Hierarchical Gaussian Process Models for Regression Discontinuity/Kink under Sharp and Fuzzy Designs

TL;DR

This paper introduces hierarchical Gaussian Process models for causal inference in Regression Discontinuity/Kink designs, offering improved estimation and uncertainty quantification, with applications to US elections.

Contribution

It develops novel hierarchical GP estimators for RD/RK, enhancing derivative estimation and uncertainty quantification over existing methods.

Findings

Hierarchical GP models outperform one-layer GP models in simulations.

Estimations reveal a significant incumbency advantage in US elections.

The methods can be extended to include covariate adjustment.

Abstract

We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) under sharp and fuzzy designs. Our estimators are based on Gaussian Process (GP) regression and classification. The GP methods are powerful probabilistic machine learning approaches that are advantageous in terms of derivative estimation and uncertainty quantification, facilitating RK estimation and inference of RD/RK models. These estimators are extended to hierarchical GP models with an intermediate Bayesian neural network layer and can be characterized as hybrid deep learning models. Monte Carlo simulations show that our estimators perform comparably to and sometimes better than competing estimators in terms of precision, coverage and interval length. The hierarchical GP models considerably improve upon one-layer GP models. We apply the proposed methods to estimate the incumbency advantage of US house elections. Our estimations suggest a significant incumbency advantage in terms of both vote share and probability of winning in the next elections. Lastly we present an extension to accommodate covariate adjustment.