Entrepreneurial types and_economic_growth

Journal of Business Venturing 25 (2010) 305–314

Contents lists available at ScienceDirect

Journal of Business Venturing

Entrepreneurial types and economic growth
Maria Minniti a,1, Moren Lévesque b,⁎
a
Strategy and Entrepreneurship Department Southern Methodist University Cox School of Business, Dallas, 75275 TX, United States
b
Department of Management Sciences University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

a r t i c l e i n f o a b s t r a c t

Keywords: Most literature on economic growth focuses on expenditure in research and development
Entrepreneur (R&D) because of its ability to produce technological change. Models based on this principle,
Entrepreneurship however, fail to account for the exceptional growth exhibited in recent year by country such as
Imitators China where R&D expenditure is virtually non-existing and for the lack of growth observed in
Economic growth
countries such as Japan where R&D expenditure is significant. We propose a model in which
entrepreneurs may be research-based (those incurring R&D expenditure) or imitators (those
not incurring R&D expenditure) and show that, when the returns to R&D expenditure are low,
such as in many emerging economies, the presence of a high number of imitative entrepreneurs
who increase competition and product supply is sufficient to generate economic growth
regardless of the distribution of activity between research-based and imitative and in spite of
low R&D expenditure.
© 2008 Elsevier Inc. All rights reserved.

1. Executive summary

The most rigorous analysis of economic growth is found in the literature originating from work by Nobel Prize Robert Solow
(1956, 1957). In his work, economic output is generated by the interaction of physical capital and labor, while output growth is
generated by technological change. This framework, however, does not explain how technological changes come about. Romer
(1990, 1994) developed further Solow's idea by endogenizing technological change. In other words, he developed a theory in
which the rate of technological change is the result of knowledge and human capital accumulated within the economy. The
literature on endogenous growth represents the state of the art on the causes and structure of economic growth and helps us
understand the spreading and emergence of technological change and its relationship to growth.
In this literature, technological change is the key variable. Thus, attention is centered on R&D expenditure without which no
technological change, and as a result no growth, are assumed possible. It has become evident, however, that these models cannot
account easily for countries such as China, where growth has been remarkable in recent years even in the absence of significant
expenditure in R&D, or such as Japan, where plenty of expenditure in R&D has generated little to no growth. We argue that the
problem arises from the fact that, in spite of being very useful and sophisticated, these models ignore entrepreneurship. Although
the relationship between entrepreneurial activity and economic growth is often given for granted, the exact nature of such a
relationship and the channels that allow entrepreneurial activity to influence growth are still unknown. With a very few recent
exceptions (Michelacci, 2003; Acs et al., 2004, 2005), there is no role for the entrepreneur in endogenous growth models.
Moreover, the characterization of technological change or innovation (the two words are used as synonymous) is not sufficiently
refined and, as a result, no sufficient attention is paid to the fact that they may result from a variety of activities only some of which
require R&D expenditure but all of which require the presence of entrepreneurs.

⁎ Corresponding author. Tel.: +1 214 768 3145.
E-mail addresses: minniti@babson.edu (M. Minniti), levesque@uwaterloo.ca (M. Lévesque).
1
Tel.: +1 781 239 4296.

0883-9026/$ – see front matter © 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.jbusvent.2008.10.002

306 M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314

The main propensity of entrepreneurs is, of course, to innovate. Innovation, however, may take very simple forms and often
consists merely in filling a market niche that has not yet been exploited or that someone else has vacated. In other words,
innovation is not synonymous with original technological discoveries requiring R&D expenditure. We argue that most existing
research neglects the crucial role played by entrepreneurs in general and by imitative entrepreneurs in particular. We take a
Kirznerian view of entrepreneurs and define them as arbitragers who are willing to incur upfront costs in the hope of realizing
profit expectations. We then distinguish between two types of entrepreneurs: Research-based entrepreneurs who incur R&D
expenditure and commercialize technological discoveries, and imitative entrepreneurs who, unlike research-based entrepreneurs,
do not incur R&D costs. Thus, in our paper, the characterizing features of entrepreneurs are their alertness to opportunities
(Kirzner, 1973; Shane and Venkataraman, 2000) and their willingness to incur upfront costs, not their involvement with original
technological discoveries which, instead, only differentiates their types.
Building on Gancia and Zilibotti (2005), we offer an analytical model and derive a set of conditions describing the dynamics of
economic growth. We show that, in equilibrium, higher economic growth is found when the number of research-based or imitative
entrepreneurs, or both, is increased. Thus we show that a relatively high quantity of imitative entrepreneurs is sufficient for growth
and suggest that, as a result, the latter may not require R&D expenditure. We also show economic growth to be higher when
(ceteris paribus) the entrepreneurial cost and/or the cost of technological change (expenditure in R&D per unit of output) are
reduced. Most importantly, we show that an increase in an economy's imitation rate has a positive effect on economic growth
when the cost of technological change is sufficiently high, and when labor employed in developing original technological
discoveries (research-based labor) and labor not employed in developing original technological discoveries (imitative labor)
exhibit different levels of productivity.
Our argument is consistent with standard trade arguments according to which countries should leverage their relative
comparative advantages. In our model, for example, the recent economic growth in China is explained, in part, by the presence of a
large number of imitative entrepreneurs in spite of negligible R&D expenditure. Our model can also account for situations in which
significant expenditure in R&D yields unsatisfactory results. In recent years, for example, countries such as Japan and Sweden have
exhibited limited growth in spite of significant R&D investments. The lack of growth in Japan or Sweden is explained, in part, by the
small percentage of R&D expenditure translated into marketable technological change.
Our work changes the way we think about the relationship between entrepreneurial activity and economic growth by suggesting
what some of the linkages between them may be and by providing a model that can accommodate observations about all
economies, from the poorest to the most developed. We replace the common wisdom that R&D expenditure is a necessary condition
for economic growth with the claim that different countries may exploit a variety of entrepreneurial comparative advantages.
We also suggest that the presence of entrepreneurs is a necessary condition for economic growth but that entrepreneurship may
take a variety of forms depending on the competitive characteristics of each country. To our knowledge, no such general model
existed before.

