Steven Durlauf, Paul Johnson and Jonathan Temple 1093A first source of correlation derives from country-specific heterogeneity. Cross-
section growth regressions assume that the error termsεiare uncorrelated with the
logyi,0terms, but this is unlikely to hold if there is country-specific unobserved
heterogeneity in output levels. If such effects were present, they would typically
imply a link betweenεiandyi,0. For this reason, a number of researchers have
investigated convergence using panel data. This leads to models of the form:
gi,t=ci+yi,t− 1 β+Zi,tγ+εi,t (23.8)where growth is now measured betweent−1 andt. This approach means that
individual (“fixed”) effects can be used to control for (time-invariant) unobserved
heterogeneity. In practice, this has often been supplemented with the use of instru-
mental variables to address the endogeneity of variables like investment rates.
Panel analyses have been conducted by Bond, Hoeffler and Temple (2001), Caselli,
Esquivel and Lefort (1996), Islam (1995, 1998) and Lee, Pesaran and Smith (1997,
1998), among others. These studies generally find that conditional convergence
takes place at higher rates than estimated in the cross-section studies. For example,
Caselliet al.(1996) report annual convergence rate estimates of 10%.
As discussed in Durlauf and Quah (1999) and Durlaufet al.(2005), panel data
approaches to convergence suffer from the problem that, once country-specific
effects are allowed, it becomes harder to interpret the results in terms of specific
economic explanations. One problem is that, once the growth model includes
individual effects, then the question of convergence is changed, at least if the goal
is to understand whether initial conditions matter; simply put, the country-specific
effects may partly reflect the effects of varying initial conditions. When studies
such as Leeet al.(1997, 1998) allow for rich forms of parameter heterogeneity
across countries,β-convergence becomes the equivalent of the proposition that
there is some mean reversion in a country’s output process. The rate of mean
reversion could be informative about the extent of diminishing returns, but not
about whether certain types of contemporaneous inequalities are increasing or
decreasing. This does not lessen the interest of these studies as statistical analyses,
but means their economic import can be unclear.
A second source of correlation between the error term and explanatory variables
is that some variables are endogenously determined. Variables such as invest-
ment rates and initial income^13 are themselves equilibrium outcomes, in the
same way as growth rates. This has led some authors to propose instrumental
variables approaches to estimatingβ. Barro and Lee (1994) analyze growth data
in the periods 1965–75 and 1975–85 using five-year lagged explanatory variables
as instruments, but find that this makes little difference to the coefficient esti-
mates. Although motivated by the possibility of measurement error, Romer (1990)
finds that estimating a growth regression using instrumental variables (IVs) elim-
inates the negative and significant coefficient on initial income typically found
when the equation is estimated by ordinary least squares (OLS). As noted above,
Caselliet al.(1996) find estimates ofβof the order of 10% – much larger than
the typical 2% of cross-section studies – using a generalized method of moments