Double Robustness for Complier Parameters and a Semiparametric Test for Complier Characteristics

We propose a semiparametric test to evaluate (i) whether different instruments induce subpopulations of compliers with the same observable characteristics on average, and (ii) whether compliers have observable characteristics that are the same as the full population on average. The test is a flexible robustness check for the external validity of instruments. We use it to reinterpret the difference in LATE estimates that Angrist and Evans (1998) obtain when using different instrumental variables. To justify the test, we characterize the doubly robust moment for Abadie (2003)'s class of complier parameters, and we analyze a machine learning update to $\kappa$ weighting.