Coppock, Alexander, and Alan S. Gerber, Donald P. Green, and Holger L. Kern. 2017. “Combining Double Sampling and Bounds to Address Non-ignorable Missing Outcomes in Randomized Experiments.” Political Analysis. 25(2): 188-206.


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.


Figure 1 from paper, showing the width of confidence intervals and identification regions as a function of second-round response rate:

Coppock et al. 2017 Figure 1