Missing data as a causal and probabilistic problem

Causal inference is often phrased as a missing data problem - for every unit, only the response to observed treatment assignment is known, the response to other treatment assignments is not. In this paper, we extend the converse approach of [7] of representing missing data problems to causal models where only interventions on missingness indicators are allowed. We further use this representation to leverage techniques developed for the problem of identification of causal effects to give a general criterion for cases where a joint distribution containing missing variables can be recovered from data actually observed, given assumptions on missingness mechanisms. This criterion is significantly more general than the commonly used "missing at random" (MAR) criterion, and generalizes past work which also exploits a graphical representation of missingness. In fact, the relationship of our criterion to MAR is not unlike the relationship between the ID algorithm for identification of causal effects [22, 18], and conditional ignorability [13].