A Theory of Knowledge Growth

A Theory of Knowledge Growth Network analysis of US patents, 1975–1999 Gianluca Carnabuci

UNIVERSITEIT

VAN

AMSTERDAM

A THEORY OF KNOWLEDGE GROWTH Network analysis of US patents, 1975-1999

Gianluca Carnabuci

Lay-out: Gianluca Carnabuci, Amsterdam Coverdesign: René Staelenberg, Amsterdam

ISBN 90 5629 403 2 NUR 741, 781

© Gianluca Carnabuci / Vossiuspers UvA, 2005 Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd, opgeslagen in een geautomatiseerd gegevensbestand, of openbaar gemaakt, in enige vorm of op enige wijze, hetzij elektronisch, mechanisch, door fotokopieën, opnamen of enige andere manier, zonder voorafgaande schriftelijke toestemming van de uitgever. Voorzover het maken van kopieën uit deze uitgave is toegestaan op grond van artikel 16B Auteurswet 1912 jº het Besluit van 20 juni 1974, Stb. 351, zoals gewijzigd bij het Besluit van 23 augustus 1985, Stb. 471 en artikel 17 Auteurswet 1912, dient men de daarvoor wettelijk verschuldigde vergoedingen te voldoen aan de Stichting Reprorecht (Postbus 3051, 2130 KB Hoofddorp). Voor het overnemen van gedeelte(n) uit deze uitgave in bloemlezingen, readers en andere compilatiewerken (artikel 16 Auteurswet 1912) dient men zich tot de uitgever te wenden. All rights reserved. Without limiting the rights under copyright reserved above, no part of this book may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the written permission of both the copyright owner and the author of the book. This research was supported by the Dutch Organization for Scientific Research, NWO grant #401-01-098.

A THEORY OF KNOWLEDGE GROWTH Network analysis of US patents, 1975-1999

ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. mr. P.F. van der Heijden ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op dinsdag 18 oktober 2005, te 10.00 uur door Gianluca Carnabuci Geboren te La Spezia, Italië

Promotiecommissie: Promotoren: prof. dr. J. Visser prof. dr. W. van Rossum Co-promotor: dr. J.P. Bruggeman Overige leden: prof. dr. J. Podolny, Harvard University prof. dr. F. N. Stokman, Rijksuniversiteit Groningen prof. dr. B. Verspagen, Technische Universiteit Eindhoven prof. dr. B. Kittel, Universiteit van Amsterdam prof. dr. R. J. Mokken, Universiteit van Amsterdam Faculteit:

Faculteit der Maatschappij- en Gedragswetenschappen

TABLE OF CONTENTS

1.

ACKNOWLEDGEMENTS

ix

INTRODUCTION

1

THE NETWORK STRUCTURE OF KNOWLEDGE GROWTH

Abstract I. The self-reinforcing growth of codified and accessible knowledge II. Public knowledge and economic growth III. Knowledge production function IV. Invention as knowledge hybridization V. The network structure of knowledge growth 2.

5 6 8 9 11 13

PATENT-BASED INDICATORS AND THE ANALYSIS OF KNOWLEDGE GROWTH

Abstract I. What is a patent? II. Knowledge spillovers III. Knowledge output IV. Knowledge domains V. The network model of knowledge growth VI. Conclusions Appendix 3.

18 18 20 22 25 26 28 29

NBER PATENT AND PATENT CITATIONS DATA

Abstract I. Patent production II. Patent citations II. I. Citations made and received II. II. Citation lags III. The NBER data as indicators of knowledge dynamics III. I. Time of patent grant

31 32 37 37 40 43 44

vi

Table of contents III. II. Area of technology III. III. Data truncation III. III. I. Comparability of truncated data III. III. II. Data truncation and measurement quality III. IV. Network evolution

4.

CHARACTERIZING THE NETWORK STRUCTURE OF US-PATENTED KNOWLEDGE

Abstract I. Network components II. Network visualization II. I. Weak ties and backbone structure II. II. The evolution of the ICT cluster III. Small-world analysis IV. Triadic census V. Conclusions 5.

49 50 51 52 57 60 63 66

THE CONCENTRATION OF KNOWLEDGE PROGRESS

Abstract I. Enduring trait or transient phase? I. I. Towards a heavy-tail distribution? Gibrat’s model I. I. I. I. I. II. Testing for cumulative advantage I. II. Converging to a common size? I. III. Domains’ steady-state sizes II. Explaining the concentration of knowledge progress III. Conclusions 6.

45 45 45 46 48

67 70 70 71 72 75 76 79 81

SPECIALIZATION AND BROKERAGE: A THEORY OF KNOWLEDGE GROWTH

Abstract I. A network representation of specialization and brokerage II. Creativity, specialization and brokerage III. Hypotheses

85 86 89 93

Table of contents

vii

IV. Statistical model V. Analysis VI. Conclusions Appendix

94 97 102 103

7.

BUILDING UPON THE FOUNDATIONS

Abstract I. Long-term effects of specialization and brokerage I. I. Between-effects estimation I. II. Level effects II. Rank re-ordering of domains’ sizes III. Risk, specialization, and brokerage IV. Niche overlap and the creative potential of structural holes V. Conclusions 8.

CONCLUSIONS

I. II. III. IV. V.

Abstract Findings Contributions to science Policy and investment implications Future research Conclusions

105 104 106 108 111 114 115 121

123 124 126 128 129 132

BIBLIOGRAPHY

133

SAMENVATTING (Summary in Dutch)

145

ACKNOWLEDGEMENTS PhD students have a tendency to take home the many difficulties, anxieties, and obsessive questions that arise in pursuit of their research project. Before introducing my thesis, I wish to thank several people who continually helped me to distinguish between my PhD project and my life at large. I want to begin by expressing my deepest gratitude to my now-wife, Elisabetta, for showing me what really matters while still supporting me wholeheartedly in my academic endeavours. And I want to thank our newborn son, Tommaso, for making life a lot more interesting while unrestrainedly encumbering my academic endeavours. I am also grateful to the friends I was lucky enough to encounter during my PhD trajectory. Dimitri, whom I met for the first time at his breakfast table after spending the night out dancing with his girlfriend, Iris, and with whom I immediately and unmistakably felt of one mind. Jonathan, whose generosity and honesty forced me to try and become a more complete person. Davide, who is one of those rare people who never demands anything from a friend, while deserving all a friend can give. Eelke, whose spontaneity and instinctive altruism I deeply admire. Jeff Prins, whose understanding of (Dutch) people helped me appreciate many otherwise bothersome aspects of my life in the Netherlands. And Erik, Jeff Powell, Elisa, Mattijs, Esther, Nicole, my colleagues at the ASSR and at the ICS, and my numerous flatmates at the Essex Summer School 2001, who made my PhD venture much more meaningful and pleasurable. A special thank you also goes to my parents, for always granting me enthusiastic and unconditional support. A number of people helped me by generously sharing their scientific knowledge, creativity, and expertise. First of all, there is my co-supervisor, Jeroen Bruggeman. Not only did Jeroen shape my PhD thesis, he shaped me as a social scientist as well. I want to particularly thank him for always being there when I needed his guidance, for educating my instinctive dislike of “bla-bla social sciences”, for correcting and improving my sloppy English, and for showing me that science and salsa dancing, and in general intellectual rigor and fun, go together superbly. Our weekly Friday lunch conversations were well-balanced blends of science and life matters, and I will miss them very much. I am also

x

Acknowledgements

deeply indebted to professor Willem Saris, for having spent a long time explaining to me the ins and outs of Structural Equation Modelling for panel data. Likewise, I want to thank professor Bernhard Kittel for introducing me to STATA and the econometrics of panel data. I am also grateful to the ASSR for accepting me as one of their PhD students, and to the ICS for allowing me in their doctoral training program. Being simultaneously part of two such excellent, yet dissimilar, research schools was extraordinarily enriching and stimulating. Finally, I want to thank my supervisors, professor Jelle Visser and professor Wouter van Rossum, for granting me the freedom to carry out my PhD in the manner I felt was best.

INTRODUCTION In its struggle against misery and subjugation to uncontrollable forces, humanity acquired extensive knowledge of how to manipulate nature. This progress would have not been possible without stocking knowledge in repositories other than biological memory. Books and other media augmented knowledge preservation and diffusion, as well as the accumulation of new ideas upon existing ones. Enhanced by increasingly powerful information and communication technologies, the stock of human knowledge exhibited an unprecedented expansion in the recent history of Western societies. The electricity grid, the combustion engine, the penicillin, the transistor, the integrated circuit, the polymerase chain reaction for replicating DNA, are but a few examples of the progress made in just the last two hundred years. This progress enhanced the transformation of pre-industrial societies into the globalized First World, leading to a formidable improvement in living standards (Mokyr 2002). Unmistakably, the knowledge generated in the West did not generally improve people’s material conditions. Rather, many regions have been suffering from the power imbalances this localized progress induced. At this point, however, there is wide consensus that also for underdeveloped economies to catch up, new and better technologies are essential. Similarly, and contrary to prevailing patterns in the history of industrialization, only by increasing our knowledge of how resources can be better utilized, we can hope for an environmentally sustainable system of economic production (NewellMcGloughlin 1999). At present, the dynamics by which new ideas accumulate upon existing ones, thereby expanding the stock of human knowledge, are not well understood. This ignorance hinders our ability to enhance and funnel knowledge growth, as much as it hampers the development of social and economic theories. The objective of this PhD thesis is to contribute to covering this gap by formulating, formalizing, and testing a theory of knowledge growth. Ultimately, knowledge growth is always driven by the same mechanism – human ingenuity – and by the same resource – existing knowledge. Starting out there, my ambition in the following

2

Introduction

chapters is to put forward a theory applicable across different empirical settings and levels of analysis. The scope of empirical studies is necessarily limited, though. Throughout this thesis, I focus my analysis on the stock of knowledge patented in the United States between 1975 and 1999, to explain why certain domains of knowledge advance faster than others. OVERVIEW My thesis proceeds as follows. In Chapter 1, I propose that the dynamics of knowledge growth can be modeled network-analytically. My approach makes it possible to describe the network of interdependencies connecting domains of human knowledge; and, in turn, to explain how the growth of each domain is affected by its embeddedness in this network. Having detailed out my network model, I conclude the chapter by formulating the research question overarching this thesis. In Chapter 2, I explain why and how the proposed network model of knowledge growth can be instantiated by patent data. These data are interesting because they describe in detail a large and important part of the technological knowledge generated in our recent history. For that reason, they have been widely used in econometric studies as empirical indicators of knowledge domains, knowledge spillovers, and knowledge output. In this thesis, I employ them to indicate all three concepts. In Chapter 3, I describe statistically the dataset used throughout the thesis, which contains information on all knowledge patented in the largest international patent office worldwide – the US Patent and Trademark Office (USPTO) – between 1975 and 1999. I conclude the chapter with a discussion of potentially problematic issues regarding the use of the USPTO data as indicators of knowledge dynamics, and solutions thereof. In Chapter 4, I instantiate the data in my network model of knowledge growth, and I characterize them network-analytically. I first analyze the entire observation period as one single network. Then, to capture its changing structure, I model the data as a time series of networks.

Introduction

3

To explain the observation that progress in US-patented knowledge is disproportionably concentrated among larger domains, in Chapter 5 I propose and test the hypothesis that an endogenous dynamics of knowledge growth – self-hybridization – systematically magnifies a domain’s inherent growth potential. In Chapter 6, I put forward the foundations of a dynamic theory of knowledge growth. My argument is that the advancement of knowledge is keyed to a dialectical relationship between knowledge specialization and knowledge brokerage. I propose that specialization and brokerage are opposite poles of one conceptual continuum, which I operationalize network-analytically as the structural holes (Burt 1992) contained within a domain’s niche of knowledge sources. Further, I argue that specialization yields efficiency in knowledge production, while brokerage yields new potential for knowledge growth. From these premises I derive three hypotheses on the effects of specialization and brokerage on domains’ growth rates, which I subsequently test. In Chapter 7, I build upon my theory of knowledge growth by deriving and testing four qualifying hypotheses. First, I argue that the effects of knowledge specialization and knowledge brokerage on domains’ growth hold in the long run as well. Second, I propose that my theory of knowledge growth also helps to explain the rank re-ordering of domains’ sizes over time. Third, I argue that knowledge specialization and knowledge brokerage have a predictable effect on the variance of domains’ growth rates, i.e. on how securely domains advance. Fourth, I posit that the knowledge productivity of a domain’s structural holes decreases with the domain’s niche overlap. In Chapter 8, I discuss the results of previous chapters and their implications for science and policy. I conclude that my proposed theory is thus far corroborated by empirical tests, and that benefits would derive from testing it on data describing knowledge growth in realms other than technology, e.g. science, and from applying it at different levels of analysis, e.g. the firm, or the State.

CHAPTER 1 THE NETWORK STRUCTURE OF KNOWLEDGE GROWTH

ABSTRACT: A large and growing stock of publicly available knowledge is a distinguishing trait of the knowledge-based economy and a necessary condition for long-term economic growth. In this chapter, I propose a network-analytical model to analyze the growth of this stock.

6

The network structure of knowledge growth

I

n recent years, the notion of knowledge-based economy has been used to indicate the increased importance of knowledge as an asset of economic production and organization in advanced economies (Bell 1973; Drucker 1993; Powell and Owen-Smith 2004). A variety of empirical phenomena testify this development. Knowledge-intensive industries have been contributing an increasing share of the total wealth generated (OECD 1996); Research & Development costs have been on the rise, and larger portions of the discoveries made by basic scientific research have resulted in technical improvements (OECD 1996); knowledge progress has transformed the dynamics of economic production and exchange in all sectors, including traditional ones (von Tunzelmann and Acha 2004); firms’ competitiveness is increasingly determined by knowledge management (Drucker 1995; Nonaka et al. 1996); the new jobs created are more knowledge-demanding than the ones that have been lost (Morris and Western 1999); returns to education have increased (Cheeseman Day and Newburger 2002); and, work is less organized within firm boundaries (Powell et al. 1996) and more within knowledge communities (Rappa and Debackere 1992). In the literature, there is consensus that the viability of the knowledge-based economy be keyed to a continually growing stock of publicly available knowledge (e.g. Eliasson 1990). The dynamics responsible for the growth of this stock, however, are still poorly understood. The goal of this chapter is to put forward a novel approach to formally represent and analyze these dynamics.

I. THE SELF-REINFORCING GROWTH OF CODIFIED AND ACCESSIBLE KNOWLEDGE The knowledge-based economy is characterized by a high degree of knowledge codification and by broadly accessible knowledge sources, and there is a reason to believe that these two features are jointly responsible for its fast and incessant knowledge expansion (Abramowitz and David 1996; Eliasson 1990; Soete 1996). Codification reduces ambiguity, and facilitates knowledge reproduction, transfer, storage, search, and interpretation; thus, codification makes possible to decouple knowledge from people, institutions, artifacts and routines, and to accumulate it into serviceable stocks (Cowan and Foray 1997). Accessibility, in turn, makes the content of these stocks available to a varied composition of ingenuities, needs, and expertise. In economic jargon, knowledge that is both

The network structure of knowledge growth

7

codified and publicly accessible is non-rival – i.e. it does not deplete with consumption – and non-excludable – i.e. it spills over to many actors. Hence, it is a public good (Arrow 1962; Romer 1986). This means that each new idea that is both codified and accessible is a possible non-consumable input for the production of multiple newer ideas and applications1, which in its turn implies that the growth of public knowledge2 is potentially self-reinforcing. Consistent with this view, substantial increases in knowledge codification and accessibility preceded the wave of technological progress initiated in western societies some two centuries ago, and regarded by some as the historical origin of the knowledge-based economy (Mokyr 2002). Noticeable examples of systematic knowledge codification carried out in those days are the compilation of technical notions in encyclopedias, the Linnaean method for identifying botanical species, and an increased use of mathematical language among scientists and engineers. At the same time, codified knowledge became more widely accessible throughout society due to the spread of alphabetization, the greater availability of cheap reading material, more efficient postal services, and a more favorable cultural and institutional atmosphere (Mokyr 2002). The body of accessible and codified technological knowledge has been growing ever since. However, due to the diffusion of powerful information and communication technologies, only in recent years has it displayed a sharp acceleration. Nowadays, all codified knowledge can be digitalized and transmitted virtually everywhere, and publicly accessible electronic networks, such as the Internet, connect an increasingly vast array of knowledge sources including books, scientific journals, and patents. In spite of the development of this “universally accessible digital library” (OECD 1996, p. 13), the characterization of knowledge as a public good has encountered opposition in the literature. Building on an intuition of Polanyi (1967), evolutionary economists and organizational scholars have argued that a 1

In Chapter 7, I will show that it is possible and useful to qualify this statement with greater precision. 2 For the sake of simplicity, in what follows I sometimes use the expression public knowledge to indicate knowledge that has the characteristics of a public good.

8

The network structure of knowledge growth

fair amount of knowledge is not, or cannot be, accurately codified (Harabi 1995; Mansfield et al. 1981). An even if it could, it could not just be utilized by everybody as an input for further knowledge production. Rather, its interpretation and elaboration would require specific and costly skills, which typically include substantial tacit knowledge (Nightingale 1998). Furthermore, a great deal of knowledge does not spill over at all into a publicly accessible stock, but is carefully kept secret within the minds or archives of its originators3 (Arundel 2001). The argument that not all knowledge is or can be a public good, however, does not collide with the argument that the accumulation of public knowledge is self-reinforcing, and that this is a key factor behind the rapid knowledge expansion characteristic of the knowledge-based economy. As I will point out in the following section, the self-reinforcing growth of public knowledge is also a necessary condition for long-term economic growth. II. PUBLIC KNOWLEDGE AND ECONOMIC GROWTH In his seminal papers (1956, 1957), Robert Solow proposed a model of economic systems that may be expressed by the following Cobb-Douglas production function4:

Y = Ae µ K α L1−α

(1)

Y is the aggregate output of an economy, K is the stock of capital, A is a constant reflecting the stock of technology, L is labor, and α is the percentage increase

µ in gross national product from a 1 % increase in capital; e , also called the Solow residual, models the rate of technological progress. Analyzing historical country data, Solow used this model to show that output growth tends to greatly outpace the weighted average increase in combined inputs. In other words, constantly technologies are invented that increase the productivity of economic systems, i.e. transform more and better output from given amounts of input. 3

Codification, in fact, may serve this purpose too, as codes can be encrypted to make knowledge incomprehensible to others. 4 The specific production function expressed by equation (1) is used only in Solow 1957, whereas the model used in Solow 1956 depends on labor-augmenting technological progress. The two models, however, are mathematically equivalent.

The network structure of knowledge growth

9

Solow’s pioneering work demonstrated that technological progress is the engine of long-term economic growth, but did not explain what sustains technological progress in the long run. So-called idea-based growth theory5 refined the Solowian approach to address specifically this issue (Jones 2004). If technology were a standard – i.e. rival and exclusive – economic good, technological progress would be declining in the long run because of resource scarcity. Hence, long-term technological progress would not be possible. In the production of technology, however, public technological knowledge is an input of primary importance, because many inventions draw on documents such as patents and scientific outlets (Romer 1993)6. And, because the growth of public knowledge is self-reinforcing, its returns tend to increase in scale, rather than decrease as with any other production factor. It follows that only a continually growing stock of publicly accessible technological knowledge can sustain long-term technological progress and, thus, long-term economic growth. In light of this, it is not surprising that economic growth remained proximate to zero for several thousand years across the globe, before it accelerated permanently in those areas and periods where technological knowledge became broadly accessible (Jones 2004). III. KNOWLEDGE PRODUCTION FUNCTION Numerous knowledge production functions have been put forward to formalize the intuition of an idea-based growth. Much like Solowian models, however, the ultimate goal of these models is to explain economic growth. Hence, rather than the growth of public knowledge, they investigate its effects. As Weitzman (1998, p. 332) notices, in these models “[n]ew ideas are simply taken to be some exogenously determined function of ‘research effort’ in the spirit of a humdrum conventional relationship between input and output”. 5

In the economics literature, this theoretical tradition is also called “New Growth theory”. The denomination “New Growth theory”, however, is broader than “ideabased growth theory”, and it includes also explanatory models that do not share the features that I refer to in what follows. 6 To say it with McCallum, this technological knowledge “is possessed by society in general and is passed on from generation to generation, in the sense that it is available to those who wish to draw upon it” (1996, p. 58)

10

The network structure of knowledge growth

A more elaborate explication of this point may facilitate the remainder of my argument. Thus, it is useful to discuss an algebraic representation of the knowledge production function proposed by Jones7. In Jones’ model, growth in the stock of technological knowledge available to an economy is determined by the following differential equation (Jones 2004):

A& t = vR At Atφ

(2)

& is the new where A is the stock of existing technological knowledge, A technological knowledge produced within a given time interval t, R A denotes investment in knowledge production, say R&D, and each R&D unit can produce v(A) new ideas at a point in time. The new knowledge that an economy is able to produce depends on the investment in R&D, R A , and on the knowledge already available to the economy, A. Parameter

φ , modeled as an exogenous constant, determines the

new knowledge generated by a unit of R&D in a given period of time, as a function of the existing stock of technological knowledge. Insofar as φ > 0, the size of publicly available knowledge favors the generation of new knowledge. This case, also known as standing on the shoulders of giants, characterizes knowledge production in the purported knowledge-based economy. The model, moreover, allows for cases in which φ < 0, describing situations of so-called fishing out. Idea-based growth theorists assume arbitrary values of

φ to derive

implications for economic growth from their models. For somebody interested in the growth of public knowledge, however,

φ is the variable to be explained.

Let us then try to grasp the concept captured by with, it is important to notice that 7

φ more precisely. To begin

φ characterizes a process that is exogenous

Although other idea-based growth models would serve equally well my objective, Jones’ has the advantage of incorporating much of the most recent theoretical and modelling developments.

