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 miss-ingness indicators are allowed. We further use this representation to leverage techniques devel-oped 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 missing-ness. 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].