A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs
A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs
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当仪器识别不同 LATE 时 2SLS 的一致方差估计器
DOI：
10.1080/07350015.2016.1186555
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发表时间：
2015
影响因子：
3
通讯作者：
Seojeong Lee
中科院分区：
文献类型：
--
作者：
Seojeong Lee
在治疗效应异质性下，工具识别工具特异性局部平均治疗效应（LATE）。对于多个工具，两阶段最小二乘（2SLS）估计量是不同LATE的加权平均值。在文献中经常被忽视的是，在2SLS被估量处评估的假定力矩条件不成立，除非这些LATE相同。如果是这样的话，传统的异方差稳健方差估计量将是不一致的，基于这种估计量的2SLS标准误将是不正确的。我推导出正确的渐进分布，并利用Hall和Inoue（2003，Journal of Economics）关于错误指定的矩条件模型的结果提出了一致的渐进方差估计量。这可以用于正确计算标准误差，而不管是否存在多个LATE。
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.