Reopening the Convergence Debate:
A New Look at Cross-Country Growth
Empirics
Francesco Caselli, Gerardo Esquivel and Fernando Lefort
1
Journal of Economic Growth, 1996.
1
Harvard University. We wish to thank Alberto Alesina, Robert Barro, John
Campbe ll, John Driscoll, Guido Imbens, Aart Kraay, David Laibson, John Leahy,
Jong-Wha Lee, Jordan Rappaport, J ose Tavares, Jaume Ventura and seminar
partecipants at Harvard University and at the Sev enth World Congress of the
Econometric Society for useful remarks. Special thanks are due to Gary Cham-
berlain, Dale Jorgenson and Greg Mankiw for illuminating conversations. The
comments of a n anon ymous referee have led to a substantial improvement of the
paper, and are also gratefully acknowledged. We are responsible for all errors.
Comments are welcome. Please write to any of the authors at: Department of
Economics, Littauer Cen ter, Harvard University, Cambridge, MA, 02138 (e-mail:
gesquiv@fas.harvard.edu).
Abstract
There are two sources of inconsistency in existing cross-country empirical
work on grow th: correlated individual effects and endogenous explanatory
variables. We estimate a variety of cross- country grow th regressions using
a generalized method of moments estimator that eliminates both problems.
In one application, we find that per capita incomes converge to their steady-
state levels at a rate of approximately 10% per year. This result stands in
sharp contrast to the current consensus, which places the convergence rate
at 2%. We discuss the theoretical implications of this finding. In another
application, we perform a test of the Solow model. Again, contrary to prior
results, we reject both the standard and the augmented version of the model.
1Introduction
Almost ten years have elapsed since William Baumol (1986) started the em-
pirical debate on economic convergence. Since then, dozens of researchers
ha ve taken up his lead on this and related topics, generating a vast litera-
ture of cross-country and cross- regional studies of economic growth and its
determinants. Instrumental in this development has been the appearance of
Maddison’s (1992) and Summers and Heston’s (1988, 1991, 1993) data sets
of world-wide aggregate series.
In fact, so vast has been the collective research effort on empirical
gro wth, and so intense the exploitation of the Summers and Heston data,
that there is a widespread feeling among macroeconomists that the industry
has entered the stage of maturit y.
1
In particular, few scholars believe that the
Summers and Heston data still harbor new answers to unsettled questions
on economic growth. On the contrary, on the specific issue of convergence,
the literature seems to have reached a broad consensus (a rare occurrence in
empirical macro).
Specifically, in a series of contributions that have shaped the research
agenda in growth empirics, Robert Barro (1991), together with Xavier Sala-
i-Martin (1991, 1992, 1995) and Jong-Wha Lee (1994a, 1994b) has argued
that countries converge to their steady-state level of per-capita income at a
slow rate of approximately 2 or 3% per year. In other words, the current
conventional wisdom is that each y ear an economy’s GDP covers slightly
more than 2% of its distance from the steady state.
2
This paper challenges the status quo, arguing that the existing em-
pirical literature on cross-country growth relies on inconsistent estimation
procedures. Consequently, the convergence rate and the other gro wth co-
efficients as obtained in existing contributions are unreliable. Instead, we
use the Summers and Heston (1991) and Barro and Lee (1994c) data to of-
fer an alternative, consistent estimate of the rate of convergence which is
approximately 10%.
There are two sources of inconsistency in existing cross-country em-
pirical work on growth, and almost all the studies of which we are aware are
plagued by at least one of these (the overwhelming majority b y both). First,
the incorrect treatmen t of country-specificeffects representing differences in
technology or tastes gives rise to omitted variable bias. In particular, it
is almost always assumed that such effects are uncorrelated with the other
1
“Not another growth regression!” has been more than one seminar participant’s cry.
2
See Sala-i-Martin (1994) for a survey emphasizing the “definitive” nature of the 2%
result.
1
right-hand-side variables. We show that this assumption is necessarily vio-
lated due to the dynamic nature of a growth regression.
Second, there exists a strong theoretical argument that at least a
subset of the explanatory variables should be expected to be endogenous.
Although this problem is generally recognized in the literature, few attempts
to con trol for it have been made. However, our regression and test results
indicate a strong role of endogeneity in driving standard results in growth
empirics.
