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 oftenconsists 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 existingresearch neglects the crucial role played by entrepreneurs in general and by imitative entrepreneurs in particular. We take aKirznerian view of entrepreneurs and deﬁne them as arbitragers who are willing to incur upfront costs in the hope of realizingproﬁt expectations. We then distinguish between two types of entrepreneurs: Research-based entrepreneurs who incur R&Dexpenditure 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 originaltechnological 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 ofeconomic growth. We show that, in equilibrium, higher economic growth is found when the number of research-based or imitativeentrepreneurs, or both, is increased. Thus we show that a relatively high quantity of imitative entrepreneurs is sufﬁcient for growthand 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) arereduced. Most importantly, we show that an increase in an economys imitation rate has a positive effect on economic growthwhen the cost of technological change is sufﬁciently high, and when labor employed in developing original technologicaldiscoveries (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 relativecomparative advantages. In our model, for example, the recent economic growth in China is explained, in part, by the presence of alarge number of imitative entrepreneurs in spite of negligible R&D expenditure. Our model can also account for situations in whichsigniﬁcant expenditure in R&D yields unsatisfactory results. In recent years, for example, countries such as Japan and Sweden haveexhibited limited growth in spite of signiﬁcant R&D investments. The lack of growth in Japan or Sweden is explained, in part, by thesmall 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 suggestingwhat some of the linkages between them may be and by providing a model that can accommodate observations about alleconomies, from the poorest to the most developed. We replace the common wisdom that R&D expenditure is a necessary conditionfor 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 maytake a variety of forms depending on the competitive characteristics of each country. To our knowledge, no such general modelexisted before.2. Introduction Most literature analyzing the mechanisms and causes of economic growth focuses on the role played by expenditure in R&Dand the resulting innovation and technological change (Goel and Ram, 1994; Griliches, 1979; Piekarz, 1983). Historically, mostcountries with sustained research investments have grown faster than others (Peretto, 1999). In recent years, however, countrieswith signiﬁcant R&D expenditure, such as Sweden and Japan have experienced little or no economic growth (Acs et al., 2005). Atthe 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 oneconomic growth. This suggests that imitation, by producing increased output consistent with existing technology developedelsewhere, is responsible for a signiﬁcant portion of the Chinese miracle. Also, Tan (2005) found that, comparing 2002 to 1990, thebusiness environment in China has become more conducive to entrepreneurial activities. This suggests that an increase inentrepreneurial 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 growthtrend in this country. They do suggest, however, that entrepreneurship may play a very important role in emerging economies andthat 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 contextof emerging economies. For this purpose, we develop a model of the relationship between entrepreneurship and economic growthapplicable 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 bybeing either research-based entrepreneurs (individuals who transform invention into marketable technological change and incur R&Dexpenditure) or imitative entrepreneurs (individuals who increase product availability and competition by replicating technologiesdeveloped elsewhere and, as a result, do not incur R&D expenditure). In other words, we argue that entrepreneurs are the lubricant atthe core of the growth process. Whether imitating an existing product or technology, or transforming a new invention into amarketable technological change, entrepreneurs are the economic actors who, by risking own resources in exchange for an expectedproﬁt, make growth possible (Schumpeter, 1934; Acs et al., 2004). By including two types of entrepreneurial activity (imitative andresearch-based), our model accounts for the accelerated growth experienced by some emerging economies in the absence of R&Dexpenses 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 (Goeland Ram, 1994; Gong and Keller, 2003). For example, in a relatively rich country, which is closer to its production possibilityfrontier, growth is generated by increases in productivity. To remain competitive, such a country will need relatively more originaltechnological discoveries. On the other hand, a country characterized by a large quantity of unused resources may increase itswealth simply by mobilizing them. This country may specialize in imitating technology developed elsewhere and, depending onthe level of development of the country and the cost of technological change, imitative entrepreneurs may be more important thanresearch-based entrepreneurs. Understanding the role of entrepreneurship for economic growth is important becausegovernments worldwide are sinking large amounts of capital in the pursuit of