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Variety, Competition, and Population in Economic Growth:
Theory and Empirics
Alberto Bucci∗
Lorenzo Carbonari†
Giovanni Trovato‡
September 14, 2016
Abstract
By considering the average density of sectors in a country’s product space, measured
by the Lafay’s net export flows-based specialization index, as an indicator of the degree of
complexity of the same country’s production structure (Hausmann and Klinger [29]), this is
the first paper that provides aggregate macroeconomic evidence on how, in the long-run, a
diverse degree of production-complexity may affect in a differential way not only economic
growth, but also the relation between economic growth, population growth and the monopolistic (intermediate) markup. On average, for the countries included in the sample, we find
that, following an increase in the number of horizontally-differentiated (intermediate) inputs
entering the aggregate production function, the specialization effect is greater than the corresponding complexity effect. In this case, the impact of population growth on economic growth
is definitely negative, whereas the influence of the monopolistic markup on the same variable
is negative.
Keywords: Economic growth; Population growth; Variety-expansion; Specialization; Complexity; Product market competition.
Jel codes: O3; O4; J1.
∗
Università di Milano, DEMM. E-mail address: [email protected]
Università di Roma “Tor Vergata”& CEIS. E-mail address: [email protected].
‡
Università di Roma “Tor Vergata”& CEIS. E-mail address: [email protected].
†
1
“The productivity-enhancing effects of horizontal innovations are not. . . obvious. . . For while having more
products definitely opens up more possibilities for specialization, and of having instruments more closely
matched with a variety of needs, it also makes life more complicated and creates greater chance of
error. . . .”
1
Introduction
Economic theory has long ago made clear that the degree of product market competition
(PMC, henceforth) and the rate of population growth, by affecting, respectively, the path of
future profits accruing to the successful innovator and the availability of researchers in an
economy, have a strong impact on economic growth (i.e., the growth of per capita income).
In order to analyze, both theoretically and empirically, how population growth and the
extent of the monopolistic markups rewarding prospective innovators may affect economic
growth, we employ a variant of the canonical semi-endogenous growth model by Jones [33],
[34]. The main reason for using that framework resides in the fact that in two companion contributions Jones (1995a,b) has provided convincing evidence against two (the AK-type and
the Research & Development, R&D-based, respectively) broad categories of fully endogenous
growth models. In particular, the evidence against the first generation of R&D-based fully
endogenous growth models (i.e., Romer [57]; Grossman and Helpman [27]; Aghion and Howitt
[5]) is especially persuasive: these models predict that economic growth is proportional to
the amount of resources invested in R&D (namely the number of researchers allocated to
this activity), however in the last few decades R&D investments have increased remarkably
in most of advanced countries, with the long-run growth rates of per capita output and total
factor productivity of these countries not showing a comparable upward trend.
In the light of this, the motivation of the present paper is twofold. The first objective is to re-examine the long-run relationship both between PMC and economic growth,
and between population growth and economic growth. In our context, the relevance of reassessing these quite age-old problems/relations has to do with the fact that (and this is
the main difference with the traditional semi-endogenous growth theory) we postulate that,
following the introduction of new varieties of horizontally-differentiated intermediate inputs
(i.e., following an improvement in the rate of technological change), a possible trade-off between productivity gains (due to more specialization) and productivity losses (due to more
production-complexity) may emerge.1 More importantly, and related to the first one, the
second objective of the present contribution is to reach some quantitative understanding of
the magnitude of the production-complexity effect related to technological progress (namely,
intermediate inputs proliferation), in comparison to the more standard specialization effect
of variety-expansion.
To have an immediate picture of the mechanisms involved in the framework we are going
to describe in our paper, consider a typical R&D-based growth model à la Romer [57] and
suppose, as in Jones [33], that there are diminishing technological opportunities in the sector
-the R&D sector- that produces new ideas for new varieties of differentiated intermediates.
Having diminishing technological opportunities means that an individual researcher becomes
1
In the canonical semi-endogenous growth model, the production-complexity effect is either non-existent at all
or (at most) very much small, and as such totally negligible.
2
less and less productive as the number of existing ideas grows up, so that in the long run (i.e.,
along a balanced growth path - BGP - equilibrium) it is possible to keep on innovating at a
constant pace only by allowing for a rise of the aggregate stock of researchers. In turn, if the
stock of researchers is proportional to population size, expanding the number of researchers
and, hence, the number of available ideas, will ultimately be possible only through an increase
of population. Thus, a larger population generates two opposing effects in our setting: the
first is negative and implies that the available aggregate GDP of the economy has to be split
among a larger number of heads, which decreases per capita income over time, while the
second is positive as a larger number of heads leads, as a consequence, to more ideas and
therefore to a greater aggregate GDP. Our model suggests that, in line with the standard
semi-endogenous growth theory, the positive effect on per capita income of a more sizeable
population always prevails over the corresponding negative effect (so that the correlation
between population and economic growth rates is unambiguously positive in the long-run) if
and only if the productivity losses arising from more production-complexity due to varietyexpansion are extremely small and littler than the related productivity gains resulting from
more specialization. In contrast, and this is a totally new result within the semi-endogenous
branch of growth theory, when the (productivity) losses arising from production-complexity
are extremely large, and larger than the corresponding (productivity) gains coming from
specialization, then having more population (hence, more researchers, and ultimately more
ideas) in the economy leads in the long-run to a lower per capita income growth rate.2 In this
case, our model also suggests that it is possible to raise the economy’s growth rate through
reducing, ceteris paribus, the incentives (instantaneous profits) to produce new ideas, which
actually occurs by a reduction in the degree of monopoly power with which the potential
innovators are rewarded. Finally, in the intermediate case where the productivity losses
arising from production-complexity due to variety-expansion are sufficiently large, but still
lower than (or equal to) the productivity gains resulting from specialization, we find that
population growth has a negative impact while the monopolistic markup has a positive
influence on economic growth (at most, both impacts are null).
From the sketch of our theoretical model, it is immediate to infer that we do not aim here
at capturing the mutual evolution of population growth, technological incentives, and per
capita income along an economic and demographic transition toward a long-run equilibrium
characterized by low fertility and mortality rates, high levels of R&D investments and persistent growth in per capita income.3 It is exactly for this reason that we use the simplest and
2
Thus, the model presented here accounts for the possibly negative long-run correlation between population
and economic growth rates in R&D-based models through a mechanism which is completely different from the one
recently suggested by Prettner [53]. Using a Romer [57]-Jones [34]’s setting, Prettner shows that an increase in
population growth, while positively influencing aggregate human capital accumulation, decreases simultaneously
schooling intensity (defined as the productivity of teachers times the public resources spent on educating each
child). The fall of schooling intensity has, in turn, a negative impact on the future evolution of aggregate
human capital. If the negative effect dominates, the resulting slowdown of aggregate human capital accumulation
eventually reduces technological progress and, therefore, economic growth. In our model there is no human capital
investment.
3
A comprehensive overview of the economic theories and consequences of the so-called demographic transition
can be found in Galor [26] and Jones and Vollrath [38].
3
most parsimonious possible setting (namely, a variant of the basic semi-endogenous growth
model) in which population growth and the intermediate sector monopolistic markup are
both regarded as exogenous variables, and focus on the relation between population change
and economic growth and between markups and economic growth along a BGP.4
In theory, our model is able to account simultaneously (and eventually for different
ranges of the parameter measuring the magnitude of the production-complexity effect) for a
non-monotonic, non-uniform relationship not only between population growth and economic
growth but also between the degree of the monopolistic markup and economic growth. This
is the most important difference between our theoretical results and those of the basic semiendogenous growth model (Jones [33]) that, instead, does not allow any analysis of the
long-run connection between PMC and economic growth.
In the econometric part of the paper, we explicitly deal with this non-monotonicity using
a Finite Mixture Model. Our estimates confirm that the most likely case found in the data is
the one in which the proliferation of new horizontally-differentiated (intermediate) inputs to
be assembled in the same aggregate production function generates a production-complexity
effect that, while important in magnitude, is ultimately lower than the corresponding specialization effect, so that population growth produces a statistically significant and negative
influence while the monopolistic markup has a statistically significant and positive impact
on long-run per capita income growth.
