# Clarifying the definition of DDD?

I am examining the triple diff (diff-in-diff-in-diff)(DDD) in a staggered setting.

Normally, when it comes to DDD, I understood that we examine the differential movement between two sub groups based on a standard (or generalized) DiD. For example, in a generalized DiD, we can examine the impact of anti-corruption laws on salary of labors. Where anticorruption laws are staggered implemented around the world.

Afterwards, from my understanding, if we want to examine the difference between the impact of this law on salary of male worker and female worker, we need to perform DDD. At that time, the general equation change from

$$Y = ai + bt + cD + epsilon$$

$$i$$ standing for each worker and $$t$$ standing for each time period.

where D equal to 1 for all observation after the year a country passed the law

to

$$Y = ai + bt + c*D*g + epsilon$$

where $$g$$ is the group for gender of worker So, I am wondering if g=1 for make worker and 0 for female worker or "." for female worker?

And I am wondering whether it is a right thinking ?

• What is $i$ and $t$ for? Sep 3 at 23:56
• i is unit and t is period, for example i is each worker and t is year Sep 4 at 0:00
• Cross-poste d at statalist.org/forums/forum/general-stata-discussion/general/… Sep 4 at 0:55
• The second-order interaction terms should be in there as well. Is treatment starting at different times? Sep 4 at 1:05
• @ThomasBilach , treatment starting at different times ( staggered implementation) Sep 4 at 1:06

I use Greek letters for coefficients. I assume you intended to include person and time dummies for DiD purposes and denoted them by $$\alpha_i$$ and $$\beta_t$$. You perhaps want to do this regression:

$$Y_{i,t} = \alpha_i + \beta_t + \gamma D_{i,t} + \delta g_i D_{i,t}$$

If male ($$g=1$$), then this person receives $$(\gamma + \delta)$$ impact from $$D$$. If female, this person's impact is $$\gamma$$. This way, you can capture the difference in the impact received by the gender.

Your original equation misses the term $$D$$, which essentially assumes that females won't get any impact. I don't think you want to impose such restrictions.

Also, you often add $$g_i$$ to regressors for regressions with interaction terms. However, $$g_i$$ will be collinear to the person fixed effect ($$\alpha_i$$); hence it should be omitted.

• Thanks for your help, so you mean g will receive value missing "." or 0 for female ? I am really curious about that Sep 4 at 3:48
• If g can be missing and you want to use the missing cases as well, then you need to create male and female variables and use them as separate regressors. Sep 4 at 4:48
• @KotaMori Aren’t we missing some of the second-order interactions, such as country times year? Sep 4 at 4:59
• @ThomasBilach That depends on data and research goals. In this particular case the $D$ variable, law dummy, would be unique within a country-year pair. Then if we add country-year fixed effect, then the coefficient for $D$ will become unidentifiable. You could possibly add the gender-time fixed effect. I think researchers may have different preferences on these terms (some prefer parsimonious specifications, others want to control as many things as possible). Sep 4 at 5:21
• @Louise Yes, that works. Sep 4 at 5:56