The network structure of knowledge growth

11

to, i.e. independent of, the dynamics of economic production. The latter can affect the resources dedicated to advancing technological knowledge, represented by Rt in equation (2), for example by influencing the dynamics of investment in R&D; and Rt , in its turn, has an impact on the future stock of knowledge At +1 . None of these, however, affect

φ . The question then becomes:

φ governed by? The answer to this question is, again, hinted at by equation (2): φ represents the transformation of publicly accessible

what process is

& – which, in their turn, knowledge inputs, A , into knowledge outputs, A become accessible inputs for further knowledge production. More precisely, denotes the productivity of this transformation process. Alternatively,

φ

φ may be

8

conceived in terms of inter-temporal spillovers . From this perspective, existing knowledge influences the future production of knowledge. The implication is the same: the greater such spillovers, the higher the returns of new knowledge that are derived from transforming the stock of existing knowledge. IV. INVENTION AS KNOWLEDGE HYBRIDIZATION To explain φ , one needs first to explicate how existing knowledge is transformed into new knowledge. Unconstrained by modeling limitations, the descriptive literature on the knowledge advancement process emphasizes its complex and stochastic nature. One principle, however, emerges from most accounts: new ideas result from novel combinations of existing ideas. In his classic book A history of mechanical inventions Abbott Payson Usher concludes: “Invention finds its distinctive feature in the constructive assimilation of preexisting elements into new syntheses, new patterns, or new configurations…” (Usher 1929, p.11). Diamond (1997) reports that in prehistorical times knowledge on how to make “ceramics” and “wooden baskets” was combined in the invention of “pottery”. Similarly, Gutenberg’s printing press resulted from pooling several existing elements of the stock of technological knowledge of his time, including paper, metallurgy, press, ink, 8

For this reason,

φ

is also referred to as “spillovers parameter”.

12

The network structure of knowledge growth

movable types, and alphabet (Diamond 1997); the concepts of “watermill” and “sail” were creatively brought together to conceive the idea of windmill (Mokyr 1990); and, Edison’s invention of the electric light bulb combined the ideas of “electricity” and “candle” to invent what he named the “electric candle” (Weitzman 1998). On somewhat more systematic bases, research on the cognitive mechanisms of knowledge creativity points out that the novelty of creative thinking resides in the ability to envision unprecedented combinations and applications to familiar ideas (Heerwagen 2005). Moreover, a similar view is put forward in Schumpeter’s conception of entrepreneur as somebody who combines existing resources in novel ways (1976), as well as by Schmookler (1966) and Romer (1994), who compared the creation of knowledge to a reordering of existing ideas. In one of the few attempts to formalize this process mathematically, Weitzman proposed that new ideas spring out of the hybridization of existing ideas, leading to a process of recombinant knowledge growth (Weitzman 1998). A metaphor for this is the production of new plant varieties by cross-pollination of existing ones. Analogously, the generation of hybrid ideas drives the advancement of knowledge. In Weitzman’s mathematical formulation, new knowledge is produced by binary pairings of ideas from a finite set, A, representing the stock of existing knowledge. Then, the number of possible creative combinations,

Z 2 (A ) , is given by the formula:

Z2 (A ) =

A (A − 1) 2

(3)

Weitzman’s conclusion is that the advancement of technological knowledge is potentially boundless, and may only be constrained by the fact that the resources necessary to process potential new ideas (most importantly, R&D) are limited. Weitzman’s model is an important development in the direction of formally representing the relationship between existing and new knowledge. However, by modeling knowledge advancement as an unconstrained combinatorial process, it incurs three evident limitations. The first is that not all combinations of ideas

The network structure of knowledge growth

13

lead to creative applications. Moreover, even if they would, one can wander with George Akerlof if the invention of “chicken ice creams” would be of any use (cited in Jones 2004, p.3). The second limitation is that knowledge advancement is a cumulative process characterized by a high degree of path dependence (Rosenberg 1994). Accordingly, ideas are typically not combined randomly, but build upon specific trajectories (Dosi 1982; Nelson and Winter 1982)9, thereby resulting in a variety of idiosyncratic domains (Hayek 1945). This leads us to the third limitation of the model: in actuality knowledge does not grow homogeneously at the same rate. Rather, some domains expand rapidly, while others advance slowly or stagnate (Scherer 1965). In view of these shortcomings, it is not surprising that Weitzman’s claim that the production of technological knowledge is bound only by R&D constraints is at odds with empirical facts: while R&D investments in the U.S. have been persistently growing since WWII, Caballero and Jaffe (1993) have shown that the number of technological ideas hybridized has declined by one third between 1960 and 1990, leading to a significant decrease in knowledge productivity. V. THE NETWORK STRUCTURE OF KNOWLEDGE GROWTH In this section, I put forward an analytical framework aimed at retaining the principle of knowledge growth by hybridization, while overcoming the three limitations of Weitzman’s model. Rather than an abstract model of unconstrained and random knowledge hybridization, I propose to represent the dynamics of knowledge growth as a network (Strogatz 2001) of actual hybridization patterns within and between domains of knowledge. Ultimately, hybridizations and ideas are the product of human ingenuity. Hence, it is important to explicate the relationship between people’s creative acts and the unit of analysis of my network approach, i.e. the knowledge domain. Such relationship rests on the fact that creative individuals do not contribute randomly to the advancement of knowledge. Rather, they strive to advance a specific

9

Although his model did not account for path-dependence, Weitzman himself was well aware that real-world technologies advance along historically determined paths “…taken from an almost incomprehensibly vast universe of ever-branching possibilities” (Weitzman 1998, p. 357).

14

The network structure of knowledge growth

knowledge domain10 in a priority race involving a loose community of individuals and organizations sharing a cognitive and normative structure (Constant 1980; Kaufman and Baer 2004; Merton 1957a, 1957b). By representing the network of hybridization patterns at the level of knowledge domains, I aim to capture what sources of public knowledge their underlying communities access in their creative endeavor11. Figure 1.1 is an example network, which describes a “snapshot” of the growth process of a hypothetical stock of public knowledge within a given time interval. The stock consists of three domains of knowledge, A, B, and C, in which, respectively, 2000, 4000, and 1000 new ideas have accumulated over the time interval. Let us focus on the ego-network of domain A’s direct contacts. The ideas generated in A resulted from the hybridization of ideas from A’s own knowledge base 2500 times, and of ideas belonging to domain B 1000 times12. (Or, equivalently, ideas spilled over 2500 times from previous to current inventions in A, and 1000 times from previous inventions in B to current inventions in A). Moreover, ideas generated in A have been subjected to hybridizations that led to new ideas in C 200 times, and in B 700 times. Formally,

a

network

N t = J t , Lt , Vt , At ,

Nt which

at

time

consists

interval of

a

t finite

is

a set

{

four-tuple, of

nodes,

}

J t = {i,..., k , q,... j}; a set of ties between the nodes, Lt = lik , t ,..., l qj , t ; a function Vt (.) mapping ties on pertaining values, usually called weights; and, a

function At (.) mapping nodes on node values. In the context of this study,

10

This is not to say that ingenious individuals cannot contribute to multiple fields at the same time, but that such exceptional individuals can contribute only negligible portions of the overall advancement of any domain of knowledge. See Kaufman and Baer (2004) for a more detailed discussion of this issue. 11 In this respect, my exercise is methodologically similar to network analyses of other aggregates, such as industries or countries. 12 The quantity of hybridizations underlying the advancement process of a domain does not correspond to the quantity of ideas produced in that same domain because any new idea can result from the hybridization of several existing ones.

The network structure of knowledge growth

15

nodes represent domains of knowledge; directed ties represent hybridizations of previous ideas from any given domain into subsequent ideas, belonging to the same or another domain; tie values indicate the number of such hybridizations; and, node values indicate the number of ideas accumulated within each domain.

2500

A (2000) 200

700

1000

500 900

3000

C (1000)

100

B (4000)

Figure 1.1 A network visualization of the hybridization process of three hypothetical knowledge domains

Unlike Weitzman’s representation of knowledge growth, the proposed network model imposes no a priori assumptions concerning the number or proportion of ideas that can be hybridized. Thus, it includes the limiting case where all possible hybridizations are carried out, as is assumed in Weitzman’s recombinant growth model. Furthermore, it imposes no a priori assumptions concerning the distribution of hybridizations across the stock of knowledge. At one extreme, ideas could be hybridized randomly across domains, corresponding to a random network. (Again, this limiting case is an assumption in Weitzman’s model). At the opposite extreme, all ideas could be hybridized exclusively within domains, which would generate a disconnected network of isolates, i.e. of independent trajectories of knowledge accumulation.

16

The network structure of knowledge growth

In actuality, growth processes generate patterns in between these two extremes. The proposed network representation offers a rigorous method to model these patterns empirically, and to theorize about their effects. The fields of graph theory and social network analysis feature a broad array of formal techniques for the analysis of networks. These can be used to analyze both the overall structure of the stock of public knowledge, and node-level properties of individual knowledge domains (Wasserman and Faust 1994). The possibility to complement the analysis of the entire network with that of its constituent nodes yields both theoretical and methodological benefits. Theoretically, as I already argued, it is desirable to conceive an explanatory model that accounts for the fact that knowledge typically advances along domain-specific trajectories of accumulation. By characterizing the (lack of) interdependencies in the growth of knowledge domains, the proposed network model lends itself to this end. Methodologically, the focus on knowledge domains increases the sources of variation in both explanans and explanandum, thus confers inferential leverage. The representation of the knowledge hybridization network within subsequent time intervals, moreover, makes it is possible to analyze formally the dynamics of knowledge growth. In this thesis, I employ this network model to answer the following research question: how do different conditions of embeddedness in the network of knowledge hybridizations affect the growth rate of individual knowledge domains? Importantly, an answer to this question would provide an explanation of both rate and direction of knowledge advancement. While the rate of knowledge advancement is investigated by relating node-level properties to the growth dynamics of individual knowledge domains, these dynamics determine the direction of knowledge advancement at the aggregate level. In the following chapter, I discuss how the proposed network model can be instantiated empirically.

CHAPTER 2 PATENT-BASED INDICATORS AND THE ANALYSIS OF KNOWLEDGE GROWTH

ABSTRACT: Patent data have become a prime source of information on the advancement of technological knowledge. In this chapter, I show why and how patent-based indicators can be employed to instantiate the network model of knowledge growth presented in Chapter 1.

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Patent-based indicators and the analysis of knowledge growth

A

lthough there is evidence suggesting that patent-like documents were used in ancient Greek cities, patents in the modern sense originated in England under King James I. Prior to this time, the crown of England would issue letters patent providing any person with a monopoly to produce certain goods or provide certain services. This power became widely abused, and courts began to limit the circumstances under which letters patent could be granted. In 1623, the Parliament restricted the crown’s power through the Statute of Monopolies, which established that monopolies could be granted only for limited periods and, most importantly, for “the sole working or making of manners of new manufacture” (Statute of Monopolies, Section 6). Nowadays, patents are granted by designated patenting authorities (often referred to as National Patent Offices), which are available in most countries. Although efforts are being made to globalize and harmonize patent law systems, at present patent rights are still limited to the State that grants the patent, and disputes are settled by national courts. In this thesis, I employ data describing utility patents issued by the United States Patent and Trademark Office (USPTO); in the following I will refer to its laws, rules, and practices. I. WHAT IS A PATENT? In the language of the USPTO statute (U.S. Code, Title 35, Part II, Chapter 10, Section 101), any person who “invents or discovers any new and useful process, machine, manufacture1, or composition of matter, or any new and useful improvement thereof, may obtain a [utility] patent.” These definitions taken together comprise practically every idea that has some productive application, including the processes for applying it, provided that it is novel and nonobvious. US courts have determined that the laws of nature, physical phenomena, and abstract ideas are not patentable. A USPTO patent grant confers “the right to exclude others from making, using, offering for sale, or selling” (U.S.Code, Title 35, Part II, Chapter 14, Section 154) the invention in the United States, or importing the invention into the United States. Patents may be granted exclusively to the original inventor(s). However, being an intellectual 1

In the congressional report that accompanied the passage of the Patent Act in 1952, the term manufacture was rephrased as “anything under the sun that is made by man.” {FN6: Sen. Rep. No. 82-1979 at 5, H.R. Rep. No. 82-1923 at 6 (1952)}

Patent-based indicators and the analysis of knowledge growth

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property right, a patent can be bought, sold, or willed to heirs. Hence, it is common for inventors to assign the rights to their inventions over to other individuals or institutions. The recipient of US patent rights – i.e. the patent assignee – may be any U.S. or foreign company or individual, or a foreign government. Generally, the term of a patent right is 20 years from the date on which the application for the patent is filed, subject to the payment of maintenance fees2. In return for the temporary legal monopoly conferred by a patent, the applicant must make full disclosure of the patented invention. Accordingly, inventions cannot be patented unless they are explicated “…in such full, clear, concise and exact terms as to enable any person skilled in the art or science to which the invention or discovery to which it pertains or with which it is most nearly connected, to make and use the same” (U.S. Code, Title 35, Part II, Chapter 10, Section 112). Hence, patents fall squarely into the category of public knowledge described in Chapter 1. Applications filed to the US Patent and Trademark Office are assigned for examination to the respective examining groups in charge of the domain of technological knowledge the invention pertains to. The examination of the application consists of a study of the application for compliance with the legal requirements, and a search through US patents, foreign patent documents, and available literature, to establish if the claimed invention is in fact novel, useful, and non-obvious. The applicant is notified of the examiner’s decision by an action. If the claimed invention is not directed to patentable subject matter, its claims will be rejected. Likewise, if the examiner finds that the claimed invention lacks novelty or differs only in an obvious manner from existing disclosed knowledge, the claims will also be rejected. The applicant has a right to amend his/her application in reply to a rejection, which may lead to a reconsideration of his/her application and, ultimately, to a final decision on the 2

As of May 2004, maintenance fees are to be paid every four years, and increase progressively: it costs $ 850 to maintain a patent in force after its fourth year, $ 1950 after its eighth year, and $ 2990 after its twelfth year. About 22% of patent owners qualify as small entities, which entitles them to fees of approximately half the figures above. (2000. Federal Register. "Rules and Regulations")

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Patent-based indicators and the analysis of knowledge growth

part of the examiner. As a result of the examination, which usually lasts about two years, about two thirds of the filed applications are found to be patentable (Griliches 1990). Then, the applicant is required to pay a fee for issuing the patent3. On the date of the grant, the patent document is disclosed to the public. Patents are lengthy documents containing a wealth of information. This includes the dates of filing and grant, a detailed description of the patented invention (where possible accompanied by drawings), a list of claims defining exactly the scope of the invention, a list of citations to existing knowledge that the invention relates to, the countries where the invention is protected, and the name and address of the applicant and of the inventor(s). In the following sections, I will describe how specific elements of the patent document can be used to instantiate the network model presented in Chapter 1. In Appendix 1, the interested reader can find an example USPTO patent front page; full patents documents can be downloaded free of charge from the World Wide Web4. II. KNOWLEDGE SPILLOVERS Patents must cite so-called prior art, i.e. all disclosed knowledge that the patented invention relates closely to. Citations to prior art have an important legal function: by recognizing what was already known at the time of the invention, they set the limits beyond which claims of novelty cannot be laid. In so doing, however, they also define the specific bits of existing disclosed knowledge the patented invention builds upon. The accuracy and completeness of the information contained in the prior art is seconded by both legal and economic reasons. US law imposes a penalty on attorneys and patent owners for failure to cite all relevant prior art. Moreover, the discovery of inaccuracies lengthens the process that leads to its grant and, hence, to the legal protection of the invention. This can have two negative economic consequences for the applicant. First, the benefits springing from the patent, such as royalties or licenses, are delayed. Second, other patents can be granted in the meanwhile that make the applicant’s obsolete and thus no longer patentable. Furthermore, a 3

The basic fee for issuing each original or reissue utility patent amounts to $1240, or $620 in case the applicant qualifies as small entity (2000. "Rules and Regulations." Federal Register.) 4 The patent archive of the USPTO can be found at http://www.uspto.gov/patft/.

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primary task of USPTO patent examiners is to crosscheck and integrate the prior art presented by applicants. In principle, prior art encompasses the entire body of relevant disclosed knowledge from the beginning of time to present. For example, in a U.S. Supreme Court case in the 1950s, the work of Benvenuto Cellini, the noted Italian artist who died in 1571, was cited in the judicial opinion as part of the prior art, invalidating a patent for the lost-wax casting of jewellery. Although prior art can include virtually any published and, sometimes, unpublished documents, in actuality the bulk of it consists of previously patented inventions. By signaling which bits of disclosed knowledge inventions draw from (Jaffe et al. 1993), patent citations are indicative of the hybridizations underlying the generation of new knowledge. In this respect, they convey information of great theoretical importance. Following the work of Jaffe and his collaborators in the nineties (e.g. Jaffe et al. 1993; Jaffe and Trajtenberg 1996; Jaffe and Trajtenberg 1998), many econometric studies have analyzed patent citations to investigate how knowledge spills over the economy5. This approach has gained further prominence in consequence of the widespread digitalization and systematization of patent data that took place in recent years. Patent citations have been used to trace knowledge spillovers within and between industries (Fai and von Tunzelmann 2001), from universities to firms (Jaffe et al. 1993), within and between firms (Jaffe 1986; Rosenkopf and Nerkar 2001), and between inventors (Jaffe et al. 2000), institutions (Jaffe and Trajtenberg 1996) and geographic regions (Jaffe et al. 1993). More recently, Batagelj (2003) has developed a network-analytic method to detect themes, i.e. trajectories of knowledge accumulation, from patent citations. These studies provided indirect evidence that patent citations indicate knowledge hybridization. Jaffe cum suis (1998) investigated this issue more directly. They interviewed patent attorneys, R&D directors, and inventors involved in a 5

It is important to notice that the terms spillover and hybridization are two connotations of the same concept: an idea that spills over in the knowledge production process is one that becomes hybridized as an input into a newer idea. While the term spillover refers to the transfer of knowledge, hybridization refers to the inventive mechanism that underlies such transfer.

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Patent-based indicators and the analysis of knowledge growth

selection of patenting processes, and estimated the relationship between these actors’ perception of knowledge spillovers and observed patterns of patent citation. Their conclusion was that, albeit noisy, patent citations are a valid measure of technology spillover. Jaffe, Trajtenberg and Fogarty (2000) refined this approach and applied it to a broader sample of inventions, reaching the same conclusion. III. KNOWLEDGE OUTPUT Since patens indicate inventions, they are commonly used to measure the advancement of technological knowledge (Griliches 1984; Scherer 1965; Schmookler 1966). The distribution of individual patent contributions, however, is known to be highly skewed: while some patents are groundbreaking inventions, others are valueless. Hence, raw patent counts are but a rough approximation of knowledge output. Numerous authors have discussed the skewness of patent values (Griliches et al. 1987; Pakes 1986; Pakes and Schankerman 1984). The general conclusion is that the accuracy of patent counts as an approximation of knowledge output increases significantly when patents are weighed by some indicator of their importance (Griliches 1990). Several strategies have been proposed to measure the importance of individual patents. One is to observe the length of continued patent protection. As patent renewal is expensive, it should indicate patent value as perceived by holders. Pakes and Schankerman (1984), Schankerman and Pakes (1986) and Lanjouw (1998) have developed models in which the observed renewal decisions are used to estimate the distribution of patent values. A drawback of this approach is that it provides no indication of value differentials among those patents that are never renewed, and among those that are renewed to full statutory term. In addition, the accuracy of renewal behavior as an indicator of patent value depends on the extent to which imperfectly informed patent holders make rational decisions and act accordingly. Lerner (1994) used the market value of biotechnology firms as a measure of the knowledge value of their respective patent portfolios. Then he estimated empirically the relationship between firms’ market value and the scope of their average patent, and concluded that the scope of a patent is indicative of its value.

Patent-based indicators and the analysis of knowledge growth

23

Focusing on the MIT’s patent applications, Shane (2001) reached a similar conclusion. He found that the scope of patents has a significant and positive impact on the probability to create new technology-based firms. Overall, however, the empirical evidence on the relationship between patent scope and patent value is mixed at best. Whereas Harhoff et al. (2003) found that the relationship is not statistically significant, Harhoff and Reitzig (2004) Guellec and van Pottelsberghe (2000, 2002) and Lanjouw and Schankerman (1997) estimated negative relationships. A host of other indicators of the importance of patents have been proposed, but none appears to be generally applicable, or to have accumulated sufficient empirical validation. Lanjouw (1998), Lanjouw and Lerner (1997), and Lanjouw and Schankerman (1999) found that more valuable patents are more likely to be enforced through lawsuits. Tong and Frame (1994) related the inventive content of a patent to its number of claims, a finding only in part corroborated by Lanjouw and Schankerman (1997, 1999). Harhoff et al. (2003) found that patent citations to scientific sources, indicating a strong knowledge base, impact patents’ monetary value. In an investigation of biotechnology and pharmaceutical patents, however, Harhoff and Reitzig (2004) did not observe a significant influence of the number of scientific citations on the probability that a patent is opposed (considered as a value indicator). Some evidence has been found that the number of jurisdictions in which patent protection is sought for a particular invention, or family size, correlates with patent value (Guellec and van Pottelsberghe 2000, 2002; Lanjouw and Schankerman 1999; Putnam 1996). However, this indicator – like others we discussed – confuses economic value and knowledge contribution of the patent. Although most indicators of the knowledge contribution of patents fall short in accuracy, validation or applicability, approaches based on the quantification of patent citations received after grant – or forward citations – seem to stand out. Citation-based measures overcome important limitations of alternative indicators. Unlike measures based on the observation of patent renewal, patent litigation, number of claims, and family size, citation-based indicators do not infer patent values from the choices of purportedly informed and rational actors. Based on an established methodology in bibliometrics (Garfield 1979), the

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Patent-based indicators and the analysis of knowledge growth

rationale of citation indicators is that the importance of any given knowledge output is determined by the impact it has on subsequent developments of knowledge. Because a patent cites another one when it builds upon it, the citations a patent receives indicate the degree to which it furthers technological progress. Thus, measures of forward citation are specifically designed to capture patents’ knowledge contribution, not patents’ economic value6. Many of the indicators proposed in the literature to assessing the importance of individual patents are based on the use of additional data sources. Often, these sources contain data on just a fraction of patents. This is the case, for example, in studies of patent renewal, market value, and patent litigation. Information on patent citations, on the contrary, is contained in the patent itself, which makes data collection generally less burdensome and, at least in principle, comparisons possible across all patents. Citation-based indicators have received empirical validation from all known studies. In an influential research, Trajtenberg used data on a clearly defined set of products (computer tomography scanners) to show that the consumers’ welfare associated with a patented invention was highly correlated with the incidence of patent citations received (1990). Using data from a survey of patent holders, Harhoff cum suis (1999) found that the number of citations received by a patent correlates positively and significantly with the value perceived by its holder, a single citation implying an estimated average value of about $1 million. Giummo (2003) examined the royalties received by patent holders at nine major German corporations and reached a similar conclusion. Hall, Jaffe and Trajtenberg (2004) analyzed the patenting activity of almost 5000 firms over a period of 30 years. They found that patent citations are indicative of firms’ intangible assets, even when controlling for raw patent counts and R&D investments. Besides indirect evidence, patent citations were found to indicate patent importance also in the studies of Albert (1991), and Jaffe, Trajtenberg and Fogarty (2000), who asked knowledgeable inventors/experts to evaluate the technological significance of selected samples of inventions.

