Do Technology and Efficiency Differences Determine Productivity?
ABSTRACT This paper investigates the forces driving output growth, namely technological, efficiency, and input changes, in 80 countries over the period 19702000. Relevant past studies typically assume that: (i) countries use resources efficiently, and (ii) the underlying production technology is the same for all countries. We address these issues by estimating a stochastic frontier model, which explicitly accounts for inefficiency, augmented with a latent class structure, which allows for production technologies to differ across groups of countries. Membership of these groups is estimated, rather than determined ex ante. Our results indicate the existence of three groups of countries. These groups differ significantly in terms of efficiency levels, technological change, and the development of capital and labor elasticities. However, a consistent finding across groups is that growth is driven mainly by factor accumulation (capital deepening).

 SourceAvailable from: Lesley Potters[show abstract] [hide abstract]
ABSTRACT: The main objective of this study is to investigate the impact of corporate R&D activities on firms' performance, measured by labour productivity. To this end, the stochastic frontier technique is applied, basing the analysis on a unique unbalanced longitudinal dataset consisting of 532 top European R&D investors over the period 2000–2005. R&D stocks are considered as pivotal input in order to control for their particular contribution to firmlevel efficiency. Conceptually, the study quantifies the technical inefficiency of a given company and tests empirically whether R&D activities could explain the distance from the efficient boundary of the production possibility set, i.e. the production frontier. From a policy perspective, the results of this study suggest that – if the aim is to leverage companies' productivity – emphasis should be put on supporting corporate R&D in hightech sectors and, to some extent, in mediumtech sectors. By contrast, supporting corporate R&D in the lowtech sector turns out to have a minor effect. Instead, encouraging investment in fixed assets appears vital for the productivity of lowtech industries. However, with regard to firms' technical efficiency, R&D matters for all industries (unlike capital intensity). Hence, the allocation of support for corporate R&D seems to be as important as its overall increase and an 'erga omnes' approach across all sectors appears inappropriate.Journal of Productivity Analysis 12/2009; 37(2):125140. · 0.87 Impact Factor  SourceAvailable from: gtap.agecon.purdue.edu[show abstract] [hide abstract]
ABSTRACT: Computable General Equilibrium (CGE) models have gained continuously in popularity as an empirical tool for assessing the impact of trade liberalization on growth, poverty and equity. In recent years, there have been attempts to extend the scope of CGE trade models to the analysis of the interaction of agricultural growth, poverty and income distribution. Conventional models ignore however the channels linking technical change in agriculture, trade openness and poverty. This study seeks to incorporate econometric evidence of these linkages into a dynamic sequential CGE model, to estimate the impact of alternative trade liberalization scenarios on welfare, poverty and equity. The analysis uses the latent class stochastic frontier model in investigating the influence of international trade on agricultural technological change and productivity. The estimated productivity gains induced from a more opened trade regime are combined with a general equilibrium analysis of trade liberalization to evaluate the direct welfare benefits of poor farmers and the indirect income and prices outcomes. These effects are then used to infer the impact on poverty using the traditional topdown approach and the Tunisian household
Page 1
Electronic copy available at: http://ssrn.com/abstract=998107
Do technology and e?ciency di?erences
determine productivity??
J.W.B. Bosa, C. Economidoua, M. Koetter∗,b,c, J.W. Kolarid
aUtrecht School of Economics, Utrecht University, Janskerkhof 12, 3512 BL,
Utrecht, the Netherlands
bUniversity of Groningen, Faculty of Economics, PO Box 800, 9700 AV
Groningen, the Netherlands
cResearch Center Deutsche Bundesbank, P.O. Box 10 06 02, G60006 Frankfurt
dMays Business School, Texas A&M University, 4218 TAMU, College Station,
Texas 778434218, USA
Abstract
This paper investigates the forces driving output growth, namely technological, e?
ciency, and input changes, in 80 countries over the period 19702000. Relevant past
studies typically assume that: (i) countries use resources e?ciently, and (ii) the un
derlying production technology is the same for all countries. We address these issues
by estimating a stochastic frontier model, which explicitly accounts for ine?ciency,
augmented with a latent class structure, which allows for production technologies
to di?er across groups of countries. Membership of these groups is estimated, rather
than determined ex ante. Our results indicate the existence of three groups of coun
tries. These groups di?er signi?cantly in terms of e?ciency levels, technological
change, and the development of capital and labor elasticities. However, a consistent
?nding across groups is that growth is driven mainly by factor accumulation (capital
deepening).
