2015b) “Uniform Inference on Quantile Effects under
- Qu, Zhongjun, Jungmo Yoon
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. In addition, we develop weak convergence results for the QRKD estimator as a local quantile process for the purpose of conducting statistical inference of heterogeneous treatment effects using the QRKD. Applying our methods to the Continuous Wage and Benefit History Project (CWBH) data, we find significantly heterogeneous positive moral hazard effects of unemployment insurance benefits on unemployment durations in Louisiana between 1981 and 1982. We find that these effects are larger for individuals with longer unemployment durations.