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I assessing the impact of anti-collusion laws on dependent variables $Y_{it}$ across the country by using generalized DiD.

The identification is:

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

where i, k, and t index firms, countries, and years respectively. $X_{ikt}$ is a vector of the different firm, country, and industry controls, while $\gamma$ and $\theta$ are firm and year fixed effects. $(pt)_{kt}$ is the $post \times treat$ variable.

The result is

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The 6 columns all use firm and year fixed effects, if not stated elsewhere. In column (1), I did not control for any independent variables. In column (2), I control for some firm and country independent variables. In column (3), I control for firm, country, and industry variables. In column (4), I control for country and firm independent variables along with firm and industry * year fixed effects. In column (5), I control for the country and firm independent variables along with firm and region * year fixed effects. In column (6), I control for some firm and country independent variables, similar to column (2) but without the U.S. firms.

I am wondering whether I can conclude that: anti-collusion laws, in general, have a weak but consistent negative impact on $Y$ ceteris paribus, on average in this situation?

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    $\begingroup$ I imagine the post-periods vary very widely across $i$. Did you actually multiply two variables in this model, or is $pt_{kt}$ one variable? $\endgroup$ Commented Jun 16, 2021 at 16:14
  • $\begingroup$ Hi @ThomasBilach , $(pt)_{kt}$ is one variable, it is $(Leniency Law)_{kt}$ in this post $\endgroup$ Commented Jun 16, 2021 at 20:25

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I am wondering whether I can conclude that: anti-collusion laws, in general, have a weak but consistent negative impact on $Y$ ceteris paribus, on average in this situation?

The conclusion more or less aligns with your results.

In all but one specification (i.e., unadjusted DiD estimate) the coefficient on the main policy variable $pt_{kt}$ is negative—and consistently so. Columns (2) – (4) suggest, to some degree, a weak, negative influence of anti-collusion laws on $y_{it}$. The policy influence is stronger once you adjust for the region-by-year effects in column (5). Results from column (6) also suggest a significant, negative policy effect, though this is at the expense of discarding all the U.S. firms.

Synthesizing the policy influence as weak yet consistently negative may veil the effects under alternative specifications. I would argue that your point estimates are more consistent across specifications than they are weak. Again, the term "weak impact" may only suffice for columns (2) – (4), though less so for column (2). In short, a more elaborate explanation may be required if you want to summarize your findings across the six specifications.

And, as always, if the $t$ values are in parentheses, then say so.

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