The Missing Link: The Knowledge Filter and Endogenous Growth

Paper to be presented at the DRUID Summer Conference 2003 on
                        CREATING, SHARING AND TRANSFERRING KNOWLEDGE.
                        The role of Geography, Institutions and Organizations.

                                   Copenhagen June 12-14, 2003

                         The Missing Link:
             The Knowledge Filter and Endogenous Growth
                                        Zoltan Acs
                      Merick School of Business, University of Baltimore

                                       David Audretsch
                                       Indiana University

                                   Pontus Braunerhjelm
                Linköping University and Centre for Business and Policy Studies

                                   Bo Carlsson
          Weatherhead School of Management, Case Western Reserve University

                                           Abstract
The intellectual breakthrough contribution of endogenous growth theory is the recognition that
investments in knowledge and human capital generate growth endogenously. This
represented a significant intellectual advance in understanding the growth process, not only
by identifying the important role that knowledge and human capital play, but also by the
unique way in which these factors impact growth. However, the empirical evidence supporting
the hypotheses derived from these models is ambiguous at best. This paper contributes to
our understanding of the growth process with new insights as regards three aspects of
knowledge and growth which, to our knowledge, have not been considered previously. First,
we explicitly introduce a link between knowledge capital and growth – the missing link in the
endogenous growth model. Second, we demonstrate that such a link influences the
exploitation of knowledge. For instance, whether regions or countries with a relatively small
stock of knowledge experience higher growth than countries more abundantly endowed with
knowledge depends on how well the transmission link works. Third, we show how the
suggested modifications of the endogenous growth model imply a set of policy prescriptions
and instruments that differs from those previously discussed in the growth theory literature.

JEL: O10, L10

Preliminary!

    The Missing Link: The Knowledge Filter and Endogenous Growth

             Zoltan Acs, David Audretsch, Pontus Braunerhjelm and Bo Carlsson1

                                                May 2003

Abstract

The intellectual breakthrough contribution of endogenous growth theory is the recognition

that investments in knowledge and human capital generate growth endogenously. This

represented a significant intellectual advance in understanding the growth process, not only by

identifying the important role that knowledge and human capital play, but also by the unique

way in which these factors impact growth. However, the empirical evidence supporting the

hypotheses derived from these models is ambiguous at best. This paper contributes to our

understanding of the growth process with new insights as regards three aspects of knowledge

and growth which, to our knowledge, have not been considered previously. First, we

explicitly introduce a link between knowledge capital and growth – the missing link in the

endogenous growth model. Second, we demonstrate that such a link influences the

exploitation of knowledge. For instance, whether regions or countries with a relatively small

stock of knowledge experience higher growth than countries more abundantly endowed with

knowledge depends on how well the transmission link works. Third, we show how the

suggested modifications of the endogenous growth model imply a set of policy prescriptions

and instruments that differs from those previously discussed in the growth theory literature.

JEL: O10, L10

1
 Zoltan Acs, Merrick School of Business, University of Baltimore, Baltimore, David Audretsch, Indiana
University. Pontus Braunerhjelm, Linköping University and Centre for Business and Policy Studies, Box 5629,

                                                                                                              1

Keywords; Endogenous growth, transmission and entrepreneurship.

11485 Stockholm (pontusb@sns.se), Bo Carlsson, Case Western Reserve University, Weatherhead School of
Management, Department of Economics, Cleveland (Bo.Carlsson@cwru.edu)

                                                                                                        2

1. Introduction

Endogenous growth theory has provided two fundamental contributions that constitute

intellectual breakthroughs. The first is that knowledge and human capital are significant

factors generating growth. The second is that they, in contrast to the more traditional factors

of physical capital and labor, impact growth endogenously. However, empirical evidence

supporting the hypotheses derived from these models is ambiguous at best: For example, why

have countries such as Japan and Sweden with high rates of R&D spending grown so slowly

during the last decades? And why have other countries less endowed with knowledge – and

often small, such as Denmark and Ireland – experienced persistent and high growth rates?2

              The purpose of this paper is to extend the basic endogenous growth model

(Romer 1986, Lucas 1988). Both Romer (1986) and Lucas (1986) assume a spillover

mechanism that is built into their models. That is, the process by which knowledge spills over

from the firm producing it for use by a third-party firm is automatic. In this paper, we go

back to Arrow’s (1962) recognition that knowledge is not at all the same thing as

economically relevant knowledge, which suggests that the spillover may not occur

automatically. Rather, this paper focuses on the spillover mechanisms generally, and

entrepreneurship in particular as a mechanism facilitating knowledge spillovers. More

precisely, we will contribute with new insight which, to our knowledge, has not been

previously considered. First, in contrast to the endogenous growth models, we will explicitly

introduce a transmission mechanism between knowledge capital and growth. Second, we will

demonstrate how such a link influences the exploitation of knowledge. For instance, whether

regions or countries with a relatively small stock of knowledge experience higher growth than

countries more abundantly endowed with knowledge depends on how well the transmission

link functions. Third, we will show how the suggested modifications of the endogenous

                                                                                                  3

growth model imply a completely different set of policy prescriptions. We will do that by

integrating growth theory with recent theoretical advances as regards industrial dynamics and

the spatial organization of economic activities.

                 Romer and others (Lucas 1988, Rebel 1991, and others) picked up the thread

suggested in the spillover literature a couple of decades earlier. They aimed at

operationalizing and explicitly introducing knowledge into models of growth. Knowledge

capital was defined as a composite of R&D and human capital, not embodied in processes or

products. Introducing accumulation of capitalized knowledge assets was then shown to be

compatible with increasing growth rates and a well-defined general equilibrium. The major

contribution – because of the properties of non-excludability and non-rivalry attached to

knowledge – of these models was to analytically demonstrate that since the marginal

productivity of knowledge capital does not diminish as it becomes available to more users,

growth may go on indefinitely.