6

Obviously, the economic value of a patent may be – and typically is – correlated

Patent-based indicators and the analysis of knowledge growth

25

IV. KNOWLEDGE DOMAINS The U.S. Patent and Trademark Office has developed an articulated system of classification (the United States Patent Classification, henceforth USPC), so that every patent can be identified by the technical content of its subject matter. As of 1999, the system consists of 418 domains of technological knowledge, or primary classes, and over 100,000 subclasses. Both are regularly revised to reflect technological progress. The first step a classifying examiner follows in the process of designating the proper classification of a patent is to establish precisely what is being claimed in the application document. Each claim in an application must be reviewed to determine which elements, or combinations of elements, are embraced by that claim. When the content of each claim has been analyzed, it may be found that the application includes two or more claims that are drawn to diverse subject matters (i.e., they are classifiable in different classes). For search and retrieval purposes, merely placing the document in each class would suffice. However, for both administrative and legal purposes within the USPTO (e.g., ensuring the examination of patent applications by the best qualified examiner on the subject matter, restricting patent applications to properly related inventions, interference or infringement searches, etc.), there is a need to designate for each patent a primary, i.e. unique, classification. This must reflect the invention information, i.e. that portion of the disclosure that, in the opinion of the classifying examiner and according to a set of well-specified criteria, most comprehensively typifies the main inventive concept of the application (Earls et al. 1997). Patent classes have been extensively used to indicate domains of technological knowledge. Powell and Snellman (2004) observed longitudinal patenting rates across patent classes to describe the changing importance of technological sectors. Jaffe, Trajtenberg and Henderson (1993) modeled patents’ technological proximity on the bases of their primary patent classification, a methodology adopted also in Almeida (1996), Jaffe and Trajtenberg (1999), Frost (2001), and Hicks cum suis (2001), and refined by Thompson and Fox-Kean (2004). Hall cum suis (2001) observed patents’ forward and backward citations across patent classes to assess, respectively, patents’ generality and originality. Similarly, with its knowledge importance and, hence, with the citations it receives.

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Patent-based indicators and the analysis of knowledge growth

Rosenkopf and Nerkar (2001) used patent citations across classes to operationalize firms’ technological exploration. Jaffe (1986) measured firms’ proximity in technology space based on the profile of classes they patented in. A similar approach was used in Maurseth and Verspagen (2002) to develop an asymmetric compatibility index between technological competences across geographic regions. In research on national systems of innovation (NSI), countries’ technological specialization is commonly measured by their revealed technological advantage, which measures the concentration of countries’ patents across patent classes (Cantwell 1989; Patel and Pavitt 1987; Patel and Vega 1999; Soete 1987). V. THE NETWORK MODEL OF KNOWLEDGE GROWTH The model of knowledge growth I proposed in Chapter 1 represents a set of knowledge domains among which hybridizations are carried out within given time intervals, resulting in knowledge growth at the level of domains. In this thesis, I use USPTO patent data to instantiate this network model. USPC patent classes provide a straightforward empirical indication of the domains of technological knowledge of US-patented inventions. Obviously, there is some degree of arbitrariness in the definition of such classes. The classification procedure described in section IV, however, guarantees standards of objectivity and accuracy that would be hard to pair by other means. My choice is to denote knowledge domains on the basis of USPC primary patent classes. There are two reasons for preferring primary classes to higher or lower aggregations. First, as said, patents can be assigned to multiple subclasses, but each patent must be assigned to a unique primary class representing its “main inventive content”. This makes it possible to partition inventions into domains. Second, there are 418 primary patent classes, which is a large yet manageable number of units. Following the literature on knowledge spillovers, I interpret patent citations as paper trails of hybridizations. Citations between patents form a directed, unweighted, acycilc network. This means that a tie from node i to node j implies the absence of a tie from j to i (previous patents cannot cite subsequent patents); and, that there is no difference in the strength of ties (a patent either cites

Patent-based indicators and the analysis of knowledge growth

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another patent or it does not). Having defined technology domains as partitions of patents, I can homomorphically map this patent-by-patent network onto a domain-by-domain network. Because each USPTO patent reports the date of grant, I can describe the network at specific time intervals. The resulting representation is a time series of directed, valued, and cyclic networks. The number of citations from domain i to domain j determines the weight of the corresponding directed tie in these networks7. Moreover, these networks admit reciprocated ties and self-referential loops (the former denote mutual hybridization between pairs of domains, and the latter denote a domain’s hybridization of ideas belonging to its own knowledge base). As a result of hybridizations, domains advance. In this thesis, I measure domains’ knowledge output following the two most widely diffused approaches in the literature. Whenever possible, I count the citations received by domains within a given time interval. I employ this measure for the analyses I will present in Chapters 6 and 7. In Chapter 5, however, I prefer to use a simple patent count instead, as this allows me to keep more neatly separated causes and effects in that context. Wrapping up, I employ patent-based indicators to instantiate the network representation of knowledge growth described in Chapter 1 as follows. The 418 USPC primary patent classes instantiate the nodes; directed ties are instantiated by the citations made from patents granted in a class within a given time interval, t, to patents granted to the same or other classes within t; tie values are instantiated by the number of these citations; and, node values are instantiated by the number of patents granted within each class (Chapter 5) or by the number of citations received by each class (Chapters 6 and 7), within t. For an illustration, let us go back to Figure 1.1 on page 15, and let us focus again on the ego-network of node A’s direct contacts. All patents represented in the network have been granted within time interval t. Patents in class A cited previous patents granted in A 2500 times and in B 1000 times. Moreover, patents granted

7

As reported, patent citations are noisy indicators of hybridization at the level of individual inventions. The aggregation of patents and citations across domains of knowledge, however, minimizes the possibly biasing effects of such noise.

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Patent-based indicators and the analysis of knowledge growth

in A have been cited by subsequent patents granted in C 200 times and in B 700 times. In total, A was granted 2000 patents and received 3400 citations8. VI. CONCLUSIONS Since Frederic Scherer’s pioneering work (1965), a sizeable body of research has used patent statistics for the analysis of knowledge dynamics. Nowadays patent and citation data have become widely established indicators of knowledge output, knowledge hybridization, and knowledge domains. In order to instantiate the network model of knowledge growth I presented in Chapter 1, I employ patent data as indicators of all three concepts. A number of issues pertaining to the instantiation of the model must still be discussed with regard to the specific patent dataset analyzed. In the following chapter, I provide a statistical description of the data used throughout this thesis.

8

Note that citations and knowledge spillovers run in the opposite direction.

Patent-based indicators and the analysis of knowledge growth: appendix APPENDIX FRONT COVER OF A USPTO PATENT

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CHAPTER 3 NBER PATENT AND PATENT CITATIONS DATA

ABSTRACT: Throughout this thesis I use the NBER Patent Citations Data files (Hall et al. 2001), which describe all patents granted by the USPTO between 1975 and 1999, as well as the citations among them. In this chapter I analyze these data statistically; on this basis, I identify a number of potentially problematic issues with regard to the instantiation of my network model of knowledge growth, and I indicate solutions thereof.

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T

he empirical analyses carried out throughout this thesis are based upon the NBER Patent Citations Data Files created by Hall, Jaffe, and Trajtenberg. The authors provided a thorough and comprehensive description of the data (Hall et al. 2001), which many of the analyses in this chapter draw from and elaborate upon. The NBER database comprises detailed information about almost 3 million U.S. patents granted between January 1963 and December 1999, and all citations among the patents granted between January 1975 and December 1999 (over 16 million). All the data were collected directly from the USPTO digital archive, except for those concerning the citations between patents granted in 1999, which come from MicroPatent. As the instantiation of my network model of knowledge growth requires data on both patents and their citations, for the purpose of this thesis I discarded the patents granted between January 1963 and December 1974 – which leaves me with 2.139.314 patents. The present chapter consists of three sections. In the first, I present a statistical analysis of patent production. In the second, my focus shifts to patent citations. In light of these analyses, in the third section I point out potentially problematic issues related to the use of the NBER data for the instantiation of my network model of knowledge growth. Furthermore, I indicate how these issues can be resolved by network and statistical modeling.

I. PATENT PRODUCTION The patent application process takes an average of about two years (Chapter 2). Table 3.1 reports more detailed statistics of the application-grant lag. The figures reveal some degree of variation around the mean. However, they also show that the portion of patents granted 2 years after filing hovers around 85%, and goes up to about 95% after 3 years. Notice that the application-grant lag is non-monotonic with respect to time, peaking at the beginning of the 1980s but shrinking to values similar to 1975 at the end of the observation period. During the same period the number of patents granted in the United States more than doubled (Figure 3.1). Patent production oscillated around 70.000 patents per year until the middle eighties, when it began to increase steadily. Due to a further acceleration started in 1997/1998, it approached 150.000 patents per year at the end of the nineties. Figure 3.2 shows that this growth has been propelled more by non-U.S. than by U.S. assignees in the last 25 years, although the

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1997/1998 acceleration seems to be due in equal measure to both. At present, with nearly as many patents assigned yearly to U.S. as to non-U.S. inventors, the USPTO is by far the most internationalized patent authority worldwide.

Lag years 0 1 2 3 4 5 6 7+ Total

Distribution of Lags (in %) 1973-75

1976-79

1980-82

1983-85

1986-89

1990-92

1.0 40.1 48.2 8.0 1.5 0.6 0.2 0.3 100.0

1.0 32.5 51.0 11.9 2.0 0.8 0.4 0.3 100.0

0.2 18.0 51.1 24.1 4.0 1.2 0.7 0.7 100.0

1.0 26.6 49.4 16.7 3.7 1.5 0.7 0.4 100.0

1.8 40.4 43.6 10.6 2.5 0.7 0.2 0.2 100.0

2.6 40.4 42.0 11.1 2.3 0.7 0.4 0.4 100.0

1973-75 Mean s.d.

1.74 0.91

Mean and standard deviation of the lag 1976-79 1980-82 1983-85 1986-89 1.88 0.93

2.25 1.02

2.05 1.02

1.76 0.90

1990-92 1.76 0.95

Table 3.1 Application-grant lag distribution by 3-year sub-periods Source: adapted from Hall et al. (2001)

Approximately 17% of all USPTO patents between 1975 and 1999 are assigned to inventors who have not (yet) granted the rights to their invention to a legal entity such as a corporation or a university. However, by far the greatest majority of patents (roughly 80%) are assigned to corporations. Of these, 53.75% are granted to U.S. companies, and 46.25% to companies located outside the U.S. territory. The remaining patents (a mere 2.8% of the total) are assigned to U.S. or foreign individuals and government agencies. These data back the view that corporations are the locus of technological innovation in

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advanced economies. Figure 3.3 shows that the predominance of corporations for patent production has been on the rise in the last quarter of a century both within and outside the United States.

Figure 3.1 Number of patents by application year Source: adapted from Hall et al. (2001)

Figure 3.2 Number of patents by grant year, US and non-US assignees Source: adapted from Hall et al. (2001)

USPTO patent and patent citations data

Figure 3.3 Share of corporate patents by application year, US and non-US assignees Source: adapted from Hall et al. (2001)

Figure 3.4 Distribution of patents by technological area and application year Source: adapted from Hall et al. (2001)

35

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USPTO patent and patent citations data

Figure 3.5 Distribution of patents by technological area and application year, as a share of total patents Source: adapted from Hall et al. (2001)

As I already discussed, the USPTO classifies each patent into one of 418 technological domains. In addition, the developers of the NBER database partitioned these domains (and the patents therein) into six macro technologyareas (Hall et al. 2001). These are Chemical; Computers & Communications (C&C); Drugs & Medical (D&M); Electrical & Electronics (Elec); Mechanical; and Others. Figure 3.4 shows the number of patents granted in each of the six technological categories over time. The figure reveals that in the 25 years observed, the areas of Chemical, Mechanical and Others have grown much less rapidly than Electrical & Electronics, Drugs & Medicals, and Computers & Communications1. This reflects a much-spoken trend in technological 1

The decline observable in all technological areas at the end of the time series is an artifact due to the application-grant lag: many of the patents applied for in the late

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production, whereby emergent fields such as ICT and health care technologies display greater dynamism than mature technologies (Hall et al.2001). This trend is captured even more clearly by Figure 3.5, which expresses the same figures as shares of total patents granted. The area of Computers & Communications appears to have risen most steeply, producing well over 15% of all patents in the late 1990s from a share of roughly 6% in 1975. Similarly, patents in the area of Drugs & Medical and, to a lesser degree, those in the field of Electric & Electronics became relatively more numerous. In contrast, the areas of Chemical, Mechanical and Others declined from roughly 74% of the total in 1975 to 51% in 1999. II. PATENT CITATIONS Patent citations contain two kinds of information necessary to instantiate my network model of knowledge growth. While the citations a patent makes indicate the hybridization it springs from, the citations a patent receives indicate its contribution to subsequent knowledge development. In this section, I describe some key patterns of patent citation in the NBER dataset. II. I. CITATIONS MADE AND RECEIVED Figure 3.6 shows the mean number of citations made and received over time. The number of citations made rose from an average of about 5 citations per patent in 1975, to about 9 at the end of the observation period. The decline in the average number of citations received per patent in recent years is a result of data truncation: patents applied for later have lower chances to be cited within the observation period. Beyond that, the average number of citations received per patent does not seem to have changed substantially over time. Figure 3.7 shows that the distribution of citations received per patent is highly skewed. The distribution is best described by the power-law function: with an R-Square of 0.89, the estimated constant is 1992 and the estimated power coefficient is -2.79. Hence, most patents receive few or no citations, while disproportionably few patents receive thousands of citations. This reflects the uneven knowledge contribution of individual patents, an issue I discussed in Chapter 2.

nineties had not yet been granted before the end of 1999.

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USPTO patent and patent citations data

Figure 3.6 Mean citations made and received by application year Source: adapted from Hall et al. (2001)

Figure 3.7 Frequency of citations received per patent

USPTO patent and patent citations data

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Figure 3.8 Mean citations made by technological area and application year Source: adapted from Hall et al. (2001)

Figure 3.8 and Figure 3.9 show, respectively, the average number of citations made and received by technological categories. The figures reveal that the technological areas Chemicals & Mechanical tend to cite more while receiving fewer citations, especially if compared to the emerging areas of Computer & Communications and Drugs & Medical. The difference in citations received is striking: the average patent in the area of Computer & Communications receives up to 12 citations, while in Drugs & Medical the average number of citations received is 10 at its peak; in contrast, patents in the traditional areas of Mechanical, Chemical and Others never receive more than 6 citations. (The area of Electrical & Electronic is in between the two groups receiving approximately 7 patents at its peak).

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USPTO patent and patent citations data

Figure 3.9 Mean citations received by technological area and application year Source: adapted from Hall et al. (2001)

II. II. CITATION LAGS There are two kinds of citation lags. Backward citation lags measure the time between the grant date of a focal patent and the grant date of the patents the focal patent cites. Conversely, forward citation lags measure the time between the grant date of a focal patent and the grant date of the patents that cite the focal patent. The NBER dataset includes the complete list of citations made by each patent granted after 1975. Hence, the entire distribution of backward citation lags can be computed for those patents. For the computation of forward citation lags, observed data are less helpful. First, they are truncated, because patents granted after the end of the observation period keep citing the patents described

USPTO patent and patent citations data

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in the NBER dataset. Second, data truncation is more severe for patents granted later in the observation period.

Figure 3.10. Distribution of backward citation lags Source: Hall et al. (2001)

Figure 3.10 shows the frequencies of backward citation lags up to 50 years back and, in the inset, the remaining tail for lags longer than 50 years; Figure 3.11 shows the cumulative distribution up to 50 years back. Note that a remarkable portion of citations is directed to patents granted many years before the citing patent. Less than 30% of the citations are made to patents between 0 and 5 years older than the citing patent, and it takes 50 years to cover 90% of all citations. Somewhat less than 50% of the citations made are directed to patents at least 10 years older than the citing patent, 25% to patents 20 years older or more, and 5% to patents that are at least 50 years older than the citing one (some citations even refer to patents that are over a hundred years old). Projecting these figures in the future, patents granted in year 2000 will receive just one third of their citations by 2005, half by 2010, and even by 2100 they will still be receiving some2. 2

Of course, it remains to be seen if the lag distribution will remain stable

42

USPTO patent and patent citations data

Figure 3.11 Cumulative distribution of backward citation lags Source: Hall et al. (2001)

Figure 3.12 shows the frequency distribution of forward citation lags for patents from selected cohorts. The figure provides a useful visual representation of both problems associated with forward citation lags. Because of truncation, the frequency of citations received drops, regardless of cohort, as the distribution approaches the maximum lag possible. Moreover, the more a patent is granted towards the end of the observation period, the more severe is the artificial decline induced by data truncation. Figure 3.12 also highlights another interesting point. As patents become obsolete, one would expect that they should receive fewer citations as time advances; however, the observed citation distributions are surprisingly flat. Take the distribution for the 1975 cohort: the frequency of citations received did not diminish until 1995 – when a decline was induced by the aforementioned data truncation. A likely explanation is that the obsolescence of cited patents was compensated for by the growth in both the number of citing patents and in the number of citations made per patent. Nonetheless, it remains striking that it took

USPTO patent and patent citations data

43

over 10 years for the 1975 patents to receive 50% of their forward citations. Even looking at data-truncated patterns, it is clear that the citation process is a remarkably lengthy one.

Figure 3.12 Distribution of forward citation lags, selected cohorts Source: Hall et al. (2001)

III. THE NBER DATA AS INDICATORS OF KNOWLEDGE DYNAMICS In the previous sections, I described statistically the processes of patent production and patent citation as observed in the NBER data. Based on these analyses, in this section I point out potentially problematic issues related to using the NBER data to instantiate my network model of knowledge growth, and I indicate solutions thereof. III. I. TIME OF PATENT GRANT To instantiate my network model of knowledge growth, domains’ knowledge output can be measured by means of patent or citation counts, while domains’ hybridization patterns can be tracked back on the basis of patent citations (Chapter 2). However, there is no natural scale within which patenting and

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USPTO patent and patent citations data

citation activities can be quantified. Accordingly, knowledge indicators based on patent and citation counts are meaningful only when used comparatively, and to the degree that appropriate comparisons are made. As we have seen, the number of patents granted yearly has substantially increased over the 25 years described by the NBER data. As patents measure knowledge output, this growth may be indicative of an increase in the production of technological inventions. However, it may also reflect changes occurred in the patent-to-invention ratio. In light of the greater role of business companies in the inventive process, for example, it is certainly plausible that the proportion of patented inventions increased over time. Furthermore, during the observation period there has been an expansion of patentable subject matters3. Similar arguments can be made with respect to the interpretation of patent citations, which also steadily increased during the 25 years observed (Figures 3.6 and 3.8). It is known, for example, that the USPTO patent archive was digitalized in the 1980s, and that this made prior art searches easier and more comprehensive. As a result, also the number of citations per patent might have increased to some degree regardless of actual dynamics of knowledge growth. The general conclusion that should be drawn from these considerations is that the comparison of patent or citation counts from different points in time may lead to wrong inferences. A conservative solution to this problem is to purge all temporal variation from estimation at the statistical level, a strategy that I implement throughout this thesis by systematically controlling for the effects of time. III. II. AREA OF TECHNOLOGY The analyses presented in the previous sections also suggest that patent and citation counts may be misleading if comparisons are made across different areas of technological knowledge. As we have seen, differences in patenting and citation patterns are substantial among the six macro technology-areas (see Figures 3.4, 3.5, 3.8, and 3.9). Unfortunately, on the basis of available data it is impossible to establish to what extent these differences reflect actual patterns of 3

Subject matters that have become patentable since the 1980s include artificially engineered genetic organisms, (some) software applications, and business methods.

