Direct and Indirect Effects Based on Difference-in-Differences With an Application to Political Preferences Following the Vietnam Draft Lottery

Abstract

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.

The elasticity of voter turnout: Investing 85 cents per voter to increase voter turnout by 4 percent

“…Moreover, we have no indication that some parties tried to introduce prepaid postage to increase the turnout probability of some specific spectrum of voters. Besides, it seems unlikely that prepaid postage changed fundamental political views, which would constitute another direct channel (for evidence on the stability of voter preferences see Deuchert, Huber and Schelker 2017).…”

Instrument Validity Tests With Causal Forests

“…For instance, the ceiling was 195 in the 1970 lottery. Note that there are some concerns regarding the randomization of the 1970 lottery (see, e.g., Fienberg 1971;Deuchert, Huber, and Schelker 2019). In this application, Y measures education (no college, some college, college), D is veteran status and Z indicates whether the individual's date of birth led to a lottery number lower than 200, which considerably increased the risk of conscription.…”

Mediation Analysis

“…In contrast to standard treatment evaluation, approaches based on so-called natural experiments have rarely been considered in causal mediation analysis. One exception is Deuchert et al (2019), who use a difference-in-differences strategy to identify direct and indirect effects within principal strata, see section "Principal Strata Effects." They to this end assume a randomized treatment, monotonicity of the (binary) mediator in the treatment, and particular common trend assumptions on mean potential outcomes across principal strata.…”

“…Invoking further common trend and effect homogeneity assumptions eventually permits identifying direct and indirect effects on mediator compilers and (if identification is obtained in all strata) on the total population, see Deuchert et al (2019). See also Huber et al (2019) and Sawada (2019), who adapt the related changes-in-changes framework of Athey and Imbens (2006) to the context of direct and indirect effects within subpopulations.…”