Key words: total factor productivity, latent class, stochastic frontier, e?ciency,
growth
JEL: O47, O30, D24, G21, C24
?We thank Clemens Kool and seminar participants at Utrecht School of Economics
for helpful comments. Michael Koetter acknowledges ?nancial support from the
Netherlands Organization for Scienti?c Research (NWO) under VENI grant number
016.075164. The opinions expressed are those of the authors. Any remaining errors
are our own.
∗Corresponding author: phone +31 50 363 3633; fax +31 (0)50 363 3850.
Email addresses: j.bos@econ.uu.nl (J.W.B. Bos), c.economidou@econ.uu.nl
Preprint submitted to Elsevier May 1, 2007
Page 2
Electronic copy available at: http://ssrn.com/abstract=998107
1Introduction
Over the past thirty years, a large amount of e?ort has been devoted to answer
ing the question why some countries perform better than others. Nonetheless,
growth di?erentials between countries still pose a puzzle to economists. Gen
erally speaking, the empirical crosscountry growth literature narrowly focuses
on the role of capital in generating economic growth (Baumol, 1986; Barro,
1991, 1996; Barro and Salai Martin, 1992, 1994; Mankiw, Romer, and Weil,
1992; Islam, 1995). However, recent work by Prescott (1998) and Hall and
Jones (1999) suggests that it is di?erences in productivity rather than capital
that account for growth di?erentials.1
Previous comparative studies on crosscountry growth can be divided into
two strands. The ?rst strand relies on (augmented neoclassical) production
functions that assume e?cient use of inputs. However, if this assumption does
not hold, parameter estimates for the marginal e?ects of inputs are biased. The
usual practice in the second strand of literature is a twostage approach. Cross
country productivity estimates are retrieved as a residual from a production
function and then regressed on a set of potential determinants of productivity
growth.2However, in the presence of ine?ciency, total factor productivity
(TFP) indices based on growth accounting or index numbers (e.g. Divisia and
Tornquist indices) are biased as well.
To avoid the aforementioned biases, in this paper we relax the assumption
that all producers are technically e?cient. We estimate a socalled stochas
tic production frontier, where unexplained variance consists of both random
noise and ine?ciency.3Optimal behavior  the technically e?cient use of the
existing production technology  is represented by a production frontier that
benchmarks a country against the maximum level of output it can achieve.
If a country produces this optimal level of output, it is e?cient and will be
on the production frontier. Given their production technology and their input
mix, some countries may be ine?cient, and consequently produce less than
their optimal output.
(C. Economidou), m.koetter@rug.nl (M. Koetter), jkolari@tamu.edu (J.W.
Kolari).
1See also Coe and Helpman (1995), Keller (1997), Miller and Upadhya (2002),
Scarpetta and Tressel (2002) and Gri?th, Redding, and Van Reenen (2004).
2See, for example, Coe and Helpman (1995), and Keller (1997) for the e?ects of
domestic and foreign R&D stocks on productivity growth. Also, see Scarpetta and
Tressel (2002), Gri?th (2004), and Cameron, Proudman, and Redding (2005) for
the e?ects of R&D, trade, and human capital on productivity growth.
3Stochastic frontier analysis (SFA) was introduced by Aigner, Lovell, and Schmidt
(1977), Battese and Corra (1977), and Meeusen and Van Den Broeck (1977).
2
Page 3
A major advantage of this Stochastic Frontier Analysis (SFA) framework is the
tripartite decomposition of productivity growth into: (1) technology changes
(i.e., shifts of the frontier over time), (2) factor accumulation (i.e., scale elas
ticity adjusted increases in factor use), and (3) ine?ciency changes (i.e., move
ments of a country towards the production frontier). Hence, SFA results pro
vide additional insights for designing policies with important welfare implica
tions. For instance, among e?cient countries productivity di?erentials can be
reduced by improving the input mix or by encouraging a faster adoption of
innovative technologies. However, ine?cient countries can also seek to improve
the e?ciency with which existing technologies are used (e.g., by improving le
gal and ?nancial systems, trade regulations, the quality of institutions, etc.).
