Causal Analysis at Extreme Quantiles with Application to London Traffic Flow Data

Treatment effects on asymmetric and heavy tailed distributions are better reflected at extreme tails rather than at averages or intermediate quantiles. In such distributions, standard methods for estimating quantile treatment effects can provide misleading inference due to the high variability of the estimators at the extremes. In this work, we propose a novel method which incorporates a heavy tailed component in the outcome distribution to estimate the extreme tails and simultaneously employs quantile regression to model the remainder of the distribution. The threshold between the bulk of the distribution and the extreme tails is estimated by utilising a state of the art technique. Simulation results show the superiority of the proposed method over existing estimators for quantile causal effects at extremes in the case of heavy tailed distributions. The method is applied to analyse a real dataset on the London transport network. In this application, the methodology proposed can assist in effective decision making to improve network performance, where causal inference in the extremes for heavy tailed distributions is often a key aim.