  Suppose that we are interested in the average causal effect of a binary
treatment on an outcome when this relationship is confounded by a binary
confounder. Suppose that the confounder is unobserved but a non-differential
binary proxy of it is observed. We identify conditions under which adjusting
for the proxy comes closer to the incomputable true average causal effect than
not adjusting at all. Unlike other works, we do not assume that the average
causal effect of the confounder on the outcome is in the same direction among
treated and untreated.