USPTO patent and patent citations data

45

knowledge growth, and to what extent they reflect data artifacts. For example, incentives to patent are known to depend on appropriability conditions that vary across technological areas (Cohen et al. 2000). Similarly, industry-specific legal and cultural practices may induce differences in the citation patterns observed across technological areas4. For these reasons, one should be mindful of comparisons based on patent and citation counts across technological areas. Again, conservative statistical modeling can eliminate the risk of unduly comparisons: throughout this thesis, I remove from estimation all variation across technological areas (hence also its possibly artificial components) by means of dummy control variables. III. III. DATA TRUNCATION Patent data are inherently truncated. This poses two methodological problems in the context of this study. The first pertains again to the comparability of observations, while the second pertains to measurement quality. I discuss these problems in turn. III. III. I. COMPARABILITY OF TRUNCATED DATA Comparisons of citation counts ought to take into account that patents granted at different points in time are subjected to differing degrees of truncation. As shown in Figure 3.12, older patents have systematically higher chances to receive citations within the observation period. Therefore, a comparison of forward citation counts over time would yield biased conclusions, and the bias would increase with differences in patents’ age. An equivalent problem occurs when backward citations are analyzed. Although the NBER data contain information on all citations made by each patent granted during the observation period, for many analyses data need to be time-partitioned. In these cases, the more a patent is granted towards the end of the observation period, the larger is the portion of its citations that is captured by the data. Thus, also in the case of backward citations comparisons that do not account for differences in the degree of data truncation will lead to wrong inferences. 4

Hall cum suis agreeably maintain that “…the differences in citations received are more likely to be “real”, since it is hard to believe that there are widespread practices that systematically discriminate between patents by technological fields when making citations” (2001, p. 18)

46

USPTO patent and patent citations data

One way to make truncated citation data comparable is to put forward a few identifying assumptions concerning the distribution of unobserved citations, and weigh truncated citation counts by the expected effects of truncation. For example, if one is willing to assume stationarity and proportionality in the distribution of citations over time, then one could estimate on the basis of observed citations how many citations each patent at each given point in time is still to receive. An alternative, and more conservative, solution consists of subjecting all observations to the same degree of data truncation. By confining citation counts to fixed time windows, this approach in effect eliminates the problem of truncation bias. Motivated by the will of being as conservative as possible in my analyses, throughout this thesis I employ the latter strategy. III. III. II. DATA TRUNCATION AND MEASUREMENT QUALITY The use of fixed time windows also makes it possible to model the evolution of the network by means of comparative statics, i.e. by comparing network parameters across subsequent cross-sectional representations. However, it exacerbates the second problem associated with data truncation: measurement quality. Patent and citation counts that are performed on truncated data may differ from their non-truncated equivalents, and the magnitude of this difference is likely to vary with the extent of the truncation. In choosing the length of time windows, then, one is confronted with a trade-off. A shorter length would result in more time points for modeling network evolution; however, a longer length would reduce measurement error. My choice is to group the patents into intervals of five years. Hence, one crosssectional image of the network is based on all citations between patents granted within the same five-year window. The choice of five years is arbitrary, but nonetheless appropriate. One reason is that other studies employing patent citations data adopted a five-year window (Podolny et al. 1996), which makes my study more easily comparable with extant literature. Another reason is that I estimated that models of knowledge growth based on five-year intervals are nearly as accurate as those based on the entire observation period. To reach this conclusion, I reckoned that temporal truncation could induce two kinds of measurement error in my network model. The first kind pertains to the

USPTO patent and patent citations data

47

representation of network configurations, and occurs insofar as domains’ citation patterns to older patents are directed to systematically different domains than their citation patterns to more recent patents. To assess empirically the severity of this problem, I employed the so-called QAP (Quadratic Assignment Procedure) regression analysis (Simpson 2001). Namely, I regressed the interdomain adjacency matrix in which both cited and citing patents are granted between 1995 and 1999, on the adjacency matrix constructed using citing patents granted in the interval 1995-1999 and cited patents granted during the entire observation period, i.e. between 1975 and 1999. This enabled me to gauge the discrepancy in the representation of network configurations resulting from using a 5-year window rather than the whole 25-year period. Table 3.2 shows the results, which indicate that the two network configurations are virtually identical5. Independent variables

Un-standardized coefficients

Intercept 5-year-window network Observations Adj. R-square Significance

-0.000792 1.000049 174306 0.999 0.000

Table 3.2 QAP regression analysis

The second kind of measurement error that temporal truncation could introduce in my network model pertains to the quantification of domains’ knowledge output. This problem is likely to be aggravated when domains’ output is measured on the basis of citation counts. As I showed, citation lags are very long, and models based on 5-year intervals capture less than 30% of all citations received. To assess the magnitude of the error induced by the truncation of 5

Strictly speaking, this conclusion is valid only for the patents granted between 1995 and 1999. However, I carried out similar QAP analyses for the earlier time intervals (I compared the network representation based on 1990-1994 patents against the one based on patents granted between 1975 and 1994; the network based on 1985-1989 patents against the one based on patents granted between 1975 and 1989; etc.) and I obtained equivalent results.

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USPTO patent and patent citations data

citation data in measuring domains’ knowledge output, I focused my attention on the patents granted between 1975 and 1979. Based on those patents, I first counted the citations domains received during the same five-year interval (i.e. between 1975 and 1979), then I counted the citations they received up to 1999, and finally I correlated the two vectors of scores. I calculated both Pearson’s correlation and Spearmans’ rho correlation of rank orders, which resulted in coefficients of 0.973 (p<0.0001) and 0.976 (p<0.0001), respectively. On the basis of these values, I concluded that the measurement of knowledge output based on five-year windows is just about as accurate as the one based on the entire observation period6. III. IV. NETWORK EVOLUTION Given the choice of five-year intervals, a maximum of twenty-one network cross-sections, each overlapping for 80% with its neighbors, could be used as observation instances for the time-series. To guarantee that relationships between networks are not artificial, however, I decided to reduce the observation instances to five non-overlapping networks. Thus, I modeled the evolving structure of patent citations between technological domains between 1975 and 1999 as a time series of five networks (based, respectively, on the patents granted in the intervals 1975 through 1979, 1980 through 1984, 1985 through 1989, 1990 through 1994, and 1995 through 1999). In the following chapter, I provide an empirical characterization of this evolving network.

6

I carried out similar analyses focusing on the other time intervals (i.e., for the patents granted in each domain between 1979 and 1984, I correlated the citations received by domains within the same 5-year interval, with the citations they received between 1979 and 1999; for the patents granted between 1985 and 1989, I correlated the citations they received within the same 5-year interval, with the citations they received between 1985 and 1999; etc.), which led the same conclusion.

CHAPTER 4 CHARACTERIZING THE NETWORK STRUCTURE OF US-PATENTED KNOWLEDGE

ABSTRACT: In this chapter, I characterize the knowledge hybridization network constructed on the basis of the NBER data. I describe the network visually, as well as by means of components, small-world, and triadic analyses.

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Characterizing the network structure of US-patented knowledge

T

he network approach can be applied to model a variety of real-world systems. In recent years, a stream of research has emerged that searches for generalities in topology and dynamics across large-scale empirical networks (Barabási 2002). Due to its vitality and highly interdisciplinary character, this line of work has been called “the new science of networks” (Barabási 2002; Watts 2004). The empirical networks analyzed include collaborative relations of film actors, the electrical power grid of the western United States (Watts and Strogatz 1998), food webs (Montoya and Solè 2002), molecular networks (Rzhetsky and Gomez 2001), fire spreading (Moukarzel 1999), epidemics (Kleczkowski and Grenfell 1999), trade patterns (Wilhite 2001), scientific collaborations (Newman 2001), the Internet (Yook et al. 2002), and the World Wide Web (Albert et al. 1999). In this chapter, I aim to contribute to this body of research by characterizing the inter-domain network of US-patent citations. This network is especially interesting because, differently from most other largescale systems, it is comprehensively described for a period as long as 25 years. By exploring the topology of the network and its evolution, I also aim to present contextual information for the analyses carried out in the following chapters.

I. NETWORK COMPONENTS Before more sophisticated analyses are performed, it is important to examine the internal components of the network under investigation. A component is a maximal sub-graph in which there exists a path between any pair of nodes. The size of a component, in turn, is the number of nodes it contains (Wasserman and Faust 1994). Thus, the analysis of components enables one to assess the degree to which a network consists of disjointed regions, and to establish which and how many nodes belong to each region. Table 4.1 shows the analysis of components for the entire period (first column), and for each of the subsequent network cross-sections (second through sixth column). As can be seen, nearly all nodes of the knowledge hybridization network belong to one giant component, and the identified smaller components are isolates – i.e. components of size 1. Hence, with the exception of a few isolated nodes, all domains of US-patented knowledge are mutually connected through direct or indirect paths of hybridization.

Characterizing the network structure of US-patented knowledge

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Number of domains per component 1975- 1975- 1980- 1985- 1990- 199599 79 84 89 94 99 Component 1 Component 2 Component 3 Component 4

418 ----------

415 1 1 1

418 -------------

416 1 1 -----

416 1 1 -----

417 1 -------

Table 4.1 Analysis of components

Because isolates preclude most network analyses, they are often removed from the analysis. In the case analyzed here, to the isolates identified in any of the network cross-sections correspond only five domains. Moreover, the patterns of knowledge hybridization and production of these isolated domains are of negligible magnitude1. This suggests that analyses can focus on the giant component at no risk of overlooking noteworthy dynamics of knowledge growth, which is the strategy I adopt throughout this thesis. After excluding the five isolated domains, the population of domains of US-patented knowledge reduces to 413 units. II. NETWORK VISUALIZATION Although the analysis of components indicates that the knowledge hybridization network is well connected, a glance at tie values shows that much of the observed connectivity results from very weak ties. In the period 1975 through 1979, roughly one third of the connections between domains consist of only one patent citation, while in the period 1995 through 1999 this proportion is about one fourth. Although in general there is no reason to overlook the role of these ties, their presence sometimes obscures the strong-tie backbone structure of the network. This is certainly the case when networks are investigated by visual inspection, as I do in this section.

1

In total, these domains account for 0.00088 % of all patents granted, 0.00047 % of all citations received, and 0.00061 % of all citation made.

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Characterizing the network structure of US-patented knowledge

To visualize the knowledge hybridization network I use NetDraw1 (Borgatti 2002), a freeware software downloadable from the Web2. NetDraw1 employs a spring-embedded drawing algorithm to represent network data in twodimensional Euclidian space: while nodes repel one another, network ties act as springs that draw connected nodes closer together. The algorithm iteratively searches for the representation of the network that minimizes the distance between connected nodes and maximizes the distance between unconnected ones. In Netdraw1, the direction of ties is represented by means of arrows, while their strength is symbolized by arrows’ thickness. II. I. WEAK TIES AND BACKBONE STRUCTURE Figure 4.1 shows the knowledge hybridization network between 1975 and 1999. Figures 4.2, 4.3, and 4.4 represent the same network without the weakest 5%, 10%, and 15% ties, respectively3. As it appears, under a pervasive surface of weak ties, the network backbone consists of a multiplicity of relatively welldefined hybridization clusters. To analyze these clusters in more detail, Figure 4.4 reports next to each node the corresponding USPTO patent class numbers4. Beginning from the Southwest region, a well-defined subgroup of domains cluster around patent class 428, denoted Stock material. Zooming in (Figure 4.5), it appears that the cluster has a star configuration around patent class 428, within which a cliquish structure is nested that includes classes 523, 524, 525, 528 – all belonging to the broadly defined area of Synthetic resins and natural rubbers. Moving North, a quasi-star is visible in which node 514 (Drug, bioaffecting and body treating compositions) is the nexus of hybridization activities for the broad area of organic compounds (comprising domains 536, 540, 544, 546, 548, 549, 564), and for some domains of chemistry (435, 530). The cluster is not a pure star because its central node is strongly connected to patent class 424, which in its turn is at the center of a small sub-cluster. Interestingly, patent classes 424 and 514 are identically denoted (Drug, bio-affecting and body treating compositions), although the hierarchy of subclasses they head is of course different. 2

The software Netdraw1 can be downloaded http://www.analytictech.com/downloadnd.htm 3 These proportions do not count loops, i.e. domains’ self-citations. 4 Patent class numbers refer to the USPTO classification scheme as of 1999.

from

Characterizing the network structure of US-patented knowledge

Figure 4.1 Hybridization network (1975-1999)

53

54

Characterizing the network structure of US-patented knowledge

Figure 4.1 Hybridization network (1975-1999), 5% weakest ties removed

Characterizing the network structure of US-patented knowledge

Figure 4.1 Hybridization network (1975-1999), 10% weakest ties removed

55

56

Characterizing the network structure of US-patented knowledge

Characterizing the network structure of US-patented knowledge

57

Figure 4.5 The stock material cluster

The third discernible sub-network in Figure 4.4 has a chain structure. This connects a dense hybridization cluster in the area of surgery (600, 604, 606, 607, 623, 128) to a triad of domains in the area of electrical devices (174, 29, 439), passing through domains related to data processing and measurement (702, 73, 324), a clique involved in telecommunications technologies (370, 375, 379, 455), and a thick chain of knowledge hybridizations in the area of computers and information technologies (709, 710, 711, 712, 365, 257, 438). In view of the well-known integration of information and communication technologies, it is interesting to analyze the evolution of this last network fragment. II. II. THE EVOLUTION OF THE ICT CLUSTER To visualize the development of the ICT cluster in more detail, I selected patent classes 370, 375, 379, 455, 709, 710, 711, 712, 365, 257, 438, and I analyzed the time-partitioned data. To establish if the hybridization of information and communication technologies has grown indeed, I needed to account for the

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Characterizing the network structure of US-patented knowledge

generalized increase in the number of citations made and received over the observation period. For that reason, I removed ties from visualization based on the distribution of the tie values observed in each of the network cross-sections: only ties whose value is greater than 5% of the highest value observed in the pertaining time period are visualized. Figures 4.6 displays the evolution of the resulting sub-network. In line with what is generally believed, the domains belonging to the areas of information and communication technologies clearly came closer together during the observation period. As it turns out, this integration process began in the middle-eighties (1985-1989). Back then, information and communication technologies became connected by a bridge originated by domain 370 (Multiplex communications), whose inventions started to hybridize a sizeable number of inventions in domain 710 (Electrical computers and digital data processing systems: input/output). Following this initial phase, new ties emerged that consolidated the ICT field by progressively eliminating structural holes (Burt 1992)5. Between 1990 and 1994, the development of Multiplex communications became dependent also on domain 709 (Electrical computers and digital processing systems: multiple computer or process coordinating), which duplicated the bridge, while redundancy increased all through the sub-network. Later yet (1994-1999), the boundary between information and communication technologies became crossed by a multiplicity of domains and in both directions, and cliquish structures began to appear. Clearly, this simple account of the emergence of the ICT field falls short in contextual information. Rather than a historical description, it is meant to give a sense of the details of the knowledge hybridization network, and of the dynamics underlying its evolution. Incidentally, however, it is worth noting that the dynamics I observed in the ICT sub-network square nicely with the rich network-based description that Powell cum suis (2004) gave of the emerging biotechnology field.

5

Chapter 6 explains in which precise ways the structural holes present in hybridization networks, and their elimination, affect knowledge growth.

Characterizing the network structure of US-patented knowledge

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Characterizing the network structure of US-patented knowledge

III. SMALL-WORLD ANALYSIS The finding that many real-world networks are small worlds aroused the interest of many scholars and conveyed a decisive input to the emergence of the new science of networks. Small worlds are neither completely ordered networks6, nor completely random ones, but exhibit important properties of both. As it turns out, these properties can be described empirically by means of two simple statistics. One is the clustering coefficient, C, which measures the degree of transitivity, or local density, of a network. The other is the characteristic path length, or average geodesic, L, which is a global measure of distance across network nodes. In ordered networks, both C and L tend to be high; hence, networks are organized around local clusters and nodes are typically connected through long chains (Figure 4.7 A). In contrast, in random networks both C and L are low, thus nodes do not cluster locally and the average distance across nodes is small (Figure 4.7 C). Small-world networks feature both high clustering, like ordered networks, and short path lengths, like random networks. As revealed by Figure 4.7 B, this somewhat counterintuitive combination is made possible by the presence of but a few ties that cut across local clusters, thereby creating shortcuts between otherwise distant network regions. In this section I investigate whether the hybridization network among domains of US-patented knowledge is a small world, with a twofold objective. First, I aim to contribute to the accumulation of evidence on the ubiquity of small-world networks. A unique feature of the empirical network analyzed here is that it is described for a period as long as 25 years, making it possible to investigate how small-world parameters evolved over time. Second, small-world networks have been shown to emerge under very general conditions (Watts and Strogatz 1998). Hence, the small-world topology can be regarded as a null hypothesis of spontaneous network organization with which the observed network can be compared. The quantification of parameters C and L is meaningful only if the system analyzed is represented by a fully connected and un-weighted network. As said, 6

Here I adopt Watts’ restrictive definition of ordered network as a regular lattice (Watts 2004)

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I removed from analysis the five domains of US-patented knowledge that were isolated at any point in time during the observation period. Therefore, all the cross-sectional representations of the hybridization network are fully connected. Ties, however, are weighted, thus I dichotomized them for this analysis.

Increasing randomness

Figure 4.7 Examples of ordered (A), small world (B), and random networks (C) Source: Watts and Strogatz (1998)

A simple statistic to assess whether an empirical network is a small world is the so-called small-world quotient (Davis et al. 2003), which is calculated as follows. Let h be an observed empirical network with n nodes and k average degree, and let r be a random network similarly characterized by n and k. Let Lh be h’ s characteristic path length, as calculated by the average geodesic distance between all pairs of nodes, and let Lr be r’ s characteristic path length7. 7

Newman, Strogatz, and Watts (2001) showed that, for random networks, the characteristic path length is approximated by ln (n ) ln (k ) . This approximation,

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Characterizing the network structure of US-patented knowledge

Furthermore, let C h be h’ s clustering coefficient, measured as the average density of nodes’ ego-network, and let C r be r’ s average clustering coefficient, given by k/n. Then, the small-world quotient, S h , is:

S h = (C h Lh )(Lr C r )

(1)

Only if S h is sizably greater than 1 can the observed empirical network be regarded as a small world. Table 4.2 reports the small-world parameters for each of the five subsequent knowledge hybridization networks and for their corresponding random networks, as well as the resulting small-world quotients. Two considerations suggest themselves. First, the network of hybridizations among domains of USpatented knowledge does reveal a small-world signature, but this is far from pronounced. Second, over the 25 years observed, the network has steadily evolved away from the characteristic topology of a small world.

1975-79 1980-84 1985-89 1990-94 1995-99

Ch

Cr

Lh

Lr

Sh

0.488 0.511 0.552 0.580 0.619

0.209 0.236 0.292 0.333 0.382

1.830 1.793 1.723 1.675 1.619

1.791 1.763 1.708 1.667 1.618

2.279 2.128 1.874 1.733 1.620

Table 4.2 The evolution of small-world parameters

however, is unbiased only in the limiting case of n >> k (in which case, moreover, the standard deviation is quite large). In the network described here, the condition n >> k is not satisfied. To calculate Lr in a sounder way, I generated 50 random networks with n and k set equal to those observed in each of the five subsequent hybridization networks (thus obtaining 250 random networks in total), and measured Lr as the average of their characteristic path length. Note that, in all time intervals,

Lr had a standard deviation smaller than 0.01.

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A closer look at the results reveals an important nuance of this process. Over time, the network’s characteristic path length has become nearly identical to the one observed for random networks, thus reinforcing a typical trait of smallworld topologies. However, also the network’s average clustering coefficient has progressively approached the values expected for random graphs. Hence, the observed departure from the small-world topology is to be attributed entirely to the relative decline in the network’s degree of local clustering. In the next section, I delve deeper into this issue. IV. TRIADIC CENSUS While a network’s clustering coefficient is defined simply as the average density of its ego-networks, the latter may be determined by a variety of triadic configurations. To understand more precisely how the knowledge hybridization network relates to the characteristic topology of small worlds, it is then useful to inspect the evolution of its triadic census (Wasserman and Faust 1994). In a directed network, there exist 16 possible triad types (see Figure 4.8), which can be distinguished on the basis of three ordered digits. The first digit is the number of node pairs connected by a bi-directional tie; the second is the number of node pairs connected by a unidirectional tie; and, the third is the number of unconnected node pairs. In those cases in which the three ordered digits are insufficient to distinguish between triad types, a letter is added which indicates D (Down), U (Up), C (Cyclic), or T (Transitive). A triadic census is the distributional analysis of these triad types. Figure 4.8 shows each triad type (i = 1, 2,…, 16) denoted by its respective code. In Table 4.3, I compare the frequency, oi , of triad type i observed in each subsequent cross-section of the knowledge hybridization network, with the frequency, ei , expected for triad type i in random networks with an identical number of nodes and ties. When (oi − ei ) ei = 0, the observed frequency of

triad type i is identical to what would be expected if the network was random. For positive and negative values, the statistic expresses the observed frequency as a percentage deviation from the expected frequency for random networks.

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Characterizing the network structure of US-patented knowledge

Figure 4.8 Triad types

As can be seen, only types 030T, 030C, 120D, 120U, 120C, 210, and 300 contribute to increasing a network’s clustering coefficient. Of these, only 210 and 300 are observed to vary dramatically from zero in the knowledge hybridization network. Hence, the two most densely connected triad types, and particularly the only fully connected one, are entirely responsible for the average clustering coefficient to be higher in the knowledge hybridization network than in a random network. This indicates that domains have a strong tendency to cluster only when they hybridize ideas bi-directionally from one another, which in turn suggests that local reciprocity, rather than clustering in general, is a distinctive feature of the knowledge hybridization network.

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Now notice how the preponderance of these two triad types decreased over the observation period. In 1999, there were roughly as many triads of type 210 as there would be in a random network, while the frequency of fully bi-directional triads collapsed from 160 to 20 times the expected frequency for random networks. Clearly, the declining incidence of these two triad types explains the progressive departure of the knowledge hybridization network from the smallworld topology. Substantively, however, the causes of this process remain unclear. One possibility is that the knowledge hybridization network has been evolving towards a more integrated topology. Albeit speculative, this conjecture seems plausible when paired with the observation that due to a generalized increase in knowledge hybridization across domains, the density of the network almost doubled during the 25 years observed8.

