  Many identification results in instrumental variables (IV) models have the
property that identification holds with no restrictions on the joint
distribution of potential outcomes or how these outcomes are correlated with
selection behavior. This enables many IV models to allow for arbitrary
heterogeneity in treatment effects and the possibility of selection on gains in
the outcome variable. I call this type of identification result
"outcome-agnostic", and provide a necessary and sufficient condition for
counterfactual means or treatment effects to be identified in an
outcome-agnostic manner, when the instruments and treatments have finite
support. In addition to unifying many existing IV identification results, this
characterization suggests a brute-force approach to revealing all restrictions
on selection behavior that yield identification of treatment effect parameters.
While computationally intensive, the approach uncovers even in simple settings
new selection models that afford identification of interpretable causal
parameters.