                 Note that emphasis in the original endogeneous growth models is on why

knowledge capital impacts growth, not how. Thus, less attention was paid to the diffusion or

transmission of knowledge and the mechanism that makes knowledge accessible to society.

Still, that is of course the critical issue in modeling knowledge-based growth. The only

attempts to model the diffusion of knowledge relate to the knowledge flows between countries

at different levels of development. In that case, countries on the technology frontier are

assumed to discover new products that follower countries imitate. Various factors are then

introduced that influence the capacity of follower countries to imitate.3 However, when it

comes to the diffusion of knowledge within countries, the endogenous growth model assumes

that there is no barrier to commercializing knowledge, i.e., spillovers are automatic and there

2
  Romer (1990) and Grossman and Helpman (1991) argues that there are scale economies in producing
knowledge, i.e. per unit labor cost of an invention will fall in larger economies. This is related to larger flows of
ideas and lower costs in relation to the size of the economy.
3
  Se Barro and Sala-i-Martin (1997) for a brief survey of these models.

                                                                                                                    4

is no distinction between knowledge and commercialized knowledge. We intend to highlight

how the transmission mechanisms work, and how knowledge can be more or less smoothly

filtered and substantiated into commercialized activities.

              The rest of the paper is organized in the following way. In the next section, a

brief survey of the dominant explanations to growth will be presented. Emphasis is on the

structure of the endogenous growth model. The following section, 3, scrutinizes the

assumptions underpinning the endogenous growth model in order to identify why - and how -

the model can be extended to incorporate spillover mechanisms that vary in their

effectiveness. Section 4 compiles existing empirical evidence linking various measures of

entrepreneurship to growth. In Section 5, the model is modified to incorporate a filter in the

spillover mechanism that determines the link between entrepreneurship and growth. Section 6

shows how these changes in the model yield completely different policy implications. Finally,

in Section 7 a summary and conclusion are provided.

2. Why do countries grow?

Contemporary theories of economic growth can be traced all the way back to mechanisms

suggested by the classical economists such as Smith, Ricardo and Malthus. But the more

coherent building blocks of modern growth theory originated in the advances made in the

beginning of the 20th century. Important cornerstones were provided by Ramsey (1928), who

explicitly introduced an intertemporal optimization economic structure, which was then

further elaborated by Fischer (1930). A more formal growth model, anchored in the

Keynesian tradition, was presented by Harrod (1939) and Domar (1946). Exogenous savings

and investment rates were paired with low substitutability of factors of production and a fixed

supply of labor. Still, it was not until the neoclassicals entered the scene, that research on

growth gained momentum.

                                                                                                 5

Neoclassical explanations of growth

A major leap forward in understanding growth stems from the work by Solow (1956) and

Swan (1956). Based on an aggregate production function exhibiting the traditional properties

(constant returns to scale, substitutability among production factors, etc.), they proposed a

general equilibrium solution to growth. In steady state, capital would grow at a rate

determined by the increase in the labor force and consumers’ rate of time preferences.

Consumers are willing to postpone consumption – i.e. save – for one period, provided that the

return on those savings is at least as large as the increases in prices (i.e., the interest rate)

during the same period. Thus, given the increase in labor supply, savings are channeled into

investments such that marginal productivity of capital complies with those conditions. As a

consequence, the rate of growth would cease when the marginal productivity of net

investments reached a certain level, i.e., steady state was attained. The model was closed, and

a well-defined and decentralized equilibrium was attained.4

                  The problem was that this did not conform to the observed increases of growth

within the last centuries. Growth accounting exercises revealed that something else was also

taking place. As shown by Solow (1957), after accounting for the contributions provided by

additional labor and capital there remained a sizeable part of growth to be explained. Solow

attributed that unexplained effect to technical progress and knowledge-enhancing processes in

general, and the effect became known as Solow’s “technical residual”. However, the

mechanisms that resulted in technical progress and knowledge accumulation were still

unspecified.

                  Hence, despite the progress made in modeling and understanding the growth

process, the model suffered from the fact that the main part of growth was determined in an

4
    See Barro and Sala-i-Martin (1997) or Gylfasson (1999) for a survey of the literature.

                                                                                                    6

exogenous manner not captured by the model. The most promising attempts in the

neoclassical tradition to account for that shortcoming were the models of Arrow (1962) and

Sheshinski (1967), suggesting that learning-by-doing was an important by-product of

production that diffused into the economy, but their models were not fully integrated into a

growth context.

               In the aftermath of the contributions provided by Solow, Arrow, and others,

research on growth by and large vanished from the academic agenda, mainly because of the

ambiguous empirical support that existing models attained.5 There was a general awareness

that the missing element was knowledge, an insight which was far from new. Scholars as far

back as Marshall (1879) had noted that “knowledge is the most prominent engine of growth,”

a view also emphasized by Hayek (1944) (1945?), Knight (1921, 1944) and McKenzie

(1959). Still, the technical complexities in incorporating knowledge into growth models

tended to discourage research in this field for a considerable time. Therefore Romer’s (1986)

proposed method to incorporate knowledge into a model of economic growth revitalized –

and initiated a new wave of – growth research.

Endogenous growth – the basic structure

The seminal contribution by Romer (1986, 1990), Lucas (1988), and their followers, was to

endogenize the knowledge-producing activity within an economy, thereby disconnecting

growth from investment in physical capital or increases in the supply of labor.

