Palgrave Handbook of Econometrics: Applied Econometrics

Sergio J. Rey and Julie Le Gallo 1263

provide sound theoretical foundations for the inclusion of spatial dependence in
β-convergence or Verdoorn models. We review some of this recent work here.
Ertur and Koch (2007) show how a spatial Durbin version of theβ-convergence
model (equation 27.6) can be obtained from a theoretical growth model with
Arrow–Romer externalities and spatial externalities that imply inter-economy tech-
nology interdependence. They start with an aggregate Cobb–Douglas production
function for economyiat timetthat exhibits constant returns to scale in labor
and reproducible physical capital:

Yi(t)=Ai(t)Kαi(t)L^1 i−α(t) (27.10)

whereAi(t)=(t)k#i(t)

N



j=i

A

γwij

j (t),

whereYi(t)is output,Ki(t)is the level of reproducible physical capital,Li(t)is the
level of labor,Nis the number of economies andAi(t)is the aggregate level of
technology of economyiat timet. This level depends on three terms. First, as
in the standard Solow growth model, Ertur and Koch (2007) assume that some
proportion of technological progress is exogenous and identical in all countries:
(t)=( 0 )eμt, whereμis the constant growth rate. Second, each economy’s
aggregate level of technology increases with the aggregate level of physical capital
per workerki(t)=Ki(t)/Li(t), and the parameter#(with 0≤#<1) describ-
ing the strength of home externalities generated by physical capital accumulation.
Finally, as these externalities may spill over to neighboring economies, it is also
assumed that there is technological interdependence generated by the level of spa-
tial externalitiesγ(with 0≤γ<1). Thewijare the usual terms of the spatial
weights matrix.
This specification yields a spatially augmentedβ-convergence model, similar to
a non-constrained spatial Durbin model, where the growth rate of real income
per worker not only depends on its own saving rate and population growth rate,
but also depends on the same variables in the neighboring economies and on
the growth rate of its neighboring economies weighted by their speed of conver-
gence. Interestingly, complete parameter heterogeneity can be allowed for when
the speed of convergence is not assumed to be identical across economies. Ertur
and Koch (2007) estimate this heterogeneous model on a set of countries using the
SALE model as in equation (27.9). Other such attempts to motivate theoretically
the presence of spatial dependence have been suggested. For instance, López-Bazo
et al. (2004) assume that the spatial externalities originate from physical and human
capital accumulation rather than knowledge, yielding aβ-convergence model with
a spatial lag term as in (27.4). Egger and Pfaffermayr (2006) decompose the speed
of convergence term into three components: one measuring the speed of conver-
gence net of spillovers, and the other two accounting for the importance of spatial
spillovers.
A similar path has recently been followed to provide theoretical foundations
for the spatial versions of Verdoorn’s law. In particular, Fingleton (2000) shows
how Verdoorn’s law including a spatial lag term can be motivated by inter-regional