In a staggered Difference-in-Differences setting, my static setting is:

Array

On the result table below, I focus on column (2) and (6)

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In these two columns, I have the same control variables sets, fixed effects sets, but only difference in sample. While columns (2) controlled for the whole sample but column (6) controlled for non-US sample.
As we can see from the Table, the coefficients of pt tell us the effect of laws stronger in US countries but weaker in non-US countries. So, I need to address this issue.

What I tried is that I add US_dummy equalling to 1 to specification (2) if this firm is in the US to the equation. But I faced the omitted issue because the information in US_dummy is carried by the year fixed effect already.

That said, I simply cannot solve the weakened results in non-US sample problem by using the US dummy in all regressions. Can you suggest me any other way to deal with this issue?