Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility
提出一种三步估计法，用于评估连续处理变量对结果变量整个分布的影响，并应用于研究父母收入对子女收入分布特征（如贫困率、方差、分位距）的因果效应。
Abstract This paper considers the effect of a continuous treatment on the entire distribution of outcomes after adjusting for differences in the distribution of covariates across different levels of the treatment. Our methodology encompasses dose‐response functions, counterfactual distributions, and ‘distributional policy effects’ depending on the assumptions invoked by the researcher. We propose a three‐step estimator that consists of (i) estimating the distribution of the outcome conditional on the treatment and other covariates using quantile regression; (ii) for each value of the treatment, averaging over a counterfactual distribution of the covariates holding the treatment fixed; (iii) converting the resulting counterfactual distribution into parameters of interest that are easy to interpret. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of the treatment. We use our method to study intergenerational income mobility where we consider effects of parents’ income on features of their child's income distribution such as (i) the fraction of children with income below the poverty line; (ii) the variance of child's income; and (iii) the inter‐quantile range of child's income–all as a function of parents’ income.