Semi-endogenous growth theory versus fully-endogenous growth theory:
a sectoral approach
ABSTRACT
In the last two decades, endogenous growth theory has generated a second
generation of models to solve the empirical paradoxes that arose from the first
generation.
These models are based on two theoretical approaches: semi-endogenous growth
theory and fully-endogenous growth theory, each with different assumptions about
technical progress, the main driver of economic growth. This paper offers, for the first
time, an analysis of the validity of the aforementioned theories in a sectoral context,
applying the most modern tests and estimation procedures for the treatment of panel
data.
1
1. Introduction
The 1990s were prolific in the development of theoretical models able to
identify the causes of economic growth. However, the variety of explanatory models
developed under different assumptions had one feature in common: the existence of
productive inputs such as technology and human capital which, under the assumption of
non-decreasing returns to scale, ensured long-term economic growth. More specifically,
the first generation endogenous growth models ensured that the sustained increase of
these inputs should accelerate TFP and per capita output growth.
The inclusion of the "ideas" in the explanation of growth, as Jones (2005) states,
resulted in the alteration of three basic assumptions: Unlike traditional inputs, ideas are
a non-rival input, which implies the existence of increasing returns to scale in the
production of final goods and, therefore, the need to raise models of imperfect
competition. The logical link between non-rivalry and increasing returns to scale led the
study of the so-called "scale effect" in growth models to be the focus of much of the
research effort in recent years.
In the first generation endogenous growth models –Romer (1990), Grossman
and Helpman (1991) and Aghion and Howitt (1992)–, the assumption of constant
returns to scale in the R&D sector implied the existence of the so-called "scale effect" in
its "strong" form: the long-run rate of TFP growth and, hence, the long-run growth rate
of per capita output were increasing functions of the growth of the knowledge stock
which was, in turn, an increasing function of the scale of the economy, quantified by the
size of the population. In the long term, therefore, it will suffice to increase the level of
resources devoted to R&D in order to increase the TFP growth rate1.
While the theoretical frameworks seemed to offer a satisfactory explanation of
economic growth, economic reality ran contrary to the theoretical prescription. Two
pieces of empirical evidence question the validity of the prevailing theoretical
framework. First, in some influential papers, Jones (1995a, 1995b) showed a new
empirical paradox by pointing out that, historically, TFP growth in developed
economies and, particularly, in the United States, has remained constant, or even
decreased, despite the continued increase in R&D expenditures and in the number of
1
Note that the strong scale effect implies that long-term positive population growth would lead to an
exponential increase in per-capita income which becomes infinite in the steady state. This is clearly an
unrealistic prediction that prompted the removal of the assumption of scale effects in Schumpeterian
growth models.
2
scientists and engineers. Second, and more recently, several empirical studies (see, for
example, Stiroh and Botsch, 2007) show that U.S. productivity underwent a continuous
acceleration at the start of this millennium, even though investment in information and
communication technology (ITC) had clearly been reduced.
What might be termed "Jones's paradox” led to the development of new
theoretical approaches that introduced certain changes in the basic assumptions of the
traditional endogenous growth model. First, the semi-endogenous growth theory,
initially proposed by Jones himself (1995b), Kortum (1997) and Segerstrom (1998)2.
This theory presupposes the existence of decreasing returns to scale in the production of
knowledge that would explain why, despite there having been a continued growth in the
technological input, TFP growth has not accelerated. Under this assumption, the
development of the semi-endogenous growth model determines that, in the long run,
TFP growth will exclusively depend on the increase observed in the population, as it is
this variable that ultimately limits the R&D employment growth rate. If a permanent
acceleration in productivity is to be observed, a continued increase in population growth
rate will also be required. In this way, the scale effect takes its weak form: it is the per
capita income level of an economy, not its growth, that is an increasing function of
population size.3
The development of semi-endogenous growth theory runs parallel with another
research trend in the Schumpeterian framework known as fully-endogenous growth
theory, which appeared initially in the works of Aghion and Howitt (1998, ch.12),
Dinopoulos and Thompson (1998) and Peretto (1998)4. They maintain the assumption
of constant returns to scale in the knowledge-creation function, admitting, however, the
existence of a sectoral differentiation process –horizontal and vertical– associated with
2
Jones (1995b) proposed this name for a model that is endogenous in the sense that long-term growth is
driven by technological progress and this, in turn, is driven by R&D investment from profit-maximizing
economic agents. In contrast to the endogenous growth models of Romer, Grossman and Helpman and
Aghion and Howitt, Jones does not recognize the influence of changes in economic policy on growth. In a
more recent paper, Dinopoulos and Sener (2007) seem to distance themselves from this designation,
calling the aforementioned models of Jones and Segerstrom "exogenous Schumpeterian-growth models
without scale effects".
3
It is obvious that the weak scale effect does not hold at present, given the levels of poverty of the nations
with the highest levels of population. However, as Jones (2005) points out, it is necessary to adjust, assess
and take into account other differences, mainly institutional, to test the existence of the weak scale effect.
In our paper this clarification does not seem necessary because we are working with developed countries
where the institutional differences or the degree of openness are not so conspicuous as to affect the
results.
4
Dinopoulos and Sener (2007) call these models "scale-invariant endogenous Schumpeterian growth
models" and divide them into horizontal product differentiation models and another, newer type based on
rent protection activities (RPA) derived from quality-ladder models.
3
economic growth. This process causes the effectiveness of the "R&D input" to be
diluted among a larger number of sectors, which explains why the TFP growth can
remain constant in spite of the continuous increase of the R&D input5. Product
differentiation prevents the population size from having a scale effect on long-run
growth, which was a characteristic of the first generation models. In addition, in the
long run, constant returns to scale in the the knowledge-creation function ensure that the
TFP growth depends on economic factors and economic policy measures, which
establishes a crucial difference with respect to the semi-endogenous growth model.
The empirical studies –such as Ha and Howitt (2007), Madsen (2008), Madsen
et al. (2009), Islam (2009), Zachariadis (2004), Ulku (2007b) and Ang and Madsen
(2009)- adopted a macroeconomic perspective and obtained evidence supporting the
Schumpeterian hypothesis6.
Sectoral studies carried out in the context of second generation endogenous
growth models have focused on the validation of the Schumpeterian hypothesis with a
common denominator: the use of different proxies for research intensity in order to
analyse the influence of this variable on productivity growth. Among them, Griffith et
al. (2003), Griffith et al (2004) Zachariadis (2003, 2004) or Ulku (2007 a) provided
evidence in favour of Schumpeterian endogenous growth theories.
Our work follows these contributions and intends to be the first in this field of
research which focuses on the sectoral level to test the validity of the two second
generation endogenous growth theories. It provides standardized information for 10
manufacturing sectors of six developed countries over 22 years, 1979-2000 (the data
used by López-Pueyo et al. (2008)). This innovation is particularly significant, since, as
Aghion and Durlauf (2009) pointed out, this is the right field to assess the usefulness of
5
Madsen (2006), however, interprets product proliferation as a "tendency to the existence of decreasing
returns to scale in the R&D stock". Indeed, the Schumpeterians recognize the pernicious effect of the
increasing complexity of the research on the R&D productivity, but acknowledge that there are other
compensatory mechanisms of this effect such as "capital deepening", the result of productivity growth,
and the "labour augmenting technological progress" which, as in the manufacturing sector, makes
workers more efficient in the R&D industry. The assumption of constant returns to scale in the R&D
stocks is maintained with these compensatory mechanisms.
6
Madsen (2008) showed that the Schumpeterian growth theory was, to a large extent, consistent with the
time series evidence, not with the cross-country evidence. Madsen et al. (2009) also supported the
Schumpeterian hypothesis and showed that Indian growth was positively associated with research
intensity and with technology spillovers transmitted through trade, the distance to the frontier and various
reforms introduced especially in the decade of the 1990s.
4
some models ―innovation-based endogenous growth models― that have been
designed in terms of companies and sectors, not in terms of aggregate economies.7
The paper is structured as follows. After this introduction, Section 2 undertakes
a brief review of the analytical implications of the various endogenous growth models.
Section 3 transfers these formulations to the empirical field, the variables and data
sources are described and the validity of those models are discussed in two phases: first,
by applying the adequate unit root and cointegration tests for the various panel data
models and, secondly, by building a model to explain the increase in TFP. Section 4
improves and extends the model, refining the measures of research intensity and
incorporating the absorptive capacity as an explanatory variable8. Finally, Section 5
discusses the main findings.
2. Basic approach of endogenous growth models
Following Ha and Howitt (2007), it is possible to synthesize each of the three
growth theories mentioned, starting from the central idea, common to the different
versions, that the explanatory role of TFP growth is equivalent to the knowledgecreation function, and that both, therefore, depend on a R&D input and on other inputs.
Thus, from a common expression, one can test various theoretical models considering
different null hypotheses about the parameters.

