Hausman test - wrong conclusion

Question

I'm performing a Hausman test in Stata 11. After the test the conclusion is to use FE panel model. In my model I have 6 variables. In FE model only one has a significant effect and in RE model 4 variables have a significant effect on the dependent variable. What do you suggest? To use FE model based on results of Hausman test or you have some other solution?

Answer 1

Statistical significance doesn't mean the model is good. In fact, in this case, it's probably a sign that it's bad.

If your model is misspecified your estimate of the model variance could be wrong. Statistical significance depends on that estimate. If that estimate is wrong, you will get erroneous t-statistics and therefore p-values and therefore, possibly, erroneously significant coefficients at your desired confidence level. I say go with what the Hausman test says.

Answer 2

You should definitely utilize the result from the Hausman test. Remember what the test does: it compares a consistent but less efficient estimator (fixed effects) to a more efficient estimator that is only consistent under the null (random effects), $$H = (\beta_{FE}-\beta_{RE})'[Var(\beta_{FE})-Var(\beta_{RE})]^{-1}(\beta_{FE}-\beta_{RE})$$ where the null of the Hausman test is that the coefficients from fixed and random effects are not systematically different. If random effects was consistent then you might expect that its coefficient estimates will not be significantly different from the fixed effects ones. Rejecting this null hypothesis means that it is unlikely for random effects to be consistent, hence fixed effects would be the better choice.

Statistical significance is not a good criterion to choose because random effects will always be more efficient than fixed effects, i.e. its coefficients' standard errors are going to be smaller. This is because random effects is a matrix weighted average of the between and the within variation in your data (fixed effects only uses the within variation and does not consider the information contained in the between variation, hence it is less efficient). For this reason you will be better off with choosing fixed over random effects if you have indication that random effects is not going to be consistent. A very precise but wrong estimate is probably less valuable to you than a less precise but more correct estimate.