Do all countries grow alike?
ABSTRACT This paper investigates the driving forces of output change in 77 countries during the period 1970–2000. A flexible modeling strategy is adopted that accounts for (i) the inefficient use of resources, and (ii) different production technologies across countries. The proposed model can identify technical, efficiency, and input change for each of three endogenously determined regimes. Membership in these regimes is estimated, rather than determined ex ante. This framework enables explorations into the determinants of output growth and convergence issues in each regime.

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ABSTRACT: Recent research has shown that there is significant crosscountry heterogeneity in the previously wellestablished relationship of finance and longrun growth. We explore this heterogeneity by estimating finite mixture models and by considering the effects of foreign and domestic lending separately. We find that bank lending does not have the same effect on growth or savings in all countries. Country characteristics such as the extent of stock market development, the degree of rule of law, and even the development of the banking sector itself vary considerably across countries and affect the productivity of bank lending in encouraging growth and savings. Furthermore, the effect of bank finance on growth and the effect of foreign bank involvement depend on 1) how well developed the banking sector is, and 2) if foreign banks are involved via loans made by affiliates located within the country or via crossborder loans. The experience of lenders with a presence in the country is important, but only once a threshold level of financial sector development is reached. In countries with underdeveloped banking sectors, the influence of foreignowned lenders relative to locallyowned banks can be detrimental to growth.07/2012;
Page 1
Do all countries grow alike?☆
J.W.B. Bosa, C. Economidoua, M. Koetterb,c,⁎, J.W. Kolarid
aUtrecht School of Economics, Utrecht University, Janskerkhof 12, 3512 BL, Utrecht, The Netherlands
bUniversity of Groningen, Faculty of Economics and Business & CIBIF, 9700 AV Groningen, The Netherlands
cResearch Center Deutsche Bundesbank, P.O. Box 10 06 02, G60006 Frankfurt, Germany
dMays Business School, Texas A&M University, 4218 TAMU, College Station, Texas 778434218, USA
a b s t r a c ta r t i c l ei n f o
Article history:
Received 1 May 2007
Received in revised form 8 June 2009
Accepted 24 July 2009
JEL classification:
C33
O33
O47
Keywords:
Growth
Efficiency
Stochastic
Frontier analysis
Latent class
Regimes
This paper investigates the driving forces of output change in 77 countries during the period 1970–2000. A
flexible modeling strategy is adopted that accounts for (i) the inefficient use of resources, and (ii) different
production technologies across countries. The proposed model can identify technical, efficiency, and input
change for each of three endogenously determined regimes. Membership in these regimes is estimated, rather
than determined ex ante. This framework enables explorations into the determinants of output growth and
convergence issues in each regime.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Over the past 30 years, significant effort has focused on providing
answers as to why some countries produce more than others. Yet,
growth differentials across countries still pose a puzzle to economists.
Standard economic models imply that the output level in an economy
depends entirely on the inputs used. For example, growth empirics
typically base crosscountry regressions on a neoclassical production
function specification (Mankiw et al., 1992; Islam, 1995), often
expanded to include various sets of additional variables in an attempt
to explain economic growth.1However, considerable disagreement
remains regarding the explanatory variables to be included in the
analyses (see Temple, 1999, for a comprehensive survey). The per
ceived failure of simple textbook models has stimulated a great deal
of interest in providing alternative theories of growth. Endogenous
growth theory emphasizes factors such as increasing returns to scale,
technology spillovers, learningbydoing, and unobserved factors
(e.g., human capital), whereas the international economics literature
(Krueger, 1998; Dollar and Kraay, 2004) stresses the openness of
countries as an important conduit for growth.
This article develops a modeling strategy and presents empiri
cal evidence that provides further insights into the determinants of
nations' growth. A structural methodology is adopted that allows for the
decomposition of output change into efficiency, technical, and input
change across a large panel of developed and developing countries. The
aim of the paper is to investigate whether all countries use the same
productionfunction,thesourcesofoutputgrowth,andifthereisevidence
of convergence. Policy implications of these results are discussed also.
Traditionally, crosscountry growth empirics have assumed the
efficient use of inputs. The strong assumption that economic units
(countries) are always efficient (i.e., they always produce at the pro
ductionpossibilityfrontier)impliesthatactualoutputisthemaximum
attainable output and that all countries are equally productive for a
given level of inputs. In reality, however, economic units may use the
bestpractice (frontier) technology with varying degrees of efficiency.
Journal of Development Economics 91 (2010) 113–127
☆ We thank Bill Greene, Subal Kumbhakar, Clemens Kool, Bart Los, Luis Orea, Mark
Sanders, Spiro Stefanou, and Marcel Timmer, as well as seminar participants at Utrecht
School of Economics and participants at the European Workshop on Efficiency and
Productivity Analysis in Lille, for their valuable discussions. We are grateful for helpful
comments and advise received by an anonymous referee and the editor, Lant Pritchett.
Michael Koetter acknowledges financial support from the Netherlands Science
Foundation NWO (VENI grant 016.075.164). The opinions expressed are those of the
authors. The usual caveat applies.
⁎ Corresponding author. University of Groningen, Faculty of Economics and Business
& CIBIF, 9700 AV Groningen, The Netherlands.
Email addresses: j.w.b.bos@uu.nl(J.W.B.Bos),c.economidou@uu.nl(C.Economidou),
m.koetter@rug.nl (M. Koetter), jkolari@tamu.edu (J.W. Kolari).
1See Barro (1991), Levine and Renelt (1992), Persson and Tabellini (1994) and
others.
03043878/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jdeveco.2009.07.006
Contents lists available at ScienceDirect
Journal of Development Economics
journal homepage: www.elsevier.com/locate/devec
Page 2
As a result, parameter estimates for the marginal effects of inputs are
biased in the presence of inefficiency. Efficient countries may increase
their output through technical change (i.e., shift of the frontier),
whereas inefficient countries may increase output by becoming more
efficient through the use of the bestpractice technology.
Here, we account for inefficiency and estimate a stochastic pro
duction frontier, which is the empirical analog of the theoretical
production possibility frontier. This modeling strategy therefore adds
structure to the unexplained residual. Under reasonable assumptions,
it disentangles the residual into inefficiency and measurement error.
Given this framework, we can decompose output changes into three
typesofchange: technical change(i.e.,shiftsof thefrontierovertime),
efficiency change (i.e., movements of a country toward or away from
the frontier), and input change (i.e., scale elasticityadjusted changes
in factor use).
A growing body of recent empirical literature has conducted ef
ficiency analyses along lines similar to that we propose in this paper,
but has used different modeling approaches. Previous studies have
decomposed output change into technical, efficiency, and input change.
For instance, Färe et al. (1994) use data envelopment analysis (DEA),
while Koop et al. (1999, 2000) and Limam and Miller (2004) apply
stochastic frontier analysis (SFA) to examine countryspecific ineffi
ciency in a number of developed and developing countries.2However,
not all countries necessarily share a single common frontier.3With
the exception of a handful of studies that allow for parameter hetero
geneity when estimating frontier production functions, the frontier
literature has largely ignored this issue.
Similarly, conventional crosscountry growth empirics mainly
examine the ‘average’ country (Temple, 1999) via a universal growth
model that governs the (per capita) output evolution in all countries.
However, if growth patterns diverge across countries, the ‘average’
country is not representative, parameter averages are less informative
about the factors that matter for a particular country (Solow, 1994),
and no country benefits from onesizefitsall policy recommenda
tions. More generally, the validity of treating all countries as a single
homogeneous group, for which the same variables have the same
effect on economic growth, seems increasingly questionable (see
Brock and Durlauf, 2001 for an extensive discussion of this issue).
In response to these concerns, a range of methodologies have been
proposed. For example, Durlauf and Johnson (1995) employ classifica
tion and regression tree analysis, which identifies threshold values
in particular economic variables (e.g., output per capita, adult literacy
rates, etc.), to determine the appropriate grouping of countries.4Rather
than classifying countries ex ante into various groups on the basis of
geographic location or threshold values of particular economic var
iables, Paap et al. (2005) and Davis et al. (2007) apply latent class
models that sort countries into different growth regimes according
to the similarities of their economic growth rates. They find that a
model with three and four groups of countries, respectively, is sta
tisticallysuperiortoamodelthatassumeseconomiesarehomogeneous.
To improve the country classification, Davis et al. (2007) explore the
conditional (i.e., on institutions, openness, and macroeconomic policy)
distribution of countries' growth rates.
Some authors in the frontier literature have attempted to account for
heterogeneity in growth patterns. In exploring the sources of output
differentialsina panelofdevelopedanddevelopingcountries,Koopetal.
(2000) and Limam and Miller (2004) controlled for the quality of
productionfactorsusingeffectivelaborandcapital,insteadofactuallabor
and capital, and estimate regional frontiers.5The geographic division of
the sample is to a certain degree subjective, as some authors readily
admit,andmodelsmaybepoorlyidentifiedbecauseofthelackofdatafor
some regions such as Africa and Asia (see Koop et al., 2000, pages 286–
287). Tsionas and Kumbhakar (2004) instead proposed a stochastic
frontier production function augmented with a Markov switching
structure to account for different technology parameters across hetero
geneous countries. Technology group membership depends on priors in
their Bayesian framework. Others, for example Koop et al. (2000),
critically view forming technology club memberships based on priors.
In this paper we allow for heterogeneous growth experiences.
Whereas most studies that classify countries apply an ex ante sorting
based on characteristics such as income and geography, we endogen
ize the sorting of countries using a latent class model. The latent class
approachsupposes a simple parametric model and uses observed data
to estimate parameter values for each regime in the model. Among
the parameters estimated is the probability that a certain country in
a particular time period is a member of one of the regimes. These
probabilities result from a (multinomial logit) sorting equation and
depend on observable characteristics. In our case these characteristics
are conditioning variables common to the growth literature (Durlauf
and Johnson, 1995; Koop et al., 2000; Papageorgiou, 2002; Davis
et al., 2007) — namely, the level of human capital, openness to trade,
financial development andtheprimarysector share.We thusestimate
a regimespecific coefficient for each production factor. Each regime
exhibits ‘conditional independence’ because each variable is statisti
cally independent of every other variable.
Hence, we advance methodology by introducing a structural and
flexible model that allows simultaneously for (i) the inefficient use
of resources, and (ii) different technologies across countries. We
augment the stochastic frontier production model with a latent class
structure, as proposed by Greene (2002a) and Orea and Kumbhakar
(2004). Using regimespecific production parameters, we identify
technical, efficiency, and input growth for endogenously determined
regimes. We introduce additional flexibility into the model by per
mitting countries to switch between regimes over time. The efficiency
of countries in different regimes is estimated simultaneously but
relative to each regime's specific frontier. The latent class stochastic
frontier model enables us to avoid the routinely imposed assumption
of a common production function for all countries but yields results
that are comparable across countries at a given point in time.
Our work relates to and extends several important studies. Paap
et al. (2005) and Davis et al. (2007) also apply latent class models
to investigate growth experiences across a panel of countries. We
extend their work by accounting for the inefficient use of resources
2Various studies also investigate the role of efficiency in explaining growth
differentials for a panel of manufacturing industries in OECD countries. See, for
instance, Koop (2001) and Kneller and Stevens (2006).
