This thesis consists of three self-contained chapters: First, I develop a method to assess the sensitivity of local average treatment effect estimates to potential violations of the monotonicity assumption. Second, we propose new confidence sets for the parameter of interest in fuzzy regression discontinuity designs that are valid in a wide range of empirically relevant settings. Third, we propose a novel class of estimators that use pre-treatment covariates more efficiently than estimators that are commonly applied in the literature of regression discontinuity designs.
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