Bounds on Extrapolated Treatment Effects in Regression Discontinuity Designs

Yuta Okamoto and Yuuki Ozaki

Papers from arXiv.org

Abstract: External validity is a central concern in regression discontinuity (RD) designs. To assess treatment effect heterogeneity and the representativeness of the conventional RD estimand, this paper studies the identifying content of monotonicity and smoothness restrictions for treatment effects away from the cutoff in both canonical and multi-cutoff RD designs. In the canonical design, monotonicity in the running variable alone has limited identifying power and generally yields only one-sided bounds. In multi-cutoff designs, by contrast, our proposed monotonicity restrictions along both the running-variable and cutoff-group dimensions yield a support-free characterization of the identified set. In both settings, smoothness restrictions may further tighten the identified set, underscoring the value of combining shape and smoothness restrictions. These sharp identified sets, or their outer approximations, are amenable to bias-aware inference and moment-inequality-based inference procedures. An empirical application illustrates the practical usefulness of our approach.

Date: 2024-12, Revised 2026-09
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