Double robustness for complier parameters and a semi-parametric test for complier characteristics

Summary We propose a semi-parametric test to evaluate (a) whether different instruments induce subpopulations of compliers with the same observable characteristics, on average; and (b) whether compliers have observable characteristics that are the same as the full population, treated subpopulation, or untreated subpopulation, on average. The test is a flexible robustness check for the external validity of instruments. To justify the test, we characterise the doubly robust moment for Abadie’s class of complier parameters, and we analyse a machine learning update to weighting that we call the automatic $\kappa$ weight. We use the test to reinterpret Angrist and Evans' different local average treatment effect estimates obtained using different instrumental variables.