3Theoretical contributions (Basu and Weil, 1998; Acemoglu and Zilibotti, 2001))
stress the ‘appropriateness’ of technology, suggesting that countries choose the best
technology available to them, given their input mix. On empirical grounds, a number
of works have emphasized that labor and capital cannot be equally productive in all
countries (Trefler, 1993; Tallman and Wang, 1994; Auerbach et al., 1994). Countries
are members of the same technology class if their marginal productivity of labor and
capital (the technology parameters that characterize the efficient production frontier)
are the same for a given level of inputs such that their input/output combinations can
be described by the same production frontier (Jones, 2005).
4A number of studies continue in this tradition. Papageorgiou (2002) extends the
work of Durlauf and Johnson (1995) by exploring whether trade can be used as a
threshold variable. Desdoigts (1999) proposes clusters based on culture, geographic
location, and OECD membership. Hobijn and Franses (2000) use a clustering method
as well, and find an abundance of convergence clusters. More recently, Bloom et al.
(2003), Canova (2004), and Sirimaneetham and Temple (2006) explore the existence
of multiple growth regimes. For instance, Sirimaneetham and Temple (2006) sort
economies into groups according to the value of an index of policy quality. Bloom et al.
(2003) argue that geographical variables determine the likelihood that a country will
be assigned to the two regimes they find. Canova (2004) takes a Bayesian approach to
examine income levels in Europe and, using initial income as a splitting variable, finds
four groups of countries.
5Koop et al. (2000) use the years of schooling embodied in the workforce to correct
for labor and agriculture and industry labor force participation to correct for physical
capital. They also allow for four different production frontiers: one for western
industrialized economies, one for East Asia, one for Latin America, and one for Africa.
Limam and Miller (2004) use the mean years of education and average age of physical
capital to account for quality of labor and physical capital, respectively. Like Koop et al.
(2000), they allow for heterogeneity by estimating regional frontiers based on five
geographic divisions: Africa, East Asia, South Asia, Latin America, and the West.
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 3
and allowing countries to change regimes. In relation to the frontier
literature, particularly studies by Koop et al. (1999, 2000), Koop
(2001), Limam and Miller (2004), Tsionas and Kumbhakar (2004),
and Kneller and Stevens (2006) which control for heterogeneity in
growth patterns across countries, we further account for heteroge
neity in the growth patterns of countries without following ad hoc
or a priori clustering. Instead, we endogenize the regime allocation
by applying a latent sorting, conditioned on growth determinants
commonly used in prior literature.
Our empirical analysis is based on a sample of 77 countries during
the period 1970–2000, whereas similar studies generally examine
fewer countries over a shorter time span (Koop et al., 1999, 2000;
Koop, 2001; Limam and Miller Koopy, 2004; Tsionas and Kumbhakar,
2004;Paap et al., 2005; Kneller and Stevens 2006; Davis et al., 2007).
We proceed with our empirical analysis with three primary questions
in mind: (i) Do all countries follow the same growth experience?;
(ii) What are the sources of growth?; and (iii) What economic theory
provides a reasonable description of the growth processes?
Our results are easy to summarize. We find no evidence that
countries follow a common growth process, nor do we find that the
growth process of each country is entirely unique. Rather, we identify
three distinct growth processes or growth regimes. First, the mature
regimewithmostobservations,whichhostsmanyEuropeancountries
and the United States is characterized by high human capital ac
cumulation. Second, the emerging regime, which contains many
Asian countries, is characterized by a relatively high level of financial
development. And third, the developing regime with many African
countries is characterized by a large primary sector share and high
degree of openness. Almost all regimes include countries from var
ious geographical regions and/or income groups. Therefore, assigning
countries ex ante to certain groups based on their income or regional
criteria is not appropriate. We do find, however, that many countries
from the same region or with the same development level cluster in
the same regime.
Efficiency is economically and statistically important. Whereas the
neoclassical paradigm assumes that countries are fully efficient, we
demonstrate the fallacy of this assumption, since efficiency levels vary
across regimes. We find countries that belong in the emerging regime
exhibit the highest level of efficiency, whereas the least efficient
countries tend to be members of the developing regime.
The driving forces of growth also vary across and within regimes.
A consistent finding across all regimes shows that input accumulation
is an important source of growth, a finding we share with Koop
et al. (1999, 2000) and Limam and Miller (2004), among others. Our
findings suggest that countries' growth patterns do not necessarily
support just one growth explanation, such as the input accumulation
view or the productivity view. Instead, explaining countries' growth
performance requires a more pluralistic interpretation.
Countries can grow within a regime bycatchingup withthefrontier
(convergence) or migrating to a better regime (switching). Our results
showthatwiththeexceptionoffewcountries,regimeallocationisfairly
stable,andcountrieschangeonlyrarelyacrossregimes.Mostmigrations
pertain to countries switching between the mature and the emerging
regime. With regard to convergence, we find strong evidence of ‘con
vergence clubs’ as different regimes converge at different rates to their
regime's steady state.
Overall, many of our findings could not have been obtained using
traditional approaches, such as imposing constant returns to scale,
ignoring inefficiency, assuming a single, common production func
tion. By adopting a flexible modeling approach, we gain additional
insightsinto policiesthatshouldfostergrowth.We findno support for
the onesizefitsall policy. More education alone, for instance, may
put countries in more advanced regimes, but for education to be
effective it needs the support of other development measures, such as
enhanced factor allocation, financial development, and trade policies.
The presence of significant inefficiency in one of the regimes fur
ther suggests that development policies geared toward a better ex
ploitation of existing technologies, rather than promoting technical
advances to push the production possibility frontier, might be bene
ficial for some countries.
The remainder of this paper proceeds as follows. Section 2 pre
sents the methodology and the econometric specification for esti
mation. Section 3 discusses the data. Empirical results are presented
in Section 4. Section 5 concludes.
2. Methodology
We first introduce a model of production that accounts for in
efficiency. We then augment the model with a latent class structure to
allow for more than one type of production. Finally, we decompose
the output change for each regime into technical, efficiency, and input
change.
2.1. A Stochastic frontier model of production
We model the performance of countries using a stochastic frontier
production model.6A frontier production function defines the maxi
mum output attainable, given the current production technology and
available inputs.
If all industries produce at the boundary of a common production
set that consists of an input vector with two arguments, physical
capital (K) and labor (L), output can be described as:
YitT= f Xit;t;β
ð Þexp vit
f g;
ð1Þ
where Yit⁎ is the frontier (optimum) level of output in country i at
time t; Xitis the vector of inputs, namely, physical capital, Kit, and
labor, Lit; f and the parameter vector β characterize the production
technology; t is a time trend variable that captures neutral technical
change (Solow, 1957); and vitis an i.i.d. error term distributed as N(0,
σv
TwoaspectsofEq.(1)areworthnoting.First,thefrontierrepresents
a set of maximum outputs fora range of inputvectors. Therefore,at any
moment in time, it is defined by observations from multiple countries,
not just one. This definition differentiates our modeling approach from
conventional empirical growth approaches in which the leader country
achievingthe highestleveloftotalfactor productivity (TFP), constitutes
the frontier (Bloom et al., 2002; Cameron et al., 2005). An implicit but
nontrivial assumption in this literature suggests that technical progress
is described by the observations of a single country over time. Second,
ourmodelingapproach treats thefrontierasstochastic byincluding the
error term vit, which accommodates noise in the data and therefore
allows for statistical inference. In this respect, it fundamentally differs
from other (nonparametric) frontier industrylevel analyses (Färe
etal.,1994;KumarandRussell,2002;LosandTimmer,2005)thatdonot
allow for random shocks around the frontier.7
Some countries, however, may lack the ability to employ existing
technologies efficiently and subsequently produce less than the fron
tier output. If the difference between optimum and actual (observ
able) output is represented by an exponential factor, exp{−uit}, then
the actual output, Yit, produced in each country i at time t can be
expressed as a function of the stochastic frontier output, Yit=Yit⁎exp
{−uit}, or equivalently:
2), which reflects the stochastic character of the frontier.
Yit= f Xit;t;β
ð
where uit≥0 is assumed to be i.i.d., with a halfnormal distribution
truncated at zero, N(0, σu
Þexp vit
fgexp −uit
fg;
ð2Þ
2), and independent from the noise term,
6Stochastic frontier analysis (SFA) was introduced by Aigner et al. (1977), (Battese
and Corra (1977), and Meeusen and van den Broeck (1977).
7For comprehensive reviews of frontier methodologies, see Kumbhakar and Lovell
(2000) and Coelli et al. (2005).
115
J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 4
vit.8Efficiency, exp{−uit} is measured as the ratio of actual over
maximum output, exp −uit
f
{−uit}=1 implies full efficiency.9
A country is inefficient if it fails to absorb the bestpractice tech
nology. In this way, our approach is comparable to conventional, non
frontier studies (Bernard and Jones, 1996a,b; Cameron et al., 2005)
that measure impediments to the absorptive capacity using TFP
changes. However, in these frameworks TFP changes cannot be sep
arated into technical change and efficiency change (Kumbhakar and
Lovell, 2000). In addition, most studies assume a single technology
attainable by all countries in the sample. Instead, we explicitly model
the possibility of different technology regimes.
g =
Yit
YitT, where 0≤exp{−uit}≤1, and exp
2.2. Latent classes
Existing literature has proposed a range of methods to tackle
heterogeneity in countries' growth experiences. A common approach
is to include country fixed effects and dynamic panel data analyses
(Islam, 1995). Although this approach controls for differences in
average growth rates, it fails to control for differences in the marginal
effects of the regressors. An alternative approach identifies groups of
countries with similar growth behavior — for instance, similar income
(Auerbach et al., 1994) or human capital levels (Durlauf and Johnson,
1995) or degrees of openness (Papageorgiou, 2002), or the same
geographiclocation (Koopet al.,2000;LimamandMiller, 2004) — and
then estimates the production functions for each cluster of countries
separately.
Our approach diverges from these studies in that we endogenize
the classification of countries into different classes (regimes) using
a latent class model. The latent class approach employs a simple
parametric model to estimate regimespecific parameters of the
model.10The probability that a country belongs to a particular regime
can be calculated from a (multinomial logit) sorting equation and
depends on observable characteristics. In line with the economic
growth literature, we distinguish between four conditioning variables
that may sort countries into different groups, which we specify in
vector V. Human capital, openness to trade, financial development,
and the share of primary sector are growth determinants that may
affect factor accumulation, efficiency change, or technical change that
are parameters in the frontier production model.
Human capital affects output through various channels.11Human
capital contributes to factor augmentation. Barro (1991), for instance,
argues that a significant part of the effect of human capital on growth
is channeled through an increase in the investment rate for physical
capital.12Human capital also enhances the effectiveness of the work
force, as it enhances the ability of the latter to learn, absorb, and work
with new technologies created by innovation efforts, thus contribut
ing to the absorptive capacity of the economy (Abramovitz, 1986;
Benhabib and Spiegel, 1994). Furthermore, it accounts for aspects of
innovation not captured by the innovation sector (e.g., R&D), in
cluding ‘learningbydoing’ and ‘onthejobtraining’ (Romer, 1989;
Redding, 1996). Therefore, human capital can affect the inputs of
production, physical capital, and labor, as well as efficiency (through
absorption of existed advanced technologies) and technical change
(through innovation), which in turn influence the economic perfor
mance of a country.
