Sergio J. Rey and Julie Le Gallo 1261extended by allowing a spatial lag term or a spatial error process. Another method-
ological problem is the fact that spatial heterogeneity (representative of spatial
convergence clubs) and spatial dependence may be observationally equivalent in a
cross-section (Abreuet al., 2005). Indeed, a cluster of high-growth regions may be
the result of spillovers from one region to another or it could be due to similarities
in the variables affecting the regions’ growth. Moreover, standard tests of structural
instability and heteroskedasticity are not reliable in the presence of spatial auto-
correlation. Therefore, as Rey and Janikas (2005) note, the existing specification
search procedures should be extended to be able to distinguish between spatial
dependence and spatial heterogeneity, while formal specification search strategies
for spatial heterogeneity have yet to be suggested.
Rather than partitioning the cross-sectional sample into regimes based on struc-
tural characteristics, parameter heterogeneity might also be country- or region-
specific. For example, Durlaufet al. (2001) allow the Solow growth model to vary
according to a country’s initial income by using the varying coefficient model sug-
gested by Hastie and Tibshirani (1993). In a spatial context, Erturet al. (2007) argue
that similarities in legal and social institutions, as well as culture and language,
might create spatially local uniformity in economic structures, which lead to sit-
uations where rates of convergence are similar for observations located nearby in
space. One possibility is to use geographically weighted regression (GWR) (Fother-
inghamet al., 2004), which is a locally linear, nonparametric estimation method
aimed at capturing, for each observation, the spatial variations of the regres-
sion coefficients. For that purpose, a different set of parameters is estimated for
each observation by using the values of the characteristics taken by the neighbor-
ing observations. For the conditionalβ-conditional convergence model (equation
27.1), this procedure allows estimation of the set of unknown parameters (βand
coefficients associated with the other structural characteristics) for each economy
of the sample:
1
T
log(yi,t 0 +T/yi,t 0 )=αi+βilog(yi,t 0 )+X1,iδ 1 i+X2,iδ 2 i+εi. (27.8)This model is estimated using weighted least squares with the weights being spe-
cific to each observation: for an observationi, the weights are a continuous and
monotone decreasing function of the distance between observationiand all other
observations. This method is useful for identifying the nature and patterns of spa-
tial heterogeneity over the observations and the results of a GWR (local estimated
coefficients, localt-statistics and measures of quality of fit) can be mapped. In a
convergence context, this method has been used by Bivand and Brunstad (2003)
for a sample of European regions and by Eckeyet al.(2007) for 180 labor mar-
ket regions in Germany. Eckeyet al. show that the German labor market regions
are moving at different speeds towards their steady-states, with the value of the
half-life increasing from North to South.
While useful for capturing heterogeneity in growth experiences in a sample of
economies, inference in this context is problematic. Indeed, Wheeler and Tiefels-
dorf (2005) show that the local regression estimates are potentially collinear even if