Identification of Regression Models with a Misclassified and Endogenous Binary Regressor
Identification of Regression Models with a Misclassified and Endogenous Binary Regressor
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识别具有错误分类和内生二元回归量的回归模型
DOI：
10.1017/s0266466621000451
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发表时间：
2022
影响因子：
0.8
通讯作者：
Hiroyuki Kasahara and Katsumi Shimotsu
中科院分区：
文献类型：
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作者：
桜井智恵子;原伸子;酒井隆史;成田洋樹;田中太郎;居神浩;進藤理香子;Hiroyuki Kasahara and Katsumi Shimotsu
本文研究了具有误分类和内生二元回归变量的非参数回归模型的辨识问题。我们证明了回归函数是非参数识别的，如果一个二元工具变量和一个二元协变量满足以下条件。工具变量校正内隐变量;工具变量必须与未观察到的真实基础二元变量相关，必须与结果方程中的误差项不相关，但允许与误分类误差相关。协变量纠正错误分类;该变量可以是结果方程中的回归变量之一，必须与未观察到的真实基础二元变量相关，并且必须与错误分类错误无关。我们还提出了一个基于混合物的框架，用于建模未观察到的异质性治疗效果与一个错误分类和内源性二元回归，并表明，治疗效果可以确定，如果真正的治疗效果与观察到的回归和另一个可观察到的变量。
We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.