# 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 1970-2000. 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).

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**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 firm-level 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 high-tech sectors and, to some extent, in medium-tech sectors. By contrast, supporting corporate R&D in the low-tech sector turns out to have a minor effect. Instead, encouraging investment in fixed assets appears vital for the productivity of low-tech 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):125-140. · 0.87 Impact Factor - SourceAvailable from: Nadia belhaj hassine
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**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 top-down 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, G-60006 Frankfurt

dMays Business School, Texas A&M University, 4218 TAMU, College Station,

Texas 77843-4218, USA

Abstract

This paper investigates the forces driving output growth, namely technological, e?-

ciency, and input changes, in 80 countries over the period 1970-2000. 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 cross-country growth literature narrowly focuses

on the role of capital in generating economic growth (Baumol, 1986; Barro,

1991, 1996; Barro and Sala-i 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 cross-country 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 two-stage 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 so-called 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), j-kolari@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

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A major advantage of this Stochastic Frontier Analysis (SFA) framework is the

tri-partite 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 less-developed 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; Demirguc-Kunt and Levine, 2001).

Our empirical analysis is based on a sample of 80 countries over the period

1970-2000. 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).

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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 cross-country 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

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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 output-oriented 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 cross-country 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 cross-sectional 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 non-parametric 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

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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+ vit|j− uit|j,

(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

Pit|j=

J

?

j=1

Π(i,j)

T?

t=1

Pit|j=

J

?

j=1

Π(i,j)Pi|j.

(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 country-speci?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 sub-optimal 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 Cobb-Douglas 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 non-negative distribution truncated at zero. Ine?ciency

is time-variant 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 re-parameterize 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

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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 right-hand-side represent technological

and e?ciency changes, respectively. The third and fourth terms represent

elasticity-adjusted 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 group-speci?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.18Country-speci?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

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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 Demirguc-Kunt 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 country-speci?c average growth rate. For robustness purposes, we also

calculated a backward-looking 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.

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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

Cobb-Douglas 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: p-values 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, over-speci?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 over-speci?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 log-likelihood 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 Demirguc-Kunt 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 (Demirguc-Kunt 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 over-proportionately 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 Sub-Saharan 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, group-speci?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

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