argued to be strong evidence in favour of convergence. Abramovitz (1986) presented similar
evidence, arguing that catch-up growth has been most prominent in the period since 1945.
This position was challenged by DeLong (1988) who argued that Baumol’s results suffered
from a sample bias, in that his analysis has been confined to a sample of countries that have
become rich and developed; if one takes a sample of countries that in 1870 seemed likely to
converge, the evidence of convergence is less clear cut. In addition, a number of studies have
presented evidence of income convergence across countries, by explicitly testing (augmented
versions of) the Solow growth model (e.g., Barro 1991, Barro and Sala-i-Martin 1992,
Mankiw et al. 1992, Islam 1995). These empirical cross-country growth analyses raised the
important question of whether countries converge to a global or rather to a local steady state,
the latter implying that convergence is conditional on cross-country differences in steady-
state characteristics. They are, respectively, referred to as unconditional (or absolute) and
conditional (or relative) convergence. This idea has been formalised by Durlauf and Johnson
(1992) and confirmed by several studies in this field, some of them suggesting the existence
of convergence clubs: groups of countries converging to different steady states (e.g., Chatterji
1992, Chatterji et al. 1993, Quah 1997).3
From this literature it follows that convergence can be understood in terms of levels
and growth rates, which translates into a distinction between so-called σ-convergence and β-
convergence (e.g., Barro 1991, Barro and Sala-i-Martin 1992). The former refers to a
decreasing variance of cross-country differences in productivity levels, while the latter
suggests a tendency of countries with relatively low initial productivity levels to grow
relatively fast, building upon the proposition that growth rates tend to decline as countries
approach their steady state. Obviously, σ-convergence and β-convergence are closely related.
A narrowing dispersion of cross-country productivity differences implies that countries with
a relatively poor initial productivity performance tend to grow relatively fast. However, as
has been argued by Quah (1993), a statistically significant inverse relationship between the
initial level and the growth rate of productivity performance can be consistent with constant
or even increasing cross-country productivity differences - a phenomenon known as Galton’s
3 For more complete surveys of the convergence debate we refer to Barro and Sala-i-Martin (1995), Broadberry
(1996), Durlauf and Quah (1999), Fagerberg (1994), Economic Journal (1996) and Islam (2003). For more
recent work on evidence of and driving forces behind convergence patterns see, for example, Baumol et al.
(1994), van Ark and Crafts (1996), Kumar and Rusell (2002), Miller and Upadhyah (2002) and Tondl (2001)
among many others.