X
g A     A 1
Q
0    1,   0
(1)
Q  L in the steady state
where g denotes growth rate, A is productivity (knowledge)9; X is a proxy for the
so-called "R&D input" (R&D expenditures, patents or number of researchers in the
semi-endogenous growth models and "R&D input adjusted for productivity" in the
Schumpeterian growth models); Q is a measure of product proliferation and L is
In the words of the authors “New growth theories such as the innovation models focus on interactions
that are defined with respect to firms and industries, not aggregate economies. For this reason,
identification of these effects is problematic when the exclusive focus in on aggregate data. The reason
for this is that the endogeneity of those aggregates that produce spillovers (e.g. as human and physical
capital) is difficult to disentangle from the effects of other aggregate determinants, e.g. the saving rate”.
(Aghion and Durlauf, 2009, pp. 24).
8
We refer –as Islam (2009) does– to R&D based absorptive capacity.
9
This paper does not go into the eternal and complex debate over the definition of TFP and technical
progress. Ha and Howitt (2007, p.736, n. 9), for instance, define productivity in labor-augmenting terms
and refer to it as TFP.
7
5
employment10. is a research productivity parameter;  is a duplication parameter (0 if
all innovations are duplications and 1 if there are no duplicating innovations), is
returns to scale in knowledge and  is the parameter of product proliferation.
Endogenous growth models can be distinguished by the parameters:  and .
The first generation endogenous growth models foresee the existence of constant returns
to scale in knowledge, that is to say, =112; there are no external effects so the rate of
generation of new ideas is independent of the knowledge stock. In these models the
product proliferation is not considered, that is, =0. So that productivity growth is
expressed as:
g A  X 
(2)
In this model, with constant returns to scale in the creation of new knowledge, a
positive growth in the input is enough to cause an acceleration of productivity, which
leads to the scale effect in its strong form: economic growth is proportional to
population size.
On the contrary, semi-endogenous theory assumes that there are diminishing
returns to scale in knowledge (that is, <1). This is the case known in literature as
"fishing out" and implies that the rate of innovation decreases with the knowledge stock
because the most important ideas arise at the beginning and, as the knowledge stock
increases, the finding of a new idea becomes less and less likely. Additionally, the
assumption of the absence of product proliferation effects (=0)13 is maintained. In
short, TFP growth is expressed like this:
g A  X  A  1
  1 (3)
so that the existence of diminishing returns to scale in the knowledge stock solves the
problem of strong scale effect that is characteristic of the first generation models. So the
scale effect takes the weak form: the increase in the productivity growth rate requires a
10
Since g A 
A
, it is possible to identify determinants of the knowledge-creation function from the
A
different models.
11
The
 parameter is important because it serves to distinguish between endogenous models and
traditional neoclassical models in which the parameter takes the value zero, which means accepting that
technical progress is exogenous.
12
As Jones (1995b, p. 766, n. 8) indicates, it is a completely arbitrary assumption, essential to ensure the
endogeneity of growth in the traditional sense.
13
However, it is possible to propose an extended semi-endogenous growth model, which combines the
existence of decreasing returns to scale in the production of knowledge and imperfect product
proliferation with β < 1. See Section 3 of this paper.
6
continued increase in the R&D input growth rate, not merely of its level. Ultimately,
long-run growth in per capita income is proportional to the population growth rate,
traditionally considered exogenous14.
Finally, the so-called fully-endogenous growth theory maintains the assumption
of constant returns to scale in knowledge characteristic of the first generation models
(=1), but assumes that the effectiveness of R&D investment decreases as the range of
products increases, =1.
X
g A    
Q

(4)
As a result, the product proliferation avoids the scale effect of the growth in
R&D inputs on productivity growth, so that, log-run growth in per capita income is
proportional to the increase in the research intensity X/Q, and not to the mere increase
of X.
14
Although population growth is often referred to as an exogenous explanatory factor, Jones (1995b)
quotes Kremer’s (1993) model as an example where population growth is endogenously determined by a
Malthusian process.
7
3. Empirical test of endogenous growth models
3.1 Empirical model approach
In order to empirically validate the model, Ha and Howitt (2007) transform (1)
with a log-linear approximation, representative of an error correction model:
 A
ln  t
 At



 1
  ln    ln X t  ln Qt  
 ln At    1,t
  



(5)
 At 
 is indeed stationary, the expression
 At 
and valid to verify the two theories, so that, if 
included in brackets must also be stationary:


  1
Et  ln X t  ln Qt  
 ln At  (6)
  


Taking into account the parameter differences that characterize the two theories,
the analytical expressions and econometric requirements of both approaches will be set
out below.
Semi-endogenous growth theory. Since, in the semi-endogenous growth
models, =0, Q is constant and, therefore, the stationarity of the term in brackets
requires