In addition to assuming that all countries are e?cient, most studies also as
sume that all countries use the same underlying production technology. The
latter assumption is questionable, especially in samples that include both de
veloped and lessdeveloped countries. Estimating a common production func
tion may lead to biased estimates of labor and capital elasticities.4Some pre
vious studies have tried to account for this bias by controlling for the quality
of inputs (Koop, Osiewalski, and Steel, 2000; Limam and Miller, 2004). Other
studies have excluded "excessively" di?erent economies or ex ante classi?ed
countries.5
In this paper, we avoid assuming a common technology by estimating group
speci?c production technologies using a latent class model. Countries in each
group share a common production technology, but technology parameters are
allowed to di?er across groups. The production functions of all groups are
estimated simultaneously together with group membership.6An attractive
feature of this model is that we can quantify the likelihood of group mem
bership. We can also condition these membership probabilities on a set of co
variates, such as human capital and ?nancial development, commonly used in
the growth literature (Mankiw, Romer, and Weil, 1992; Benhabib and Spiegel,
1994; King and Levine, 1993; DemirgucKunt and Levine, 2001).
Our empirical analysis is based on a sample of 80 countries over the period
19702000. We identify three groups, that are characterized by di?erent e?
ciency levels, labor and capital elasticities, and levels of technological change.
A consistent ?nding across these three groups is that growth is driven mainly
by factor accumulation (capital deepening). While the level of ine?ciency is
substantial in one of the three groups, ine?ciency changes are modest in all
three groups of countries. Consequently, whereas group membership appears
4Moreover, if unobserved technological di?erences are not properly treated, they
may be incorrectly identi?ed as ine?ciency.
5See Orea and Kumbhakar (2004) for criticism.
6In addition, we need not impose constraints on technology parameters. See Tsionas
and Kumbhakar (2004).
3
Page 4
to be closely related to e?ciency, productivity change itself is driven more
by capital deepening than by e?ciency changes. An important policy impli
cation of our ?ndings is that highly ine?cient countries need to increase their
e?ciency to gain the full productivity bene?ts of capital accumulation.
The remainder of the paper proceeds as follows. Section 2 presents the method
ology and econometric speci?cation for estimation. Section 3 introduces the
data. Empirical results are presented in section 4. Section 5 concludes.
2Methodology
In this section, we begin by explaining how ine?ciency is taken into account
by using a stochastic frontier model. We then describe how to account for dif
ferences in technology parameters using a latent class version of the stochastic
frontier model. Finally, we present the empirical speci?cation and our decom
position of TFP growth into e?ciency, factor augmentation, and technological
change.
2.1Accounting for ine?ciency
The crosscountry growth literature de?nes a production set consisting of the
capital stock Kitand labor Lit. All N countries (i = 1,...,N) in T periods
(t = 1,...,T) produce real output Yitusing the same production function f,
which can shift over time as a result of technological change (Solow, 1957).
For a given period t, output di?erences are explained by di?erences in the
endowments of Kitand Lit, and possibly by increasing or decreasing returns
to scale.
We can specify a general production function by combining the production
set together with the production technology characterized by function f and
a parameter vector β:
Yit= f(Kit,Lit,t;β) · exp{?it},
(1)
where Yitis the output level in country i at time t, β is a vector of parameters
to be estimated, and exp{?it} is the exponentiated error term. In keeping with
Solow (1957), we add a time trend variable t, which is assumed to capture neu
tral technological change. If all countries produce e?ciently, Yitis the optimal
output.
However, as already mentioned, some countries may lack the ability to employ
existing technologies as e?ciently as possible and consequently produce less
4
Page 5
than the optimal output. The actual (observable) output (Yit) produced in
each country i at time t is then better described by the following stochastic
frontier production function:7
Yit= f(Kit,Lit,t;β) · exp{vit} · exp{−uit},
where the deterministic kernel of the production frontier f(Kit,Lit,t;β) is
multiplied by an exponentiated measure of outputoriented ine?ciency −uit
and an exponentiated noise term vit.8Ine?ciency is allowed to vary over time,
and two countries with identical input levels Kitand Litmay produce di?erent
levels of output if they di?er in their ability to e?ciently employ the available
production technology. We can write equation (2) in logs as:
(2)
yit= α + β?xit+ vit− uit,
(3)
where lower case letters denote natural logs, and x is a vector comprising
production factors. E?ciency (TEit) is de?ned as the ratio of actual output,
yit− uit, over optimal output, yit. It ranges between 0 (fully ine?cient) and
1 (fully e?cient), where TEit of 0.9 implies that a country produces only
90 percent of optimal output. Countries that are fully e?cient operate on
the stochastic production frontier. Their output can only change if either the
production frontier shifts through technological change or if their endowments
of Kit and Lit change. Countries below the frontier can also increase their
output by increasing their e?ciency.
