Quantile Treatment Effects in the Regression Kink Design

This paper studies identification, estimation, and inference of quantile treatment effects in the fuzzy regression kink design with a binary treatment variable. We first show the identification of conditional quantile treatment effects given the event of local compliance. We then propose a bootstrap method of uniform inference for the local quantile process. This bootstrap method is fast and is robust against common optimal choices of bandwidth parameters. We provide practical guidelines as well as a formal theory. Simulation studies show accurate coverage probabilities for tests of uniform treatment significance and treatment heterogeneity.


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