Learning low‐dimensional structure in house price indices

Abstract

AbstractHouse price indices (HPIs) are statistical measures of real estate price dynamics in defined geographic regions over defined periods of time. HPIs are important metrics that help policymakers, mortgage lenders, real estate investors, and bank regulators monitor market conditions and manage risk. HPIs that are local, reliable, and timely are essential in understanding connections between housing markets and the broader economy. In this article, we examine the algorithmic construction of Zillow's Home Value Index (ZHVI), an HPI built on black box machine learning algorithms. To provide deeper statistical insight into ZHVI than afforded by its black box construction, we develop a Bayesian generative meta‐model that approximates the black box construction of ZHVI series in 100 metropolitan areas (metros). Each ZHVI series is modeled with a global trend, a finite mixture of Gaussian processes, and a local component. We find that there are three shared dynamic patterns across the 100 markets in our analysis, and we utilize this shared latent structure to forecast ZHVI in each metro 12 months ahead. Our clustering strategy has two advantages: (i) it allows us to construct composite HPIs where member metros are learned from the data rather than predetermined; and (ii) it allows us to estimate the relative contributions of cluster‐level and metro‐specific components to a metro's ZHVI, providing a novel statistical attribution of real estate market dynamics.