In my difference-in-difference setting , I examine the impact of anticorruption laws on firms' asset growth of all countries all over the world after the laws are implemented in each country.
I normally control for firm and industry * year fixed effects in this case following existing literature.
However, I reckon that the impacts of laws will be different between developed and developing countries. Therefore, I am thinking of using subsample tests. There are two ways of conducting a subsample test are: (1) divide the whole sample into two subsamples and then run the main regression for all subsamples or (2) add the interaction for one subsample and see the difference by reading the interactive coefficients by running the regression.
Regarding the method (2) in double diff, we call it diff-in-diff-in-diff or triple diff. And (2) is preferred compared to (1).
So, what I want to ask is, if in the main specification, I control for firm and industry * year fix effects, so what fixed effects I should control when I perform the triple diff to examine the additional impact of laws on developed countries?
From this answer of Thomas, it seems that I only need to add the second level interaction terms. I deem the regression should be adjusted as below
$$ Y_{iast} = \gamma_{st} + \lambda_{at} + \eta_{as} + \delta L_{ast} + u_{iast}, $$
where $Y_{iast}$, which denotes the asset growth of each firm i in developed country group $a$ in country $s$ and year $t$
Up to this point, I do not know what I should do next to know what are the fixed effects should be controlled.