2. Introduction

Most literature analyzing the mechanisms and causes of economic growth focuses on the role played by expenditure in R&D
and the resulting innovation and technological change (Goel and Ram, 1994; Griliches, 1979; Piekarz, 1983). Historically, most
countries with sustained research investments have grown faster than others (Peretto, 1999). In recent years, however, countries
with significant R&D expenditure, such as Sweden and Japan have experienced little or no economic growth (Acs et al., 2005). At
the same time, countries such as China have shown that significant rates of growth are possible with virtually no R&D expenditure
(Hsiao and Shen, 2003; Mah, 2005).
Using a large panel data set, for example, Yao (2005) has shown that Chinese exports and FDI have a strong and positive effect on
economic growth. This suggests that imitation, by producing increased output consistent with existing technology developed
elsewhere, is responsible for a significant portion of the Chinese miracle. Also, Tan (2005) found that, comparing 2002 to 1990, the
business environment in China has become more conducive to entrepreneurial activities. This suggests that an increase in
entrepreneurial attitudes, generated by increased incentives, has also contributed to economic growth in China. Of course,
macroeconomic growth is an extremely complex phenomenon, and a few facts about the economy do not explain the recent growth
trend in this country. They do suggest, however, that entrepreneurship may play a very important role in emerging economies and
that the type of entrepreneurship observed in those countries may be somewhat different from that observed in developed ones.
Our research question consists in asking how and if entrepreneurial activity contributes to economic growth in the specific context
of emerging economies. For this purpose, we develop a model of the relationship between entrepreneurship and economic growth
applicable not only to emerging economies but to all countries regardless of their level of development. Consistently with Kirzner
(1973,1997), we describe entrepreneurs as arbitragers willing to incur an upfront cost in the hope to realize their profit expectations by
being either research-based entrepreneurs (individuals who transform invention into marketable technological change and incur R&D
expenditure) or imitative entrepreneurs (individuals who increase product availability and competition by replicating technologies
developed elsewhere and, as a result, do not incur R&D expenditure). In other words, we argue that entrepreneurs are the lubricant at
the core of the growth process. Whether imitating an existing product or technology, or transforming a new invention into a
marketable technological change, entrepreneurs are the economic actors who, by risking own resources in exchange for an expected
profit, make growth possible (Schumpeter, 1934; Acs et al., 2004). By including two types of entrepreneurial activity (imitative and
research-based), our model accounts for the accelerated growth experienced by some emerging economies in the absence of R&D
expenses as well as for the lack of growth in countries with high levels of R&D expenditure.

M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 307

Whether imitative entrepreneurs or research-based entrepreneurs are more important depends on the type of country (Goel
and Ram, 1994; Gong and Keller, 2003). For example, in a relatively rich country, which is closer to its production possibility
frontier, growth is generated by increases in productivity. To remain competitive, such a country will need relatively more original
technological discoveries. On the other hand, a country characterized by a large quantity of unused resources may increase its
wealth simply by mobilizing them. This country may specialize in imitating technology developed elsewhere and, depending on
the level of development of the country and the cost of technological change, imitative entrepreneurs may be more important than
research-based entrepreneurs. Understanding the role of entrepreneurship for economic growth is important because
governments worldwide are sinking large amounts of capital in the pursuit of policies that, lacking such understanding, may
have little if any effect on the macroeconomic conditions of a country (Easterly, 2005).
Although our theoretical model is rooted in endogenous growth theory, our argument is consistent with a growing body of
empirical literature which, in recent years, has studied the relationship between entrepreneurial activity and economic growth.
Wennekers and Thurik (1999), for example, have suggested the existence of a U-shaped relationship between number of self-
employed and stages of economic development. Similarly, van Stel et al. (2005) have found that entrepreneurial activity by early
stage entrepreneurs affects economic growth, but that this effect depends upon the level of per capita income. This suggests that
entrepreneurship plays a different role in countries in different stages of economic development. Dana (1997) has shown that the
business environment in Uruguay does not lend itself to the reproduction of entrepreneurial policies that have been successful in
Argentina in spite of many similarities across the two countries. Finally, Giamartino (1991) has argued that when one considers
many developing economies around the world, it is not unreasonable to conclude that the status of internal and external
components varies widely across countries and within regions of countries and that these differences may lead to different
experiences in economic development and entrepreneurship. All these works support our argument that entrepreneurship comes
in a variety of forms and plays different roles in countries in different stages of economic development.

