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  • Difference-in-difference with multiple types of interventions

    I am trying to measure the impact of a road rehabilitation project on road-receiving vs non-receiving households. I have a panel data of two time periods. The project was run for some settlements and not for the others.

    I use this code:
    Code:
     xtreg y i.time##i.treat HHtimevariantcontrols, i(settl) fe vce(cluster settl)
    time and treat are dummies, respectively time for before(0) and after(1) and treat for not receiving new road(0) and receiving new road(1). This code works fine.

    However, the complication comes when I want to measure different types of interventions. There were three different types of roads rehabilitated: access roads (small), nearby major road(big) or both(combined). I have a categorical variable roadtype = 1 if only small road was rehabilitated, =2 if only big and =3 if combined.

    I want to measure the impact of these different types of road rehabilitation.
    Code:
     xtreg y i.time##i.treat##i.roadtype HHtimevariantcontrols, i(settl) fe vce(cluster settl)
    I tried using three way interaction term, but the interactions drop because of collinearity. It might be a silly question but could you please point out where do I have a mistake? Thanks a lot!
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