Steven Durlauf, Paul Johnson and Jonathan Temple 1109favor of non-neoclassical models, but care must be taken to control for the long-run
effects of differences in preferences and other structural characteristics.
More formally, successful empirical work on the convergence issue requires the
distinction between initial conditionsρi,0and structural characteristicsθi,0. Steady-
state effects of the former imply the existence of convergence clubs, but steady-state
effects of the latter do not. In order to make this distinction we modify (23.18) and
say that countriesiandjexhibit convergence if:
lim
t→∞‖μ(logyi,t|ρi,0,θi,0)−μ(logyj,t|ρj,0,θj,0)‖=0ifθi,0=θj,0. (23.23)The corresponding modification to the notion of convergence in expected value is:
lim
t→∞E(logyi,t−logyj,t|ρi,0,θi,0,ρj,0,θj,0)=0ifθi,0=θj,0, (23.24)and the other convergence concepts discussed above can be similarly modified.
While conceptually clear, the distinction between initial conditions and struc-
tural heterogeneity is potentially difficult in practice. Typically, researchers have
treated initial human and physical capital stocks as instances of initial conditions,
and other variables as representing structural heterogeneity – for example, those
that often appear as controls in cross-country growth regressions, a practice that
is problematic if these variables are, in fact, endogenously determined by initial
conditions.
Disentangling the respective roles of structural heterogeneity and initial con-
ditions in determining growth performance remains one of the most important
challenges for the convergence literature. Economic theory does not always pro-
vide a guide to the relevant control variables, let alone the appropriate distinction
between variables that capture structural heterogeneity and those that should be
classed as initial conditions. It is also important to emphasize that none of the
statistical definitions of convergence discussed above is necessarily of any intrinsic
interestper se; each is useful only to the extent that it can illuminate some eco-
nomically interesting notions of convergence such as that in (23.24). The failure
to distinguish between convergence as an economic concept and convergence as
a statistical concept has led to much confusion in the growth literature.
23.8 Conclusions
The empirical convergence literature contains many interesting findings and has
helped to identify a number of important generalizations about cross-country
growth behavior. At the same time, it has yet to reach any sort of consensus
on the deep economic questions for which the statistical analyses were designed.
It is not difficult to highlight some of the relevant problems. The fundamen-
tally nonlinear nature of endogenous growth theories renders the conventional
cross-section and panel convergence tests inadequate as ways to discriminate
between the main classes of theories. Evidence of convergence clubs may simply
be evidence of deep nonlinearities in the transitional dynamics towards a unique