Combining Double Sampling and Bounds to Address Non-Ignorable Missing Outcomes in Randomized Experiments

Missing outcome data plague many randomized experiments. Common solutions rely on ignorability assumptions that may not be credible in all applications. We propose a method for confronting missing outcome data that makes fairly weak assumptions but can still yield informative bounds on the average treatment effect. Our approach is based on a combination of the double sampling design and non-parametric worst-case bounds. We derive a worst-case bounds estimator under double sampling and provide analytic expressions for variance estimators and confidence intervals. We also propose a method for covariate adjustment using post-stratification and a sensitivity analysis for non-ignorable missingness. Finally, we illustrate the utility of our approach using Monte Carlo simulations and a placebo-controlled randomized field experiment on the effects of persuasion on social attitudes with survey-based outcome measures