  Learning a causal effect from observational data is not straightforward, as
this is not possible without further assumptions. If hidden common causes
between treatment $X$ and outcome $Y$ cannot be blocked by other measurements,
one possibility is to use an instrumental variable. In principle, it is
possible under some assumptions to discover whether a variable is structurally
instrumental to a target causal effect $X \rightarrow Y$, but current
frameworks are somewhat lacking on how general these assumptions can be. A
instrumental variable discovery problem is challenging, as no variable can be
tested as an instrument in isolation but only in groups, but different
variables might require different conditions to be considered an instrument.
Moreover, identification constraints might be hard to detect statistically. In
this paper, we give a theoretical characterization of instrumental variable
discovery, highlighting identifiability problems and solutions, the need for
non-Gaussianity assumptions, and how they fit within existing methods.
