Can I report fixed and random effects outcomes in one paper?

Question

I am a health economist working with panel data for a paper I am working on, I use Hausman tests to determine if I should use fixed or random effects estimators in my analysis, for some outcomes random effects are supported, for others fixed are. For the main table of results in my paper would it be acceptable to report the results of the fixed effects models for those outcomes that the hausman suggests should use a fixed effects estimator and the results of the random effects estimator for those outcomes that a random effects estimator is suggested for? Are there any examples of this approach in the literature?

Best.

Answer 1

The Hausman test merely tests whether the fixed-effect model provides results that are statistically different from those of the random-effect model. I would keep in mind that FE models are always more flexible, because you don't impose any assumption on the distribution of the unobservables. Conversely, if you were sure that the distribution of the unobservables are correct, the RE model would be preferable, as RE estimates are more efficient in this case.

As, in economics, we are rarely sure about the distribution of the unobservables, I would personally show the results in FE in one table for all outcomes, and report in another table the results with RE for those outcomes for which the Hausman test does not reject the null hypothesis. Of course, here, we're in the realm of judgement and opinion, and I'm just giving my own. Your solution, which consists of mixing methods for different outcomes, may be viewed by referees as a way to conceal some results.