1282 Spatial Analysis of Economic Convergence
The space-time Moran HDR in the lower right panel of Figure 27.7 provides a
composite view of the spatial dynamics over this period. Here the spatial lag for
incomes in 2000 is conditioned on state income in 1929. In contrast to the Moran
HDR for 1929, the mode of the conditional lag distributions in 2000 display lin-
ear independence for low and moderate values of income in 1929. Moreover, in all
cases, the respective modes of the conditional lag distributions have moved towards
the overall average income value, with the convergence being upward for the con-
ditional distributions below one, and downward for conditional distributions for
y 1929 >1.0.
27.4 Conclusion
The previous two sections have reviewed a rapidly evolving body of literature
concerned with spatial analysis of economic convergence. In both the formal
confirmatory work and more recent exploratory data analysis, the unique chal-
lenges that spatially organized data pose continue to attract much attention. In
this section we offer some final thoughts and identify some remaining outstanding
issues for future research.
In the study of regional economic convergence it has become abundantly clear
that spatial dependence tends to be the rule rather than the exception in regional
income and product series. As a result, there is a growing recognition of the impor-
tance of treating this form of dependence in both formal confirmatory econometric
models as well as in newer exploratory methods of data analysis.
While spatial autocorrelation and spatial dependence have attracted the majority
of the attention in the literature, spatial heterogeneity has also been recognized as
an important dimension of many regional series. In general terms, however, the
treatment of spatial heterogeneity is more easily done using traditional (that is,
a-spatial) econometric methods, while spatial dependence has necessitated a new
body of models and methods.
Despite the growing awareness of spatial dependence and heterogeneity in
empirical work, most studies tend to focus on only one type of spatial effect. Work
on developing specification strategies within spatial econometrics (Anselin and
Rey, 1991; Anselin and Florax, 1995; Floraxet al., 2003) has provided guidance to
practitioners on how to detect and discriminate between different forms of spatial
dependence, yet similar approaches to deal with alternative forms of geographical
heterogeneity are lacking. Durlauf and Johnson (1995) use regression trees to exam-
ine whether international growth data obey a single Solow-type growth model or if
there are specific sub-groups or regimes with distinct parameter values. They find
evidence of substantial geographic homogeneity within the subgroups. That is,
model parameters are found to vary across the regional regimes but are assumed
to hold for all economies within a given regime. As acknowledged by Durlauf and
Johnson, there is no asymptotic theory available to access the statistical signifi-
cance of the identified regimes. An additional qualification offered is that there is
the possibility that the parameter heterogeneity could hold within each regime as
well as across the regimes. Moreover, the question of how to deal with the joint
presence of spatial dependence and spatial heterogeneity remains unanswered.