(oi − ei ) ei

Triad Type

003 012 102 021D 021U 021C 111D 111U 030T 030C 201 120D 120U 120C 210 300

1975-79 0.71 -0.52 2.71 -0.81 -0.82 -0.83 0.39 0.40 -0.89 -0.91 9.28 0.14 0.08 -0.07 9.71 160.40

1980-84 0.89 -0.48 2.32 -0.80 -0.80 -0.82 0.26 0.26 -0.88 -0.91 6.95 -0.02 -0.07 -0.19 6.75 100.22

1985-89 1.31 -0.40 2.00 -0.78 -0.80 -0.81 0.01 0.10 -0.89 -0.91 4.28 -0.29 -0.26 -0.39 3.69 48.55

1990-94 1.79 -0.34 1.88 -0.76 -0.80 -0.80 -0.11 0.01 -0.89 -0.92 3.09 -0.43 -0.37 -0.49 2.35 30.03

1995-99 2.54 -0.24 1.90 -0.74 -0.81 -0.80 -0.24 -0.04 -0.90 -0.93 2.30 -0.54 -0.45 -0.60 1.43 19.41

Table 4.3 Longitudinal triadic census

8

Network density increased from 0.2066 in the time interval 1975-1979, to 0.3787 in the time interval 1995-1999

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Characterizing the network structure of US-patented knowledge

V. CONCLUSIONS The hybridization network among domains of US-patented knowledge appears to be well connected, although under the thicket of weak ties, its backbone structure features a rather long chain of connections with some dense clusters. The network also shows traits of the small-world topology, most of which is due the tendency of domains to form local clusters via reciprocation of hybridization patterns. However, the longitudinal analysis clearly points out that the structure of the network has been evolving away from the characteristic topology of small worlds.

CHAPTER 5 THE CONCENTRATION OF KNOWLEDGE PROGRESS

ABSTRACT: The size distribution of the domains of US-patented technological knowledge obeys an exponential law, revealing a disproportionable concentration of progress among larger domains. My analyses suggest that this phenomenon is explained by the combination of two factors. First, domains’ trajectories of growth have inherently different potentials. Second, differences in domains’ potentials are magnified by a mechanism – domains’ selfhybridization – endogenous to the process of knowledge growth. I conclude that the observed concentration of progress reflects dynamics of knowledge growth that are more general than the specific case analyzed, and should be factored in investment decisions and policies.

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The concentration of knowledge progress

H

aving characterized the hybridization network in which the 413 domains of US-patented technological knowledge are embedded (Chapter 4), I now would like to quantify the knowledge output generated in each domain during the observation period. Both simple and citationweighed patent counts can be employed to this end (Chapter 2). Although the latter method is known to yield more accurate estimates, here I prefer to use simple patent counts. As will become clear, this choice provides a more straightforward way to disentangle causal dynamics in the context of the analyses presented1. I regard the amount of knowledge produced within a given domain as its size. Figure 5.1 shows a scatter plot of domains’ size, as measured by the number of patents granted within the observation period, against domains’ rank, in linear (A) and semi-logarithmic (B) scale. The data follow a straight line in the semilogarithmic plot, indicating that domains’ sizes are distributed exponentially (Dragulescu and Yakovenko 2001).

Figure 5.1 Distribution of domains’ size semi-logarithmic (B) scale

1

in

linear (A)

and

All the analyses presented in this chapter have also been performed using citationweighed counts, instead of simple patent counts, which led to equivalent results.

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This impression is confirmed by Figure 5.2, which reports a probability plot of the observed size distribution against the theoretical exponential distribution. Ordinary Least Square regression of the logarithmic transform of domains’ rank on domains’ size makes it possible to establish statistically how closely the data fit an exponential function. The regression yielded an R-Squared of 0.963, indicating very close fit.

Figure 5.2 Plot of the observed probability distribution against the expected exponential probability distribution

In this chapter, I first show that the observed concentration of knowledge progress is an enduring characteristic of US-patented knowledge growth. Then, inspired by the analytical framework outlined in Chapter 1, I identify a general mechanism of concentration in knowledge progress, and I test its hypothesized effects. I conclude with a discussion of the scope and implications of my findings.

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The concentration of knowledge progress

I. ENDURING TRAIT OR TRANSIENT PHASE? To examine how the observed size distribution changed over time, I timepartitioned the data into five subsequent cross-sections as described in Chapter 3 (pp.44 - 46), and I again regressed the log of domains’ rank on domains’ size. The data turned out to be well described by an exponential distribution during each of the time intervals, with R-Squared deviating only slightly from the one estimated for the entire observation period. This suggests that the exponential distribution reflects a stable and enduring trait in the growth of US-patented knowledge. Distributional analyses, however, could obscure long-term changes. For this reason, in the following three sub-sections I turn my attention to domains’ growth patterns. Namely, I test if domains grow in a way that is compatible with the emergence of heavy-tail distributions or, in contrast, if they show signs of convergence towards a common size; and, I investigate how the observed concentration of knowledge progress is likely to change as domains approach a steady-state size. I. I. TOWARDS A HEAVY-TAIL DISTRIBUTION? There is increasing evidence that two distributions, power-law and lognormal, are ubiquitous in many realms of reality. Both distributions are highly skewed, with tails heavier than in the exponential, and apply to systems wherein concentration of resources is extreme. A classic example is the distribution of income in capitalist societies, which Pareto showed to obey a power-law in the upper tail (1897). Other well-known cases are the size distribution of cities (Gabaix 1999), firms (Gibrat 1931), human sexual contacts (Liljeros et al. 2001), the World Wide Web (Albert et al.), usage of words (Zipf 1949), and citations received by scientists (Lotka 1926). The ubiquity of power-law and lognormal distributions led scholars to investigate their generative processes in detail. Not unexpectedly, it turned out that the two distributions are inherently related, and represent the equilibrium solutions of a wide-ranging growth mechanism (Mitzenmacher 2003). The distinctive feature of this mechanism, which in the literature has been interchangeably termed law of proportionate effect (Gibrat 1931), cumulative advantage (Price 1980), Gibrat’s law (Simon

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1955), and Matthew effect (Merton 1968), is that the size of an object affects positively its subsequent growth. I. I. I. GIBRAT’S MODEL In his seminal book (1931), Gibrat was the first to provide a general mathematical model of growth by cumulative advantage. His model shows that, given a fixed population, the size of its units will converge to a lognormal distribution when growth dynamics are driven by a stochastic multiplicative component. Formally, let si denote the size of population unit i, t denote time, and ε be a stochastic term; then Gibrat’s law of proportionate effects can be expressed as:

sit − sit − ∆t = ε it sit − ∆t Gibrat assumed that

(1)

ε it is independent of sit ; that ε it features no significant

inter-temporal correlation; and, that there is no interaction between units. Given that:

sit = si 0 (1 + ε i1 )(1 + ε i 2 )...(1 + ε it ) ,

(2)

the logarithm of sit follows a random walk. Because in a short period of time

ε it can be regarded as small, the approximation ln (1 + ε it ) = ε it is justified.

Then, taking logs: T

ln sit ≅ ln si 0 + ∑ ε it

(3)

t =1

Due to central limit theorem, after a sufficiently long time the logarithm of units’ size will converge to a normal distribution; that is, units’ size will converge to a lognormal distribution.

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Gibrat’s model has been extended in a multiplicity of directions. One general conclusion that can be drawn from these studies is that growth by cumulative advantage does not necessarily lead to a lognormal size distribution, but often results in a power-law distribution instead. For example, Simon and Bonini (1958) showed that sizes converge to a power-law distribution if entry dynamics and the principle of preferential attachment are introduced in Gibrat’s model. Kesten (1973) showed that a power law distribution results from integrating Gibrat’s purely multiplicative mechanism with an additive term. In Levy and Solomon (1996a), a power-law distribution is obtained by imposing a lowerbound size on Gibrat’s model. Other extensions of Gibrat’s model that lead to the same general conclusion have been proposed, among others, by Manrubia and Zanette (1999), Nirei and Souma (2002), Cordoba (2002), Levy and Solomon (1996b), Sornette and Cont (1997), Sornette (1998), and Blank and Solomon (2000). I. I. II. TESTING FOR CUMULATIVE ADVANTAGE Thus, Gibrat’s model is an elegant representation of the basic mechanism behind the ubiquitous lognormal and power-law distributions. Moreover, it provides a straightforward method to test empirically if the mechanism of cumulative advantage is at work. As shown in (3), processes of cumulative advantage take place when units’ growth rates are unrelated to their current size and only depend on the sum of idiosyncratic shocks. Then, the following logarithmic specification can be used to test for growth processes driven by cumulative advantage:

ln sit − ln sit −1 = α + β ln sit −1 + u it

(4)

where u it is a random variable that satisfies the following conditions:

E (u it sit − s , s > 0)

=0

⎧σ 2 ⎪ E (u it u jt sit − s , s > 0) = ⎨ ⎪0 ⎩

i = j, otherwise

t =τ

The concentration of knowledge progress In equation 4, if

73

β < 0 , Gibrat’s law can be rejected, and the process is mean

β ≅ 0 , Gibrat’s law is confirmed, and cumulative advantage is at work. The case β > 0 can be regarded as a transient phase of a Gibrat-like

reverting2. If

process, whereby the process of cumulative advantage leads to explosive growth paths, which may endure for a short period but not indefinitely (Cefis et al. 2005). The model specification described by (4) has been widely used to test Gibrat’s law. However, the model assumes that unit effects are homogeneous – i.e. that

α i = α or, equivalently, that σ 2 (α i ) = 0 . Hence, under the hypothesis that Gibrat law does not hold, all units are assumed to converge to the same steadystate size. Because I have no reason to believe this to be an appropriate assumption in the case of knowledge domains, I use the Breusch and Pagan Lagrange multiplier (1980) to test the homogeneity assumption that

σ 2 (α i ) = 0 . The test clearly rejects the null hypothesis of homogeneity (ChiSquared = 60.20; Probability > Chi-Squared = 0.000); thus, the use of model (4) for the analysis of my data would overestimate my parameter of interest, β , whenever

β < 0 (Goddard et al. 2002).

In principle, additional covariates on the right hand side of (4) may eliminate the heterogeneity of individual effects, thereby making it possible to estimate β correctly. However, the possible sources of unit heterogeneity are so many that this strategy is hardly viable in practice. A more effective approach is then to use the panel structure of the data to model unit fixed-effects, thus removing all cross-sectional variation from estimation. In this case, (4) is reformulated as a variable-intercept model:

ln sit − ln sit −1 = α i + β ln sit −1 + u it

2

(5)

Note that the dependent variable in equation (4) is expressed as a difference of logarithms; hence, it approximates percentage change.

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The concentration of knowledge progress

Being interconnected in a network, domains of knowledge are by definition nonindependent units. If not appropriately accounted for, this non-independence may result in correlated residuals across units, and therefore bias the standard error of the estimated statistical relationships. A methodologically sound solution is to model explicitly this source of non-independence, known in the literature as network autocorrelation, in the statistical equation (Leenders 2002). To test whether the growth of US-patented technological domains between 1975 and 1999 has been characterized by the mechanism of cumulative advantage, I followed this strategy, and augmented equation (5) with a covariate capturing network autocorrelation. In order to model network autocorrelation, a weighting matrix of dyadic interdependences, W, needs to be specified. Typically, W reflects the network connections, whereby each (valued) dyadic tie determines the extent to which the response variable of a contact node affects the response variable of the focal node. The response variable of each node is then weighted on the basis of this dyadic inter-dependence score, and summed across all contacts for each of the nodes. The outcome is a node-level score of network autocorrelation, which is then employed as a regressor in the statistical equation. As a result of this procedure, the degree to which network connections induce network autocorrelation can be estimated and controlled for. Applied to my domain-by-domain knowledge network, this procedure estimates the degree to which the percentage growth of focal domain i is affected by the percentage growth of contact domains j. The weight that j’s growth has on i’s growth is determined by the number of citations between i and j. I computed this domain-level score of network autocorrelation and included it in two alternative specifications of model (5): one in which the growth of contacts j is assumed to have a contemporaneous effect on i’s growth, and the other in which the effects of j’s growth are supposed to be strongest after one period3.

3

Because these two specifications yielded qualitatively identical results, I only report the model with contemporaneous network autocorrelation.

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Table 5.1 reports the results: net of network autocorrelation (which turned out to be inconsequential), domains’ growth rates decreased significantly with domains’ size. This is in stark contradiction with the hypothesis of cumulative advantage, and indicates that domains’ observed growth patterns are not compatible with the emergence of heavy-tail size distributions. Dependent variable: domains’ growth rate Coefficient Std. Error t-value Sig. Intercept Network autocorrelation Domains’ size

1.854 0.001 -0.290

Number of units Periods Num. Observations F Prob. > F R-Squared within R-Squared between R-Squared overall ρ*

413 4 1652 78.57 0.0000 0.1127 0.0382 0.0032 0.7294

0.141 0.002 0.023

13.19 0.46 -12.51

0.000 0.644 0.000

Table 5.1 Variable-intercept regression of domains’ size on domains’ growth rates. * = fraction of variance due to domains’ fixed-effects.

I. II. CONVERGING TO A COMMON SIZE? The negative value of β in model (5) implies that a process of mean-reversion is afoot in the distribution of US-patented knowledge across domains. This reversion, however, means neither that domains have been converging to a common size, nor that they will. As indicated by the Breusch Pagan Lagrange multiplier test of homogeneity, there are significant domain-specific effects, revealing permanent differences across domains’ growth paths, which in model (5) are accounted for by a variable-intercept specification. Hence, the estimated negative relationship between domains’ current size and subsequent growth rate

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The concentration of knowledge progress

expressed by

β should be interpreted as evidence that domains tend towards

different steady-state sizes. Model (5) lends itself to a substantive interpretation of why domains cannot converge to a common size. The model says that growth rates decline similarly across all domains as these grow larger, while domains’ initial growth rates are significantly different. A metaphor for this is a group of cars consuming the same amount of fuel per kilometer, but beginning their trip with different amounts of fuel in their tank. Likewise, all domains progressively exhaust their growth potential, but they differ in their initial endowment. Differences in domains’ inherent growth potential can be explained in several ways, the most obvious one being that possibilities of technological developments are, at least in part, determined by idiosyncratic technical and physical constraints. This point, albeit sometimes shadowed by sociological and economic discourse, is central to theories of technical change (Nelson and Winter 1982; Rosenberg 1994), and is reflected in historiographic accounts of technological development (e.g. Mokyr 2002). I. III. DOMAINS’ STEADY-STATE SIZES In the last two sections I described the overall picture: on the one hand, domains’ growth dynamics are incompatible with the emergence of heavy-tail size distributions while, on the other, there are permanent differences across domains that prevent them from converging to a common size. Now, I would like to turn to a more detailed view, and ask whether we should expect the observed concentration of knowledge progress to increase or decrease as domains approach their steady-state size. To get a more nuanced inspection of the available data, I propose to complement the results obtained under model (5) with the estimation of the following model:

∑( t

ln s it − ln s it −1 ) T −1

= λ +τ

∑

ln s it −1

t

T

+u

(6)

The concentration of knowledge progress where T is the number of observed time points, estimated, and u is an error term.

77

λ and τ are parameters to be

In model (6) longitudinal observations are collapsed into domains’ means over time, thus the only variance left is between domains. For this reason, this model is also referred to as the between-effects estimator. As it results in substantial loss of information, the between-effects estimator is not much used in practice. However, in combination with model (5), it can shed light on the nature of domains’ observed size differences. Figure 5.3 helps illustrate how.

Figure 5.3 Hypothetical size-growth plots featuring negative within-domain effects, and negative (A) and positive (B) between-domain effects

Both Figure 5.3 A and B represent sets of hypothetical domains of knowledge whose growth paths display both domain-specific effects (the data points are clustered within domains), and a mean-reverting process towards domainspecific steady state sizes (the clusters follow a negative slope). In other words, both figures represent situations that are perfectly compatible with the estimates obtained for US-patented knowledge domains, i.e.

α i ≠ α , and β < 0 in

model (5). The difference between A and B is in the patterns observed between domains, represented in each figure by the long line interpolating the clusters, and whose slope is captured by parameter τ in model (6). As can be seen, in A

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The concentration of knowledge progress

this line has a negative slope, thus τ < 0 , whereas in B its slope is positive, thus

τ > 0 . This means that in A, domains that are on average larger over the observation period display a lower average growth rate; in contrast in B, larger domains also display a higher average growth rate. As I will try to explain, this implies that in A, larger domains have on the average less potential for future hybridization and growth, whereas the opposite is true for B. To illustrate why this is the case, let me again refer to Figure 5.3. Notice that that the zero-point on the Y-axis indicates the point where domains do not grow, i.e. where they reach their steady-state size4. As can be seen, in A part of the observed size differences between larger and smaller domains is due to larger domains having exploited, on average, more of their growth potential. While larger domains are bound to grow yet relatively modestly or even to shrink to reach their steady-state size, smaller domains will reach their steady-state size only after growing a great deal more. Thus, one can expect size differences to diminish as domains approach their steady-state sizes, leading to a decrease in the concentration of knowledge progress. In B the situation is reversed. Here the domains that have been observed to be smaller during the observation period are, on average, closer to or larger than their steady-state size. Accordingly, in this case the concentration of knowledge progress among large domains will increase as domains approach their steady-state size5. The estimates of model (6) for the US-patent data are reported in Table 5.2: controlling for network autocorrelation, domains’ average size is positively associated with domains’ average growth rate (i.e. τ > 0 ), and the relationship is highly significant. It follows that the growth paths of the domains of USpatented knowledge conform to the situation sketched in Figure 5.3.B, thus 4

Accordingly, when domains are above this point their sizes grow, and when they are below their sizes shrink. Clearly, this representation abstracts away from time. 5 To get back to the car metaphor introduced earlier, in A larger domains are like cars that have proceeded a longer way but have less fuel left in their tank. In B, in contrast, larger domains are like cars that have gone a longer way, and still have more fuel in their tank than other cars. By the time all cars are left without fuel, in A the cars that were lagging behind will have caught up to some degree, whereas in B they will be left even further behind.

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knowledge progress will become even more concentrated among large domains as domains approach their steady-state size. Dependent variable: domains’ growth rate Coefficient Std. Error t-value Sig. Intercept Network autocorrelation Domains’ size

-0.074 -0.006 0.029

Number of units Periods Num. Observations F Prob. > F R-Squared within R-Squared between R-Squared overall

413 4 1652 9.00 0.0001 0.0205 0.0420 0.0025

0.045 0.004 0.007

-1.64 -1.31 4.03

0.102 0.192 0.000

Table 5.2 Between-effects regression of domains’ size on domains’ growth rates.

II. EXPLAINING THE CONCENTRATION OF KNOWLEDGE PROGRESS On the basis of the analyses presented so far, there remains little doubt that the observed concentration of knowledge progress among larger domains reflects a continuing feature in the advancement of US-patented knowledge. Without delving deeper into the causes of this phenomenon, however, it is impossible to establish its generality beyond the empirical case observed. According to model (5), domains’ steady-state sizes are determined by two parameters: a domain-specific intercept, and the relationship between domains’ size and growth. The first of these two parameters, as I have argued, can be interpreted as the growth potential inherent in domains’ path of development: clearly, domains’ inherent growth potentials have a bearing on their steady-state size. The second of these two parameters – the size-growth relationship – determines the degree to which domains’ inherent growth potentials are realized.

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The concentration of knowledge progress

To see why, consider the following two limiting cases. If domains’ growth rates decay infinitely fast as a function of domains’ size, then the size of all domains drops to zero regardless of domains’ inherent growth potential. In contrast, if domains’ growth rates do not decay with domains’ size at all (as is the case with processes of cumulative advantage), then domains’ inherent growth potentials will be perpetually amplified. I posit that there exists a mechanism, integral to the process of knowledge growth, which intervenes in the size-growth relationship so as to systematically boost concentration in knowledge progress. My argument is the following. Knowledge grows along trajectories of hybridization because hybridizations occur consistently more often within than between domains of knowledge6. Accordingly, the number of self-hybridizations domains yield, and the knowledge output resulting from them, should increase proportionally to domains’ size. If this is the case, then domains’ self-hybridizations counter the tendency of growth rates to decay with domains’ size and, thereby, magnify the size differences induced by domains’ inherent growth potentials. For that reason, I expect the mechanism of self-hybridization to reinforce the concentration of knowledge progress. In statistical jargon, my argument is that domains’ self-hybridizations mediate the size-growth relationship. This hypothesis is corroborated if two conditions are met. The first is that domains’ size and self-hybridizations must be positively correlated. This is clearly the case with my data: on average, during the 25 years observed, the Pearson correlation coefficient between the log of domains’ size – as measured by number of patents – and the log of domains’ self-hybridizations – as measured by number of self-citations – has been 0.942. The second condition is that the effects of size and self-hybridizations are counteracting, resulting in a stronger negative effect of size on growth when the effect of selfhybridizations are controlled for. A straightforward way to test whether this second condition is met is to augment model (5) with the log of domains’ selfcitations. Due to the very high correlation between domains’ size and self-

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hybridization, however, the resulting model specification exhibited high multicollinearity (highest VIF = 18.2). Therefore, I preferred to augment model (5) with the raw count of self-citations instead. This reduced the correlation between the regressors to 0.599, thereby eliminating the problem of multicollinearity (highest VIF = 1.54)7. Table 5.3 reports the results of the analysis: net of the productive effect of self-hybridizations, the negative effect of domains’ size on domains’ growth increases by roughly one fourth (compare Table 5.3 with Table 5.1). This clearly indicates that also the second condition necessary for the corroboration of my hypothesis is met. Dependent variable: Domains’ growth rate Coeff. Std. Error t-value Sig. Intercept Network autocorrelation Domains’ size Domains’ self-hybridizations

2.235 0.001 -0.365 2.3e-04

Number of units Periods Num. Observations F Prob. > F R-Squared within R-Squared between R-Squared overall ρ*

413 4 1652 67.54 0.0000 0.1408 0.0322 0.0017 0.7710

0.151 0.002 0.025 4.3e-06

14.82 0.33 -14.21 6.36

0.000 0.740 0.000 0.000

Table 5.3 Variable-intercept regression of domains’ size and domains’ selfhybridization, on domains’ growth rates. * = fraction of variance due to domains’ fixed-effects.

6

In my data, for example, domains’ self-citations – indicating self-hybridizations – are roughly half of all citations, and approximately 217 times more frequent than would be expected if hybridizations occurred randomly across domains. 7 Notice that I also estimated the model in which both domains’ size and selfhybridization are logarithmically transformed, obtaining qualitatively identical results.