               The basic structure of the model was as follows: At the micro-level, knowledge,

just like any other good, is produced by profit-maximizing firms, i.e., knowledge production

is endogenized. At the macro-level, the production of knowledge carries obvious implications

for growth. It is channeled into growth through two main mechanisms: First, firms run their

5
 See also Kaldor (1961) and Denison (1967). See Rostow (1990) for a survey of the contributors to neoclassical
growth theory.

                                                                                                             7

firms more efficiently, and, second, knowledge spills over across firms acting as a shift factor

in their production functions. Both effects tend to increase firm-level productivity.

                The endogenous growth models do provide a micro-economic foundation for

explaining the mechanisms that promote growth at the macro-level. Still, emphasis in these

models is on the macro effects, i.e., growth at the national/global level. Our concern is that the

too simple microeconomic setting in these models misguides policy-makers and renders

empirical testing much more hazardous. We believe that a deeper understanding of the micro-

processes is decisive in order to understand how growth is manifested at the macro-level. We

will therefore, in some detail, describe the underlying assumptions and mechanisms in the

basic endogenous growth model before proposing several extensions of the model.

3. The basic assumptions of the endogenous growth model

The knowledge-based growth models have three cornerstones: spatially constrained

externalities, increasing returns in the production of goods, and deceasing returns in the

production of knowledge. These drive the results of the model. They rely on assumptions

related to technology, firm characteristics, the spatial dimension, and knowledge. We will

now in some detail examine these assumptions in order to motivate the extensions of the

model we consider necessary in order to better understand growth in a knowledge economy.

Assumptions on technology

The assumed technology implies that – despite convexity in goods production – an optimum

growth rate exists because production of knowledge is characterized by (strongly) diminishing

returns to scale. Hence, doubling the inputs to research will not double the amount of

knowledge produced.6 The result is an upper bound of knowledge that can be used in the

6
 On the firm level, empirical evidence has been presented that a concave relation prevails between firm
performance and knowledge investment (Braunerhjelm 1999).

                                                                                                          8

production of goods. On the other hand, the production of goods is characterized by

increasing returns to scale associated with increasing marginal productivity of knowledge,

holding all other inputs constant. Still, even though growth rates may increase monotonically

over time, the increase in the rate of growth is constrained by the decreasing returns to scale

in knowledge production. The outcome is a well-specified competitive equilibrium model.

                More precisely, in its simplest dynamic form, i.e., a two-period model, the

research technology of a representative firm i in period 1 to produce knowledge is foregone

consumption:7

                                 c1i = e1 − k1i              (1)

Period one consumption (c1i) is consequently the exogenously given endowment of

consumption goods (e1i) minus the part of the endowments that is used to produce firm-

specific ki in the first period. The technology that transforms consumption goods into firm-

specific knowledge k is simply assumed to exist and is not explicitly modeled in a behavioral

sense.

                In the second period, the knowledge (ki) produced in period 1 is used as input in

production of consumption goods. The production function F is assumed to be twice

differentiable and, in addition to ki, employs a fixed vector x representing all other factors of

production used by the firm. Finally, firms benefit from spillovers originating in all other

                                                   n
firms’ (n) knowledge investment, ( K = ∑ k i ) , since each individual firm cannot appropriate
                                                  i =1

all the knowledge they produce in period 1. The production function is shown in equation 2,

7
  In the two-period model with finite consumers, the concavity assumption is not required on knowledge
production (constant returns to scale technology would also work), but in the infinite time horizon model it is.

                                                                                                                   9

F ( k i , x, K ) ,                                          (2)

                F1 ≥ 0, F12 ≤ 0, F2 ≥ 0, F22 ≤ 0, F3 ≥ 0, F32 ≥ 0

It has the following properties: First, the production function is concave and homogeneous of

degree one as a function of ki and x, holding K constant, but convex in all arguments.8

Second, the production function is assumed to exhibit globally increasing marginal

productivity of knowledge from a social point of view. The implication is that production is

convex in ki for a social planner who is assumed to have the ability to set ki at the optimum

level. Or, to put it differently, the aggregate production function for the whole economy is

characterized by increasing returns to ki, i.e., it is a strengthening of the increasing return

assumption on knowledge (K).

                Assuming utility maximizing agents, the above assumptions on production

technology ensure that this dynamic model – in contrast to other models where consumption

would grow towards infinity – results in a tractable, stable and competitive equilibrium with

increasing returns to scale.

Assumptions on firms

For modeling reasons there are generally good reasons to simplify when it comes to firm

characteristics. A common assumption in general equilibrium models is that each individual –

or unit of labor – can be considered identical to a firm. Basically, in the endogenous growth

models the scale and number of firms are indeterminate.9 However, firms are also assumed to

8
  Any concave function can be kept homogeneous by adding an additional factor to x that exempts production
revenue. That, as Romer (1986) notes, could be entrepreneurial reward.
9
  In principle, from the social planners view, the number of firms could range from a large number of atomistic
firms to one single firm. Subsequent models have elaborated on somewhat more sophisticated market and firm
structures, even though symmetry conditions remains (Fujita and Thisse 2002).

                                                                                                              10

be price-takers, which implicitly means that there are many firms operating in competitive

markets, and earning zero profits.

                Even though the numbers of firms, entry rates and the scale of operation cannot

be determined in the model, the following assumptions are typically imposed -- the number of

firms is given (i.e., equals the number of individuals), no entry occurs (labor being constant),

and all firms operate at the same level.10 In principle, these models typically assume what

amounts to a “representative” firm, and which is supposed to capture microeconomic

behavior.

