Two-stage least squares with treatment-covariate interactions for treatment effect heterogeneity
含处理与协变量交互项的两阶段最小二乘及处理效应异质性AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接讨论工具变量、LATE 与服从者处理效应异质性的识别解释。
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含处理与协变量交互项的两阶段最小二乘及处理效应异质性
- 研究问题
- 当工具变量仅在给定协变量后有效时，含处理交互项的两阶段最小二乘系数何时能够解释为服从者中的处理效应异质性？
- 方法与思路
- 作者在 LATE 框架下分析交互式两阶段最小二乘，将其因果解释与工具倾向得分乘协变量的线性条件联系，并研究去均值设定。
- 材料陈述的贡献
- 摘要称对任意结局生成过程的一致解释具有必要充分条件，并给出倾向得分取值数量限制及去均值交互估计 LATE 的结果。
- 阅读关注点
- 应核对必要充分结论的量词范围、协变量维度与饱和设定，以及条件随机化和无条件随机化的区别，避免将回归交互系数直接因果化。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出全部正则条件或有限样本证据，结论不能脱离其工具有效性框架使用。
原文摘要
Treatment effect heterogeneity with respect to covariates is common in instrumental variable (IV) analyses. An intuitive approach, which we call the interacted two-stage least squares (2sls), is to postulate a working linear model of the outcome on the treatment, covariates, and treatment-covariate interactions, and instrument it using the IV, covariates, and IV-covariate interactions. We clarify the causal interpretation of the interacted 2sls under the local average treatment effect (LATE) framework when the IV is valid conditional on the covariates. Our main findings are threefold. First, we show that the coefficients on the treatment-covariate interactions from the interacted 2sls are consistent for estimating treatment effect heterogeneity with respect to covariates among compliers for any outcome-generating process if and only if the product of the IV propensity score and covariates are linear in the covariates, referred to as the linear IV-covariate interactions condition. Second, assuming that the covariate vector has dimension K and includes a constant term, we show that the linear IV-covariate interactions condition holds only if the IV propensity score takes at most K distinct values. As a result, this condition is difficult to satisfy beyond two special cases: (a) the covariates are categorical with K levels, or (b) the IV is randomly assigned. These results underscore the difficulty of interpreting regression coefficients from specifications with treatment-covariate interactions when the covariates are not saturated and the IV is not unconditionally randomized, absent correct specification of the outcome model. Third, as an application of our theory, we show that the interacted 2sls with demeaned covariates is consistent for estimating the LATE under the linear IV-covariate interactions condition.