This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

中文翻译：

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分类错误的工具变量分位数回归

本文研究了工具变量分位数回归模型（Chernozhkov 和 Hansen，2005，计量经济学73, 245–261; 2013年，经济学年度回顾, 5, 57–81) 采用二元内源性处理。当不直接观察治疗状态时，它提供两种识别结果。第一个结果是，值得注意的是，结果变量对工具变量的简化形式的分位数回归提供了随机单调性条件下结构分位数处理效果的下限。这个结果是相关的，不仅当处理变量受到错误分类时，而且当处理变量的任何测量不可用时。第二个结果是治疗状态测量错误时的结构分位数函数；尖锐识别集的特征是在广泛使用的测量误差假设下的一组矩条件。此外，