In this paper I revisit the interpretation of the linear instrumental variables (IV) estimand as a weighted average of conditional local average treatment effects (LATEs). I focus on a situation in which additional covariates are required for identification while the reduced-form and first-stage regressions may be misspecified due to an implicit homogeneity restriction on the effects of the instrument. I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under a weaker version of monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere. The problem of negative weights disappears in the interacted specification of Angrist and Imbens (1995), which avoids misspecification and seems to be underused in applied work. I illustrate my findings in an application to the causal effects of pretrial detention on case outcomes. In this setting, I reject the stronger version of monotonicity, demonstrate that the interacted instruments are sufficiently strong for consistent estimation using the jackknife methodology, and present several estimates that are economically and statistically different, depending on whether the interacted instruments are used.

翻译：本文重新审视了线性工具变量（IV）估计量作为条件局部平均处理效应（LATE）加权平均的解释。我聚焦于这样一种情境：识别需要额外协变量，而简化式回归与第一阶段回归可能因工具效应的隐含同质性限制而被错误设定。我证明，在单调性的弱化版本下——即当某些协变量值存在依从者但无违抗者，而其他协变量值存在违抗者但无依从者时——部分条件LATE的权重为负，且IV估计量不再能被解释为因果效应。Angrist与Imbens（1995）提出的交互项设定避免了错误设定问题，且在实际应用中似乎未被充分利用，该设定可消除负权重问题。我通过审前羁押对案件结果因果效应的应用研究阐明了上述发现。在该设定中，我拒绝了较强版本的单调性假设，证明交互项工具在刀切法框架下足够强以实现一致估计，并展示了多组经济与统计上存在显著差异的估计结果——差异取决于是否采用交互项工具。