Steven Durlauf, Paul Johnson and Jonathan Temple 1103income distributions as well as the ergodic distribution implied by the model. Con-
sistent with Quah (1996c, 1997), they find bimodality to be a pervasive feature of
the sequence of distributions for about 100 years, even though the ergodic distri-
bution is unimodal. Hence, even if bimodality eventually disappears, it may persist
for a long time, as Quah notes in his response to Kremeret al.(2001).
There are some possible limitations to the use of distributional dynamics in
reaching conclusions about substantive economic questions, especially when con-
vergence is the main focus of interest. It is true that multiple modes in a distribution
are consistent with the hypothesis of non-convergence, as they can be a conse-
quence of multiple steady states. But they can also arise in the Solow model if, for
example, there are multiple modes in the distribution of investment rates or popu-
lation growth rates. Hence multimodality is not sufficient for concluding in favor
of the existence of convergence clubs. Moreover, the existence of meaningful clubs
also requires some degree of immobility within the distribution, so that countries
in the vicinity of a mode will tend to remain there for extended periods.
A further point is that, while multimodality and immobility provide evidence of
a lack of global convergence in the form of convergence clubs – groups of countries
that converge locally but not globally – convergence clubs may be relevant even if
the unconditional distribution of GDP per capita is unimodal. We can summarize
some of these points by observing that the distribution dynamics literature typi-
cally investigates the shape and evolution of the whole cross-country distribution
of per capita income at particular points in time, whereas economic debates about
convergence are partly about the shape of the long-run or ergodic distributionfor
a given country.
23.5.1 Structural analysis
A final approach to convergence is to take a theoretical model with multiple steady-
states and calibrate it to cross-country data. Graham and Temple (2006) carry out
this kind of exercise for a two-sector general equilibrium model. The combina-
tion of increasing returns to scale in one sector (manufacturing and services) and
intersectoral capital and labor mobility gives rise to multiple steady-states. They
calibrate the model to data for 127 countries, and find that about a quarter are in a
low-output equilibrium. The income differences across the equilibria are sizeable,
and imply that multiplicity is capable of explaining up to a quarter of the cross-
country dispersion in the logarithm of GDP per worker. Given the importance of
structural models in business cycle analysis, it is remarkable how little work of this
type has appeared in the convergence literature.
23.6 Time series approaches to convergence
Time series approaches to convergence are based on direct evaluation of the per-
sistence or transience of income per capita differences between economic units,
for example between pairs of countries or regions. This approach permits precise
statistical definitions of hypotheses about convergence, but has the disadvantage
of not being explicitly linked to particular growth theories.