  1
Et  ln X t  
 ln At  (7)
  


to be stationary. Following Ha and Howitt (2007), the stationarity of expression (7)
implies that lnX and lnA should be integrated of the same order and, if they are not
stationary, there should be a cointegrating relationship between them with a
cointegrating vector [1,    1  ] where, if it is assumed that <1, the second element in
  
the vector is strictly negative.
Fully-endogenous growth theory. The Schumpeterian approach maintains the
assumption of constant returns to scale (=1) but admits the pernicious effect of product
proliferation, =1. The combination of the two restrictions implies that the expression
Et =lnX - lnQ (8)
representative of the R&D input adjusted by the product proliferation must be
stationary.
8
As stated in Madsen (2008), the following cointegration model nests both
previous versions:
ln X t   ln Qt   ln At  e 2,t
(9)
where   (1   ) .
The Schumpeterian growth theory presupposes that   0 and   1 , whereas the
semi-endogenous growth theory implies that   0 and   0 , e2,t being the stationary
error term. The application of the cointegration test to this expression will allow us to
know which of the two approaches is the most consistent with the data, although, as
Madsen (2008) points out, the existence of a cointegrating relationship between the
variables A, X and Q is a necessary although not sufficient condition to conclude that
the TFP growth is explained by either model.
For this reason and following Madsen (2008), different estimations of the TFP
growth equation have been carried out in this paper. The basic regression takes the
form:
X
 ln At   ln  t
 Qt
 Amax  A
   
  
 ln X t    t 1 max t 1

At 1
 1 


   t (10)


where Amax represents, for each sector, the TFP value in the country which is the
technological leader in each of the years under study.
Equation (10) nests the Schumpeterian theory (extended to allow for the
gravitation of TFP towards the leading edge technology) and semi-endogenous theory.
As is well known, Schumpeterian growth theory foresees that and  >0, whereas
the semi-endogenous growth theory assumes that and  >0.
After the description of the variables and data sources in Section 3.2, Section 3.3
will be devoted to the empirical estimation of these models.
9
3.2. Variables and data sources
The data used in this paper are the result of an intensive effort to improve the
calculation of TFP and obtain comparable measures both between sectors and between
countries. Hence, the empirical analysis is performed only for the industrial
manufacture of the developed countries for which the information available is detailed
and homogeneous enough. This condition, of course, must be taken into account when
interpreting the results presented in the following paragraphs.
The data cover the period 1979-2001 and comprise ten aggregations of the
manufacturing sector in six countries. The sectors considered were “Food products,
beverages and tobacco” (15–16); “Textiles, textile products, leather and footwear” (17–
19); “Pulp, paper, paper products, printing and publishing” (21–22); “Chemicals and
chemical products” (24); “Rubber and plastic products” (25); “Other non-metallic
mineral products” (26); “Basic metals and fabricated metal products” (27–28);
“Machinery and equipment (n.e.c.)” (29); “Electrical and optical equipment” (30–33)
(ICT) and “Transport equipment” (34–35). The countries analysed were Finland,
France, Italy, the United States, Canada and Spain.
As the endogenous variable, we have taken the logarithm of TFP (A), that is, the
change in output not explained by changes in the use of inputs– expressed in index
form:
1

1


 2 ( sˆz  s )(ln Lz  ln L)  (1  2 ( sˆz  s ) (ln K z  ln K ) 


