KNOWLEDGE DYNAMICS:
Reconciling Competing Hypotheses from Economics And Sociology*
Anne Marie Knott*
The Wharton School
of the University of Pennsylvania
2023 Steinberg Hall-Dietrich Hall
Philadelphia, PA 19104-6370
Phone: (215) 573-9628
Fax: (215) 898-0401
knott@wharton.upenn.edu
Bill McKelvey
Anderson School at UCLA
110 Westwood Plaza
Box 951481
Los Angeles, CA 90095-1418
Phone: (310) 825-7796
Fax: (310) 206-3337
mckelvey@anderson.ucla.edu
June 22, 1999
* Please address all correspondence to the senior author, Anne Marie Knott.
The authors would like to thank Dan Levinthal and participants at the Reginald Jones Center seminar series for helpful
comments during development of this research. We would also like to acknowledge financial support from the
Huntsman Center for Emerging Technologies.
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KNOWLEDGE DYNAMICS:
Reconciling Competing Hypotheses from Economics And Sociology
Abstract
Our goal is to reconcile competing null hypotheses from sociology and economics with respect to
knowledge flow—sociology assumes that knowledge flow is viscous, whereas economics assumes
knowledge flows fluidly thereby discouraging investment in its creation. The concern is that the
two fields’ attendant prescriptions might cancel one another. Our vehicle for reconciliation is a
simulation of knowledge flow that embodies empirical regularities emerging from studies in both
fields. Through simulation we find that both fields are partially correct. More importantly we
find that the fields’ prescriptions for knowledge growth, rather than canceling one another,
actually complement one another.
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1. INTRODUCTION
Both economics and sociology agree that innovation and human capital formation normally
improves social welfare, but they differ in starting assumptions. In general, economics studies
knowledge creation—How can public policy create incentives for firms to create new knowledge?
Sociology, on the other hand, looks at knowledge diffusion—How can institutions get individuals
to share their own knowledge and adopt that of others? Corresponding to these goals, the two
fields have opposing null hypotheses regarding the flow of knowledge. In general, economists
hold that knowledge flows freely—the challenge is to impede knowledge flow. In contrast,
sociologists generally hold that knowledge is inert—the challenge is to facilitate knowledge flow.
The null hypothesis that each field has adopted makes sense given its respective approach to
innovation. Economists worry that firms will not invest in knowledge creation if they can not
appropriate the returns from those investments. The greatest threat to appropriation is the relative
ease with which knowledge can be transferred. Sociologists suspect that organizations will not
share knowledge if they derive benefit from controlling it. They also see firms as comprised of
boundaries around individuals and subunits that act as barriers to information flow. The problem
with the opposing null hypotheses is that they may lead to contrary prescriptions that may
potentially offset one another, such that neither innovation nor growth occurs. Thus, it is
important to understand the relative correctness of each field’s null hypothesis. Are economists
correct that knowledge flow is fluid, or are sociologists correct that knowledge is inert?
We take a step toward resolving the debate by studying the impact of the driving assumptions,
given various firm and industry conditions. Our approach begins with harvesting a set of stylized
facts or known empirical regularities of knowledge flow from both literatures so as to develop a
simple model of knowledge dynamics. We focus on empirical regularities spreading across
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several fields of research and introduce a computational modeling approach so as to study the
dynamics in between the extremes of the economists’ and sociologists’ assumptions—the range of
dynamics more likely to be of use by managers interested in speeding up human capital
appreciation within their firm, but worried about possible increased flow out to competitors. Thus,
we try to answer questions regarding the inherent state of knowledge in a firm or an industry and
the effects of various stimuli on knowledge growth in firms or in an industry. The method we use
is an interacting agent model derived from the “spin glass” family of models frequently used in
physics (Fischer and Hertz, 1993).
In this article we: (1) highlight the debate; (2) resolve the debate such that research findings
from the two literatures may be constructively integrated toward a theory of knowledge dynamics
between the two extremes; and (3) provide some new insights that might guide public as well as
managerial policy. We begin by reviewing the sociology of science, diffusion, technology
economics, and management of technology literatures, setting out the empirical regularities as we
go. Then we propose a formal model of knowledge dynamics that we evaluate through computer
simulation. We validate the simulation relative to the empirical regularities and then utilize it to
explore the dynamics affecting knowledge growth. Results and Discussion follow.
2. COMPARING THE PERSPECTIVES
2.1 Sociology of Science and Organization
Sociological perspectives on knowledge flow are probably best exemplified by the sociology of
science and the study of bureaucratic structure. Sociology of science is concerned with the
interrelationship of science and society. How has science influenced values, education, class
structure, ways of life, political decisions, and ways of looking at the world? How has society, in
turn, influenced the development of science itself (Kaplan, 1964)? Organizational sociology has
3
uncovered significant deleterious effects of bureaucratic structure that inhibit the flow of
information across organizational boundaries.
Sociology of science emerged in the early twentieth century as an outgrowth of studies of the
history of invention and technology (Ogburn, 1922; Usher, 1929; Gilfillan, 1933; Merton 1938).
Sociology was ripe for a theory of science around the turn of the century, as technology formed a
major force that threatened, or at least affected, society. Since its inception the sociology of
science has come to be characterized as the “old” and “new” schools. Old sociology of science is
best represented by the 240 or so published papers and classic book (1963) by Price and a second
edition that includes nine later papers (1986; reissued by Columbia University Press with a
foreword by Robert K. Merton and Eugene Garfield). Price’s papers document the quantitative
study of science, what he called “scientometrics,” and particularly the study of citation indices.
New sociology of science studies science as a social phenomenon, paying particular attention to
the social construction aspects of scientific truth claims as characterized by the postmodernist
literature (Mirskaya, 1990; Lynch,1993; Hilgartner and Brandt-Rauf, 1994, Pels, 1994; Murphy,
1994; Fuller, 1995a, b; Barnes, Bloor, and Henry, 1996). The impetus for new sociology of
science was undoubtedly Kuhn’s 1962 book, The Structure of Scientific Revolutions, with the
works of Hanson (1958) and Feyerabend (1970) also instrumental. Mulkay’s 1969 paper, “Some
aspects of cultural growth in the natural sciences” sits as a dividing point between old and new—
between the quantitative and functionalist views of Merton (1942) and the relativist/postmodernist
views of post Kuhnian and postmodern sociology of science. Since we are interested in the causes
of knowledge flow dynamics and whatever empirical regularities exist, needless to say, new
sociology of science has little to offer once it moved into studying the social aspects of truth
claims. This explains why most of the research we cite dates before new sociology of science.
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Up until about the 20th century most people, while knowing that change occurs, tended to think
of stability as more normal and preferable than change (Dubin, 1958: 117). Partly this was
because U. S. society was rural dominated and more homogeneous and change occurs least readily
in less heterogeneous and rural societies (Berelson and Steiner, (1964: 615–616). However the
combined effects of technological development coupled with consequent social change stemming
from the industrial revolution and the growth of factory employment in urban centers transformed
all aspects of human life at ever more rapid speed and magnitude (1964: 615–617). The general
public’s conception shifted to one in which change was more normal than stability, as well as more
desirable. Further impetus came with World War II, as science attained political importance, both
because it formed a major element in the national budget, and because it produced technology with
substantial societal implications, e.g., the atomic bomb(Hiskes and Hiskes, 1986).
Given technology as the major source of change and science at the heart of technology, a
sociology of science emerged to deal with the patterns of change likely to affect society (Barber,
1952; Barber and Hirsch, 1962; Hiskes and Hiskes, 1986; Fuller 1993). Thus, understanding the
rate of technological change became a significant goal of sociology of science. Another objective
was to identify and promote factors that lead to change.
2.1.1 Knowledge Creation Process
Sociology of science holds that knowledge accumulates. Exponential growth in several
measures of scientific activity comprises the primary evidence supporting this view. Sociologists
view invention as the cumulative synthesis of many individual items, though the magnitude of
each item is small. Thus, scientific growth is largely a diffusion process: accretion of many small
innovations each building upon prior innovations (Crane, 1972). Ogburn (1922) goes so far as to
contend that when the necessary cultural base is in place, invention is inevitable—if one inventor
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does not create the new device another will. He offers as supporting evidence the frequency of
independent simultaneous invention. This is confirmed more recently by Kuhn (1959), and is
evident in the account of the biologists’ search for the DNA “double helix” molecule (Watson,
1968).
