldridge]

Clara: Especially with very aggregated data, you should use fixed effects unless the estimates are too imprecise to learn anything useful. FE is the most robust of the three estimators because it allows all time-varying explanatory variables to be arbitrarily correlated with the country heterogeneity. Unless randomization occurs (very unlikely at the country level) it is rare that you'd feel comfortably assuming the x(i,t) are uncorrelated with the country heterogeneity.

Having said that, there are a few issues to consider. First, xttest0 is purely a test of positive serial correlation. It's sold as a test of random effects versus pooled OLS but that's just not true. xttest0 is based on estimating a common serial correlation coefficient across all pairs. Especially if there's negative serial correlation across some time periods, xttest0 could easily not reject even though you should be allowing for an unobserved effect. If you're using, say, country growth rates, there could easily be negative serial correlation in the shocks.

If you are to do a robust Hausman test, it should be robust to serial correlation, too. I like the Mundlak regression where you add the time averages of all time-varying explanatory variables and use pooled OLS and cluster. This is easy with a balanced panel, a bit trickier if unbalanced. With balanced where z1 ... zJ are time-constant controls:

xtset country year
egen x1bar = mean(x1), by(country)
...
egen xKbar = mean(xK), by(country)
reg y x1 ... xK z1 ... zJ i.year x1bar ... xKbar, vce(cluster country)
test x1bar ... xKbar
xtreg y x1 ... xK z1 ... zJ i.year x1bar ... xKbar, re vce(cluster country)
test x1bar ... xKbar

Pooled OLS and RE when you add the xjbar are identical, so it doesn't matter which you use.

Again, if FE with clustered standard errors is giving you useful answers, use that!