  Complete randomization allows for consistent estimation of the average
treatment effect based on the difference in means of the outcomes without
strong modeling assumptions on the outcome-generating process. Appropriate use
of the pretreatment covariates can further improve the estimation efficiency.
However, missingness in covariates is common in experiments and raises an
important question: should we adjust for covariates subject to missingness, and
if so, how? The unadjusted difference in means is always unbiased. The
complete-covariate analysis adjusts for all completely observed covariates and
improves the efficiency of the difference in means if at least one completely
observed covariate is predictive of the outcome. Then what is the additional
gain of adjusting for covariates subject to missingness? A key insight is that
the missingness indicators act as fully observed pretreatment covariates as
long as missingness is not affected by the treatment, and can thus be used in
covariate adjustment to bring additional estimation efficiency. This motivates
adding the missingness indicators to the regression adjustment, yielding the
missingness-indicator method as a well-known but not so popular strategy in the
literature of missing data. We recommend it due to its many advantages. We also
propose modifications to the missingness-indicator method based on asymptotic
and finite-sample considerations. To reconcile the conflicting recommendations
in the missing data literature, we analyze and compare various strategies for
analyzing randomized experiments with missing covariates under the design-based
framework. This framework treats randomization as the basis for inference and
does not impose any modeling assumptions on the outcome-generating process and
missing-data mechanism.
