Bayesian regression discontinuity design with unknown cutoff

TL;DR

This paper introduces LoTTA, a Bayesian method for regression discontinuity design that estimates causal effects even when the cutoff point is unknown or uncertain, improving local inference accuracy.

Contribution

The paper proposes a novel Bayesian approach, LoTTA, that accounts for unknown cutoff locations in RDD, enhancing the validity of causal effect estimates.

Findings

LoTTA effectively estimates treatment effects with uncertain cutoffs.

The method improves inference accuracy in real-world HIV treatment data.

LoTTA integrates prior knowledge to handle cutoff uncertainty.

Abstract

The regression discontinuity design (RDD) is a quasi-experimental approach used to estimate the causal effects of an intervention assigned based on a cutoff criterion. RDD exploits the idea that close to the cutoff units below and above are similar; hence, they can be meaningfully compared. Consequently, the causal effect can be estimated only locally at the cutoff point. This makes the cutoff point an essential element of RDD. However, the exact cutoff location may not always be disclosed to the researchers, and even when it is, the actual location may deviate from the official one. As we illustrate on the application of RDD to the HIV treatment eligibility data, estimating the causal effect at an incorrect cutoff point leads to meaningless results. The method we present, LoTTA (Local Trimmed Taylor Approximation), can be applied both as an estimation and validation tool in RDD. We use a Bayesian approach to incorporate prior knowledge and uncertainty about the cutoff location in the causal effect estimation. At the same time, LoTTA is fitted globally to the whole data, whereas RDD is a local, boundary point estimation problem. In this work we address a natural question that arises: how to make Bayesian inference more local to render a meaningful and powerful estimate of the treatment effect?