1258 Spatial Analysis of Economic Convergence
there is a debate on the assumed endogeneity and exogeneity of this specification
(Kaldor, 1975; Rowthorn, 1975a, 1975b).
In a spatial context, as mentioned previously, the case of a spatial lag model
with additional endogenous variables is straightforward since it can be estimated
by 2SLS. However, the estimation of a model with a spatial error process and
endogenous variables is not possible with the usual ML approach. In this case,
Fingleton and Le Gallo (2008) have extended the Kelejian and Prucha (1998) fea-
sible generalized spatial two-stage least squares (FGS2SLS) estimator to account for
endogenous variables due to system feedback, given an AR or a MA error process.
Angerizet al. (2008) use this strategy in the Verdoorn context. Alternatively, rather
than modeling the error process, Kelejian and Prucha (2007) have suggested a non-
parametric heteroskedastic and autocorrelation consistent (HAC) estimator of the
variance-covariance matrix in a spatial context (SHAC), which can be computed for
general regression models allowing for endogenous regressors, their spatial lags and
exogenous regressors. This methodology may also prove useful in spatial economet-
ric growth studies. Coupled with this is an extensive taxonomy of simultaneous
equation frameworks for spatial process models, recently suggested by Rey and
Boarnet (2004), that appears well-suited to convergence research.
Finally, the problem of model uncertainty has been raised by Brock and Durlauf
(2001), Fernandezet al. (2001), Doppelhoferet al. (2004) and Sala-i-Martin (1997).
This problem can arise from several sources. First, the selection of appropriate
conditioning variables is a difficult issue in convergence models and involves a
trade-off between the arbitrary selection of a small number of variables, which may
imply some omitted variables bias, and the introduction of a larger set of variables
with a number of econometric problems such as endogeneity or multicollinearity.
Second, as is typical in all regression models, we also face parameter uncertainty.
Fernandezet al. (2001) and Doppelhoferet al. (2004) employ Bayesian model
averaging techniques that can accommodate both model and parameter uncer-
tainty. In a convergence framework, they find that the posterior distribution of
βcomputed across alternative specifications assigns all probability mass to the
negative half interval. This results in strong support to the convergence hypoth-
esis. However, LeSage and Fischer (2007) point out that in a spatial setting an
additional source of model uncertainty arises: one also has to specify the appropri-
ate weights matrixWthat defines connectivity between regions. In other words,
the estimates and associated inferences in spatial growth regressions are not only
conditional on the set of explanatory variables employed but also on the chosen
spatial weights matrix. Extending the approach of LeSage and Parent (2007), LeSage
and Fischer (2007) derive a Bayesian model comparison approach that simultane-
ously specifies the spatial weights structure and the explanatory variables in spatial
Durbin models, with an application to the convergence process among European
regions.
27.2.3 Dealing with heterogeneity
In this section, we deal with heterogeneity problems and how the literature has
considered them in conjunction with spatial autocorrelation. We consider the