2.2Accounting for di?erences in technology parameters
A handful of studies have examined crosscountry growth di?erentials using
stochastic frontier models. Koop, Osiewalski, and Steel (1999) study the deter
minants of output growth for a panel of relatively homogenous OECD coun
tries.9They ?nd that capital accumulation accounts for most of the growth.
Technological change plays a secondary role, and the role of e?ciency growth
is small. Subsequent studies analyze more countries and (consequently) at
tempt to control for crosssectional heterogeneity. Koop, Osiewalski, and Steel
(2000) and Limam and Miller (2004) control for the quality of production fac
tors using e?ciency units of labor and capital.10Both studies ?nd that factor
accumulation accounts for most of the TFP growth in all groups of countries.
7See Kumbhakar and Lovell (2000).
8In this respect we di?er from nonparametric studies (Färe, Grosskopf, Norris,
and Zhang, 1994; Kumar and Russell, 2002; Los and Timmer, 2005).
9They use a Bayesian model to obtain more robust results for their small sample.
10Koop, Osiewalski, and Steel (2000) use the years of schooling embodied in the work
force to correct labor, as well as agriculture and industry labor force participation to
correct physical capital. Limam and Miller (2004) use mean years of education and
5
Page 6
Tsionas and Kumbhakar (2004) suggest that one should account for cross
sectional heterogeneity as well as (time) variation by estimating di?erent tech
nology parameters for di?erent groups of countries. They estimate an SFA
model with a Markov switching structure.11Their results support the ex
istence of two regimes, where most of the developed countries belong to a
?rst regime characterized by negative growth and high e?ciency. Developing
countries belong to a second regime, characterized by positive growth and low
levels of e?ciency. The regimes di?er mostly with respect to their capital in
tensity. As they explain, regime switching can occur in their framework due
to the choice of priors in their Bayesian framework. Developing countries that
switch from the second to the ?rst regime do so by accumulating capital.
We follow a related approach, that does not require us to formulate priors.
Instead, we model the regime allocation as a latent class problem. In equation
(2), all countries share the same technology parameter vector β. Orea and
Kumbhakar (2004) and Greene (2005) have suggested latent class frontier
models as a way of relaxing this assumption. Following Greene (2005), we can
write a latent class stochastic frontier model (LCFM) as:
yit= α + β?
jxit+ vitj− uitj,
(4)
where technology parameters β are allowed to vary across an a priori speci
?ed number of groups j = 1,..,J. Greene (2005) demonstrates that country
speci?c probabilities of belonging to a group j can be estimated with a multino
mial logit model. The conditional likelihood averaged over classes for country
i is:
Pi=
J
?
j=1
exp(πjz?)
J ?
m=1exp(πmz?)
T?
t=1
Pitj=
J
?
j=1
Π(i,j)
T?
t=1
Pitj=
J
?
j=1
Π(i,j)Pij.
(5)
Parameters for equations (4) and (5) can be obtained by estimating the joint
likelihood incorporating production and probability parameters as described
in detail in Greene (2005).12An attractive feature of this model is that we
average age of physical capital to account for quality of labor and physical capital,
respectively.
11Note that alternative approaches exist to allow for heterogeneity across countries'
production technologies. The simplest approach is to estimate countryspeci?c fron
tiers. However, since relative e?ciency measures cannot be compared when derived
from di?erent benchmarks, another approach is to use ?xed or random e?ects panel
frontier models. While many panel models require a rigid dynamic structure on inef
?ciency, alternatives suggested by Greene (2005) and Kumbhakar and Lovell (2000)
leave enough ?exibility on the time trend of e?ciency to be appropriate. However,
these models limit heterogeneity across countries to the intercept.
12We use this model suggested by Greene (2005) because the alternative approach
by Orea and Kumbhakar (2004) is suboptimal for our purposes. In their words, "...
6
Page 7
can quantify the likelihood of group membership. We can also condition these
membership probabilities on a set of covariates zi.
