标题： 2SLS在工具变量识别不同LATE时的相合方差估计量 显示英文标题

标题： A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

摘要： 在处理效应异质性下，一个工具变量识别的是特定于该工具变量的局部平均处理效应（LATE）。 当存在多个工具变量时，两阶段最小二乘法（2SLS）估计量是不同LATE的加权平均。 文献中常被忽视的是，除非这些LATE相同，否则在2SLS估计量处的假设矩条件并不成立。 如果是这样，传统的异方差稳健方差估计量将是不一致的，基于此类估计量的2SLS标准误也将是错误的。 我推导了正确的渐近分布，并通过使用Hall和Inoue（2003，计量经济学杂志）关于错误设定矩条件模型的结果，提出了一种一致的渐近方差估计量。 这可以用来正确计算标准误，无论是否存在多个LATE。 显示英文摘要

摘要： Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroskedasticity-robust variance estimator would be inconsistent, and 2SLS standard errors based on such estimators would be incorrect. I derive the correct asymptotic distribution, and propose a consistent asymptotic variance estimator by using the result of Hall and Inoue (2003, Journal of Econometrics) on misspecified moment condition models. This can be used to correctly calculate the standard errors regardless of whether there is more than one LATE or not.