# Isotonic Regression Discontinuity Designs

## TL;DR

This paper investigates isotonic regression at boundary points within regression discontinuity designs, revealing inconsistency issues and proposing boundary-corrected estimators with practical bootstrap methods, demonstrated through Monte Carlo simulations and an application to U.S. House elections.

## Contribution

It introduces boundary-corrected estimators for isotonic regression at boundary points and shows their advantages over traditional methods in regression discontinuity analysis.

## Key findings

- Boundary correction improves estimator consistency.
- Bootstrap methods work without subsampling for boundary estimators.
- Shape restrictions enhance finite-sample performance.

## Abstract

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 corrected 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 apply the isotonic regression discontinuity designs to estimate the causal effect of incumbency in the U.S. House elections.