Referencing this Q/A, Andy offers two models that return the DiD lift estimate.
Eq1: =([|=,=2]−[|=,=1])−([|=,=2]−[|=,=1])
Eq2: =1+2(treat)+3(time)+(treat⋅time)+
From appearances, the in eq1 is the same as in eq2, which is the lift attributable to treatment exposure under parallel trends assumption.
[|=,=2] = 1+2+3++
[|=,=1] = 1+2+
[|=,=2] = 1+3+
[|=,=1] = 1+
So, the following should be true: = [ (1+2+3++) - (1+2+)] - [ (1+3+) - (1+) ]. Doing some algebra, both sides are reduced to = . Great!
Question
However, suppose that the duration of pre-start period and post-start period varied by individual in the natural experiment.
My questions are:
- Is this allowed?
- What is the appropriate modeling choice?
