Do School Districts Affect NYC House Prices? Identifying Border Differences Using a Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs

Abstract

What is the premium on house price for a particular school district? To estimate this in New York City we use a novel implementation of a geographic regression discontinuity design (GeoRDD) built from Gaussian processes regression (kriging) to model spatial structure. With a GeoRDD, we specifically examine price differences along borders between “treatment” and “control” school districts. GeoRDDs extend RDDs to multivariate settings; location is the forcing variable and the border between school districts constitutes the discontinuity threshold. We first obtain a Bayesian posterior distribution of the price difference function, our nominal treatment effect, along the border. We then 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). We test for nonzero LATE with a calibrated hypothesis test with good frequentist properties, which we further validate using a placebo test. Using our methodology, we identify substantial differences in price across several borders. In one case, a border separating Brooklyn and Queens, we estimate a statistically significant 20% higher price for a house on the more desirable side. We also find that geographic features can undermine some of these comparisons. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORDS:

• Bayesian testing
• Causal inference
• Gaussian processes
• Housing market
• Kriging
• Regression discontinuity

Supplementary Materials

(1) Why the Projected 1D RDD Approach Can Lead to Spatial Confounding, (2) Handling Nonspatial Covariates, (3) Additional LATE Estimands and Simulations, (4) Alternate Tests for Non-Zero Treatment Effect, and (5) Additional Testing Details for NYC School Districts Application.

This research was supported by the National Science Foundation Graduate Research Fellowship Program under grant no. 1144152, by the National Science Foundation under grant no. 1461435, by DARPA under grant no. FA8750-14-2-0117, by ARO under grant no. W911NF-15-1-0172, and by NSERC. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation, DARPA, ARO, or NSERC.

Army Research Office;Defense Advanced Research Projects Agency;

NOTE: The spatial coordinates of the $i\text{th}$ treatment unit are denoted by ${\mathit{s}}_{iT}$, and those of the $j\text{th}$ control unit by ${\mathit{s}}_{jC}$, while ${\mathit{b}}_i$ denotes the $i\text{th}$ sentinel location along the border.

Additional information

Funding

Army Research Office; Defense Advanced Research Projects Agency;