Regression Discontinuity Design with Many Thresholds

TL;DR

This paper develops new estimators for average treatment effects in regression discontinuity designs with multiple cutoffs, allowing for more general heterogeneity and improving inference on meaningful population effects.

Contribution

It introduces a consistent, asymptotically normal estimator for ATEs under non-parametric heterogeneity and proposes a parametric approach for fuzzy designs with multiple cutoffs.

Findings

Estimator converges at root-n rate.

Identification is impossible without parametric assumptions in fuzzy case.

Proposed methods outperform existing approaches in complex RD settings.

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.