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 effect 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. Imposing random treatment assignment along with specific common trend (and further) assumptions identifies 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. We provide an empirical application based on the Vietnam draft lottery, where we analyse the impact of the random draft lottery number on political preferences. The results suggest that a high draft risk due to the lottery leads to a relative increase in mild preferences for the Republican Party, but has no effect on strong preferences for either party or on policy contents. Moreover, the increase in Republican support is mostly driven by the direct effect.