Terence C. Mills and Kerry Patterson xxixof neighborhood, proximity to parks, schools, measures of environmental quality,
and so on, that are critical in assigning a value to a house. These characteristics
lead to the specification of a hedonic price function to provide an estimate of the
marginal willingness to pay (MWTP) for a characteristic; a related aim, but one
not so consistently pursued, is to retrieve the implied inverse demand function
for house characteristics. Two key problems in the estimation of hedonic house
price functions, in particular, are spatial dependence and spatial heterogeneity. As
Anselin and Lozano-Gracia note, spatial dependence, or spatial autocorrelation,
recognizes the importance of geographical or, more generally, network space in
leading to a structure in the covariance matrix between observations. Whilst there
is an analogy with temporal autocorrelation, spatial autocorrelation is not simply
an extension of that concept, but requires its own conceptualization and methods.
Spatial heterogeneity can be viewed as a special case of structural instability; two
(of several) examples of heterogeneity are spatial regimes (for example, ethnically
based sub-neighorhoods) and spatially varying coefficients (for example, different
valuations of housing and neighborhood characteristics). In this chapter, Anselin
and Lozano-Gracia provide a critical overview of methods, such as spatial two-stage
least squares and spatial feasible GLS, a summary of the literature on spatial depen-
dence and spatial heterogeneity, and discussion of the remaining methodological
challenges.
In Chapter 27, Serge Rey and Julie Le Gallo consider an explicitly spatial analysis
of economic convergence. Recall that Chapter 23, by Durlaufet al., is con-
cerned with the growing interest in the econometrics of convergence; for example,
whether there was an emergence of convergence clubs, perhaps suggesting “win-
ners and losers” in the growth race. There is an explicitly spatial dimension to
the evaluation of convergence; witness, for example, the literature on the con-
vergence of European countries or regions, the convergence of US states, and so
on. Rey and Le Gallo bring this spatial dimension to the fore. The recognition of
the importance of this dimension brings with it a number of problems, such as
spatial dependence and spatial heterogeneity; these problems are highlighted in
Chapter 26, but in Chapter 27 they are put in the context of the convergence of
geographical units. Whilst Rey and Le Gallo consider what might be regarded as
purely econometric approaches to these problems, they also show how exploratory
data analysis (EDA), extended to the spatial context, has been used to inform the
theoretical and empirical analysis of convergence. As an example, a typical focus
in a non-spatial context is onσ-convergence, which relates to a cross-sectional
dispersion measure, such as the variance of log per capita output, across regions or
countries. However, in a broader context, there is interest in the complete distri-
bution of regional incomes and the dynamics of distributional change, leading to,
for example, the development of spatial Markov models, with associated concepts
such as spatial mobility and spatial transition. EDA can then provide the tools to
visualize what is happening over time: see, for example, the space-time paths and
the transition of regional income densities shown in Figures 27.5 and 27.6. Rey and
Le Gallo suggest that explicit recognition of the spatial dimension of convergence,
combined with the use of EDA and its extensions to include the spatial element,