A Bayesian Nonparametric Causal Model for Regression Discontinuity Designs

Abstract: For non-randomized studies, the regression discontinuity design (RDD) can be used to identify and estimate causal effects from a "locally-randomized" subgroup of subjects, under relatively mild conditions. However, current models focus causal inferences on the impact of the treatment (versus non-treatment) variable on the mean of the dependent variable, via linear regression. For RDDs, we propose a flexible Bayesian nonparametric regression model that can provide accurate estimates of causal effects, in terms of the predictive mean, variance, quantile, probability density, distribution function, or any other chosen function of the outcome variable. We illustrate the model through the analysis of two real educational data sets, involving (resp.) a sharp RDD and a fuzzy RDD.