  Consider the problem of estimating the causal effect of some attribute of a
text document; for example: what effect does writing a polite vs. rude email
have on response time? To estimate a causal effect from observational data, we
need to adjust for confounding aspects of the text that affect both the
treatment and outcome -- e.g., the topic or writing level of the text. These
confounding aspects are unknown a priori, so it seems natural to adjust for the
entirety of the text (e.g., using a transformer). However, causal
identification and estimation procedures rely on the assumption of overlap: for
all levels of the adjustment variables, there is randomness leftover so that
every unit could have (not) received treatment. Since the treatment here is
itself an attribute of the text, it is perfectly determined, and overlap is
apparently violated. The purpose of this paper is to show how to handle causal
identification and obtain robust causal estimation in the presence of apparent
overlap violations. In brief, the idea is to use supervised representation
learning to produce a data representation that preserves confounding
information while eliminating information that is only predictive of the
treatment. This representation then suffices for adjustment and can satisfy
overlap. Adapting results on non-parametric estimation, we find that this
procedure is robust to conditional outcome misestimation, yielding a low-bias
estimator with valid uncertainty quantification under weak conditions.
Empirical results show strong improvements in bias and uncertainty
quantification relative to the natural baseline.