 (11)
ln Arz  (ln Vz  ln Vr )  
 1

1


 ( sˆr  s )(ln Lr  ln L)  (1  ( sˆr  s ) (ln K r  ln K )
2


 2

where V is the gross value added; r, z are two different observations (e.g., sector-country
r and sector-country z in the same year or the same sector-country in two different
years); L is employment, ŝ is an estimate of the share of labour income in the value
added; s is the average estimate of the shares of labour income in the value added; K is
the physical capital stock; and
ln X 
1
M
M
 ln X
n 1
n
, where M is the total number of
observations.
10
The TFP index used is the Tornqvist index, transformed using the Elteto-KovesSzulc (EKS) method15. This index is superlative, because it can be derived from a
determined form of the production function (quadratic or translogarithmic). The index
took base 100 in 1997 for each individual (the sectors of the different countries),
because we chose that year to express the monetary magnitudes in real terms.
Value added, employment and gross fixed capital formation data were taken
from the STAN database of the OECD.
The figures of the value added were expressed in local 1997 currency units using
STAN volume indexes, except in the case of sectors 30–33 (Electrical and optical
equipment), for which hedonic prices were used. Hedonic prices were available at the
Industry Labour Productivity Database of the Gröningen Growth and Development
Center (GGDC). Subsequently, the figures of the value added were converted into 1997
US dollars using the unit value ratios (UVR), published by the GGDC in the
Manufacturing Productivity and Unit Labour Cost Database.
Likewise, to take into account the different position of the countries in the cycle
and to facilitate international comparisons, the value added was adjusted by the output
gap of the manufacturing sector of each country, calculated by the Hodrick-Prescott
smoothing method, as López Pueyo et al. (2008) propose.
As for capital, gross fixed capital formation at current prices was taken from the
STAN database. The variable was expressed in real units of 1997 and converted into US
dollars of the same year, using the gross fixed capital formation PPP of the different
countries calculated by the OECD. With these figures, the accumulated physical capital
stocks were calculated by applying the perpetual inventory method frequently used in
the empirical literature.
The labour factor was approximated by the number of hours worked in the
sectors of the countries analysed, according to the information published by the GGDC.
Two variables representing the R&D input were considered: business R&D
expenditures (R), taken from the OECD ANBERD database and deflated using the
OECD producer price index for manufactures and, secondly, the ratio of R&D
expenditures and TFP (R/A), a variable used in Schumpeterian models to reflect the
increasing complexity associated with the innovative process.
15
For multilateral comparisons in panel data (with spatial and temporal dimensions, as in this paper), the
best indices are chain volume type –such as those of Fisher and of Törnqvist (to avoid the bias of the
fixed weighted indices) – transformed by means of the Elteto-Koves-Szulc (EKS) method –as Caves et al.
(1982) did– so that they are transitive.
11
Two variables were incorporated as measures representing product proliferation:
(A/L), that is, TFP adjusted for hours worked, and V, the value added adjusted by cycle.
So the variable research intensity (that discounts the effect of product proliferation on
the R&D investment efficiency) was measured by the variables (R/AL) and (R/V).
3.3. A first approach: Results of unit root and cointegration tests
A first step to test whether the second generation endogenous growth theories
are consistent with the data is to analyze whether the variables involved in the various
versions are stationary and, if they are not, whether there is a cointegrating relationship
between them.
As described in Section 3.1, to test the semi-endogenous growth model, a
cointegration model has been proposed (assuming TFP growth is stationary), in which
variable X is R (estimate 12a) or, alternatively, R/A (estimate 12b)
lnAijt=0ij+1lnXijt+ijt
(12)
From this expression, in which i denotes the sector and j denotes the country and
the rest are the known variables, the prediction of the semi-endogenous growth model is
that 1>0 and the error term is stationary.
Additionally, following Madsen (2008), an extended semi-endogenous growth
model has been proposed by including two variables representing the product
proliferation (Q). They are the TFP adjusted by labour variable (AL in estimate 13a),
and variable V, which measures the sectoral value added (estimate 13b).
lnAijt=0,ij+1lnXijt++2lnQijt+ijt
(13)
If the semi-endogenous growth theory is true, it is expected that 1>0 and 2=0.
Finally, the Schumpeterian hypothesis has been tested by means of the following
expression:
lnXijt=0,ij+1lnQijt+ijt
(14)
where, again, the R&D expenditures flow (R) is used as a proxy for knowledge input
and two variables are used as a proxy for product proliferation: TFP adjusted for
employment (AL in estimate 14a) and sectoral value added (V in estimate 14b). The
prediction, in this specific case, is that 1=1 and that the error term is stationary.
All the models have been estimated using data from the six countries and ten
sectors described in Section 3.2, taking 1979-2001 as the time period. The technique
12
used is Dynamic Ordinary Least Squares (DOLS), developed by Stock and Watson
(1993), which takes into account, and corrects, the endogeneity bias and serial
correlation. The results are given in Table 2, but previously the results of the unit root
test applied to all the variables involved in the models are presented in Table 1.
As is well known, the test developed by Im et al. (2003) (IPS), which is
frequently used in empirical applications to assess the stationarity of the series, assumes
the independence of the different individuals of the sample. This assumption has been
questioned by some scholars, especially when working with a sample of developed
countries where the existence of influences common to all members is taken for granted.
This dependence is the logical result of the globalization phenomenon which has been
observed in recent decades and which generates a significant degree of interaction in the
panel data, especially in regressions in which we work with a group of developed
countries16.
In the second column of Table 1, the dependence of each variable taken
individually is analysed by means of Pesaran's (2004) CD test, with the aim of deciding
which unit root test should be applied in each case. To calculate the CD statistic of each
variable, 60 autoregressive models were previously estimated, one for each individual in
the sample, using Schwarz’s (1978) BIC lag selection criterion. Since the vast majority
of the models selected were AR (1) models and the matrix required to implement the
CD test should be a balanced matrix, we chose to incorporate a single lag for all models,
thus obtaining a residue matrix of dimension 22*60 on which the CD test is applied. As
can be deduced from Table 1, the cross-independence hypothesis is rejected for all the
variables in the model, whether they be expressed in levels or in first differences;
consequently the unit root test applied has been Pesaran’s (2007) in all cases.
The Pesaran test of the null hypothesis that ln A has a unit root is not rejected. The
variable to which scholars have paid most attention, productivity growth (ln A), also
presents an unequivocal result, since the null hypothesis of a unit root is always
rejected.
This is a significant finding in our research: as in other studies carried out with
more aggregate data, the "TFP change" variable calculated at the country-sector level is
stationary for the period 1979-2001, which means admitting the constancy of the TFP
growth rates of the sample under study.
16
The cross-dependence may have its origins in unobservable common factors that are part of the error
term, in the spatial dependence, or in idiosyncratic pair-wise dependence of the error terms.
13
Table 1. Cross-dependence test (Pesaran, 2004) and
Unit Root Test (Pesaran, 2007)
Variable
CD
Pesaran
(2004)
Decision
lnA
26.74
TD
-1.97 (-1.97)
I(1)
ln
13.61
TD
-3.06 (-3.06)
I(0)
lnR
16.55
TD
-1.98 (-1.98)
I(1)
lnR
6.72
(0.00)
13.91
TD
-2.93 (-2.93)
I(0)
TD
-2.06(-2.06)
I1)
TD
-3.13 (-3.13)
I(0)
TD
-2.18 (-2.18)
I(1)
TD
-3.11(-3.11)
I(0)
TD
-2.19 (-2.19)
I1)
TD
-3.13 (-3.13)
I(0)
TD
-2.06 (-2.06)
I(1)
TD
-3.11(-3.11)
I(0)
TD
-2.00(-2.00)
I(1)
TD
-3.11(-3.11)
I(0)
lnR/A
lnR/A
lnR/AL
lnR/AL
lnR/V
lnR/V
LnAL
LnAL
Ln V
LnV
Pesaran (2007)
Decision
(0.00)
(0.00)
(0.00)
(0.00)
10.77
(0.00)
14.26
(0.00)
13.38
(0.00)
12.04
(0.00)
1213
(0.00)
24.53
(0.00)
17.07
(0.00)
37.49
(0.00)
13.89
(0.00)
Notes: A denotes TFP, R is R&D expenditures; R/A is productivity-adjusted R&D expenditure; AL is TFP adjusted for
hours; and V is sectoral value added.
Number of observations: 1320
In the meantime, what has been the behaviour of the technological variables? Do
they also show constant growth rates or do these rates tend to accelerate? To answer
these questions, the Pesaran test has been applied to the two variables representing the
technological input. The first, R, includes the sectoral R&D expenditures in each
country, while the second, R/A, refers to productivity-adjusted R&D expenditure (R/A),
a measure with which some growth models (e.g., Aghion and Howitt, 1998) recognizes
the force of increasing complexity. That is, as technology advances, it takes an everincreasing R&D expenditure just to keep innovation at the same rate.17
17
Models that incorporate this specification belong to the first generation of endogenous growth models,
and maintain the assumption of constant returns to knowledge. When R&D input is adjusted for
productivity, it is assumed that the negative impact of the increasing complexity on the productivity
growth rate is offset by the positive effect of other factors such as capital deepening associated with
innovation or greater labour efficiency.
14
As we can see, the results are identical for both variables and for TFP. The R&D
input variables are I(1) whereas their differences clearly allow us to reject the null
hypothesis of a unit root with the stationarity test.
Having proved the non-stationarity of the variables involved in the model, the
validity of the semi-endogenous approach requires us to demonstrate that there is a
cointegrating relationship between the two variables. To do this, we initially have
applied the ADF test developed by Kao (1999). The results, included in the second
column of Table 2, show that the null hypothesis of no cointegration is not rejected,
which invalidates the semi-endogenous growth approach (specifications 12a and 12b).
However, when the Pedroni (1997) test is applied, it rejects the null hypothesis of no
cointegration with a p-value of 0.00.
Table 2. Tests of cointegration
Estimate
(12a)
(12b)

a


b

(14a)
ADF
Kao
-0.08
(0.46)
0.42
(0.33)
-2.70
(0.00)
-2.40
(0.00)
-2.88
(0.00)

(14b)

