Luc Anselin and Nancy Lozano-Gracia 1243using data on 33,494 transactions of single-family detached houses sold between
January 2001 and December 2003 in the City of Toronto; 10% of this sample is
taken out for out-of-sample validation. The MWR is an alternative to the locally
weighted regression (LWR) (and therefore GWR) in which a window (neighbor-
hood) is defined at every location. All points inside the window, and only those
points, are used to estimate the parameters for each observation. Therefore, in
contrast to LWR/GWR, a constant weight is given to all observations within the
window, ignoring observations outside the window. Similarly, MWK uses a local
spatial covariance structure that varies at every point in the sample (Haas, 1990).
In this example, MWR and GWR provide the most accurate results in terms
of prediction, while MWK produces very poor results in terms of out-of-sample
prediction.
Overall, the explicit incorporation of spatial heterogeneity in hedonic specifica-
tions illustrates the need to better understand the nature of market segmentation
and the complex interactions between location and the value of individual house
characteristics.
26.7 Concluding remarks
The contribution of spatial econometrics to hedonic analysis is not limited to
improving the quality and precision of the estimates obtained, as reviewed in the
previous sections. Spatial econometric methods also provide additional insight for
policy analysis. In this concluding section, we focus on two aspects in particular,
the notion of the spatial multiplier and its implications for the interpretation of
welfare effects, and the use of spatially explicit simulations to assess the impact of
non-marginal changes in characteristics.
As outlined in detail in section 26.2.1, the marginal implicit price derived
from the hedonic price equilibrium may be interpreted as a measure of a house-
hold’s marginal utility. Therefore, the derivative of the hedonic price equilibrium
equation with respect to the characteristic of interest forms the basis for the
estimation of MWTP.
In a non-spatial log-linear model, this MWTP equals the estimated coefficient
for the characteristic of interestzktimes the price (P), or:
MWTP̂z
k=∂P
∂zk=βˆzkP. (26.45)As shown in Kimet al. (2003), in a spatial lag model this is no longer the case.
Instead, a spatial multiplier effect needs to be accounted for to accurately compute
the MWTP. Specifically, in the case of a uniform change in the amenity across all
observations, the MWTP can be shown to be:
MWTP̂ =βˆz
kP(
1
1 −̂ρ)
, (26.46)witĥρas the estimate of the spatial autoregressive coefficient.