Steven Durlauf, Paul Johnson and Jonathan Temple 1101similar conclusion using the Duclos, Esteban and Ray (2004) polarization index.
Maasoumi, Racine and Stengos (2007) find that the distributions of growth rates for
OECD and non-OECD member countries are persistently different between 1965
and 1995, with the OECD distribution’s variance reducing over time whereas the
non-OECD distribution appears to be becoming less concentrated.
The methods discussed above permit comparison of distributions at different
points in time, but are not explicitly dynamic. In most of these contributions,
the process describing the evolution of the cross-country distribution of per
capita income over time is not specified or described. Quah (1993a, 1993b,
1996a, 1996b, 1996c, 1997) introduced methods into the growth literature for
studying the evolution of distribution dynamics, in order to illuminate issues
of mobility, stratification, and polarization that are typically obscured by the
standard regression approaches used for testing the convergence hypothesis. In
addition, a description of the process governing the evolution of the cross-
country income distribution enables analysis of the long-run tendencies implied
by that process, through computation of long-run or ergodic distributions.^23
One way of studying distribution dynamics is to assume that the process describ-
ing the evolution of the distribution is described by a time-invariant and first-order
Markov chain.^24 Using cross-country per capita income data from the early 1960s
through to the mid 1980s, Quah (1993b) takes this approach. He finds that the ele-
ments on the main diagonal of the estimated transition matrix are often close to
unity, indicating a high degree of persistence, or lack of mobility, within the distri-
bution. Moreover, the implied ergodic mass function is bimodal or “twin-peaked.”
Together, these findings of persistence and bimodality could be seen as consistent
with the presence of multiple basins of attraction or “convergence clubs.”
Evidence of bimodality in the long-run cross-country distribution of per capita
incomes is also found by Kremer, Onatski and Stock (2001), who update Quah’s
analysis using more recent data. However, their point estimates imply that most
countries will ultimately move to the high-income state, and they are unable to
reject the hypothesis that there is a single right-hand peak in the long-run distribu-
tion. Quah (2001) observes that the imprecision of their estimates of the ergodic
distributions is sufficiently large that it is not possible to reject a wide range of
null hypotheses about their shape, including, as it is the point estimate, that of
bimodality.
Feyrer (2003) observes that the development traps implied by the “twin peaks”
finding could stem from traps in the accumulation of physical or human capital
or in total factor productivity (TFP). He uses a combination of Quah’s methods
and those of development accounting to examine this question, based on data
from 1970 to 1989. In particular, he examines whether the possible bimodality in
the distribution of GDP per capita can be traced to bimodality in the distributions
of aggregate TFP (measured as a residual), the capital-output ratio, or the average
level of human capital, measured in the usual way as a Mincerian function of years
of schooling. If traps in the accumulation of physical capital are, for example,
an important proximate cause of the bimodality in the distribution of output per
capita, the distribution of the capital-output ratio should also be bimodal. Feyrer’s