To operationalize the model in equations (4) and (5), we need to specify a
functional form. Following Kumbhakar and Wang (2005), we prefer a translog
speci?cation over a CobbDouglas speci?cation due to the latter's superior
?exibility (Du?y and Papageorgiou, 2000). Unlike Koop et al. (1999, 2000),
we explicitly account for technology shifts in the frontier. That is, we include
a trend variable t with interaction terms that allows us to identify the contri
bution of technological change to TFP growth. The reduced form of equation
(4) is then:
lnYit= αj+ β1jlnKit+ β2jlnLit+1
+1
+ δ1jlnKitt + δ2jlnLitt + vit− uit.
Random error vitis iid with vit∼ N(0,σ2
variables. The ine?ciency term is iid with uit∼ N(0,σ2
vit. It is drawn from a nonnegative distribution truncated at zero. Ine?ciency
is timevariant and estimated from E(uit?it), the conditional distribution of
u given ? (Jondrow, Lovell, Van Materov, and Schmidt, 1982).13E?ciency
(TEit) is calculated as [exp(−uit)] and equals one for a fully e?cient country.14
2β11jlnK2
it
2γ11jt2
2β22jlnL2
it+ β12jlnKitlnLit+ γ1jt +1
(6)
v) and independent of the explanatory
u) and independent of
Recent studies that compare total factor productivity changes seek to account
for di?erences in the quality of production factors by including, for exam
ple human capital and/or ?nancial development as additional variables in the
production set.15In line with Koop, Osiewalski, and Steel (2000), we model
human capital and ?nancial development as factors that a?ect the labor and
capital elasticities. Thus, we expect that both human capital and ?nancial
development in?uence output indirectly by improving the quality of labor and
capital. Hence, we consider an extension of our latent class model, where hu
man capital and ?nancial development are included as conditioning arguments
ziin equation (5) that help predict group memberships of individual countries.
In doing so, we can test whether these factors explain di?erences in production
technology.16
time variation [of e?ciency] in this model is deterministic and evolutionary, which
might or might not be restrictive" (p. 172). Put di?erently, in contrast to the model
employed here, the uit's are not free to develop unrestricted over time in their model.
13Note that we do not impose any time trend on ine?ciency, which is allowed to
freely vary over time.
14To estimate the log likelihood function we reparameterize σ2= σ2
λ =σu
σv.
15This approach has been criticized by Benhabib and Spiegel (1994).
16Note that we do not test whether these factors explain di?erences in growth de
velopments of individual countries.
u+ σ2
vand
7
Page 8
2.3TFP decomposition
Total factor productivity change
·
TFP equals the rate of change of output
·
K and
L. We follow Kumbhakar and Lovell
·
Y
less the rate of change of inputs
(2000) and use the reduced form of the production frontier to decompose TFP
changes into three elements. Di?erentiating equation (6) with respect to time
yields:
·
·
TFP =∂ lnf(K,L,t;β)
∂t
−∂u
∗1
L
∂t+∂ lnf(K,L,t;β)
∂ lnK
dL
dt.
∗1
K
dK
dt
+∂ lnf(K,L,t;β)
∂ lnL
(7)
The ?rst and second terms on the righthandside represent technological
and e?ciency changes, respectively. The third and fourth terms represent
elasticityadjusted factor augmentation of capital and labor, respectively.
The rate of technical change is given by
·
TCit > 0 represents an upward shift of the production frontier.17
By taking the partial derivatives of our general index of technical change t
with respect to production factors K and L, we can distinguish between pure
·
TCPU
·
TCit= ∂ lnf(Kit,Lit,t)/∂t in equa
tion (7).
technical change (
it), capital augmenting technical change (
·
TCL
capital and labor elasticities are allowed to vary across groups j, technical
change estimates are groupspeci?c as well.
·
TCK
it), and
labor augmenting technical change (
it) (Baltagi and Gri?n, 1988). Since
Next, consider the rate of change of e?ciency
where e?ciency levels TEitare estimated simultaneously with factor elastici
ties, for all groups j.18Countryspeci?c e?ciency estimates are time variant,
such that a country that adopts an innovative technology but has not yet ac
quired the necessary skills to use it e?ciently may initially have a fairly low
TEitcompared to a country which invented the technology. Successful dissem
ination of that technology should be re?ected in e?ciency increases over time
as followers catch up to innovation leaders. Note that in the latent class pro
duction frontier model, each country's change in e?ciency is measured against
·
TE = ∂TEit/∂t in equation (7)
17Alternatively, many researchers model technical change by estimating separate
frontiers per year and then disentangle output changes due to changed parameters
from those due to changing variables. As discussed shortly, this is particularly prob
lematic for the estimated ine?ciency terms uit.
