When to use Hausman test to choose between Fixed Effects or Random Effects?

[Kieran Davies]

I want to use fixed effects to estimate the impact that a fiscal council's presence has on country macroeconomic forecast errors.

xtreg rgfe L.fc L.fri L.og L.debt, fe
estimates store fixed
xtreg rgfe L.fc L.fri L.og L.debt, re
hausman fixed 

 chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       32.51
                Prob>chi2 =      0.0000

The above tells me that fixed effects is preferred to random effects, which makes theoretical sense.
1) Is it then appropriate to use the fixed effects model with time dummies included without having to test once again or should I follow the same process as above for the model with time dummies included?
2) Should I perform this test for each specification of my model, e.g. if I include a fiscal council independence index as another explanatory variable, or only for my baseline regression?

I also have another problem. When estimating the impact that a fiscal council's presence has on budget balance forecast errors, a Hausman test indicates that random effects are preferred but when estimating the impact on absolute budget balance forecast errors, fixed effects are preferred. Theoretically, it seems I should use fixed effects for both since I expect the unobserved individual effects to be correlated with the other explanatory variables (e.g. a country's attitude towards fiscal discipline is likely to determine whether or not a fiscal council is instituted). How would I overcome this? Would it be best to go ahead with random effects even though I don't think the assumptions for it are satisfied?

[Andrew Musau]

1) Is it then appropriate to use the fixed effects model with time dummies included without having to test once again or should I follow the same process as above for the model with time dummies included?

If you want to test the fixed effects model with time dummies (two-way fixed effects), then the equivalent random effects model is a two-way random effects model. This you cannot do from results obtained using xtreg as the command does not allow more than one random effect.

2) Should I perform this test for each specification of my model, e.g. if I include a fiscal council independence index as another explanatory variable, or only for my baseline regression?

Yes, as the test looks at differences between coefficient pairs, so adding extra variables may change the result that you obtain.

I also have another problem. When estimating the impact that a fiscal council's presence has on budget balance forecast errors, a Hausman test indicates that random effects are preferred but when estimating the impact on absolute budget balance forecast errors, fixed effects are preferred. Theoretically, it seems I should use fixed effects for both since I expect the unobserved individual effects to be correlated with the other explanatory variables (e.g. a country's attitude towards fiscal discipline is likely to determine whether or not a fiscal council is instituted). How would I overcome this? Would it be best to go ahead with random effects even though I don't think the assumptions for it are satisfied?

The point of the Hausman test is that you should allow the sample data to determine what is the appropriate model and not assume this a priori. One of the first papers to explore these issues in Economics was Owusu-Gyapong (The Review of Economics and Statistics, 1986). It is a very good read, so you should take a look at it.

[Phil Bromiley]

It also depends on whether your theory is a within-panel theory or an across-panel theory.