3. Theoretical background

In standard models, the long-run rate of economic growth was determined by assuming a constant rate of technological change
(Solow, 1956, 1957). Although very useful in many instances, these models failed to explain the origins of growth as technological
change remained exogenous to the economic context. Endogenous growth theory solved this issue by including mechanisms that
link human capital to the creation of new technologies so that technological progress is no longer outside the model but, rather, is
determined by the characteristics of the economy described by the model (Jovanovic and Rob, 1989; Romer, 1990). In these models,
R&D expenditure produces knowledge which, in turn, leads to technological change and growth. The knowledge generated by
technological changes spills over to other individuals thereby increasing their ability to produce additional inventions. Thus, a
positive externality is set in motion that allows sustainable and possibly increasing technological change over time (Romer, 1986).
Although already in 1934 Schumpeter had put entrepreneurship at the core of economic development, with a very few
exceptions, entrepreneurs have been excluded from formal models of economic growth. In fact, for a long time, scholars working
with analytical models neglected entrepreneurship and simply treated it as part of the residuals that cannot be attributed to any
measurable productive input (Baumol, 1993). Only very recently, a few attempts have been made to better understand what the
distinctive characteristics of the entrepreneurs are (Lazear, 2005) and to incorporate the role of the entrepreneur in the growth
process (Acs et al., 2004, 2005).
Among studies that consider the role of the entrepreneur, Michelacci (2003) proposes a model of endogenous growth in which
technological change requires both researchers, who produce inventions, and entrepreneur who transform them into innovation,
that is into economically viable ventures. Michelacci shows that when entrepreneurs appropriate too little rents from innovation,
too few resources are allocated to entrepreneurship and, as a result, returns to R&D are low because of this lack of entrepreneurial
skills. Along similar lines, Acs et al. (2004) argue that one of the breakthroughs contributed by endogenous growth theory is the
idea that investments in human capital create economic growth through the spillover of knowledge. They also claim that
endogenous growth theory does not explain how or why spillovers occur and that the missing link is the mechanism converting
knowledge into ‘economically relevant' knowledge. Within this context they suggest the existence of a filter between knowledge
and economic knowledge and identify entrepreneurship as the mechanism that reduces such knowledge filter. Thus, they focus on
the relationship between knowledge and commercializable knowledge.
As in the works discussed above, the recent growth literature that does include entrepreneurs focuses on their role as agents
who bring research-based technological discoveries to the market. We complement this approach by taking a broader view of
entrepreneurship and developing a model of growth that, in addition to including a distinctive role for entrepreneurs, can be
applied even to countries in which little or no formal R&D exists and virtually no original technological discovery takes place. The
argument we develop follows Howitt (2000), according to whom, the further behind its production possibility frontier a country is
initially, the larger is the number of entrepreneurial opportunities.
Technically, analytical models of economic growth spun off from Romer's work are of two types: models with vertical
innovation (e.g. Aghion and Howitt, 1992), and models with expanded variety (e.g. Acemoglu and Zilibotti, 2001). In a vertical
innovation framework, the expected rate of growth of the economy depends exclusively on the economy wide amount of
technological change, which in turn results from competition among research firms that generate innovations. Research firms are
motivated by the prospect of monopoly rents that can be captured when a successful innovation is patented. But those rents, in
turn, are destroyed by the next innovation, which renders obsolete the existing good. The basic intuition behind these models is the
Schumpeterian idea of creative destruction.


In an expanded variety framework, on the other hand, an innovation consists of the technological knowledge required to
manufacture a new good that does not displace existing ones. Thus, innovation takes the form of an expansion in the variety of available
products. The underlying growth assumption is that the availability of more goods, either for final consumption or as intermediate
inputs, raises the material well-being of people. This class of models is the most recent in the endogenous growth literature. Among
others things, they lend themselves to several applications and offer the advantage of being mathematically tractable.
We propose a modified version of an expanded product variety model (Gancia and Zilibotti, 2005; Jovanovic and MacDonald, 1994)
in which economic growth is achieved thank to the activity of entrepreneurs and through a combination of research-based
entrepreneurship, which increases productivity and product variety, and imitative entrepreneurship, which increases competition and
product supply thereby reducing prices and promoting efficiency. We assume the existence of an intermediate good sector and a final
good sector. The latter is competitive and produces a homogenous final good. The intermediate good sector, instead, is non competitive
and includes a variety of non-homogeneous (and therefore non-substitutable) goods which enjoy economic profits. Specific
intermediate goods, however, can be imitated. When this happens, they lose their monopolistic position and generate zero economic
profits.
Two types of entrepreneurs are considered in our model: Research-based entrepreneurs who are involved in commercializing
original technological discoveries and imitative entrepreneurs who mobilize resources to expand existing markets. Research-based
entrepreneurs exploit profit opportunities by producing research-based intermediate goods and incur R&D expenditure to develop
such goods, while imitative entrepreneurs imitate existing products and exploit the profit opportunities presented by the non
competitive nature of the intermediate goods sector. Imitative entrepreneurs also contribute to economic growth by increasing
competition and promoting efficiency. Their entry in the market increases product quantity thereby reducing prices and drives the
economic profits associated to the specific good to zero. Both types of entrepreneurs, research-based and imitative, face a variable
entrepreneurial cost consisting of the expense necessary to set up and operate the business. Research-based entrepreneurs, however,
incur an additional expenditure necessary to finance the R&D needed to develop the innovation. Research-based entrepreneurs are
willing to incur R&D expenditure because their goods will enjoy a monopoly position at least until they are copied.

