I have a staggered Difference-in-Differences setting as below when examining the impact of laws implemented in different countries in different time periods: Array



When running the regression with Y is firms' asset growth, the result is as below Array



As we can see from the Table, the coefficients of the Leniency Law variable decrease in magnitude and losing the significant levels as well.

My senior friend told me one way to deal with this problem is to ignore column (6), but adding a dummy variable called US_dummy for every specification from (1) to (5). US_dummy equalling to 1 if this firm is in the US.

However, when I run the regression, I faced the omitted problem, which is explained here

I am wondering why I need to control for US_dummy variable like that and how to overcome the omitted issue here.

My solution is instead of controlling for US_dummy, I may control for US_pt, which equals US_dummy*pt. I am wondering whether I am falling into any fallacy?