Instrumental Variable Methods for Conditional Effects and Causal Interaction in Voter Mobilization Experiments

In democratic countries, voting is one of the most important ways for citizens to influence policy and hold their representatives accountable. And yet, in the United States and many other countries, rates of voter turnout are alarmingly low. Every election cycle, mobilization efforts encourage citizens to vote and ensure that elections reflect the true will of the people. To establish the most effective way of encouraging voter turnout, this article seeks to differentiate between (1) the synergy hypothesis that multiple instances of voter contact increase the effectiveness of a single form of contact, and (2) the diminishing returns hypothesis that multiple instances of contact are less effective or even counterproductive. Remarkably, previous studies have been unable to compare these hypotheses because extant approaches to analyzing experiments with noncompliance cannot speak to questions of causal interaction. I resolve this impasse by extending the traditional instrumental variables framework to accommodate multiple treatment–instrument pairs, which allows for the estimation of conditional and interaction effects to adjudicate between synergy and diminishing returns. The analysis of two voter mobilization field experiments provides the first evidence of diminishing returns to follow-up contact and a cautionary tale about experimental design for these quantities. Supplementary materials for this article are available online.