Hausman test in Eviews 6, error?

[zinco]

Hi all,

I realize de Hausman test for random effects in Eviews 6 and Stata 10, and the results appear differentes!

I used the database of Gujarati (Basic Econometric), where investment is dependent of firm value and kapital (1935-1954), and the cross section firms are GE, US, GM, WEST.

Here is the Stata output, which X2 p-value is 0.9678:

---------I--- Coefficients ----I
-----------(b)-----------(B)--------------(b-B)-------sqrt(diag(V_b-V_B))
----------fixed-----------.------------Difference-----------S.E.

F------0.107948-----0.107655-----0.0002926--------0.0048738
C------0.346162-----0.345710-----0.0004513--------0.0025204


Here is the Eviews output, which X2 p-value is 0.4785:

Variable-----Fixed---------Random------Var(Diff.)----Prob.

F-----------0.107948------0.107655-----0.000022----0.9500
C-----------0.346162------0.345710-----0.000002-----0.7132

Observe that the coefficients estimated are the same in the two softwares, but their difference is not the same. If you make the counts, you will see that Stata comput it right (0.107948 - 0.107655 = 0.0002926).

Becasue of this I think that Eviews 6 compute the hausman test wrong...

What do you think?

[EViews Gareth]

I'm at home, so can't look into this in detail at the moment (but will do on Monday...).

However I will point out a few things..

The Var(Diff.) that EViews reports is not the difference between the coefficients, but rather the variance of the difference. I suppose this lines up with the sqrt(diag(V_b-V_B)) term that Stata reports, although they report the SD of the difference, not the variance.

Following that, the differences are possibly due to the way that degrees of freedom are factored into the variance/sd calculations. Stata often uses a different DoF correction from EViews.

[EViews Glenn]

Gareth is correct about the Var(diff) column, which reports the variance of the different not the difference.

I've taken a look at the results for these data, and there are differences in the overall test statistic between EViews and Stata (which the original poster didn't elaborate on, EViews has a p-value of .48, Stata has a p-value of .90). In essence, the difference in results comes from a subtle difference in how the random effects coefficient covariances are computed by the two programs. (The original poster will note when looking at S.E.s of the random effects coefficients that they are slightly different between the two packages.)

I haven't verified this directly, but here is my analysis of the issue (based partly on notes and partly on recollection).

The random effects coefficient covariance estimates require an estimator of the innovation variance which determines scaling. Consistent estimates of this variance, along with the estimates of the variance of the random component are computed as part of the GLS step (by default, Swamy-Arora in EViews). In keeping with one convention for EGLS, EViews uses the GLS estimate of the innovation variance when it forms an estimate of the coefficient covariance; in essence, EViews uses a strict EGLS covariance estimator based on the initial EGLS transformation. Alternately, one could obtain a subsequent estimate of the innovation variance from the residuals from the estimated transformed model. I believe that this is the method used by Stata.

Generally, provided that the models are correctly specified, the differences between these two approaches should be small; indeed, in this case they lead to only small differences in the test statistics for the direct analysis of the coefficients of the RE model. The differences are, however, large relative to the variance of the difference between the fixed and random effects coefficients (which is very small in this case) so that they matter a bit more for the Hausman test statistic (though in neither program we do not reject the null). There isn't a right answer to which method of computing the RE coefficient covariance is correct. Both methods are consistent under the assumptions of the model. That they offer somewhat different results for the Hausman test is unfortunate, but again the two estimators reach the same conclusion.

I will make a note to consider adding an option for this particular computation since I can see it being an issue.

I hope that this answers your question.

[zinco]

Thanks for the answers,

Accepting your orientations and suggestions, I realized the random effects model according to the 3 methods available in Eviews 6: Swamy-Arora (default); Wallace-Hussain; and Wansbeek-Kapteyn.

Each method results in a different variance and a different p-value of the Hausman test. For exemple, in this specific case, the p-value calculated by Wallace-Hussain method is 0.998, nearest to the Stata p-value.

My question is answered, I think this topic is finished.

Thanks!