Hierarchical Regression Discontinuity Design: Pursuing Subgroup Treatment Effects

TL;DR

This paper introduces hierarchical RDD (HRDD), a Bayesian method that improves estimation of subgroup treatment effects in regression discontinuity designs by borrowing strength across subgroups, leading to more stable estimates.

Contribution

The paper proposes HRDD, a hierarchical Bayesian approach with a pseudo-model and Gibbs sampling, to enhance subgroup treatment effect estimation in RDD.

Findings

HRDD yields more stable estimates than standard RDD for subgroups.

Simulation and real data show HRDD's superior performance in treatment effect estimation.

Automatic bandwidth selection improves model robustness.

Abstract

Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically suffers from small subgroup-wise sample sizes, which makes the estimation results highly instable. To solve this issue, we introduce hierarchical RDD (HRDD), a hierarchical Bayes approach for pursuing treatment effect heterogeneity in RDD. A key feature of HRDD is to employ a pseudo-model based on a loss function to estimate subgroup-level parameters of treatment effects under RDD, and assign a hierarchical prior distribution to ''borrow strength'' from other subgroups. The posterior computation can be easily done by a simple Gibbs sampling, and the optimal bandwidth can be automatically selected by the Hyv\"{a}rinen scores for unnormalized models. We demonstrate the proposed HRDD through simulation and real data analysis, and show that HRDD provides much more stable point and interval estimation than separately applying the standard RDD method to each subgroup.