Assumptions on knowledge

As shown above, all firms are assumed to employ firms-specific knowledge (ki) in the

production of goods. The knowledge produced is there forever; it is a non-depreciating stock,

and hence zero research by a firm means that ki is constant. The first question to address

concerns the firm-specificity issue. If firms are symmetric – the same size and producing the

same goods – why then is firm-specific knowledge necessary? The straightforward

interpretation is that even though diversity in knowledge prevails, the same consumer good is

produced. In other words, there may be many ways to produce the same good. Still, that does

not seem to contribute much to the model.

                Rather the assumption of firm-specificity is necessary to justify that only part of

the produced knowledge spills over and is utilized by other firms. The reason is that if

knowledge at the firm level was identical, then spillovers would be direct and involve 100

percent of the produced knowledge. Hence, there would be no incentive to invest in

knowledge and subsequently no, or at least less, growth. Thus, this assumption is necessary

10
  One obvious advantage is that these simplifications mean that subscripts/indexes can be avoided and that the
inclusion of a representative, symmetric firm allows technical generalizations.

                                                                                                             11

for the dynamics of the model, but it does not seem to be consistent with the microeconomic

set-up.

             The aggregated stock of knowledge that generates spillovers to other firms is

defined as a disembodied public good – it is available in books, etc. –, while the other part

remains firm-specific. It affects all firms in the same way, i.e., by shifting production upwards

even though all other production factors are held constant. The classification of knowledge is

easy to accept -- a perfectly accessible part consisting of already established knowledge

elements obtainable via scientific publications, patent applications, etc. on the one hand, and a

novel, tacit element on the other hand, contained within firms and individuals. The part that

does not correspond with empirical observations refers to the spatial dimension.

Assumption on the spatial dimension

A principal assumption in the theory of endogenous growth is that the total stock of

knowledge (K) is evenly distributed across space. However, this assumption is not supported

in the literature on geographic knowledge spillovers. New technological knowledge (the most

valuable type of knowledge) usually contains a strong element of tacitness that makes

accessibility bounded by geographic proximity and by the nature and extent of the interaction

among agents in agglomerated areas. A host of recent empirical studies have confirmed that

knowledge spillovers are geographically bounded (Jaffe 1989, Jaffe, Trajtenberg and

Henderson 1993, Audretsch and Feldman 1996, Anselin, Varga and Acs 1997, Keller 2002).

             To conclude, in the endogenous growth models the opportunity to exploit

knowledge spillovers accruing from aggregate knowledge investment is not adequately

explained. In essence, these models assume that knowledge – defined as codified R&D –

automatically transforms into commercial activities, or what Arrow (1962) classifies as

economic knowledge. However the imposition of this assumption lacks intuitive as well as

                                                                                                12

empirical backing. It is one thing for technological opportunities to exist but an entirely

different matter for them to be discovered, exploited and commercialized.

The missing link

So far we have not mentioned the growth mechanism suggested by the Austrian school, that

is, innovative entry, reorganization and rationalization of existing firms, and exits

(Schumpeter 1911, Hayek 1945). However, these ingredients have to be integrated into the

endogenous growth process in order to grasp the interdependency between knowledge,

opportunity and commercialization.11

               New knowledge –in the form of products, processes or organizations – leads to

opportunities that agents exploit commercially. Such opportunities are hence a function of the

distribution of knowledge within and between societies. But more important is that

opportunities rarely present themselves in neat packages; rather they have to be discovered

and packaged. Precisely for that reason the nexus of opportunity and enterprising individuals

is crucial in order to understand economic growth.

               It implies that knowledge (K) by itself may be only a necessary condition for the

exercise of successful enterprise in a growth model. The ability to transform new knowledge

into what Arrow identified as economic knowledge that becomes a commercial opportunity

requires a set of skills, aptitudes, insights and circumstances that is neither uniformly nor

widely distributed in the population. Moreover, empirical findings seem to suggest that entry

and entrepreneurship are important links between knowledge creation and the

commercialization of such knowledge, particularly at the early stage when knowledge is still

fluid.

11
  Aghion and Howitt (1991) make an attempt but fail to disclose the diffusion mechanism. An interesting
approach is suggested by Eliasson (1991), introducing the experimentally organized economy.

                                                                                                          13

4. An Empirical Regularity

Above we attempted to identify the weaknesses in the endogenous growth models through a

careful investigation of assumptions underlying these models. We believe that the fragile

empirical support that endogenous growth models attain is associated with a far too

mechanistic view on the transmission of knowledge. Simple correlation between R&D-

expenditure and GDP-growth reveals no systematic relationship (Figure 1).

              In this section we will point to the missing link in current models as evidenced

in numerous empirical studies. A series of recent studies have ascertained a statistical

regularity between various measures of entrepreneurial activity, most typically startup rates,

and economic growth. Other measures sometimes include the share of SMEs, and self-

employment and business ownership rates. The most common measure of growth relates to

employment changes over time, but other measures, have also been used. Regardless of the

measure of entrepreneurship or the geographic unit of observation (city, region, state, or

country), these studies have invariably identified the existence of a positive relationship

between entrepreneurship and subsequent economic growth.

              In a recent study, Acs (2002) examines the relationship between startup rates

and economic growth for 348 U.S. regions for the 1990s (Figures 2–5). He finds compelling

evidence that startup rates are positively related to regional growth rates. The statistical

relationship between entrepreneurship and growth is found to be stronger than for other

regional characteristics, such as human capital, income levels, and population growth. These

results have been confirmed in other studies (Acs 2003, Reynolds 1999).

              Other studies have not found such a clear-cut relationship between

entrepreneurship and growth, suggesting that no general pattern exists across developed

                                                                                               14

countries.12 Rather, they have provided evidence for the existence of distinct and different

national systems, suggesting that there is more than one way to achieve growth, at least across

different countries. Convergence in growth rates seems to be attainable by maintaining

differences in underlying institutions and structures.

