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

We study low dimensional complier parameters that are identified using a binary instrumental variable $Z$, which is valid conditional on a possibly high dimensional vector of covariates $X$. We characterize the doubly robust moment function for the entire class of complier parameters defined by Abadie (2003) by combining two classic formulations: the Wald formula and the $\kappa$ weight. In particular, we reinterpret the $\kappa$ weight as the Riesz representer to the Wald formula, which appears to be a new insight. The main result includes new cases such as average complier characteristics. We use the main result to propose a hypothesis test, free of functional form restrictions, to evaluate (i) whether two different instruments induce 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. By developing this hypothesis test, we equip empirical researchers with a new robustness check.