Bayesian Modeling of a High Resolution Housing Price Index
Advisor: Emily Fox
The housing market is a large part of the economy. In the United States, roughly fifty percent of household wealth is in residential real estate. Understanding how the value of housing changes over time is important to policy makers, consumers and real estate professionals. Existing methods for constructing housing indices are computed at a coarse spatial granularity, such as metro regions, which can mask or distort price dynamics apparent in local markets, such as neighborhoods and census tracts. A challenge in moving to estimates at, for example, the census tract level is the sparsity of spatiotemporally localized house sales observations. Our work aims at addressing this challenge by leveraging observations from multiple census tracts discovered to have correlated valuation dynamics. We start by considering individual time series that represents house sales from every census tract in Seattle. Our proposed Bayesian nonparametric approach then builds on the framework of latent factor models to enable a flexible, data-driven method for inferring the clustering of correlated census tracts. The resulting hierarchical Bayesian model in essence provides a form of multiple shrinkage, sharing information between related time series based on the inferred dependence structure. We explore various methods for scalability and parallelizability of computations, yielding a housing valuation index at the level of census tract rather than zip code, and on a monthly basis rather than quarterly. We also discuss some future directions for including road network structure in the valuation procedure.