How do our results compare with those of the existing theoretical and empirical literatures on the two issues (the links between markups-economic growth, and between population
growth-economic growth, respectively)? Although economists have been studying for a long
time the effects of an increase in the intensity of PMC and in population growth on productivity growth, these questions still remain to a large extent unsettled. Unlike the traditional
Schumpeterian [59] view, more recent theoretical research (both industrial organization- and
macro- based5 ) finds mixed results in the correlation between product market competition
and economic growth, and the existing empirical evidence confirms the non-monotonicity of
this relation.6 In this regard, Aghion et al. [2] analyze a model of Schumpeterian growth with
4
In more detail, we do not illustrate here any new mechanism(s) able to command an economy’s take-off
from a “stagnant-equilibrium steady state”into a self-sustaining “growth-equilibrium steady state”, during which
the portion of full income eventually spent on R&D-investment-related activities (thus, economic growth) and
population ageing ultimately rise, while fertility and mortality fall. Instead, using the simplest framework in
which R&D activity plays a significant and explicit role, our goal is to show that the sign of the links between
population and economic growth rates and between markups and economic growth, respectively, can ultimately
be ascribed to the contrast of two different effects (specialization vs. production-complexity) that the introduction
of new varieties of intermediate inputs, a proxy for the rate of technological progress, can yield.
5
An excellent review of these two branches of the literature on product market competition, incentives to
innovate, and economic growth can be found in Aghion and Griffith [4]. In particular, the third chapter of their
book extends the endogenous growth model from the first chapter. At the end of their analysis, the authors claim
that, for some parameter values, the steady-state aggregate innovation intensity of their model is correlated in an
inverted-U-shaped manner with the degree of competition.
6
While Nickell [52] and Blundell et al. [14]-[15], for instance, find that competitive pressures encourage
innovation and, therefore, have a positive effect on productivity growth in a long-run perspective, other papers
(notably, Aghion et al., 2005) show that the relationship between competition and growth is non-monotonic, i.e.
inverted U-shaped, in the data.
4
step-by-step innovation and no leapfrogging.7 In their theoretical framework, each intermediate sector is assumed to be duopolistic with respect to production and research activities,
and competition is proxied by the Lerner Index (or price-cost margin). In obtaining a nonmonotonic, empirically inverted-U relationship between product market competition and
innovation/growth, they use UK panel-data on patents generated by matching the NBER
patents database to accounting data (from Datastream) on firms listed on the London Stock
Exchange.8
Our model is different from Aghion et al. [2]’s contribution because technical change takes
the form of an expansion in the number of available varieties of intermediate inputs in our
analysis and also because we are interested in analyzing the possible impacts of population
change on economic growth.
Similarly to the relationship between PMC, innovation and productivity growth, so far
a complete agreement about the sign of the long-run correlation between population and
economic growth rates has not emerged yet, both theoretically and empirically.9 While according to Kuznets ([43], p. 328): “. . . Population growth [. . . ] produces an absolutely larger
number of geniuses, talented men, and generally gifted contributors to new knowledge whose
native ability would be permitted to mature to effective levels when they join the labor force”,
proponents of the view that population growth is detrimental to economic growth (Solow
[61]; Coale and Hoover [21]; Barro [10]; and Mankiw et al. [48]) found their argument on
the belief that an increase in population leads to a dilution of reproducible resources. More
recently, a negative effect of population growth on economic growth is also found in the data
by Li and Zhang [46] and Herzer et al. [31]. Finally, there are also strong arguments advocating that it is a better economic performance to cause an increased population growth rate.
Blanchet [12] is among those who use this claim to explain the presence of an insignificant
correlation between economic and population growth rates.10
Summing up, concerning the relation between population and economic growth rates, it
seems that the main argument of the path-breaking paper by Kelley and Schmidt [40] still
continues to hold today. Using both cross-section and time-series data, these two authors
have indeed provided compelling evidence that the impact of population growth on per
capita income growth has changed over time (it has been statistically not significant in the
sixties and the seventies and statistically significant, large and negative in the eighties),
7
See also Aghion et al. [3] and Acemoglu and Akcigit [1] for comparable examples of Schumpeterian growthframeworks with step-by-step innovation. In particular, Aghion et al. [3], by developing an industry model, find
that a firm’s response of innovation to increased competition is non-monotonic as it depends on how far it is from
the world technology frontier.
8
Aghion et al. [2] explain theoretically such a relation through the interplay between two opposing effects, the
“Escape-Competition”and the “Schumpeterian”effect, respectively.
9
See Sala-i-Martin et al. [58], who find in the data that the sign of the whole impact of population growth on
economic growth is ambiguous.
10
Using a sample of 78 countries covering the period from 1965 to 1990, Williamson ([62], pp. 113-115) shows
that there is no significant relationship between population and economic growth rates. This outcome is consistent
with the “neutralist”position. However, he also shows that the result is sensitive to the empirical specification
employed as, when the log of life-expectancy in 1960 and two further variables controlling for economic geography
are added, population growth is shown to generate a positive and significant impact on GDP per capita growth,
which would support the “optimist”position.
5
and varies with the level of economic development (it is generally negative in less developed
countries and can be positive for some developed countries). Kelley and Schmidt [40] explain
these results by the fact that the impact of population change on economic development
may be drastically different in sign depending on which specific component of population
growth is affected by a given demographic shock: an increase of population growth attained
through a rise of fertility has a monotonically negative consequence on economic growth,
whereas the same increase of population growth achieved through a decline of mortality has
a monotonically positive influence on the growth rate of real per capita income. This has
profound implications for the analysis, as it suggests that the composition of a simultaneous
rise of fertility and decline of mortality, both leading to a higher population growth rate,
is in theory an important explanation of the emergence of a non-monotonic, non-uniform
relationship between population and economic growth rates.
This work is especially related to Bucci [18] [19], Bucci and Raurich [20], Ferrarini and
Scaramozzino [25], and Maggioni et al. [47]. Unlike Bucci [18], it is not an objective of this
article to emphasize the growth effects of the so-called returns-to-specialization (Benassy
[11]) and their role in shaping the link between population growth-economic growth and
between markups-economic growth. Moreover, contrary to Bucci [18], we pay no attention
here to how the type of agents’ intertemporal utility (whether Millian, Benthamite, or an
intermediate case between the two) might ultimately affect the relationship between population and economic growth rates. Differently from Bucci [19], instead, we analyze here
a semi-endogenous growth model without (intentional or unintentional) human capital accumulation with the objective of studying simultaneously, and within the same framework,
the interactions between long-run economic growth, on the one side, and population growth
and markups, on the other. In particular, the present paper formally demonstrates that
having (exogenous or endogenous accumulation of aggregate) human capital within a semiendogenous-type growth framework is not essential in yielding the result of a non-uniform
relation between population and economic growth rates. Unlike Bucci and Raurich [20], we
do not aim at explaining the differential impact that in the long-run a given change in the
population growth rate may have on economic growth through: (i) Either the nature (i.e.,
whether fully-endogenous or not) of the process of economic growth, (ii) Or the peculiar
engine(s) driving economic growth (human capital, R&D, or both).