policies that, lacking such understanding, mayhave 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 ofempirical 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 earlystage entrepreneurs affects economic growth, but that this effect depends upon the level of per capita income. This suggests thatentrepreneurship plays a different role in countries in different stages of economic development. Dana (1997) has shown that thebusiness environment in Uruguay does not lend itself to the reproduction of entrepreneurial policies that have been successful inArgentina in spite of many similarities across the two countries. Finally, Giamartino (1991) has argued that when one considersmany developing economies around the world, it is not unreasonable to conclude that the status of internal and externalcomponents varies widely across countries and within regions of countries and that these differences may lead to differentexperiences in economic development and entrepreneurship. All these works support our argument that entrepreneurship comesin 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 technologicalchange remained exogenous to the economic context. Endogenous growth theory solved this issue by including mechanisms thatlink human capital to the creation of new technologies so that technological progress is no longer outside the model but, rather, isdetermined 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 bytechnological changes spills over to other individuals thereby increasing their ability to produce additional inventions. Thus, apositive 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 fewexceptions, entrepreneurs have been excluded from formal models of economic growth. In fact, for a long time, scholars workingwith analytical models neglected entrepreneurship and simply treated it as part of the residuals that cannot be attributed to anymeasurable productive input (Baumol, 1993). Only very recently, a few attempts have been made to better understand what thedistinctive characteristics of the entrepreneurs are (Lazear, 2005) and to incorporate the role of the entrepreneur in the growthprocess (Acs et al., 2004, 2005). Among studies that consider the role of the entrepreneur, Michelacci (2003) proposes a model of endogenous growth in whichtechnological 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 entrepreneurialskills. Along similar lines, Acs et al. (2004) argue that one of the breakthroughs contributed by endogenous growth theory is theidea that investments in human capital create economic growth through the spillover of knowledge. They also claim thatendogenous growth theory does not explain how or why spillovers occur and that the missing link is the mechanism convertingknowledge into ‘economically relevant knowledge. Within this context they suggest the existence of a ﬁlter between knowledgeand economic knowledge and identify entrepreneurship as the mechanism that reduces such knowledge ﬁlter. Thus, they focus onthe 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 agentswho bring research-based technological discoveries to the market. We complement this approach by taking a broader view ofentrepreneurship and developing a model of growth that, in addition to including a distinctive role for entrepreneurs, can beapplied even to countries in which little or no formal R&D exists and virtually no original technological discovery takes place. Theargument we develop follows Howitt (2000), according to whom, the further behind its production possibility frontier a country isinitially, the larger is the number of entrepreneurial opportunities. Technically, analytical models of economic growth spun off from Romers work are of two types: models with verticalinnovation (e.g. Aghion and Howitt, 1992), and models with expanded variety (e.g. Acemoglu and Zilibotti, 2001). In a verticalinnovation framework, the expected rate of growth of the economy depends exclusively on the economy wide amount oftechnological change, which in turn results from competition among research ﬁrms that generate innovations. Research ﬁrms aremotivated by the prospect of monopoly rents that can be captured when a successful innovation is patented. But those rents, inturn, are destroyed by the next innovation, which renders obsolete the existing good. The basic intuition behind these models is theSchumpeterian idea of creative destruction.
308 M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 In an expanded variety framework, on the other hand, an innovation consists of the technological knowledge required tomanufacture a new good that does not displace existing ones. Thus, innovation takes the form of an expansion in the variety of availableproducts. The underlying growth assumption is that the availability of more goods, either for ﬁnal consumption or as intermediateinputs, raises the material well-being of people. This class of models is the most recent in the endogenous growth literature. Amongothers 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-basedentrepreneurship, which increases productivity and product variety, and imitative entrepreneurship, which increases competition andproduct supply thereby reducing prices and promoting efﬁciency. We assume the existence of an intermediate good sector and a ﬁnalgood sector. The latter is competitive and produces a homogenous ﬁnal good. The intermediate good sector, instead, is non competitiveand includes a variety of non-homogeneous (and