We propose to solve these problems by using a panel data, general
method of moments estimator. The basic idea is the following. First, we
rewrite the growth regression as a dynamic model in the level of per capita
GDP. Second, w e tak e differences in order to eliminate the individual effect.
Third, we instrument the right-hand-side variables using all their lagged val-
ues. The last step eliminates the inconsistency arising from the endogeneity
of the explanatory variables, while the differencing removes the omitted vari-
able bias. This estimation procedure is adapted from those described in
Holtz-Eakin, Newey and Rosen (1988) and Arellano and Bond (1991).
We use this estimator to revisit two prominent lines of research in
growth empirics. First, we reconsider the empirical case for the Solow (1956)
model. We use as a bench mark the results in Mankiw, Romer and Weil
(1992), which are obtain ed by a method (ordinary least squares in a cross-
section regression) that exposes them to both omitted variable and endogene-
it y bias. We find that eliminating these biases leads to striking changes in
results. For example, Mankiw, Romer and Weil get an estimate of the capital
share in output of 0.75. Since this is too high relative to the national-account
figure of about 1/3, they reject the model in favor of an augmented version
that includes human capital in the production function. Instead, with our
procedure w e find a value of 0.10 for the capital share in the basic model.
Thus, we also reject, but for the opposite reason, namely, that the capital
share is too low. This obviously implies that we reject the augmented version
as w ell. By comparing our results to those in Knight, Loayza and Villanueva
(1993), Loayza (1994) and Islam (1995) — which, we argue, feature a correct
treatment of the correlated individual effect, but are still affected by endo-
geneity bias — we also find that both sources of inconsistency have a large
impact on standard regression results.
Oursecondapplicationisinthetradition of the “determinants of
gro wth” equations. The approach consists in regressing the growth rate of
output on a broad set of explanatory variables (including the initial level of
GDP). Although growth theory is used as a guide for the choice of possible
regressors, the specification is quite general, and cannot be interpreted as the
reduced form of a single model.
2
We take as our starting point the Barro and Lee (1994a) specification,
which can be considered the curren t bench mark in this line of research.
3
Relative to this bench mark, the new estimator involves dramatic changes
in the magnitude and sign of several coefficien ts. The most striking result
concerns the implied estimate of the convergence coefficient. As mentioned
at the outset, correcting for endogeneity and omitted variable bias induces a
jump in the estimate of convergence from 2-3% to about 10% per year.
4
The main implication of a high rate of conditional convergence is that
economies spend most of their time in a neighbourhood of their steady state.
As a consequence, we interpret the large differences in observ ed levels of per
capita GDP as arising from differences in steady-state levels, rather than
from differences in the position of countries along similar transitional paths.
We also present some evidence that substantial differences in technology may
play an important role in generating this dispersion in steady-state levels.
The finding of an extremely high rate of convergence is generally at
odds with theories of growth that do not feature a steady-state lev el of out-
put. However, this still leaves a variety of neoclassical growth models that
do feature convergence. We argue that, in general, it is difficult to recon-
cile extremely fast convergence with “augmented” versions of the production
function. In other words, our results tend to indicate that the relevant no-
tion of capital is restricted to physical capital only. On the other hand, open
economy extensions of the standard neoclassical model generally feature a
higher speed of convergence, other things equal, than their closed economy
counterparts. These considerations lead us to regard some open economy
3
The specifications in Barro and Lee (1994b) and Barro and Sala-i-Martin (1995, ch.
12) are extremely similar.
4
An independent paper b y Paul Evans (1995) shares some of the features of ours. In
particular, after emphasizing the consistency problems associated with growth regressions,
he proposes to take first-differences, and to use lagged output as an instrument. He also
finds high convergence. There are, however, important differences. First, he studies a
cross-section, rather than a panel of countries. Second, he only instruments with output
lagged one period. As a consequence, his estimates are not very precise (he reports a
confidence interval for the convergence rate of 3.15 to 100 percent a year). Third, he only
estimates an univariate regression of current on lagged output, and retrieves the coefficients
on other explanatory variables by an ad hoc procedure that, among other things, requires
him to assume that the individual effect is uncorrelated with those variables. The more
general GMM procedure we adopt does not require the individual effect to be uncorrelated
with any of the right hand side variables. Finally, Evans does not apply the consistent
estimator to the whole range of growth regressions that we present. Rather, he confines
himself to a single specification, i.e. the augmented Solow model.
3