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III. CONCLUSIONS In this chapter, I showed that a stable and continuing feature in the growth of US-patented knowledge is that it concentrates disproportionably among larger domains. This tendency is explained by the combination of two factors: domains’ trajectories of growth have inherently different growth potentials, whose effects on domains’ steady-state sizes are magnified by the endogenous mechanism of self-hybridization. As it is hard to conceive of a process of knowledge growth in which either of these two factors would not be at work, I reckon that the observed concentration of progress reflects dynamics of knowledge growth that are more general than the specific case analyzed.

Figure 5.4 Scatterplot of domains’ rank position in the first (1975-79) and last (1995-99) time intervals

A straightforward implication that can be derived from my research is that, ceteris paribus, it is advantageous to invest in larger domains of knowledge.

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83

There is a limit to this prescription, though: if private investors and policymakers focus their resources among larger domains, thereby accelerating their transition to their steady-state size, at some point smaller domains could become relatively more productive investments. Moreover, the tendency of knowledge progress to concentrate among larger domains is far from a deterministic process. This point is visualized in Figure 5.4, wherein domains’ rank orders are plotted at the beginning (X-axis) and at the end (Y-axis) of the observation period. As can be seen, although the distribution of progress has remained stable over the observation period, there has been a substantial rank re-ordering within the distribution. Likewise, the size advantage induced by the endogenous mechanism of self-hybridization explains only a fraction of the variance in domains’ growth rates (Table 5.3). In the following chapters, I hope I will be able to show that factors other than size play a crucial role in determining domains’ growth rates as well as the rank reordering displayed in Figure 5.4.

CHAPTER 6 SPECIALIZATION AND BROKERAGE: A THEORY OF KNOWLEDGE GROWTH

ABSTRACT: In this chapter, I employ the network framework presented in Chapter 1 to make sense of an unresolved paradox: is knowledge growth favored by knowledge specialization or by knowledge brokerage? I propose to reconcile the functions of specialization and brokerage into a dynamic explanation, thereby laying the foundations of a theory of knowledge growth. The empirical analysis supports the derived hypotheses, which encourages me to develop the theory further.

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Specialization and brokerage: a theory of knowledge growth

T

he view that specialization favors the advancement of knowledge lies at the core of modern economic thinking, being central in the work of Adam Smith (Smith 1776), Amasa Walker (Walker 1867), Allyn Young (Young 1928) and Alfred Marshall (Marshall 1936)1. More recently, however, also the notion that brokerage of diverse specialties propels knowledge has become widely accepted in the literature (Scherer 1964; Sutton and Hargadon 1996)2. Thus far, the relationship between knowledge specialization and knowledge brokerage has remained unexplained. However, specialization and brokerage appear to exclude each other, because specializing in a particular domain impairs brokering many, and vice-versa. The goal of this chapter is to show how this apparent contradiction can be resolved, and how the functions of both knowledge specialization and knowledge brokerage can be integrated into one dynamic theory of knowledge growth. The chapter proceeds as follows. I begin by defining specialization and brokerage network-analytically (Section I) and, subsequently, I explicate how their underlying mechanisms of knowledge growth can be reconciled in a dynamic explanation (Section II). On these bases, in the third section I derive three testable hypotheses. Then, in the fourth section, I select the inferential models, which I employ to test the hypotheses in the fifth section. In the last section, I discuss the results. I. A NETWORK REPRESENTATION OF SPECIALIZATION AND BROKERAGE In line with the analytical framework outlined in Chapter 1, I regard knowledge specialization and knowledge brokerage as specific patterns of knowledge hybridization. Intuitively, domains are specialized when they advance by hybridizing closely related ideas, whereas they are brokering if their progress springs from the combination of unrelated ideas. In this section, I formalize

1

Xiaokai Yang and Siang Ng (1998) report that the advantages of specialization for invention were spelled out even before the work of Adam Smith, for example in the French Encyclopedia published in 1701, in Maxwell (1721), and Tucker (1755; 1774). 2 Interestingly, also this idea dates back to at least Adam Smith’s work: “When the mind is employed about a variety of objects it is some how expanded and enlarged” (quoted in Burt 2004, p. 350).

Specialization and brokerage: a theory of knowledge growth

87

these concepts network-analytically, thereby making them less ambiguous and more tractable. The starting point is the conception of a domain’s niche as a sub-network comprising a focal domain, its contact domains, the valued and directed ties linking the focal domain to its contacts, and the valued and directed ties linking contact domains among each other3. Structural holes indicate a lack of connections between nodes within such sub-networks. In the context of this study, the structural holes in a domains’ niche measure the degree to which that domain hybridizes ideas from domains that do not hybridize ideas from one another or from the focal domain. Then, the brokerage of a domain is captured by the structural holes in its niche and, conversely, a domain’s specialization is captured by its lack of structural holes. To measure on a continuous scale the brokerage4, Bit , of a focal domain, i, within a given interval of time5, t, I adapted Burt’s model of network brokerage (1992) as in equation (1):

(

Bit = 1 − piit + ∑ pijt + ∑q piqt pqjt j

)

2

(1)

where:

piit =

3

hiit Σ j hijt

This conception of niche as a relationally defined position in a network is similar to the one employed, at the level of the patent, by Podolny and Stuart (1995). 4 To avoid unnecessary complications, in the following I will often use either the term specialization or the term brokerage, leaving their duality implicit. It remains understood that specialization means lack of brokerage, and brokerage means lack of specialization. 5 Note that t indicates a time interval, not a point in time.

88

pijt =

Specialization and brokerage: a theory of knowledge growth

hijt

*

h jit

∑ hiq ∑ h jx t

q

piqt =

p qjt =

t

x

hiqt + hqit

(

Σ j hijt + h jit

)

hqjt + h jqt

(

Σ z hqzt + hzqt

)

In this model, j and q are variables for the nodes in i’s niche, and i ≠ j ≠ q; for nodes in j’s niche x is used, x ≠ j; and z stands for nodes in q’s niche, z ≠ q ≠ j; h is the number of ideas belonging to the right-hand subscript domain, used in hybridizations belonging to the left-hand subscript domain. Then, piit is the proportion of self-hybridizations within domain i, relative to all hybridizations carried out by i; pijt is the proportion of ideas belonging to domain j that are hybridized in advancing i, weighed by the proportion of ideas that j hybridizes from i; and, the term within the inner summation indicates the redundancy of i’s contact domains, i.e. how closely related they are to both i and i’ s other contacts. Bit is zero when i advances by hybridizing ideas only from one fully specialized knowledge source, either itself or another, so when there are no structural holes in its niche; it approaches one when i hybridizes ideas from many mutually-unrelated knowledge sources6.

6

My model of network brokerage differs from Burt’s in two ways. First, I account for the role of loops, i.e. domains’ self-hybridizations, with the term piit. Second, Burt calculates pijt by an additive term. This can lead to paradoxical conclusions in the context of my study, because, if i does not hybridize ideas from j while j does hybridize ideas from i, changes in j may still affect the computation of i’s brokerage and specialization. To correct this problem, I use a multiplicative term to calculate pijt; by doing this, I make the role of j’s hybridization of ideas from i conditional on the proportion of ideas that i hybridizes from j.

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89

The concept of structural holes makes it possible for any given hybridization network to compare the degree of specialization versus brokerage of each of the nodes. In order to understand and model actual knowledge development, it is useful to look into the dynamic version of this cross-sectional view. The specialization of a domain, i, between two subsequent time intervals, t-1 and t, increases with hybridizations carried out that reduce the structural holes in i’s niche relative to t-1. In turn, hybridizations reduce i’s structural holes when they are path-dependent, i.e. reinforce already established ties in i’s niche. As can be seen in equation (1), this can happen in three ways. First, the proportion of selfhybridizations increases ( piit − piit −1 > 0 ) . Second, i’s hybridizations to other

( ( )

domains become more concentrated Σ j pijt

2

(

− Σ j pijt −1

)2 > 0). Third, the

domains that i hybridizes from become more redundant, i.e. they hybridize larger proportions from one another or from i

(Σ q piq pqj t

t

)

− Σ q piqt −1 p qjt −1 > 0 .

To understand under which conditions the beneficial effects of specialization and brokerage can be expected, one needs to explicate how their characteristic patterns of knowledge hybridization enhance knowledge growth. I address this issue in the next section. II. CREATIVITY, SPECIALIZATION AND BROKERAGE A popular view sees creative thinking as a mode of reasoning in which enlightened thoughts spring to mind without being cued, but this turns out to be more of a myth than a representation of reality. Mastery of the subject matter is necessary both to appreciate and to pursue the potential of a creative thought (Simonton 2000; Walberg 1988), and it conduces to absorptive capacity (Cohen and Levinthal 1990). Mastery, albeit necessary, can be achieved only at the price of high fixed learning costs (Hayes 1989; Simonton 1991), as it typically takes years of preparation before even the most talented individuals can become proficient in any given domain (Weisberg 1993)7. It follows that it is efficient to spread fixed learning costs over a larger knowledge output, thus to 7

Mastery does not exclude serendipity but, as Pasteur said, “chance favors the prepared mind.”

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hybridize as many ideas as possible from an unchanging set of related knowledge domains. The reverse is also true. Hybridization of ideas from a broad set of unrelated knowledge domains is an inefficient mode of knowledge production because it involves higher learning costs associated with a given level of knowledge output. For these reasons, I conclude that: Proposition 1

Specialization yields efficiency in knowledge production

While mastery of the subject matter makes it possible to appreciate and pursue the potential for developing new ideas, the novelty of hybridizations resides in the useful relations they establish between yet unrelated ideas (Weisberg 1993). Cross-fertilizing transfers of ideas typically occur by shifting mental models through analogies, metaphors, or other cognitive mechanisms (Holyoak & Thagard 1995). Regardless of the mechanisms involved, it is the exposition to ideas from different domains and applications that prompts unexplored mental representations and makes novel hybridizations visible (Anderson & Thompson, 1989). A well-known example is Gutenberg’s printing press, which resulted from creatively pooling his knowledge of paper, metallurgy, press, ink, movable types, and the alphabet, among others (Diamond 1997). The literature abounds of similar accounts of other inventions, both old and new (Mokyr 2002). More systematic empirical evidence is reported by Dunbar (1996), who showed that scientists in laboratories with a greater diversity of scientific backgrounds are better able to solve problems by conceiving new ideas. Benefits of brokering a diversity of knowledge sources, and developing a proficiency at it, can be gained beyond laboratories. Hargadon (2002) and Burt (2004) found that individuals and organizations brokering between unrelated regions of their social network come up with more innovative ideas. Because the diversity of ideas someone is exposed to is determined by the diversity of the knowledge sources one learns from and strives to improve upon, we expect that hybridizing ideas from unrelated knowledge domains develops the ability to identify novel hybridizations. Proposition 2

Brokerage yields new hybridization potential

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By clarifying the specific mechanisms through which specialization and brokerage enhance knowledge growth, Propositions 1 and 2 connect to and enrich extant literature. Consider Thomas Kuhn’s theory of knowledge (1962). This theory states that knowledge typically advances by long trajectories of cumulative refinements, or normal science. In this mode of knowledge growth, mopping up and puzzle solving operations push forward the frontier of knowledge incrementally. Although normal science can generate a great deal of progress for some time, it invariably exhausts creativity. When stagnation looms, manifesting itself through an increasing number of anomalies and insoluble problems, only radical departure from the core principles – a paradigm shift – can bring new momentum to the progress of knowledge. Kuhn’s theory captures dynamics of knowledge growth that appear to take place well beyond the realm of science. A central tenet of evolutionary economics is that trajectories of technological knowledge follow analogous patterns of advancement (Dosi 1982; Nelson and Winter 1982). This view is backed by empirical evidence from many industries that long periods of incremental technical improvement are interrupted by short periods of radical and disruptive innovation – a pattern termed punctuated equilibrium (Tushman and Anderson 1986; Abernathy and Utterback 1978). However general, Kuhn’s theory of knowledge growth does not specify why normal knowledge production leads to stagnation, or why new thrust for knowledge advancement follows radical departures from existing trajectories of accumulation. In my network representation, the trajectory of development of a knowledge domain (in technology, science, or other realms) at any point in time is determined by the domain’s niche of knowledge sources. Normal knowledge advancement consists of path-dependent hybridizations that progressively exploit the structural holes comprised in a domain’s established niche, thereby increasing its specialization. This mode of knowledge advancement is efficient – which explains why it is the normal (i.e. predominant) one. However, by progressively depleting a domain’s structural holes, it exhausts its creative sources. Paradigm shifts, on the contrary, result from hybridizations that initiate relations with knowledge sources previously outside a domain’s niche, thereby expanding its structural holes. By connecting ideas from yet unrelated domains of knowledge, path-breaking hybridizations prompt unexplored perspectives,

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which may yield potentially fruitful veins for new hybridizations of ideas. Advancement is in no way guaranteed, though: path-breaking hybridizations are both costly and risky from a cognitive and an institutional perspective, and many holes are likely to be inconsequential dead-ends. In some cases, however, a new process of normal knowledge advancement catches on that reaps the value inherent in the new knowledge structure opened up. Then a sequence of cumulative hybridizations materializes the inventive potential by exploiting the newly created tie(s), signaling a paradigm shift. Besides making possible to explain macro-dynamics of knowledge growth in terms of precise network conditions, Propositions 1 and 2 also complement the notion that at the micro level, knowledge production is maximized by balancing knowledge exploitation and exploration (March 1991). Exploitation, which consists of harvesting as much value as possible from one’s knowledge base, appears to be the predominant strategy of knowledge production in both humans and firms. In organizational sociology and psychology, the acquisition of new knowledge is regarded as conditional upon one’s existing competencies (March and Simon 1958). Similarly, according to Cohen and Levinthal's (1990) concept of absorptive capacity, firms’ ability to assimilate and integrate new technological knowledge depends on their past R&D. In the long run, however, exploitation cannot sustain knowledge growth; hence, some degree of exploration beyond one’s established competencies is necessary (Kogut and Zander 1992; Henderson and Cockburn 1994; Rosenkopf and Nerkar 2001; Teece et al 1997). Albeit useful, the notions of exploitation and exploration are markedly abstract, which hinders their use for scientific theory and research. My network-structural perspective fleshes out these two notions. Exploitation consists of hybridizations that deplete the existing structural holes in a pathdependent niche of knowledge sources; thus, exploitation implies making efficient use, and thereby progressively exhausting, the creative potential inherent in an established knowledge base. Exploration, in contrast, consists of hybridizations that break outside the current niche; thus, exploration implies

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high learning costs, along with a possibility to discover new potentially creative structural holes8. While connecting with extant literature, my network approach provides a novel explanatory framework and methodology for analyzing the process of knowledge advancement. In the following section, I derive three testable hypotheses about the effects of knowledge specialization and knowledge brokerage, which resolve the contradiction in the literature and may lay the foundations for a full-fledged theory of knowledge growth. III. HYPOTHESES I have argued that path-dependent hybridizations yield efficiency in knowledge production. These are hybridizations that deplete the structural holes in a domain’s established niche, thereby increasing its specialization. Hence, I expect that domains that increase their specialization between two points in time grow faster in that time period: Hypothesis 1

Changes in specialization are positively associated with domains’ growth rates

However, the structural holes of any niche are finite. This leads to two further testable implications. The first is that higher specialization is associated with slower growth, because more hybridization opportunities have already been exploited in specialized domains, and fewer opportunities are left for subsequent hybridizations. Conversely, brokering domains should have greater potential for upcoming hybridizations and, thus, for growth. Hypothesis 2

8

Levels of specialization are negatively associated with domains’ growth rates

Typically, empirical research on structural holes at the person or firm level is based on the analysis of, respectively, person-by-person and firm-by-firm networks. Incidentally, it is important to notice that other operationalizations are possible and, arguably, more suitable to the analysis of structural holes in knowledge niches. In the concluding chapter of this dissertation, this issue will be discussed in greater detail.

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Specialization and brokerage: a theory of knowledge growth

The second implication is that path-dependent hybridizations should yield marginally decreasing returns. Unlike hypothesis 2, the argument here is not that specialized knowledge offers fewer possibilities to hybridize, but that possible hybridizations have a more limited innovative potential. The higher the level of specialization, the more hybridization possibilities consist of refinements of current ideas in a mopping-up fashion. On the other hand, hybridizations in brokering domains spring on average from more distant cross-fertilizations, resulting in greater knowledge advancement. Hypothesis 3

The positive effect of changes in specialization on domains’ growth rates decreases with levels of specialization

In order to design a solid test of my hypotheses, a number of issues need to be accounted for in the statistical model. I discuss them in the next section. IV. STATISTICAL MODEL To measure domains’ size, in this chapter I used the number of citations domains received within each time interval. Accordingly, my dependent variable – domains’ growth rate – is calculated as the percentage change in citations received by each domain between subsequent time intervals. The number of citations received by a domain is determined by the number of patents granted within that domain, weighed by the number of citations each of these patents received. Thus, my dependent variable takes into account the specific knowledge contribution of individual patents (Chapter 2) 9. Both patents and citations increased rapidly during the observation period, and it is impossible to establish what part of this increase reflects dynamics of knowledge growth, and what part reflects artificial changes in the data (Chapter 2). As panel data have both a longitudinal and a cross-sectional dimension, a 9

As the attentive reader will remember, in Chapter 5 I measured domains’ size by a simple patent count. This choice was made in order to distinguish more clearly the effect of domains’ self-hybridizations – measured by domains’ self-citations – on domains’ size. Here, domains’ self-hybridizations are not modeled; thus, I can improve the measurement of domains’ size by taking into account patents’ citations.

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conservative solution is to model all unit-invariant time-specific effects by means of period-dummy variables. In order to sort out the possibility that timerelated artifacts could alter the estimation of the hypothesized relationships, this is the strategy I adopted in my analyses. Estimations might also be altered by unaccounted cross-sectional correlation. In the case of my knowledge network, I reckoned there exist two possible sources of cross-sectional correlation. First, as suggested by Hall cum suis (2001), domains’ growth dynamics may be affected by the broader technological area they belong to (Chapter 2). To account for this, I included a set of dummy variables representing the six macro-technological categories defined by the NBER 1-digit classification. Second, cross-sectional correlation may result from dynamics of network autocorrelation (Leenders 2002), which I modeled by means of a domain-level score of network inter-dependence (see Chapter 5, p. 74). Because observations are repeated on the same units, panel data typically have a nested structure: observations within units are more likely to be similar than observations between units. Ignoring this nested structure may lead to biased estimates and incorrect standard errors. A general form of statistical models that do account for unit heterogeneity is:

Yit = α i + X i't β + ε it

(2)

where i = 1,...,N; t = 1,...,T The main difference between (2) and a standard regression equation is represented by term

α i , denoting unit-specific factors. I considered a number of

alternative approaches to modeling

α i . First, I ran a simple OLS regression on

the pooled data. This approach seemed reasonable because my dependent variable is expressed as a change variable, and thus in effect accounts for unobserved domain-specific differences. Second, I removed all between-domain variance from the estimation by taking unit-demeaned variable transformations.

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Specialization and brokerage: a theory of knowledge growth

This approach, known as fixed-effects or within estimation, is equivalent to modeling

α i as a set of i = {1,…, N} domain-dummy variables. Thus, its

estimates are based exclusively on the variance observed within domains over time. The third approach I employed is to model

α i as random draws from a

wider population, which results in a random-effects model, and leads to:

α i = α + ηi

(3)

and, in turn, to

Yit = α + X i't β + η i + ε it The domain-specific factors are now denoted

(4)

η i (instead of α i ) to emphasize

that they are modeled as a random component of the same type as the error ε it – i.e. as a distribution characterized by its mean and variance – rather than constant parameters as in the fixed-effects specification. The random-effects model estimates the coefficients from weighted unit-demeaned variable transformations, where the weight, 0 < θ < 1, is determined by:

⎞ ⎛ σ ε2 ⎟ θ = 1− ⎜ 2 ⎜ σ + Tσ 2 ⎟ η ⎠ ⎝ ε

(5)

Because θ is calculated by partitioning the variance into its longitudinal and its cross-sectional components, estimations in the random-effects model take into account both within-unit and between-units effects. For that reason, the randomeffects specification is more efficient than the fixed-effects one; moreover, it makes possible to estimate jointly time-invariant and unit-invariant variables. In the three models I just presented, it is assumed that the data are homoskedastic and that all serial correlation is accounted for. To assess to what degree my estimates of interest are affected by these assumptions, in my fourth

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model I assumed them to be violated, and tested the hypothesized relationships on this basis. To do this, I modeled panel-level heteroskedasticity and a firstorder autoregressive (AR1) error covariance structure10, and I employed a Feasible Generalized Least Squares (FGLS) estimator. V. ANALYSIS On the basis of the Breusch-Pagan Lagrange multiplier test (1980) of the pooled regression against the random-effects model, it turned out that the pooled OLS model may not be consistent – the null hypothesis of identical disturbances is rejected (Chi-square = 29.58; Prob. > Chi-square = 0.0000). For that reason, I report the results obtained under the pooled OLS model in appendix. Estimations for the remainder three models are reported in Table 6.1.

Intercept Network autocorrelation Domain size 1985 through 1989 1990 through 1994 1995 through 1999 Computers & Communications Drugs & Medical

10

Dependent variable: domains’ % growth rate Random-effects FGLS Fixed-effects 0.71*** 0.31*** 0.28*** (0.13) (0.06) (0.02) 0.00 -0.00 -0.00 (0.00) (0.00) (0.00) -9.3e-07 -1.7e-06 1.3e-06 -06 -06 (5.2e ) (2.9e ) (8.8e-07) 0.35*** 0.37*** 0.33*** (0.04) (0.04) (0.01) 0.11** 0.13*** 0.11*** (0.05) (0.04) (0.01) 0.29*** 0.32*** 0.24*** (0.05) (0.04) (0.02) 0.84*** 0.66*** (0.07) (0.05) 0.94*** 0.69*** (0.11) (0.06)

I follow Beck and Katz (1995), who make a strong argument in favor of modeling the coefficient of the first-order temporal correlation as common to all panels.

