Causal inference by quantile regression kink designs

The quantile regression kink design (QRKD) is proposed by empirical researchers, but its causal interpretation remains unknown. We show that the QRKD estimand measures a weighted average of heterogeneous marginal effects at respective conditional quantiles of outcome given a designed kink point. We also derive limit processes for the QRKD estimator to conduct statistical inference on heterogeneous treatment effects using the QRKD. Applying our methods to the Continuous Wage and Benefit History Project (CWBH) data, we find heterogeneous positive causal effects of unemployment insurance benefits on unemployment durations. These effects are larger for individuals with longer unemployment durations.