therefore non-substitutable) goods which enjoy economic proﬁts. Speciﬁcintermediate goods, however, can be imitated. When this happens, they lose their monopolistic position and generate zero economicproﬁts. Two types of entrepreneurs are considered in our model: Research-based entrepreneurs who are involved in commercializingoriginal technological discoveries and imitative entrepreneurs who mobilize resources to expand existing markets. Research-basedentrepreneurs exploit proﬁt opportunities by producing research-based intermediate goods and incur R&D expenditure to developsuch goods, while imitative entrepreneurs imitate existing products and exploit the proﬁt opportunities presented by the noncompetitive nature of the intermediate goods sector. Imitative entrepreneurs also contribute to economic growth by increasingcompetition and promoting efﬁciency. Their entry in the market increases product quantity thereby reducing prices and drives theeconomic proﬁts associated to the speciﬁc good to zero. Both types of entrepreneurs, research-based and imitative, face a variableentrepreneurial 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 arewilling to incur R&D expenditure because their goods will enjoy a monopoly position at least until they are copied.4. Growth model with imitation4.1. 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 totallabor size L. Agents earn income by supplying labor and derive utility from consumption. On the consumption side, agentspreferences are described by an isoelastic utility function which they maximize by selecting the optimal consumption plan givenan intertemporal budget constraint. In other words, individuals want to maintain living standards over their life time. Thus, theyallocate their resources so that the rate of growth in their consumption over time is directly proportional to the interest rate theyhave 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 rateat 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 goodand a non competitive sector for the production of intermediate goods. The production of the ﬁnal good depends on labor employedfor 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,twhere 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 ofintermediate goods available at t, and xj,t the quantity of intermediate good j at t. This speciﬁcation describes different intermediategoods (production inputs) as imperfect substitutes without implying that any of them is better than the others. All intermediategoods 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, entrepreneurswilling to incur R&D expenditure may introduce original technological changes thereby increasing productivity and intermediategoods variety. Imitative entrepreneurs produce imitative intermediate goods, research-based entrepreneurs produce research-basedintermediate goods. Both imitative and research-based entrepreneurs incur entrepreneurial costs, ce, consisting of set up and ﬁnancingcosts. In addition to entrepreneurial costs, each research-based entrepreneur is subject to R&D expenditure. That is, to a ﬁxed sunk costci required to develop a research-based intermediate good variety. Although they incur the additional R&D cost, research-basedentrepreneurs 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 ourargument. 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. Inline with the growth literature, the crucial distinction between imitative and research-based entrepreneurs is the amount of R&D expenditure per unit of outputwhich is uncorrelated to size.
M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 309Table 1Notation summary.Notation DescriptionLabor 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 tTime-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 tGrowth rates • At/At = δ[βLx,t + Li,t] ≡ δLe,t Law of motion for innovation at t • Ct/Ct = [rt − ρ]/θ An agents 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 thehomogeneous 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 : ð1ÞThe entrepreneurial labor force consists of all labor force for imitative intermediate goods plus a fraction, β, of labor forceemployed in R&D. In fact, not all attempt to develop original technologies come to fruition, and not all inventions are marketable orbrought to market. This is an important point of our model since it incorporates the differential effect that alternative types ofentrepreneurs have on markets and reﬂects how different entrepreneurial types are behind the growth dynamics of someemerging 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 onpeople. Thus, we assume that the development of research-based intermediate goods only requires labor and that potentialresearch-based entrepreneurs beneﬁt from observing the stock of intermediate goods already existing in the economy by obtainingideas for new goods.3 This means that the design of a unit measure of research-based intermediate good requires anentrepreneurial labor input equal to 1/(δAt), in other words, that the productivity of research-based entrepreneurial laborincreases 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 ofresearch-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 laboremployed 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 ; ð2Þwhere δ N 0 represents the productivity of the entrepreneurial sector and β allows us to account for the possibility of differentproductivities 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 intertemporalexternality.
