On Mis-Measured Binary Regressors: New Results and Some Comments on the Literature
On Mis-Measured Binary Regressors: New Results and Some Comments on the Literature
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关于误测的二元回归量：新结果和对文献的一些评论
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发表时间：
2015
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通讯作者：
Camilo García
中科院分区：
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作者：
Francis J. Ditraglia;Camilo García
本文研究了使用离散工具变量来识别内生的、误测的、二进制处理的因果效应。我们开始表明，唯一现有的识别结果，这种情况下，出现在Mahajan（2006），是不正确的。因此，在这个模型中的识别仍然是一个悬而未决的问题。我们开始证明，治疗效果是基于条件的第一时刻的信息，无论该仪器可能采取的值的数量是不确定的。我们继续推导出一种新的部分识别结果的基础上，条件二阶矩，可用于测试的存在下的错误分类，并构建简单的和翔实的治疗效果的界限。在某些特殊情况下，我们实际上可以单独基于二阶矩信息获得处理效果的点识别。当这是不可能的，我们表明，添加条件三阶矩信息点识别的治疗效果和测量误差的过程。
This paper studies the use of a discrete instrumental variable to identify the causal effect of a endogenous, mis-measured, binary treatment. We begin by showing that the only existing identification result for this case, which appears in Mahajan (2006), is incorrect. As such, identification in this model remains an open question. We begin by proving that the treatment effect is unidentified based on conditional first-moment information, regardless of the number of values that the instrument may take. We go on to derive a novel partial identification result based on conditional second moments that can be used to test for the presence of mis-classification and to construct simple and informative bounds for the treatment effect. In certain special cases, we can in fact obtain point identification of the treatment effect based on second moment information alone. When this is not possible, we show that adding conditional third moment information point identifies the treatment effect and the measurement error process.