Abstract

Given a standard endogenous treatment effect model, we propose nonparametric estimation and inference procedures for the distribution and quantile functions of the potential outcomes among compliers, as well as the local quantile treatment effect function. The preliminary distribution function estimator is a weighted average of indicator functions, but is not monotonically increasing in general. We therefore propose a simple monotonizing method for proper distribution function estimation, and obtain the quantile function estimator by inversion. Our monotonizing method is an alternative to Chernozhukov et al. (2010 Chernozhukov, V., Fernández-Val, I., Galichon, A. (2010). Quantile and probability curves without crossing. Econometrica 78(3):1093–1125.[Crossref], [Web of Science ®] , [Google Scholar]) and is arguably preferable when the outcome has unbounded support. We show that all the estimators converge weakly to Gaussian processes at the parametric rate, and propose a multiplier bootstrap for uniform inference. Our uniform results thus generalize the pointwise theory developed by Frölich and Melly (2013 Frölich, M., Melly, B. (2013). Unconditional quantile treatment effects under endogeneity. Journal of Business & Economic Statistics 31(3):346–357. doi:https://doi.org/10.1080/07350015.2013.803869[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Monte Carlo simulations and an application to the effect of fertility on family income distribution illustrate the use of the methods. All results extend to the subpopulation of treated compliers as well.

摘要

给定一个标准的内生治疗效果模型，我们提出了非参数估计和推断程序，用于编制者之间潜在结果的分布和分位数函数，以及局部分位数治疗效果函数。初步分布函数估计量是指标函数的加权平均值，但一般不是单调递增的。因此，我们提出了一种简单的单调化方法来进行适当的分布函数估计，并通过反演获得分位数函数估计量。我们的单调化方法是 Chernozhukov 等人的替代方法。( 2010 年 Chernozhukov, V. , Fernández-Val, I. , Galichon, A. ( 2010 )。没有交叉的分位数和概率曲线。计量经济学78(3): 1093 – 1125。[Crossref], [Web of Science ®]  , [Google Scholar] ) 并且当结果有无限支持时可以说是更可取的。我们展示了所有估计量都以参数速率弱收敛到高斯过程，并提出了一个乘法器引导来进行均匀推理。因此，我们的统一结果概括了 Frölich 和 Melly ( 2013) 开发的逐点理论 Frölich，M.，Melly，B.（2013 年）。内生性下的无条件分位数处理效果。商业与经济统计杂志31(3): 346 – 357。doi：https://doi.org/10.1080/07350015.2013.803869 [Taylor & Francis Online]、[Web of Science®]  、[Google Scholar]）。蒙特卡洛模拟和生育率对家庭收入分配影响的应用说明了这些方法的使用。所有结果也延伸到处理过的编译器的亚群。