Regression Discontinuity Design with Many Thresholds

40 Pages Posted: 10 Jan 2016 Last revised: 31 Mar 2019

See all articles by Marinho Bertanha

Marinho Bertanha

University of Notre Dame - Department of Economics

Date Written: March 29, 2019

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. This paper proposes a consistent and asymptotically normal estimator for such ATEs 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 for a specific choice of tuning parameters. Identification in the fuzzy case, with multiple cutoffs, is impossible unless heterogeneity follows a finite-dimensional function of cutoff characteristics. Under parametric heterogeneity, this paper proposes an ATE estimator for the fuzzy case that optimally combines observations to maximize its precision.

Keywords: Regression Discontinuity Designs, Multiple Cutoffs, Average Treatment Effect, Alternative Asymptotics, Peer-effects

JEL Classification: C14, C21, C52, I21

Suggested Citation

Bertanha, Marinho, Regression Discontinuity Design with Many Thresholds (March 29, 2019). Available at SSRN: https://ssrn.com/abstract=2712957 or http://dx.doi.org/10.2139/ssrn.2712957

Marinho Bertanha (Contact Author)

University of Notre Dame - Department of Economics ( email )

Notre Dame, IN 46556
United States

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