4. Growth model with imitation

4.1. Consumption and production

Our starting point is the expanded variety model of Gancia and Zilibotti (2005), which, in turn, is a simplified version of Romer
(1990) as it abstracts from investments in physical assets. In this model, infinitely lived agents form a population of constant total
labor size L. Agents earn income by supplying labor and derive utility from consumption. On the consumption side, agents'
preferences are described by an isoelastic utility function which they maximize by selecting the optimal consumption plan given
an intertemporal budget constraint. In other words, individuals want to maintain living standards over their life time. Thus, they
allocate their resources so that the rate of growth in their consumption over time is directly proportional to the interest rate they
have to pay net of the discount rate representing the rate at which consumption in the future is viewed as less valuable than
•
present consumption. Formally, such a consumption plan satisfies the Euler equation Ct/Ct = [rt − ρ]/θ, where rt is the interest rate
at time period t, ρ the discount rate, and 1/θ the intertemporal elasticity of substitution of consumption.
On the production side, the expanded variety model includes a competitive sector for the production of a homogenous final good
and a non competitive sector for the production of intermediate goods. The production of the final good depends on labor employed
for its production as well as quantity and variety of intermediate goods. Formally, the production function is Yt = L1 − α ∫At xα dj,
y,t 0 j,t
where Ly,t is the labor force employed in the production of the final good at t, 1 − α ∈ (0,1) its elasticity, At a measure of the number of
intermediate goods available at t, and xj,t the quantity of intermediate good j at t. This specification describes different intermediate
goods (production inputs) as imperfect substitutes without implying that any of them is better than the others. All intermediate
goods have diminishing marginal products. Table 1 summarizes all mathematical notation used in the paper.

4.2. The role of research-based and imitative entrepreneurship

We complement the existing expanded variety models by distinguishing the role of the entrepreneurial labor and non-
entrepreneurial labor. Entrepreneurs produce intermediate goods and exploit profit opportunities in one of two ways: First,
entrepreneurs can imitate an existing intermediate good thereby increasing competition and product supply. Second, entrepreneurs
willing to incur R&D expenditure may introduce original technological changes thereby increasing productivity and intermediate
goods' variety. Imitative entrepreneurs produce imitative intermediate goods, research-based entrepreneurs produce research-based
intermediate goods. Both imitative and research-based entrepreneurs incur entrepreneurial costs, ce, consisting of set up and financing
costs. In addition to entrepreneurial costs, each research-based entrepreneur is subject to R&D expenditure. That is, to a fixed sunk cost
ci required to develop a research-based intermediate good variety. Although they incur the additional R&D cost, research-based
entrepreneurs have an incentive to innovate rather than imitate because expected profits from innovations are, at least temporarily,
monopoly profits.2
2
It should be noted that imitative entrepreneurship is not synonymous with small business ownership and that firm size is irrelevant with respect to our
argument. In fact, as illustrated by the biotech industry in the United States, many small businesses are very research-based, whereas many larger firms are not. In
line with the growth literature, the crucial distinction between imitative and research-based entrepreneurs is the amount of R&D expenditure per unit of output
which is uncorrelated to size.


Table 1
Notation summary.

Notation Description
Labor components
L Total labor size of a population
Ly,t Labor force employed in the production of the final good at t
Lx,t Labor force employed in R&D at t
Li,t Labor force employed for imitative intermediate goods at t
Le,t = βLx,t + Li,t Entrepreneurial labor force at t
Time-invariant variables
β Portion of research labor transformed into research-based intermediate product
ρ Discount rate
1/θ Intertemporal elasticity of substitution of consumption
1−α Elasticity of the labor force employed in the production of the final good
δ Productivity of the entrepreneurial sector
ce Entrepreneurial cost
ci Cost of innovation
µ Entry cost (i.e. cost of labor per innovation)
Time-variant variables
rt (r in equilibrium) Interest rate at t
pj,t Unit price of intermediate good j at t
xj,t Quantity of intermediate good j at t
wt Wage rate at t
At Measure of the number of intermediate goods available at t
mt = Li,t/Le,t (m in equilibrium) Imitation rate at t
πj,t = pj,t xj,t − xj,t − ce xj,t − ci (π in equilibrium) Profit from research-based intermediate good j at t
πY = Ly,t α ∫At xα dj − wtLy,t − ∫At pj,t xj,tdj
t
1−
0 j,t 0 Profit from the final good at t
Yt = L1 − α ∫At xα dj
y,t 0 j,t Production function at t
Growth rates
•
At/At = δ[βLx,t + Li,t] ≡ δLe,t Law of motion for innovation at t
•
Ct/Ct = [rt − ρ]/θ An agent's consumption plan at t
γ Rate of growth in equilibrium

Total labor force, L, which is assumed constant over time, is distributed between labor force used for the production of the
homogeneous final good Ly,t, labor force Lx,t employed in R&D, and labor force employed for imitative intermediate goods Li,t.
Consequently,

L zLy;t + Lx;t + Li;t : ð1Þ

The entrepreneurial labor force consists of all labor force for imitative intermediate goods plus a fraction, β, of labor force
employed in R&D. In fact, not all attempt to develop original technologies come to fruition, and not all inventions are marketable or
brought to market. This is an important point of our model since it incorporates the differential effect that alternative types of
entrepreneurs have on markets and reflects how different entrepreneurial types are behind the growth dynamics of some
emerging economies. The total entrepreneurial labor force, denoted by Le,t, thus adds to βLx,t + Li,t.
For simplicity, and since the core of our paper is to show how different types of entrepreneurs matter for growth, we focus on
people. Thus, we assume that the development of research-based intermediate goods only requires labor and that potential
research-based entrepreneurs benefit from observing the stock of intermediate goods already existing in the economy by obtaining
ideas for new goods.3 This means that the design of a unit measure of research-based intermediate good requires an
entrepreneurial labor input equal to 1/(δAt), in other words, that the productivity of research-based entrepreneurial labor
increases with At, since 1/(δAt) becomes smaller as the number of intermediate goods increases. Therefore, each potential
•
research-based laborer who has an impact on the market contributes δAt to the change in technological innovation, At.
Research-based entrepreneurs (and corresponding labor), however, are not the only ones to contribute to technological change.
Imitative entrepreneurs contribute too albeit indirectly. In fact, the existence of imitative entrepreneurs threatens the rent of
research-based entrepreneurs and gives them incentives to continue innovating to stay ahead of competition. Thus, when the role
•
of imitation is considered, the rate of growth in technological knowledge, At /At, not only depends on the entrepreneurial labor
employed for research-based purposes, but also on imitative labor (since the latter increases the incentive to innovate). As a result,
the law of motion for innovation is described by

