1260 Spatial Analysis of Economic Convergence
mixture distribution for the predictive density of per capita output (Canova, 2004),
among others.
It is noteworthy that Durlauf and Johnson (1995), by endogenizing the split-
ting using the regression tree method, point out the geographic homogeneity
within each group. This is even more bound to happen in a regional context,
as regional economies are often characterized by strong geographic patterns. In
Europe, the core–periphery pattern has frequently been underlined as representa-
tive of a form ofspatial heterogeneity. In a regression context, spatial heterogeneity
can be reflected by spatially varying coefficients, that is, structural instability,
and/or by spatially varying variances across observations. With this observation
in mind, several attempts aimed at analyzing spatial convergence clubs have been
suggested. A first strand of papers just usea priorispatial regimes. For example,
Neven and Gouyette (1995) define two regimes: Northern and Southern European
regions. Ramajoet al. (2008) split their sample of European regions between the EU
cohesion-fund countries (Ireland, Greece, Portugal and Spain) and all the others.
Using a model with groupwise heteroskedasticity, two spatial regimes and spatial
dependence, they show that, over 1981–96, there was a faster conditional con-
vergence speed in regions belonging to cohesion countries than in the rest of the
regions. A similar strategy has been adopted by Roberts (2004) on a sample of
British counties, by distinguishing between northern and southern counties.
Others explicitly take into account the spatial dimension of the data and use
exploratory spatial data analysis to detect spatial regimes. These techniques are
described in more detail in the following section. We note here that Erturet al.
(2006) use Moran scatterplots (Anselin, 2006), based on the initial per capita
GDP of a sample of European regions, to determine spatial clubs. Two clubs are
constructed this way: HH (High–High) regions and LL (Low–Low) regions, corre-
sponding respectively to regions with High (Low) initial per capita GDP surrounded
by regions with High (Low) initial per capita GDP. Atypical regions (that is, regions
classified as High–Low or Low–High) are eliminated from the sample as they are
not numerous enough to constitute a club. Alternatively, Le Gallo and Dall’erba
(2006), Dall’erba and Le Gallo (2008) and Fischer and Stirböck (2006) prefer the use
of Getis–Ord statistics (Ord and Getis, 1995), applied to initial per capita GDP, that
lead to a two-way partitioning of the sample: spatial clusters of high values of per
capita GDP (corresponding to positive values of the statistic) and spatial clusters of
low values of per capita GDP (corresponding to negative values of the statistics). We
can think of these methods as being “semi-endogenous,” as the number of clubs
is fixed (four in the case of Moran scatterplots and two in the case of Getis–Ord
statistics) but the economies are endogenously allocated to the clubs.
The endogenous detection of convergence clubs in data characterized by spatial
autocorrelation remains a serious problem, as the properties of the methods already
suggested (regression trees, and so on) remain unknown in the presence of spatial
autocorrelation. A first step in this direction is described in the paper by Basile and
Gress (2005), who suggest a semiparametric spatial autocovariance specification
that simultaneously takes into account the problems of nonlinearities and spatial
dependence. To that end, Liu and Stengos’ (1999) nonparametric specification is