A Nonparametric Bayesian Methodology for Regression Discontinuity Designs

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.

40 pages, 5 figures, 5 tables

References in corpus (6)

• Rates of contraction of posterior distributions based on Gaussian process priors
• Inference in Regression Discontinuity Designs with a Discrete Running Variable
• Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth
• A Nonparametric Bayesian Methodology for Regression Discontinuity Designs
• A Simple Adjustment for Bandwidth Snooping
• A Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs: Do School Districts Affect NYC House Prices?

Cited by in corpus (6)

• A Nonparametric Bayesian Methodology for Regression Discontinuity Designs
• Noise-Induced Randomization in Regression Discontinuity Designs
• A Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs: Do School Districts Affect NYC House Prices?
• The Local Randomization Framework for Regression Discontinuity Designs: A Review and Some Extensions
• Kernel-based Partial Permutation Test for Detecting Heterogeneous Functional Relationship
• V-Splines and Bayes Estimate