Anisotropic Autocorrelation in House Prices

Abstract

This paper examines anisotropic spatial autocorrelation in single-family house prices and in hedonic house price equation residuals using a spherical semivariogram and transactions data for one county in the Philadelphia, Pennsylvania MSA. Isotropic semivariograms model spatial relationships as a function of the distance separating properties in space. Anisotropic semivariograms model spatial relationships as a function of both the distance and the direction separating observations in space. The goals of this paper are: (1) to determine whether there is spatial autocorrelation in hedonic house price equation residuals; and (2) to empirically examine the validity of the isotropy assumption. We estimate the parameters of spherical semivariograms for house prices and for hedonic house price equation residuals for 21 housing submarkets within Montgomery County, Pennsylvania. These housing submarkets are constructed by dividing the county into 21 groupings of economically similar adjacent census tracts. Census tracts are grouped according to 1990 census tract median house prices and according to characteristics of the housing stock. We fit the residuals of each submarket hedonic house price equation to both isotropic and anisotropic sepherical semivariograms. We find evidence of spatial autocorrelation in the hedonic residuals in spite of a very elaborate hedonic specification. Additionally, we have determined that, in some submarkets, the spatial autocorrelation in the hedonic residuals is anisotropic rather than isotropic. The empirical results suggest that the spatial autocorrelation in Montgomery County single-family house price equation residuals is anisotropic in submarkets where residents typically commmute to a regional or local Central Businss District (CBD).

Keywords: spatial autocorrelation, house price indices