Á Â Ã
At =At = δ βLx;t + Li;t uδLe;t ; ð2Þ

where δ N 0 represents the productivity of the entrepreneurial sector and β allows us to account for the possibility of different
productivities from the research-based (Lx,t) and imitative sector (Li,t). The rate of original technological discovery or, consistently

3
In other words, consistently with the endogenous growth literature we assume the existence of innovation spillovers that generate a positive intertemporal
externality.


with the endogenous growth literature, the rate of innovation is thus a linear function of total employment in entrepreneurship
and its distribution between imitation and research. Without loss of generality, the coefficient associated with imitative
entrepreneurs in the brackets equals 1 because the parameters δ and β allow the model to account for different productivities for
imitative and research-based entrepreneurs. In fact, these parameters can be used to view the probability of success for imitators as
being δ, whereas that of research-based entrepreneurs as being δβ (which is smaller than δ as β b 1).
For the purpose of evaluating the effect of imitation on economic growth, we also define an imitation rate parameter. This
allows us to account for those research-based intermediate goods that become imitated and whose monopoly position is eroded by
imitation. For simplicity, we assume that on any given time period t this erosion occurs at a constant rate, so that a fraction mt of
research-based intermediate goods becomes competitive. This imitation rate corresponds to the ratio of imitative entrepreneurs to
entrepreneurial labor force, i.e. mt = Li,t / Le,t.4 Clearly, a strong patent protection can be considered as a reduction in the imitation
rate mt (Judd, 1985).5 The separation of research-based and imitative intermediate goods is important because these two types of
intermediate goods yield different profits.

4.3. Entrepreneurial profits

Due to competition, the unit price of imitative intermediate good j at t, pj,t, is 1 + ce, its standardized production cost, and profit
πj,t is zero. For research-based intermediate goods, which enjoy a monopoly position (albeit temporarily), instead, the profit of the
entrepreneur producing variety j at t is

πj;t = pj;t xj;t −xj;t −ce xj;t −ci : ð3Þ

pj,t is obtained from optimizing the profit of the final good producer with respect to the demand for intermediate good j (i.e. xj,t).
This profit is a linear combination of revenues, labor costs, and costs of intermediate input with πY = Ly,t ∫0 t xα dj − wtLy,t − ∫0 t pj,t
t
1-α A
j,t
A
1 − α α −1 6
xj,t dj, where wt is the wage rate. It follows that the price of research-based intermediate good j at t is given by pj,t = αLy,t 2 xj,t .
Substituting this demand function into the profit in Eq. (3) and maximizing that profit with respect to xj,t lead to xj;t = α 1−α Ly;t and
2 −1
hence pj,t = [1 + ce]/α. Substituting back the latter into the demand function leads to xj;t = α 1−α ½1 + ce Š1−α Ly;t uxt .
As expected, the price of a research-based intermediate good is above that of an imitative intermediate good (since α b 1).
1 −1
Consequently, it makes sense for the amount of imitative intermediate good (which equals α 1−α ½1 + ce Š1−α Ly;t from substituting,
1−α α −1
instead, pj,t = [1 + ce] into the demand function pj,t = αLy,t xj,t ) to be larger than the amount xt of research-based intermediate
good. Thus, the profit from a research-based intermediate good is
1+α −α
πj;t = πt = ½1−α Šα 1−α ½1 + ce Š1−α Ly;t −ci : ð4Þ

Eq. (4), along with the Euler equation and Eqs. (1) and (2), allow us to determine at equilibrium the laws of motion (rates of
change) for consumption, production and innovation in this economy and, therefore, to describe how the economy grows as a
result of its productive structure and, in particular, of the role played by both types of entrepreneurs.

5. Balanced growth equilibrium

Most models of economic growth use the concept of balanced growth equilibrium in order to study the dynamic changes and
instabilities produced in the economic system by changes in some key variables. In the balanced growth equilibrium the capital
intensity of the economy, that is its capital stock divided by its total output, is constant while other variables such as real GDP and
output per worker are allowed to change. The balanced growth equilibrium is useful because it shows where the economy tends to
converge and stabilize. In other words, it provides a point of reference so that dynamic changes toward and away from this stable
growth pattern can be compared. Without the balanced growth equilibrium to serve as a reference point, the causes and
implications of changes in economic variables such as consumption, production, and interest rates could not be isolated.
In our model, at the balanced growth equilibrium, the rates of growth in consumption, production and innovation all equal a
• • •
constant γ, that is Ct/Ct = Yt/Yt = At/At = γ. In addition, the three sectors (final good labor, research-based labor, and imitative
labor) must employ constant proportions of the labor force over time. In such equilibrium, the time dimension is removed and
the various labor force components, Ly, Lx, Li, become time-independent. As a result, production and profits are constant over time.
The interest rate is also assumed constant over time, and from the Euler equation described earlier for consumption, we have
r = ρ + θ γ.
Free entry in the market requires the present discounted value (PDV) of expected profit from an innovation to equal its entry
cost, where the latter is measured as that innovation's labor cost. Since both research-based entrepreneurs and imitators influence