18Note that since we do not impose any particular trend on uit, e?ciency can ?uc
tuate freely over time. As an alternative, consider the model by Battese and Coelli
(1988), where TEit= ui· γ · exp{−γ(t − T)}. Here the parameter γ is identical for
all countries, and TE is either constantly increasing or constantly decreasing.
8
Page 9
the frontier of the group j to which it belongs.
Lastly, in equation (7) the rate of change in factor augmentation is given
by the sum of the scale elasticity of capital
·
it= ∂ lnf(K,L,t;β)/∂ lnK ∗
SK
(1/K)(dK/dt) and labor
plied with changes in factor use, respectively.19The rate of change in fac
tor augmentation can vary for two reasons: pure factor accumulation and
input factor elasticities. For example, if a country exhibits constant returns to
scale, changes in the level of input factors do not in?uence the rate of change
of TFP. In turn, if labor exhibits, for example, increasing returns to scale
?∂ lnf(K,L,t;β)
the rate of change of TFP.
·
SL
it= ∂ lnf(K,L,t;β)/∂ lnL ∗ (1/L)(dL/dt) multi
∂ lnL
?
> 1, an increase in the labor force
?1
L
dL
dt
?
> 0 further increases
Table 1
Total factor productivity decomposition
MeasureCalculation from Equation (7)
·
TCK
·
TCL
it
δ1lnKit
it
δ2lnLit
·
TCPU
it
γ1+γ11t
·
TCPU
·
TCit
·
TEit
it+
·
TCK
it+
·
TCL
it
(exp(−uit))/(exp(−uit−1)) − 1
β1+β11lnK + β12lnL + δ1t
·
it
·
it
SK
SL
β2+β22lnK + β12lnK + δ2t
·
SK
SL
it
·
TCit+
TEit+
Sit
·
Sit
it+
·
·
TFPit
··
In sum, in equation (7) we decompose the rate of change in total factor pro
·
TFPit into a technical change component, a technical e?ciency
component, and a scale component, all of which are conditioned on di?er
ent technology parameters for j groups of countries. Table 1 summarizes this
decomposition for our empirical speci?cation in equation (6).
ductivity
19For expositional ease we dropped group indices j but note that these scale prop
erties are allowed to vary conditional on most likely group membership.
9
Page 10
3Data
We construct a panel data set consisting of 80 countries over the period 1970
2000.20Annual data are retrieved from various sources. Descriptive statistics
are included in Table 5 in the Appendix. Output (Y) in terms of real gross
domestic product and labor force (L) data are obtained from the Penn World
Tables, version 6.1 (PWT 6.1). Total output is given by the product of the
real per capita GDP, measured in 1996 international purchasing power parity
dollars (chain index), and the national population numbers. Our capital stock
(K) series is computed with a perpetual inventory method following Hall and
Jones (1999).21Data on human capital, measured as the average years of
education of the population that is 25+ years old, are retrieved from Barro
and Lee (2001). Finally, data on the ?nancial development, measured as the
amount of deposits held in the ?nancial system as a percentage of GDP, are
taken from DemirgucKunt and Levine (2001).
4Results
In this section we report speci?cation tests, discuss e?ciency levels and scale
elasticities, and provide decomposition results.
4.1 Speci?cation tests
Before we discuss the importance of ine?ciency and di?erences in technology
in explaining growth, we must ?rst choose our preferred speci?cation. We do
so in four steps and report results in Tables (2) and (6).
First, we test whether accounting for ine?ciency can improve our analysis. To
do so, we estimate a ?xed e?ect production frontier (FEM). In estimating the
frontiers, we use the following standard parameterizations: σ = (σ2
and λ = σu/σv, where λ is the ratio of ine?ciency and random noise (Coelli,
Rao, and Battese, 1998). We then test whether the ine?ciency parameters
u+ σ2
v)1/2,
20The list of countries included is provided in the Appendix.