If growth in social welfare is the end, and invention the means, one merely needs to facilitate
diffusion of the existing knowledge base to ensure efficient discovery of the inevitable invention.
Diffusion mechanisms, thus, become the main focus of empirical studies in sociology of science.
The science citation index has become a major data source for the investigation of the growth and
the diffusion of knowledge since it provides a clear listing of prior innovations.
A number of empirical regularities emerge from the examinations of scientific citations:
1.
The growth of science as a whole follows a logistic curve, and while the total cost of research has increased by
a factor of 4.5 since World War II, output has merely doubled. Further the growth of important contributions
(heavily cited papers) has remained constant over the same period. “Thus we are multiplying lesser talents
faster than the highest ones with half the scientific advance” (Price, 1963: 91). (Diminishing returns)
2.
Output (complete papers per person) is highest for large groups and for solos (Price, 1963: 132). (U-shape
productivity)
3.
Per capita science activity in a country correlates with per capita wealth and level of economic development
(Price, 1963: 43). (Wealth effect)
4.
Competition (number of specialists attacking problem) increases when agreement about the importance of a
field increases (Hagstrom, 1965). (Density dependence).
2.1.2 Stimulus to Knowledge Creation
A parallel theme hinting that progress may not be inevitable, is the stimulus to invention—the
extent to which invention is socially determined versus the inherent development of science.
Ogburn (1922) acknowledges that necessity (social pull) plays a role in invention, but argues
necessity is insufficient without a cultural base, and not necessary, as evidenced by frivolous
invention. This view is not universally held. Price for example, holds that the greatest and most
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useful advances in our technologies have come not from applied research, but from “basic research
aimed at furthering understanding and curiosity” (1963: 155).
Stein (1962) presents research findings indicating that personality factors also bear on
knowledge creation, independent of culture or the basic/applied continuum. Why individual
scientists do what they do is “little science” (Price, 1986). As the century ends, the concerns about
the practices and social impact of “big science” have become more pronounced as people worry
that big science has been stimulated beyond reason and to the exclusion of other factors affecting
modern society—particularly the impact of the military/industrial symbiosis, hi-tech weapons and
weapons of mass destruction, and chemical pollutants (Steneck, 1975; Reingold, 1979; Hiskes and
Hiskes, 1986; Bell 1992).
2.1.3 Diffusion of Innovation
A related literature dealing with the diffusion of innovation outside science draws conclusions
similar to those of the sociology of science. Diffusion research grows out of the rural sociology
studies of the 1940s that examined the diffusion of agricultural innovation—the most influential
study being Ryan and Gross's (1943) investigation of the diffusion of hybrid corn seed. The
research spans a number of disciplines including education (adoption of learning innovations),
public health (adoption of health practices), communication (awareness of media events),
marketing (the adoption of new products), and geography (role of spatial distance in technology
adoption) (Rogers, 1995). The principal theme of this literature is that widespread adoption, even
of an idea with obvious advantages, is often difficult. The research examines the factors affecting
the rate of adoption, with a goal of devising policies that speed the adoption process.
There are two important differences between the sociology of science and diffusion literatures.
Sociology of science is fundamentally interested in the creation of new knowledge, whereas the
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diffusion literature is concerned with the exploitation of existing knowledge. Therefore, because
the sociology of science view is that creation is inevitable, given sufficient prior accumulation and
diffusion, it follows that creation of new knowledge directly is isomorphic with the adoption of
existing prior knowledge. Consequently, this distinction disappears—both see diffusion as critical.
The second distinction is that while both literatures examine knowledge flow between individuals,
sociology of science restricts attention to scientists embedded in the scientific institutional context,
whereas the diffusion literature, perhaps because of its breadth, examines the implications of
diffusion among individuals independent of any institutional context.
Rogers (1995) develops a set of empirical regularities from review of approximately 4000
diffusion publications:
1.
Diffusion follows a logistic curve, where the rapid growth phase is prompted by adoption of the innovation by
opinion leaders (Tarde, 1903) (Logistic growth)
2.
Imitation (adoption by one individual prompted by the adoption of another individual) is most frequent
between individuals who share similar attributes (Technical proximity/homophily).
3.
The very nature of diffusion requires that some heterophily exists, else there is nothing to diffuse (Heterophily)
4.
Innovators and early adopters differ from later adopters in that they have higher education, social status,
upward mobility, wealth, IQ, ability for abstract thought, ability for rational thought, and empathy. In
addition, their communication patterns differ from later adopters. In particular, they have more exposure to
mass media, engage in more information seeking, have more social ties, and are more cosmopolitan (Wealth
effect)
5.
Diffusion is a function of geographic distance (Hagerstrand, 1952) (Geographic proximity)
2.1.4 Boundary Effects
While earlier diffusion findings were mostly about individuals independent of institutional
context, now increasing numbers of individuals work in organizations. Thus, diffusion among
individuals is more a function of diffusion across organizational boundaries. Weber’s (1947) ideal
bureaucracy rests on division of labor, clear role definition, specialization, formalization, and
centralization (with decentralization allowed if accompanied by appropriate rules). According to
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“rational” organization design (Scott, 1998), the ideal bureaucracy is synonymous with clearly
designed specialized roles and departments with accompanying rigid and impervious boundaries.
In a comparative analysis of four countries Ben-David (1960) shows that the rate of innovation is
hindered by strongly centralized organization structure and facilitated by loose and competitive
structures. He also shows that innovation benefits from a diversity of roles. Mulkay (1969)
concludes that though Kuhn’s (1962) normal science may progress adequately in bureaucratized
structures, innovation is more apt to flourish when diverse roles are brought together, and when
cross-fertilization is fostered by researchers occupying dual or multiple roles.
Another recent view of bureaucratic effects is given by Pennings (1987: 208). He cites
evidence that boundary spanning individuals (dual roles) are “crucial for the adoption of
CAD/CAM in a production system. He also notes that high incidences of professionals and
professional networks and a “loosely federated structure” aid the spread of innovations. Other
innovation researchers also emphasize the importance of boundary-spanning gatekeepers
(Pettigrew, 1973; Moch and Morse, 1977; and Ettlie, 1985). Boundary spanning is seen as
essential to fostering innovation in Japanese firms (Nonaka, 1990), where information redundancy
across departments as associated with a shared division of labor in which individuals are able to
more broadly define their roles, thus partially negating the impermeable boundary effects of
bureaucratic structure. The boundary spanners are the people who shore up homophily in firms
where division of labor, specialized roles, and departmentalization all work to foster heterophily.
Mohrman and Mohrman (1993) also report that bureaucratic structure and controls impede
innovation and that rigid bureaucratic forms are antithetical to innovation. Boundaries negate the
effects of physical or technical proximity. Leonard-Barton (1995) and Ashkenas et al. (1995) echo
these results. Organizational elements that reduce or compensate for narrow role specializations,
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reduce departmental boundary blocks to information flows, build interdepartmental networks,
build role diversity and the interaction of employees playing multiple roles, and keep employees in
close contact with external parties, that is, closer to competitive pressures and inputs from outside
the organization, all work to enhance innovation (physical and technical proximity effects).
2.2 Technology Economics
Economic perspectives on knowledge flow are best captured by economics of technology. The
economics of technology literature was motivated by the link that (Solow, 1957) demonstrated
between innovation and productivity growth. Its primary goal is to understand the conditions that
facilitate innovation. The work is generally at the level of industries or the economy. The insights
gained from work in this field are used to guide government policy, primarily through intellectual
property law, antitrust regulation and national investment.
The economics of technology literature focuses on two hypotheses, both of which are attributed
to Schumpeter (1942). The first hypothesis is that large firms are more likely to innovate than
small firms. This is essentially an hypothesis regarding firms’ capacity to innovate. The second
hypothesis is that monopolists are more likely to innovate than firms without market power. This
is essentially a hypothesis regarding firms’ incentives to innovate.