After more than two centuries from Adam Smith [60]’s notable book, in which the specialization/division of labor was considered the key source of productivity growth, Kremer
[42] has proposed another (the so-called “O-Ring”) complementary view of the process of
economic development. This view is based on the observation that the number of tasks
included in a given production process is the major determinant of its degree of complexity:
more complex technologies are those incorporating more tasks and, then, more possibilities of
errors. Another important conclusion of Kremer [42] is that when firms select among diverse
technologies with different tasks, in equilibrium they will choose by taking into account the
amount of “capabilities”they own: firms endowed with more capabilities will decide to use
technologies requiring a larger number of tasks. This may explain why in general “rich countries specialize in complicated products”(Kremer [42] , p. 563). The core implication of all
this is that the proliferation of tasks/components/different inputs included in the same production process may ultimately yield opposing effects on long-run economic development and
6
growth, due to the differential role played simultaneously by specialization and productioncomplexity. In the model we are going to present in the next sections, the balance between
positive (specialization) and negative (production-complexity) productivity-consequences related to an expansion in the number of varieties of (intermediate) inputs involved in a given
production process is found to be important in affecting simultaneously the sign of the
long-run correlations between population and economic growth, and between markups and
economic growth. This is in line with the “O-Ring”theory of economic development, according to which for some countries (especially those using particularly “complicated”production
processes) it may well be that the productivity-gains from more specialization are overcome
by the associated productivity-losses due to a more complex production organization. More
specifically, our paper shows that when this happens, we should observe (with respect to the
opposing case) not only a different level of the growth rate of per capita income but also,
and perhaps more importantly, a changing relation between economic growth, population
growth and markups across countries.
In order to (indirectly) measure production-complexity, some economists (Hausmann and
Klinger [29]; Hidalgo et al. [32]; Hausmann and Hidalgo [28]) have developed a model that,
by the use of trade-data, now consents to have a broad appraisal of that effect. The idea put
forward by these economists is based on the notion of product space, which can be thought
of as a forest, with sectors representing trees and countries being monkeys. A large distance
between any two trees means that monkeys cannot easily jump from one to the other: in this
case the sectors corresponding to those two trees are so different in terms of their patterns
of specialization that, at a country-level, a revealed comparative advantage in one sector is
not necessarily associated with a revealed comparative advantage in the other sector. By
contrast, whenever two trees stay very close to each other, specialization in either of the
two sectors typically leads the same country to specialize in the other, as well. At the same
time, however, the degree to which sectors are close to each other (the so-called average
product density) can also be viewed as a proxy for the degree of complexity of a country’s
production structure in that an economy with a high average product density must possess
all the necessary capabilities and technical competences to produce simultaneously within
a thicker area of activities: in sum, the closer two sectors are to each other, the easier it
is for a country to specialize in both of them, while simultaneously the more complicated
(in terms of required competencies) it becomes for the same country to produce in both
industries. By exploiting these ideas, and following the methodology illustrated by Lafay
[44], Ferrarini and Scaramozzino [25] have used data on net trade flows to compute an
average product density index for a cross-section of 89 countries over the period 1990-2009.
For these countries, they separately estimate, through a panel data GLS model, the impact
of a larger product density on the level and the growth rate of GDP per capita. For the
whole sample, density has a positive and significant coefficient on the level of GDP per
capita (countries occupying the denser areas of the product space have on average higher
GDP per capita, with causality going from the former to the latter). However, when the
sample is split by income levels, it is observed that density positively affects GDP per capita
in middle/low income countries, while it dampens per capita income for the group of highincome countries. Concerning the growth regressions (that examine the relationship between
product density and economic growth by including the initial level of GDP per capita as a
7
regressor), instead, the authors find that for the whole sample of countries the coefficient
on density is still positive and significant. This result remains true when the sample is
split by aggregated income groups (high vs. middle/low income countries). However, by
considering six different geographical regions separately, it is observed that only for Europe
and North America the coefficient on the density variable is significantly negative. All in
all, in line with the “O-Ring”theory of economic development, the evidence presented by
Ferrarini and Scaramozzino [25] supports very well the idea that, especially for advanced
countries, it can be the case that the productivity-gains from more specialization are smaller
than the associated productivity-losses due to increased complexity in production. Unlike
Ferrarini and Scaramozzino [25], we focus solely on advanced (OECD) countries, employ a
different econometric technique, and analyze how the balance between production-complexity
and specialization (induced by input proliferation) contributes to affect not only the rate of
economic growth, but also the joint long-run relation between population growth, economic
growth, and markups.
Finally, by using a sample of Turkish manufacturing firms between 2003 and 2008, Maggioni et al. [47] have recently studied the link between complexity and volatility at the
firm-level. Their main conclusion is that firms producing more complex goods (i.e., goods
requiring a wider set of diverse and exclusive capabilities, see Hausmann and Hidalgo [28])
enjoy higher output stability. Differently from Maggioni et al. [47], we employ here a macrolevel perspective and focus on the role of product/country complexity on aggregate economic
growth, rather than firms’ output volatility. In this sense, we believe that our analysis does
represent a nice complement to Maggioni et al. [47]’s contribution.
This article is structured as follows. In section 2 we present the theoretical model with
the objective of illustrating the differential impact that population growth and markups may
have on long-run economic growth depending on the relative degree of production-complexity.
In section 3, we perform our empirical analysis. In particular, in this section we present our
econometric strategy, describe the employed dataset, discuss the econometric results, and
provide robustness checks. As usual, the last section (section 4) summarizes, concludes and
proposes new possible directions for future research.
2
The Model
The model presented in this section is a version of Romer [57], with four relevant differences.
The first concerns the shape of the aggregate technology:
"
#αm
Z Nt
1
1−α
1/m
Yt = LY t
(xit )
di
with
0 < α < 1 and m > 1
(1)
Ntβ 0
This production function formalizes the idea (Aghion and Howitt, [6], Chap. 12, equation
12.4, p. 407) that:
“. . . The productivity-enhancing effects of horizontal innovations are not
. . . obvious. . . For while having more products definitely opens up more possibilities
for specialization, and of having instruments more closely matched with a variety
of needs, it also makes life more complicated and creates greater chance of error
...”
8
In equation (1), LY is the labor input employed in the production of the homogeneous final
good Y , xi is the quantity of the i − th variety of differentiated capital goods/intermediate
inputs, N is the existing number of these inputs, and m > 1 is a technological parameter that
determines the elasticity of substitution between any generic pair of varieties of differentiated
capital goods, equal to m/(m − 1). A decrease in m, by increasing the substitutability
between durables, leads to tougher competition across capital-goods producers and to lower
prices. Thus, m can be used as a (inverse) measure of the degree of competition in the
intermediate product market. In a moment, we show that m is, indeed, the optimal markup
on the production marginal cost in the durables sector (see equation (5)). As a whole, the
aggregate production function (1) displays constant returns to scale to private and rival
inputs (LY and xi ) and allows disentangling the measure of product market concentration
(m) from the factor-shares in GDP (α and 1 − α).11
Depending on its magnitude, parameter β summarizes the different effects that innovation
may have on GDP. In particular, when positive, β is meant to capture the detrimental effect
on Y of having a larger number (N ) of intermediate-input varieties to be assembled in the
same manufacturing process. This is the (production-) complexity effect. This effect contrasts
with the traditional and positive specialization effect that is reflected by the upper bound of
the integral within the square bracket of equation (1).12
As a matter of fact, under symmetry - i.e., xi = x > 0 ∀i ∈ [0, N ] - and with LY > 0
and N ∈ [0, ∞), equation (1) suggests that an increase in N may have either a positive (i.e.,
β < 1, the specialization gains are larger than the possible losses due to more complexity in
production), or a negative ( i.e., β > 1, the specialization gains are smaller than the possible
losses due to more complexity in production), or else no impact at all on ( i.e., β = 1,
the specialization gains are exactly offset by the possible losses due to more complexity in
production).13
Using equation (1), it is possible to compute the inverse demand function for the i − th
intermediate:
"
pit =
αL1−α
Yt
1
Ntβ
Z
#αm−1
Nt
(xit )
0
1/m
di
1
Ntβ
1−m
xitm
(2)
The second difference with respect to Romer [57] is related to the technology for producing
intermediates. We now postulate that monopolistically competitive firms have access to the
same one-to-one technology employing solely labor as an input (as in Grossman and Helpman
11
Since final output is produced competitively under constant returns to scale to rival inputs, at equilibrium
LY and xi are rewarded according to their marginal productivities. Hence, for given N , (1 − α) is the share of Y
going to labor and α (the complement to one of the labor-share) is the share of total GDP going to intermediate
inputs.
