What is the common way to separate panel sample by a variable varying by year?

[Phuc Nguyen]

I have panel data on firms in 3 countries (e.g., 100 firms in 3 countries in 5 years, and event happen at the 3rd year in all countries at the same time). For an example, for each firms I have 4 variables, including:

y x1 x2 profitability

(while y is dependent variable and the rest are independent variables). I am examining the impact of a law on y by using differences-in-differences. There is a theory that suggests that the law has more impact on firms' with high profitability. Therefore, I want to test the impact of laws on a sample of firms with high profitability. However, each firms has 5 profiatbility (given my sample period is 5). So is there any conventional way or widely-used approach to getting a high-profitability subsample in such a case?

[George Ford]

The law applies to everyone, so it's not DD. It's just a difference in the mean effects.

Several approaches come to mine. Mean profitability prior to law; profitability in year prior to law. Might think about the coef of variation to mark firms with variable profitability. As for groups, maybe above mean/median, or tails. Maybe take bottom quartile and top quartiles (or thirds) and exclude the middle or treat as a category.

Might try FMM and let the computer decide.

Another approach might be let the threshold of high profitability vary (in a loop) and see which threshold provides the highest R2.