Simple Tests for Selection: Learning More from Instrumental Variables

We provide simple tests for selection on unobserved variables in the Vytlacil-Imbens-Angrist framework for Local Average Treatment Effects (LATEs). Our setup allows researchers not only to test for selection on either or both of the treated and untreated outcomes, but also to assess the magnitude of the selection effect. We show that it applies to the standard binary instrument case, as well as to experiments with imperfect compliance and fuzzy regression discontinuity designs, and we link it to broader discussions regarding instrumental variables. We illustrate the substantive value added by our framework with three empirical applications drawn from the literature.