310 M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314with the endogenous growth literature, the rate of innovation is thus a linear function of total employment in entrepreneurshipand its distribution between imitation and research. Without loss of generality, the coefﬁcient associated with imitativeentrepreneurs in the brackets equals 1 because the parameters δ and β allow the model to account for different productivities forimitative and research-based entrepreneurs. In fact, these parameters can be used to view the probability of success for imitators asbeing 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. Thisallows us to account for those research-based intermediate goods that become imitated and whose monopoly position is eroded byimitation. For simplicity, we assume that on any given time period t this erosion occurs at a constant rate, so that a fraction mt ofresearch-based intermediate goods becomes competitive. This imitation rate corresponds to the ratio of imitative entrepreneurs toentrepreneurial labor force, i.e. mt = Li,t / Le,t.4 Clearly, a strong patent protection can be considered as a reduction in the imitationrate mt (Judd, 1985).5 The separation of research-based and imitative intermediate goods is important because these two types ofintermediate 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 proﬁtπj,t is zero. For research-based intermediate goods, which enjoy a monopoly position (albeit temporarily), instead, the proﬁt of theentrepreneur producing variety j at t is πj;t = pj;t xj;t −xj;t −ce xj;t −ci : ð3Þpj,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 6xj,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 −1hence pj,t = [1 + ce]/α. Substituting back the latter into the demand function leads to xj;t = α 1−α ½1 + ce 1−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 −1Consequently, it makes sense for the amount of imitative intermediate good (which equals α 1−α ½1 + ce 1−α Ly;t from substituting, 1−α α −1instead, pj,t = [1 + ce] into the demand function pj,t = αLy,t xj,t ) to be larger than the amount xt of research-based intermediategood. Thus, the proﬁt from a research-based intermediate good is 1+α −α πj;t = πt = ½1−α α 1−α ½1 + ce 1−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 ofchange) for consumption, production and innovation in this economy and, therefore, to describe how the economy grows as aresult 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 andinstabilities produced in the economic system by changes in some key variables. In the balanced growth equilibrium the capitalintensity of the economy, that is its capital stock divided by its total output, is constant while other variables such as real GDP andoutput per worker are allowed to change. The balanced growth equilibrium is useful because it shows where the economy tends toconverge and stabilize. In other words, it provides a point of reference so that dynamic changes toward and away from this stablegrowth pattern can be compared. Without the balanced growth equilibrium to serve as a reference point, the causes andimplications 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 imitativelabor) must employ constant proportions of the labor force over time. In such equilibrium, the time dimension is removed andthe 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 haver = ρ + θ γ. Free entry in the market requires the present discounted value (PDV) of expected proﬁt from an innovation to equal its entrycost, where the latter is measured as that innovations 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 competitorswho 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. Inorder 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 theentrepreneurial labor force, presumably because more units of intermediate good j are then produced.
M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 311the research-based sector and technological change, the PDV of expected proﬁt is calculated as a weighted average of the positiveexpected proﬁt from a research-based intermediate good with (from Eq. (4)) πt = π in equilibrium and zero expected proﬁt froman 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 inequilibrium the imitation rate mt has its time dimension removed. In other words, we use the imitation rate m, which is calculatedas the ratio of imitative entrepreneurs to total entrepreneurial labor force, as a proxy for the proportion of imitative intermediategoods 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−mπ = μ or, equivalently from rsubstituting r = ρ + θ γ, Eq. (4), and rearranging both sides, h 1+ α −α i ½1−m ½1−α α 1−α ½1 + ce 1−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 equalsto the PDV of expected proﬁt from innovating divided by that innovations labor cost. Eq. (5) allows us to explore next how changesin a countrys 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 growthrate that can be used to analyze how a change in research-based or imitative labor (or both) affects growth. This expression for thegrowth rate can also be substituted in Eq. (5) to study further how changes in the labors environment affect the growth rate. Á ASpeciﬁcally, γ = Att = δ½βLx + Li (Eq. (2)) shows that the growth rate γ increases in both research-based and imitative labor sincethey 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, whereasMichelacci (2003) shows that the growth rate does not necessarily increase as the amount of resources devoted to researchaugments. Michelacci argues that there needs to be a balance between entrepreneurial and research activities. In fact, lowentrepreneurial rents from research are associated with low returns to R&D (and hence growth) because of a lack of resourcesallocated to entrepreneurs who can implement those innovations. In our formulation, a tradeoff similar to Michelaccis existsbetween 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−m 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−mL = Ly + Lx + Li and the above equalities, the ﬁnal good labor force becomes Ly = L− δ m + β . As a result, the growth rate canbe expressed as ½1−m 1+α −α μ ½1−α α 1−α ½1 + c 1−α L−c −ρ e i γ= −α h i: ð6Þ ½1−m 1+α ½1−m θ+ δμ ½1−α α 1−α ½1 + c 1−α e m+ βCeteris paribus, the growth rate decreases with an increase in the entrepreneurial cost (ce), the cost of innovation (ci), the laborcost per unit of innovation (μ), or the discount rate (ρ). But the growth rate increases with an increase in the productivity of theentrepreneurial sector (δ), the portion of research labor transformed into research-based intermediate products (β), the size oftotal 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 theequation represents the proﬁt rate and the right-hand side the effective cost of capital. All else equal, an increase in entrepreneurialcost, cost of research, or labor cost per unit of research-based intermediate goods decreases the proﬁt rate but does not affect the costof capital and, as a result, the growth rate should decrease. On the other hand, an increase in the discount rate does not affect theproﬁt rate but increases the cost of capital, which should also yield a diminished growth rate. Furthermore, all else equal, an increasein either productivity in the entrepreneurial sector, portion of R&D labor transformed into marketable inventions, or size of totallabor force increases the proﬁt rate but keeps unchanged the cost of capital and, as a result, the growth rate should increase. Last, anincrease 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 canbe 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, thisinequality holds when the intertemporal elasticity of substitution of consumption (1/θ) exceeds 1 and the growth rate exceeds the discount rate (ρ), and alsowhen the growth rate is sufﬁciently large. Finally, even when this sufﬁcient condition is violated, it is still possible to derive conditions under which imitationincreases 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 deﬁnedexclusively as research-based labor. Also, regardless of how abundant they are, all resources have always an opportunity cost and the trade off suggested byMichelacci is universal. Furthermore, in our model, Inequality (1) does not force the change in labor to be directed exclusively to imitative or research-based usessince 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 consistentwith our framework. As the entrepreneurial labor force shrinks or expands, new markets and new industries might be destroyed or created. Although businessand industry churning is an important phenomenon, this is not the core element of our arguments.
