  Unobserved confounding is a central barrier to drawing causal inferences from
observational data. Several authors have recently proposed that this barrier
can be overcome in the case where one attempts to infer the effects of several
variables simultaneously. In this paper, we present two simple, analytical
counterexamples that challenge the general claims that are central to these
approaches. In addition, we show that nonparametric identification is
impossible in this setting. We discuss practical implications, and suggest
alternatives to the methods that have been proposed so far in this line of
work: using proxy variables and shifting focus to sensitivity analysis.
