1218 Spatial Hedonic Models
for the characteristic. The general form of this expression is as in equation (26.4).
This second stage is especially important when interest centers on the effect of
non-marginal changes in the characteristic.
One important problem associated with this second stage is identification
(Palmquist, 1991; Freeman, 1999). This is primarily a result of the fact that the
prices used in the second-stage inverse demand function are not actually observed,
but derived from the coefficient estimates in the first stage (the hedonic price func-
tion). Also, the MWTP is computed as a function of at least one of the explanatory
variables used in the price specification. In order to be able to separately identify
the inverse demand function, it is necessary that additional variables (demand
shifters) be included in the second stage.
Furthermore, the attribute variable (amount of the characteristic) is an explana-
tory variable in both the first and second stage and is thus endogenous. This follows
because the selection of a point on the hedonic price function simultaneously
determines the level of the characteristic and the marginal price associated with it.
This endogeneity must be taken into account in the second stage estimation, typi-
cally by using instrumental variables. The instruments should be truly exogenous
to the model, which in practice may be difficult to establish.
One solution to the identification problem, suggested by Palmquist (1991), is to
use information from spatially or temporally distinct sub-markets. The rationale
behind this is that the heterogeneity between the sub-markets provides sufficient
variability to identify a demand function for the characteristic. This is estimated by
taking marginal prices from different sub-markets as well as demand shifters that
vary sufficiently across the sub-markets (e.g., income).
Apart from the identification issue for the demand function (the second stage),
sub-markets should also be explicitly considered when spatial heterogeneity inval-
idates the assumption of a single equilibrium. After defining meaningful spatially
delineated sub-markets, a separate hedonic price function should be estimated
for each.
In practice, interest has focused on the first stage of the hedonic model and on
estimation of MWTP for various characteristics. An important body of applications
pertains to the valuation of amenities, such as environmental quality, access to
open space and views. Very few spatial econometric applications have carried out
the second stage of estimating the inverse demand function. Recent exceptions are
Beronet al. (2004) and Brasington and Hite (2005).
26.3 Spatial models
Increasingly, applied econometric work dealing with hedonic house price mod-
els has taken an explicit spatial econometric perspective. Some recent examples
include Basu and Thibodeau (1998), Dubinet al. (1999), Bell and Bockstael (2000),
Bowenet al. (2001), Bourassaet al. (2003), Kimet al. (2003), Beronet al. (2004), Pace
and LeSage (2004), Brasington and Hite (2005), Anselin and Le Gallo (2006), Neill
et al. (2007) and Anselin and Lozano-Gracia (2008). This work focuses, in partic-
ular, on the treatment of market interactions or unobserved neighborhood effects