1100 The Econometrics of Convergence
Others have estimated the density of the cross-country distribution using mix-
ture models, based on weighted sums of component distributions.^20 Multiple
components, like multiple modes, can be indicative of multiple steady-states in
the dynamic process describing the evolution of per capita income. Paap and van
Dijk (1998) fix the number of components at twoa priori, based on the bimodality
of histograms of their data, and then use goodness-of-fit tests to select the shapes
of the component distributions. They study mobility between the components
by assigning each country to a component in each year according to the maxi-
mal conditional probabilities of component “membership,” computed using their
parameter estimates. They find only limited mobility across components: most of
the countries initially assigned to the poorer component remain so throughout the
sample period. Pittau, Zelli and Johnson (2008) estimate mixture models of the dis-
tribution of GDP per worker at five-year intervals from 1960 to 2000.^21 They use
goodness-of-fit and likelihood ratio (LR) tests to conclude that a three-component
mixture is the preferred model. As in Paap and van Dijk (1998), they find little
mobility between components, and so interpret their results as evidence of the
presence of multiple steady-states, contrary to the convergence hypothesis. The
results of Davis, Owen and Videras (2007), who fit a mixture model that allows
for conditioning on a typical set of proximate growth determinants, suggest that
these results are robust to cross-country variation in those variables.
Bloom, Canning and Sevilla (2003) also derive a mixture model for logyi,t. They
argue that, if long-run outcomes are determined by fundamental forces alone, the
relationship between income levels and exogenous variables ought to be unique.
If there are multiple steady-states, so that initial conditions play a role in long-run
outcomes, the relationship will not be unique. Instead, under suitable regularity
conditions, it will be described by a two component mixture model if there are two
steady-states and if large shocks and resultant movements between steady-states
are sufficiently infrequent.^22 Using 1985 income data from 152 countries with the
absolute value of the latitude of the (approximate) center of each country as the
fundamental exogenous variable, they are able to reject the null hypothesis of a
single regime model in favor of the alternative of a model with two regimes. The
regimes correspond to a high-level (“manufacturing and services”) steady-state, in
which income does not depend on latitude, and a low-level (“agricultural”) steady-
state in which income does depend on latitude, perhaps through its influence
on climate and agricultural productivity. Further, the probability of being in the
high-level steady-state is found to rise with latitude.
Other analyses of the distributions of income and growth have focused on
the differences in these distributions across time and across sub-sets of countries.
Anderson (2004) uses stochastic dominance methods to compare distributions at
different points in time and to construct measures of polarization, arguably the
antithesis of convergence. Using nonparametric estimates of the cross-country dis-
tribution of per capita income, he finds increased polarization – shifts in probability
density mass that increase disparities between relatively rich and relatively poor
economies – between 1970 and 1995. Pittau, Zelli and Johnson (2008) reach a