Missing data are frequently encountered in the statistical analysis
of randomized experiments. In this article, I propose
statistical
methods that can be used to analyze randomized experiments with
a
nonignorable missing binary outcome where the missingdata
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 the German
election
experiment where researchers are worried that the act of voting
may
increase the probability of participation in the postelection
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 nonignorability
assumption and compare it with the existing alternative
approaches
in the literature. I then derive the maximum likelihood
estimator
and its asymptotic properties, and discuss possible estimation
methods. Furthermore, since the proposed identification
assumption
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 proposed methodology is extended to the
analysis of randomized experiments with noncompliance. Although
the
method introduced in this article may not directly apply to
randomized
experiments with nonbinary outcomes, I briefly discuss possible
identification strategies in more general situations.
