Hausman test chi-square

[Jo Smith]

Hi,
I have a quick query, the following is the result from Hausman teat, so which one should I take in order to consider to choose between fixed effect and random effect method.

Test: Ho: difference in coefficients not systematic

chi2(21) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 66.73
Prob>chi2 = 0.0000
(V_b-V_B is not positive definite)


Is it 66.73 then random is appropriate
or Prob>chi2 = 0.0000 then fixed much suitable?

Thanks very much

[Carlo Lazzaro]

Jo:
looking at Prob>chi2 is simply another way to look at chi2: at its face value the hausman test favours the fixed effect specification.
As far as the (V_b-V_B is not positive definite) message, you may want to test the result of -hausman- against those provided by a robust hausman test (please, seehttp://www.stata.com/statalist/archi.../msg00053.html).

[Joshua D Merfeld]

If I could just add to this (and a comment I've added to many previous posts on Hausman tests): please do not just run a Hausman test and use the results to select your specification. There are many reasons the Hausman test could reject the null that have nothing to do with our true test of interest (measurement error, for instance, which is much worse in fixed effects). Ask yourself: is it at all possible that the panel heterogeneity is correlated with my explanatory variables? If so, you need to use fixed effects. (Moreover, a negative variance is a known issue in empirical work with Hausman tests.)

But to answer your question, Carlo is spot on. The results favor a fixed effects specification.