1
$\begingroup$

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 ?

$\endgroup$
5
  • 1
    $\begingroup$ What is $i$ and $t$ for? $\endgroup$
    – Kota Mori
    Commented Sep 3, 2021 at 23:56
  • $\begingroup$ i is unit and t is period, for example i is each worker and t is year $\endgroup$ Commented Sep 4, 2021 at 0:00
  • $\begingroup$ Cross-poste d at statalist.org/forums/forum/general-stata-discussion/general/… $\endgroup$
    – Nick Cox
    Commented Sep 4, 2021 at 0:55
  • 1
    $\begingroup$ The second-order interaction terms should be in there as well. Is treatment starting at different times? $\endgroup$ Commented Sep 4, 2021 at 1:05
  • $\begingroup$ @ThomasBilach , treatment starting at different times ( staggered implementation) $\endgroup$ Commented Sep 4, 2021 at 1:06

1 Answer 1

3
$\begingroup$

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.

$\endgroup$
9
  • $\begingroup$ Thanks for your help, so you mean g will receive value missing "." or 0 for female ? I am really curious about that $\endgroup$ Commented Sep 4, 2021 at 3:48
  • 1
    $\begingroup$ 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. $\endgroup$
    – Kota Mori
    Commented Sep 4, 2021 at 4:48
  • $\begingroup$ @KotaMori Aren’t we missing some of the second-order interactions, such as country times year? $\endgroup$ Commented Sep 4, 2021 at 4:59
  • $\begingroup$ @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). $\endgroup$
    – Kota Mori
    Commented Sep 4, 2021 at 5:21
  • 1
    $\begingroup$ @Louise Yes, that works. $\endgroup$
    – Kota Mori
    Commented Sep 4, 2021 at 5:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.