Testing instrument validity for LATE identification based on inequality moment constraints

We derive testable implications of instrument validity in just identified treatment effect models with endogeneity and consider several tests. The identifying assumptions of the local average treatment effect allow us to both point identify and bound the mean potential outcomes of the always takers under treatment and the never takers under nontreatment. The point-identified means must lie within their respective bounds, which provides us with four testable inequality moment constraints. Finally, we adapt our testing framework to the identification of distributional features. A brief simulation study and an application to labor market data are also provided.