A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs
指出在工具变量识别不同局部平均处理效应时，传统异方差稳健方差估计量不一致，并基于Hall和Inoue(2003)的误设定矩条件模型结果，提出了一致的渐近方差估计量，用于正确计算标准误。
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 heteroscedasticity-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.