Isotonic regression discontinuity designs

This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the isotonic regression is inconsistent in this setting and derive the asymptotic distributions of boundary cor-rected estimators. Interestingly, the boundary corrected estimators can be bootstrapped without subsampling or additional nonparametric smoothing which is not the case for the interior point. The Monte Carlo experiments indicate that shape restrictions can improve dramatically the finite-sample performance of unrestricted estimators. Lastly, we estimate the causal effect of incumbency in U.S. House elections via the isotonic regression discontinuity design. & COPY; 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper examines the estimation and inference of isotonic regression at the boundary point, which is crucial for analyzing monotone regression discontinuity designs. The paper demonstrates that isotonic regression is inconsistent in this context and provides the asymptotic distributions of boundary-corrected estimators. Interestingly, the boundary-corrected estimators can be bootstrapped without subsampling or additional nonparametric smoothing unlike the interior point. Monte Carlo experiments indicate that shape restrictions can significantly enhance the finite-sample performance of unrestricted estimators. Finally, the paper estimates the causal effect of incumbency in U.S. House elections using isotonic regression discontinuity design.