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. The tests allow 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. The tests are quite simple; undergraduates after an introductory econometrics class should be able to implement these tests. We illustrate our tests with two empirical applications: the impact of children on female labor supply from Angrist and Evans (1998) and the impact of training on adult women from the Job Training Partnership Act (JTPA) experiment.