# A Nonparametric Bayesian Methodology for Regression Discontinuity Designs

## TL;DR

This paper introduces a Bayesian Gaussian process regression approach for regression discontinuity designs, offering a flexible and uncertainty-aware alternative to local linear regression, with proven consistency and promising empirical performance.

## Contribution

It develops a Gaussian process-based Bayesian methodology for regression discontinuity, improving flexibility and uncertainty quantification over traditional local linear regression.

## Key findings

- Method is consistent in estimating treatment effects.
- Simulation shows better coverage and mean squared error.
- Applied to NBA draft data with meaningful insights.

## Abstract

One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We propose a Gaussian process regression methodology that acts as a Bayesian analog to LLR for regression discontinuity designs. Our methodology provides a flexible fit for treatment and control responses by placing a general prior on the mean response functions. Furthermore, unlike LLR, our methodology can incorporate uncertainty in how units are weighted when estimating the treatment effect. We prove our method is consistent in estimating the average treatment effect at the threshold. Furthermore, we find via simulation that our method exhibits promising coverage, interval length, and mean squared error properties compared to standard LLR and state-of-the-art LLR methodologies. Finally, we explore the performance of our method on a real-world example by studying the impact of being a first-round draft pick on the performance and playing time of basketball players in the National Basketball Association.