                However, the results obtained for earlier periods seem to have changed in later

decades. For instance, Audretsch and Fritsch (2002) find that different results emerge for the

1990s, as compared to the 1980s, for Germany. Based on the compelling empirical evidence

that the source of growth in Germany has shifted away from the established incumbent firms

during the 1980s to entrepreneurial firms in the 1990s, it would appear that a process of

convergence is taking place between Germany and the United States. Despite remaining

institutional differences, the relationship between entrepreneurship and growth is apparently

converging in both countries. These results are consistent with the findings of Audretsch and

Keilbach (2003), who estimate a production function model for German regions based on data

from the 1990s.

                The positive relationship between entrepreneurship and growth at the regional

level is not just limited to the United States and Germany in the 1990s. For example, Fölster

(2000) examines not just the employment impact within new and small firms but on the

overall link between increases in self-employment and total employment in Sweden during

1976–1995. By using a Layard-Nickell framework, he provides a link between micro

behavior and macroeconomic performance and shows that increases in self-employment

shares have had a positive impact on regional employment growth in Sweden.13 Hart and

Hanvey (1995) link measures of new and small firms to employment generation in the late

12
   For instance, Audretsch and Fritsch (1996) found that in both the manufacturing and the service sectors a high
start-up rate in a region was found to lead to a lower and not a higher rate of growth in Germany in the 1980s.
13
   On the firm level, Braunerhjelm (1996) has shown how growth and entry is related to knowledge investment
in Swedish firms.

                                                                                                              15

1980s for three regions in the United Kingdom. They find that employment creation came

largely from SMEs.

              Callejon and Segarra (1999) use a data set of Spanish manufacturing industries

between 1980 and 1992 to link new-firm birth rates and death rates, which taken together

constitute a measure of turbulence, to total factor productivity growth in industries and

regions. They adopt a model based on a vintage capital framework in which new entrants

embody the edge technologies available and exiting businesses represent marginal obsolete

plants. Using a Hall type of production function, which controls for imperfect competition and

the extent of scale economies, they find that both new-firm startup rates and death rates

contribute positively to the growth of total factor productivity in regions.

              But also at the national level a positive statistical relationship between

entrepreneurship and economic growth has been identified. For example, Thurik (1999)

provided empirical evidence from a 1984–1994 cross-sectional study of the 23 countries that

are part of the Organization for Economic Co-operation and Development (OECD), that

increased entrepreneurship, as measured by business ownership rates, was associated with

higher rates of employment growth at the country level. Similarly, Audretsch et al. (2002) and

Carree and Thurik (1999) find that OECD countries exhibiting higher increases in

entrepreneurship also have experienced greater rates of growth and lower levels of

unemployment.

              In a study for the OECD, Audretsch and Thurik (2002) undertake two separate

empirical analyses to identify the impact of changes of entrepreneurship on growth. Each one

uses a different measure of entrepreneurship, sample of countries and specification. This

provides some sense of robustness across various measures of entrepreneurship, data sets,

time periods and specifications. The first analysis measures entrepreneurship in terms of the

relative share of economic activity accounted for by small firms. It links changes in

                                                                                                16

entrepreneurship to growth rates for a panel of 18 OECD countries spanning five years to test

the hypothesis that higher rates of entrepreneurship lead to greater subsequent growth rates.14

               The second analysis uses a measure of self-employment as an index of

entrepreneurship and links changes in entrepreneurship to unemployment at the country level

between 1974 and 1998. The different samples including OECD countries over different time

periods reach consistent results; increases in entrepreneurial activity tend to result in higher

subsequent growth rates and a reduction of unemployment (Figure 6).

5. The knowledge filter, entrepreneurs and endogenous growth

We concluded in section 2 that the basic shortcoming of the endogenous growth model is that

it fails to recognize that only some of the aggregate stock of knowledge production (K) –

normally R&D – is economically useful and that even economically relevant knowledge (Kc)

is not necessarily exploited (or exploited successfully) if the transmission links are missing.

We also noted that some part of the general stock of knowledge is not in the public domain

and may not spill over easily from one carrier (actor) to another. Most knowledge, regardless

of whether it is in the public or private domain, requires a certain absorptive capacity on the

part of the recipients in order for successful transmission to occur. This suggests that there is a

filter between the stock of knowledge (K) and economically useful knowledge (Kc). Not only

does K vary among countries and regions; the transmission capacity of the filter also varies.

The empirical evidence presented in the previous section suggests that the degree of

entrepreneurial activity is shaped by the thickness of this filter; a higher degree of

entrepreneurial activity reflects a greater share of the ideas flowing through the filter and

being transformed from Arrow’s knowledge into his economic knowledge.

14
  The Global Entrepreneurship Monitor (GEM) Study (Reynolds et al., 2000) also established an empirical link
between the degree of entrepreneurial activity and economic growth, as measured by employment, at the country
level.

                                                                                                          17

Consequently, despite the gains in terms of transparency and technical ease

obtained by imposing strong assumptions in the endogenous growth models, these advantages

have to be measured in relation to the drawbacks of deviations from real world behavior. In

our view, the result has been that the endogenous model fails to incorporate one of the most

crucial elements in the growth process; transmission of knowledge through entrepreneurship,

entry and exit, and the spatial dimension of growth. The presence of these activities is

especially important at the early stages of the life cycle while technology is still fluid.

   Thus, a closer connection between the endogenous growth models with models of

entrepreneurship seems necessary. In particular, as noted by Thornton (2003), knowledge is

developed in certain regions where individual agents that choose to act upon acquiring new

knowledge will most likely become entrepreneurs:

   “entrepreneurship is increasingly the domain of organizations and regions, not individuals.

