Causal Inference for Quantile Treatment Effects - Weighted Quantile Treatment Effects (WQTE)

Sep 4, 2026

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Environmental analyses often target rare, high-impact events such as floods, heatwaves, droughts, or extreme pollution levels, yet most causal inference methods emphasize mean effects. This work develops a general estimator for population quantile treatment (exposure) effects, the weighted quantile treatment effect (WQTE), and a balancing-weight framework based on the propensity score. Asymptotic properties are proved, and propensity score regression plus two weighting approaches are compared via simulations. The methods estimate 95% QTE for phosphorus effects on copper concentration in the Bavarian Danube catchment.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages34

Reading Time1 h 26 min

AccessFree to download

Introduction

Quantile treatment effects in environmental extremes

Weighted QTE (WQTE) and balancing weights

Estimation methods and asymptotic properties

Simulation study and application example

Causal Inference for Quantile Treatment Effects arXiv :2 109 .03757v1 [ stat .ME] 8 Sep 2021 Shuo Sun 1 , Erica E. M. Moodie 1 , and Johanna G. Ne´a2 1 Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montre´al, QC, Canada 2 Department of Mathematics and Statistics, McGill University, Montre´al, QC, Canada Abstract Analyses of environmental phenomena often are concerned with understanding unlikely events such as 􀀃oods, 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 de􀀂ne 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. Keywords: quantile treatment effect, weighted quantile treatment effect, propensity score, quantile regression 1 Introduction Environmental disturbances can lead to changes in the frequency or intensity of unusual environmental events such as 􀀃oods, droughts, wild􀀂res, hurricanes, and air pollution. Heuristically, an unlikely event can be seen as the occurrence of a value of an environmental variable that is above (or below) a threshold near the right (or left) tail of its historical distribution. Learning about the distributional causal effect beyond the average impact of speci􀀂c interventions on environmental outcomes is often important for planning and policy-making. For example, chronic exposure to high levels of heavy metal can result in several consequences in the human body, such as liver and kidneys damage, leading to gradually progression of physical, muscular, and neurological degenerative processes that imitate diseases such as Parkinson’s disease and Alzheimer’s disease (Jaishankar et al., 2014) . Heavy metal pollution often correlates with eutrophication in aquatic ecosystems (L´opez-Flores et al., 2003), where agricultural activity (e.g., fertilizers) is one of the major sources of phosphorus – an element directly associated with eutrophication – in aquatic ecosystems (Carpenter et al., 1998; Ekholm et al., 2000) . Thus a policy-maker might be interested in the causal effect of a potential source of eutrophication (e.g., phosphorus) on heavy mental concentration on the tail (or some high quantile) of the underlying distribution. In many areas of environmental science research, conventional methods based on correlation and regression are common data-based tools to analyze relationships. However, such approaches provide few insights into the causal mechanisms which might help discover and quantify the causal interdependence. In order to study causal relationships, causal inference techniques are needed; due to the increasing availability of observational and simulation data, there is a growing interest in these techniques in the environmental sciences literature. For example, Kretschmer et al. (2016) investigated possible Arctic mechanisms which could be pivotal to understand northern hemisphere mid-latitude extreme winters in Eurasia and North America. Arctic teleconnection patterns are much less understood than their tropical counterparts and different climate models provide partially con􀀃icting results, thus the data-driven causal analyses are especially important (Shepherd, 2016;

FAQs

What problem does the paper address in causal inference for environmental studies?

It addresses the limitation of existing causal inference focused on means by targeting causal effects at quantiles, which are crucial for rare or extreme environmental events.

How does the paper define and construct the main estimand?

It defines the population quantile treatment (or exposure) effects and introduces the weighted QTE (WQTE) using a general class of balancing weights built with the propensity score.

Which estimation strategies are proposed and how are they evaluated?

The paper proposes and compares propensity score regression with two weighted methods based on the balancing weights, studying their finite-sample behavior through simulations and applying them to a river pollution dataset.

Sep 4, 2026

Upload by Liam