  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.

Methodology