Different types of fixed effects

Hey! :)

I am stuck at understanding the difference between different types of fixed effect models. In particular, what is the difference between:
  1. A two way fixed effect model in the form of Yit = αi + γt + βXit, where ai is the time fixed effect and yt the entity fixed effect. In the literature this is called two-way fixed effect most of the time
  2. A fixed effect model in the type of Yit = αγit + βXit where the time fixed effects and the entity fixed effects are combined in "one" estimator. That would mean you would have a time-entity dummy for each combination. Are there any paper regarding this kind of fixed effect model? Is this even a fixed effect approach?
Some explanation would be really nice.
Thank you!
what does βXit represent? given you have time effects is this repeated measures model?

Whether or not any of the coefficients is random effect or not is really something that is specified by you based on desired output/goals, although there are certain conventions about what types of things ought to be treated as random effects in certain cases.


Fortran must die
I disagree that whether a coefficient is random or not depends on your design. It depends on reality, and can be tested for instance in multilevel analysis. If a variable varies with some group effect then it is random (to cite one example). If not its fixed.
yeah i guess if you have data these sort of things are subject to analysis, but the model itself is not really dependent on reality, since it is just a mathematical idea. If you stick a variable in the random statement, you have a random effect.