   These organizations and regions are environments rich in technological opportunity and

   resources and they have been increasing in numbers and in varieties—be they technology

   licensing offices, bands of angels, venture capital firms, corporate venturing programs, or

   incubator firms and regions. These environments explicitly influence individuals by

   teaching them how to discover and exploit technological opportunities. These

   environments also specifically influence new ventures, providing resources to increase

   their rate of founding and survival. However, how these environments spawn new

   entrepreneurs and create new businesses remains relatively understudied.” (Thornton 2003,

   p. 401).

Thus, the region and environment in which agents operate are crucial for the outcome. The

fact that knowledge-producing inputs are not evenly distributed across space implies that

                                                                                               18

regions (and countries) may not grow at the same rate, not (only) because they have different

levels of investment in knowledge but (also) because they exploit knowledge at different

rates. Even if the stock of knowledge were freely available, including the tacit and non-tacit

parts, the ability to transform that knowledge into economic knowledge, or commercialized

products, would not be. Hayek (1945) pointed out that the central feature of a market

economy is the partitioning of knowledge or information about the economy.

              The key is that this knowledge is diffused in the economy and is not a given or a

free good at everyone’s disposal. Thus, only a few know about a particular scarcity, or a new

invention, or a particular resource lying fallow or not being put to best use. This knowledge is

idiosyncratic because it is acquired through each individual’s own circumstances including

occupation, on-the-job routines, social relationships, and daily life. It is this particular

knowledge, obtained in a particular knowledge base that leads to profit-making insight. The

dispersion of information among different economic agents who do not have access to the

same observations, interpretations or experiences, has implications for economic growth.

Since this is not recognized in the endogenous growth model, we will suggest a different set

of assumptions and outline an alternative structure of the model.

An entrepreneurship-based endogenous growth mode: The assumptions

In order to remedy the limitations of the endogenous growth model and to specify the nature

of the transmission mechanism that generates a diffusion of knowledge, we propose the

following assumptions.

1       New firms are assumed to be the (only) mechanism to transmit knowledge (K). K is

        transformed into economically relevant knowledge (Kc) via spillovers, exploited in

        new ventures regardless of whether the knowledge that is drawn from the stock of

                                                                                                 19

knowledge is new or existing knowledge and whether it is scientific knowledge or

        some other kind of knowledge. Existing firms may learn and thereby add to their firm-

        specific knowledge, but we think of the results of such learning as taking the form of

        new ventures. This means that if there are no startups (whether as genuinely new

        entities or as new entities within existing firms), there is no spillover and hence no

        growth.

2       Each new firm represents a new idea. A new idea (innovation) represents any kind of

        new combination of new or existing knowledge, as suggested by Schumpeter (1911).15

        An important implication of this assumption is that firms are heterogeneous, not only

        in the size dimension but in terms of all characteristics such as absorptive capacity,

        strategy, technology, product range, and all aspects of performance (profitability,

        productivity, etc.). New entrants, being less experienced than incumbents, often make

        mistakes and also fail. As a result, a high entry rate is necessary to sustain long-term

        growth.

3       There are no interregional spillovers, only local (Audretsch and Feldman 1996,

        Anselin, Varga and Acs 1997, Keller 2002). Access to the stock of knowledge is

        assumed to be equal to all local entities, but the success in converting general

        knowledge into economically useful firm-specific knowledge depends on the

        absorptive capacity of each firm and hence firm characteristics. Both public and

        private knowledge is subject to spillover. Thus, in order to tap into the knowledge base

        in Silicon Valley, you have to be located in Silicon Valley. (By contrast, the

15
  See also Knight (1921), Hannan & Freeman (1989/1990), Acs & Audretsch (1990), Winter , and Williamson
(1981, 1985).

                                                                                                      20

information generated in Silicon Valley can be accessed at any location with no cost

       disadvantage.)

4.   The conditions for new entry and hence knowledge transmission vary across regions.

     Policy and previous history (path dependence) determines the entrepreneurial climate in

     the form of infrastructure, regulation, attitudes, networks, technology transfer

     mechanisms, etc.

A simple theoretical framework

The combined result of these assumptions, when added to the endogenous growth model, can

be characterized as a filter (here defined in terms of entrepreneurship) that determines the rate

at which the stock of knowledge (K) is converted into economically useful firm-specific

knowledge (Kc):

0 ≤ Kc/K ≤ 1

Two conditions thus are decisive for an increasing stock of knowledge (through R&D and

education) to materialize in higher economic growth; first, knowledge has to be economically

useful and, second, an economy must be endowed with factors of production that can select,

evaluate and transform knowledge into commercial use, i.e., entrepreneurs. If these conditions

are not fulfilled, an increase in the knowledge stock may have no impact on growth.

Similarly, regions with smaller knowledge stocks may experience higher growth than regions

more abundantly endowed with knowledge due to superior links to the market.

                                                                                               21

The basic structure of the model implies that we have two types of firms. First

we have incumbent firms (I) which have a history and have accumulated knowledge over

their life-time,

                                 ∞                        n     I

               k iI, j ,t = f ( ∫ k iI, j ,t , K ) ,    ∑k = K I
                                                         i, j
                                t =0

At each given point in time firm-specific knowledge of the incumbent firms i in industry j

depend on their previous investment in knowledge and the size of K at time t. The already

accumulated firm-specific knowledge within the incumbent firms has two implications for

their ability to exploit new knowledge spillovers from K: first, the size of accumulated firm-

specific knowledge determines their capacity to draw on spillovers (their absorptive capacity),

second, the degree of firm specificity constrains the absorption of knowledge spillovers.

Hence, the incumbent firms’ ability to exploit spillovers is determined by path-dependence

and the specificity of the accumulated knowledge.