12
In equation (1) we observe that if β < 0, then there is no (production-) complexity-effect, since this parameter
would amplify the positive effect of specialization emerging from the upper bound of the integral inside the square
bracket. A fortiori, this is also true when β = 0 (again, in this case we would end up with the sole, traditional
specialization-effect in the square bracket). Therefore, in order to model explicitly a (production-) complexity-effect
arising from an increase of N some positive β is needed.
13
We do not make any ad hoc assumption on the sign and the magnitude of β.
9
[17] Chap. 3):14
∀i ∈ [0, N ]
xit = lit
N ∈ [0, ∞)
(3)
where li is the amount of labor required in the production of the i−th durable, whose output
is xi . Thus, the marginal cost of production is the wage. For given Nt , equation (2) implies
that the total amount of labor employed in the intermediate sector at time t, LIt , is given
by:
Nt
Z
Z
Nt
lit di = LIt
xit di =
(4)
0
0
Under the assumption that there exists no strategic interaction across intermediate firms,
maximization of the generic i − th firm’s instantaneous profit leads to the traditional markup
rule:15
∀i ∈ [0; Nt ]
pit = mwIt = mwt = pt
(5)
This expression says that the price is the same for all intermediate goods i and equal
to a constant markup (m) on the marginal production cost (wt ). In this model all labor
(L) is employed to produce, respectively, consumption goods (LY ), durables (LI ), and ideas
(LN ). Since it is assumed to be perfectly mobile, at equilibrium all labor will be rewarded
according to the same wage rate, i.e., wY t = wIt = wN t ≡ wt . The hypothesis of symmetry
(i.e., xi and pi equal across i) leads to:
xit = xt =
πit = α
m−1
m
LY t
Nt
1−α LIt
Nt
LIt
Nt
α
∀i ∈ [0; Nt ]
α[m(1−β)−1]
Nt
(4’)
∀i ∈ [0; Nt ]
= πt
(6)
The third difference with respect to Romer [57] is related to the aggregate R&D technology:
1
Ṅt = LλN t Ntφ
with N (0) > 0, χ > 0, 0 < λ ≤ 1, φ < 1
(7)
χ
where χ is a technological parameter, Nt is the number of ideas already invented and LN t
is the labor input employed in research. The fourth and last difference we introduce in
this model with respect to Romer [57] is that population grows at a positive, constant
L˙t
and exogenous rate, L
≡ n > 0.16 Equation (7) stems from the criticism of strong scale
t
effect one may find in the first-generation of Schumpeterian growth models (see Jones [34],
14
We show that our results would not change if physical capital (as opposed to labor) is assumed to be the
only input into the production of intermediate goods (as in Romer [57]). A formal proof can be obtained from
the authors upon request.
»
–αm−1
RN
15
More precisely, we assume that each of these firms is so small that it takes 1β 0 t (xit )1/m di
as given,
Nt
hence:
∂
∂xit
»
1
Ntβ
–αm−1
Nt
(xit )1/m di
=0
Z
0
16
We simplify further the analysis by assuming that the aggregate labor-force equals the total population.
Under this assumption per capita and per-worker variables do coincide.
10
equation (6), p. 765; Jones [37], equation (16), p. 1074). In equation (7), the parameters
λ and φ denote, respectively, the returns to the labor input employed in research and the
intertemporal spillover coming from the accumulated stock of (disembodied) knowledge.
When φ < 1, higher values of N imply that the same amount of R&D resources (research
labor) generates a lower growth rate of ideas, i.e., there exist diminishing technological
opportunities. The presence of diminishing technological opportunities is key to the removal
of the strong scale effect in the first-generation of Schumpeterian growth models: since
individual researchers become less and less productive as the level of disembodied knowledge
(N ) increases, it is possible to maintain a constant rate of innovation only by increasing the
number of researchers. This, in turn, is possible solely if the economy’s population grows at
a positive rate. Because the R&D sector is competitive, there is free entry into this market:
wN t =
where
Z
VN t =
∞
πτ e −
Rτ
t
1 Ntφ
VN t
χ L1−λ
Nt
r(s)ds
dτ
(8)
with τ > t
(9)
t
In equations (8) and (9), VN t is the market value of the generic i − th blueprint, π is the
instantaneous profit of the i − th intermediate firm, r denotes the real rate of return on
households’ asset holdings (to be introduced in a moment) and wN t is the wage rate going
to one unit of research labor-input.
2.1
Households
The number of infinitely lived households of this economy is constant and normalized to one.
Hence, the size of population/labor-force coincides with the size of the single dynastic family
(L). The representative household uses savings (forgone consumption) to accumulate assets,
taking the form of ownership claims on firms. Thus,
Ȧt = (rt At + wt Lt ) − Ct
with A(0) > 0
(10)
In equation (10), A, C and L denote, respectively, household’s asset holdings, consumption and labor-input, w is the real wage and r is the real rate of return on A.17 According to
this equation, household’s investment in assets (the left hand side) equals household’s savings (the right hand side). In turn, household’s savings are equal to the difference between
household’s income (the sum of interest income, rA, and labor income, wL) and household’s
consumption (C). Given the above expression, the law of motion of per capita assets is:
ȧt = (rt − n)at + wt − ct
with a(0) > 0
(11)
C
with a ≡ A
L and c ≡ L representing per capita asset holdings and per capita consumption,
respectively. With a constant inter-temporal elasticity of substitution (CIES) instantaneous
utility function, the objective of the household is to maximize, under the usual budget
constraint, the discounted utility of per capita consumption of all its members:
17
Notice that, in this economy, all labor is employed and at equilibrium obtains the same wage, w.
11
Z
max
{ct ,at }t=+∞
t=0
U
+∞
c1−θ
−1
t
1−θ
≡
0
s.t.
!
e−(ρ−n)t dt
(12)
(11)
a(0) given
with θ > 0 and ρ > n > 0. In equation (12) we have normalized population at time 0 to
one, L(0) = 1. The representative dynastic family chooses the optimal path of per capita
t=+∞
consumption {ct , at }t=0 , taking the interest rate rt and the wage rate wt as given. The
assumption that ρ > n > 0 ensures that U is bounded away from infinity if c remains
constant over time. The solution to this problem gives the usual Ramsey-Keynes rule:
γc ≡
2.2
ċt
1
= (rt − ρ)
ct
θ
(13)
The labor market and the BGP equilibrium
Since labor is fully employed and distributed across production of consumption goods, production of intermediates and invention of new ideas, at equilibrium the following equalities
must hold:
LY t + LN t + LIt
= Lt
wY t = wN t = wIt
= wt
∀t ≥ 0
(14)
(15)
Equation (14) says that at equilibrium total supply (the right hand side) and total demand
(the left hand side) of labor must be equal. In the model, labor is a homogeneous factorinput, i.e., it can be employed interchangeably in the three sectors of the economy. Thus,
labor will continue to move across these sectors until wage equalization is attained (equation
(15)). Moreover, in equilibrium, aggregate household’s asset holdings (A) must equalize the
aggregate value of firms:
At = Nt VN t
(16)
where VN t is given by equation (9) and satisfies the no-arbitrage condition:
V̇N t = rt VN t − πt
(17)
In the model, the i-th idea allows the i-th intermediate firm to produce the i-th variety
of durables. This explains why in equation (16) total assets (A) equal the number of profitmaking intermediate firms (N ) times the market value (VN ) of each of them (equal, in turn,
to the market value of the corresponding idea). On the other hand, the no-arbitrage condition
suggests that the return on the value of the i-th intermediate firm rt VN t must equal the sum
of the instantaneous monopoly profit accruing to the i-th intermediate input producer (π)
and the capital gain/loss matured on VN t during the small time interval dt (i.e., V̇N t ).
We can now move to a formal definition and characterization of the balanced growth path
(BGP) of this model.
