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Causal Inference without Control Units

A fundamental tenet of research design is the necessity of control units: units of analysis that have not been assigned the treatment/program of interest. However, there are many applications where it is not possible to withhold treatment due to ethical concerns, logistical constraints, costs due to the disruption of business practices, or sometimes the potential for political fallout. In this work, we develop front-door difference-in-differences estimators that allow the estimation of treatment effects without control units. To validate the approach, we use data from 19 get out the vote (GOTV) experiments, and 4 sites of the Job Training Partnership Act Study (JTPA). We show that using only the treated units from these studies, we can provide informative bounds, and in some cases hit experimental benchmarks. We also illustrate the approach with an application to Florida's early in-person voting program. We find evidence that the program had small positive effects on turnout in 2008 and 2012. This provides a counterpoint to recent claims that early voting had a negative effect on turnout in 2008.