21We use a depreciation rate of 6% and utilize average growth over the ?rst ten
years to get a countryspeci?c average growth rate. For robustness purposes, we also
calculated a backwardlooking capital stock using data from 1960 onwards. Results
are qualitatively similar. Our capital stock series has a wider coverage than the PWT
6.1 variable for capital stock per worker, which is only available for 62 countries from
1965 onwards. Where the two series overlap, the correlation coe?cient between their
log levels is 0.97.
10
Page 11
λ and σ are signi?cantly di?erent from zero (see Table 6 in the Appendix)
and whether all parameters are jointly signi?cantly di?erent from zero (see
the Wald test in Table 2). Both tests show that ine?ciency matters, which
implies that we improve upon standard production function estimations.
Second, we test whether our translog function form is indeed preferred to a
CobbDouglas speci?cation. Again, Wald tests for the joint signi?cance of the
additional parameters involved in estimating a translog production function
are included in Table 2. Our results are consistent with Koop, Osiewalski, and
Steel (1999), who also ?nd support for the translog speci?cation.
Table 2
Speci?cation tests
ModelFEMUncond. LCFM Cond. LCFM
Classes3434
Hypotheses:
No ine?ciency
Cobb Douglas
No additional classes
HC and FD
Identical group parameters on:
lnK
lnL
lnK ∗ lnK
lnL ∗ lnL
lnK ∗ lnL
t
t ∗ t
lnK ∗ t
lnL ∗ t
σ
λ
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.830
0.000
0.000
0.000
0.984
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
Notes: pvalues of Wald tests for joint hypotheses. n/a: not available. FEM: ?xed e?ect
panel frontier model. Cond. (Uncond.) LCFM: (unconditional) latent class frontier model,
conditional on human capital and ?nancial development. σ =?
Third, we must select the number of groups in our latent class production
frontier model. Theoretically, the maximum number of groups is only limited
by the number of cross sections, i.e. the number of countries in our study.
Empirically, overspeci?cation problems preclude even much smaller group
numbers. Greene (2005) suggests to test downward to identify the number of
groups discernible in the data. In our sample, four is the maximum number
of groups j for which neither multicollinearity nor overspeci?cation prohibits
σ2
u+ σ2
v
?1/2, and λ = σu/σv.
11
Page 12
convergence of the maximum likelihood estimator. Hence, in Tables 2 and 6
we compare estimation results from speci?cations with three and four groups.
Our results are in favor of a speci?cation with three groups. This speci?cation
has a higher loglikelihood value. As shown at the bottom of Table 6, for the
speci?cation with four groups, parameter estimates of both groups one and
four as well as these groups' respective membership probabilities are not sig
ni?cantly di?erent from zero. Finally, while Wald tests for joint signi?cance
of parameters cannot be rejected for either speci?cation, signi?cance tests for
individual coe?cients' di?erence across groups are rejected for the speci?ca
tion with four groups. For our preferred speci?cation with three groups, the
Wald tests shown in Table 2 clearly reject the joint identity of technology
parameters across groups.22
Fourth and last, we test whether our group allocation is conditional on hu
man capital and ?nancial development. The role of both variables in explaining
growth di?erentials is commonly tested (see Benhabib and Spiegel (1994), de la
Fuente and Domènech (2000), and DemirgucKunt and Levine (2001)).23Our
latent class frontier model allows us to add to these tests by exploring whether
the average probability of countries belonging to our j groups is a?ected by
human capital (HC) and ?nancial development (FD). Put di?erently, we can
test whether di?erences in technology parameters for our groups are explained
by these additional factors. In the rightmost columns of Table 6 in the Ap
pendix, we show conditional latent class results for both three and four groups
(where the last group is always the reference group). In line with Kneller and
Stevens (2003), our results show that neither human capital nor ?nancial devel
opment have discriminatory power to discern group membership probabilities
in di?erent technology groups. This result need not contradict most ?ndings
in the literature, which emphasize the relevance of both variables for economic
growth. In fact, Wald tests of the joint insigni?cance of parameters on FD
and HC reported in table 2 cannot be rejected despite the model's inability to
generate statistically signi?cant point estimates. We conclude that these vari
ables may have an impact on growth when speci?ed directly as production
factors. However, they cannot predict group membership.
22The constrained speci?cation with four groups and identical group parameters was
inestimable, thus lending further support for our preferred speci?cation. In addition
to the joint equality tests of individual parameters shown in Table 2, we also test
between all possible pairs of groups, e.g. whether groups three and four have the
same capital elasticities. These results again show that our preferred speci?cation
with three groups has the highest discriminatory power.
