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.

翻译：我们用一种二维工具变量Z$Z来研究低维遵守者参数,该变量以可能的高维矢量为条件,以共变方美元为条件。我们对Abadie(2003年)所定义的整个类别的遵守者参数的双重强势时刻功能作了描述,将两种经典配方组合在一起:Wald公式和$\kappa重量。特别是,我们重新解释作为Riesz代表方的Riesz重量,这似乎是一个新的洞察力。主要结果包括诸如平均遵守者特征等新案例。我们使用主要结果提出假设测试,不附带功能形式限制,以评价(一)两种不同的仪器是否平均以相同的可见特征诱导遵守者,(二)遵守者是否具有与普通人口相同的可见特征。我们通过开发这一假设测试,我们为经验研究人员提供了一种新的稳健性检查。