Another important conduit of growth is international trade.13
Openness to trade promotes the efficient allocation of human and
capital resources through comparative advantage and increases their
productivity. It further facilitates the dissemination of knowledge
and technological progress.14In particular, exporting may involve
some learning effects due to exposures to international contacts with
buyers and customers. These effects likely foster knowledge and
technology spillovers, such as access to technical expertise including
new product designs and new production methods.15Imports of qual
ity foreign capital goods also serve as a means to acquire foreign
technology through reverse engineering.16Therefore, we include
opennessto tradein our analysisas a latentregimemembershipprob
ability determinant.
Financial intermediaries shape the economic performance of a
countrybychoosingwhichfirmsgettousethesociety'ssavings.Awell
developed financial sector can increase the marginal productivity of
capital by allocating funds to the projects for which the marginal
product of capital is highest by collecting information to evaluate
alternative investment projects (Greenwood and Jovanovic, 1990) and
by inducing investors to invest in riskier but more productive tech
nologies via risk sharing (Schumpeter, 1934; Pagano, 1993). In the
absence of banks, households can guard against idiosyncratic liquidity
shocks only by investing in productive assets that can be promptly
liquidated, which causes them to forgo investments that are more
productive but also more illiquid. This inefficiency can be considerably
reduced by banks, which pool the liquidity risk of depositors and invest
most of their funds in more illiquid and more productive projects.17
Because it affects the productivity of inputs, efficiency, and technical
change in an economy, we also include financial development as a
latent regime membership probability determinant.
Finally, inefficient factor markets may affect the growth perfor
mance of a country. To understand why, consider dual economy
effects. The marginal product of similar factors may not be equal
within a country due to reallocation impediments, such as labor in
an agricultural sector, which typically is less than perfectly mobile.
Vollrath (forthcoming) and Temple (2005) argue that the primary
sector share can affect growth in (at least) two ways. First, a large
primary sector can negatively affect growth if labor productivity is
low in this sector. The same influence may hold for its effect on (labor
augmenting) technical change. Second, a high primary sector share
increases the effect of reallocation impediments and thereby reduces
the efficiency with which countries produce. Therefore, we let a
country's group membership be codetermined by sectoral structures
when estimating factor shares and, more important, groupspecific
technical inefficiency levels.18
8We decompose the residual in Eq. (2), exp{vit}exp{− µit}, and identify its
components, exp{vit} and exp{− uit}, by reparameterizing λ in the maximum
likelihood procedure, where λ(= σu/σv) is the ratio of the standard deviation of
efficiency over the standard deviation of the noise term, and σ (= (σu
composite standard deviation. The frontier can be identified by the λ for which the log
likelihood is maximized (see Kumbhakar and Lovell, 2000).
9Countries also may be inefficient if they use an input mix for which the prices of
inputs are not equal to the marginal returns to these inputs. Measuring this ‘allocative’
efficiency requires accurate input price data, which are particularly difficult to measure.
Therefore, we do not consider allocative efficiency and use the term efficiency only to
refer to technical efficiency.
10Throughout this paper, we use the terms ‘class’ and ‘regime’ interchangeably.
11Ontheeffectofhumancapitalongrowth,seeNelsonandPhelps(1966),Abramovitz
(1986), Lucas (1988), Romer (1989), Benhabib and Spiegel (1994), and (Cameron et al.,
2005).
12This evidence receives further support from Krueger and Lindahl (2001), and
Cannon (2000).
2+σv2)1/2) is the
13Classical references include BenDavid and Loewy (1998), Edwards (1998), and
Frankel and Romer (1999).
14These arguments are illustrated in the endogenous growth models offered by
Young (1991), Grossman and Helpman (1991), and Eicher (1999).
15For instance, the purchase of an input requires some degree of customization or
extended coordination between the seller and the buyer. Pack and Saggi (2001)
develop a model in which the sellers have an incentive to provide technology to
buyers, even if that technology may spill over to other sellers and buyers.
16When countries successfully imitate highquality imported goods, they gain more
insight into how these goods are engineered and how to improve them. Connolly
(1998) discusses this ‘learningtolearn’ effect.
17For empirical evidence, see King and Levine (1993), Easterly (1999), and Beck et al.
(2000), among others.
18We thank the editor for suggesting the primary sector share as a latent regime
membership probability determinant.
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 5
In our empirical specification, human capital (H), openness to
trade (T), financial development (F), and the primary sector share (P)
condition the allocation of countries to a specific regime. Within each
regime, countries share the same set of parameters, as in Eq. (2).
However, each regime also has its own set of parameters. Note that
conditioning group membership on this vector V affects all parts of
the growth decomposition for three reasons. First, countries are now
compared to the frontier of ‘their’ estimated peer group and thus
likely to be more efficient compared to a single frontier approach.
Second, factor elasticities of both capital and labor will be different
since the slope of regimespecific production frontiers will differ in V
too. Third, each frontier can now shift at their own pace, thereby
allowing for different technical change per regime. To estimate Eq. (2)
we must specify the functional form of the production frontier.
Specificationtestsfavoratranslogspecificationproductionfunction.19
In turn, for a translog specification with a general index of technical
change specified by means of time dummies Dt (see Baltagi and
Griffin, 1988) and regimes z(=1,..,Z), we can write a latent class
stochastic frontier as:
lnYit= βz+ β1jzln Kit+ β2jzln Lit+1
+1
2β22jzlnL2
+ δktjzln KitDt+ δltjzlnLitDt+ vitjz− uitjz′
2β11jzln K2
it
it+ β12jzln KitlnLit+ γtjzDt
ð3Þ
To operationalize Eq. (3), we must allocate each observation it
to a regime z. This is done by first making the contribution of each
observation to the likelihood function conditional on its regime mem
bership. The unconditional likelihood then can be averaged over the
latent classes using the prior probability of membership in a class
(regime) as weights of the membership in class z.
In our conditional latent class frontier model, regime membership
probability conditional on the vector V (consisting of the four con
ditioning variables, H, F, T, and P) determines regime membership.
Greene (2005) shows these conditional probabilities can be estimated
using a multinomial logit model:
θit=
exp Vitθz
ð
z = 1exp Vitθz
Þ
PZ
ðÞ;
ð4Þ
where θ measures the odds of belonging to regime z, conditional on
the values of the set of conditional variables Vit.
The resulting system of Eqs. (3) and (4)) is estimated by maxi
mizing iteratively back and forth between posterior group probabil
ities from Eq. (4) and the (weighted) loglikelihood function used to
estimate Eq.(3).20The likelihoodmaximization in Eq. (3) dependsnot
only on inputs and outputs per industry but also on efficiency (λ and
σ). Therefore, in contrast to a priori clustering on the basis of some
individual proxy, both the technology parameters β and efficiency u
can be determined endogenously through latent sorting into Z classes.
In summary, we redefine the production frontier as a latent class
frontier characterized by a system of equations: Z stochastic production
frontiers and a multinomial logit model with conditioning variables
(human capital, openness to trade, financial development, and the pri
mary sectorshare)that accounts for the sorting (of countries) into each
of the Z regimes.
An important feature that distinguishes our modeling approach
from previous latent class studies (Greene, 2002a,b, 2005; Orea and
Kumbhakar, 2004) is that we allow countries to switch regimes over
time. For our sample of 77 countries observed over a maximum of
31 years, we define six different time periods: 1970–1974, 1975–
1979, 1980–1984, 1985–1989, 1990–1994, and 1995–2000. Eqs. (3)
and (4)) are estimated on annual data, and observations for some
years may be missing. Within each period, observations per country
are not independent because the country must fall within one of
the regimes during that period, and the probability of being in a
regime depends on the average of the variables used to estimate
regime membership.21However, across periods, observations on a
single country are treated as independent. For example, n moving
from t=5 (the last year of the period 1970–1974) to t=6 (the first
year of the period 1975–1979), a country is treated as a different
i in our panel dimension it and can switch regimes.
The advantage of this approach is that a country can be in one
regime in one period and in another regime next period.22As a result,
the regime allocation of a country is not restricted, and a country's
allocation in a given period is independent of its allocation in other
periods.This flexibilityadds an importantdimension toour analysisof
the components of countries' growth in that we can study regime
migrations. We turn next to decomposing output growth for different
regimes.
2.3. Decomposing output growth
A key aim of this paper is to relate our results to some of the major
macroeconomic debates about why and how some countries grow
faster than others. We therefore decompose output growth for each
regime into three components: input growth, represented by move
ments along the frontier; technical growth, reflected by shifts of the
production frontier; and efficiency growth, captured by movements
toward (or away from) the production frontier as countries absorb
and implement bestpractice technologies and reduce (or increase)
technical inefficiencies.
We take logs and totally differentiate Eq. (2) with respect to time,
which yields a convenient expression of output growth for every
regime, z:
gr Yit
ðÞ =
:Yit
Yit
=Aln fit
At
−Auit
At
+ eK
it
:
Kit
Kit
+ eL
it
:
Lit
Lit
;
ð5Þ
where εit
output with respect to the inputs, physical capital and labor,
respectively, and the dotted variables refer to time derivatives.23
The first term,Alnfit
where TCit>0 indicates an upward shift of the production frontier
(technical progress). Technical change can be attributed to capital
change (TCit
inputs in the form of pure technical change (TCit
−Auit
represents a reduction in inefficiency. Because we allow inefficiency
to vary freely over time, the time evolution of our efficiency term is
Kand εit
Ldenote the partial elasticity of the stochastic frontier
At, corresponds to technical growth, TCit=
Aln fit
At,
K) or labor change (TCit
L), or it may be independent of the
P). The second term,
Auit
At, corresponds to efficiency change, ECit= −
At, where ECit>0
19We test whether a translog is preferable to a Cobb–Douglas specification, which
appears in most prior literature. Our tests (see Section 4.1) support a translog
specification. Estimations of specifications with more flexible functional forms (Fourier
flexible) suffered from multicollinearity problems.
20The likelihood function is LF i;tjz
1
σzϕ
σj
and ϕ and Φ are the probability density and cumulative distribution functions of
standard normal distribution, respectively (see Greene, 2005).
ðÞ = f YitjKit;Lit;t;βz;δz;σz;λz
ðÞ =Φ λjeitjz
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
??
Φ 0
ð Þ
eitjz
??
, where ɛitz=Yitz − f(Kitz, Litz, t; βz), λz=σujj
σvjz, σz=
σ2
ujz+ σ2
vjz
q
,
21In this modeling approach the allocation of a country in a regime in a specific
period depends on the period averages of the conditioning variables. We consider this
to be in line with theory, as we expect the allocation of a country in, for example, the
period 1990–1994 to depend on the average level of human capital (and the other
conditioning variables) in that period, rather than the initial level in 1970.
