Luc Anselin and Nancy Lozano-Gracia 1219through the incorporation of spatial dependence and on the use of model spec-
ifications that allow for spatial heterogeneity in the form of submarkets. Several
different model formulations and estimation methods have been applied, reflecting
the richness of the spatial methodology (Anselin, 2006).
The motivation for incorporating spatial effects into the specification of a hedo-
nic house price model is based on two main concerns. One, which we refer to as
substantive, is that the model form is intended to capture either interaction effects,
market heterogeneity, or both. The other is more pragmatic and we refer to it
as anuisance, in that spatial autocorrelation in omitted variables, or unobserved
externalities and heterogeneities, are relegated to the error term. In dealing with
spatial dependence, these two perspectives are reflected in thelaganderrormod-
els (Anselin, 1988). In addressing spatial heterogeneity, varying coefficient models
and spatial regimes reflect substantive models, whereas various specifications for
heteroskedasticity deal with nuisance effects.
The econometric treatment of these two types of effects differs considerably.
Substantive models require a new class of estimation methods and specification
tests, whereas nuisance models are simply special cases of a non-spherical error
variance-covariance matrix. The consequences of ignoring these effects differ as
well. Omitting substantive effects when they should be included results in model
misspecification. Consequently, the estimates of the remaining parameters will be
biased and inconsistent, and inference may be spurious. In a hedonic context,
this implies that conclusions about the marginal price of specific characteristics
(e.g., environmental improvements) may be wrong. On the other hand, nui-
sance effects are primarily a problem of efficiency. Ignoring those effects when
present will yield biased estimates of standard errors in a traditional ordinary
least squares (OLS) regression if the proper adjustments are not carried out. This
will yield biased t-tests and misleading indications of precision. Since the co-
efficient estimates in hedonic models are used in further calculations (e.g., of
marginal willingness to pay), it remains important to have correct measures of
standard errors in order to properly address uncertainty in a policy decision making
context.
One additional complexity with spatial models is that spatial dependence and
spatial heterogeneity are often difficult to distinguish in a cross-sectional setting.
The properties of specification tests and estimators developed for one type of effect
are affected by the presence of the other type. In practice, one typically addresses
one type of spatial effect first, carries out specification tests for remaining problems
and subsequently addresses those if warranted.
In this section, we review the main model specifications and estimation methods
that have been applied in hedonic studies. Here, we only focus on the basic proper-
ties and do not intend to duplicate the extensive methodological reviews provided
in Anselin and Bera (1998) and Anselin (2006), among others. We also limit our
discussion to the most commonly used specifications. For spatial (and space-time)
dependence, these are the lag and error models, as well as some recently suggested
semiparametric approaches. For spatial hetereogeneity, we cover the treatment of
discrete (regimes) and continuous (varying coefficients) spatial heterogeneity.