Extrapolation in Regression Discontinuity Design Using Comonotonicity

TL;DR

This paper introduces a new method for extrapolating causal effects in regression discontinuity designs using comonotonicity, applicable to multiple covariates and providing estimands for weighted average effects.

Contribution

It proposes a novel approach leveraging comonotonicity for extrapolation in RDD, with estimation via local linear regression, extending causal inference capabilities.

Findings

Effective in extrapolating causal effects beyond the treatment margin.

Applicable to both multiple covariates and single running variable settings.

Demonstrated utility through evaluation of summer school policies.

Abstract

We present a novel approach for extrapolating causal effects away from the margin between treatment and non-treatment in sharp regression discontinuity designs with multiple covariates. Our methods apply both to settings in which treatment is a function of multiple observables and settings in which treatment is determined based on a single running variable. Our key identifying assumption is that conditional average treated and untreated potential outcomes are comonotonic: covariate values associated with higher average untreated potential outcomes are also associated with higher average treated potential outcomes. We provide an estimation method based on local linear regression. Our estimands are weighted average causal effects, even if comonotonicity fails. We apply our methods to evaluate counterfactual mandatory summer school policies.