22Orea and Kumbhakar (2004) also propose a latent class frontier model. The subtle
difference between the models of Greene (2002a,b, 2005) and that of Orea and
Kumbhakar (2004) is described by Orea and Kumbhakar (2004, p.172). In the latter,
the log density (likelihood function) for an individual (or a country, here) is defined as
the same over all time periods in the model. In contrast, it defined for each individual
at each time t in the model of Greene (2002a,b). To allow countries to switch regimes,
we use the latent class model specified by Greene (2002a,b, 2005).
23For clarity, we delete the latent regime subscript z in this section.
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 6
not captured by a specific functional form (see Jondrow et al., 1982).
We approximateAuit
last two terms, ek
it it
ICL
itit
factor accumulation or changes in input factor elasticities. For example,
if a country exhibits constant returns to scale, changes in the level of
input factors do not influence the rate of change of output growth. If
laborexhibits,forexample,increasingreturnstoscale
anincreaseinthelaborforce
Lit
of output growth.
Table 1 summarizes the output growth decomposition for every
regime, z, based on the production function specified in Eq. (3).
Atby the growth rate of uitover time (uit− uit − 1
:
Kit
Kit+ el
:
Lit
Lit. The input change can vary for two reasons: pure
uit − 1
). The
it+
:
Lit
Lit, capture the input change, ICit= ICK
it= ek
:
Kit
Kit+ el
Aln f K;L;t;β
ð
AlnLit
Þ
??
= 1,
:
Lit
??
0 furtherincreasestherateofchange
3. Data
Our sample consists of 77 countries over the period 1970–2000.
The countries included in our sample are listed in Table A.3 in the
Appendix A. Annual data are retrieved from various sources. Output
(Y), measured as real gross domestic product (GDP), is constructed
from the Penn World Tables, version 6.1 (PWT 6.1), by taking the
product of the real per capita GDP, measured in 1996 international
purchasing power parity (PPP) dollars (chain index) and the national
population numbers. Labor force (L), measured in millions, is also
taken from the Penn World Tables. The computation of capital stock
(K) series, in 1996 international PPP dollars, follows the perpetual
inventory method in Hall and Jones (1999).24
To estimate the number of regimes and respective membership
probabilities, we rely on four conditioning variables commonly used
in the economic growth literature. Data on human capital (H), mea
sured as the average years of education of the population that is
at least 25 years old, are retrieved from Barro and Lee (2001).25
Openness to trade (T), measured as the sum of exports and imports
relative to GDP, is obtained from the World Bank World Development
Indicators (2006). From the samedata source,we retrieve the primary
sector share (P) relative to total GDP. Finally, as a proxy for financial
development (F), we use the amount of deposits held in the financial
systemas a percentage of GDPprovided in Beck et al. (2000).26Table 2
contains the descriptive statistics.
4. Results
First, we examine whether there is a single production function.
That is, we test whether there is one universal model that can
adequately describe the growth experience of all countries. Second,
we present a tripartite output growth decomposition for countries
with similar growth experiences, according to their identified regime.
We relate these results to macroeconomic debates about whether
input accumulation or productivity drives output growth and to the
convergence hypothesis.
4.1. Is there a universal production function?
We start by investigating whether countries in our sample can be
described by a common production function. In estimating the latent
class frontier model defined by Eqs. (3) and (4), we first must
determine the number of regimes, Z. Multiple regime endogenous
growth models (Azariadis and Drazen, 1990; Kejak, 2003) merely
suggest the possibility of multiple steady states or growth regimes,
without being explicit about the exact number of regimes. Without
theoretical guidance into the ‘optimal’ number of regimes, we must
rely on statistical methodologies. We determine the number of re
gimes in our preferred specification by following the suggestions
provided by Orea and Kumbhakar (2004) and Greene (2005).
We formally test for the optimal number of regimes, Z, using log
likelihood ratio tests and the Akaike and Schwartz Bayesian
information criteria (AIC and SBIC, respectively), as we outline in
Table A.1 in the Appendix A. The preferred specification has the
highest loglikelihood value and the lowest AIC or BIC values. The test
results in Table A.1 favor a specification with three regimes over those
specifications with two.27Hence, our conditional latent class model
defined by Eqs. (3) and (4) supports the existence of three regimes.28
Table 3 below contains the estimated parameters for the translog
production function with a time trend (top panel), efficiency param
eters (middle panel) and membership probability parameters (bot
tom panel) for each of the three regimes we identify: emerging (A),
mature (B) and developing (C). Before explaining in subsequent sec
tions in greater detail the growth process and further characteristics
that give rise to this taxonomy, we test whether the parameter esti
mates differ significantly across regimes using Wald tests for joint
equality across regimes (A, B and C) (see the top panel of Table A.2
Table 1
Decomposition of output growth.
:
Yit
Yit= TCit+ ECit+ SCit
TCit= TCP
TCK
TCL
TCP
ECit= −
ICit= SEK
ICK
it
ICL
it
it+ TCK
it+ TCL
it
it= δktlnKit
it= δltlnLit
it= γt
uit− uit −1
uit −1
it+ SEL
it= ek
it= el
it
K̇it
Kit;where eK
L̇it
Lit; where eL
it= β1+ β11lnKit+ β12lnLit+ δktDt
it= β2+ β22lnLit+ β12lnKit+ δltDt
24We use a depreciation rate of 6% and the average growth over the first 10 years to
determine a countryspecific average growth rate. For robustness we also calculate a
backwardlooking capital stock using data from 1960 onwards. The results are
qualitatively similar. Our capital stock series has wider coverage than the PWT 6.1
variable for capital stock per worker, which is only available for 62 countries after
1965. When the two series overlap, the correlation coefficient between their log levels
is 0.97.
25Workers in different countries have different levels of skills. Typically, these skills
develop through education and experience. The lack of data about the latter prompts
us to measure education according to the years of schooling embodied in the labor
force. Given missing annual data, we use a linear interpolation per year. Assuming that
human capital is constant per fiveyear period does not change the results
qualitatively.
26See Beck et al. (2000) on February 21, 2006.
Table 2
Descriptive statistics.
MeanStd. dev.
Output (Y)
Capital (K)
Labor (L)
Human capital (H)
Openness to trade (T)
Financial development (F)
Primary sector share (P)
250.332
69.429
16.474
5.444
62.730
38.072
13.768
737.888
221.566
42.174
2.834
38.574
27.610
11.972
There is 1913 observations for 77 countries between 1970 and 2000.
27Three is a maximum number of regimes at which neither multicollinearity nor
over specification prohibits convergence of the maximum likelihood estimator. An
unconditional threeregime specification without further group determinants Z is
rejected, as are the Cobb–Douglas and translog specifications with a linear time trend.
These results are available on request.
28In response to comments of an anonymous referee, we also specified a latent class
model with the conditioning vector, V, as part of the deterministic kernel of the latent
class model, similar to some crosscountry growth regression literature in which
explanatory variables such as human capital, openness to trade, and financial
development enter directly into the production function. Just as the additional
interaction of time and squared terms discussed before, this specification suffers from
over identification, multicollinearity, and convergence problems and therefore cannot
be estimated.
118
J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 7
in the Appendix A). Low pvalues less than 1% demonstrate that
parameters are jointly significantly different across the three regimes.
However, statistically significant differences for the parameters
in the production function are insufficient to assess whether the
specification of multiple regimes with their own production frontiers
is important for analyzing the output growth of countries. The middle
panel of Table 3 shows that inefficiency matters too. For regime C, the
efficiency parameter, λ(=σu/σv, the ratio of the standard deviation of
efficiency over the standard deviation of the noise term), is 2.053 and
significant at the 1% level. As such, inefficiency is approximately twice
as great as noise in this regime. The same result holds for regime B,
where inefficiency is oneandahalf times times the size of noise (λ
is 1.525) and significant at the 1% level. In regime A, however, the
production process is fully efficient, as exemplified by the insignifi
cance of λ.
Finally, the bottom panel of Table 3 demonstrates the importance
of the conditioning variables. The use of a multinomial logit spe
cification implies an estimation of membership likelihood relative to
the reference group, orregime C here. Financialdevelopment, primary
sector share, and openness to trade have significant effects on the
probability of belonging to regime A. For regime B human capital,
primary sector share, and openness to trade are significant. For
example, an increase in financial development (human capital) of 1%
increases the probability of belonging to regime A (B) by 1.04%
(1.53%).29Wald tests (see the bottom panel of Table A.2 in the
Appendix A) show that the joint effect of a change in all four regime
determinants on the probability of belonging to regime A differs from
its effect on the probability of belonging to regime B. However, the
coefficients for human capital and the primary sector share are not
significantly different between regimes A and B. Financial develop
ment, in turn, is critical distinguishing between regimes A and B. The
effect of financial development on regime A membership is both
higher and more significant. These results confirm the importance
of the mix of regime determinants. Individual determinants (e.g.,
financial development) may be important, but the interaction be
tween regime determinants is especially crucial to identify relevant
peer groups of countries.
To explore differences among the three regimes further, we
present each regime's factor elasticities, εit
estimates, uit, and the marginal rate of technical substitution, MRTS, in
Table 4.
As Table 4 clearly shows, there are differences between regimes A
and B on the one hand and regime C on the other. The latter regime,
which is the smallest in terms of number of observations, has all the
characteristics of a less developed regime. Average inefficiency is
more than 10%, and the productivity of capital, as measured by the
capital elasticity (εit
with a very low marginal rate of technical substitution. Regime A
exhibits the highest labor elasticity and is almost 100% efficient.
Capital elasticity is highest in regime B, which also has the highest
marginal rate of technical substitution. The differences in factor
elasticities across regimes are also statistically significant, as shown in
the middle panel of Table A.2 in the Appendix A.
The relatively lower values of elasticities of capital and labor in
regime C can be explained in conjunction with Table 3. Regime A has
the highest level of financial development, whereas regime B exhibits
the highest level of human capital, as the bottom panel of Table 3
shows. More human capital and a better developed financial system
should contribute to the productivity of capital and labor and there
fore increase the probability of that country belonging to a regime
with higher capital or labor elasticity. The average values for these
conditioning variables confirm the status of the lesser developed
regime C, which is characterized by a low level of human capital and
financial development.
More pronounced differences exist between the primary sector
share of regimes A and B compared to regime C. The share of the
relatively unproductive and often inefficient agricultural sector
(Vollrath, forthcoming) is the highest in regime C. A high share of
this relatively unproductive sector increases the probability that a
country in such a regime exhibits low productivity of capital and labor
due to existing inefficiencies. Regime C is also characterized by a high
openness to trade and the association of this trait with lower elas
ticities of labor and capital supports some existing concerns about the
benefits of openness to trade for developing countries. If market or
Kand εit
L, technical efficiency
K) is less than half that of the other regimes, in line
29We calculate probabilities by taking the exponent of the coefficients from the
bottom panel of Table 3.
Table 4
Factor elasticities, efficiency, and marginal rate of technical substitution.
