The quantile regression kink design (QRKD) is proposed by empirical
researchers as a potential method to assess heterogeneous treatment effects
under suitable research designs, but its causal interpretation remains unknown.
We propose causal interpretations of the QRKD estimand. Under flexible
heterogeneity and endogeneity, the sharp and fuzzy QRKD estimands measure
weighted averages of heterogeneous marginal effects at respective conditional
quantiles of outcome given a designed kink point. Read More