Sensitivity of Quantile Treatment Effects to Small Shifts in Covariate Distributions

Music City Center 

This paper evaluates how small perturbations in covariate distributions affect Quantile Treatment Effect (QTE). We introduce a new metric to quantify the sensitivity of QTE to such shifts across various quantile levels. We propose corresponding point and variance estimators and establish the asymptotic properties. The performance of our method is supported by simulation studies. Additionally, we apply our approach to the 2017-2018 National Health and Nutrition Examination Survey (NHANES) data, and find that counterfactually increasing the proportion of females in the population significantly reduces the QTE at lower percentiles, indicating that maintaining a sufficient vitamin D level is particularly effective in increasing bone mineral density for males with lower bone mineral density.

causal inference

counterfactual analysis

quantile treatment effects

unconditional quantile

influence functions 

Section on Nonparametric Statistics