Direct and indirect effects based on difference-in-differences with an application to political preferences following the Vietnam draft lottery

This paper proposes a difference-in-differences approach for disentangling a total treatment effect on some outcome into a direct impact as well as an indirect effect operating through a binary intermediate variable - or mediator - within strata defined upon how the mediator reacts to the treatment. We show under which assumptions the direct effects on the always and never takers, whose mediator is not affected by the treatment, as well as the direct and indirect effects on the compliers, whose mediator reacts to the treatment, are identified. We provide an empirical application based on the Vietnam draft lottery. The results suggest that a high draft risk due to the lottery leads to a relative increase in the support for the Republican Party and that this increase is mostly driven by those complying with the lottery outcome.