Sergio J. Rey and Julie Le Gallo 1259convergence literature here as these problems have been mainly encountered in
this context. First, unobserved heterogeneity is one of the most common problems
related with conditional convergence models, in particular due to technological
differences between economies. Given the difficulty in accounting for technolog-
ical differences in a cross-sectional framework (Islam, 2003), an alternative tactic
is to resort to the panel data approach to eliminate unobservable economy-level
heterogeneity. For that purpose, a dynamic panel data model with individual fixed
effects has been suggested by Islam (1995). Panel data techniques have several
advantages. They allow controlling for unobserved heterogeneity in the initial
level of technology and omitted variables that are persistent over time. Moreover,
endogeneity bias, common in convergence equations as stated above, may also
be rectified by estimating the panel data convergence model using Arrelano and
Bond’s (1991) GMM procedure.
Inclusion of spatial autocorrelation in this context has investigated been by few
authors to date. One possibility is to get rid of spatial autocorrelation in order to
apply the usual estimators. This strategy has been adopted by Badingeret al. (2004),
who propose a two-step estimation procedure. First, they apply the filtering tech-
nique suggested by Getis and Griffith (2002) that separates the spatially correlated
component from the data. Second, standard GMM estimators are used to provide
inference on convergence. However, the properties of the estimators obtained in
this two-step procedure are unknown. Moreover, this approach assumes that spa-
tial autocorrelation is only a nuisance, whereas the following section shows how
spatial autocorrelation can be considered as a component of the growth process in
its own right. In their suggestion to deal with spatial autocorrelation directly, Arbia
and Piras (2005) analyze the European growth process by including a spatial lag
variable or a spatial error term in a convergence model with region fixed effects.
The spatial parameters are assumed to be fixed over time and the model is esti-
mated using ML. One drawback of this method is that consistent estimation of the
individual fixed effects is not possible asN→∞, due to the incidental parameter
problem (Anselinet al., 2008).
Heterogeneity may also concern the regression parameters. While absoluteβ-
convergence is frequently rejected for large samples of countries and regions, it is
usually accepted for more restricted samples of economies belonging to the same
geographical area. This observation can be linked to the presence of convergence
clubs: there is not only one steady-state to which all economies converge. Rather,
there may be multiple, locally stable, steady-state equilibria. Therefore, a con-
vergence club is a group of economies whose initial conditions are near enough
to converge toward the same long-term equilibrium. It is noteworthy that the
hypothesisβ<0 can be consistent with non-converging alternatives, such as a
threshold growth model with multiple steady-states (Azariadis and Drazen, 1990).
The determination of those clubs, when they exist, is then a critical issue. In this
respect, some selecta prioricriteria, such as initial per capita gross domestic prod-
uct (GDP) cut-offs (Durlauf and Johnson, 1995). On the contrary, endogenous
methods of club detection are quite diverse and include regression trees (ibid.),
projection pursuit methods (Desdoigts, 1999), Bayesian methods that identify a