4
While in Gancia and Zilibotti (2005) the imitation rate is a fixed parameter, our formulation allows us to endogenize this rate.
5
The possibility of obsolescence also increases the incentives to innovate. An entrepreneur innovates more trying to stay ahead of imitators and competitors
who can make her obsolete. One could, however, also argue that the entrepreneur innovates less because she thinks that she will be imitated or made obsolete. In
order to introduce a clear distinction between the effect of imitation and obsolescence, the model would have to include alternative forms of patenting rights.
6
When Eq. (1) holds as an equality then Ly,t = L − Le,t − [1 − β]Lx,t and the price of research-based intermediate good j at t decreases with the size of the
entrepreneurial labor force, presumably because more units of intermediate good j are then produced.


the research-based sector and technological change, the PDV of expected profit is calculated as a weighted average of the positive
expected profit from a research-based intermediate good with (from Eq. (4)) πt = π in equilibrium and zero expected profit from
an imitative intermediate good. As a result, the PDV of expected profit is the ratio of [1 − m]π to the real interest rate r, where in
equilibrium the imitation rate mt has its time dimension removed. In other words, we use the imitation rate m, which is calculated
as the ratio of imitative entrepreneurs to total entrepreneurial labor force, as a proxy for the proportion of imitative intermediate
goods and, clearly, 1 − m as a proxy for the proportion of research-based intermediate goods.7 With μ representing the entry cost
(i.e. the cost of labor per innovation), the balanced growth equation can be formally written as ½1−mŠπ = μ or, equivalently from
r
substituting r = ρ + θ γ, Eq. (4), and rearranging both sides,
h 1+ α −α
i
½1−mŠ ½1−α Šα 1−α ½1 + ce Š1−α Ly −ci
= ρ + θγ: ð5Þ
μ

Thus, when balanced growth takes place, the interest rate is (among other things) proportional to the rate of growth and equals
to the PDV of expected profit from innovating divided by that innovation's labor cost. Eq. (5) allows us to explore next how changes
in a country's labor environment affect the rate of growth of that country.

5.1. Growth rate and its sensitivity

At balanced growth equilibrium, the law of motion for technological knowledge (Eq. (2)) provides an expression for the growth
rate that can be used to analyze how a change in research-based or imitative labor (or both) affects growth. This expression for the
growth rate can also be substituted in Eq. (5) to study further how changes in the labor's environment affect the growth rate.
Á
A
Specifically, γ = Att = δ½βLx + Li Š (Eq. (2)) shows that the growth rate γ increases in both research-based and imitative labor since
they both constitute entrepreneurial labor which, according to Eq. (2), augments the rate of technological innovation. Acs et al.
(2004) also derive a positive relationship between growth and both research-based labor and entrepreneurial labor, whereas
Michelacci (2003) shows that the growth rate does not necessarily increase as the amount of resources devoted to research
augments. Michelacci argues that there needs to be a balance between entrepreneurial and research activities. In fact, low
entrepreneurial rents from research are associated with low returns to R&D (and hence growth) because of a lack of resources
allocated to entrepreneurs who can implement those innovations. In our formulation, a tradeoff similar to Michelacci's exists
between imitative and research-based labor (as per Eq. (2) based on the parameter β, which weights the contribution of research-
based labor relative to that of imitative labor).8
γ ½1−mŠ γ
Further, given Eq. (2) and m = βLx L+ Li , it is straightforward to verify that Lx = δ β h and Li = im. Given the resource constraint
i
δ
γ ½1−mŠ
L = Ly + Lx + Li and the above equalities, the final good labor force becomes Ly = L− δ m + β . As a result, the growth rate can
be expressed as

½1−mŠ 1+α −α

μ ½1−α Šα
1−α ½1 + c Š1−α L−c −ρ
e i
γ= −α
h i: ð6Þ
½1−mŠ 1+α ½1−mŠ
θ+ δμ ½1−α Šα
1−α ½1 + c Š1−α
e m+ β

Ceteris paribus, the growth rate decreases with an increase in the entrepreneurial cost (ce), the cost of innovation (ci), the labor
cost per unit of innovation (μ), or the discount rate (ρ). But the growth rate increases with an increase in the productivity of the
entrepreneurial sector (δ), the portion of research labor transformed into research-based intermediate products (β), the size of
total labor force (L), or the intertemporal elasticity of substitution of consumption (1/θ).
The effects of a change in any of these parameters on the growth rate can be seen intuitively from Eq. (5). The left-hand side of the
equation represents the profit rate and the right-hand side the effective cost of capital. All else equal, an increase in entrepreneurial
cost, cost of research, or labor cost per unit of research-based intermediate goods decreases the profit rate but does not affect the cost
of capital and, as a result, the growth rate should decrease. On the other hand, an increase in the discount rate does not affect the
profit rate but increases the cost of capital, which should also yield a diminished growth rate. Furthermore, all else equal, an increase
in either productivity in the entrepreneurial sector, portion of R&D labor transformed into marketable inventions, or size of total
labor force increases the profit rate but keeps unchanged the cost of capital and, as a result, the growth rate should increase. Last, an
increase in intertemporal elasticity of substitution of consumption keeps unchanged the profit rate but decreases the cost of capital,
which should yield an increased growth rate. (Proofs for these results are straightforward and thus omitted.)

7
We use m as a proxy for the percentage of imitated goods in order to estimate the PDV of expected profit. In our framework, however, this percentage can
be endogenously derived and shown to equal m/[γ + m], where γ is the growth rate. As long as mρ − γm[1 − θ] − γ2 b 0, all our results are robust. That is, this
inequality holds when the intertemporal elasticity of substitution of consumption (1/θ) exceeds 1 and the growth rate exceeds the discount rate (ρ), and also
when the growth rate is sufficiently large. Finally, even when this sufficient condition is violated, it is still possible to derive conditions under which imitation
increases growth.
8
Noticeably, the fact that in our model labor is the only productive input does not limit the role played by creativity. In fact, a portion of labor is defined
exclusively as research-based labor. Also, regardless of how abundant they are, all resources have always an opportunity cost and the trade off suggested by
Michelacci is universal. Furthermore, in our model, Inequality (1) does not force the change in labor to be directed exclusively to imitative or research-based uses
since our model also includes a portion of labor force used in the production of final goods. The creation of new markets and new industries is also consistent
with our framework. As the entrepreneurial labor force shrinks or expands, new markets and new industries might be destroyed or created. Although business
and industry churning is an important phenomenon, this is not the core element of our arguments.