Definition 1. A BGP equilibrium in this economy is an equilibrium-path along which:
12
(i) all variables depending on time grow at constant (possibly positive) exponential rates;
(ii) the sectoral shares of labor employment (sj =
Ljt
Lt ,
with j = Y, I, N ) are constant.
The following results do hold in the BGP equilibrium (algebraic details are in the online
appendix, not intended for publication, where we also compute the BGP allocation of labor
across the final output, intermediate and research sectors and check for the respect of the
transversality condition):
Ṅt
≡ γN = Ψn
Nt
ẏt
ċt
ȧt
γy ≡
= γc ≡
= γa ≡
= ΦΨn
yt
ct
at
r = θΦΨn + ρ
(18)
(19)
(20)
where:
Φ ≡ α [m(1 − β) − 1] R 0
and
Ψ≡
λ
1−φ
>0
Equation (18) gives the BGP equilibrium growth rate of the economy’s number of intermediate input varieties (N ). According to equation (19), real income (y), consumption (c)
and asset holdings (a), all expressed in per capita terms, grow at the same constant rate in
the BGP equilibrium. Equation (20) gives the BGP value of the real rate of return on asset
holdings (r). It is evident from these equations that, for any ρ > n > 0, θ > 0 and Ψ > 0,
ρ
.
γN is always positive whereas r is positive as long as Φ is sufficiently large, i.e., Φ > − θΨn
Instead, for the common BGP growth rate of the economy (19) to be positive, Φ needs to be
strictly greater than zero, which implies that we would restrict our analysis to the case where
0 < β < m−1
m < 1. In other words, our theory suggests that along a BGP the economy’s
growth rate can be positive only if the production-complexity effect (as summarized by β) is
sufficiently low and smaller than the corresponding specialization effect. This is compatible
with the basic semi-endogenous growth model (see Jones [33]), where (intermediate-)input
proliferation yields no production-complexity effect at all. However, since the main objective
of the present paper is to study the macroeconomic (growth) effects of intermediate inputvariety proliferation, in what follows we do not limit ourselves to the very restrictive case in
which 0 < β < m−1
m < 1. Instead, we present the results of our model in their more general
form without imposing any ex-ante restriction on the magnitude of parameter β.18 These
results are summarized in the following proposition.
Proposition 1. Along the BGP we observe that:
1. Sign(γy ) = Sign(Φ);
∂γ
2. Sign ∂ny = Sign(Φ);
3. Real per capita income growth is equal to zero in the absence of any population change
(i.e., when n = 0);
18
As a matter of fact, in our regressions we deal with negative per capita GDP growth rates, as well (see table
3).
13
4. Sign
∂γy
∂m
depends on whether β is greater, smaller, or else equal to one.
Proof. The proof of the first part of the proposition is immediate when one takes into account
that in the model Ψ > 0 and n > 0. To prove the second part of the proposition, notice that:
∂γy
∂n = ΨΦ. To prove the third result, we observe that in equation (19) γy = 0 if n = 0. The
same equation (19) also implies that:


 Ψn [α(1 − β)] > 0 if β < 1
∂γy
≡
Ψn [α(1 − β)] = 0 if β = 1

∂m

Ψn [α(1 − β)] < 0 if β > 1
Using the definition of Φ and equation (19), we also obtain that:
- if 0 < β <
- if β =
- if
m−1
m
m−1
m ,
m−1
m ,
then: Φ > 0, γy > 0,
then: Φ = 0, γy = 0,
∂γy
∂n
< β < 1, then: Φ < 0, γy < 0,
- if β = 1, then: Φ < 0, γy < 0,
- if β > 1, then: Φ < 0, γy < 0,
∂γy
∂n
∂γy
∂n
∂γy
∂n
> 0 and
= 0 and
∂γy
∂n
∂γy
∂m
< 0 and
< 0 and
< 0 and
∂γy
∂m
∂γy
∂m
∂γy
∂m
> 0;
= 0;
∂γy
∂m
> 0;
= 0;
< 0.
Specifically, proposition 1 tells us that the impact of the intermediate sector markup on real
per capita growth crucially depends on the sign of (1 − β). If β < 1, the specialization gains
obtained from an expansion in input variety are larger than the possible losses due to more
∂γ
complexity in production and ∂my > 0. If β > 1 , the specialization gains are smaller than
∂γ
the possible losses due to more complexity in production and ∂my < 0. Finally, when β = 1,
the specialization gains are exactly offset by the possible losses due to more complexity
∂γ
in production and ∂my = 0. Therefore, a decrease in m, by increasing the elasticity of
substitution across intermediate inputs and, hence, the toughness of competition in this
industry, can imply a lower, or a higher, or else no effect at all on per capita income growth
(PMC and economic growth are ambiguously correlated in sign in the model).
Although the result that in the absence of demographic change (n = 0) growth in real
per capita incomes is equal to zero is a distinctive characteristic of basic semi-endogenous
growth models (Jones [34]), our setting also includes other features that cannot be found
in canonical semi-endogenous growth theory. The most important of these features is that,
unlike Jones [34] (p. 767, equation (8)) where γN = γy = Ψn, in our model the relation
between γN and γy is mediated by Φ ≡ α [m(1 − β) − 1]. Thus, while in Jones [34] (p.780,
equation (A1)) β = 0, and hence Φ ≡ α(m − 1) > 0, in our model Φ can also be negative.
This occurs, for any given m > 1, when β is sufficiently large, β > (m − 1)/m ∈ (0, 1), i.e., if
the (production-) complexity effect related to an increase in N is strong enough, which can
ultimately lead to negative growth rates of per capita income when the innovation activity
expands. Moreover, since n affects positively γN (as in Jones, [34]), an increase in the rate
of population growth can also imply (when Φ < 0, or with a complexity effect particularly
strong) a negative impact on per capita income growth.
Our model differs from Jones [34] also because in equation (19) the growth rate of the
economy depends not only on the growth rate of population (n) and the parameters φ, λ
and β, but also (among others) on m. This specific difference with respect to Jones [34]
14
can be ascribed to the fact that in our model we have: (i) postulated that intermediate
firms produce with labor (rather than forgone consumption) and, more importantly, (ii)
disentangled the intermediate firms’ gross markup of price over the marginal production cost
from the factor-input shares in GDP. It can be easily demonstrated (see on-line Appendix
B) that, using the Jones’ assumptions, our model can exactly reproduce the BGP growth
rate of the Jones’ economy.
3
Quantitative analysis
From the theoretical analysis developed in the previous section, three main testable predictions emerge.
Case I When the possible losses due to more complexity in production are extremely
small, and lower than the specialization gains from innovation (i.e., an expansion in input-variety), then per capita real GDP growth rate is positively
correlated to the population change and the intermediate sector markup, i.e.,
∂γy
∂γy
∂n > 0 and ∂m > 0.
Case II When the possible losses due to more complexity in production are moderately large, but still lower or, at most, equal to the specialization gains from
innovation (i.e., an expansion in input-variety), then per capita real GDP
growth rate is negatively correlated to the population change and positively
∂γ
∂γ
correlated to the intermediate sector markup, i.e., ∂ny ≤ 0 and ∂my ≥ 0.
Case III When the possible losses due to more complexity in production are very big,
and definitely larger than the specialization gains from innovation (i.e., an
expansion in input-variety), then per capita real GDP growth rate is negatively correlated to the population change and the intermediate sector markup,
∂γ
∂γ
i.e., ∂ny < 0 and ∂my < 0.
The three testable predictions obtained from our theory and listed above are summarized
by table 1.
The rest of the paper confronts these predictions with the data. In particular, how the magnitude of β (in our setting a measure of the production-complexity effect due to intermediate
inputs proliferation) may affect the interaction between population growth and economic
growth, and between markups and economic growth, respectively. In doing this, we abstract
λ
. Since this term must be positive, this choice entails, at most, an attenuation
from Ψ ≡ 1−φ
bias in our estimates. As we will see later on, our empirical results corroborate the theoretical predictions and document, at least for a group of countries, a positive role for population
change in economic development.19
We proceed now by discussing the econometric strategy, then we illustrate the dataset
and the main findings of our contribution.