-3.02
(0.00)
Equation
Pedroni
(1997)
-14.44
(0.00)
-14.12
(0.00)
-12.27
(0.00)
-12.27
(0.00)
-15.16
(0.00)
-14.82
(0.00)
-14.05
(0.00)
-13.74
(0.00)
-15.04
(0.00)
-14.71
(0.00)
-16.47
(0.00)
-16.11
(0.00)
Semi-endogenous growth model
lnAijt=0,ij+lnRijt+ijt
(5.58)
Semi-endogenous growth model
lnAijt=0,ij-lnR/Aijt+ijt
(-2.07)
Extended semi-endogenous growth model
lnAijt=0,ij+lnRij,t++lnALij,t+ijt
(3.19)
(17.96)
Extended semi-endogenous growth model
.
lnAijt=0,ij+lnRij,t++lnVij,t+ijt
(9.20)
(0.26)
Schumpeterian growth model
.
lnRijt=0,ij+lnALijt+ijt
(3.67)
Schumpeterian growth model
lnRijt=0,ij+lnVijt+ijt
(0.43)
Notes: A denotes TFP, R is R&D expenditures; R/A is R&D expenditures adjusted by TFP; AL is TFP adjusted by hours;
and V is sectoral value added.
Number of observations: 1320
This mixed evidence about the semi-endogenous hypothesis is also found in
other empirical studies. Ha and Howitt (2007) and Madsen (2008) obtained mixed
15
results from the use of different R&D input variables. Ha and Howitt (2007) suggested
that semi-endogenous growth theory is not consistent with the long-run evidence when
the null hypothesis that R&D input variables contain a unit root is not rejected at 5%
significance level.18 In any case, under the assumption they are I(1), the Johansen test
could not reject the hypothesis that there was no cointegrating relationship. Madsen
(2008) also did not find a cointegrating relationship between the logarithm of R&D
expenditures or patents on the one hand, and the TFP, on the other, using the DF test
proposed by Kao.
In the extended semi-endogenous growth model proposed in specification 13a,
the results of the unit root test show that the variables expressed in levels are not
stationary. Both the test of Kao (1999) and the test of Pedroni (1997) show that the null
hypothesis of no cointegration between lnA and the two explanatory variables (lnAL and
lnR) are rejected. Both are significant at 1%, with respective elasticities of 0.05 and
0.67.
By contrast, specification 13b, in which product proliferation is assessed by the
sectoral value added (V) does not provides good results. Even if one accepts that the
variable is I(1) –as deduced from the IPS test (2003) and Pesaran (2007)– and maintains
a cointegrating relationship with ln A as both the tests of Kao (1999) and Pedroni (1997)
show, the variable is not significant.
Thus, the evidence calls into question the validity of the simple semiendogenous growth model, but supports the extended model, when product proliferation
–an eminently Schumpeterian variable– is incorporated and approximated by ln AL.
Finally, according to Ha and Howitt (2007), in the absence of statistical
significance in the parameters, it enough to test the stationarity of ln R/AL and ln R/V to
support the Schumpeterian model. In our case, as shown in Table 1, the variables R/ AL
and R/V are not stationary but they are in differences. Given this result, the next step, in
line with the suggestion of Madsen (2008), is to assess whether there is a cointegrating
relationship between them.
The existence of a cointegrating relationship is confirmed in specifications 14a
and 14b, with the Kao (1999) and Pedroni (1997) tests, although the product
differentiation variable is significant only in model 14a. Therefore, the results suggest
18
Ha and Howitt (2007) find that the ADF test rejects the null hypothesis of a unit root in ln X for two
R&D inputs (the number of workers engaged in R&D in G5 countries and productivity-adjusted R&D
expenditure) while it is not rejected either for R&D employees in the U.S. or the lnA. In differences, the
null hypothesis of the existence of a unit root is rejected in all cases.
16
the validity of the Schumpeterian approach where the proxy for product differentiation
is AL, the same as is found in the analysis of Ha and Howitt (2007) (with seven proxies
of product differentiation) and in Madsen (2008) (with three different variables,
regardless of whether the proxy for R&D input is R&D expenditures or patents).
However, in estimate 14a, the parameter of product proliferation (AL) although
significantly different from 0 is also significantly different from 1, which is inconsistent
with the Schumpeterian hypothesis. Madsen (2008) also obtained this result, but he did
not believe that this evidence was sufficient to deny the validity of the fully-endogenous
growth model, given the difficulty of capturing product proliferation in its entirety.
In sum, the stationarity and cointegration analysis carried out so far, allows us to
deny the validity of the semi-endogenous growth model, recognize the validity of a
hybrid model in which the existence of diminishing returns is accompanied by product
proliferation and suggest the validity of the Schumpeterian approach with certain
limitations as product differentiation does not yield the expected parameter near unity.
3.4. Explanatory model of TFP growth
The existence of a cointegrating relationship between the variables A, X and Q is
a necessary but not a sufficient condition to conclude that TFP can be explained by
either of the two models.
Therefore, the stochastic version of equation (10) is estimated by OLS in this
section, with different specifications of the equation representing TFP growth and, thus,
complementing the cointegration estimates to test whether the predictions of second
generation models are consistent with the data.
The model is based on Howitt's (2000) theoretical proposal that nations that
carry out R&D will converge in growth rates whereas those that do not will have no
long-term growth. Empirically, following Saxena et al. (2008), the explanatory model
can be enriched by: a) the acquisition of technology through international technology
spillovers which are transmitted through trade or other means and whose ability to
explain economic growth has been amply recognized in the abundant literature that
followed the publication of the work of Coe and Helpman (1995) the absorptive
capacity generated internally, directly related to the investment in technology at the
sectoral-country level and, finally c) the capacity to grow and catch up with the leader
countries, independent of the international economic relations that are established via
17
foreign direct investment or international trade. Griffith et al. (2004) founnd R&D to be
statistically and economically important in both technological catch-up and innovation.
Expression (15) nests the two second generation growth models and includes
additional explanatory factors, such as international technological spillovers (Xf) and the
distance to the technological frontier (DF)19.
 ln Aijt   0,ij  1 ln X
d
i jt
Xd
  2  ln X ijt   3 ln  d
Q
f

Xf
   4 ln 

Qf
 ijt


  ijt  5 DFij  ijt (15)


The Schumpeterian prediction is 1=2=0 and 3>04>0, 5>0. The semiendogenous growth hypothesis provides 1>0, 2>0 and 34=5=0.
Estimates of (15) is performed in five-year differences to filter out the influences
of the business cycle and transitional dynamics on TFP growth. Xf was proxied, as
proposed by Coe and Helpman (1995), by the annual technology expenditure of
individual countries weighted by the accumulated percentage of imports of products of
sector i that arrive from country h into country j and then multiplied by the average
openness of country j during the period.
The R&D conducted in each sector-country is assessed with the five-year
average of (R/AL), (R/V). Estimates also included a variable that contains the foreign
research intensity weighted by import penetration (mR/AL).
Finally, the distance to the technological frontier for each sector-country is
defined in two alternative forms which are denoted DF1 and DF2, where
 A  Ai
DF1ijt =  max
 Amax


