Academic journal article Real Estate Economics

Predicting Spatial Patterns of House Prices Using LPR [Local Percentile Rank] and Bayesian Smoothing

Academic journal article Real Estate Economics

Predicting Spatial Patterns of House Prices Using LPR [Local Percentile Rank] and Bayesian Smoothing

Article excerpt

This article is motivated by the limited ability of standard hedonic price equations to deal with spatial variation in house prices. Spatial patterns of house prices can be viewed as the sum of many causal factors: Access to the central business district is associated with a house price gradient; access to decentralized employment subcenters causes more localized changes in house prices; in addition, neighborhood amenities (and disamenities) can cause house prices to change rapidly over relatively short distances. Spatial prediction (e.g., for an automated valuation system) requires models that can deal with all of these sources of spatial variation. We propose to accommodate these factors using a standard hedonic framework but incoporating a semiparametric model with structure in the residuals modeled with a partially Bayesian approach. The Bayesian framework enables us to provide complete inference in the form of a posterior distribution for each model parameter. Our model allows prediction at sampled or un sampled locations as well as prediction interval estimates. The nonparametric part of our model allows sufficient flexibility to find substantial spatial variation in house values. The parameters of the kriging model provide further insights into spatial patterns. Out-of-sample mean squared error and related statistics validate the proposed methods and justify their use for spatial prediction of house values.


Hedonic models of house prices are plagued by inadequate specification of spatial price processes. It is known that house prices vary dramatically over space, but this is difficult to model. Dubin (1992) defines the problem: "Most hedonic estimations show few significant coefficients on the neighborhood and accessibility variables" (p.433). It follows that there are many unmeasured spatial variables omitted from the hedonic equation. Dubin summarizes literature attempting to deal with the problem through the early 1990s. (1)

We view spatial variation in house prices as the sum of many causal factors. Two categories of causal factors may be modeled in the mean function: (2) (1) House prices change relatively slowly over long distances due to access to major points of interest such as the downtown (CBD), an airport, or an ocean beach; (2) Employment subcenters, school districts, higher elevations, a water view and the like require more proximity to influence house prices. These variables cause spatial patterns that work over shorter distances than the first category.

Mills and Hamilton (1984, especially Chapter 6) summarize "new urban economics" theory for category 1 spatial patterns; these are the factors giving shape to the skyline and presumed to cause major changes in house prices. (3) According to this theory, we can expect distances measured to the CBD and other major points of interest to influence house values over the entire metropolitan area.

Anas, Arnott and Small (1998) emphasize the growing complexity of urban areas in their summary of literature dealing with both categories of spatial variables. Technological change and deregulated global competition drive subcenter development. Many subcenters containing substantial portions of metropolitan employment give rise to cross-commuting patterns. It is reasonable to expect that such a complex pattern will reduce the distance over which any subcenter can influence the mean function of house prices.

A third category of causal variables (3) includes physical and political variables that cause neighborhood house prices to be spatially autocorrelated. For example, subdivision approvals lead to neighborhoods being developed at about the same time and with similar building characteristics. Can and Anselin (1998) and Gillen, Thibodeau and Wachter (2001) discuss a number of variables omitted from categories 2 and 3 that can be modeled with spatial autocorrelation. …

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