Testing instrument validity for LATE identification based on inequality moment constraints

This paper proposes bootstrap tests for the validity of instrumental variables (IV) in just identified treatment effect models with endogeneity. We demonstrate that the IV assumptions required for the identification of the local average treatment effect (LATE) allow us to both point identify and bound the mean potential outcomes (i) of the always takers (those treated irrespective of the instrument) under treatment and (ii) of the never takers (never treated irrespective of the instrument) under non-treatment. The point identified means must lie within their respective bounds, which provides four testable inequality moment constraints for IV validity. Furthermore, we present simulations on the finite sample behavior of various tests and empirical applications to labor market and economic development data. Finally, we show how to increase testing power by imposing mean dominance assumptions and propose a method to check for effect homogeneity across subpopulations