and DF2ijt =
 ijt5
 Amax

 Ai

 (16)
 ijt5
In the first case, the distance to the technological frontier is measured for each
individual (sector-country) as a ratio whose numerator is the difference between the
value of the TFP of the leader and the value of the TFP of each sector-country and
whose denominator is the value of the TFP of the leader. All variables are measured at
the beginning of each quinquennium (t-5). In the second case, the distance to the
technological frontier is defined as the ratio value of the TFP of the leader and the value
of the TFP of each sector-country (at the beginning of the quinquennium).
In this way, the sample is reduced to 240 observations for the period from 1979
to 1999.
19
We refer to autonomous technological transfer or catch-up to the technological frontier.
18
The first obvious result of the estimation of equation (15), shown in Table 3, is
the positive and significant effect of the increase in R&D investment within the country
(variable Rd) on TFP growth. This result provides support for the semi-endogenous
growth theory. The growth in imports of foreign technology (Xf variable), as a reflection
of the international technological spillovers, also exerts a positive influence on all the
estimates, especially in estimates where distance is measured by the DF1 variable. This
latter result also confirms the proposed semi-endogenous approach.
Table 3. An explanatory model of the TFP growth
Estimate
(15a)
(15b)
(15c)
(15d)
Xd=Rd
Xf=Rf
(X/Q)d=R/AL
0.03*
0.01**
-0.10***
-0.05***
0.60***
(2.29)
(1.71)
(-8.09)
(-3.64)
(8.21)
0.03**
0.01**
-0.12***
-0.04***
0.63***
(2.55)
(1.83)
(-8.47)
(-3.35)
(8.60)
0.02*
0.01*
-0.10***
-0.06***
0.21***
(1.62)
(1.47)
(-7.85)
(-4.46)
(9.26)
0.02**
0.01*
-0.11***
-0.05***
0.22***
(1.82)
(1.57)
(-8.15)
(-4.20)
(9.57)
(X/Q)d=R/V
(X/Q)f=R/V
DF1
DF2
R2
0.23
0.24
0.25
0.26
A denotes TFP, R is domestic R&D expenditures, Rf represents the foreign R&D expenditures, AL is PTF adjusted for
employment, V is sectoral value added and DF is the distance to the technological frontier.
*, ** and *** denote that the variable is significant at a 1, 5 and 10%, respectively.
Number of observations: 240
The results for the X/Q variable are surprising because it is clearly significant but
has an unexpected negative sign. This is a result which should be considered carefully,
given that, in many empirical studies, the X/Q variable has a negative and significant
impact on per capita output or on productivity and, in many other papers, it is not
significant. Saxena et al. (2008), for instance, obtained this same sign for a variable for
the research intensity in India, measured as the ratio between patents and labour force.
Ulku (2007a) obtained a negative and non-significant coefficient for the R&D intensity
variable (defined as the ratio of R&D expenditures over output) for one of the four
sectors considered in his study (Machinery and Transport). Ulku (2007b) verified that,
in the large market OECD economies, an increase in the share of researchers in the total
labour force negatively affects the per capita output growth. The author interpreted this
as the existence of diminishing returns in the number of researchers in terms of per
capita output in these countries. Islam (2009) verified that the R&D intensity was not a
19
significant variable when it was measured as R/Y, R/AL, PA/L and PG/L.20 Madsen
(2008) also did not find a clear relationship between research intensity (measured by
R&D expenditure) and TFP growth in OECD countries.
It seems necessary, therefore, to analyse this result in greater depth. It may have
come about due to a problem of multicollinearity, to the difficulties presented by an
adequate measurement of product differentiation or, in an extreme case, that it is
necessary to abandon the assumption of constant returns to scale in research intensity
and replace it with the assumption of diminishing returns to research intensity.
Finally, the coefficient that accompanies the distance to the technological
frontier is, no doubt, the one which offers the most outstanding results, with a clearly
positive and significant influence on TFP growth, suggesting the existence of
conditional convergence in the sample studied: the farther a sector is from the
technology frontier, the higher its potential for accelerating productivity growth. That
coefficient is representative, as Griffith et al. (2003) indicated, of the influence of
institutions, government policy, the level of human capital or trade openness, among
other variables. From a theoretical point of view, the importance of the distance to the
frontier was considered in the models of Aghion and Howitt (1998) and Howitt (2000)
in which the size of an increasing quality innovation depends on how the distance to the
technological frontier is measured.
4. A new explanatory model with "effective" research intensity
These results on the proxies for national and foreign product differentiation have
led us to propose a new empirical model which introduces two important innovations to
approximate the value of X/Q.
First, instead of including R&D expenditures in the numerator, in line with the
extensive literature developed from Coe and Helpman (1995), technological stocks (Sd)
are considered. Furthermore, in the denominator, two proxies for product
differentiation, hours worked (L) and the number of employed (N), were incorporated.
Having calculated the ratios Sd/L and Sd/N for all the years of the sample, the
research intensity is assessed by two measures. The first is calculated as the five-year
20
Where R is R&D expenditures; L the labour force; Y the GDP; PA patent applications and PG granted
patents.
20
log difference of the logarithm of Sd/L, and the second as the five-year log difference of
the logarithm of Sd/N.
These new variables are proxied for the net or “effective” research intensity
whose increase reflects that the rise in R&D expenditure has been sufficient to
compensate for and/or encourage three factors: the depreciation of capital (considered
when quantifying the numerator, Sd), the increase in the stock of knowledge and product
proliferation.
Consequently, the equation to be estimated is
 ln Aijt   0,ij  1 ln
X ijtd
  2  ln
X ijtf
f
d
 X efect

 X efect


   DF   (16)


  3  ln



ln
4
5
ijt
ijt
 Qf 
 Qd 

 ijt

 ijt
The results of equation (16), which incorporates the so-called "effective”
research intensity, are shown in Table 4, where again these estimates are presented with
two possible values of distance to the frontier.
Table 4. Effective research intensity and TFP growth
Estimate
(16a)
(16b)
(16c)
(16d)
Xd=Rd
Xf=Rf
(X/Q)d=
(X/Q)d=
(X/Q)f=
(X/Q)f=
(Sd/L)d
(Sd/N)d
(Sf/L)
(Sf/N)
DF1
DF2
0.01
0.01
0.13***
0.09***
0.66***
(1.16)
(0.93)
(4.29)
(2.94)
(8.59)
0.01
0.01
0.10***
0.12***
0.24***
(0.46)
(0.87)
(3.66)
(3.89)
(9.87)
0.01
0.01
0.10***
0.09***
0.66***
(1.09)
(0.90)
(3.38)
(2.69)
(8.51)
0.01
0.01
0.08***
0.12***
0.24***
(0.42)
(0.83)
(2.83)
(3.68)
(9.88)
R2
0.17
0.20
0.16
0.20
Notes: Rd and Rf represent domestic and foreign R& D expenditure; Sd and Sf are the domestic and foreign
technological stocks: L is hours worked by the labour force; N is the number of employees and DF1 and DF2 are the
two measures used to approximate the distance to the technological frontier.
*, ** and *** denote that the variable is significant at a 1, 5 and 10%, respectively.
Number of observations: 240.
It can be seen that, regarding the first two explanatory factors, the results
obtained with the new model are clearly different to those previously obtained. The
variables representing the increase in R&D expenditure and technological spillovers
lose their significance whereas the variables that proxy the effective research intensity
observed in the five years are significant and clearly show the expected positive sign.
On the contrary, the results for the distance to the technological frontier variable
are practically identical to those obtained previously. The variable is clearly positive
21
and shows the greatest significance of all those included in the model. This result is
common to all empirical studies that incorporate a proxy for the distance to the frontier
and, as pointed out above, it reflects the advantages, in economies with high levels of
integration, of the most backward countries with respect to the leaders.
Associated with this advantage is the absorptive capacity, a concept which refers
to the ability of nations to exploit the leaders’ knowledge. Howitt and Mayer-Foulkes’s
(2005) Schumpeterian model updated the concept under the name of "implementation
capacity”. This approach assumes that technical progress is the main determinant of
productivity growth in the long run and that technology transfer depends on "effective
skills", which in turn depend on the degree of development of the country and on the
distance to the technological frontier. Thus, the tendency to converge with the leader
will depend on the ability of the countries to implement modern technologies developed
elsewhere, the only ones with enough qualifications to develop the so-called "modern
R&D". The sample of developed countries used in this paper can be considered part of
the group of nations capable of absorbing foreign technology; this differentiates them
from lagging countries, in which insufficient starting conditions erode their absorptive
capacity and keep their growth rates far from those located at the technological frontier.
Two factors have traditionally been considered as major determinants of the
ability to absorb and implement foreign technology, namely, human capital, which
Abramovitz highlighted in 1986, and the national technological capability, considered
by Griffith et al. (2003, 2004), among others.
In our paper, which has not been provided with adequate data about human
capital at the sectoral level, various measures of absorptive capacity have been
examined, all of them based on R&D data. This absorptive capacity is measured by the
interaction between research intensity and the distance to the frontier. Research intensity
is measured in three alternative ways in which R&D expenditure appears as flow (R/Y)
or stock (Sd/L, Sd/N). The interaction between these three variables and two
specifications of the distance to technological frontier, DF1 and DF2, allows us to
obtain six proxies of absorptive capacity.
For reasons of space, Table 5 shows the results obtained from estimating
equation 17 when the effective research intensity is measured by Sd/N and the distance
to the frontier by DF2, very similar to those obtained when Sd/L and DF1 are used.
22
 Xd
 efect
f
d
 ln A  
   ln X    ln X    ln
ijt
0, ij
1
ijt
2
ijt
3
 Qd

