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.

This paper derives the limit distribution of the rescaled sum of the reciprocal of the positive part of a random walk with continuously distributed innovations, and of the rescaled sum of the reciprocal of the absolute value of a random walk with continuously distributed innovations. It also considers this statistic for the case of a simple random walk, and shows that the limit distribution is different for this case.