Regime ARegime BRegime C
Capital elasticity (εit
Labor elasticity (εit
Technical efficiency (uit)
MRTS
Observations
K)0.570
0.396
0.999
2.198
689
(0.086)
(0.160)
(0.000)
(3.182)
0.658
0.299
0.953
2.500
919
(0.116)
(0.114)
(0.024)
(0.874)
0.255
0.556
0.898
0.699
305
(0.119)
(0.326)
(0.058)
(10.060)
L)
There is 1913 observations for 77 countries over the period 1970–2000. All calculations
are based on latent classspecific parameter estimations evaluated at the mean.
Standard deviations in parentheses. MRTS is the marginal rate of technical substitution,
calculated as the ratio of scale elasticityadjusted capital to labor change.
Table 3
Latent class frontier estimation results.
Regime
ABC
VariableCoeff.Coeff.Coeff.
Latent technology regime parameters
Constant
−0.669
ln K
ln L
ln K2
−0.050
ln L2
−0.124
ln K×ln L
D2
D3
D4
D5
D6
ln K×D2
ln K×D3
ln K×D4
ln K×D5
ln K×D6
ln L×D2
−0.159
ln L×D3
−0.030
ln L×D4
−0.325
ln L×D5
−0.172
ln L×D6
−0.295
(0.106)⁎⁎⁎
(0.012)⁎⁎⁎
(0.017)⁎⁎⁎
(0.005)⁎⁎⁎
(0.007)⁎⁎⁎
(0.006)⁎⁎⁎
(0.034)⁎⁎⁎
(0.030)⁎⁎⁎
(0.031)⁎⁎⁎
(0.031)⁎⁎⁎
(0.034)⁎⁎⁎
(0.012)⁎⁎⁎
(0.017)⁎⁎
(0.016)⁎⁎⁎
(0.014)⁎⁎⁎
(0.015)⁎⁎⁎
(0.018)⁎⁎⁎
(0.024)
(0.022)⁎⁎⁎
(0.019)⁎⁎⁎
(0.020)⁎⁎⁎
−0.334
0.394
0.579
0.036
0.000
0.018
0.098
0.338
0.194
0.243
0.207
0.103
0.133
0.169
0.185
0.147
−0.222
−0.350
−0.372
−0.442
−0.369
(0.019)⁎⁎⁎
(0.011)⁎⁎⁎
(0.017)⁎⁎⁎
(0.005)⁎⁎⁎
(0.008)
(0.006)⁎⁎⁎
(0.022)⁎⁎⁎
(0.023)⁎⁎⁎
(0.023)⁎⁎⁎
(0.024)⁎⁎⁎
(0.025)⁎⁎⁎
(0.014)⁎⁎⁎
(0.015)⁎⁎⁎
(0.014)⁎⁎⁎
(0.016)⁎⁎⁎
(0.016)⁎⁎⁎
(0.020)⁎⁎⁎
(0.021)⁎⁎⁎
(0.020)⁎⁎⁎
(0.023)⁎⁎⁎
(0.020)⁎⁎⁎
−1.015
0.403
0.204
0.024
0.279
−0.065
0.373
0.195
−0.141
0.163
0.093
0.081
−0.011
−0.120
−0.210
−0.190
−0.088
0.118
0.238
0.031
0.213
(0.150)⁎⁎⁎
(0.056)⁎⁎⁎
(0.075)⁎⁎⁎
(0.015)⁎⁎⁎
(0.016)⁎⁎⁎
(0.012)⁎⁎⁎
(0.145)⁎⁎⁎
(0.151)
(0.159)
(0.154)
(0.148)
(0.043)⁎⁎
(0.046)
(0.055)⁎⁎⁎
(0.061)⁎⁎⁎
(0.064)⁎⁎⁎
(0.075)
(0.075)
(0.082)⁎⁎⁎
(0.077)
(0.075)⁎⁎⁎
0.471
0.659
0.060
0.681
0.439
0.599
0.446
0.679
0.031
0.032
0.214
0.140
0.168
Efficiency parameters
σ
λ
0.115
0.011
(0.004)⁎⁎⁎
(1.119)
0.139
1.525
(0.008)⁎⁎⁎
(0.282)⁎⁎⁎
0.275
2.053
(0.020)⁎⁎⁎
(0.469)⁎⁎⁎
Regime membership probability parameters
Constant3.276
Human capital0.176
Financial
development
Primary sector
share
Openness
to trade
Observations689
(1.085)⁎⁎⁎
(0.158)
(0.016)⁎⁎⁎
2.528
0.425
0.022
(1.079)⁎⁎⁎
(0.157)⁎⁎⁎
(0.016)
Reference group
Reference group
Reference group0.039
−0.095(0.025)⁎⁎⁎
−0.094(0.025)⁎⁎⁎
Reference group
−0.031(0.006)⁎⁎⁎
−0.027(0.006)⁎⁎⁎
Reference group
919305
Standard errors in parentheses; the data refer to 1913 observations on 77 countries over
the period 1970–2000; Dk, k=2, 3, 4, 5, and 6 are time dummies for the periods 1970–74,
1975–79, 1980–84, 1985–89, 1990–94, and 1995–2000, respectively; σ[=(σu
and λ[=σu/σv] are efficiency parameters; the loglikelihood value is 1119.54; significance
at the 10/5/1% levels (⁎/⁎⁎/⁎⁎⁎).
2+σv
2)1/2]
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 8
institutional imperfections exist, such openness actually can lead to
underutilization of human and capital resources, concentration in
extractive economic activities, and specialization away from techno
logically advanced increasingreturns sectors (Grossman and Help
man, 1991; Sachs and Werner, 1999; Rodriguez and Rodrik, 2001).
Therefore, it is not surprising that the (least) developed economies in
regime C exhibit low productivities of capital and labor.
Estimates in Table 4 also reveal significant heterogeneity in the
elasticities of inputs across regimes. We find almost constant returns
to scale in all regimes, as most of crosscountry regressions assume
when examining growth differentials (Mankiw et al., 1992). However,
in regime C capital elasticity is lower than labor elasticity, which
contrasts with results from the growth empirics literature that reports
a marginal product of capital as high as 0.60 (Mankiw et al., 1992).
Furthermore, efficiency levels are statistically significant and different
for every regime. Overall, we conclude that there is no average or
representative country. Also, all countries do not operate at the fully
efficient production frontier. Instead, we find different regimes of
countries, each with its own specific characteristics. Rather than
merely assigning countries to groups, we find support for using the
four conditioning variables jointly to determine the allocation of a
country to regimes A, B, or C.
Another distinctive feature of our model is the possibility that a
country may change regimes over time. This raises the question if and
how often countries do change membership over time. We depict
regime migrations in Table 5 including the frequency and absolute
numberofregimeallocationchangesbetweenanytwotimeperiods.30
While the migration pattern observed may appear rather dynamic,
imposingregimestickinessbynotpermittingregimeswitchesimplied
counterintuitive country groupings in an earlier version of this paper,
presumably reflecting changing technology and group determinants.
We prefer here to permit countries to follow different growth
processes due to regime switches similar in spirit to Jerzmanowski
(2006), rather than imposing the rigid assumption of unique
equilibrium growth per country.
Most observations are located on the diagonal of Table 5, which
indicates that overall countries appear to change relatively rarely in
terms of their production structure. At the same time, especially for
countries in regimes A and B a stable group allocation seems difficult.
Different technology regimes appear to be relevant for some
countries' growth processes at different times. We checked if some
countries are ‘borderline’ cases in the sense that our model allocated
them to regimes A or B with a conditional probability that is close to
50%, the conventional cutoff level in the multinomial logit model of
Eq. (4). However, the conditional probability of group membership is
very high in almost all cases. In fact, it is above 90% for more than 90%
of the sample. Hence, the relatively high frequency of regime switches
between regimes A and B is not the result of our model's flexibility.
This active migration pattern across technology regimes is to some
extent in line with Jerzmanowski (2006). Using a Markowregime
switchingmodel, henotes thatalmostall countries in hissample ‘visit’
each of the growth regimes identified there on the basis of output
perworker growth dynamics alone. In this sense, the frequency of
migrations we observe does not seem excessive. It is also important
to note that most migrations between the two fairly developed
technology regimes A and B involve countries that switch back and
forth (see also Table A.3). Of the 79 (42+37) switches between
regimes A and B, approximately 60% pertain to countries that change
back and forth.31Put differently, 36 out of 42 moves from A to B (27
out of 37 from B to A) are accounted for by the same countries, which
may simply be hard to classify. In line with Jerzmanowski (2006), we
also find that regime migrations are rarely a viable strategy to escape
poverty traps, since exiting the worst performing regime C for good is
rare. Most extreme upgrades from regime C to A are followed either
by gradual (for example Rwanda) or straight (for example Togo)
‘downgrades’ back to the regime C. Finally, as shown in the last
column of Table 5, few countries move from regimes A and B to
regime C.
A natural question that arises at this point pertains to which
countries belong to which regime and how plausible the allocations
are. Table A.3 in the Appendix A provides a list of the countries and
shows regime memberships for each of the six periods across which
they are permitted to switch regimes. Each country in our sample in
each period joins the regime for which it has the highest conditional
probability. Most countries belong to either one or two regimes over
the entire sample period. Regime B is the most populated followed by
regime A.
To confirm the plausibility of our classification, we provide Table 6,
which shows the difference between the subjective and objective
probabilitiesofbeingaregimemember.Thesubjectiveprobabilityisthe
ratio of the number of years a country has been a member of a regime
to the total number of years it appears in the sample. The objective
measure is calculated as the product of the number of years a country
appears in the sample and the relative size of the regimes (e.g., 689/
(689+919+305) for regime A). We calculate both probabilities
after determining the regimes. A positive number in Table 6 indicates
that countries from a certain region are more likely to be members of a
regime than if the regions were randomly distributed across regimes.32
The evidence in Table 6 shows that geography matters. Our
classification justifies, to a certain extent, the regional classification
argument (countries in the same geographical region may have
similar endowments, such as natural resources). Asian countries are
most likely to be members of regime A, whereas regime B is very
likely to contain European countries. All regions are underrepresented
in the laborintensive and inefficient regime C, with the notable
exception of Africa (mainly subSaharan countries). A few Asian and
Latin American countries, such as Pakistan, Indonesia, and Honduras,
Table 5
Migration matrix.
To regime
ABCTotal
From regime
A
54.37
(56)
26.24
(37)
17.02
(8)
34.71
(101)
40.78
(42)
72.34
(102)
12.77
(6)
51.55
(150)
4.85
(5)
1.42
(2)
70.21
(33)
13.75
(40)
100
(103)
100
(141)
100
47
100
(291)
B
C
Total
Numbers denote the percentage probability of moving from regime to another. The
number of countries per cell appears in parentheses.
30Since we distinguish six episodes, we have five migration matrices but display only
the aggregate, unconditional migration probabilities.
31Finland and Trinidad and Tobago migrate in and out of these two regimes a total of
three times.
32We exclude Oceania from the table due to few observations.
Table 6
Do geography and income matter?
RegionRegime ARegime BRegime C
Africa
Americas
Asia
Europe
−0.102
0.044
0.239⁎⁎
−0.073
−0.283⁎⁎⁎
0.060
−0.162⁎
0.215⁎⁎⁎
0.385⁎⁎⁎
−0.104⁎⁎
−0.077⁎
−0.142⁎⁎⁎
Income level
Output per capita15.749 (12.480)17.977 (13.885)3.048 (5.156)
Numbersrefertothedifferencesbetweentheconditionalandunconditionalprobabilitiesof
being a regime member. Differences between conditional and unconditional probabilities
are tested using a twosided ttest. Significance at the 10/5/1% levels (⁎/⁎⁎/⁎⁎⁎).
