Fixed effect Differences

[Kevin Dan]

Hi everyone,

Could anyone explain to me what is the difference between including, for example, country fixed effect + year fixed effect compared to including country-year fixed effect?

Thank you in advance.

[FernandoRios]

Hi Kevin
at its core, its the same as deciding to include a gender dummy (2) and a marital status dummy (2), vs adding the interactions between gender and marital status (4 categories).
With panel data, however, if you try to interact the time variable with panel variable, there will be NO variation left, and you cant identify anything. That is why that is not done.
HTH

[Kevin Dan]

Dear Rios,
thanks a lot for your explanation. There is a question I cannot explain by myself. Let's say we estimate a gravity model to find the impact that a free trade agreement variable on trade. The control variables can be the GDP of the importer and exporter. If including the country-year fixed effect, the GDP variable will be dropped. I understand why. But if we use country fixed effect and year fixed effect, the GDP variable can still stay in the regression. I cannot explain why, as I think the country fixed effect will capture the time-invariant terms and year fixed effect captures the time-variant term, then how GDP can still be included? There should be no variant left to estimate the coefficient of GDP.

Below are the regression for two cases:
trade_{x.i,t} = \alpha_0 + \alpha_1 FTA_{x.i,t} + country-year fixed effect + u_{x.i,t}
trade_{x.i,t}= \alpha_0 + \alpha_1 FTA_{x.i,t} + \alpha_2 GDP_{x,t}+ \alpha_3 GDP_{i,t} + country fixed effects + year fixed effect+ u_{x.i,t}

with x and i are exporter and importer.

[FernandoRios]

Couple of options
1) in this kind of models, you actually have 3 levels of fixed effects
year
Origin country
destination country
So, adding D_country#year fixed effect will still leave variation in origin country GDP.

2) There is something wrong in your data.

My guess is 1) but 2) has been known to happen
HTH