312 M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 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 fourparameters, and of Acs et al. (2004) for ρ and L. Nevertheless, our model illustrates the additional effects on growth of δ, β, ce andci. 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 betweengrowth and the portion of research-based labor actually transformed into marketable innovations (β). These two parameters allowus to separate the productivity of research-based entrepreneurs from that of imitative entrepreneurs. Acs et al. (2004) also derive apositive 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 toweigh (via δ and β) in the technological change equation (Eq. (2)) how research-based entrepreneurs fare compared to imitativeentrepreneurs. As discussed next, this weighting leads to new ﬁndings on how a change in the imitation rate (m) affects the growthrate. Finally, existing expanded variety models do not take into consideration cost differential faced by different types ofentrepreneurs, namely entrepreneurial and innovation costs, ce and ci, respectively. These costs play an important role indetermining the expected proﬁt of a research-based intermediate good. As a result, they are also important in characterizing theimpact 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 decreasethe growth rate. The intuition is that a higher imitation rate leads to a smaller percentage of research-based labor relative toentrepreneurial labor ([1-m] diminishes) but a larger expected proﬁt for any research-based intermediate good (π increases). Thislarger 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−m = L− δβ + mγ ½1−β), which in turn increases π (as per Eq. (4)). Consequently, the resulting PDV of expected δ β γ βproﬁt 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−m ), we verify that an increase in the imitation rate may have a positive effect on growth δ βwhen 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, whenresearch-based and imitative entrepreneurs have the same productivity (δ), a large number of imitative entrepreneurs relative tothe overall number of entrepreneurs no longer increases expected proﬁt for research-based intermediate goods. As a result, thetradeoff between a smaller percentage of imitative entrepreneurs relative to the total number of entrepreneurs and a largerexpected 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 asthe imitation rate increases. In other words, that the lower the patent protection, the lower is the growth rate. Our results differbecause, in our model, contributions to technological innovation from research-based entrepreneurs and, indirectly, from imitativeentrepreneurs 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 isparticularly useful for analyzing how entrepreneurial activity interacts with growth and under what conditions alternative types ofentrepreneurial behavior lead to growth. We also suggest that this type of models provide a useful and mathematically tractableframework 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 alertindividuals who are willing to incur costs in exchange for expected proﬁts. Second, our model is applicable to countries in any stageof 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; countriesmentioned 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 thepresence of a sufﬁcient amount of either type of entrepreneurship has a positive effect on the growth pattern of the economy. Infact, the relative distribution of entrepreneurs across these two categories does not inﬂuence the growth rate, what matters is thata country has a relatively high absolute number of at least one type of entrepreneurs. Furthermore, our model suggests that whenthe cost of producing original technological discoveries (innovation) is high, a country can experience economic growth byfocusing 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 imitativeentrepreneurs. In our model, the imitation rate would increase since research-based entrepreneurship would decrease relative to imitative entrepreneurship. As aresult, the growth rate would increase when the cost of innovation is sufﬁciently high (imitative entrepreneurship yields better country-level returns), butdecrease when research-based and imitative entrepreneurs have the same productivity.
