Title: Estimation and inference for distribution functions and quantile functions in endogenous treatment effect models
Authors: Yu-Chin Hsu - Academia Sinica (Taiwan)
Tsung-Chih Lai - Feng Chia University (Taiwan) [presenting]
Robert Lieli - Central European University and Magyar Nemzeti Bank (Hungary)
Abstract: Two-step nonparametric estimators are proposed for the distribution functions of potential outcomes among the group of compliers in an endogenous treatment effect model. Our estimator is monotonically increasing and bounded between zero and one. The monotonizing method we propose is an alternative to a previous one and it is easier to implement. We obtain the quantile function by inverting the estimated distribution function and show that both the distribution and the quantile estimators converge weakly to zero-mean Gaussian processes. For uniform inference, we propose a multiplier bootstrap procedure to approximate the limiting processes. Our methods generalize the pointwise results, and we also discuss the case for the treated compliers. Monte Carlo simulations and an application to the effect of fertility on family income distribution illustrate the usefulness of our results.