Distinguishing Residential Submarkets

This article examines the possibility of dividing an urban housing market into a set of component submarkets in a way that is consistent with existence of one or more equilibrium hedonic pricing relationships. This is done by estimating an hedonic mixture model for the observed price. Two types of mixture model are estimated. The first is a standard fixed proportions mixture model, while the second is a spatially contextual mixture model. In both specifications, the null hypothesis of a single unified housing market is easily rejected. The exact number of submarkets is less clear, because some of the submarkets are too thin to obtain reliable regression estimates. Despite the results confirming multiple submarkets, my overall conclusion is that the prices for the vast majority of houses are described well by one or two equilibrium pricing relationships. 1.0 Introduction This article is concerned with the possibility of dividing an urban housing market into a set of component submarkets. There is a growing literature on this topic. A central question in this literature is: What constitutes a (sub)market? In the literature, there are two basic approaches to defining housing submarkets. The most common approach is based on the notion that housing submarkets are composed of housing units which are close substitutes to each other, but which are poor substitutes for housing units in other submarkets (Grigsby, et al., 1987; Rothenberg et al., 1991). This definition of housing submarkets is expressed empirically through the classification housing units into submarkets based on their observed characteristics. For this reason, I refer to it as the market segmentation approach. Classification methodologies used to segment the market range from ad hoc definitions of submarkets to statistical methods, such as principal components, factor analysis or cluster analysis. The latter set of methodologies are based on a variety of housing and neighbourhood attributes, such as location, size, lot dimensions, view, etc. (Bourassa et al., 1997; Dale-Johnson, 1987; Kendig, 1976; Kennedy, 1995; MacLennan and Tu, 1996; Smith and Kroll, 1989). The other approach to defining submarkets is based on the premise that the law of one price must hold for all housing units within a housing submarket; that is, units with the same attributes must have the same price. This means all housing units in a submarket have the same hedonic price ffinction. The corollary of this premise is that housing submarkets are distinguished by violations of the law of one price and, hence, differences in hedonic price ffinctions. This approach has not been used previously to define submarkets. Instead, it has been used to test whether a given segmentation of an urban housing market is valid. Examples of this procedure may be found in Bajic (1985), Dale-Johnson (1987), Gabriel (1984), Goodman (1981) and Schnare and Struyck (1976). Both these approaches are incomplete. The market segmentation approach suffers from both theoretical and empirical problems. First, it does not take the product-differentiated nature of the housing market into account. The key point of the seminal article by Rosen (1974) is that, under suitable conditions, a competitive equilibrium can exist in a product-differentiated market, whereby products with different characteristics are in demand/supply equilibrium across a unified market. Note that substitutability of the differentiated products is subsumed within the hedonic pricing relationship generated by the competitive equilibrium. Hence, the substitutability of housing units only becomes an issue at the margin where the hedonic relationship breaks down. This complicates empirical work considerably, as market segmentation rules based on housing attributes may not be linked in a meaningful way to housing submarkets. To resolve this problem, some form of market test needs to be built into the segmentation