1232 Spatial Hedonic Models
observations is conceptualized (for details, see Anselin, 2002). The most widely
used framework is referred to as lattice analysis, due to the fact that considerable
early work in this area pertained to regularly spaced or gridded observations (e.g.,
Besag, 1974). In lattice analysis, the observations are discrete spatial units that
exhaust the space, such as contiguous census tracts or counties. The main dis-
tinction is that the notion of interpolation is not supported, since observations
are available on all spatial units in the “population.” Asymptotics are based on a
notion of expanding domain, i.e., growing the sample by adding additional units
at the edge. In contrast, in so-called geostatistical analysis (Cressie, 1993), obser-
vations are a sample from a continuous surface. The main objective is to extract
the characteristics of the continuous surface, so that interpolation (spatial predic-
tion) can be carried out. The proper asymptotics are referred to as infill asymptotics
and can be conceived of as increasing the density of sampling. Importantly, the
two forms of asymptotics are different and properties that hold under one do not
necessarily hold under the other (see, e.g., the discussion in Lahiri, 1996).
Hedonic house price studies are typically based on a sample of individual sales
transactions or appraisals, and seldom include the full population. This is only
the case in analyses for aggregate spatial units, such as census tracts or counties.
Because of the nature of the sales sample, a geostatistical perspective should be the
preferred approach. However, in practice, most empirical work is couched in a lat-
tice perspective, using the standard spatial lag and spatial error specifications with
spatial weights derived from contiguity or nearest neighbor criteria. This aspect is
seldom highlighted, but it does raise potential problems in terms of the asymptotics
necessary to obtain the consistency of estimators. For example, when a simple con-
tiguity weights matrix is used between the locations of sales transactions (e.g., by
using Thiessen polygons to define neighboring sales), a lattice approach assumes
that the observed houses are the only houses in the population. In other words, the
effect of theneighborsshould be interpreted as the effect of neighboringsales, but
not of neighboring properties. When the sales only constitute a sample of all trans-
actions, the underlying assumption becomes that the effect of sampled neighbors
is the same as that of the unobserved true neighbors. The validity of this assump-
tion rests on the degree of spatial homogeneity of the housing market, in terms
of both house and household characteristics. Without further information, this is
very difficult to verify in practice.
26.4.2 Endogeneity
The issue of endogeneity in the estimation of demand equations that arise from a
nonlinear hedonic price schedule is a familiar problem (see, e.g., Palmquist, 2005).
Much less common is the focus on endogeneity in the estimation of the hedonic
price equation itself. In the context of spatial hedonic models, this has received
some attention, specifically in the study of the valuation of the contribution of air
quality (and, to a lesser extent, of school quality).
There are two different perspectives on the endogeneity problem. In one, atten-
tion focuses on a specific house characteristic and the degree to which this is truly
exogenous. For example, this would not be the case if air quality is correlated with