Thank you!!

Thank you!

Was thinking that D is a time variant status that turns on at certain T but only for certain groups- so G doesn’t always mean treatment until the treatment kicks in. (This could be totally off though!!)

And I guess signs of parallel trends prior to post-period would be an indicator that U2 is unlikely (no other factors dependent on both time and group)

3/3 "Parallel trends":
T and G (time and group) only affect the outcome Y through D; i.e., no

U2->Y
T->U2
D->U2

U2 being some other confounder (another policy that is group/time dependent that might lead to non-parallel trends)

2/ D->Y (treatment affects outcome)
T->Y; T->D (time affects outcome, time affects treatment)
G->Y; G->D (group affects outcome, group affects treatment)
U->G (unobserved factors affect group membership)

1/ Here's the working one in my brain:
D = treatment
T = time
G = group membership (treatment vs. comparison)
U = unobserved confounders

They have been extremely consistent in this regard!!

same!!!

So good to see you Chloe and hear about your new work!

really important work, Lucy and team! thanks for sharing.

Thank you so much!!