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Page 9
are also allocated to regime C, but they eventually exit this worst
performing regime and enter either regime A or B. In addition, we find
some evidence in favor of the importance of similar production
structures (countries with similar level of development, such as
income per capita, may have similar structures of production). Table 6
shows that highincome countries (e.g., European, and the United
States) tend to be members of regime B, mediumincome countries
(e.g., Asian nations) often appear in regime A, and lowincome
countries (e.g., African nations) are mostly in regime C.
Our classification can therefore, to some extent, be compared with
studies that apply similar methodologies (e.g., stochastic frontier
analysis) but base their country allocation ex ante on geography
(Koop et al., 2000; Limam and Miller, 2004). However, in every region
some countries may behave very differently from other countries in
the same geographical region. For example, as Davis et al. (2007)
argue, purely based on geography, the Philippines would be placed
with other countries in East Asia, although its development is much
more akin to that of many Latin American countries. This observation
is supported by our classification. Other studies, for example, Paap
et al. (2005) and Davis et al. (2007), use latent class analysis and
allocate countries based on multiple conditioning variables, in line
with our approach. However, these studies do not consider the pos
sibility that countries can move over time to a more (less) advanced
regime, which is a realistic scenario.
In summary, three main findings emerge from our analysis so far.
First, all countries do not follow a common growth process, nor is the
growth process of any country entirely unique. Instead, we find three
distinct growth processes or, equivalently, three growth regimes. In
addition,wefindthatsomecountriesovertimeimprove(ordeteriorate)
their production and move to a more (less) advanced regime.
Second, (in)efficiency, which has been widely ignored by con
ventional growth empirics, is statistically important in our study and
quantitatively different across regimes. We find that countries from
regime A are fully efficient, whereas the least efficient countries
appear in regime C. This division implies that development policies
for some countries geared toward a better exploitation of existing
technologies, rather than augmenting new ones, may be beneficial.
Third, membership in a certain regime depends on the joint effect
of multiple factors — namely, human capital, openness to trade,
financial development, and primary sector share. Our results clearly
show that no single factor can explain the allocation of countries to a
certain regime.
To shed more light on the growth experience of the three regimes,
especially the quite ‘similar’ regimes A and B, we turn next to the
decomposition of output growth for every regime.
4.2. How do countries grow?
Having identified the number of regimes and their characteristics,
we next consider how countries in each regime grow. Therefore, we
decompose output growth per regime into three components: input
growth, technical growth, and efficiency growth, as in Eq. (5). To
allow for potential heterogeneity in growth patterns within regimes,
we identify high, medium, and lowgrowth countries according to
the 33rd and 66th percentiles of the overall growth distribution as
cutoff points in each regime. In Table 7 we present the break down
of countries in each regime according to their growth performance.
Fig. 1 graphically presents a more detailed decomposition of technical
change and factor accumulation.
In the comparison of regime B with regime A in Section 4.1, we
noted that the differences between their conditioning variables and
theircoefficients appeared marginal.However,we cautionedagainsta
comparison of individual variables and coefficients and emphasized
the multivariate effect of the conditioning variables. We confirm this
latter point by realizing that output growth decomposition in Table 7
is markedly different for each regime.
We identify regime A as the emerging regime, which contains
many Asian countries and has the most productive labor among all
regimes as well as a relatively high level of financial development
and human capital that is somewhat lower than that for countries
in regime B. The output growth decomposition in Table 7 also re
veals that countries in regime A grow primarily as a result of factor
accumulation and technical change.33As Fig. 1 shows, the former
effect consists predominantly of capital accumulation, whereas the
latter influence consists mostly of pure technical change (especially in
the highgrowth countries in this regime). These results confirm the
importance of financial development in facilitating capital accumu
lation, through both domestic savings and foreign capital (Pagano,
1993) as well as in reallocating capital to firms that generate the
greatest technical change (Schumpeter, 1934). Efficiency change is
positive but very small in this highly efficient regime.
We can relate these findings about regime A to the ongoing debate
aboutthesourcesoftheimpressiveoutputgrowthperformanceofsome
East Asian countries. Some studies (Young, 1994) argue that East Asian
countries grow primarily through factor accumulation, whereas others
(PackandPage,1994)pointtotheroleoftheproductivityofinputs.Our
results suggest that factor accumulation is important but technical
change is a key factor overall, especially for highgrowth countries.
Regime B is the mature regime, which contains many European
countries and the United States, has the highest output per capita,
indicates an important role for human capital, and achieves the
highest capital elasticity of all regimes. Output growth for countries in
this regime is driven by factor accumulation, especially through
increases in the capital stock. Such increases may result from a high
human capital stock, which increases the rate of investment (Barro,
1991; Krueger and Lindahl, 2001; Sianesi and Reenen, 2003). The
regime is also characterized by negative technical change, largely due
to laboraugmenting technical regress, as we show in Fig. 1. The main
explanation for the negative technical change in the lowgrowth
Table 7
Output growth decomposition.
Regime A
High MediumLowTotal
gr(Yit)
TCit
ECit
SCit
N
0.309
0.217
0.003
0.067
325
(0.193)
(0.194)
(0.012)
(0.029)
0.075
0.012
0.002
0.061
161
(0.038)
(0.039)
(0.011)
(0.023)
−0.108
−0.170
0.004
0.057
203
(0.085)
(0.091)
(0.020)
(0.023)
0.123
0.055
0.003
0.063
689
(0.227)
(0.220)
(0.015)
(0.026)
Regime B
HighMediumLowTotal
gr(Yit)
TCit
ECit
SCit
N
0.210
0.123
−0.001
0.073
211
(0.069)
(0.086)
(0.013)
(0.023)
0.058
−0.003
0.000
0.061
371
(0.036)
(0.040)
(0.015)
(0.018)
−0.069
−0.124
−0.004
0.059
337
(0.077)
(0.090)
(0.022)
(0.024)
0.042
−0.018
−0.002
0.063
919
(0.120)
(0.119)
(0.018)
(0.022)
Regime C
HighMediumLowTotal
gr(Yit)
TCit
ECit
SCit
N
0.302
0.225
0.008
0.047
165
(0.126)
(0.153)
(0.042)
(0.031)
0.069
0.017
0.004
0.048
74
(0.036)
(0.050)
(0.030)
(0.026)
−0.157
−0.191
−0.003
0.037
66
(0.158)
(0.158)
(0.051)
(0.032)
0.136
0.085
0.004
0.045
305
(0.222)
(0.217)
(0.042)
(0.030)
Standard errors in parentheses. High growth >66th percentile of the total growth
distribution. Low growth <33rd percentile of the total growth distribution. N is the
number of observations in each regime. Variables are as defined in Table 1.
33Some lowgrowth countries in this regime exhibit technical regress. For example,
Brazil exhibits technical regress in the early 1990s. Since 1989 was the first
presidential election after 29years of military rule, technical regress may reflect the
burden of setting these decades of economic mismanagement straight.
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 10
subsample of regime B is the (temporary) migration of countries from
regimes A and C (e.g., South Africa and Indonesia) to regime B. The
same is true for the small negative efficiency change.
Finally, we characterize regime C as the developing regime. It
contains many African countries, with very low output per capita, a
high degree of openness to trade, and a large primary sector share.
Output growth for these countries results from technical change,
efficiency change, and factor accumulation. The latter is fairly modest
and involves both capital and labor accumulation. Technical and
efficiency change are important, but as Table 7 shows, they have the
greatest effect on highgrowth countries. From Fig. 1, we observe that
technical change in highgrowth countries in this regime is both pure
and laboraugmenting. In contrast, lowgrowth countries in the
developing regime experience both pure and laboraugmenting
technical regress, which implies an inward shift of their production
possibility frontier. The latter may initially seem odd. However, the 66
observations in this lowgrowth subsample include primarily obser
vations of Uganda and Rwanda in the early 1990s (which were
marked by various conflicts in The Great Lakes region), Congo at the
end of the same decade (the time of the Second Congo War), Zambia
(during 1986–1994 when it suffered one of the highest debt burdens
due to the collapse in the price of copper), and other subSaharan
countries in Africa that have suffered from various political, health,
and/or natural disasters during these years. Both the group allocation
of our model and the implication of the actual destruction of some
economies' production possibilities thus seems logical.
Recall that the share of the relatively unproductive and often
inefficient agricultural sector (Vollrath, forthcoming) is the highest in
regime C. The negative relationship between output per capita and
primary sector share across our regimes may reflect a dual economy
reallocation problem (Vollrath, forthcoming; Caselli, 2005). Labor in
the agricultural sector, which tends to be less than perfectly mobile,
may lead to factor market misallocations that seriously hamper
growth if labor productivity in this sector falls too low.
RegimeC is alsocharacterized bya highdegree of openness totrade,
which should contribute positively to growth such as through the
knowledge spillovers from importing and exporting (Edwards, 1998;
BenDavid and Loewy, 1998; Frankel and Romer, 1999). However, the
effects of trade on growth depend on the composition of exports in
particular. Hausmann et al. (2007) develop an index that measures the
‘quality’ of countries' export baskets and provide evidence that only
countries that produce and export highproductivity goods perform
better in terms of growth. Imports only enhance growth when they
include highquality foreign capital goods, which embody advanced
foreign technology, and when anadequate level of humancapital exists
to perform reverse engineering and possibly improve on the imported
technology (Connolly, 1998). These two conditions rarely can be met in
lowincome, developing countries. Furthermore, with market or
institutional imperfections, openness can lead to the underutilization
of resources, concentration in extractive economic activities, or spe
cialization away from technologically advanced, increasingreturns
sectors (Grossman and Helpman, 1991; Sachs and Werner, 1999;
Rodriguez and Rodrik, 2001).34Our results therefore support the
positiveeffectsofopennessongrowththroughtechnologyspilloversfor
highgrowth countries, as well as the composition and market/
institutional imperfections arguments for lowgrowth countries in
regime C. We do not find unequivocal support for the exportled
growth hypothesis in our sample. Crosssectional studies that rely on
the‘average’countrythusappeartoobscuretheimportanceofdifferent
growth regimes and the potential heterogeneity within a regime.
The output growth decomposition thus leads to several important
conclusions. Though the forces that drive growth differ across regimes,
capital accumulation is consistently an important component of growth
across all the regimes. This finding is consistent with the results of
several prior studies (Koop et al., 1999, 2000; Koop, 2001; Limam and
Miller, 2004; Davis et al., 2007). However, it differs from Solow (1956)
who found that capital accumulation accounts for between oneeighth
and onequarter of total output growth in the United States, whereas
34According to Grossman and Helpman (1991), a country may specialize in a non
dynamic sector as a result of its openness, which causes it to lose out on the longrun
benefits of increasing returns. The underlying imperfection involves the contracts or
financial markets that induce people to follow a myopic notion of static comparative
advantages. Sachs and Werner (1999) also develop a model in which specialization in
extractive, naturalresource sectors diverts the economy from achieving technological
progress. In this case the underlying imperfection is the institutional weakness that
encourages naturalresource depletion for quick gains among only certain societal
groups. Finally, Rodriguez and Rodrik (2001) review the theoretical arguments
regarding why openness might be detrimental to developing countries.
