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Title: Testing identifying assumptions in a fuzzy regression discontinuity design Authors:  Yoichi Arai - GRIPS (Japan)
Yu-Chin Hsu - Academia Sinica (Taiwan)
Toru Kitagawa - University College London (United Kingdom) [presenting]
Ismael Mourifie - University of Toronto (Canada)
Yuanyuan Wan - University of Toronto (Canada)
Abstract: A new specification test is proposed for the validity of fuzzy regression discontinuity designs (FRD-validity). We derive a new set of testable implications for FRD-validity which is characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off. We show that it exploits all the information in data useful for screening out violation of FRD-validity. Our approach differs from and complements the existing approaches that test continuity of the distributions of running variables and baseline covariates at the cut-off since ours focuses on the distribution of observed outcome and treatment status. We show that the proposed test controls size in large sample uniformly over a large class of distributions, is consistent against all fixed alternatives, and has non-trivial power against local alternatives. Two empirical applications illustrate uses of our test.