19
This result substantially departs from the existing literature on the topic, which finds general lack of correlation between population and real per capita growth rates (see Herzer et al. [31] and Li and Zhang [46] and Kelley
and Schmidt [40] among others).
15
Table 1: Summary of the theoretical predictions
>0
∂γy
∂m
>0
m−1
m
∂γy
∂n
=0
∂γy
∂m
=0
<β<1
∂γy
∂n
<0
∂γy
∂m
>0
0<β<
Case II
β=
Case II
3.1
∂γy
∂n
Case I
m−1
m
m−1
m
Case II
β=1
∂γy
∂n
<0
∂γy
∂m
=0
Case III
β>1
∂γy
∂n
<0
∂γy
∂m
<0
Econometric strategy
In this section, we estimate different models that are consistent with our theory. The econometric approach we follow allows to test the behavior of per capita GDP growth dynamics,
under the assumption that unobserved heterogeneity affects parameters estimation. In particular, we employ a finite mixture model (FMM), relaxing the hypothesis of IID residuals
(see Aitkin [7] and Alfò et al. [8], among others), and allowing for correlated random terms.20
In such a model, the random component captures the impact of unobserved country-specific
variables, limiting the effects of the omitted variable bias. It is worth noticing that FMM allows also to deal with the unobserved heterogeneity due to the non-monotonic, non-uniform
relationship between regressors and response, as predicted by our theory.
According to the Generalized Linear Models framework (see McCullagh and Nelder [49]),
the empirical counterpart of equation (19) can be written as:
T
E(γit |nit , mit ) = ω0i + mT
i ω1i + ni ω2i
(21)
where γi,t is the per capita GDP growth rate, mT
i is the vector measuring the product between
intermediate sector markup and population change, nT
i is the vector of the population growth
21
The parameters ω1i and ω2i capture the country-specific
rates, for country i at time t.
unobserved factors that affect per capita GDP growth, through population change and its
interaction with intermediate sector markup. Finally, ω0i captures the unobserved countryspecific factors related with other variables not included in the model.
Equation (21) entails a data generation process for per capita GDP growth that can be
20
Assuming that some of the fundamental covariates were not included into the model specification, and that
their joint effects can be accounted by adding latent variables to the linear predictor, it is possible to relax the
assumption of IID residuals (Aitkin [7], McLachlan and Peel [51]).
21
In this section, the subscript y on the per capita GDP growth rate γ is omitted for notational simplicity.
16
affected by some hidden factors, underlying the relationship between mit and nit . Conditionally to the regression parameters η i = [ω0i , ω1i , ω2i , σi2 ]T , the probability density function
of γit is given by:
fγi = f (γit |η i ) =
T
Y
(
t=1
)
1
2
p
exp − 2 (γit − ω0i − ω1i mit − ω2i nit )
2σi
2πσi2
1
(22)
We assume that parameters in η i can be empirically described by random variables, with
unspecified probability function, and cluster-specific variances σi . In this way, equation (22)
takes explicitly into account the between countries random terms correlation.
The nonparametric maximum likelihood estimator (NPMLE) of the distribution is discrete (Laird [45], Heckman and Singer [30]), with at a finite number of locations and masses.
This implies that the country-specific latent variables are modeled as measures of the difference between country i-th’s covariates and their sample mean. We assume that γit is a
conditionally independent realization of the potential per capita GDP growth, given the set
of random factors, which varies over countries and accounts for both individual variation and
dependence among country-specific rates of growth.
Let now ui denote the set the country-specific unobservable factors that affect mit and nit ,
T
T
i.e., ui = [uT
ω0 , uω1 , uω2 ]. Treating the latent effects as nuisance parameters, and integrating
them out, we obtain the following likelihood function:
L (·) =

n Z
Y
i=1

U


fγi dG(η)

(23)
where U is the support for the latent variables space G(u), i.e., U is the discrete probability
measure on the space η i , with k = 1, . . . , K support points, each of them with probability
PK
πk = π1 , . . . , πK with k=1 πk = 1. McLachlan and Peel [51] stress that the mixture reduces to a simple homogenous regression when U degenerates in a single support point with
probability πk = 1. By introducing an undefined random distribution of parameters, this
specification allows to estimate unbiased coefficients for population growth and its interaction with intermediate sector murk-up, conditional to the effects of additional unobserved
environmental variables. Our goal is to find the best discretization of the conditional log
likelihood, given the data generating process of the response variable (Dempster et al. [22],
McLachlan and Krishnan [50], among others).
Equation (23) can be approximated by the sum of finite number (K) locations:
L (·) =
(K
I
Y
X
i=1
)
f (γi |mi , ni , uk )πk
=
(K
I
Y
X
i=1
k=1
)
[fik πk ]
(24)
k=1
where f (γi |mi , ni , uk ) = fik denotes the response distribution in the k-th component of
the finite mixture. Locations uk and corresponding masses πk (prior probabilities) represent unknown parameters while the optimal number of cluster K is estimated via penalized
17
likelihood criteria. This implies that:

n

n
K
K

XX
∂ log[L (η)]
∂` (η) X X 
∂ log fik
 πk fik  ∂ log fik
=
=
=
wik

 K
P
∂η
∂η
∂η
∂η


i=1 k=1
i=1 k=1
πk fik
(25)
k=1
where wik represents the posterior probability that the i − th unit comes from the k − th
component of the mixture. The corresponding likelihood equations are weighted sums of
those of an ordinary log-linear regression model, with weights wik . Solving these equations
for a given set of weights, and updating the weights from the current parameter estimates,
we define an Expectation Maximization (EM) algorithm (see, for instance, McLachlan and
Peel [51], and Alfò et al. [8] for the computation of EM in growth contest).
3.2
The data
In this section, we provide a description of our data and discuss the procedures adopted to
merge information from different sources in a single dataset.
First, we get data on real per capita GDP growth, population growth and exchange rate
(to convert all the monetary values in constant PPP US$) from the Penn Table database.22
Second, in order to construct a measure for the markup in the intermediate sector, we use
the EUKLEMS database, which collects data on output, productivity, employment (skilled
and unskilled), physical capital at industry level, for all European Union member states
and for five of the high developed countries (US, Japan, Korea, Canada and Australia)
from 1970 to 2007.23 At the lowest level of aggregation, data are collected for 72 industries
according to the European NACE revision 1 classification. We proxy the intermediate sector
with the sum of the following industries: basic metals and fabricated metal; electrical and
optical equipment; electricity; gas and water supply; machinery; other non-metallic mineral;
rubber and plastics; textiles; textile; leather and footwear; transport and storage; transport
equipment; wood and cork.
We then compute the markup index for the intermediate sector, of country i at time t,
as follows:
Gross Outputit
mit =
(26)
Total Labor Costsit + Total Capital Costsit
In our regressions, m is an index set equal to 1 in the base year 1995.
Third, the variable “research-labor”has been identified through an aggregate measure of
investment in research activity: we use the Gross Domestic Expenditure in R&D, converted
in constant PPP US$, as in Bottasso et al. [16].24
22
Time span: 1970-2007, 2005 as reference year. PWT 8.0 Alan Heston, Robert Summers and Bettina Aten,
Penn World Table Version 8.0, Center for International Comparisons of Production, Income and Prices at the
University of Pennsylvania. For more information on the Penn Table database the interested reader can refer to
the following web page: https:http://www.rug.nl/research/ggdc/data/pwt/.
23
For more information on the EUKLEMS database the interested reader can refer to the following web page:
http://www.euklems.net/.
24
The primary source of these data is EUROSTAT. In the case of missing data, Bottassio et al. [16] collect
information either from the OECD-STAN database or, for some countries, from EUROSTAT on Business Ex-
18
Fourth, the “number of ideas already invented”, i.e., a country stock of knowledge, has
been measured through the patent applications to the European Patent Office, collected by
EUROSTAT.25 In the robustness checks, we use the number of citation weighted patents
filed in each year at the USPTO.
