A Spatial Model of Housing Returns and Neighborhood Substitutability

William N. Goetzmann Yale School of Management
Matthew Spiegel University of California at Berkeley, Haas School of Business

This paper presents a new spatial model for analyzing return indices for infrequently traded assets, and applies it to housing data. Within many asset classes, particularly real estate, one expects there to exist a spatial correlation in deviations from the index due to omitted explanatory variables in the econometric model. This error structure can be useful in estimating location-specific indices, whether that location is defined in terms of geography or exposure to common economic or social factors. The econometric design presented in this paper allows the use of distance, broadly defined, to accurately estimate housing return series at the level of individual zip code neighborhoods in the San Francisco Bay area. While a paucity of transactions data would normally make this impossible, the use of spatial and factor correlations provide sufficient information to estimate zip code level returns.

We use these indices to examine the degree to which housing market participants in one major metropolitan statistical area view neighborhoods as substitutes. Using distance defined in terms of geographical proximity, median household income, average educational attainment and racial composition, we find that median household income is the salient variable explaining co- variance of neighborhood housing returns. Racial composition and educational attainment, while significant are much less influential and geographical proximity is nearly meaningless. Our methodology has applications to a range of infrequently traded assets, including bonds, commercial real estate and collectibles. The approach may be viewed as an extension of "non- parametric" spatial correlation models. In the non-parametric approach a distance function and decay rate are exogenously specified. In a spatial model one estimates the distance metric and uses statistical rules to obtain the resulting decay rates. The results of our analysis of housing substitutability in the San Francisco Bay area have implications for estimates of the covariance of housing returns within metropolitan areas. In particular, low covariances imply gains to diversification for lenders, equity-holders and tax authorities.