Sergio J. Rey and Julie Le Gallo 1283Spatial dependence and heterogeneity do not exhaust the class of spatial effects
that confront the regional convergence literature. The issue of the appropriate spa-
tial scale has largely been ignored as the specification of the geographical unit of
analysis has tended to be based on data availability rather than theoretical con-
cerns. In the context of convergence research, the geographical unit has varied
from countries, to regions, states and metropolitan areas (Drennan, 2005). As a
vast literature in spatial analysis has demonstrated (cf. Wong and Amrhein, 1996),
the modifiable area unit problem can give rise to inferences that are not robust to
changes in the spatial scale and aggregation of the data.
The aggregation issue can also be confounded with the regional heterogeneity
question. As work by Miller and Genc (2005) demonstrates, alternative definitions
of regional groupings can lead to different inferences regarding the speed of con-
vergence. Similarly, Rey (2004a) shows that changes in regional definitions can
have similar impacts on measuring regional inequality dynamics. In these stud-
ies the groups are taken exogenously with regard to administrative boundaries,
yet the possibility of endogenously determining these groupings was touched on
in section 27.2.3. Regionally constrained clustering algorithms (Rey and Anselin,
2007) could be used to determine spatially explicit convergence clubs.
In existing studies of regional convergence, the underlying spatial structure has
been assumed time invariant. Over the short run, the assumptions that the bound-
aries of economies, spatial weights matrices, and the composition of convergence
clubs are unchanging, are likely to be plausible. However, as the period under con-
sideration lengthens, such assumptions become increasingly untenable. A critical
area for future research will be the integration of evolving spatial structure into
formal growth models and distribution dynamics approaches.
Closely related to the issue of spatial scale is the relationship between regional
inequality dynamics and personal income distribution dynamics. In the case of the
US we have witnessed an apparent paradox of convergence over the last 150 years
at the state and regional scales, yet strong evidence of growing polarization in per-
sonal and household income distributions (Jones and Weinberg, 2000). Regional
patterns in personal income inequality, that is, the spatial distribution of personal
income distributions, has attracted some attention (Bishopet al., 1994; Levernier
et al., 1995; Partridgeet al., 1996; Morrill, 2000). However, the link between con-
vergence in the mean of these distributions (that is, regional convergence) and
the evolution of increasing inequality between individuals within these distribu-
tions remains largely unexplored and is an important avenue for future research.
In particular, the relationship between spatial clustering at one scale and the pace
of convergence at a higher spatial scale has received only limited attention (Janikas
and Rey, 2008).
Finally, although we organized our review along the dimensions of confirma-
tory and exploratory analysis, we see these approaches as complements rather
than substitutes. We can identify several areas where cross-fertilization between
these literatures is likely to lead to new advances. The first is the use of ESDA
methods applied to regional data series to identify interesting new patterns from
which suggestions for new types of theories and hypotheses about the spatial
nature of economic convergence may emerge. Rather than seeing ESDA as a case of