Finally, in order to identify a country’s underlying complexity in production, we use
alternative indexes, i.e. the Network Trade Index and density measures, based on Lafay
index and Balassa index, provided by Ferrarini and Scaramozzino [25].
Our final dataset consists of a sample that includes 23 OECD countries (Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, The Netherlands, Poland, Portugal, Slovak, Slovenia, Spain,
Sweden, United Kingdom and USA), with a time span ranging from 1970 to 2007. Table 2
presents summary statistics. Table 3 shows that all countries in the sample experienced a
positive average real GDP per capita growth rate, along the period under observation. Since
we are dealing with OECD countries, this is not surprising. At the same time, the same
table also shows that the same countries (with the only exception of Ireland and Slovenia)
have experienced over time some negative annual real GDP per capita growth rates, as well.
3.3
Results
Tables 4 provides the estimation results for equation (21), using the annual real GDP per
capita growth rate as a dependent variable. Columns (1) and (2) report OLS fixed effects
and Feasible GLS estimates, respectively. In the OLS fixed effects model, inference is biased
because of the residuals non-normality (i.e., the Shapiro-Wilk test rejects the normality hypothesis with a value 0.988 and a p-value=0.000). The FGLS model allows for heterogeneous
variance in the residuals and takes into account the possible correlation between the covariates. In both models, the marginal effects of population change and its interaction with
the intermediate sector markup on per capita GDP growth are consistent with our second
theoretical prediction. This suggests that, on average, for the countries in the sample, the
specialisation effect is greater than the complexity effect.
Columns (3), (4), and (5) report the Finite Mixture Model (FMM) estimates, where we
relax the assumption of global normality of the residuals. Using the AIC, we identify three
clusters of countries, i.e., K = 3 in equations (24) and (25), listed along with summary
statistics for n and m in tables 6-8. The Shapiro-Wilk normality test on the residuals had
p-value=0.056 in cluster 1, 0.241 in cluster 2, and 0.830 in cluster 3. FMM parameter
estimation provides the same results of the previous models, with respect to the second
cluster of countries.
Results of models (1), (2) and (4) are consistent with the second prediction of our theoretical model. In particular, the location k = 2 of the Finite Mixture Model identifies a cluster
penditure on R&D. The authors notice that “only in the case of Sweden, Norway and New Zealand the amount
of missing data was substantial and we had to rely on linear interpolation: for this reason, as a robustness check
we have also performed our analysis after excluding these countries”.The full dataset is available at the following
web page: http://qed.econ.queensu.ca/jae/2015-v30.2/bottasso-castagnetti-conti/bcc-data.zip.
25
Data are available at the web page: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=pat_
ep_nic&lang=en.
19
of countries for which the potentially large losses due to the complexity in production are
lower than the specialization gains arising from innovation (see table 7). Table 7 shows that
those countries are characterized by higher (average) population growth and intermediate
sector markup and a lower (average) GDP growth (7.185 annual percentage points against
8.098 and 9.272). Results from the Finite Mixture Model (3) indicate also that exists a group
of countries, those of locations k = 1 and k = 3, whose sources of growth dynamics are not
captured by our theoretical model (see tables 6 and 8). Finally, parameter estimation for
countries in cluster 3 provides not significant results, even though the signs of the effects of
population change and intermediate sector markup on economic growth in this cluster are
compatible with the third prediction of our theoretical model.
It is wise noticing that, in our regression, we consider only three random components (i.e.,
the intercept, population growth and its interaction with the intermediate sector markup).
The set of unobserved differences between countries is, however, potentially larger and multidimensional. Our approach, then, has the limit of representing a multi-dimensional phenomenon on a reduced dimensional scale. This is proven by the fact that the variance of the
latent effects is high in all clusters (see table 4).
To examine whether the increase in production complexity influences the cluster membership, we estimate the following multinomial logit model:
P r{Cluster = 1, 2, 3} = log
πic
πiC
= %0C + %1C ntiC + %2C R&DC
(27)
PC
where: πic is the probability that the country i belongs to cluster c, with c πic = 1, for
each country i; %0C is the intercept; nti is our proxy for complexity in production; R&D is
the expenditure on Research & Development activities, in percentage of GDP.26
The second cluster (FMM, k=2) is the reference group for the odds. Results are reported
in table 9. In line with our theory, our estimates show that an increase of complexity in
production (here captured by an increase of nti) increases the odds for cluster 3 (FMM, k=3)
- where ∂γy /∂n < 0 - while reduces that for cluster 1 (FMM, k=1) - where ∂γy /∂n > 0. This
implies that, ceteris paribus, the higher the degree of complexity of a country’s production
structure, the lower probability that population growth acts as an engine for real per capita
GDP growth. Notice finally that, surprisingly, the R&D variable does not play any significant
role in the cluster membership probability.
26
As in Ferrarini and Scaramozzino [25], we employ the Network Trade Index (nti) as a measure of the intensity
of trade among countries participating in the international production networks (see also Ferrarini [24]). The net
index is defined as follows:
t
t
Xijk
− Mijk
(28)
nettijk = t
t
Xijk + Mijk
t
t
where Xijk
is country i’s exports of product k to country j, in year t and Mijk
is country i’s imports of product
k from country j. By construction, the nti ∈ [−1, 1]. A nti index equal to 1 indicates pure exports (and the
highest comparative advantage); a nti index equal to -1 indicates pure imports (and the highest comparative
disadvantage); finally, a nti index equal to 0 indicates balanced trade.
20
3.4
Robustness checks
In order to check the robustness of our results to different model specifications, in this section
we briefly present all the alternatives we have estimated and compare the results with the
baseline specification presented in the previous section.27
First of all, we run our regressions using the 5-year average real GDP growth rate as
dependent variable. This has been done with the objective of getting rid of possible shortrun business-cycle effects. Estimation results are provided in table 5. In this case, parameters
estimation through OLS Fixed Effects and Feasible GLS is in line with that presented in the
previous section and the AIC suggests four groups for the Finite Mixed Model. The main
difference with the previous results is that we can now identify a group of countries (namely,
Hungary, Ireland and Poland), which have actually the highest (average) per capita GDP
growth rate along the period under observation, that experience a positive impact both of
population change and the intermediate sector markup on economic growth, as predicted by
the first testable implication of our theoretical model.28
We control also for other measures of GDP. As mentioned at the top of tables 4 and 5,
our dependent variable, i.e. the (annual and the 5-year average) real GDP growth rate, has
been computed using the expenditure-side real GDP at chained PPP (rgdpe ), provided by
the Penn World Tables 8.0. Alternatively, we employ the rate of change of the real GDP
using national-accounts growth rates (rgdpna ) and the GDP per capita growth provided
by the World Bank. Although some modifications occur in the composition of the clusters,
our results do not change significantly.
We run our regressions also using different measures of intermediate sector markup. As
usual, when dealing with index numbers, results can be dependent on the base year. Since
we are examining long-run changes, we use an alternative base year, the 1985. We don’t find
any significant change in our estimates.
Finally, we estimate the multinomial logit model using the (logarithm of 5-year average
of the) country product density, according to the Lafay product space definition, to proxy
for complexity in production. The average density provides a measure of how fungible a
country’s capabilities are in terms of adjustment to complex production structures.29 Even
in this case, we do not obtain any significant change in our estimates.
4
Concluding remarks
This paper has re-assessed how the changing degree of production complexity (i.e., the number of horizontally-differentiated intermediate inputs entering the same aggregate production
function of a country) can ultimately affect not only the long-run growth rate of per capita
27
As our results are robust to the alternative specifications used, for the sake of brevity we do not present and
discuss in detail all the parameter estimates. However, they are available upon request from the authors.
28
Ireland is included by Durlauf et al. [23] (pag. 566, table 2) in the group of “fifteen growth miracles”.
