Statistical analysis of randomized experiments with non‐ignorable missing binary outcomes: an application to a voting experiment

Summary.  Missing data are frequently encountered in the statistical analysis of randomized experiments. I propose statistical methods that can be used to analyse randomized experiments with a non‐ignorable missing binary outcome where the missing data mechanism may depend on the unobserved values of the outcome variable itself even after taking into account the information in the fully observed variables. The motivating empirical example is a German election experiment where researchers are worried that the act of voting may increase the probability of participation in the post‐election survey through which the outcome variable, turnout, was measured. To address this problem, I first introduce an identification strategy for the average treatment effect under the non‐ignorability assumption and compare it with the existing alternative approaches in the literature. I then derive the maximum likelihood estimator and its asymptotic distribution and discuss possible estimation methods. Furthermore, since the identification assumption proposed is not directly verifiable from the data, I show how to conduct a sensitivity analysis based on the parameterization that links the key identification assumption with the causal quantities of interest. Finally, the methodology proposed is extended to the analysis of randomized experiments with non‐compliance. In addition, although the method that is introduced may not directly apply to randomized experiments with non‐binary outcomes, I briefly discuss possible identification strategies in more general situations.