98

Specialization and brokerage: a theory of knowledge growth Fixed-effects

Random-effects

FGLS

-1.01*** (0.36) 1.49*** (0.39) -1.65** (0.69)

0.10 (0.07) 0.07 (0.06) 0.14** (0.06) -0.37*** (0.12) 1.92*** (0.34) -1.69*** (0.56)

0.08*** (0.02) 0.03 (0.02) 0.10*** (0.02) -0.20*** (0.05) 2.16*** (0.30) -2.23*** (0.70)

413 4 1652

413 4 1652

374.46 0.0000 0.1015 0.3676 0.2117

1116.45 0.0000

Electronic Mechanical Others Specialization ∆ Specialization Specialization * ∆ Specialization Number of units Periods Num. Observations F Prob. > F Wald chi-sqaure Prob. > chi-square R-Squared within R-Squared between R-Squared overall Corr. ( η i , Χ b )

413 4 1652 17.90 0.0000

0.1042 0.0198 0.0608 -0.1212

Table 6.1 The dynamic effects of specialization on knowledge growth under the fixed-effects, random-effects, and FGLS specifications. Standard errors in parenthesis. *** = p < 0.001, ** = p < 0.01, * = p < 0.05

Before examining the results from a theoretical point of view, let me discuss their reliability. The first noteworthy element is that directions and significance levels of the estimated coefficients are nearly identical in all three models. This is a reassuring starting point, because the estimates are based upon different assumptions and modeling specifications. To be sure, the fixed-effects model is

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99

a conservative approach that generates consistent estimates with panel data (Hsiao 2003). In contrast, random-effects models are not consistent if the unobserved unit-specific factors,

η i , are significantly correlated with the

regressors, Χ b . As reported in Table 6.1, the estimated correlation coefficient between

η i and Χ b is relatively low in my case, amounting to a mere -0.1212.

Whether so much correlation induces inconsistent estimates in the randomeffects specification can be formally established by means of a Hausman specification test (1978). This tests the null hypothesis that there is no systematic difference between the coefficients estimated by a random-effects specification and its fixed-effects counterpart. As the null hypothesis cannot be rejected (Chi-square = 6.63; Prob. > Chi-square = 0.4687), it can be safely concluded that also the random-effects specification yields consistent estimates. Let us now turn to the analysis of the results. The first rows of Table 6.1 report estimates of the intercept and the control variables. In line with the analyses of Chapter 5, network autocorrelation is not an issue, and domains’ size has a negative effect on domains’ subsequent growth rates. However, here the effects of domains’ size are far from significant, revealing that part of the variance apparently explained by size finds a deeper explanation in the present model. Reflecting the generalized increase in patenting and citation rates, domains grew over the years relative to their size (reference: years 1975 through 1979). This trend is not smooth over the observation period, though, as domains’ percentage growth rates declined in the beginning of the nineties. Domains in the areas of Drugs & Medicals grew most rapidly, followed by those belonging to Computer & Communications (reference category: Chemicals). Somewhat more surprisingly, third in rank is the miscellaneous category Others, not Electrical & Electronics. This appears to contradict the distinction made by Hall cum suis (2001) between traditional and emergent areas, whereby the area Others would belong to the former while Electrical & Electronics to the latter (see Chapter 3, p. 37). The difference in results is explained by a difference in focus; while I investigate the growth of individual domains within each macro area, Hall cum suis study the growth of the macro areas themselves. Jointly, the results revealed by these two approaches seem to indicate that, compared to

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Specialization and brokerage: a theory of knowledge growth

Electrical & Electronics, the growth observed in the area Others is to a larger extent due to small domains. As smaller domains are likely to be less mature, the analysis presented here provides an interesting nuance to our understanding of emergent fields. The last three rows of the upper part of Table 6.1 test my hypotheses: in all model specifications, all three hypotheses are supported. As expected, specialized domains exhibit slower growth rates than brokering ones (hypothesis 2), although increasing specialization is positively associated with domains’ growth rates (hypothesis 1); moreover, the positive effect of increasing specialization decreases as domains specialize (hypothesis 3). The support of the hypotheses under all estimated models is not only indicative of their robustness, but also of their generality. As captured by the fixed-effects specification, the dialectical relationship of knowledge specialization and knowledge brokerage explains how the growth rate of each individual domain changes over time. In addition to changes in each domain’s growth rates, however, certain domains grow on average faster than others. The random-effects model shows that the hypothesized effects of knowledge specialization and knowledge brokerage hold true also when these cross-sectional differences are taken into account; and, when both period and area dummy variables are included in the model. Furthermore, while the fixed-effects model makes possible to generalize the estimated relationships to the population of observed effects, generalizations within the random-effects framework refer to the universe of all possible effects. Finally, the Feasible Generalized Least Squares model demonstrates that the hypotheses are corroborated even when the data are assumed to be heteroskedastic and serially correlated. A more in-depth analysis of the interactive effect of levels and changes in domains’ specialization reveals theoretically important nuances emerged from the estimation11. Figure 6.1 shows the effects of changes in specialization on domains’ growth when levels of specialization are highest or lowest12. In both cases, changes in specialization are positively associated with domains’ growth 11

Estimates are based on the random-effects specification. This drawing was made using the “Interact” STATA routine developed by Kittel (2004).

12

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101

rates. However, while the benefits of increases in specialization are weak and non-significant when domains are maximally specialized (t-value = 0.67), they are strong and highly significant when domains broker between disconnected sources (t-value = 5.61). This reflects precisely the predictions of my theory: path-dependent hybridizations are productive, but their productivity disappears in the absence of structural holes.

Figure 6.1. The effects of changes in specialization for maximally specialized and maximally brokering domains

VI. CONCLUSIONS Extant literature suggests that both knowledge specialization and knowledge brokerage should positively affect knowledge growth, which appears to be a contradiction because specialization and brokerage are opposite poles of one conceptual continuum. I showed that the beneficial effects of knowledge specialization and knowledge brokerage are dynamically intertwined, which on the one hand resolves the paradox, and on the other hand lays the foundations of a theory of knowledge growth. The more a domain advances by progressively specializing, the more efficiently it exploits the creative potential inherent in its niche of knowledge sources, and thus the faster it grows. Increasing specialization implies depletion of structural holes, though, which in its turn

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means that the more a domain is specialized, the smaller is the future growth potential left in its niche. Conversely, brokering domains tend to be endowed with more hybridization opportunities. Furthermore, hybridization of specialized knowledge largely consists of mopping-up and puzzle-solving operations, whereas hybridization of brokering knowledge typically yields more innovative ideas. Accordingly, the beneficial effect of progressive specialization decreases with domains’ degree of specialization. In the next chapter, I will develop this theory further.

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Specialization and brokerage: a theory of knowledge growth: appendix APPENDIX

THE EFFECTS OF SPECIALIZATION ON DOMAINS’ GROWTH UNDER THE POOLED OLS SPECIFICATION Dependent variable: domains’ % growth rate St. Err. t-value Sig. Coeff. Intercept Network autocorrelation Domain size 1985 thru 1989 1990 thru 1994 1995 thru 1999 Computers & Communications Drugs & Medical Electronic Mechanical Others Specialization ∆ Specialization Specialization * ∆ Specialization Number of observations F Prob. > F R-Squared

0.307 -0.000 -1e-06 0.367 0.131 0.326 0.842 0.935 0.092 0.065 0.136 2.036 -0.341 -1.831 1652 33.86 0.0000 0.2118

0.0543 0.0037 2e-06 0.044 0.044 0.047 0.064 0.093 0.057 0.048 0.048 0.346 0.109 0.562

5.67 -0.15 -0.63 8.31 2.92 6.92 12.97 10.01 1.61 1.37 2.82 5.88 -3.12 -3.26

0.000 0.879 0.526 0.000 0.004 0.000 0.000 0.000 0.108 0.172 0.005 0.000 0.002 0.001

CHAPTER 7 BUILDING UPON THE FOUNDATIONS

ABSTRACT: In this chapter, I extend my theory of knowledge growth in four directions. First, I bring evidence that the hypothesized effects of knowledge specialization and knowledge brokerage on domains’ growth hold in the long run. Second, I show that my theory of knowledge growth also helps to explain the changes observed in the rank order of domains’ sizes over time. Third, I demonstrate that knowledge specialization and knowledge brokerage also have an effect on how securely domains advance, i.e. on the variance of their growth rates. Fourth, I show that the creative potential inherent in a domain’s structural holes decreases with competitive pressure on the domain’s niche, and I thereby qualify a widespread assumption in the economics literature.

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Building on the foundations

I

n Chapter VI, I used the notion of structural hole to explicate a key dynamics of knowledge growth, and to represent it in terms of precise and measurable network conditions. This enabled me to lay the foundations of a theory of knowledge growth, whereby rates of knowledge growth are explained by the dialectical relationship of knowledge specialization and knowledge brokerage. In this chapter, I build upon the foundations of my theory of knowledge growth in four directions, which I analyze in turn.

I. LONG-TERM EFFECTS OF SPECIALIZATION AND BROKERAGE So far in this thesis, the primary goal of inferential models has been to explain changes occurred between subsequent 5-year-long time intervals. This approach made it possible to test the hypotheses at the core of my theory of knowledge growth. However, it also funneled the focus of analysis on relatively short-term dynamics. In this section, my objective is to test whether my proposed theory also holds in the long run. I envisioned two ways to test the hypothesized effects of knowledge specialization and knowledge brokerage from a longer-term perspective. First, I re-estimated them within a between-effects framework and, second, I expressed them in terms of relationships between level variables1. I. I. BETWEEN-EFFECTS ESTIMATION In the first of these two approaches – the between-effects estimator – longitudinal observations are collapsed into domains’ means over time, and a standard OLS regression is estimated on the transformed variables. This simple transformation shifts the focus of analysis from the variation observed between subsequent 5-year intervals, to changes occurred over the entire observation period, i.e. 25 years. Thus, it makes it possible to cast within a longer-term framework the three hypotheses describing the dialectical relationship of knowledge specialization and knowledge brokerage that I already tested from a short-term perspective (Chapter 6, pp. 93-94). To enhance comparability with previous models and to avoid biases in the estimation, also in this model I included a covariate capturing network autocorrelation, one indicating domains’

1

Although my data cover the 25 years between 1975 and 1999, I have only five observation instances at my disposal to model changes over time. This prevents me from employing unit-root tests and co-integration models.

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107

size, and a set of dummy variables representing the six macro-technological categories defined by the NBER 1-digit classification2. Table 7.1 reports the results of the analysis. As was found in previous models (both in Chapter 5 and Chapter 6), there is no notable network autocorrelation. Domains’ size has a positive, albeit insignificant, effect on domains’ growth, confirming that larger domains need to grow more than smaller ones before they reach their steady-state size (Chapter 5, pp. 78-79). Not surprisingly, the effects of macro-technological areas are similar to the ones estimated within a shortterm framework: domains belonging to the area of Drugs and Medicals grew fastest, followed by those in the fields of Computers and Communications and, in turn, by those in the miscellaneous category Others (reference category: Chemicals). Coeff.

St. Err.

t-value

Sig.

0.52

0.06

8.90

0.000

Network autocorrelation

-4.2 e-02

7.1 e-02

-0.60

0.549

Domain size

-1.4e-06

3.6e-06

-0.39

0.700

Computers & Communications

0.82

0.08

10.68

0.000

Drugs & Medical

0.91

0.11

8.32

0.000

Electronic

0.07

0.07

1.09

0.278

Mechanical

0.05

0.06

0.89

0.376

Others

0.12

0.06

2.09

0.037

Intercept

2

Because in the between-effects framework longitudinal changes are removed, period-dummy variables cannot be estimated.

108

Building on the foundations Coeff.

St. Err.

t-value

Sig.

Specialization

-0.28

0.13

2.12

0.034

∆ Specialization

3.11

0.83

3.75

0.000

Specialization * ∆ Specialization

-3.00

1.10

-2.72

0.007

Number of units Periods Number of observations F Prob. > F R-Squared within R-Squared between R-Squared overall

413 4 1652 23.83 0.0000 0.0237 0.3721 0.1615

Table 7.1 The dynamic effects of specialization on knowledge growth under the between-effects model.

The last three rows of the upper part of the table report the estimates pertaining to the hypothesized effects of knowledge specialization and knowledge brokerage. All three hypotheses are corroborated. In line with Hypothesis 1, the more a domain increased its specialization between 1975 and 1999, the faster was its growth. Confirming Hypothesis 2, the higher was a domain’s average level of specialization over the observation period, the slower was its growth. And, as predicted by Hypothesis 3, the higher was a domain’s level of specialization between 1975 and 1999, the less additional increases in specialization favored its growth. Thus, my theory of knowledge growth is supported even if one shifts the focus of the analysis from 5-year intervals to a time span as long as 25 years. I. II. LEVEL EFFECTS The second strategy I employed to test the validity of my proposed theory from a long-term perspective, is to reformulate the hypothesized effects of knowledge specialization and knowledge brokerage in terms of relationships between level-

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109

variables. Clearly, not all my hypotheses can be expressed by means of levelvariables. However, the focus on level effects does provide a valid test of one of the building blocks of my theory: the hypothesis that progressive specialization yields faster knowledge growth. My reasoning is simple. If domains that increase their specialization feature higher growth rates on average, then the higher is the level of specialization domains have reached, the larger should be the knowledge output they have accumulated. In other words, the more domains have specialized, the larger they should have become. I tested this hypothesis by means of a random-effects model3, which I augmented with the usual set of control variables. The resulting estimates are reported in Table 7.2. Unlike previous models, network autocorrelation4 exerts a discernible, albeit insignificant, negative effect5. From the level-variables perspective adopted here, the effect of the generalized increase in patenting and citation activities occurred over the observation period is clear-cut. Relative to the initial time interval (1975-1979), domains received progressively larger amounts of citations. The coefficients of the period-dummy variables give a sense of this increase: if between 1980 and 1984 domains received on average roughly 800 more citations than between 1975 and 1979, this increase became an order of magnitude greater in the last time interval (1995-1999).

3

I tested the consistency of this model by means of a Hausman (1978) specification test. The null hypothesis of no systematic difference between the coefficients estimated by a random-effects specification and its fixed-effects counterpart cannot be rejected (Chi-square = 2.19; Prob. > Chi-square = 0.8223). Thus, it can be safely concluded that the random-effects specification yields consistent estimates. 4 Clearly, the covariate capturing network autocorrelation differs from previous models, as now it is computed on the basis of the dependent variable used in the present model, which is domains’ size, not domains’ growth. 5 This estimate suggests that the more a domain is connected to large domains, the smaller is its knowledge output. Because I cannot conceive any straightforward interpretation of this finding, I prefer to remain theoretically agnostic, and stick to the methodological standpoint from which this parameter was designed: as a means to control for the inter-dependence of units characteristic of network data.

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Building on the foundations

Intercept

Dependent variable: domains’ size Coeff. St. Err. t-value Sig. 778.6 997.0 0.78 0.435

Network autocorrelation

-5.0e-07

4.1 e-07

-1.23

0.218

1980 through 1984

835.8

474.6

1.76

0.078

1985 through 1989

3117.4

477.2

6.53

0.000

1990 through 1994

5951.5

479.9

12.40

0.000

1995 through 1999

12179.3

498.5

24.43

0.000

Computers & Communications

3050.3

1461.0

2.09

0.037

Drugs & Medical

9123.5

2091.9

4.36

0.000

Electronic

1398.9

1298.4

1.08

0.281

Mechanical

-3161.8

1065.9

-2.97

0.003

Others

-3417.4

1062.4

-3.22

0.001

Specialization

8443.2

1755.3

4.81

0.000

Number of units Periods Number of observations Wald chi-squared Prob. > chi-squared R-Squared within R-Squared between R-Squared overall

413 5 2065 862.14 0.0000 0.3246 0.1489 0.2332

Table 7.2 The level-effect of specialization on knowledge growth.

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Interestingly, there are some differences in the effects that the six macrotechnological areas have on domains’ knowledge output on the one hand, and on domains’ growth rates on the other (compare with Table 6.1, pp.97-98). In line with my analysis of growth rates, domains belonging to Drugs & Medical turned out to be the largest ones, receiving an average of over 9000 citations per time interval more than the reference category Chemicals. However, the only other area wherein domains received significantly more citations than the category Chemicals is the field of Computers & Communications, while domains in the fields Mechanical and Others even received significantly less citations. This partial rank re-ordering in the estimated productivity of macro-technological areas relative to my previous findings reflects a difference in focus. My analysis of growth rates emphasized that, between 1975 and 1979, the domains belonging to the area Chemicals grew more slowly than virtually all other areas. The analysis presented here, in contrast, emphasizes that in the Chemicals sector domains still yielded relatively large knowledge outputs over the observation period – a finding that conceivably reflects the productivity of the Chemical sector in earlier phases of the knowledge advancement process. The last row of Table 7.2 reports the test of my hypothesis. As predicted, domains’ level of specialization is positively associated with domains’ knowledge output, and the relationship is highly significant. This result indicates that the beneficial effect of increasing specialization manifests itself also in terms of accumulated knowledge outputs: the higher the degree of specialization reached, the larger the domain became. II. RANK RE-ORDERING OF DOMAINS’ SIZES As shown in Figure 5.4 (p. 82), positions in the rank-order of domains’ sizes changed substantially over the observation period. In the graph, dots along the diagonal represent domains that conserved their rank position between the first (1975-1979) and the last (1995-1999) time intervals. The more a dot is located below the diagonal, the more positions it moved up; conversely, the more a dot is above the diagonal, the more positions it lost. My theory of knowledge growth should be able to explain these dynamics of rank re-ordering.

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The theory asserts that specialized domains grow slower than brokering domains because they have less hybridization opportunities left in their path-dependent niche of knowledge sources. Moreover, the hybridizations carried out in specialized domains are to a large extent mopping up and puzzle solving operations, while in brokering domains they are more likely to generate radical innovations. For both these reasons, domains initially endowed with greater brokerage opportunities should have greater chances to climb up the size rankhierarchy over time. To test this hypothesis statistically, I first calculated the difference between domains’ rank position in the time interval 1975-1979, and their rank position in the time interval 1995-1999. The resulting variable counts the number of positions each domain gained (positive values) or lost (negative values) between the beginning and the end of the observation period; thus, it corresponds precisely to the rank re-ordering visualized in Figure 5.1. Subsequently, I carried out an OLS regression to estimate the effects of domains’ initial degree of specialization6 on this measure of rank re-ordering. To avoid unduly alterations in the estimation, I included in the statistical model control variables capturing the effects of network autocorrelation7, domains’ initial size, and the macrotechnology area domains belong to. Table 7.3 reports the results of this analysis. Not surprisingly, domains’ initial size is negatively associated with changes in domains’ rank position: the higher the initial position in the size rank order, the lower the chance to further move up. In line with previous models, network autocorrelation does not play a noticeable role. In all technological categories domains significantly improved their rank position relative to the reference category Chemicals, which confirms the declining importance of the latter sector. Interestingly, domains in the area Computers & Communications gained more positions than domains in the field of Drugs & Medicals. This appears to be in disagreement with previous analyses, which consistently showed that domains in the area of Drugs & Medicals had the highest average growth rates over the observation period (see, 6

I.e., domains’ degree of specialization between 1975 and 1979. Also in this case, the covariate capturing network autocorrelation is constructed on the basis of the dependent variable used, i.e. domains’ rank-reordering. 7

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113

e.g., Table 7.1). There is a straightforward explanation for this apparent discrepancy, though. Domains in the area of Computers & Communications are on average much smaller than those in the area Drugs & Medicals (Table 7.2); and, because of the exponential distribution of domains’ sizes, it is disproportionably more difficult to climb the upper region of the size-rank ordering than it is to climb its lower region (Chapter 5). Dependent variable: change in rank position St. Err. t-value Sig. Coeff. Intercept

2.617

8.4

0.310

0.757

Domains’ size

-0.005

0.001

-4.764

0.000

Network autocorrelation

4e-05

0.000

0.516

0.606

Computers & Communications

153.6

11.4

13.432

0.000

Drugs & Medical

142.9

16.3

8.734

0.000

Electronic

31.9

10.0

3.187

0.002

Mechanical

16.9

8.4

2.001

0.046

Others

30.0

8.4

3.535

0.000

Specialization

-73.1

17.4

-4.207

0.000

Number of units Number of observations R-Squared

413 413 0.435

Table 7.3 The effect of specialization on the rank re-ordering of domains’ sizes. OLS regression

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The last row of the upper part of the table shows that the hypothesized effect of knowledge specialization (and, hence, of knowledge brokerage) is corroborated. The relationship between a domain’s initial level of specialization and the number of rank-positions it subsequently moved up is negative and highly significant. Thus, my theory of knowledge growth helps explain also the rank reordering of domains’ sizes displayed in Figure 5.1. III. RISK, SPECIALIZATION, AND BROKERAGE In this section, I attempt to extend my theory of knowledge growth by considering the risk associated with knowledge specialization versus knowledge brokerage. As said, specialized domains tend to grow more slowly than brokering ones because they have less upcoming hybridization opportunities left, a large portion of which consists of mopping-up and puzzle-solving hybridizations. Now I would like to reverse this argument to show that the advancement of specialized domains is more secure than the advancement of brokering domains. While the hybridization of specialized knowledge usually does not result in groundbreaking inventions, it typically follows a more established and more legitimate path of knowledge advancement. For that reason, I posit that ideas springing from specialized domains are less likely to be inconsequential dead-ends, and run lower risks of being rejected or ignored. Conversely, for brokering domains, a relatively larger portion of hybridizations is likely to turn out worthless, or to encounter cognitive and institutional obstacles associated with a lack of legitimacy. This reasoning leads straightforwardly to a testable hypothesis: brokering domains should exhibit larger variance in knowledge growth rates than specialized domains. To test this hypothesis, I selected two groups of domains from my data: the 10% domains having highest average brokerage and the 10 % domains having highest average specialization over the period of observation. Then, I formally tested the null hypothesis that the two groups would have homogeneous variances in growth rates by means of Levene’s test (1960). To account for possible fixed effects in the growth patterns of domains, I expressed my dependent variable in deviations from unit means; hence, all differences between domains are removed from estimation, and the only variance left is within domains over time.