29
Ferrarini and Scaramozzino [25] compute the density index for sector j in country i as a weighted average of
the trade specialization indicators, where the weights are the proximities of sector j with all the other sectors.
Then the average density of country i is obtained as an average of the density indexes across all sectors of the
country.
21
income, but also the relation between the latter variable, population growth, and the degree of product market competition (PMC). Building upon Romer [57] and Jones [33] we
have developed a variant of the basic, well-known semi-endogenous growth model capable
of explaining why we may observe (as suggested by the already available empirical evidence) a non-uniform correlation between population growth/economic growth and between
economic growth/markups. The theoretical explanation offered by our model is based on
the idea that introducing new varieties of intermediate inputs generates a tension between
productivity-gains due to more specialization and productivity-losses due to the presence
of a more complex production process. The composition of these two differential effects
of technological progress represents in the model the basis for the occurrence of a potentially non-monotonic correlation between population growth/economic growth and between
PMC/economic growth.
The empirical analysis presented in the second part of the paper suggests that a different
degree of production complexity yields in the long-run a different growth rate of per capita
income and, more importantly, a diverse impact of, respectively, population growth and PMC
on economic growth. In particular, using the annual real GDP per capita growth rate as a
dependent variable, OLS and FGLS models show the specialization effect of (intermediate)input-proliferation is larger than the corresponding production-complexity effect, so that the
marginal effects of population change and the intermediate sector markup on per capita GDP
growth are consistent with the second theoretical prediction of our model (negative impact
of population growth, and positive influence of markups on economic growth). Once the
unobserved heterogeneity has been taken into account (via FMM), it is possible to identify
the countries for which these results hold (Canada, France, Netherlands, Slovenia, Spain,
UK, and US). These countries are characterized, with respect to the rest of the sample, by
the highest (average) population growth rate and the lowest (average) level of markups and
per capita GDP growth. The use of the 5-year average real per capita GDP growth rate
as dependent variable confirms our previous results. The only difference is that in this case
our empirical model identifies a new cluster of countries (Hungary, Ireland, and Poland) in
which the marginal effects of population change and the intermediate sector markup on per
capita GDP growth are both positive, consistently with the first theoretical prediction of our
model. This fact, together with the observation that these three countries have enjoyed the
highest (average) GDP per capita growth rate along the period under observation, induces
us to believe that in these economies population growth and R&D incentives (in the form
of greater instantaneous monopolistic profits/markups accrued to the successful innovators)
can ultimately act as a powerful source of long-run productivity growth.
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26
Figure 1: Empirical cumulative functions
27
28
intermediate sector markup index (1995=1)
population growth rate (pop)
real per worker GDP growth rate based on
expenditure-side real GDP at chained PPP (rgdpe )
real per worker GDP growth rate based on
national-accounts growth rates (rgdpna )
real per capita GDP growth rate
R&D expenditure (% GDP)
Net Trade Index
m
n
γy
γc
R&D
nti
γy/na
Description
Variable
PWT 8.0
World Bank
Ferrarini and Scaramozzino [25]
PWT 8.0
EUKLEMS
PWT 8.0
PWT 8.0
Source
Table 2: Summary statistics
660
484
335
660
660
660
660
Obs.
0.027
1.769
4.539
2.064
1.277
0.507
2.309
Mean
0.030
0.747
3.312
1.830
0.727
0.460
2.628
Std. Dev.
-0.100
0.390
0.741
-9.830
0.152
-0.269
-11.912
Min
0.125
3.913
14.500
9.850
5.597
2.018
10.610
Max
Table 3: Descriptive statistic on annual GDP per capita growth rate
Country
Australia
Austria
Belgium
Canada
Czech Republic
Denmark
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Japan
Netherlands
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
United Kingdom
United States
Min
Mean
Max
-4.713
-2.704
-4.568
-1.872
-2.510
-3.349
-3.644
-5.023
-3.790
-4.564
-1.134
0.595
-5.239
-2.822
-4.025
-0.451
-11.912
-0.129
0.531
-3.804
-3.911
-5.907
-2.144
1.636
2.138
2.086
1.369
2.637
1.766
2.653
2.015
2.188
2.500
2.707
3.743
2.380
2.593
1.892
4.567
2.531
3.836
2.591
2.688
2.484
2.395
1.566
7.308
5.614
6.742
3.849
6.052
5.573
7.467
6.085
8.123
7.380
9.883
7.424
7.525
8.782
6.395
9.406
9.944
10.610
6.168
7.800
7.220
7.160
3.661
29
Table 4: Results I, country level data
(1)
OLSFE
(2)
FGLS
(3)
FMMk=1
(4)
FMMk=2
(5)
FMMk=3
Dependent variable: annual real per capita GDP growth rate(rgdpe )
m∗n
n
0.819***
-1.079*
0.672***
-1.348***
-1.752***
5.022***
1.564***
-2.424***
-0.008
-0.744
constant
σk
2.347***
2.443***
1.507***
2.173
2.374***
2.040
2.967***
2.986
∂γy
∂n
-0.071*
-1.041***
2.936***
-0.579***
-0.760
∂γy
∂m
0.374***
0.307***
-0.414***
1.062***
647
2.109
106
2.050
225
γy
obs.
647
Significance levels:* : 10% **: 5% *** 1%. Colors: case I, case II, case III.
30
-0.005
2.592
316
Table 5: Results II, country level data
(1)
OLSFE
(2)
FGLS
(3)
FMMk=1
(4)
FMMk=2
(5)
FMMk=3
(6)
FMMk=4
Dependent variable: 5-years real per capita GDP growth rate(rgdpe )
m∗n
n
0.083**
-0.113**
0.058***
-0.157**
1.098***
-1.300***
0.223**
-0.353**
-0.294*
0.599***
-0.028
0.102*
constant
σk
0.316***
0.335***
0.752***
0.178
0.323**
0.178
0.219***
0.178
0.375***
0.178
∂γy
∂n
–0.077*
-0.132***
0.675***
-0.065**
0.281**
-0.133
∂γy
∂m
0.120**
0.085*
0.396***
0.124**
-0.083**
-0.017
597
5.608
44
2.957
130
2.77
293
3.004
130
γy
obs.
597
Significance levels:* : 10% **: 5% *** 1%. Colors: case I, case II, case III.
Table 6: FFM, cluster 1 (k=1)
Country
n
m
Austria
Denmark
Germany
0.288
0.281
0.146
1.215
1.415
0.931
mean
std. dev.
0.238
0.080
1.187
0.243
Note: Model with the annual real GDP growth
rate as dependent variable.
31
Table 7: FFM, cluster 2 (k=2)
Country
n
m
Canada
France
Netherlands
Slovenia
Spain
United Kingdom
United States
1.135
0.550
0.644
0.198
0.750
0.244
1.008
0.934
1.483
1.398
1.072
1.380
0.914
0.952
mean
std. dev.
0.647
0.354
1.162
0.249
Note: Model with the annual real GDP growth
rate as dependent variable.
Table 8: FFM, cluster 3 (k=3)
Country
n
m
Australia
Belgium
Czech Republic
Finland
Greece
Hungary
Ireland
Italy
Japan
Poland
Portugal
Slovak Republic
Sweden
1.369
0.235
-0.007
0.374
0.587
-0.226
0.966
0.296
0.502
-0.047
0.554
0.110
0.361
1.401
1.394
1.362
0.941
2.158
1.929
0.935
0.846
0.912
3.213
1.196
3.404
1.282
mean
std. dev.
0.390
0.429
1.613
0.846
Note: Model with the annual real GDP growth
rate as dependent variable.
32
Table 9: Multinomial Logit Model for cluster membership
Cluster 1
nti
R&D
constant
%
s.e.
-0.121∗∗∗
0.051
0.185
0.357
-0.027
0.746∗∗∗
Cluster 3
nti
R&D
constant
%
s.e.
0.124∗∗∗
0.239
-1.869∗∗∗
0.048
0.250
0.508
Significance levels :
∗ : 10%
33
∗∗ : 5%
∗ ∗ ∗ : 1%