  Analyses of environmental phenomena often are concerned with understanding
unlikely events such as floods, heatwaves, droughts or high concentrations of
pollutants. Yet the majority of the causal inference literature has focused on
modelling means, rather than (possibly high) quantiles. We define a general
estimator of the population quantile treatment (or exposure) effects (QTE) --
the weighted QTE (WQTE) -- of which the population QTE is a special case, along
with a general class of balancing weights incorporating the propensity score.
Asymptotic properties of the proposed WQTE estimators are derived. We further
propose and compare propensity score regression and two weighted methods based
on these balancing weights to understand the causal effect of an exposure on
quantiles, allowing for the exposure to be binary, discrete or continuous.
Finite sample behavior of the three estimators is studied in simulation. The
proposed methods are applied to data taken from the Bavarian Danube catchment
area to estimate the 95% QTE of phosphorus on copper concentration in the
river.