2.2.1 Firm Size
There are number of factors tending to support Schumpeter’s first hypothesis. The advantages
of large firms include the ability to hold a diversified portfolio of projects, R & D scale economies,
cross fertilization of ideas, cheaper capital (through use of internal financing for risky products),
complementary assets, stronger incentives for process improvements (due to larger base for
spreading costs), serendipity (with more people there is greater likelihood that someone will
recognize the value of an innovation), and more avenues for exploiting output.
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There is an equally impressive set of factors suggesting that large firms are actually at a
disadvantage in innovation. These, however, are organizational rather than economic issues, and
thus may have received less attention in the early economics literature. These factors include the
communication overhead of large size, a higher status of management jobs versus engineering jobs
in large firms (thus drawing away the more experienced R & D professionals into management
ranks), decision making filters, bias against imagination that drives away talent, and conservatism.
Early challenges to the large firm hypothesis come from (Jewkes, Sawers and Stillerman, 1958)
and (Hamberg, 1963). These studies indicate that less than 30% of major innovations come from
large firms. This leads to a modified hypothesis by Hamberg: that large firms are likely to be
minor sources of radical invention but major sources of improvement inventions. This view does
not necessarily refute the firm size hypothesis—the cumulative effect of many small inventions
may be greater than a smaller number of major innovations.
Cohen and Levin (1989) develops a set of empirical regularities that summarize the conclusions
from the firm size studies:
1.
The likelihood of conducting R & D and the level of R&D spending increase monotonically with business unit
size. (Business unit size explains approximately two thirds the variance of R&D expenditures.) (Wealth effect)
2.
R & D productivity (output/expenditures) declines with firm size and, thus, smaller firms account for a
disproportionately large share of invention relative to their size (Geographic and technical proximity).f
The empirical regularities seem to imply that arguments in favor of both sides of the firm size
hypothesis have merit. The arguments in favor of large size pertain to efficiency advantages.
Large firms recognizing their efficiency advantages, are willing to spend more. This resembles the
wealth hypothesis in the sociology and diffusion literatures. Arguments in favor of small size
pertain to effectiveness advantages. Small firms provide environments more conducive to
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invention, and therefore produce more invention per dollar than do their large firm counterparts.
This finding resembles the proximity arguments in the sociology and diffusion literatures.
2.2.2 Monopoly Power
The second Shumpeterian hypothesis is that monopoly power is conducive to invention.
Monopoly power conveys two advantages for innovation. First, it insures appropriability for the
investment a priori (incentive effect), and second, it provides profits posteriori to support further
innovation (capacity effect). The counter-argument is that (1) once the monopolist is enjoying a
rent stream, it has reduced its incentive to innovate, because it cannibalizes a portion of that rent
stream (Arrow, 1962; Asher, 1964; Baldwin,1969; Demsetz, 1969); and (2) incentives to invest in
innovation are reduced if the new ideas are easily expropriated by competitors. It is here more
than anywhere that economists differ from sociologists. While sociologists see diffusion as
“good” because it spreads good ideas throughout society, economists see diffusion negatively as
expropriation of a firm’s ideas by competing firms. Therefore, though they agree with sociologists
that diffusion aids broader social welfare, economists worry that expropriation discourages firms
from investing, turning a “positive” into a “negative.” Thus, in what follows we often will appear
to be interchanging “diffusion” with “expropriation”—same process, but different spin.
Schumpeter’s second hypothesis has enjoyed much greater attention than his first. The
economic concern is that because knowledge is a public good (is not consumed in use), and
because its transfer is frictionless, the broader social returns to R&D may exceed the returns to
private firms, reducing their incentive to continue investing in innovation. Thus, in the absence of
intervention, R&D may fall below socially optimal levels (Arrow, 1962; Hirshleifer, 1971). Two
options are open to policy makers under these circumstances. The first is patents (to increase the
certainty that a firm may appropriate the full value of its investment); the second is enlightened
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anti-trust policies (that recognize that the less efficient resource allocations under monopoly may
be offset by the long term benefit of growth in economic welfare).
Theoretical development of the second hypothesis examines competition among potential
innovators engaged in an R&D race. The main questions are how profits, costs, and intensity of
rivalry determine the speed of innovation (Kamien and Schwartz, 1982). The incentives to
innovate consist of the “carrot” of innovation profits and the “stick” of lost profits in the event a
rival innovates first. The main conclusions from the theoretical literature are:
1.
A new good that does not supplant an existing one will appear more rapidly than a replacement good
(Diminishing returns).
2.
The greater the loss from rival precedence, the sooner development will take place (Wealth effect).
3.
Rivalry decreases development time up to a threshold number of rivals, thereafter it increases development
time (as added numbers of players tends to dissipate appropriability) (Density dependence).
4.
Incumbents invest less than entrants when innovation is uncertain, yet they invest more than entrants when
innovation is certain (Gilbert and Newberry, 1982; Reinganum, 1983, 1985; Salant, 1984; Katz and Shapiro,
1987). The factor inhibiting incumbent investment is the fact that they already enjoy a rent stream, thus they
primarily invest only to protect it (Causal ambiguity).
The general conclusions from the economic models of innovation are that rivalry and
appropriability interact. Competition for an appropriable return leads to over-investment, while
non-appropriability or absence of competition leads to under-investment.
Empirical research tends to support the theoretical conclusions. Scherer (1980) finds that
insulation from competitive pressure discourages innovation. Scherer (1965), Scott (1984), Levin
et al. (1987) all found an inverted U relationship between innovation and rivalry. Scherer (1965)
found maximum patent counts for a four-seller concentration ratio between 0.50 and 0.51—
indicating that appropriability effects are U-shaped. However this relationship tends to disappear
when additional variables are added to account for technological opportunity and other factors
influencing innovation (Levin et al., 1985).
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2.3 The Management of Technology Synthesis
Our investigation shows that while the goals of both sociology of science and economics of
technology are essentially the same—increased social welfare through innovation—the fields are
markedly different in other respects. These differences are summarized in Table 1. The most
notable differences for our purpose of reconciling views of knowledge flow, pertain to the patterns
and stimuli of innovation. As to the pattern of innovation, sociology believes innovation is
continuous (follows gradual accumulation)—thus to generate innovation, we merely need to
diffuse prior knowledge. In contrast, economics believes innovation is discontinuous. Thus to
generate innovation, we need to create incentives. With respect to the stimulus to innovation,
sociology believes innovation is a byproduct of the accumulation of knowledge. Economics
believes it is the result of deliberate strategies by key individuals to innovate.
(Insert Table 1 about here)
A synthesis of these two perspectives occurs to some extent, in the management of technology
literature. Writers through the 1950s and 1960s have goals similar to economics of technology,
but techniques more closely aligned with sociology of science. Management theorists are
interested in problems of worker satisfaction and productivity, with of goal of enhancing both.
They apply both qualitative and quantitative methods to the examination of product developments.
Qualitative methods characterize communication patterns and other elements of project structure.
Quantitative methods examine outcomes such as success rates and development times as a
function of a number of project characteristics. (Gordon, Marquis et al., 1962, Kornhauser, 1953;
Bennis, 1956; Shepard, 1956; Glaser, 1964; Allen, 1977).
A similar synthesis of sociology and economics occurs in more recent work in management of
technology with respect to notions of progress. Whereas sociology tends to see progress as
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cumulative and incremental, and economics see progress as episodic, management of technology
accounts for both in its life-cycle perspective. Technology life-cycles are punctuated by radical
innovations (episodes), but progress through incremental innovation thereafter (Abernathy and
Utterback, 1978; Abernathy and Clark, 1985; Anderson and Tushman, 1990). Thus, writers in the
management of technology field have adopted a view wherein the radical innovations are viewed
as acts of insight (by key individuals) involving the synthesis of items derived from prior acts of
insight. Progress consists of acts of insight of differing degrees of importance converging toward a
massive synthesis. While the intervening succession of events is orderly and logical, the
punctuated intervals are indeterminate (Usher, 1929).