Our findings about the effects of μ, ρ, L, and 1/θ on growth rate confirm the results of Gancia and Zilibotti (2005) for all four
parameters, and of Acs et al. (2004) for ρ and L. Nevertheless, our model illustrates the additional effects on growth of δ, β, ce and
ci. First, while Gancia and Zilibotti (2005) suggest a positive relationship between economic growth and productivity of research-
based labor, we argue for a positive relationship between growth and productivity of the entrepreneurial sector (δ), and between
growth and the portion of research-based labor actually transformed into marketable innovations (β). These two parameters allow
us to separate the productivity of research-based entrepreneurs from that of imitative entrepreneurs. Acs et al. (2004) also derive a
positive relationship between growth and both the efficiency of research-based labor and the efficiency of entrepreneurial labor.
Their formulation, however, neglects the role of imitative entrepreneurs whose consideration in our model, instead, allows us to
weigh (via δ and β) in the technological change equation (Eq. (2)) how research-based entrepreneurs fare compared to imitative
entrepreneurs. As discussed next, this weighting leads to new findings on how a change in the imitation rate (m) affects the growth
rate. Finally, existing expanded variety models do not take into consideration cost differential faced by different types of
entrepreneurs, namely entrepreneurial and innovation costs, ce and ci, respectively. These costs play an important role in
determining the expected profit of a research-based intermediate good. As a result, they are also important in characterizing the
impact of a change in the imitation rate on growth.

5.2. Impact of imitation on the growth rate

The rate of imitation influences the rate of growth. Specifically, an increase in the rate of imitation (m) can increase or decrease
the growth rate. The intuition is that a higher imitation rate leads to a smaller percentage of research-based labor relative to
entrepreneurial labor ([1-m] diminishes) but a larger expected profit for any research-based intermediate good (π increases). This
larger profit, at equilibrium, is due to a positive impact of m on the labor force used for the production of the final good
h i
(Ly = L− γ m + ½1−mŠ = L− δβ + mγ ½1−βŠ), which in turn increases π (as per Eq. (4)). Consequently, the resulting PDV of expected
δ β
γ
β
profit from an innovation ([1 − m]π) can be augmented or diminished. Using logarithmic transformations of both side of Eq. (5)
(after substituting Ly = L− γ ½m + ½1−mŠ Š), we verify that an increase in the imitation rate may have a positive effect on growth
δ β
when the cost of innovation is relatively high. A formal proof of this result is presented in the Appendix.
We further note that if the portion of research-based labor transformed into marketable innovations (β) equals 1, then,
regardless of the cost of innovation, an increase in the imitation rate leads to a decreased growth rate. The intuition is that, when
research-based and imitative entrepreneurs have the same productivity (δ), a large number of imitative entrepreneurs relative to
the overall number of entrepreneurs no longer increases expected profit for research-based intermediate goods. As a result, the
tradeoff between a smaller percentage of imitative entrepreneurs relative to the total number of entrepreneurs and a larger
expected profit for a research-based intermediate good disappears.
In a version of their model including limited-patent protection, Gancia and Zilibotti (2005) found that the growth rate decreases as
the imitation rate increases. In other words, that the lower the patent protection, the lower is the growth rate. Our results differ
because, in our model, contributions to technological innovation from research-based entrepreneurs and, indirectly, from imitative
entrepreneurs create a tradeoff that can make high levels of imitation desirable (e.g., when the cost of innovation is sufficiently high).

6. Conclusion and future research

In this paper we present a simple endogenous growth model with expanded variety. We argue that our framework is
particularly useful for analyzing how entrepreneurial activity interacts with growth and under what conditions alternative types of
entrepreneurial behavior lead to growth. We also suggest that this type of models provide a useful and mathematically tractable
framework for analyzing the determinants of long-run growth and cross-country convergence.
We believe our contribution to be twofold. First, our model puts entrepreneurs at the center of the growth process and shows,
in a formal context, their importance in the economy. Specifically, we show that at the core of economic growth is the action of alert
individuals who are willing to incur costs in exchange for expected profits. Second, our model is applicable to countries in any stage
of development and is able to account for situations such as those observed in China as well as those observed in Japan or Sweden.
Clearly, it is not our intention to advocate the Chinese case as an example for other countries. This is a theoretical paper; countries
mentioned in the text are just used as examples and others, of course, could have been used.
We also suggest that entrepreneurial activity may take the form of either imitative or research-based labor and that the
presence of a sufficient amount of either type of entrepreneurship has a positive effect on the growth pattern of the economy. In
fact, the relative distribution of entrepreneurs across these two categories does not influence the growth rate, what matters is that
a country has a relatively high absolute number of at least one type of entrepreneurs. Furthermore, our model suggests that when
the cost of producing original technological discoveries (innovation) is high, a country can experience economic growth by
focusing on imitation. This is consistent with standard economic reasoning about gains from trade and the division of labor.9

9
An important issue related to the distribution of entrepreneurial types concerns what would happen if intellectual protection (IP) laws were not enforced.
Except for products likely to generate strong first mover advantages, lack of IP laws would eliminate the advantage enjoyed by research-based over imitative
entrepreneurs. In our model, the imitation rate would increase since research-based entrepreneurship would decrease relative to imitative entrepreneurship. As a
result, the growth rate would increase when the cost of innovation is sufficiently high (imitative entrepreneurship yields better country-level returns), but
decrease when research-based and imitative entrepreneurs have the same productivity.