23In fact, we considered a broader range of proxies, including the attainment levels
(for the 15+ and 25+ population) and average years of education of the population
that is 15+ years old (Barro and Lee, 2001). We also considered the amount of private
credit as a percentage of GDP (DemirgucKunt and Levine, 2001). In unreported
results, our ?ndings are qualitatively similar.
12
Page 13
In sum, our tests show that we indeed need to account for ine?ciency and
di?erences in technology parameters. Our preferred speci?cation is an uncon
ditional latent class model with three groups. Individual capital and labor
elasticities are similar to previous ?ndings in the literature yet statistically
di?erent across groups. Group membership is not conditional on human capi
tal and ?nancial development.
4.2E?ciency and scale elasticity levels
The next step involves exploring to what extent the technology parameters
and e?ciency levels of our groups di?er. Table 7 in the Appendix reports the
classi?cation of the three groups with di?erent production technologies. Figure
1 visualizes the geographical grouping of countries.
Our latent class model yields a classi?cation of countries that is in line with
many previous studies that identify the U.S. and economies with a similar
market structure as the economic leaders. At the same time, we should note
that the most e?cient countries (compared to the relevant peer group's tech
nology) need not be those with the highest levels of income. In fact, while
mean real GDP in Table 3 is highest for group one, some countries in this
group have low levels of income but employ their technology very e?ciently.
This explains why our classi?cation is at times substantially di?erent from,
for example, the World Bank's taxonomy.
As the TFP decomposition in Table 3 shows, group one is the most e?cient
compared to its own frontier. Also, factor accumulation is only marginally
(during the 1970s) enhanced by positive scale elasticity. Mean technological
change over the three decades is slightly negative at 0.71 percentage points.
Hence, this group has all the characteristics of a mature economy.
13
Page 14
Figure 1. Three groups of countries with di?erent production technologies
Group 2
Group 3
Group 1
Notes: See Table 7 for the list of sample countries in each group.
14
Page 15
In contrast, Table 3 shows that group two enjoys increasing returns to scale,
implying that pure factor accumulation contributed overproportionately to
output. E?ciency levels are also fairly high for this group. And, technical
change is again negative on average. This group primarily consists of countries
located in continental Europe, Australasia and South America, as well as
Japan. In principle, these countries may try to catch up with the leader group
through factor accumulation. Whether they indeed do is discussed in the next
subsection.
Like group two, scale elasticities are important for group three. In fact, over
time this group evolves from producing with slightly negative scale elastici
ties to producing with highly positive scale elasticities, even surpassing group
two. However, in this group the amount of output wasted due to ine?cient
production is high (approximately 20 percent of real GDP). This group con
sists mainly of countries located in SubSaharan Africa and Southeast Asia.
While this indicates that policies aimed at reducing ine?ciency warrant fur
ther exploration, two important caveats need to be noted. First, whether each
individual country in this group should invest in reducing ine?ciency or in
enhancing factor accumulation or technology depends on the costs of each
respective strategy. Our current analysis suggests that both strategies should
be considered seriously, but does not lead to a preferred strategy. Second, the
two strategies may be related. Countries that try to adopt better production
technologies may temporarily experience low e?ciency levels.
On average, groupspeci?c e?ciency is fairly persistent. While our e?ciency
levels per decade indicate that mean e?ciency changes in each group were
small over time, within each group there are interesting developments. For
example, Figures 3 and 4 in the Appendix illustrate that some countries with
low levels of e?ciency in 1970 (e.g. Kenya or Venezuela) manage to improve
their e?ciency during the 1980s and 1990s. Over the same sample period,
e?ciency decreases in other economies (e.g. Thailand). Policies aimed at in
creasing e?ciency may be either absent due to high implementation costs, or
they may be unsuccessful.
In sum, our three groups di?er signi?cantly in terms of their e?ciency and
scale elasticity levels. Group one is mainly characterized by constant returns
to scale and high levels of e?ciency over time. Group two is almost as e?cient
as group one but exhibits increasing returns to scale. In contrast, group three
is the least e?cient and exhibits increasing returns to scale. We next calculate
each component's contribution to TFP changes.
15
View other sources
Hide other sources
 Available from James Kolari · Jan 4, 2013
 Available from SSRN
 Available from uu.nl