Another, perhaps more powerful, synthesis of the sociological and economic perspectives
occurs with the consolidation of empirical results from the three fields (including management of
technology). Table 2 is an effort to summarize and classify these results by phenomenon (rows),
level of analysis (columns) and source literature (font). The table clearly indicates that empirical
regularities emerge despite the theoretical differences across the fields. The conclusions we draw
from the table are first, that neither null hypothesis (knowledge inert vs. knowledge free-flowing)
dominates the results. The second conclusion we draw is that the empircal regularities transcend
levels of analysis. While this is what we would expect if knowledge is “atomistic”, as most of us
would tend to believe, we now have some confidence that we have captured an entity for which it
is possible to characterize fundamental flow properties. The third conclusion we draw is that the
composite view given by the three fields offers us a multidimensional view of knowledge
dynamics that is empirically grounded. These empirical findings pertain to the patterns of
innovation (logistic growth within field, versus episodic growth across fields; bi-modal
distributions of entities’ outputs), entities’ capacity to innovate (wealth effects, proximity effects),
15
as well as entities’ incentives to innovate (diminishing returns to innovative activity, density
dependence of innovative output).
(Insert Table 2 about here)
A final conclusion we draw is that the joint effect of the nine principles is virtually impossible
to discern via simple intuition—some causes are linear; some are nonlinear; and there are several
of each. We have no theory governing how the various effects interact. Given this, How could a
manager decide what the optimal level of investment is? How could a government policy advisor
or an international development agency or and industry consortium work to assure an optimal level
of knowledge in a given industry? How could an international alliance of global firms chart a
course of investment in R&D for the alliance? To help unravel the countervailing effects of the
nine principles, we employ the empirical regularities as specifications for a computational model
of knowledge flow. For reasons outlined below we think a computational simulation is especially
appropriate for better understanding knowledge flow dynamics.
3. TOWARD A THEORY OF KNOWLEDGE DYNAMICS
3.1 Why modeling?
Logical positivism (Ayer, 1959) and logical empiricism (Kaplan, 1964) were abandoned by
philosophers three decades ago (Suppe, 1977). Three replacement epistemologies have emerged
since then: scientific realism (Aronson, Harre, and Way, 1994; de Regt, 1994), the semantic
conception (Suppe, 1989, Thompson, 1989), and evolutionary epistemology (Hahlweg and
Hooker, 1989; Rescher, 1990). Some essential features of this new view of epistemology are
brought to light by (McKelvey, 1999c) under the label, “Campbellian Realism.” This term
signifies Campbell’s life-long interest in evolutionary epistemology and scientific realism
(Campbell, 1959; Campbell, 1974; Campbell, 1988). That Campbell the behavioral/social
16
scientist is deeply involved in this rereading of epistemology is critical for organization scientists
because there is a tendency in some circles to eschew “normal science” epistmology because it is
judged irrelevant to organization science (Perrow, 1994; Burrell, 1996; Chia, 1996).
Drawing as it does on the three replacement epistemologies, Campbellian realism sets up a
number of standards for effective science. Several of these assert a “model-centered science” in
which the critical importance of the coevolutionary development of the theory–model link is
highlighted. Though (Suppe, 1977) accepts that the semantic conception does not insist on
“formal” mathematical or computational models as opposed to more qualitative formulations, the
more effective sciences, Suppe, and most scientific realists (Bhaskar, 1975; Aronson, Harre, and
Way, 1994; de Regt, 1994) and semantic conception adherents (Lloyd, 1988; Suppe, 1989;
Thompson, 1989) accept the idea that theories benefit considerably if their nuances are developed
in association with more formal modeling approaches. Pfeffer (1997: 195) offers an additional
motive for a model-centered science—simplicity. Models have a way of forcing investigators
toward more parsimonious theories.
3.2 Goals for the Model
Given a Campbellian realist epistemology, we pursue the development of a theory of
knowledge dynamics using a computational models. The primary goal for using this model is to
conduct a “crucial experiment”(Stinchcombe, 1968) of the opposing null hypotheses of economics
and sociology regarding knowledge flow. Does knowledge inherently flow freely (economics), or
is it inherently inert (sociology)?
We also hope to understand the links between the nine principles governing the input variables
and the patterns of output, so that we can generate policy recommendations—what should the
population configuration be if we want rapid knowledge diffusion (social welfare), and what is the
17
appropriate configuration if we want to increase a firm’s innovation rate, or inhibit diffusion (firm
appropriability). At a minimum, the model should generate behavior consistent with the empirical
regularities regarding knowledge flow—so that we can understand the system producing these
behaviors. Given consistency with the empirical regularities, our level of confidence in the
computational experiment is increased.
Assuming the foregoing objective is reached—the model generates behavior consistent with the
existing empirical regularities—we can then use the model to experiment with resource
combinations that would be difficult to play around with in the real world. And a computational
experiment platform also allows us to meet another standard of effective science, that is, to explore
the “if this then that” aspects of our theory. Do the causal principles we identify have the effects—
in our model at least—that we would predict?
Finally, a computational agent-based model fits the assumption base of organization or
innovation behavior. The actors/entities involved are NOT uniform; their idiosyncratic differences
are stochastic and have nonlinear effects. Further, the number of variables we have in the model,
coupled with their nonlinearity, makes a closed form mathematical solution extremely unlikely,
giving the advantage to a computational simulation.
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3.3 Modeling Approach
According to a review by (Carley, 1995) a variety of computational models appear in
organization science—nearly 100 model applications are reviewed. Mostly these models represent
idealizations of individual or organizational decision processes designed to replicate the decision
processes of specific individuals or firms. These are “thick” models, to adopt the parlance of
Geertz (1971), in that they attempt to represent in considerable detail the target decision processes.
More recently a different “thin” (agent-based) approach to modeling appears in the literature
(Carley and Newell, 1994). Thin models make very few assumptions, or impose very few rules,
about how individual agents decide. They simply expect agents to “stay the same” or “change”—a
simple binary choice. As compared to thick, qualitative, in depth studies of a small sample of
human behavior, thin studies use a few proxy variables across a large sample. Thick and thin
models each have their advantages. Generally as sciences have (1) reached down toward the most
basic particles, molecules, agents, or components (generally called microstates); (2) have accepted
that microstates behave stochastically rather than uniformly; and (3) expect nonlinear dynamics,
scientists have more frequently adopted “thin” agent-based models (McKelvey, 1997).
Sometimes called “adaptive learning models,” agent-based models figure more prominently in
the organizational learning literature, an early application being by (Cohen, March, and Olsen,
1972). Recently many more applications appear in this literature (Durfee, 1988; Masuch and
LaPotin, 1989; March, 1991; Carley and Svoboda, 1996; Cohen, 1996; Warglien, 1996; Padgett,
1997; Prietula, Carley, and Gasser, 1998). Organizational adaptive learning also appears in
applications of Kauffman’s NK model by Levinthal (1997) and McKelvey (1999a, b) that are
rooted in the physicists’ spin glass models (Fischer and Hertz, 1993) and the computer scientists’
19
cellular automata models (Weisbuch, 1993). Applications of the biologists’ genetic algorithm
model (Mitchell, 1996) also now appear in the management literature (Bruderer and Singh, 1996).
Our model is a derivative of the spin glass. We start with an n x n lattice of firms and their
interconnections. Spin glasses model the rate at which the total energy level of a lattice declines as
individual agents (vertices) attempt to reduce their energy in response to current states of their
neighboring agents. This model type fits our needs since we are interested in the total knowledge
growth of all firms comprising the lattice. Spin glass models are frequently used when a quantity
such as energy and fitness (or knowledge) is expected to (respectively) decrease or increase. As
you will see, the equations we use leave agents with essentially two choices at each of many time
periods. At each time period each of our agents has a stochastically driven choice of expropriating
knowledge from another firm (or not) or creating new knowledge on its own (or not).
3.3.1 Macro and Micro Variables and their Interdependence
3.3.1.1 Microvariables. We begin by defining a set of heterogeneous entities in a population (i
= 1 to n). While these entities could be individuals, organizations, industries or even economies
(as depicted in Table 2), and while our model intends to capture all such levels of analysis, here
forward we will define the entities to be firms. Each firm is characterized by an initial endowment
of knowledge, Ki, random normally distributed—thus some firms initially “know more” than other
firms. This characterization is intended to capture wealth effects in the empirical regularities.