               The second type of firms refers to start-ups, i.e., the entry of new firms. These

differ from incumbents since knowledge is not governed by path-dependence and history to

the same extent. Rather it builds on an entrepreneur’s ability to exploit an opportunity arising

from aggregate spillovers,

                                           n     S

               k = f (K ) ,
                    S
                   i ,t                  ∑ki
                                                       = KS

Start-ups entering the market thus produce genuinely new products. Note that K S in period 1

becomes encapsulated in K I in the subsequent periods. At the aggregate level

                                                                                                   22

(region/country), we would argue that the relation between K S in the previous period and

K I in the current period reflects the presence of entrepreneurship in an economy.

                Both types of firms thus contribute to the exploitation of knowledge spillovers,

albeit in different ways. Thereby they will narrow the gap between total spillovers (K) and the

share of those knowledge spillovers that are commercialized. Yet, a complete mapping

between Kc and K – implying perfect information in an unbound state space – is unrealistic.

Rather, we postulate that

K c = K cI + K cS ,

where

K cI = θK , K cS = λK ,0 ≤ θ , λ p 1 ,

hence,

K ≥ K c = K cI + K cS

and

K c = (θ + λ ) K ,

assuming for the moment that spillovers are independent of the spatial dimension. We can

think of θ as the absorptive capacity of incumbent firms and λ as a proxy for entrepreneurship

within an economy. 16 In accordance with assumptions 1 and 2, the production function

described above (equation 2) then has to be modified to account also for entrepreneurship,

16

Χοµπαρε Ροµερ σ (1990) ρεασονινγ τηατ χοστ οφ αν ινϖεντιον δεχρεασεσ ασ αν εχονοµψ αχχυµυλατ
εσ µορε ιδεασ. Ηερε ωε ωουλδ αργυε τηατ τηε χοστ οφ (ορ ποσσιβιλιτψ το) εντερινγ τηε µαρκετ ισ λοω
ερ ισ τηερε ηασ βεεν α λαργε νυµβερ οφ εντριεσ ιν πρεϖιουσ περιοδσ. Ορ, σιµιλαρ το Ροµερ σ (1986)
ασσυµπτιον ιν τηε ινφινιτε ηοριζον ϖερσιον, ωηερε εαχη φιρµ ισ ασσυµεδ το ηαϖε τεχηνολογιεσ τηα
τ δεπενδ. Here it implies that λ=   f (k iS,t −1 ) .

                                                                                               23

F (k i , x, λK )

Thus, if entrepreneurship is non-existent in an economy, knowledge spillovers will not

provide the same solution as in the endogenous growth model with automatic and all

encompassing spillovers. In fact, it will then reduce to the neoclassical growth model. In

addition, it is obvious that it is not only the size of K and the absorptive capacity of incumbent

firms that matter but also the presence of entrepreneurs as captured by λ.

               If we introduce a spatial dimension, at the regional level, where the “home”

region is denoted by h and the foreign “region” by f, then whether F jh,r ≥ F j f,r depends on the

relative magnitude of commercialized knowledge,

K ch ≥ K cf or , λh K h ≥ λ f K f ,

implying that a smaller endowment of knowledge (K) may be compensated for by a larger

degree of entrepreneurial activity (λ) within an economy. We could also – by inserting

subscript j for industry – account for industry differences. (A more formal model is developed

in the appendix).

5. Policy Implications

The policy focus of the neoclassical growth models was on deepening capital and augmenting

it with labor (Solow, 1956). Thus, the policy debate revolved around the efficacy of

instruments designed to induce capital investment, such as interest rates and tax credits, along

with instruments to reduce the cost of labor, such as reduced income and payroll taxes and

increased labor market mobility.

                                                                                                 24

A significant and compelling contribution of the endogenous growth theory was

to refocus the policy debate away from the emphasis on enhancing capital and labor with a

new priority on knowledge and human capital – in particular through a combination of taxes

and subsidies. As Lucas (1993) concluded, “The main engine of growth is the accumulation

of human capital – of knowledge – and the main source of differences in living standards

among nations is differences in human capital. Physical capital accumulation plays an

essential but decidedly subsidiary role.”

              Lucas also elaborates on specific policy instruments designed to enhance

investments in human capital and knowledge, “Human capital accumulation takes place in

schools, in research organizations, and in the course of producing goods and engaging in

trade.” Thus, the policy debate to generate growth revolves around the efficacy of such

instruments as universities, education, public and private investments in research and

knowledge, training programs, and apprentice systems.

              By contrast, the extension of the endogenous growth model suggested in this

paper implies the central, although not exclusive, role played by a very different set of policy

instruments. This policy focus is on instruments that will reduce the filter that generates a

wedge between K and Kc, or between knowledge and economic knowledge. Such policies are

targeted to enhance the spillover of knowledge and focus on enabling the commercialization

of knowledge. Examples of such policies include encouraging new-firm startups. As

Lundström and Stevenson (2001, p. 19) suggest, “Entrepreneurship policy consists of

measures taken to stimulate more entrepreneurial behavior in a region or country… We define

entrepreneurship policy as those measures intended to directly influence the level of

entrepreneurial vitality in a country or a region.”

                                                                                                25

While the different specific types of policies being implemented to enhance

knowledge spillovers are too numerous to be identified and listed here, David Storey (2003)

has identified examples, which are provided in Table 1.

       The second element of the new set of growth policies designed to enhance the spill-

over of knowledge and reduce the gap between knowledge and economic knowledge involves

the locus of such policies, which are increasingly at the state, regional or even local level. The

last decade has seen the emergence of a broad spectrum of enabling policy initiatives that fall

outside of the jurisdiction of the traditional federal regulatory agencies.

