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

Bibtex citation

  title = {Combining Double Sampling and Bounds to Address Nonignorable Missing Outcomes in Randomized   Experiments}, 
  author = {Coppock, Alexander and Gerber, Alan S. and Green, Donald P. and Kern, Holger L.}, 
  year = {2017}, 
  journal = {Political Analysis}, 
  volume = {25}, 
  number = {2}, 
  pages = {188–206},
  DOI = {10.1017/pan.2016.6}, 
  publisher = {Cambridge University Press}