The literature on regression kink designs develops identification results for average effects of continuous treatments (Nielsen et al., 2010, American Economic Journal: Economic Policy 2, 185–215; Card et al., 2015, Econometrica 83, 2453–2483), average effects of binary treatments (Dong, 2018, Jump or Kink? Identifying Education Effects by Regression Discontinuity Design without the Discontinuity), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019, Journal of Econometrics 210, 405–433), but there has been no identification result for quantile-wise effects of binary treatments to date. In this article, we fill this void in the literature by providing an identification of quantile treatment effects in regression kink designs with binary treatment variables. For completeness, we also develop large sample theories for statistical inference, present a practical guideline on estimation and inference, conduct simulation studies, and provide an empirical illustration.

中文翻译：

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回归扭结设计中的分位数处理效果

关于回归扭结设计的文献开发了连续处理的平均效果的识别结果（Nielsen 等，2010，美国经济杂志：经济政策2, 185–215; 卡等人，2015 年，计量经济学83, 2453–2483），二元处理的平均效果（Dong，2018，Jump or Kink？通过没有间断的回归不连续设计识别教育效果）和连续处理的分位数效果（Chiang 和 Sasaki，2019，计量经济学杂志210, 405-433），但迄今为止还没有确定二元处理的分位数效应的结果。在本文中，我们通过在具有二元处理变量的回归扭结设计中提供分位数处理效果的识别来填补文献中的这一空白。为了完整起见，我们还开发了用于统计推断的大样本理论，提出了估计和推断的实用指南，进行了模拟研究，并提供了实证说明。