 Xd
 efect
  DF  l ln
5 ij
6 
Qd

Xf

 efect

   4  ln
 Q f

 ijt



 

 ijt
(17)


 DFij   ijt

 ijt
Table 5. Effective research intensity, absorptive capacity and TFP growth
Xd=R
Estimate
(17a)
(17b)
(17f)
Xf=Rf
(X/Q)d=
(X/Q)f=
(Sd/N)
(Sf/N)
DF2
Cab1=
Cab2=
Cab3=
R/Y*DF2
Sf/L*DF2
Sf/N*DF2
0.005
0.006
0.08***
0.13***
0.24***
-0.25
(0.34)
(0.83)
(2.82)
(3.75)
(9.80)
(-0.77)
0.01
0.005
0.10***
0.09***
0.24***
4.25***
(0.80)
(0.81)
(3.31)
(2.76)
(10.25)
(2.75)
0.01
0.005
0.10***
0.09***
0.24***
0.002***
(0.85)
(0.81)
(3.38)
(2.60)
(10.18)
(2.73)
R2
0.20
0.23
0.23
Notes: Rd and Rf represent the domestic and foreign R&D expenditures; Sd and Sf are the domestic and foreign
technology stocks; N is the number of employees; DF2 is the distance to the technology frontier and Cab is
absorptive capacity.
*, ** and *** denote that the variable is significant at the 1, 5 and 10% respectively.
Number of observations: 240.
The new model confirms the results observed in the former. In all specifications,
the increase in domestic technological effort and international spillovers are not
significant. By contrast, the domestic and foreign “effective research intensity” and the
distance to the frontier are significant and show the expected positive sign in all cases.
Absorptive capacity, in two of the three models, is clearly significant and shows the
expected positive sign. Overall, the results confirm those obtained by Griffith et al.
(2003, 2004), among others, who found a significant and positive relationship between
the absorptive capacity measured with a variable that incorporates R&D and TFP
growth.
The estimated coefficient of the absorptive capacity (Cab1) is statistically
insignificant at conventional significance levels, as in other empirical studies, such as
Madsen et al. (2009) and Islam (2009). These scholars consider that the results for this
variable are very sensitive to the model specification and to the measurement of
innovative activity and product variety, as well as to the problems of multicollinearity
that are frequent in the models.
23
5. Conclusions
The purpose of this paper is to test whether second generation endogenous
growth models are consistent with the data of ten productive sectors in six developed
economies during the period 1979-2001.
As observed in other empirical studies, the results suggest the constancy of TFP
growth rates accompanied by a growing trend in the temporal series of different
technological inputs. This evidence, as is well known, contradicts the requirements of
the first generation models and leads us to assess which of the two second generation
proposals conforms more closely to the empirical evidence. Having proved the
existence of cross-dependence in the sample units, the results of unit root and
cointegration tests suggest the validity of a hybrid theoretical framework, which adds a
proxy for product proliferation to the semi-endogenous approach.
The estimation of econometric models gives results that are consistent with those
found in other empirical studies. The variables proposed by the semi-endogenous
growth model (growth in domestic technological effort and in international spillovers)
are significant in models where research intensity is measured in the traditional way, as
a ratio between a measure of the R&D flow and a measure of product proliferation. In
these cases, however, research intensity shows a negative influence on productivity
growth, common in the empirical literature, but without theoretical justification.
On the contrary, the empirical evidence supports the Schumpeterian productivity
growth model when it is dependent on the effective research intensity (computed taking
into account the depreciation of the technological stock over time) and on the distance
to the technological frontier. The high significance of the latter, eminently a
Schumpeterian variable, suggests the necessity of a deeper analysis of the distance to
the technological frontier and the role of human capital and institutions as determinants
of benefit from the advantage of backwardness.
In an attempt to go deeper into this line of research, the estimation of an
extended model is performed, incorporating variables that proxy the absorptive
capacity, most of which are significant and show the expected positive sign.
What these results mean in relation to the economic policy suited to developed
countries? The Schumpeterian paradigm considers a crucial distinction in the economic
policies to be adopted depending on the distance between a sector or a country and the
24
technological frontier. Those far from the frontier should adopt economic policy
measures to ensure catching up and the possibility of imitating the leaders. Such
measures, however, will not promote growth in countries near the frontier which have
exhausted the effectiveness of such kind of policies. This is the case of the developed
countries included in this analysis, particularly the European ones. In the 1980s, many
European countries had already converged in terms of per capita income and in terms of
the ratio between capital and labour with the global technological frontier. In this
context, a new pattern of intervention becomes necessary. The inability to carry out this
shift correctly explains, according to Acemoglu et al. (2002), the unsatisfactory growth
performance of Europe when compared to the United States.
The exhaustion of the old growth model based on factor accumulation and
technological imitation demands the shift to an alternative source of growth: innovation.
No doubt the innovative model requires, firstly, the promotion of R&D investment and,
following our results, the effort must be big enough to promote "effective research
intensity”. This new variable reflects that the rise in R&D expenditure has been
sufficient to compensate for and/or encourage three factors: the depreciation of capital,
the increase in the stock of knowledge and product proliferation.
Nevertheless, scholars of growth advocate supplementing this policy with the
promotion of other indirect sources of innovation and growth such a competition,
investment in tertiary education, reduction of credit constraints and flexibility in labour
markets.
Future extensions of the present work will try to research the role of these
