Abstract

This article studies the relationship between the two most-used quantile models with endogeneity: the instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen 2005 Chernozhukov, V., and Hansen, C. (2005), “An IV Model of Quantile Treatment Effects,” Econometrica, 73, 245–261.[Crossref], [Web of Science ®] , [Google Scholar]) and the local quantile treatment effects (LQTE) model (Abadie, Angrist, and Imbens 2002 Abadie, A., Angrist, J., and Imbens, G. (2002), “Instrumental Variable Estimates of the Effect of Subsidized Training on the Quantile of Trainee Earnings,” Econometrica, 70, 91–117. DOI:10.1111/1468-0262.00270.[Crossref], [Web of Science ®] , [Google Scholar]). The key condition of the IVQR model is the rank similarity assumption, a restriction on the evolution of individual ranks across treatment states, under which population quantile treatment effects (QTE) are identified. By contrast, the LQTE model achieves identification through a monotonicity assumption on the selection equation but only identifies QTE for the subpopulation of compliers. This article shows that, despite these differences, there is a close connection between both models: (i) the IVQR estimands correspond to QTE for the compliers at transformed quantile levels and (ii) the IVQR estimand of the average treatment effect is equal to a convex combination of the local average treatment effect and a weighted average of integrated QTE for the compliers. These results do not rely on the rank similarity assumption and therefore provide a characterization of IVQR in settings where this key condition is violated. Underpinning the analysis are novel closed-form representations of the IVQR estimands. I illustrate the theoretical results with two empirical applications.

摘要

本文研究具有内生性的两个最常用分位数模型之间的关系：工具变量分位数回归（IVQR）模型（Chernozhukov和Hansen 2005 切尔诺茹科夫（V.）和汉森（C）。（2005），“分位数处理效应的IV型，”计量经济学，73，245 - 261。[Crossref]，[Web of Science®]，[  Google Scholar]）和局部分位数处理效果（LQTE）模型（Abadie，Angrist和Imbens2002 Abadie，A.，Angrist，J。和Imbens，G。（2002年），“在对见习收益的位数资助培训的工具变量估计” 经济计量学，70，91 - 117。DOI：10.1111 / 1468-0262.00270。[Crossref]，[Web of Science®]， [Google Scholar]）。IVQR模型的关键条件是等级相似性假设，这是对不同治疗状态下各个等级演变的限制，在此条件下可以识别总体分位数治疗效果（QTE）。相比之下，LQTE模型通过对选择方程的单调性假设来实现识别，但仅识别符合条件子集的QTE。本文显示，尽管存在这些差异，但两个模型之间存在紧密联系：（i）IVQR估计值对应于转换位数的编译器的QTE，并且（ii）平均治疗效果的IVQR估计值等于本地平均处理效果与综合QTE加权平均值的凸组合。这些结果不依赖于等级相似性假设，因此可以在违反此关键条件的环境中提供IVQR的表征。分析的基础是IVQR估计值的新颖封闭形式表示。我用两个经验应用说明了理论结果。