Further, each firm has a location in physical space, Gi, as well as technological space, Ti. The
location in physical space is intended to represent geographic location (e.g., Silicon Valley versus
Buffalo). The technical location captures the location of the firm in technological space, e.g.,
pharmaceuticals are close to chemicals, but far from electronics. Some notion of physical space is
necessary to incorporate the empirical regularity that transfers take place more efficiently over
20
short distances (geographic proximity). A notion of technical space is necessary to incorporate the
empirical regularity that transfers take place more fluidly between firms that share a common
knowledge base (technical proximity/homophily).
“Tension” between firms dictates the extent and direction of knowledge flow between them.
The tension is a function of physical proximity, Gij, and technological proximity, Tij, —the shorter
the distance between two entities, the more likely it is that they will share information. Tension is
also a function of the “knowledge differential” or differences in the amount of knowledge between
the entities (Ki – Kj). Knowledge differential captures the intuition that if two entities have the
same knowledge, there is no need for transfers to take place (requisite heterophily).
3.3.1.2 Actions Taken Each Period. Each period firms potentially gain knowledge in each of
two ways. First they have the opportunity to invest in new knowledge—knowledge creation.
Second, they have the opportunity to gain existing knowledge from other entities—knowledge
expropriation.
3.3.1.2.1 Knowledge Creation. True investment behavior is potentially quite complex. Firms
may invest merely to compensate for the obsolescence of the existing knowledge. In fact, a recent
study indicates that almost all R&D investment in the pharmaceutical industry is that required to
compensate for obsolescence (Knott and Bryce, 1998). Firms may invest because they can afford
to, based on the profits from the prior period (capacity to invest). Alternatively, firms may invest
because their future profits are threatened (incentive to invest). Moreover, as the technology
economics literature indicates, these threats to future profits are multifaceted. We make two
simplifying assumptions in the model’s investment rule. First, we consider only net investment,
that is, we consider only investments exceeding those required to maintain the value of the existing
asset stock (net investment = total investment – depreciation from prior period). Second, we
21
model only threat-induced investment, where threat is defined as a loss in the firm’s relative
knowledge stock. Firms make net investments in an effort to preserve their share of the total
knowledge in the industry. This behavioral assumption captures the stylized fact that innovation is
an n-shaped (inverted u) function of industry concentration. We believe that the underlying
mechanism producing the n-shaped function in concentrated industries is the zero-sum nature of
competition—your gain comes at my expense and therefore I am inclined to invest in retaliation.
Firms are always under tension to invest in creation as long as the knowledge stock is growing,
because the growth in the stock in and of itself, causes them to lose share.
Further, we believe there is causal ambiguity in knowledge creation. While firms may make
investments, there is uncertainty regarding the amount of new knowledge these investments will
yield. We thus model knowledge creation by firm i in period t as a random percentage,, of the
lost share, where is Beta distributed with p = 25 and q = 25. The choice of Beta Distribution is
driven by the need to bound the distribution at 0 and 1, but a desire to control the variance:

 
 K i t 1   K it
Cit   

K i t 1    K it


 i 1,n
  i 1,n


 

    K it 
  i 1,n 

(1)
where: Cit = new knowledge created by firm i in period t
 = random number (from a Beta distribution)  [25, 25] representing causal ambiguity
Kit = knowledge stock of firm i in period t
If equation 2 yields a negative value, which is the case if firm i enters period t having gained
share, Cit is set to zero.
3.3.1.2.2 Knowledge Expropriation. Also in each period, firms have the opportunity to
expropriate existing knowledge from neighbors (we do not distinguish between unintentional
leakage and intentional sharing). There are two basic issues regarding implementation of
22
expropriation dynamics. The first issue is how many host firms a focal firm i, can expropriate
from in a given period. The second issue is how firms choose hosts. With respect to the issue of
number of host firms, we assume that firms have limited information capacity, and therefore
restrict attention to a single firm at a time. With respect to the issue of host choice, there are two
basic approaches. An omniscient approach assumes that firms are able to compute the expected
expropriation from each of the potential hosts, then choose the host offering the maximum
expropriation. This approach assumes that firms are able to rank order potential hosts in terms of
their total knowledge, Kij. This is not unreasonable, since firms can compare products and make
assumptions about the level of underlying technological expertise. Further, firms know which of
their rivals in the industry are competing in the same arena, Tij, and they certainly know physical
proximity, Gij.
To be conservative, we nevertheless adopt a naïve approach. The logic driving our choice of
the naïve approach is one of firms’ extractive opportunities. We assume that even if firms know
which host has the greatest expropriation potential, they may not have an opportunity to extract
knowledge from that host. We suppose instead that firms come in contact with rivals randomly,
and that each contact presents an opportunity for expropriating rival knowledge.
Thus expropriation for firm i in a given period is defined by random choice of firm j, with the
knowledge differential between the two firms defined as Kij = Kj – Ki, and the attenuation crossing
technical and geographic space, defined as squared Euclidean distance: (Gij2 + Tij2). Further we
assume that there is causal ambiguity in the expropriation process. Firm i may not know which of
the host’s knowledge is valuable, or may not be completely effective in expropriating the
knowledge. Thus firm i is not necessarily able to extract the entire surplus of j’s knowledge. We
23
operationalize causal ambiguity with a random number , that like  is Beta distributed,
representing the share of differential knowledge that firm i is able to extract.

Eit    K jt  Kit 



/  gij2  tij2  

(2)
 
where: Eit = knowledge expropriated by firm i in period t
=random number  [25, 25] representing causal ambiguity
tij = technical proximity between firm i and firm j
gij = geographic proximity between firm i and firm j
If equation 1 yields a negative value, true if i has more knowledge than j, Eit is set to 0.
3.3.1.3 Micro and Macro Outputs. For convenience, geographic location and technical location
are held constant in the model. One can imagine that entities may migrate to areas with greater
potential for knowledge expropriation, but we assume that plant location and technical specialty
represent durable commitments. The primary variables that evolve over time, are the knowledge
stocks of the individual entities, and the cumulative knowledge of the population. These primary
variables generate derivative changes in the knowledge differential between neighbors, and in the
propensity to invest in new knowledge.
3.3.1.4 Assumptions. Implicit in the model are a number of assumptions. First, we assume for
the moment that there is unlimited capacity in the communication channel, that is, there is no
upper bound on the flow rate of information between two firms. (Earlier we assumed some
capacity constraint in restricting expropriation to a single host firm). Second, we assume that the
number of firms in the industry is fixed—no entry or exit. Our other assumptions have been
mentioned in the discussion of variables: investment is driven by loss of relative knowledge stock,
expropriation is from a single firm, and firms do not migrate either geographically or technically.
These are simplifying assumptions that may be relaxed in subsequent analyses.
24
3.3.2 Simulation Dynamics
The simulation evaluates an industry of 100 firms random uniformly distributed in physical and
technical space. Firms are endowed with initial knowledge stocks that are random normally
distributed. Each firm’s knowledge stock is updated in each period t, for both creation Cit
(equation 1) and expropriation Eit, (equation 2):
K
it 1
 K C  E
it
it
it
(3)
The simulation is repeated for 50 periods, or until knowledge growth ceases. Frequently
knowledge growth does not cease after 50 periods, but we believe two and a half generations is a
duration consistent with the assumption that growth is driven by the creation/diffusion process
rather than by some external shock. The entire model as described here and in the foregoing
section is depicted in the flow diagram in Figure 1.
Each simulation is seeded with a set of initial conditions. The initial conditions that the
experimenter controls are the density of the geographic and technical space and heterophily of
firms’ knowledge endowments. Population density is manipulated through specification of the
geography/technology space. The nominal value for each is length 10. Thus, firms are populated
in a 10  10 lattice. Heterophily is manipulated through specification of the standard deviation of
firm knowledge. The nominal value for  is 500, with  of 2000 knowledge units (= 0.25 In
addition to the experimental control of the initial conditions, randomness is introduced by the
simulation’s draws for each firm’s location, Gi and Ti, and initial knowledge, Ki.
3.4 Testing
There are two types of tests of the simulation. Validation testing to ensure simulation integrity
and hypothesis testing to conduct the crucial experiment These are each discussed below.
25
3.4.1 Validation
Validation requires that the simulation is well behaved and matches the empirical regularities it
attempts to capture (Table 3). We test the basic function of the simulation by running a baseline.
