1240 Spatial Hedonic Models
The main methodological problem is then how to delineate the submarkets. In
the literature, this has been approached in a number of different ways. Examples
include the use of political boundaries, such as census tract, zip code zone or county
boundaries (see, e.g. Goodman, 1981; Goetzmann and Spiegel, 1997; Brasington
and Hite, 2005), or subjectively determined areas defined by real estate agents or
appraisers (e.g., Bourassaet al., 2003, 2007). Alternatives rely on the application of
statistical techniques, such as principal component and cluster analysis (Bourassa
et al., 1999, 2003, 2008), including model-based clustering (Dayet al., 2004), hier-
archical models (Goodman and Thibodeau, 1998, 2003), and mixtures of linear
models (Ugarteet al., 2004). In addition to geographical boundaries, physical char-
acteristics of a property, such as the number of rooms, the lot and floor area, and
the type of property, have also been used to define sub-markets.
In practice, most attempts to account for this type of spatial heterogeneity
include dummy variables for each sub-market in the hedonic specification, rather
than estimating a separate hedonic equilibrium for each sub-market (e.g., Bourassa
et al., 2007). The inclusion of sub-market dummies may improve the predictive
power of the model, which is usually the stated objective. However, it does not fully
account for parameter heterogeneity, which may be important for identification
purposes.
Representative examples of the prior selection of sub-markets are the work of
Bourassa and co-authors. For example, in Bourassaet al. (2003), sub-markets
defined by real estate agents are compared to those derived from the application
of principal components and cluster analysis for 8,421 house sales transactions in
Auckland, New Zealand, in 1996. Specifically, factor scores obtained using princi-
pal components are used ink-means cluster analysis, which results in sub-markets
that do not impose contiguity. In terms of out of sample prediction, the geograph-
ically defined sub-markets used by appraisers outperform those based on statistical
criteria. Also, for mass appraisal purposes, urban boundaries seem to be better as
definitions of spatial sub-markets.
Further comparative evidence is provided in Bourassaet al. (2008), where alter-
native specifications of sub-markets are evaluated using a sample of 13,000 housing
transactions for Louisville, Kentucky. Districts defined by local property tax assess-
ment, as well as a classification of census tracts generated by principal components
and cluster analysis, are used to derive sub-markets. For the purposes of mass
appraisal, both the use of sub-market dummy variables as well as geostatistical
methods increase the predictive accuracy of hedonic models.
In contrast to this spatial fixed effects approach, Allenet al. (1995) suggest
that the differences between the sub-markets identified may be treated as random
effects. The specific application is a study of an aggregate residential rental market.
Through this approach, the authors allow for the possibility of individuals consid-
ering more than one property type in their choice set, while still considering an
aggregated rental market, instead of modeling each sub-market independently.
Goodman and Thibodeau (1998), on the other hand, suggest that submarkets
should not be imposed but specified explicitly using a hierarchical approach. For
example, they use 28,939 single-family property transactions in Dallas, Texas,