I'm trying to work out the effect of treatment on a group using a counterfactual approach. However, I don't know how I can infer the treatment start date for the comparison group.
For both groups I have a time point from which on they are eligible for treatment. I'm using kernel matching to match both groups on pre-treatment characteristics (i.e. from the time they became eligible). I don't want to use 1:1 matching because then I can't bootstrap the standard errors of the impact estimates.
I want to measure outcomes relative to the treatment start. For that I will have to estimate a pseudo treatment start for the counterfactual. How can it be done?
I thought of some sort of reverse matching (matching the treatment to the control as a weight on the treatment start date distribution), but not sure whether this could work.