Under an endogenous binary treatment with heterogeneous effects and multiple instruments, we propose a two-step procedure for identifying complier groups with identical local average treatment effects (LATE) despite relying on distinct instruments, even if several instruments violate the identifying assumptions. We use the fact that the LATE is homogeneous for instruments which (i) satisfy the LATE assumptions (instrument validity and treatment monotonicity in the instrument) and (ii) generate identical complier groups in terms of treatment propensities given the respective instruments. We propose a two-step procedure, where we first cluster the propensity scores in the first step and find groups of IVs with the same reduced form parameters in the second step. Under the plurality assumption that within each set of instruments with identical treatment propensities, instruments truly satisfying the LATE assumptions are the largest group, our procedure permits identifying these true instruments in a data driven way. We show that our procedure is consistent and provides consistent and asymptotically normal estimators of underlying LATEs. We also provide a simulation study investigating the finite sample properties of our approach and an empirical application investigating the effect of incarceration on recidivism in the US with judge assignments serving as instruments.

翻译：在具有异质性效应的内生二元处理变量与多个工具变量条件下，我们提出一种两步程序，用于识别在依赖不同工具变量时具有相同局部平均处理效应（LATE）的受控组，即便部分工具变量违反识别假设。我们利用如下事实：工具变量的LATE同质性要求其满足以下两个条件：（i）符合LATE假设（工具变量有效性与处理变量关于工具变量的单调性），且（ii）生成基于各自工具变量具有相同处理倾向的受控组。我们提出的两步程序首先对倾向得分进行聚类，其次识别具有相同简约式参数的IV组。在多元性假设（即每个具有相同处理倾向的工具变量集中，真正满足LATE假设的工具变量构成最大群体）下，该程序能够以数据驱动方式识别真实工具变量。我们证明该程序具有一致性，并能给出潜在LATE的相合且渐近正态估计量。此外，我们通过蒙特卡洛模拟考察方法的有限样本性质，并以美国司法系统中法官指派作为工具变量，实证研究监禁对累犯的影响。