A Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs: Do School Districts Affect NYC House Prices?

Abstract

Most research on regression discontinuity designs (RDDs) has focused on univariate cases, where only those units with a "forcing" variable on one side of a threshold value receive a treatment. Geographical regression discontinuity designs (GeoRDDs) extend the RDD to multivariate settings with spatial forcing variables. We propose a framework for analysing GeoRDDs, which we implement using Gaussian process regression. This yields a Bayesian posterior distribution of the treatment effect at every point along the border. We address nuances of having a functional estimand defined on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). The Bayesian estimate of the LATE can also be used as a test statistic in a hypothesis test with good frequentist properties, which we validate using simulations and placebo tests. We demonstrate our methodology with a dataset of property sales in New York City, to assess whether there is a discontinuity in housing prices at the border between two school district. We find a statistically significant difference in price across the border between the districts with p=0.002, and estimate a 20% higher price on average for a house on the more desirable side.

A nonparametric Bayesian methodology for regression discontinuity designs

“…Because GPR has been widely used in spatial statistics (Banerjee et al, 2014;Cressie, 2015), it may be particularly suitable for geographic RDDs. We explore the use of our GPR methodology for geographic RDDs in Rischard et al (2018).…”

Kernel-based Partial Permutation Test for Detecting Heterogeneous Functional Relationship

“…Most existing methods focus mainly on the case with univariate covariates. Recently, Branson et al (2019) and Rischard et al (2018) proposed Bayesian approaches utilizing Gaussian processes, and extended the regression discontinuity design to multivariate settings with spatial covariates.…”