Estimation and inference for distribution and quantile functions in endogenous treatment effect models
针对标准内生处理效应模型，提出对依从者潜在结果分布函数和分位数函数的非参数估计与推断方法，包括局部分位数处理效应函数，并给出单调化处理、弱收敛结果及自助法推断。
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: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.