Fig. 1. Mean output growth components of technical change and factor accumulation.
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J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 11
productivityaccounts for more thanhalf ofoutputgrowth inmost other
countries.35We find instead that growth in high and mediumgrowth
countriesacrossallregimesresultsfromtechnicalchange,andgrowthin
lowgrowth countries is mainly driven by factor accumulation. There
fore, we find support for the technical changedriven growth explana
tion.Overall,ourresultsdonotsupportauniformexplanationofgrowth.
Thesetupofourmodelallowscountriestoswitchregimes.Asimple
waytoshedmorelightonthefactorsthatdetermineregimemigrations
is to test if the covariates we used to predict group membership differ
significantly between those countries that move and those that stay
within regimes. In Table 8 weindicate whether, for those countries that
change regimes, each of the conditioning variables is significantly
different than the values for the rest of the countries in the regime from
which the country has departed. We use two tests: a parametric ttest
and a nonparametric Kruskal–Wallis rank test. Table 8 reports the p
values from these tests for each transition depicted in Table 5. The
numberofobservationsequalsthenumberofcountriesmoving(e.g.,42
moving from A to B) multiplied by the number of years in the period
prior to moving (e.g., 5 such that N=42×5=210). A positive
(negative) sign indicates that the conditioning variable is higher
(lower) than that of the other countries in the regime. For example, in
the second column of the first section of Table 8, the pvalues of 0.0104
and 0.0042 and significance levels of 5% and 1% indicate that countries
that moved from regime A to regime C had significantly lower human
capital levels than did countries that remained in regime A.
From the last two columns of Table 8, we observe that increases in
financial development (for migrations to regime B) and human capital
(for migrations to regime A) are important strategies with which
countries can ‘escape’ from regime C. In addition, as countries in that
regime develop, their primary sector share decreases, and they may
become less dependent on exports (resulting in a lower openness to
tradeasitismeasuredhere).ThistoomakescountriesinregimeCmore
likely to move to migrate to regimes A and B. Countries that migrate
from regimeB toregimesA have a relatively low level of human capital.
In addition to human capital, a poor financial development and a
relatively large primary sector share contribute to migrations from
regime A and B to regime C.
Yet regime migrations are not the only way in which countries can
improve their performance. Within each regime, less technologically
advanced countries can grow faster than advanced ones because they
only need to copy the technology of the latter. This notion underlies
muchoftheconvergenceliterature.Intheirreviewoftheconvergence
literature, Durlauf et al. (2005) find that the estimation of conver
gence rates can be improved by augmenting the Solow–Swan model
with human capital (Mankiw et al., 1992), by considering regional
convergence clusters (Mankiw, 1995; Quah, 1996), and by employing
econometric advancements such as panel data analysis (Islam, 1995).
Still, many studies continue to find either no or considerably different
convergence rates.
Apossibleexplanationforthispersistentconvergencepuzzlemaybe
the neglect of different regimes. Countries may converge (at different
rates) within but not necessarily across regimes, as we argue here. To
test for convergence, we replicate the modeling and estimation
approach of the seminal work of Mankiw et al. (1992). We only differ
fromtheoriginalanalysisofMankiwetal.(1992)inonerespect.Wenot
only test for convergence for the whole sample, but also for each of the
regimes identified by our conditional latent class model. To examine
convergence we estimate the following convergence equation from
Mankiw et al. (1992):
lny t ð Þ
y 0
ð Þ= 1− eλT
− 1 − eλT
??
α
1 − α
ð
?
Þln s ð Þ− 1− eλT
ln y0
ð
??
α
1 − α
ðÞn + g + δ
ðÞ
?
Þ;
ð6Þ
where y is output per worker, t and 0 indicate the end and start of the
respective period, s is the share of income saved and assumed to be
invested,andδ andgdenote theexogenous depreciation, respectively.
Following the convergence literature, we choose a joint rate for δ and
g of 6%.36The working population evolves at rate n, which we observe
from the data. According to the last term in Eq. (6), countries with
lower initial output per worker should grow faster. The pace of
convergence is implied by λ.
We estimate Eq. (6) for all countries during the whole sample
period, as in Mankiw et al. (1992), as well as for each fiveyear period,
as in Barro and SalaiMartin (1992). Subsequently, we repeat the
estimations for each regime.
The top panel of Table 9 reports the estimates of Eq. (6) for the full
sampleof77countriesduringtheperiod1970–2000andforthesixsub
periods.Theinitialincomecoefficientisnegativeandinlinewiththeory.
The diagnostics (sample size and R2) indicate fairly good explanatory
power. For the whole sample period the annual convergence rate
implied by a λ of 2.4% is in line with previous evidence.37
Our conjecture that the existence of different regimes has
important implications for convergence also receives support from
the regimespecific parameters. Longrun estimates of initial income
coefficients, reported in the rightmost column of Table 9, imply
convergence rates that range from 2.1% in the fairly developed regime
B to 4.4% in the poorly performing regime C.38Since laggard countries
are predicted to converge faster, this illustrates that imposing the
assumption of an identical steady state underestimates convergence
ratesforsome,mostlylessdeveloped,countries.Thekeyfindingofthis
analysisis thatcountries convergeto their ownregimespecific steady
state and the rate of convergence differs from regime to regime.
Convergence results per regime across the whole sample period
are also subject to a caveat. Grouping countries to one regime for the
entire period requires allocations based on mean regime member
ships. A country that appears in regime A for three intervals and then
three intervals in group C would be allocated to regime B.39Most
35Christensen and Cummings (1981), Dollar and Sokoloff (1990), King and Levine
(1994), and Kim and Lau (1996) report similar results.
Table 8
Migrating countries and their regime determinants.
Movement
A to BA to CB to AB to CC to AC to B
(N)(210)(25)(185)(10)(40)(30)
Human capital
Sign
ttest
Rank test
+
0.3239
0.1523
−
0.0104⁎⁎
0.0042⁎⁎⁎
−
0.0000⁎⁎⁎
0.0003⁎⁎⁎
−
0.0000⁎⁎⁎
0.0000⁎⁎⁎
+
0.0056⁎⁎⁎
0.9465
−
0.9765
0.3484
Financial development
Sign
ttest
Rank test
−
0.0841⁎
0.8435
−
0.0015⁎⁎⁎
0.0000⁎⁎⁎
−
0.6749
0.8185
−
0.0000⁎⁎⁎
0.0000⁎⁎⁎
−
0.5140
0.9233
+
0.0002⁎⁎⁎
0.0005⁎⁎⁎
Primary sector share
Sign
ttest
Rank test
−
0.1276
0.0062⁎⁎⁎
+
0.0003⁎⁎⁎
0.0001⁎⁎⁎
−
0.1293
0.3351
+
0.0000⁎⁎⁎
0.0000⁎⁎⁎
−
0.0000⁎⁎⁎
0.0000⁎⁎⁎
−
0.0378⁎⁎
0.0415⁎⁎
Openness to trade
Sign
ttest
Rank test
+
0.9494
0.4874
+
0.0000⁎⁎⁎
0.0000⁎⁎⁎
−
0.1817
0.0007⁎⁎⁎
+
0.8936
0.8955
+
0.7739
0.4589
−
0.0231⁎⁎
0.0227⁎⁎
Significance at the 10/5/1% levels (⁎/⁎⁎/⁎⁎⁎).
36Changing (δ+g) between 2.5% and 9.5% in increments of fifty basis points does
not alter our results qualitatively.
37Overall, the other coefficients are also consistent with theoretical predictions:
faster population growth reduces the growth of per worker income and higher savings
facilitate growth significantly.
38See Islam (1995), Caselli et al. (1996), and Jones (1997) for evidence.
39Results shown here are based on the arithmetic mean of the groups to which the
countries are allocated during the maximum of the six periods, as shown in Table A.3
in the Appendix A.
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Page 12
countries do not switch regimes, which can mitigate some of these
concerns. We can account more explicitly for possibly different
convergence speeds. To this end we estimate Eq. (6), similar to Barro
and SalaiMartin (1992), for each of the different episodes in the
latent class frontier model to identify the regimes.
The pertinent columns in Table 9 confirm the dispersion of
convergence rates.40In regime B there is convergence across most
periods at a pace of 2%. In contrast, the fully efficient and primarily
technological changedriven regime A only exhibits signs of strong
convergence during the 1980s. The absence of significant estimates of
convergence in each period in regime C likely reflects the low number
of observations.
Overall, aggregate convergence might be deceptive to the extent
that withinregime estimates differ significantly across both regimes
and time periods. Our results thus might explain why some studies
continuetofindmixedevidenceabouttheexistenceandmagnitudeof
convergence.Thatis,itmaybeduetotheirneglectofdifferentregimes.
5. Conclusion
Thestandardneoclassicalgrowthliteratureassumesthat:(i)coun
tries use resources efficiently, and (ii) that the underlying production
technologyis the same for all countries.In this paper we address these
issues by estimating a stochastic frontier model augmented with a
latent class structure. Hence, we explicitly account for inefficiency and
allow for production technologies to differ across groups of countries.
In contrast with many crosscountry growth studies, we estimate
membership in groups instead of determining ex ante which countries
should be compared.
Our empirical analysis is based on a sample of 77 countries over a
thirtyyear period. The results support the existence of three regimes
of countries. First, a large, or mature regime that is comprised of many
mature economies, such as the U.S. and European countries. It
is characterized by high output per capita, high human capital
accumulation, high capital elasticity, and some level of inefficiency.
The second regime, the emerging regime, contains primarily emerg
ing (developing) countries, mostly Asian, and is characterized by
productive labor, relatively welldeveloped financial system, and a
high efficiency level. Finally, the third regime, the developing regime,
includes the least developing countries, mostly African, and is
characterized by very low output per capita, a high degree of open
ness to trade, a large primary sector share, and high inefficiency.
The driving forces of growth vary across regimes also. Growth in
the mature regime depends primarily on factor accumulation in
general and capital in particular, whereas the key generator of growth
in the emerging regime is (pure) technical change. Growth in the
developing regime depends on both (pure and laboraugmenting)
technical change and the accumulation of labor. Overall, our results
support a rather pluralistic explanation of growth experiences in the
countries in our sample. We also find evidence that input accumu
lation is a reasonable description of the growth process for some
countries (in certain regimes) and of productivity (efficiency and
technology) developments for others.
Our findings strongly suggest several different growth processes,
which means that onesizefitall policy prescriptions based on
standard oneclass results cannot prescribe the right medicine for
40The additional effects of saving and population and technical change, as well as
depreciation, differ too. Here we focus on the implications of different technology
regimes for income convergence.
Table 9
Convergence regressions.