different indirect sources of innovation in the sectoral performance of developed
countries.
References
Abramovitz, M.A., 1986. Catching Up, Forging Ahead and Falling Behind,
Journal of Economic History 46, 385-406.
Acemoglu, D., Aghion, P., Zilibotti, F., 2002. Distance to Frontier, Selection and
Economic Growth, Working Paper 9066, National Bureau of Economic Research,
Massachusetts.
Aghion, P., Durlauf, S., 2009. From Growth Theory to Policy Design. Working
Paper 57, The International Bank for Reconstruction and Development/The World
Bank, Commission on Growth and Development, Washington.
Aghion, P., Howitt, P., 1992. A model of Growth through Creative Destruction.
Econometrica 60, 2, 323-351.
25
Aghion, P., Howitt, P., 1998. Endogenous Growth Theory. The MIT Press,
Cambridge.
Ang, J., Madsen, J., 2009. Can Second Generation Endogenous Growth Models
Explain the Productivity Trends and Knowledge Production in the Asian Miracle
Economies? MPRA Paper 175-43, Munich University Library, Munich.
Caves, D.W., Christensen, L.R., Diewert, W.E., 1982. The economic theory of
index numbers and the measurement of input, output, and productivity. Econometrica
50, 6, 1393–1414.
Coe, D.T., Helpman, E., 1995. International R&D spillovers. European Economic
Review 39, 5, 859–887.
Dinopoulos, E., Sener, F., 2007. New Directions in Schumpeterian Growth
Theory. In Hanusch, H. and A. Pyka (Eds.): Elgar Companion to Neo-Schumpeterian
Economics, Edward Elgar Publishing, Cheltenhaºm, pp. 688-704.
Dinopoulos, E., Thompson, P., 1998. Schumpeterian Growth without Scale
Effects. Journal of Economic Growth 3, 4, 313-335.
Griffith, R., Redding, S., van Reenen, J., 2003. R&D and Absorptive Technology.
Theory and Empirical Evidence. Scandinavian Journal of Economics 105, 1, 99-118.
Griffith, R., Redding, S., van Reenen, J., 2004. Mapping the Two Faces of R&D:
Productivity Growth in a Panel of OECD Industries. The Review of Economics and
Statistics 86, 4, 883-895.
Grossman, G.M., Helpman, E., 1991. Innovation and Growth in the Global
Economy. MIT Press, Cambridge.
Ha, J., Howitt, P., 2007. Accounting for Trends in Productivity and R&D: A
Schumpeterian Critique of Semi-Endogenous Growth Theory. Journal of Money, Credit
and Banking 39, 4, 733-774.
Howitt, P., 2000. Endogenous growth and cross-country income differences.
American Economic Review 90, 829–846.
Howitt, P., Mayer-Foulkes, D., 2005. R&D, implementation and stagnation: a
Schumpeterian theory of convergence clubs. Journal of Money, Credit and Banking 37,
1, 147-177.
Im, K.S., Pesaran, M.H., Shin, Y. (2003). Testing for unit roots in heterogeneous
panels. Journal of Econometrics 115, 1, 53-74.
Islam, M.R., 2009. R&D Intensity, Technology Transfer and Absorptive Capacity,
Discussion paper 13/09, Department of Economics, Monash University, Caulfield East.
Jones C. I., 1995 a. Time Series Test of Endogenous Growth Models. Quaterly
Journal of Economics 110, 2, 495-525.
Jones C. I., 1995 b. R&D Based Models of Economic Growth. Journal of Political
Economy 103, 4, 759-784.
Jones C. I. 2005. Growth and Ideas. In: Aghion, P., Durlauf, S. N. (Eds.),
Handbook of Economic Growth, vol.1B, Elsevier, B.V., Amsterdam, pp. 1064-1109.
Kao, C., 1999. Spurious Regression and Residual-Based Test for Cointegration in
Panel Data. Journal of Econometrics 90, 1, 1-44.
Kortum, S., 1997. Research, Patenting, and Technological Change. Econometrica
65, 6, 1389-1419.
Kremer, M., 1993. The O-ring theory of economic development. Quaterly Journal
of Economics 108, 3, 551-575.
López-Pueyo, C., Barcenilla-Visús, S., Sanaú, J., 2008. International R&D
spillovers and manufacturing productivity. A panel data analysis. Structural Change and
Economic Dynamics 19, 152-172.
26
Madsen, J.B., 2006. Are there Diminishing Returns to R&D? EPRU Working
Paper Series 06-05, Economic Policy Research Unit (EPRU), University of
Copenhague, Copenhague.
Madsen, J. B., 2008. Semi-endogenous versus Schumpeterian growth models:
testing the knowledge production function using international data. Journal of Economic
Growth 13, 1, 1-26.
Madsen, J.B., Saxena, S., Ang, J. B., 2009. The Indian growth miracle and
endogenous growth, Journal of Development Economics (article in press, available at
doi:10.1016/j.jdeveco.2009.06.002).
Pedroni, P., 1997. Panel Cointegration: Asymptotic and Finite Sample Properties
of Pooled Time Series Tests with an Application to the PPP hypothesis. New Results.
Indiana University Working Paper in Economics. Indiana University, San Diego.
Peretto, P., 1998. Technological Change and Population Growth. Journal of
Economic Growth 3, 4, 283-311.
Pesaran, M. H., 2004. General diagnostic tests for cross section dependence in
panels. IZA, Discussion Papers 1240, Institute for the Study of Labor, Cambridge
University, Cambridge.
Pesaran, H. M., 2007. A simple panel unit root test in the presence of cross-section
dependence. Journal of Applied Econometrics 22, 2, 265-312.
Romer, P.M., 1990. Endogenous Technological Change. Journal of Political
Economy 98, 5, S71-S102.
Saxena, S., Madsen, J.B., Ang, J., 2008. Which Second Generation Endogenous
Theory Explains Long-Run Growth of a Developing Economy? Working Paper,
Department of Economics, Monash University, Clayton Victoria (available at
http://amw2008.econ.usyd.edu.au/pdfs/G-4_Shishir_Saxena.pdf).
Schwarz, G., 1978. Estimating the dimension of a model. The Annals of Statistics
6, 461-464.
Segerstrom, P. S., 1998. Endogenous Growth Without Scale Effects. American
Economic Review 88, 5, 1290-1310.
Stiroh, K. J., Botsch, M., 2007. Information Technology and Productivity Growth
in the 2000s. The German Economic Review 8, 2, 255-280.
Stock, J.H., Watson, M.W., 1993. A Simple Estimator of Cointegrating Vectors
in Higher Order Integrated Systems. Econometrica 61, 4, 783-820.
Ulku, H., 2007 a. R&D, Innovation and Growth: Evidence from Four
Manufacturing Sectors in OECD. Oxford Economic Papers 59, 13, 513-535.
Ulku, H., 2007 b. R&D, innovation and output: evidence from OECD and
nonOECD countries. Applied Economics 39, 3, 291-307.
Zachariadis, M., 2003. R&D, Innovation, and Technological Progress: A Test of
the Shumpeterian Framework without Scale Effects. Canadian Journal of Economics
36, 3, 566-586.
Zachariadis, M., 2004. R&D Induced Growth in the OECD. Review of
Development Economics 8, 3, 423-439.
27