Time-invariant variables and negative value in Hausman specification test

[Sav Sarantis]

Dear Statalists,

I have a panel dataset on which I have run various OLS, fixed-effects and random-effects regressions. I am unsure whether FE or RE would be more appropriate for my needs, and so am attempting to use a Hausman specification test to decide. However, I have run into a few problems:

1) I have some time-invariant control variables which I'd ideally like to include, but are not essential. Obviously I can only include these in the RE model. When comparing the FE and RE models in the Hausman test, do they have to have exactly the same specification? Or should I include the time-invariant variable in the RE model?

2) Given this problem, I have run two Hausman tests; one in which the time-invariant variables are included in the RE specification and one in which they are not. The FE model is identical in both of these, with the time-invariant variables omitted.

In the first, where the time-invariant models ARE included, I am left with a chi2=0.99. I am interpreting this to mean that the coefficients are suitably similar, and so to use the RE model as it is efficient ("Hausman test, model 1" below).

In the second, where the time-invariant models ARE NOT included, I am given a negative chi2=-1.21. Does this mean that my RE model has a larger parameter estimate variance? Implying that FE is actually more efficient? ("Hausman test, model 2" below).


I am unsure as to which of these tests would be more appropriate.
I am using Stata/SE 12.0 for Mac.

Many thanks,

Sav

[Sav Sarantis]

I should mention, using: hausman fe re, sigmamore
hausman fe re, sigmaless
hausman fe re, alleqs constant

all result in a positive (and insignificant) chi2 value. I understand that the sigmamore and signaless commands tells Stata to use the covariance matrix from one of the RE/FE models, but am unsure as to how this will impact how I interpret the results?

Thanks again!

[Mark Schaffer]

Sav,

sigmamore and sigmaless ensure that you will have a positive statistic in finite samples.

As for time-invariant regressors: the way the Hausman test works is via a vector of contrasts between the FE and RE coeffs in common. The time-invariant regressors don't appear in the FE estimation, so they won't contribute directly to the test stat. But they contribute indirectly, because their inclusion/exclusion changes all the RE coeffs.

--Mark

[Carlo Migli]

I have an analogue problem, with the AR(1) model, and in this case it is not allow to use sigmamore or to apply the suest routine. How can I solve?!