Variable1970–1974 1975–19791980–19841985–19891990–19941995–2000 1970–2000
All
ln y0
ln (n+g+δ)
ln (s)
ln α
N
R2
Implied λ
−0.029
0.104
0.075⁎
0.423
45
0.060
0.006
−0.062⁎⁎⁎
0.052
0.050
0.471⁎
50
0.181
0.013
−0.085⁎⁎⁎
−0.319⁎
0.100
−0.674⁎⁎
58
0.198
0.018
−0.086⁎⁎⁎
−0.495⁎⁎⁎
0.130⁎⁎⁎
−1.234⁎⁎⁎
65
0.521
0.018
−0.024
−0.105⁎
0.143⁎⁎
−0.484⁎⁎⁎
74
0.259
0.005
0.005
−0.340⁎⁎⁎
−0.085⁎⁎⁎
−0.477⁎⁎⁎
76
0.196
−0.001
−0.528⁎⁎⁎
−0.532
1.056⁎⁎⁎
−2.119⁎⁎
77
0.563
0.024
Regime A
ln y0
ln (n+g+δ)
ln (s)
ln α
N
R2
Implied λ
−0.037
0.478⁎
0.153
1.204⁎
21
0.201
0.008
0.025
−0.221⁎⁎
−0.110
0.073
13
0.439
−0.005
−0.187⁎⁎⁎
−0.208
0.251⁎⁎⁎
−0.560
21
0.543
0.041
−0.141⁎⁎⁎
−0.694⁎⁎⁎
0.197⁎⁎
−1.737⁎⁎⁎
21
0.642
0.030
−0.053
−0.266⁎⁎⁎
0.074
−0.598⁎⁎⁎
27
0.502
0.011
−0.043
−0.392⁎⁎⁎
−0.027
−0.623⁎⁎
29
0.198
0.007
−0.663⁎⁎⁎
−0.998⁎⁎
0.962⁎⁎⁎
−2.664⁎⁎⁎
51
0.756
0.035
Regime B
ln y0
ln (n+g+δ)
ln (s)
ln α
N
R2
Implied λ
−0.126⁎⁎
0.032
0.139⁎⁎
0.216
16
0.373
0.027
−0.099⁎⁎⁎
0.019
0.043
0.480
26
0.491
0.021
−0.122⁎⁎⁎
−0.269
0.209⁎⁎⁎
−0.759⁎
26
0.445
0.026
−0.100⁎⁎⁎
−0.501⁎⁎⁎
0.121⁎
−1.194⁎⁎⁎
37
0.466
0.021
−0.085⁎⁎⁎
−0.121⁎⁎
0.220⁎⁎⁎
−0.568⁎⁎⁎
36
0.463
0.018
0.005
−0.417⁎⁎⁎
−0.040
−0.812⁎⁎
36
0.301
−0.001
−0.482⁎⁎⁎
−0.485
0.999⁎⁎⁎
−2.066
17
0.584
0.021
Regime C
ln y0
ln (n+g+δ)
ln (s)
ln α
N
R2
Implied λ
−0.293⁎
−1.580⁎⁎
0.164⁎⁎
−3.974⁎⁎
8
0.726
0.069
0.220
0.133
0.116
0.378
11
0.55
−0.040
−0.155
−2.863⁎
0.186
−7.307⁎
11
0.499
0.034
0.026
−0.384
0.081
−0.991
7
0.671
−0.005
−0.007
0.408⁎⁎
0.069
0.824
11
0.434
0.001
0.263
0.080
−0.158
0.546
11
0.443
−0.039
−0.747⁎⁎⁎
−1.302⁎⁎⁎
−0.001
−2.252⁎⁎
9
0.852
0.044
Ordinary least square estimates of Eq. (6); ln y0is the log of initial per capita output; the savings rate, s, is approximated by the investment share of GDP in fixed capital; δ+g=0.06;
n is the observed average annual growth of the working population; the number of observations is in parentheses. Significance at the 10/5/1% levels (⁎/⁎⁎/⁎⁎⁎).
124
J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 13
Table A.1
Specification tests for determining the number of regimes.
Model Conditional Log likelihood
AIC BIC
3regime latent class frontier
2regime latent class frontier
3regime latent class frontier
4regime latent class frontier
No
Yes
Yes
Yes
1018.390
639.791
1119.540
no convergence
−1894.790
−1177.580
−2081.080
−1500.280
−894.205
−1642.120
Akaike Information Criterion (AIC)=ln AIC=2m−2ln LF(z), Schwartz Bayesian Information Criterion (SBIC)=−2ln LF(z)+m·ln(n); LF(j) is the likelihood value for Z groups, m is
the number of parameters in the model, and n the number of observations. The preferred specification has the lowest AIC or the lowest SBIC. See also Orea and Kumbhakar (2004).
Table A.2
Tests for equality of parameters between regimes.
Regimes Variable(s)TestStatistic pvalueHypothesis
Latent regime parameters
A and B
A and C
B and C
A, B and C
Translog production function
Translog production function
Translog production function
Translog production function
Wald
Wald
Wald
Wald
40.983
7.261
14.240
50.456
0.000
0.007
0.000
0.000
Rejected
Rejected
Rejected
Rejected
Ancillary parameters on production traits
A and B
A and C
B and C
A and B
A and C
B and C
Capital elasticity (εitz
Capital elasticity (εitz
Capital elasticity (εitz
Labor elasticity (εitz
Labor elasticity (εitz
Labor elasticity (εitz
K)
K)
K)
L)
L)
L)
ttest
ttest
ttest
ttest
ttest
ttest
−16.754
47.183
52.170
14.316
−10.326
−20.460
0.000
0.000
0.000
0.000
0.000
0.000
Rejected
Rejected
Rejected
Rejected
Rejected
Rejected
Regime membership probability parameters
A and B
A and B
A and B
A and B
A and B
Human capital (H)
Financial development (F)
Primary sector share (P)
Openness to trade (T)
H, F, P and T
Wald
Wald
Wald
Wald
Wald
0.057
144.980
0.020
6.360
183.553
0.811
0.000
0.888
0.012
0.000
Not rejected
Rejected
Not rejected
Rejected
Rejected
Null hypothesis tested at the 5% significance level is the equality of parameters between classes. Means and standard deviations for εit
standard errors for H, F, P, and T can be found in Table 2.
Kand εit
Lcan be found in Table 4. Coefficients and
Table A.3
Regime membership.
Period70–7475–7980–8485–8990–9495–00Period70–7475–7980–8485–8990–9495–00
CountryRegionCountryRegion
AfricaAmericas
Algeria
Benin
Botswana
Cameroon
Congo, Republic of
B
C
B
B
C
Argentina
Bolivia
Brazil
Canada
Chile
B
B
B
B
B
A
A
A
B
A
B
A
C
B
B
C
B
C
B
A
A
A
AAB
A
A
B
A
B
A
A
(continued on next page)
any country. More education alone, for instance, may put countries in
more advanced regimes, but for education to be effective other
development measures, such as enhanced factor allocation, financial
development, or trade policies, are required.
The presence of fairly persistent and economically significant
inefficiencies in the operations of bestpractice technologies, espe
cially in the regime with mostly developing countries, has important
policy implications. For countries in the developing regime, develop
ment efforts geared toward developing the skills to exploit existing
technologies may be better than promoting the dissemination of new
technologies alone. Further research into the relative costs and bene
fits of policies promoting either technical change or efficiency im
provements is warranted.
This implication ties in with our finding regarding the dynamics
of regimes, which we investigate by accounting for regime migra
tions. Few countries appear able to maintain their upgrades to faster
growing regimes. Because the determinants of group membership do
not differ significantly between countries that shift regimes and those
that stay, we believe that additional research into the determinants
of regime switches, rather than membership would be fruitful. Our
results show that most migrations pertain to countries switching
between the mature and the emerging regime. The intragroup
convergence patterns also reveal that countries from the mature and
emerging regimes primarily improve by catching up with the leader
countries in their own groups. Among the least developing economies
though, such catchup patterns are absent. Both the periods and pace
ofconvergencediffer,at timessubstantially, rangingbetween1.8%and
4.1% per year. Thus, we find evidence of convergence to their own
regime for most countries, but our results support in particular
different convergence clubs around the world.
Appendix A
125
J.W.B. Bos et al. / Journal of Development Economics 91 (2010) 113–127
Page 14
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Table A.3 (continued)
Period 70–74 75–7980–84 85–8990–9495–00Period 70–74 75–79 80–8485–89 90–9495–00
Country RegionCountry Region
Egypt
Gambia, The
Ghana
Kenya
Lesotho
Malawi
Mali
Mauritania
Mauritius
Mozambique
Rwanda
Senegal
South Africa
Togo
Tunisia
Uganda
Zambia
A
C
C
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C
A
C
C
C
C
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A
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B
C
C
C
C
A
A
B
B
C
C
C
C
B
A
C
B
A
C
A
C
C
A
C
B
B
C
C
C
Colombia
Costa Rica
Dominican Republic
Ecuador
El Salvador
Guatemala
Guyana
Honduras
Mexico
Panama
Paraguay
Peru
Trinidad and Tobago
United States
Uruguay
Venezuela
A
B
B
A
B
B
A
B
B
B
A
A
A
A
B
B
A
A
A
B
B
B
A
A
A
B
B
B
A
A
A
B
A
B
A
A
C
B
B
B
B
B
A
B
A
B
C
C
C
A
B
C
A
A
A
A
B
B
A
B
B
B
A
B
B
B
B
A
A
A
B
B
B
A
B
AAA
A
C
B
A
C
A
C
C
C
C
A
C
A
C
B
C
B
C
A
C
B
B
A
A
B
C
C
BB
B
B
A
B
BB
CAB
Europe
B
B
B
A
A
Asia
Austria
Belgium
Denmark
Finland
France
Germany
Greece
Hungary
Iceland
Italy
Netherlands
Norway
Poland
Portugal
Spain
Sweden
Switzerland
United Kingdom
B
B
B
B
A
B
B
A
A
B
B
B
B
B
B
B
B
B
A
B
B
B
B
C
B
B
A
B
A
B
B
A
A
B
A
B
B
A
A
B
B
A
B
A
B
B
B
B
B
B
B
Bangladesh
Hong Kong
India
Indonesia
Iran
Japan
Jordan
Malaysia
Pakistan
Philippines
Sri Lanka
Syria
Thailand
Turkey
AA
A
B
A
A
A
B
A
A
B
B
A
B
A
A
A
A
A
A
B
A
A
C
B
C
B
B
B
C
A
A
B
B
B
B
B
B
A
B
A
A
B
A
B
B
A
B
A
A
A
B
A
B
A
A
B
B
A
B
A
ABA
B
C
B
B
B
B
B
A
B
B
B
A
C
A
A
B
A
B
B
A
A
B
B
CCC
A
A
B
B
B
B
B
A
B
B
B
B
Oceania
BAustralia
New Zealand
B
B
B
B
B
B
B
B
A
B
ABAA
Notes: most likely regime membership allocations per fiveyear period to the emerging (A), mature (B), and developing (C) groups. Probabilities obtained from Eq. (4) conditional
on period averages of human capital, financial development, primary sector share, and openness to trade. Total (annual) observations per regime A, B, and C, respectively, are 689,
919, and 305.
AfricaAmericas
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