       Sternberg (1996) documents how the success of a number of different high-technology

clusters spanning a number of developed countries is the direct result of enabling policies,

such as the provision of venture capital or research support. For example, the Advanced

Research Program in Texas has provided support for basic research and the strengthening of

the infrastructure of the University of Texas, which has played a central role in developing a

high-technology cluster around Austin (Feller, 1997). The Thomas Edison Centers in Ohio,

the Advanced Technology Centers in New Jersey, and the Centers for Advanced Technology

at Case Western Reserve University, Rutgers University and the University of Rochester have

supported generic, precompetitive research. This support has generally provided diversified

technology development involving a mix of activities encompassing a broad spectrum of

industrial collaborators.

       The Edison Technology Program of Ohio was established by the State of Ohio, as a

means of transferring technology from universities and government research institutes to new

firm startups Carlsson and Braunerhjelm (1999) explain how the Edison BioTechnology

Center has served an important dual role as a “bridging institution” between academic

research and industry and between new startups and potential sources of finance. The Edison

Centers in particular, try to link the leading universities and medical institutions, businesses,

                                                                                                26

foundations, to civic and state organizations in Ohio in order to create new business

opportunities. Several centers exist across the state. The Edison Program has also established

a bridging institution to support polymer research and technology in Ohio. Carlsson and

Braunerhjelm (1999) credit the program for the startup of new high technology firms in

Ohio.17

           Other examples of enabling policies targeted to promote knowledge spillovers are

evidenced by the plethora of science, technology and research parks. Lugar and Goldstein

(1991) conducted a review of research parks and concluded that such parks are created in

order to promote the competitiveness of a particular region. Lugar (2001, p. 47) further noted

that, “The most successful parks…have a profound impact on a region and its growth.” A

distinct example of this effect is found in the Research Triangle Park in North Carolina.

           The traditional industries in North Carolina – furniture, textiles, and tobacco – had all

lost international competitiveness, resulting in declines in employment and stagnating real

incomes. In 1952, only Arkansas and Mississippi had lower per capita incomes. According to

Link and Scott (2003, p. 2), a movement emerged to use the rich knowledge base of the

region, formed by the three major universities – Duke University, the University of North

Carolina-Chapel Hill and North Carolina State. This movement, though it initially consisted

only of businessmen looking to improve industrial growth, was subsequently spearheaded by

the Governor’s office (Link, 1995).

           Empirical evidence shows that the initiative creating Research Triangle has led to

fundamental changes in the region. Link and Scott (2003) document the growth in the number

of research companies in the Research Triangle Park as increasing from none in 1958 to 50 by

the mid-1980s and to over 100 by 1997. At the same time, employment in these research

companies increased from zero in the late 1950s to over 40,000 by 1997. Lugar (2001)

17
     See also Braunerhjelm and Carlsson (1999) and Braunerhjelm et al (2000).

                                                                                                  27

attributes the Research Triangle Park with directly and indirectly generating one-quarter of all

jobs in the region between 1959 and 1990, and shifting the nature of those jobs towards high

value-added knowledge activities.

       Such enabling policies reducing the filter between knowledge and economic

knowledge are not restricted to the U.S. One of the most interesting examples of the new

enabling spillovers policy involves the establishment of five EXIST regions in Germany,

where startups from universities and government research laboratories are encouraged

(BMBF, 2000). The program has the explicit goals of (1) creating an entrepreneurial culture,

(2) the commercialization of scientific knowledge, and (3) increasing the number of

innovative start-ups. Five regions were selected among many applicants for START funding.

These are the (1) Rhein-Ruhr region (bizeps program), (2) Dresden (Dresden exists), (3)

Thueringen (GET UP), (4) Karlsruhe (KEIM), and (5) Stuttgart (PUSH!). Evidence of similar

effects has also been shown to be at work in Sweden (Lindelöf 2002, 2003).

       These programs promoting entrepreneurship in a regional context are typical of the

new enabling policies to promote entrepreneurial activity. While these entrepreneurial policies

are evolving, they are clearly gaining in importance and impact in the overall portfolio of

economic policy instruments. Whether they will ultimately prove to be successful remains the

focus of coming research. The point to be emphasized in this paper is that entrepreneurship

policies are important instruments in the arsenal of policies to promote growth. They

represent an alternative not only to the set of instruments implied in the neoclassical growth

theory, but also the endogenous growth theory. As this paper suggests, while generating

knowledge and human capital may be a necessary condition for economic growth, it is not

sufficient. Rather, a supplementary set of policies focusing on enhancing the conduits of

knowledge spillovers also play a central role in promoting economic growth.

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Conclusion
A careful examination of the basic structure of the knowledge-based endogenous growth

model reveals that the model is limited because of the assumption that knowledge not only

automatically spills over but also that it is automatically transformed from knowledge to

economic knowledge. Such an assumption violates the basic premise of Arrow’s (1962)

insights into the economics of knowledge. In this paper we argue that these misspecifications

also account for the somewhat ambiguous empirical results the model has generated in

explaining growth differences across countries. Endogenous growth models typically ignore

the propensity for knowledge to be transmitted through a filter when being transformed into

commercializable economic knowledge.

             We also have demonstrated how a new series of empirical regularities provides

compelling, systematic empirical evidence linking measures of entrepreneurship to economic

growth. Taking this statistical regularity as our departure point, we suggest that the

endogenous growth model needs to be modified in order to incorporate the knowledge filter

consitituting a wedge between knowledge and economic knowledge. To achieve this end, we

have suggested an extension to the endogenous growth model that we believe will narrow the

gap between the model and real world behavior. That implies a whole new set of policy

conclusions. A future research agenda needs to be developed to submit this new modified

growth model based on the knowledge filter to empirical testing.

Appendix
(under progress)

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