We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.

翻译：我们开发了新的匹配估计量，用于在连续处理条件下估计因果分位数暴露响应函数及分位数暴露效应。我们给出了目标参数的识别结果，并建立了导出估计量的渐近性质。我们引入了两步估计程序：第一步，通过广义倾向得分匹配构建匹配数据集，调整可测量的混杂因素；第二步，对匹配集拟合核分位数回归。我们还推导了匹配估计量方差的一致估计量。通过模拟研究，我们在不同场景下将所提方法与现有替代方案进行了比较。我们将该方法应用于2012-2014年间的医疗保险索赔数据，估计了美国本土各邮政编码区域PM$_{2.5}$暴露对住院时长的因果效应。