M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314 313 Overall, the model highlights how entrepreneurship matters for growth and that, in its absence, the presence of a large amountof labor employed in R&D does not necessarily guarantee that the beneﬁts of this expenditure will arrive on the market, since thatdepends on β, that is on the percentage of research-based labor transformed into marketable innovations. Thus, problems withgrowth in Japan or Sweden may be linked to low level of entrepreneurial activity. On the other hand, our model suggests that, incountries such as China, growth is generated by imitative entrepreneurs who, in the face of high costs of innovation, specialize inincreasing 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 ouranalysis and, in fact, supports and strengthens our claim. The supply of inexpensive labor per se is neither sufﬁcient nor necessaryto explain the Chinese miracle. What matters is the fact that this labor is mobilized to generate signiﬁcant increases in economicgrowth without the support of extensive R&D expenditure. Thus, China provides a perfect example of our argument: It is thepresence of imitative entrepreneurs that, by mobilizing this abundant resource, creates growth. This is further supported by thefact that many countries with an abundant supply of low wage labor (such as many African economies) are stuck in low economicgrowth traps. This is due to the fact that entrepreneurial costs in those countries are prohibitively high primarily because of thelack 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, additionalwork is needed to identify more in details the determinants of a country take-off (beginning of the emergence process) and ofcross-country convergence and divergence (Ethier, 1982; Martin and Sunley, 1998). Our model allows us to touch upon thequestion of how institutions, entrepreneurial behavior and technological discovery interact. In fact, if a crucial element of growth isthe presence of a sufﬁcient number of entrepreneurs, it becomes important to understand what institutional arrangements aremore 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 orconstraining efforts at generating sustainable growth. The underlying logic of the connection between institutions andentrepreneurial behavior is the realization that institutions provide a framework that guides activity, removes uncertainty andmakes the actions of others predictable. Institutions inﬂuence the behavior of all individuals and the same individuals, with thesame motivations, will tend to act very differently under different sets of institutions (Minniti, 2005). This has major implicationsfor the way we understand economic change and progress or the lack thereof. As Baumol (1990) indicates, the institutionalenvironment of a society will determine the relative payoffs attached to various opportunities. As such, the institutionalenvironment will direct entrepreneurial activity toward those activities with the highest payoff. Unfortunately, these activities maybe productive, unproductive, or destructive. In this paper we have begun analyzing how productive entrepreneurial activitiespromote 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 beginthe task.Acknowledgement The authors gratefully acknowledge ﬁnancial supports from the A. Blank Center for Entrepreneurship, the W. Glavin Centerfor Global Management, and the Center for Women Leadership at Babson College, and from an NSF ADVANCE InstitutionalTransformation Grant, SBE-0245054, Academic Careers in Engineering and Science (ACES) at Case Western Reserve University. Wethank 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⁎ forwhich ln A(x;η) − ln B(x;η) = 0. Furthermore, if @ ½lnAðx; ηÞ−lnBðx; ηÞ @ ½lnAðx; ηÞ−lnBðx; ηÞ b0 and N0; ðA1Þ @x @η ⁎then @x N0. Now, in our context x = γ, η = m, @η h −α h i i ½1−m ½1−m ½1−α α 1−α ½1 + ce 1−α L− γ m + 1+α δ β −ci A= and B = ρ + θγ: ðA2Þ μ It follows that −α ½1−α α 1−α ½1 + ce 1−α 1 m + ½1−m 1 +α @ ½lnA−lnB δ β θ =− h i − ; ðA3Þ @γ −α ½1−α α 1−α ½1 + ce 1−α L− γ m + ½1−m −c 1 +α ρ + θγ δ β i
314 M. Minniti, M. Lévesque / Journal of Business Venturing 25 (2010) 305–314which is negative, and −α ½1−α α 1−α ½1 + ce 1−α γ β −1 1+α 1 @ ½lnA−lnB 1 δ =− + h i : ðA4Þ @m 1−m −α ½1−α α 1−α ½1 + ce 1−α L− γ m + ½1−m −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 ofinnovation (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 froman increase in the imitation rate.ReferencesAcemoglu, D., Zilibotti, F., 2001. Productivity differences. Quarterly Journal of Economics 116, 563–606.Acs, Z.J., Audretsch, D.B., Braunerhjelm, P., Carlsson, B., 2004. The missing link: The knowledge ﬁlter and entrepreneurship in endogenous growth. Center for Economic Policy Research, London. CEPR Discussion paper No. 4783.Acs, Z.J., Audretsch, D.B., Braunerhjelm, P., Carlsson, B. 2005. The knowledge spillover theory of entrepreneurship. 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