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

Causal Inference for Quantile Treatment Effects