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 non-negativity of point- identifiable complier’s outcome densities. Our specification test infers this testable implication using a variance-weighted Kolmogorov-Smirnov test statistic. Implementation of the proposed test does not require smoothing parameters, even though the testable implications involve non-parametric densities. 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.
Centre for microdata methods and practice