Population individual treatment effect that is defined at a specific quantile . It is the difference between potential outcomes and

In this plot, QTE is the 10% percentile treatment effect: the difference between 10th percentile of and the 10th percentile of .

It is generally more robust towards outlier than average treatment effect (e.g. median)

Interpretation

A quantile effect is a claim about what happens to a distribution, not individuals. A median effect is a claim about the difference between typical people (Y1 vs. Y0). — but not what happened to any single person.