Overall, the model highlights how entrepreneurship matters for growth and that, in its absence, the presence of a large amount
of labor employed in R&D does not necessarily guarantee that the benefits of this expenditure will arrive on the market, since that
depends on β, that is on the percentage of research-based labor transformed into marketable innovations. Thus, problems with
growth in Japan or Sweden may be linked to low level of entrepreneurial activity. On the other hand, our model suggests that, in
countries such as China, growth is generated by imitative entrepreneurs who, in the face of high costs of innovation, specialize in
increasing the supply of existing intermediate goods thereby mobilizing unused resources.
Noticeably, the availability of a large amount of resources such as in the case of Chinese labor, is perfectly consistent with our
analysis and, in fact, supports and strengthens our claim. The supply of inexpensive labor per se is neither sufficient nor necessary
to explain the Chinese miracle. What matters is the fact that this labor is mobilized to generate significant increases in economic
growth without the support of extensive R&D expenditure. Thus, China provides a perfect example of our argument: It is the
presence of imitative entrepreneurs that, by mobilizing this abundant resource, creates growth. This is further supported by the
fact that many countries with an abundant supply of low wage labor (such as many African economies) are stuck in low economic
growth traps. This is due to the fact that entrepreneurial costs in those countries are prohibitively high primarily because of the
lack of appropriate political institutions. In other words, in other developing countries where labor is also relatively inexpensive,
entrepreneurs do not start businesses because they do not see benefits from establishing them.
Of course, far from closing the field, the current paper provides many opportunities for future research. For example, additional
work is needed to identify more in details the determinants of a country take-off (beginning of the emergence process) and of
cross-country convergence and divergence (Ethier, 1982; Martin and Sunley, 1998). Our model allows us to touch upon the
question of how institutions, entrepreneurial behavior and technological discovery interact. In fact, if a crucial element of growth is
the presence of a sufficient number of entrepreneurs, it becomes important to understand what institutional arrangements are
more conducive to entrepreneurial behavior (Boettke and Coyne, 2007) and how countries become stuck in institutional traps
(Rivera-Batiz and Romer, 1991).
Only in the past few decades have academics and policymakers focused on the role that institutions play in the facilitating or
constraining efforts at generating sustainable growth. The underlying logic of the connection between institutions and
entrepreneurial behavior is the realization that institutions provide a framework that guides activity, removes uncertainty and
makes the actions of others predictable. Institutions influence the behavior of all individuals and the same individuals, with the
same motivations, will tend to act very differently under different sets of institutions (Minniti, 2005). This has major implications
for the way we understand economic change and progress or the lack thereof. As Baumol (1990) indicates, the institutional
environment of a society will determine the relative payoffs attached to various opportunities. As such, the institutional
environment will direct entrepreneurial activity toward those activities with the highest payoff. Unfortunately, these activities may
be productive, unproductive, or destructive. In this paper we have begun analyzing how productive entrepreneurial activities
promote growth and that they can be either research-based or imitative in nature. Many more questions remain to be answered.
We believe that our argument on the variety of entrepreneurial types and our formal framework provide useful tools to begin
the task.

Acknowledgement

The authors gratefully acknowledge financial supports from the A. Blank Center for Entrepreneurship, the W. Glavin Center
for Global Management, and the Center for Women Leadership at Babson College, and from an NSF ADVANCE Institutional
Transformation Grant, SBE-0245054, Academic Careers in Engineering and Science (ACES) at Case Western Reserve University. We
thank the editor and reviewers for valuable comments and suggestions. All errors are ours.

Appendix A. Impact of imitation on the growth rate

We first note that for two positive functions A and B, finding x⁎ for which A(x;η) − B(x;η) = 0 is equivalent to finding x⁎ for
which ln A(x;η) − ln B(x;η) = 0. Furthermore, if

@ ½lnAðx; ηÞ−lnBðx; ηÞŠ @ ½lnAðx; ηÞ−lnBðx; ηÞŠ
b0 and N0; ðA1Þ
@x @η
⁎
then @x N0. Now, in our context x = γ, η = m,
@η

h −α
h i i
½1−mŠ
½1−mŠ ½1−α Šα 1−α ½1 + ce Š1−α L− γ m +
1+α
δ β −ci
A= and B = ρ + θγ: ðA2Þ
μ

It follows that

−α

½1−α Šα 1−α ½1 + ce Š1−α 1 m + ½1−mŠ
1 +α
@ ½lnA−lnBŠ δ β θ
=− h i − ; ðA3Þ
@γ −α
½1−α Šα 1−α ½1 + ce Š1−α L− γ m + ½1−mŠ −c
1 +α
ρ + θγ
δ β i


which is negative, and

−α

½1−α Šα 1−α ½1 + ce Š1−α γ β −1
1+α
1
@ ½lnA−lnBŠ 1 δ
=− + h i : ðA4Þ
@m 1−m −α
½1−α Šα 1−α ½1 + ce Š1−α L− γ m + ½1−mŠ −ci
1+ α
δ β

Therefore, the right-hand side of Eq. (A4) can be positive or negative (recall that β b 1). We note, however, that a high cost of
innovation (ci high) is likely to make this right-hand side positive and thus ∂γ⁎/∂m N 0, i.e. the growth rate is likely to increase from
an increase in the imitation rate.

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