The baseline consists of a simulation seeded with the nominal values of each parameter as outlined
above (technical and geographic space = 10  10, firm knowledge endowments are drawn from a
population with = 0.25with causal ambiguity in both creation and expropriation (are nonzero))We examine single runs of the nominal case to verify the integrity of the growth and
convergence paths.
Next we examine that the simulation exhibits density dependence and heterophily effects. We
test sensitivity to density by distributing the initial population of firms in technical and geographic
space of varying density from 0.25 firms per unit area (Gi = Ti, = 20, so 100 firms are populated in
a space of 400 square units) to 8.0 firms per unit area (Gi = Ti, = 3.53, so 100 firms are populated
in a space of 12 square units). We test sensitivity to initial heterophily by varying the initial
dispersion of population knowledge from = 62.5 (0.3125) to = 1500 (0.75 ). Tests of
density dependence and heterophily effects are based on 100 runs for each specification of initial
conditions.
3.4.2 Crucial experiments
We conduct the crucial experiment of the opposing economics and sociology null hypotheses
by examining shares of knowledge after 50 periods (or after reaching equilibrium, whichever
occurs sooner) under a range of conditions. The range of conditions includes the validation cases
as well as a full complement of interactive cases. The interactive cases combine three levels of
density from validation with four levels heterophily from validation. Again, results for each case
are based on 100 runs for each specification of initial conditions.
26
If knowledge amounts held by all firms in the lattice are equal after 50 periods (defined as zero
variance of knowledge shares across firms), then economics is correct that knowledge flows
freely—and therefore comes to an equilibrium of equal shares. If, however, there is variance after
a reasonable time for the system to achieve equilibrium—defined as some firms retaining more
knowledge than others—then sociology is correct that knowledge is friction-laden—some firms
can keep other firms from expropriating what they have.
Since the ultimate goal of both fields is maximum knowledge growth, and the null hypotheses
are merely beliefs fueling prescriptions to achieve that end, an alternative crucial experiment
examines the prescriptions. Here we compare the relative impact of expropriation—diffusion—
mechanisms (sociological prescription) and creation—incentive—mechanisms (economic
prescription) on knowledge growth. We do so by alternately deleting each mechanism from the
baseline, to examine its marginal contribution to knowledge growth.
4. RESULTS
4.1 Validation
Validation requires that the simulation is well behaved and matches the empirical regularities it
attempts to capture (Table 3).
4.1.1 Baseline
The first such validation is a functional test of a baseline with moderate density (1 firm per unit
area), and moderate heterophily (= .25). Figure 2 presents results for a single run of the
baseline simulation. The results indicate three things of interest. First, total industry knowledge
grows by a factor of 10 over the 50 periods (an annual growth rate of 4.7%). While 4.7% growth
is on the high side for real GDP growth (a plausible correlate for knowledge growth), it is within a
reasonable range. Second, the growth while episodic, follows a logistic profile—growing slowly
27
at first, then more rapidly, before beginning to saturate. Finally, while there are outliers, there is a
general trend toward convergence (50% of firms hold 0.5% market share). Examination of single
runs over the parameter space indicate that the simulation is similarly well-behaved, thus we
proceed with formal validation.
4.1.2 Density Dependence
The main behaviors not explicitly designed into the simulation that it should exhibit are density
dependence and heterophily effects. We validate the effects of density, by running simulations
over a range of densities, with all other input conditions held at their nominal values. Comparison
of these results indicates that the simulation behaves according to the empirical regularities.
Figure 3 shows that knowledge grows more rapidly as industry density increases. Industry
knowledge grows at an annual rate of 1.5% in the low density case of .25 firms per unit area. In
contrast it grows at an annual rate of 57% for the high density case of 8 firms per unit area.
Moreover, the relationship between growth and density is monotonic, as we expect. Thus the
simulation appears to have captured density dependence.
4.1.3 Heterophily
We validate another form of “proximity”—one in which proximity is defined by the amount of
knowledge (initial share heterophily), rather than by the type of knowledge (technical distance).
For example, even though all firms in the pharmaceutical industry utilize the same technical
knowledge, some firms invest more heavily in R&D, and thus have more knowledge (and greater
knowledge share). While there is the issue of requisite level of knowledge (similar to absorptive
capacity), we do not model it in the simulation. The main effect of share heterophily in the
simulation is that it increases the tension of one firm to extract knowledge from another firm, that
28
is, the “knowledge differential,” Kij, between firms. As the population becomes more
heterophilous, the expected value of Kij, measuring the tendency toward expropriation, increases.
We validate the effects of heterophily, by running simulations over a range of initial share
dispersions, holding all other input conditions at their nominal values. Comparison of these results
indicates that the simulation behaves according to the empirical regularities. Figure 4a shows that
knowledge grows more rapidly as initial dispersion increases. Industry knowledge grows at an
annual rate of 3.0 % in the low heterophily case of = 62.5 (= 0.3125). In contrast it grows at
an annual rate of 9.2 % for the high heterophily case of = 1500 (= 0.75). Moreover, the
relationship between growth and density is monotonic, as we expect. Thus the simulation appears
to have captured heterophily effects.
Note that while initial heterophily has an impact on growth, its effect is small relative to
density, and it exhibits diminishing returns. Increases in initial heterophily beyond = 750 ( =
0.375) have little effect on growth. This is likely due to the fact that the dynamic process itself
creates and destroys heterophily, thus the initial heterophily loses its significance except in
extreme cases.
4.1.4 Interactive Cases
As a final validation we examine the interactive effects of density and heterophily. We run
simulations that simultaneously vary density and heterophily. This test goes beyond validation in
that the empirical regularities have no prediction regarding the interaction. Figure 5 indicates that
density is the dominant factor affecting knowledge growth. This is consistent with the findings
from the separate tests of density and heterophily. In fact it appears that variance in growth
attributed to heterophily is within the range of noise for the simulation.
29
4.1.5 Validation Summary
The simulation design, the baseline results, as well as the combined results for density and
heterophily tests, provide some confidence that we have developed a simulation that at least to a
first approximation captures the empirical regularities of real world knowledge flow. Given
confidence that the simulation represents the real world, we can proceed with the crucial
experiments.
4.2 Crucial Experiments
4.2.1 Crucial Experiment of the Null Hypothesis
We conduct a crucial experiment of the null hypothesis by examining final shares of the
knowledge stocks for each of the conditions tested under simulation. These results are given in
Figure 6. The results indicate that for ALL conditions, the knowledge stock fails to converge to an
equilibrium of equal shares. This result supports the sociology null hypothesis in that the
knowledge appears to exhibit friction—firms can keep other firms from expropriating all their
knowledge. However, the prior results support the economics null hypothesis in that knowledge is
clearly flowing among firms at a reasonable pace (as evidenced by its growth). This “paradox” of
sorts may explain the persistence of the opposing null hypotheses.
Beyond the basic result that shares fail to converge, there is value in examining the relative
convergence under the various conditions. Figure 6a examines convergence across density; Figure
6b examines convergence across initial heterophily, Figure 6c examines convergence for the
interactive cases. Each figure depicts the terminal dispersion (expressed as the standard deviation)
of the shares of knowledge held by firms after 50 periods. In all cases the mean share after 50
periods was the expected value of 1% (total stock divided by 100 firms).
30
Figure 6a indicates that shares are more likely to converge under low density. While we might
have expected the opposite result—high density/close proximity leading to wholesale imitation, it
appears that what is driving behavior in close proximity is something more complex. Since
knowledge flows so freely in close proximity (less loss over distance), shares change more rapidly,
thereby increasing the pressure to create. This model interpretation is supported by theoretical
arguments and empirical evidence regarding increased innovation in coevolutionary pockets, such
as Silicon Valley, where there are strong proximity effects (Porter 1990).
Figure 6b indicates that heterophily, as we have defined it (initial differences in knowledge held
by firms), operates inversely to density. In some sense, both density and heterophily are capturing
“closeness”. Density captures closeness in physical space and type of knowledge, heterophily
captures closeness in the amount of knowledge. While Figure 6a indicated that closeness (in type
of knowledge) prevented convergence, Figure 6b indicates that closeness (in amount of
knowledge) facilitates convergence. It appears that when firms are close in the amount of
knowledge there is little opportunity to gain from expropriation, thus there is little opportunity for
consequent share changes that would stimulate creation. Figure 6c seems to indicate that density
effects dominate heterophily effects.
