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Title: Regression discontinuity with many thresholds Authors:  Marinho Bertanha - University of Notre Dame (United States) [presenting]
Abstract: Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs computed over general counterfactual distributions of individuals rather than simply the observed distribution of individuals local to existing cutoffs. A consistent and asymptotically normal estimator for such ATEs is proposed when heterogeneity follows a non-parametric function of cutoff characteristics in the sharp case. The proposed estimator converges at the minimax optimal rate of root-n. Identification in the fuzzy case with multiple cutoffs is impossible unless heterogeneity follows a finite dimensional function of cutoff characteristics. Under parametric heterogeneity, an ATE estimator for the fuzzy case is proposed that optimally combines observations to maximize its precision.