# What should we conclude when the significance levels are different but the signs are similar among coefficients on a variable of interest?

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

The identification is:

$$Y_{it}$$ = $$\alpha$$ + $$\beta$$ $$(pt)_{kt}$$ + $$\deltaX_{ikt}$$ + $$\theta_t$$ + $$\gamma_i$$ +$$\epsilon_{it}$$

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

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?

• 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? Commented Jun 16, 2021 at 16:14
• Hi @ThomasBilach , $(pt)_{kt}$ is one variable, it is $(Leniency Law)_{kt}$ in this post Commented Jun 16, 2021 at 20:25

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