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In a staggered Difference-in-Differences setting, Dasgupta, 2019 has a formula for such a static setting is

$Y_{it}$ = $\alpha$ + $\beta$ $pt_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$ (1)

where $i$, $k$, and $t$ index firms, countries, and years respectively. $X_{ikt}$ is a vector of the different firm, country, and industry control, while $\gamma$ and $\theta$ are firm and year fixed effects.

When replicating table 3 in his paper, I focus on columns (2) and (6). 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.

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As we can see from the Table, the coefficients of $pt_{kt}$ tell us the effect of laws stronger in US countries but weaker in non-US countries. The number of observations for spec (2) is 194,000 and 154,000 for spec (6). So, I need to address this issue

What I tried is that I add US_dummy equalling 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?

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