# Quantile Treatment Effects in Regression Kink Designs

## TL;DR

This paper establishes the first identification results for quantile treatment effects of binary treatments within regression kink designs, along with large sample inference methods and practical guidelines.

## Contribution

It fills a gap by providing identification and inference methods for quantile effects of binary treatments in regression kink designs, which was previously unaddressed.

## Key findings

- Identification of quantile treatment effects for binary treatments in regression kink designs.
- Development of large sample inference theories.
- Provision of practical estimation and inference guidelines.

## Abstract

The literature on regression kink designs develops identification results for average effects of continuous treatments (Card, Lee, Pei, and Weber, 2015), average effects of binary treatments (Dong, 2018), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019), but there has been no identification result for quantile-wise effects of binary treatments to date. In this paper, 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 and a practical guideline on estimation and inference.