  In a general set-up that allows unmeasured confounding, we show that the
conditional average treatment effect on the treated can be identified as one of
two possible values. Unlike existing causal inference methods, we do not
require an exogenous source of variability in the treatment, e.g., an
instrument or another outcome unaffected by the treatment. Instead, we require
(a) a nondeterministic treatment assignment, (b) that conditional variances of
the two potential outcomes are equal in the treatment group, and (c) a
resistant population that was not exposed to the treatment or, if exposed, is
unaffected by the treatment. Assumption (a) is commonly assumed in theoretical
work, while (b) holds under fairly general outcome models. For (c), which is a
new assumption, we show that a resistant population is often available in
practice. We develop a large sample inference methodology and demonstrate our
proposed method in a study of the effect of surface mining in central
Appalachia on birth weight that finds a harmful effect.
