Luc Anselin and Nancy Lozano-Gracia 1233other unobserved characteristics of the house. Alternatively, if the house purchase
decision is taken jointly with the assessment of environmental quality, endogeneity
would also result. Similarly, sorting by house purchasers when there is heterogene-
ity in their preference functions associated with different pollution levels would
result in endogeneity of the air quality variable. This aspect was treated extensively
in a recent paper by Chay and Greenstone (2005), in the context of an application
where air quality is measured by total suspended particles. They suggest the use of
instrumental variables to obtain consistent estimates. While considerable care is
taken in addressing these specification problems, the model itself is estimated at a
fairly aggregate spatial scale of US counties.
Bayeret al. (2006) follow Chay and Greenstone (2005) by considering the pos-
sibility that local air pollution is correlated with unobserved local characteristics.
They address this form of endogeneity by using the contribution of distant sources
to local air pollution as an instrument. However, this study is also carried out at the
spatially aggregate county level, and could therefore suffer from ecological fallacy.
The potential correlation of specific house or household characteristics with
unobserved errors is considered by Gibbons (2003). Using a semiparametric model,
the potential endogeneity of educational composition is accounted for by using the
postcode-sector proportion of households in social housing as an instrument for
educational composition.
In the second perspective, endogeneity follows as a consequence of an “errors
in variables” problem. This is a special case of the change in support problem due
to the limited number of sample points for air pollution. As a result, the “obser-
vations” of air quality at individual house locations are actually the result of a
statistical spatial interpolation process with its own prediction error. In Anselin
(2001b), it was pointed out that the spatial structure of the prediction error is likely
to lead to correlation with the overall model disturbance term and thus to the famil-
iar simultaneity bias. Anselin and Lozano-Gracia (2008) elaborate on this idea and
estimate a spatial lag hedonic price equation using spatial two-stage least squares
(2SLS), including additional instrumental variables to address the endogeneity of
the air quality variable. Specifically, they use the components of a polynomial in
the coordinates of the house locations as instruments.
Irrespective of the actual source of the endogeneity, the use of instrumental
variables for some of the characteristic variables will yield consistent estimates.
However, in the absence of optimal instruments, the precision of these estimates
(and of the resulting computations of MWTP and other related measures) may be
improved upon. This remains a subject of future investigation.
26.5 Empirical evidence: spatial dependence
The first attempts to incorporate spatial considerations into empirical hedonic
house price studies consisted of including distance from the central business dis-
trict as an explanatory variable in the model specification. While appropriate for
monocentric cities, this is less suitable for polycentric areas, such as the Los Ange-
les metropolitan area. This resulted in several empirical studies reporting either