The basic result of the crucial test of the null hypothesis still holds—knowledge stock fails to
converge to an equilibrium of equal shares—supporting the sociology null. However, knowledge
is clearly flowing among firms at a reasonable pace (as evidenced by its growth)—supporting the
economics null. Given the equivocal results, it becomes more important to conduct the
comparative test of the two fields’ opposing prescriptions for knowledge growth. We do that next.
31
4.2.2 Comparative test of prescribed growth mechanisms
The baseline simulation incorporates both fields’ prescriptions for growth—the economics
prescription of endorsing incentives for firm investment in knowledge creation, and the sociology
prescription of endorsing mechanisms that diffuse knowledge more rapidly. The economics
prescription is embodied in the creation mechanism; the sociological prescription is embodied in
the expropriation mechanism. We conduct a comparative test of the two mechanisms by
examining the marginal effects of deleting each prescribed growth mechanism relative to the
baseline. The test reveals that expropriation (the sociology prescription) is more effective in
achieving industry knowledge growth than is creation (the economics prescription), given the way
we have modeled each. A baseline simulation with both mechanisms (without causal ambiguity in
either mechanism) yields annual knowledge growth of 29.1%. Deleting the creation mechanism
(leaving only expropriation) yields 14.6% growth; deleting the expropriation mechanism (leaving
only creation) yields only 8.1% growth (Figure 5). Given a goal of maximum knowledge growth,
there is some support for the prescription of expropriation. Note however, that the knowledge that
is “growing” with expropriation is the total knowledge held by firms, rather than new knowledge
(unless we believe, as sociology of science has, that new knowledge is inevitable from widespread
diffusion of existing knowledge).
The most significant results in these tests are their magnitudes relative to the baseline. A
baseline that incorporates both the economics and sociology mechanisms, but holds everything
else constant, yields over twice the annual growth of either mechanism in isolation (and more than
the sum of the two mechanisms by themselves). The higher growth from interactively applying
both mechanisms (as in the baseline configuration) suggests that it is possible that there is an
optimal combination of expropriation and creation that maximizes long term growth.
32
5. DISCUSSION
Our goal in this study is to reconcile the competing null hypotheses of sociology and economics
with respect to knowledge flow and knowledge growth—sociology assumes that knowledge flow
(diffusion) is highly viscous whereas economics assumes knowledge flows too easily and therefore
discourages firms from investing in its creation. The concern is to obviate the potential problem
that the two fields’ prescriptions might cancel one another out. Our vehicle for reconciliation is a
simulation of knowledge flow that embodies empirical regularities emerging from empirical
studies in both fields (as well as from the integrative field, management of technology). The
empirical regularities themselves are interesting because they are remarkably similar across the
fields despite their dissimilar data bases.
Our simulation results provide some insight into why the competing perspectives persist despite
the fact that they appear countervailing in the respective economics and sociology literatures. The
baseline simulation reveals that knowledge flows fluidly (supporting the economics null
hypothesis), but that such flow does not lead to an equilibrium of homogenous firms with zero
growth (supporting the sociology null hypothesis). Thus each field is partially correct.
We probe these findings further by examining the two fields’ prescriptions for knowledge
growth—sociology’s diffusion (expropriation) and economics’ creation. Because the prescriptions
stem from opposing hypotheses regarding knowledge flow one might suspect they too oppose one
another. However, our results suggest just the opposite. Rather than canceling one another, we
find that the combination of both mechanisms generates more than twice the growth of either
mechanism in isolation. This is a possible explanation for why the opposing null hypothesis have
persisted. Each field assumes the presence of the other field’s mechanism, and thus focuses on the
remaining challenge.
33
The reason the two mechanisms are mutually reinforcing is that each becomes exhausted in
isolation. Expropriation relies on heterophily for knowledge growth, but each time a firm’s
knowledge grows, the gap between its knowledge and that of the host firm closes. Ultimately,
expropriation consumes all heterophily, leaving no suitable host firms from which to expropriate
knowledge. However, each expropriation event leads to a change in all firms’ shares (either
directly or by increasing the total knowledge stock, and therefore the share of any firm that has not
gained knowledge). These share changes threaten firms with lost share and thereby stimulate
creation. This creation then produces additional knowledge and heterophily to fuel further
expropriation as well as creation. Thus, integration of the fields of economics and sociology
seems to point to a growth solution that is superior to either field’s isolated solution. The
economics prescription augments the dynamics the sociologists point to and the sociology
prescription does the same for the dynamics concerning economists.
Our results are necessarily sensitive to our particular implementation of the empirical
regularities. In particular, we chose naïve expropriation (random choice of a single host). Our
results would likely change if we increase the number of hosts or the manner in which they are
selected. Similarly we choose threat induced creation (firms invest when their share of industry
knowledge decreases). An alternative implementation is creation driven by capacity (size/profits).
This too will affect our results. Other conditions also could be delineated.
We began by translating a set of stylized facts into nine principles comprising a theory about
knowledge flow dynamics. Through the use of a computational model we have taken a seemingly
disparate set of stylized facts and principles stemming from decades of empirical research and
shown that a constructive integration is possible. Our integration of the various linear and
nonlinear principles suggests a way toward reconciling the contrary economics and sociology
34
perspectives regarding knowledge flow dynamics. Even though their null hypotheses about
knowledge flows are diametrically opposed, the prescriptions from each field actually complement
each other. We find that growth prescriptions taking advantage of both perspectives will dominate
those of either field in isolation.
Though our language has focussed on firms and industries, the empirical regularities indicate
that knowledge phenomena are remarkably similar across several levels of analysis. Thus we think
that the insights here, once confirmed, may be generalizable to phenomena described by all three
literatures: diffusion among individuals, organizational knowledge creation and acquisition, and
the use of knowledge at industry levels of competition among firms.
We have demonstrated that a computational approach to formalized modeling can play a
constructive role in organization science. In this instance we have focused on testing experimental
adequacy (McKelvey 1999c)—using a model to test the causal nuances among variables that are
essential to predictive theory. Given the number of stylized facts—nine—and their mixed linearity
and nonlinearity, a computational model is particularly well suited to the phenomena. This said,
however, the problem of ontological adequacy remains. Though the constituent “model
structures” (McKelvey 1999c)—that is, the structural elements of our model such as the lattice,
density dependence and proximity effects, and the rules governing agent behaviors in our model—
rest on the empirical regularities we discovered in the literature, the integrated behavior of the
elements depicted in our model have not been confirmed by real world behavior, or even via
human experiments. We do not know for a fact that real world outcomes would appear as
predicted by our simulation. Further research in this regard is called for.
Knowledge dynamics and knowledge management are increasingly important in organization
science, management, and strategy (Teece 1987; Leonard-Barton 1995; Ashkenas et al. 1995;
35
Myers 1996; Boisot 1998). Seemingly “old” sociology is has more to say about knowledge
dynamics than “new” sociology. And it is clear from our Table 2 that old sociology matches up
very well with much more recent work in economics. This suggests that Pfeffer’s (1993, 1995)
worries about the inroads of economics are well taken but irrelevant. As consumers of stylized
facts, we simply scoured them up from wherever we could find them—in this case old sociology
and new economics. While new sociology might be interesting to sociologists, it is a distraction
that increasingly makes much of that field irrelevant to organization science and strategy.
Scientists select facts from wherever, as we have done. If economists supply facts and sociologists
do not…… It does not take a rocket scientist to figure out why cites of economists are growing.
As our model demonstrates, economics is winning these days because it creates and diffuses and
doesn’t worry about expropriation. New sociology does not create and thus does not have to worry
about expropriation—there is nothing there to expropriate—as we discovered.
36
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46
Table 1. Contrasting the perspectives
Goal
Perspective
Unit of analysis
Unit of innovation
Relevant
environment
Diffusion premise
Incentive premise
Sense of progress
Stimulus to
innovation
The innovator
Ownership
Sociology of Science
How and why does knowledge
grow?
