Causal inference by quantile regression kink designs

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 a causal interpretation of the QRKD estimand. Under flexible heterogeneity and endogeneity, the QRKD estimand measures a weighted average of heterogeneous marginal effects at respective conditional quantiles of outcome given a designed kink point. In addition, we develop weak convergence results for the QRKD estimator as a local quantile process for the purpose of conducting statistical inference on heterogeneous treatment effects using the QRKD. Applying our methods to the Continuous Wage and Benefit History Project (CWBH) data, we find significantly heterogeneous positive causal effects of unemployment insurance benefits on unemployment durations in Louisiana between 1981 and 1983. These effects are larger for individuals with longer unemployment durations.