Palgrave Handbook of Econometrics: Applied Econometrics

1224 Spatial Hedonic Models

units belong to, such as a census tract or block group. This rests on the assump-
tion that the spatial range of the unobserved heterogeneity/dependence is specific
to each spatially delineated unit. In practice, there may indeed be spatial units
(such as school districts) where such a spatial fixed effects approach is sufficient
to correct the problem. However, the nature of omitted neighborhood variables
tends to be complex, as is the definition of the correct “neighborhood,” and in
many instances the fixed-effects approach will be insufficient to remove all residual
spatial autocorrelation.

26.3.1.3 Other models of spatial dependence

In addition to the familiar spatial lag and spatial error models just outlined, a num-
ber of other techniques have been adopted to deal with spatial effects in hedonic
house price functions. We briefly review here semiparametric approaches.
An alternative way to account for space in a hedonic regression is to incorporate
it directly in the hedonic price function in the form of a trend surface, while main-
taining the assumption of constant marginal prices across space. In a parametric
approach, this would consist of including a polynomial in theX,Ycoordinates
of the observations as explanatory variables in the hedonic equilibrium equation.
This could also be combined with a fixed-effects approach in the form of dummy
variables for administrative units, such as zip code or census tracts.
A semiparametric alternative, first discussed by Clappet al. (2002), includes, in
addition to the usual hedonic variables, a nonparametric functionf(Xc,Yc)of the
location of the observations. This is to model the omitted spatial variables in the
mean function, rather than relegating them to the error term. Formally, this yields:

P=Xβ+f(Xc,Yc)+ε. (26.18)

This function may be estimated using standard nonparametric techniques such as
local polynomial regression. The Nadaraya–Watson estimator is the method most
frequently used in the literature.
Clappet al.suggest estimating this model in an iterative fashion consisting of
two main steps. First, the parameters of all house characteristics are estimated
using OLS. In a second step, the residuals from this regression are fitted using
Bayesian or local polynomial regression techniques. The first step thus yields OLS

residualsηˆ^0 as:

ηˆ^0 =P−Xβˆ^0. (26.19)

In a first iteration, these residuals are then smoothed using a Nadaraya–Watson
estimator, as:

η ̄^0 =

∑q

i= 1

Kh(Xci−X 0 )Kh(Yci−Y 0 )(ηˆ^0 )

∑q

i= 1 Kh(Xci−X^0 )Kh(Yci−Y^0 )

. (26.20)

Then, the estimated residuals from a first iteration are obtained as:

0 ˆ

=η

0 ˆ

−η

0 ̄

. (26.21)