Well, it has long been, and remains, my position that these modeling decisions should not be made based on statistical tests. Of course, that won't get you very far if you are working in a discipline that very strongly believes the opposite and you are hoping to publish your work. The fact that different tests will give conflicting advice on the matter is only one of the reasons for my view.
Suffice it to say, if you need to estimate effects of some time-invariant variables (n.b.: if you need to estimate their effects to accomplish your research goals then, by definition, they are not "control" variables) then you cannot do that in a fixed-effects model. Linearj algebra is not suspended by any statistical test. You can, in a sense, have your cake and eat it too by using a hybrid model, implemented in -xthybrid-, by Francisco Perales and Reinhard Schunck, available at SSC. This will enable you to separately estimate the within-panel effects (which is what you would get from -fe-) and the between-panel effects (which is what you would get from -be-, and which is a component of what -re- gives you).
Suffice it to say, if you need to estimate effects of some time-invariant variables (n.b.: if you need to estimate their effects to accomplish your research goals then, by definition, they are not "control" variables) then you cannot do that in a fixed-effects model. Linearj algebra is not suspended by any statistical test. You can, in a sense, have your cake and eat it too by using a hybrid model, implemented in -xthybrid-, by Francisco Perales and Reinhard Schunck, available at SSC. This will enable you to separately estimate the within-panel effects (which is what you would get from -fe-) and the between-panel effects (which is what you would get from -be-, and which is a component of what -re- gives you).
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