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We develop new matching estimators for estimating causal quantileexposure-response functions and quantile exposure effects with continuoustreatments. We provide identification results for the parameters of interestand establish the asymptotic properties of the derived estimators. We introducea two-step estimation procedure. In the first step, we construct a matched dataset via generalized propensity score matching, adjusting for measuredconfounding. In the second step, we fit a kernel quantile regression to thematched set. We also derive a consistent estimator of the variance of thematching estimators. Using simulation studies, we compare the introducedapproach with existing alternatives in various settings. We apply the proposedmethod to Medicare claims data for the period 2012-2014, and we estimate thecausal effect of exposure to PM$_{2.5}$ on the length of hospital stay for eachzip code of the contiguous United States.

Estimating causal quantile exposure response functions via matching