Positive
Scientist
New knowledge
Scientific field--Society
Technology Economics
How to increase innovation
(to thereby economic growth)
Normative
Firm
Invention
Industry--Economy
Necessary to facilitate growth of
knowledge
Scientists intrinsically motivated
(seek recognition or priority)
Cumulativism (incremental)
Mechanistic determinism
Response to necessity (market
pull)
Foci of interest determined by
social forces
Many inventors trying to solve
problem, each contributing small
piece
Priority rights
Suppresses incentives to innovate
(by reducing appropriability)
Innovation requires incentives
(appropriability)
Transcendentalism (episodic)
Mystic determinism
Arises from immanent
development of science
(technology push)
Great man, act of insight
Property rights
47
Table 2. Summary of empirical regularities across levels of analysis and academic fields
LEVEL OF ANALYSIS
PATERNS of GROWTH
Logistic growth of
innovation
Individual
(Tarde 1903)
(Rogers 1962; Rogers
1995)
Organization
Episodic growth
Bifurcation
bi-modal equilibria
(Cohen and Levinthal
1990)
(Madsen )
(Knott and Bryce 1998)
(Jewkes, D. et al. 1958;
Hamberg 1963; Cohen
and Levin 1989)
Diminishing returns
INCENTIVES
CAPACITY TO INNOVATE
CAUSAL FACTORS
Density dependence
Wealth effects
Sharing/spillovers
technical proximity
/homophily
heterophily
/external ties
geographic
proximity
Industry/Field
(Mansfield 1958)
(Price 1961;1963)
(Foster 1986)
(Crane 1972)
(Holton 1962)
(Abernathy and
Utterback 1978)
(Anderson and
Tushman 1990)
Country/Economy
(Schumpeter 1934;
Schumpeter 1942)
(Romer 1986)
(Price 1961;1963)
(Scherer 1965; Scott
1984; Levin, Cohen et
al. 1985)
(Price 1961; 1963;
Hagstrom 1965)
(Rogers 1962; 1995)
(Rogers 1962; 1995)
(Coleman, Katz et al.
1966)
(Price 1961; 1963)
(Rogers 1962; 1995)
Cohen, 1989 #26
(Lieberman 1987)
(Jaffe 1986; Jaffe 1993;
Adams and Jaffe 1996)
(Price 1961; 1963)
(Burt 1997)
(Crane 1972)
(Hagerstrand 1952)
(Allen 1977)
(Darr, Argote et al.
1997)
(Jaffe 1986; 1993;
Adams and Jaffe 1996)
(Frost 1997)
Economics literature
Sociology literature
Management literature
Key to Phenomena:
Logistic growth-Typically growth follows an S-curve under nominal conditions (slow initially, acceleration, then
deceleration toward saturation).
Episodic growth-Knowledge growth exhibits periods of incremental growth interspersed with discontinuities. While
the discontinuity conditions are not well defined, they are most likely when fields shift technologies
Bifurcation-Under some conditions (not well defined) populations segregate into clusters of high knowledge and low
knowledge
Diminishing returns-At some point, additional investments are less effective in producing new knowledge
Density dependence-Knowledge growth appears to be an n-shaped function of density: with two few firms, knowledge
grows slowly and appears linear (rather than logistic) because firms have little to learn from one another, and pose
little threat to one another. Similarly with too many firms, firms have little incentive to produce new knowledge
(because of diminishing returns)
Wealth effects-Entities that are well-endowed make greater investments in knowledge
Technical proximity-Entities that are similar are more likely to share knowledge
Heterophily-However, if entities are too similar (i.e., they have identical knowledge) there is nothing to share
Geographic proximity-Knowledge is more readily shared by entities in close physical proximity
48
Table 3. Treatment of each of the empirical regularities in the simulation
Empirical regularity
Treatment
Logistic growth
Tested in validation: Kt should take this form under the baseline
Episodic growth
Defer to follow-on: Requires multi-population study
Bi-modal equilibria
Defer to follow-on: Should emerge under some conditions (not yet
known)
Built into model design: Model assumes firms invest sufficiently to
overcome diminishing returns
Tested in validation: Vary technical and geographic space
parametrically, expect higher growth in denser space
Built into model design: Firms with greater share of knowledge
create more absolute knowledge on average
Built into model design: Built into design of expropriation
mechanism-expropriation inverse function of distance
Tested in validation: Vary distribution of knowledge endowment
parametrically, expect higher growth with greater heterophily
Diminishing returns
Density dependence
Wealth effect
Proximity effects
Heterophily
49
Figure 1. Simulation Flow Diagram
Birth of
population
i=1 to n
Gi=Ti=[25,25],
Ti= B[0,t]
Ki = N()
Create new knowledge
Cit =  [(K i(t-1) /  Ki(t-1)) – (K it /  K it)] * ( K it)
Appropriate existing knowledge
Eit =  [(Kjt- Kit) / [(gij2 + tij2)]
Update stocks
Kit+1 = Kit+ Eit +
Cit
Yes
> 50 periods?
Plot distribution
of knowledge
shares
STOP
Plot distribution
of knowledge
shares
STOP
No
Share
convergence?
50
Figure 2. Results from single run to show growth and share evolution
Figure 2a. Growth in knowledge stock
Knowledge stock
Nominal Case
2.50E+06
2.00E+06
1.50E+06
1.00E+06
5.00E+05
0.00E+00
0
20
40
Years/Periods
Figure 2b. Beginning histogram of knowledge shares
35
30
25
20
15
10
5
0.0015625
0.0046875
0.0078125
0.0109375
0.0140625
0.0171875
0.0203125
0.0234375
0.0265625
0.0296875
0.0328125
0.0359375
0.0390625
0.0421875
0.0453125
0.0484375
0.0515625
0.0546875
0.0578125
0.0609375
0.0640625
0.0671875
0.0703125
0.0734375
0.0765625
0.0796875
0.0828125
0.0859375
0.0890625
0.0921875
0.0953125
0.0984375
Figure 2c. Ending histogram of knowledge shares
50
40
30
20
10
0.0015625
0.0046875
0.0078125
0.0109375
0.0140625
0.0171875
0.0203125
0.0234375
0.0265625
0.0296875
0.0328125
0.0359375
0.0390625
0.0421875
0.0453125
0.0484375
0.0515625
0.0546875
0.0578125
0.0609375
0.0640625
0.0671875
0.0703125
0.0734375
0.0765625
0.0796875
0.0828125
0.0859375
0.0890625
0.0921875
0.0953125
0.0984375
60
51
Annual knowledge growth
Figure 3. Effects of density on knowledge growth
0.60
0.50
0.40
mean
0.30
std dev
0.20
0.10
0.00
0
2
4
6
Density (firms per unit area)
8
10
52
Annual knowledge
growth
Figure 4. Effects of heterogeneity on growth
0.10
0.08
0.06
0.04
mean
stdev
0.02
0.00
0
500
1000
1500
2000
Dispersion in initial knowledge (mean=2000)
53
Mean annual knowledge growth
Figure 5. Interactive effects on knowledge growth
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
h=500
h=250
h=1500
0
5
Firms per square area
10
54
Figure 6a. Effects of density on share convergence*
Share dispersion after 50
periods
*Note mean share = .01
0.035
0.030
0.025
0.020
0.015
mean
std dev
0.010
0.005
0.000
0
5
10
Density (firms per unit area)
Share Dispersion
after 50 Periods
Figure 6b. Effects of heterogeneity on
convergence
0.030
0.020
mean
0.010
stdev
0.000
0
500
1000
1500
2000
Initial dispersion in firm knowledge
Final Dispersion (standard
deviation) in knowledge shares
Figure 6c. Interactive effects on share convergence
0.04
0.03
h=250
h=500
0.02
h=1000
h=1500
0.01
0
0
5
Firms per square area
10
55
Mean annual growth
Figure 7a. Effects of prescriptions on growth
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Unambiguous
Expropriation
Ambiguous
Expropriation
No
Expropriation
Unambig
Causal
ambiguity
None
Creation conditions
Figure 7b. Effects of prescriptions on convergence
Mean sigma share
0.05
0.04
0.03
Unambiguous
Expropriation
0.02
Ambiguous
Expropriation
0.01
No
Expropriation
0.00
Unambig
Causal
ambiguity
Creation conditions
None