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What is the benefit of including two fixed effects (say one for state and one for year), versus including a state fixed effect, a year fixed effect, and a joint state-year fixed effect?

Isn't the joint fixed effect perfectly collinear with the two separate fixed effects?

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yes it is. Which is why there are constraints on the model parameters (or rather you take linear combinations of the parameters for inference... google for contrast coding). In general, the idea is that with the joint state-year fixed effects you are testing whether the response between two states is the same for any given year and vice versa, so then you can only focus on the differences across years/states independently. This is the fundamental idea behind the ANOVA kind of analysis approach.

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  • $\begingroup$ What about when deciding on which fixed effects to include as controls? Will one method give different estimates for the coefficient of interest than the other? $\endgroup$ – gannawag Apr 30 '16 at 20:42

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