Steven Durlauf, Paul Johnson and Jonathan Temple 1111
that both diminishing returns and technology transfer are important contributors to
the convergence process. See also Bernard and Jones (1996) and Barro and Sala-i-Martin
(1997).
- That limt→∞yEi,t=yiE,∞follows fromλi>0. This long-run independence ofyEi,tfrom
yiE,0implies that initial conditions do not matter in the long run – an interpretation of
convergence that we discuss below.
- In parallel to equation (23.1), limt→∞(yi,t−yEi,∞Ai,0egit)=0, so that again the initial
value of output per worker does not affect its long-run value.
- This assumption is made, for example, by Mankiwet al.(1992), who argue thatAi,0
reflects not just technology, which they assume to be constant across countries, but
country-specific influences on growth, such as resource endowments, climate and insti-
tutions. They assume these differences vary randomly across countries, independently
of the determinants of the steady-state level of output per worker.
- Barro and Sala-i-Martin (2004, Chs. 11, 12) implementβ-convergence tests for a variety
of datasets. As pointed out by DeLong (1988), the use of homogeneous groups runs the
risk ofex postsample selection, especially if the homogeneity relates to final outcomes.
In particular, he views the Baumol (1986) finding of unconditionalβ-convergence over
1870–1979 among a set of countries that were affluent in 1979, as tending to overstate
the true degree of convergence. DeLong extends the sample to include countries with
similar starting positions in 1870, but which have been less successful since, and this
weakens the evidence for convergence.
- In both Jones and Manuelli (1990) and Kelly (1992), steady-state growth occurs with-
out exogenous technical change, but initially poor economies grow more quickly as
β-convergence requires.
- As Barro and Sala-i-Martin (1992) note, while there is some variation in estimated conver-
gence rates, estimates generally range between 1% and 3%. They attribute this variation
to unobserved heterogeneity in steady-state values; but to the extent that it is correlated
with variables included in the regressions, this heterogeneity implies the parameter esti-
mates are inconsistent. Panel studies such as Islam (1995), Caselliet al.(1996) and Lee,
Pesaran and Smith (1998) have found more rapid rates of convergence.
- For example, Barro and Sala-i-Martin (1991) present results for US states and regions
as well as European regions; Barro and Sala-i-Martin (1992) for US states, a group of
98 countries and the OECD; Mankiwet al.(1992) for several large groups of countries;
Sala-i-Martin (1996a, 1996b) for US states, Japanese prefectures, European regions, and
Canadian provinces; Cashin (1995) for Australian states and New Zealand; Cashin and
Sahay (1996) for Indian regions; Persson (1997) for Swedish counties; and Shioji (2001)
for Japanese prefectures and other geographic units.
- As Durlaufet al.(2005) document, the number of suggested control variables is now
almost as large as the number of countries in the world.
- Den Haan (1995) is an especially sophisticated discussion.
- See Abramovitz (1986), Baumol (1986), DeLong (1988), Romer (1990) and Temple (1998).
- An appendix to Durlauf and Johnson (1995) discusses the application of regression tree
methods to the issue of locating multiple regimes in growth models. Breimanet al.(1984)
contains a detailed general treatment of regression tree methods. While these methods
suffer from the lack of a well-developed asymptotic theory for testing the number of
regimes present in a dataset, they are consistent in the sense that, under relatively weak
conditions, the correct model will be revealed as the sample size grows to infinity, if
there are a finite number of regimes.
- Papageorgiou and Masanjala (2004) observe that Durlauf and Johnson’s findings could be
due to misspecification of the aggregate production function. They estimate a version of
the Solow model based on a constant elasticity of substitution (CES) production function
rather than the Cobb–Douglas, following findings in Duffy and Papageorgiou (2000),
and ask whether or not Durlauf and Johnson’s multiple regimes remain under the CES
