A Test for Instrument Validity

This paper develops a specification test for instrument validity in the heterogeneous treatment effect model with a binary treatment and a discrete instrument. The strongest testable implication for instrument validity is given by the condition for nonnegativity of point-identifiable compliers' outcome densities. Our specification test infers this testable implication using a variance-weighted Kolmogorov-Smirnov test statistic. The test can be applied to both discrete and continuous outcome cases, and an extension of the test to settings with conditioning covariates is provided.