1238 Spatial Hedonic Models
autocorrelation leads to biases for the estimated risk measures that range between
37% and 167%.
Munroe (2007) combines geovisualization of single-family residential site prices,
exploration of univariate and bivariate measures of spatial autocorrelation, and
spatial econometric estimation of a hedonic model, to identify factors that are
likely to affect the land value in Mecklenburg County, North Carolina.
Finally, Anselin and Lozano-Gracia (2008) consider the endogeneity from an
errors in variable problem of the interpolated air pollution variable. Furthermore,
they provide the first empirical application of the HAC estimator suggested in
Kelejian and Prucha (2007). By reporting standard errors and 95% confidence inter-
vals, they compare the estimates from spatial and non-spatial models. Although
statistical differences are mainly seen between estimates that ignore (or not) endo-
geneity, they point out that the spatial models allow for a distinction between
direct and multiplier effects in the estimation of benefits associated with marginal
changes in house characteristics, which is not possible in the standard non-spatial
specification.
An interesting set of studies has focused on comparing the performance of geo-
statistical and lattice spatial econometric models, with particular attention given
to the estimates in the hedonic price equation and out of sample prediction. For
example, Miltinoet al. (2004) compare a conditional autoregressive model (CAR)
and a SAR model with a geostatistical model and a linear mixed effects model. The
parameters of these four specifications are estimated using a relatively small sam-
ple, consisting of 293 dwelling sales in Pamplona, Spain. Coefficient estimates are
very similar across models. Using AIC and BIC information criteria, the CAR model
seems to be a better alternative than the SAR model, but differences do not appear
to be significant. Miltinoet al. (2004) suggest that using a linear mixed effect model
may be a better alternative, because this type of model avoids the problems asso-
ciated with the selection of an appropriate weights matrix. A similar comparison
for a larger dataset remains to be carried out.
Caseet al. (2004) find superior out of sample prediction performance for three
spatial models relative to OLS using 50,000 house sales observations for Fairfax
County, Virginia. Bourassaet al. (2007) extend this work by also including an OLS
model that includes dummy variables for different sub-markets. This is assessed
for 4,880 house sales from Auckland, New Zealand. Specifically, they compare
the performance of a geostatistical model, lattice spatial models, and a standard
model with dummy variables (spatial fixed effects) for mass appraisal purposes. The
addition of sub-market dummy variables seems to outperfom both geostatistical
as well as lattice models in terms of out of sample predictions. However, these
conclusions may need to be put into perspective, since the sub-market models
considered did not include spatial effects (see also section 26.6). To some extent
then, the spatial and dummy variable specifications are not directly comparable.
Also, for lattice models, the notion of out-of-sample prediction is complicated
when some observations are removed from the original dataset. Since this alters
the specification of the weights matrix, additional uncertainty is introduced, which
needs to be taken into account (see also section 26.4.1.2).