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95% conf. int. Groups

N

T Obs

Mean

Std dev

Std Error

Min

Max

High brokerage

41

4

164

0.000

0.698

0.054

-0.10

0.10

High specialization

41

4

164

0.000

0.425

0.033

-0.06

0.06

Levene statistic Significance

13.05 0.000

Table 7.3 Levene test of homogeneity of variance. Ten percent most highly brokering domains versus ten percent most highly specialized ones.

Table 7.3 reports the results of the analysis. As predicted, over the observation period the variance in growth rates was strikingly larger for brokering domains than it was for specialized ones, and the difference is highly significant according to Levene's test. The high variance in the performance of brokering domains shows the associated risk, whereas specialization is relatively safe. A glance at the confidence intervals for the means gives a sense of how differently the two modes of knowledge production operate: within a 95% confidence interval, the growth rates observed for brokering domains deviate nearly twice as much from their mean as specialized domains do. IV. NICHE OVERLAP AND THE CREATIVE POTENTIAL OF STRUCTURAL HOLES In the economics literature, knowledge is commonly held a non-rival resource (e.g. Romer 1993). The notion of knowledge non-rivalry, however, is ambiguous. For some scholars, it means that knowledge is a non-rival end product (the knowledge necessary to build the wheel does not diminish with the number of people who obtain it, or with the number of times it is applied). For other scholars, it means that knowledge is a non-rival input in the production of new knowledge (knowledge of how to build the wheel can be fruitfully utilized infinitely many times for the production of newer inventions). Some among the

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most influential developments in the recent history of economic theory, such as the idea-based growth theory (Jones 2004) and Weitzman’s theory of recombinant knowledge growth (1996, 1998), adopt the latter conception. Importantly, these theoretical developments are not only relevant from an academic point of view, but provide a framework within which a great deal of economic policies worldwide is designed (Carnabuci, forthcoming). I argue that the view that existing knowledge is a non-rival input in the production of future knowledge is in part unwarranted, and should be qualified more precisely. If new ideas spring from the novel combination of existing ideas, it follows that the less novel is the combination of ideas, the smaller should be the creative potential inherent in their hybridization. Thus, although I agree that ideas can in principle be hybridized infinitely many times, I posit that their value as an input for knowledge production should decrease to the degree that they are employed in recurrent combinations. This argument can be applied to the level of knowledge domains, thus it can be formalized and tested within my network framework. To capture the extent to which ideas are hybridized in recurrent combinations at the level of knowledge domains, I employ the concept of niche overlap8. With regard to my knowledge network, this concept indicates to what degree the niche of knowledge sources a domain hybridizes from is similar to the niches of other domains; or, equivalently, it indicates to what degree the structural holes contained in a domain’s niche are also brokered by other domains. I propose to calculate the dyadic niche overlap of a domain j on another domain i, α

jit

, as the proportion

of i’s hybridizations that i and j carry out from the same knowledge sources within the same time interval. Formally,

α jit =

∑ H irt ∩ H jrt r

∑ H irt r

8

In the literature, this notion has also termed crowding (Podolny et al. 1996) and diffuse competition (Bruggeman et al. 2003).

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where j ≠ i ≠ r , t is a time interval, and H stands for the set of hybridizations carried out by the domain in the left-hand subscript, from ideas belonging to the domain in right-hand subscript. Figure 7.1 presents an example. Within t, domain i hybridized 100 times ideas belonging to domain r1 , 50 times ideas in

r2 , and 60 times ideas in r3 . Meanwhile, domain j hybridized 20 times ideas in r1 , 90 times ideas in

r2 , and 75 times ideas in

r4 . Thus,

α jit = (20 + 50 ) 210 = 0.3 .

j

i

100 20

90 50

r1

r2

60

75

r3

r4

Figure 7.1 Niche overlap of two hypothetical domains

This network-analytic measure of dyadic niche overlap is continuous, it is normalized within the interval [0, 1], and it takes into account units’ size

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differences – i.e. it is asymmetric9. Thus, it meets the conditions necessary for a correct operationalization of the concept of dyadic niche overlap (Sohn 2001). The overall overlap i’s niche is subjected to, Ait , can then be simply calculated as the sum of its dyadic niche overlaps:

Ait = ∑ α jit j ≠i

My reasoning is that the higher is a domain’s overall niche overlap, the more the structural holes contained in its niche are also brokered by other domains and, therefore, the less productive should be its hybridizations. Two testable hypotheses can be derived from this argument. The first is that domains characterized by a higher niche overlap should exhibit slower growth rates; the second is that increases in domains’ niche overlap should exert a negative effect on domains’ growth rates. Notice how these two hypotheses single out different nuances of the same causal mechanism: while the first emphasizes the structural effects of niche overlap, the second focuses on the role of its short-lived changes. To estimate the hypothesized effects of domains’ niche overlap on domains’ growth rates, I included in the statistical model the usual set of control variables, as well as the covariates capturing the dynamic effects of knowledge specialization and knowledge brokerage. To establish if estimating this model within a random-effects framework would yield consistent parameter coefficients, I again performed a Hausman specification test (1978). The test results turned out not to be conclusive, though (Chi-square = 15.26; Prob. > Chisquare = 0.0841); for that reason, in Table 7.4 I report the results obtained under both the random-effects and the fixed-effects frameworks.

9

For an illustration of the latter point, let me calculate the niche overlap of i on j in the case represented in Figure 7.1: α ijt = (20 + 50) / 185 = 0.378. As can be seen, because the total number of hybridizations carried out by j is smaller than i’s, the overlap of i on j is larger than the overlap of j on i.

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Dependent variable: domains’ % growth rate Random-effects Fixed-effects Sign. Coeff. St. err. Sign. Coeff. St. err. Intercept

1.256

0.198

0.000

0.554

0.083

0.000

Network autocorrelation

0.001

0.003

0.781

-2e-04

0.003

0.940

Domain size

-5e-06

5e-06

0.350

-8e-06

3e-06

0.015

1985 through 1989

0.390

0.042

0.000

0.396

0.042

0.000

1990 through 1994

0.157

0.048

0.001

0.172

0.044

0.000

1995 through 1999

0.363

0.058

0.000

0.397

0.048

0.000

Computers & Communications

0.795

0.075

0.000

Drugs & Medical

0.931

0.107

0.000

Electronic

0.107

0.066

0.105

Mechanical

0.095

0.055

0.085

Others

0.180

0.056

0.001

Specialization

-1.874

0.428

0.000

-0.686

0.144

0.000

∆ Specialization

1.015

0.400

0.011

1.69

0.343

0.000

Specialization * ∆ Specialization

-2.013

0.688

0.004

-2.088

0.564

0.000

Niche overlap

-0.010

0.003

0.001

-0.005

0.001

0.000

∆ Niche overlap

-0.008

0.001

0.000

-0.006

0.001

0.000

120

Building on the foundations Fixed-effects

Random-effects

Number of units Periods Num. Observations F Prob. > F Wald chi-sqaure Prob. > chi-square R-Squared within R-Squared between R-Squared overall

413 4 1652 17.90 0.0000

413 4 1652

Corr. ( η i , Χ b )

-0.2228

0.1271 0.0593 0.0857

426.21 0.0000 0.1204 0.3896 0.2319

Table 7.4 The effects of niche overlap on knowledge growth under the fixedeffects and the random-effects specifications

Let me begin by noticing that qualitatively, the fixed-effects and the randomeffects specifications yield virtually identical results. The only noticeable discrepancy is represented by the negative effect of domains’ size, which is significant only in the random-effects model10. The estimates of period-effects are in line with previous models of domains’ growth rates. The same applies to 10

I reckon that this discrepancy may have two causes. First, the estimate generated under the random-effects specification is inconsistent because domains’ fixedeffects are correlated with the regressors (a problem that does not occur in the fixedeffects specification – see Chapter 6, p. 98). Second, the six macro-technology areas, which are not modeled in the fixed-effects specification, mediate the effect of domains’ size. In an attempt to delve deeper into the causes of this discrepancy, I removed from the random-effects specification the set of area-dummy variables, and I re-estimated the model parameters. The effect of domains’ size became insignificant (t-value = 0.63; significance = 0.528) as in the fixed-effect model, suggesting that the macro-technology areas domains belong to do mediate the effect of size. It then became interesting to compare the estimates of Table 7.4 with those of the random-effects model reported in Table 6.1 (pp. 97-98). As can be seen, in the latter model the effect of domains’ size is not significant. Because the only difference between the random-effects models presented in Table 6.1 and in Table 7.4 is that the latter accounts for the effects of niche overlap, it can be concluded that also niche overlap mediates the effect of domains’ size.

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the effects of the six macro-technology areas, with the notable exception of the field Mechanical, wherein for the first time domains turned out to grow faster than in the reference category Chemicals. Interestingly, this result suggests that an important reason for the sluggish growth of the area Mechanical is the niche overlap of its domains. With the three parameters capturing the intertwined effects of knowledge specialization and knowledge brokerage are associated the excepted coefficient estimates, indicating that these effects are net of dynamics of niche overlap. The estimates pertaining to the hypothesized effects of niche overlap are reported in the last two rows of the upper part of the table. As expected, the higher the niche overlap domains are subjected to at a given point in time, the slower their subsequent growth; and, changes in domains’ degree of niche overlap are negatively associated with changes in domains’ growth rates. These results confirm that the creative potential inherent in a domain’s niche of knowledge sources decreases to the degree that its structural holes are also brokered by other domains. Therefore, the assumption that knowledge is a nonrival input of knowledge production should be qualified as follows: existing knowledge can be hybridized infinitely many times, but its value as an input of knowledge production decreases to the degree that ideas are hybridized in recurrent combinations. V. CONCLUSIONS In this chapter, I extended my theory of knowledge growth in four directions. First, I brought evidence that the hypothesized dialectical relationship of knowledge specialization and knowledge brokerage holds true even if one investigates long-term dynamics of knowledge growth. Second, I showed that my proposed theory of knowledge growth also helps explain the rank reordering of domains’ sizes. Third, I demonstrated that also the risk associated with knowledge growth depends on the hypothesized effects of knowledge specialization and knowledge brokerage. Fourth, I showed that the knowledge productivity of a domain’s structural holes decreases with the domain’s niche overlap, which made possible to qualify with greater precision the widespread and influential assumption that knowledge is a non-rival input of knowledge production.

CHAPTER 8 CONCLUSIONS

Abstract: I summarize the findings of the previous chapters and discuss their implications for science and policy. In the end, I indicate promising lines of future research.

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Conclusions

M

y objective was to explain why some domains of knowledge grow faster than others. In addressing this issue, I attempted to shed light on both the rate and the direction of knowledge advancement: the factors causing growth rates to vary at the level of individual knowledge domains determine the direction of knowledge growth at the aggregate level. To explain variation across domains’ growth rates, I elaborated upon the notion that new ideas result from hybridizations of existing ideas. Accordingly, I proposed that the growing stock of human knowledge be represented as an evolving network of knowledge domains interconnected through hybridizations. This approach made possible to formalize the dynamics of knowledge growth network-analytically, which in turn provided a more rigorous model for empirical analyses and for theory building. I. FINDINGS At the most general level, this thesis demonstrated that the progress of knowledge domains depends on their embeddedness within the knowledge hybridization network. Differences in the configuration of domains’ patterns of hybridization cause knowledge productivity to vary across domains. This finding is important because it sets the stage for a novel explanatory framework in the analysis of knowledge growth, which this thesis has only begun to draw up on. Chapter 4 showed that the hybridization network among domains of USpatented knowledge features traits of the purportedly ubiquitous small-world topology, most of which is due the tendency of domains to form local clusters via reciprocation of hybridization patterns. However, my analysis also pointed out that the network has been steadily evolving away from the characteristic small-world structure. In Chapter 5, I brought evidence that larger domains of knowledge have a structural advantage compared to smaller ones due to the endogenous mechanism of self-hybridization. By mediating the effect of domains’ inherent growth potentials, self-hybridizations systematically amplify the size differences

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between small and large domains, and lead knowledge progress to concentrate disproportionably among the latter. In Chapter 6, I laid the foundations of a dynamic theory of knowledge growth, according to which the advancement of knowledge depends on a dialectical relationship between knowledge specialization and knowledge brokerage. The chapter started out by operationalizing the concepts of knowledge specialization and knowledge brokerage in terms of (lack of) structural holes in a domain’s niche of knowledge sources. The more a domain hybridizes ideas from mutually interconnected knowledge sources – i.e. the fewer are the structural holes in a domain’s niche – the higher is the domain’s degree of knowledge specialization. Conversely, the more a domain advances by hybridizing ideas from unconnected knowledge sources – i.e. the more are the structural holes contained in its niche – the higher is the domain’s degree of knowledge brokerage. Having formalized these concepts network-analytically, I argued that knowledge specialization yields efficiency in knowledge production, while knowledge brokerage yields new potential for knowledge growth. From these simple premises I derived three testable hypotheses, which were corroborated by the data. First, a domain embedded in a niche of knowledge sources that brokers between many structural holes is endowed with greater hybridization potential, thus grows faster on the average. Second, the more a domain advances by depleting the structural holes in its path-dependent niche – i.e. the more it specializes –, the more efficiently it hybridizes existing knowledge, and thus the faster it grows. Third, hybridization of specialized knowledge largely consists of mopping up and puzzle solving operations, whereas hybridization of brokering knowledge typically involves more innovative combinations of ideas. For that reason, the beneficial effect of increasing specialization decreases with domains’ degree of specialization. In Chapter 7, I built upon this dynamic theory of knowledge growth in four directions. First, I provided evidence that the hypothesized dialectical relationship of knowledge specialization and knowledge brokerage holds also in the long run. Second, I showed that my proposed theory explains the rank reordering of domains’ sizes over time. Third, I demonstrated that knowledge specialization and knowledge brokerage also have an effect on how securely domains advance. Fourth, I showed that the creative potential inherent in a

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domain’s structural holes decreases with competitive pressure on that domain’s niche. II. CONTRIBUTIONS TO SCIENCE Some scholars, mainly economists, argue that knowledge growth is enhanced by specialization (Marshall 1936; Smith 1776; Walker 1867; Young 1928), whereas others, mainly sociologists, argue in favor of knowledge brokerage (Burt 2004; Hargadon 2002; Sutton and Hargadon 1996). These two views seem mutually excluding, because specialization and brokerage are the opposite poles of one conceptual continuum. This thesis puts forward a theory of knowledge growth that reconciles the functions of knowledge specialization and knowledge brokerage in a dynamic explanation. Thereby, it resolves this apparent paradox and it indicates a point of connection between economic and sociological theories. This thesis also contributes to theories of economic growth. Economists agree that long-term economic growth crucially depends on productivity, which in turn is keyed to knowledge growth (Carnabuci, forthcoming). However, they are yet unable to model the causes and dynamics of knowledge growth. On the one hand, scholars in the orthodox neoclassical tradition simply take knowledge as an exogenous parameter (Solow 1956). On the other hand, scholars in the tradition of idea-based growth theory model knowledge as an endogenous variable (Jones 2004), but they fail to specify the conditions that determine knowledge production rates (Chapter 1, pp. 7-8). The network theory of knowledge growth advanced in this thesis is a step towards modeling in greater depth the factors responsible for long-term economic growth. It was 1962 when Thomas Kuhn published The structure of scientific revolutions. In that book, the author proposed a theory of knowledge that impacted deeply not only contemporary philosophy of science, but also theories of evolutionary economics (Dosi 1982; Nelson and Winter 1982) and of technology dynamics (Tushman and Anderson 1986; Abernathy and Utterback 1978). Albeit highly evocative, Kuhn’s conception of knowledge growth is metaphoric and descriptive. This thesis embeds Kuhn’s conception in a network

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model, thereby rendering it less ambiguous and more suitable to scientific research and theorizing. It is widely held that a balanced combination of exploitation and exploration maximizes human and organizational knowledge (March 1991; March and Simon 1958; Cohen and Levinthal 1990; Kogut and Zander 1992; Henderson and Cockburn 1994; Rosenkopf and Nerkar 2001; Teece et al. 1997). This thesis contributes to this line of reasoning by making available a network-analytical conceptualization of exploitation and exploration, as well as an explanation of their relationship to knowledge growth. This thesis also adds to the new science of networks (Barabasi 2002; Watts 2004), in three ways. First, it presents a comprehensive analysis of a yet unexplored large-scale empirical network, the network of US-patent citations between technology domains. Second, and different from all previous studies in the field, it analyzes the evolution of this network over a time span as long as 25 years. Such a longitudinal perspective turned out to be highly informative, revealing that although the network does exhibit signs of the purportedly ubiquitous small-world topology, these signs became progressively weaker as the network evolved. Third, this thesis shows how the method of triadic census can be applied to delve deeper into the analysis of small-world parameters. Prior to this thesis, social network analysis has been applied to patent data in order to study success differentials among inventions (Podolny and Stuart 1995) and among organizations (Podolny et al. 1996). This thesis extends this line of inquiry to the level of knowledge domains. Furthermore, this thesis contributes to the field of social network analysis at large by expanding the body of network-analytic measures available for future research. Finally, this thesis contributes to the sociology of knowledge. In recent decades, the postmodernist notion that knowledge dynamics are unpredictable, because they are “…the contingent product of various social, cultural and historical processes” (Woolgar and Ashmore 1988, p. 1), became widespread among sociologists. As a consequence, the sociological analysis of knowledge became largely confined to either merely descriptive exercises, or to unfalsifiable

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Conclusions

theoretical speculations (e.g. Latour 1987). The diffusion of this a-scientific approach seems especially detrimental in light of the caesura it generated with the fruitful tradition of middle-range sociology of knowledge developed by Robert K. Merton and his collaborators (e.g. Merton 1957). This thesis demonstrates that, to some relevant extent, the dynamics of knowledge are predictable. What is more, these dynamics can be modeled formally, quantified empirically, and explained by means of falsifiable theories. III. POLICY AND INVESTMENT IMPLICATIONS A first practical implication that can be drawn from this thesis is that, because progress tends to concentrate disproportionably among larger domains of knowledge, it is generally advantageous to invest in larger domains than in smaller ones. There is a limit to this prescription, though. If one were confronted with a situation wherein, unlike US-patented knowledge at the turn of the last century, smaller domains are to grow more than larger ones to reach their steady-state size, then one would be better off investing in smaller domains. The results of this thesis also indicate that it is wiser to invest in domains embedded in knowledge niches rich in structural holes. For the same reason, policies should be designed that stimulate specialized domains to draw ideas from sources outside their path-dependent niche. Investments in path-breaking hybridizations carry a greater risk, and there is little guarantee as to whether they will pay off. Moreover, they require a further process of specialization to become productive. A lack of path-breaking connections, however, will depress the chance of making revolutionary inventions, and will inevitably lead to stagnation in the long run. In evaluating knowledge investments, one should also be mindful that the contribution of structural holes to the growth prospects of a domain decreases with the degree to which other domains broker those same holes. Thus, investments should be directed towards domains endowed with relatively unique niches of knowledge sources. When the goal of the policy-maker is to favour the advancement of technological knowledge at large, this thesis suggests that productivity gains would result from maintaining a balance between dense areas of knowledge hybridization and structural holes between these dense areas. It might be that

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this balance is achieved by invisible hand, as complex networks have a selforganized tendency to evolve into clusters-and-holes structures, and such processes can hardly be influenced externally (Barabasi 2002). Nonetheless, policies could aim at modifying the structure locally, in favour of immediate exploitation of structural holes, or to invest in the generation of new structural holes for future benefits. As a final point, I would like to spend a few words on how these suggested policies could be implemented. It seems to me that the most direct way is the strategic allocation of resources across areas and projects of research. For example, R&D investments ought to be concentrated on those ventures that promise either to create path-breaking hybridizations between specialized areas, or to exploit specific development opportunities from highly brokering domains. Policies of knowledge growth, however, could also be implemented by means of more indirect strategies, and most importantly by promoting educational and training programmes that effectively combine disciplinary specialization with interdisciplinary brokerage. Whereas the importance of integrating disciplinarity and interdisciplinarity has been long recognized (Messer-Davidow et al. 1993), little progress has been made in the direction of explaining how this can be done in a way that maximizes human creativity. This thesis suggests that optimal combinations of disciplinary and interdisciplinary education can be designed only on the basis of dynamic and contingent analyses. The objective of the policy maker must not be to deliver the right proportions of disciplinary specialization and inter-disciplinary openness at all times and for all disciplines. Rather, the objective should be to provide students engaged in highly specialized disciplines with knowledge of domains that are sufficiently distinct from their own; and, in contrast, to teach students of highly brokering disciplines the principles and methods necessary to develop their fragmented knowledge into a cumulative specialty. IV. FUTURE RESEARCH The theory of knowledge growth presented in this thesis was corroborated on the basis of data describing all knowledge patented in the United States between 1975 and 1999. In order to establish the generality of the theory and to increase its empirical content (Lakatos 1970), predictions should be derived that apply to

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different empirical settings or levels of analysis. I would like to suggest three further applications of the theory whose validity can be straightforwardly tested. I am convinced that my proposed theory of knowledge growth can also be employed to explain scientific progress. Certainly, technology and science operate differently due to the differing incentives, values, and norms shaping inventive activity in these two realms of knowledge production. These differences, however, have no bearing on the explanatory mechanism of my proposed theory. My conjecture is that the incentives, norms, and values prevailing in the realms of science versus technology will manifest themselves in the configuration of their pertaining knowledge hybridization networks. Nevertheless, I expect the effects of these networks on knowledge growth to be similar in both science and technology. The first line of future research that I would like to suggest, then, is to test whether my proposed theory of knowledge growth also explains why certain scientific disciplines grow faster than others. Such a test could be straightforwardly carried out by means of bibliometric data, which are abundant (and in some cases freely available) on the World Wide Web. Following a consolidated empirical and theoretical literature (Glanzel 2004), article citations could be taken as indicative of hybridizations of scientific knowledge, and bibliographic classifications of scientific disciplines could be used to indicate knowledge domains. A second line of future research that I regard as viable and potentially useful consists of linking explicitly my theory of knowledge growth to theories of economic growth. As said (Chapter 1, pp. 7-8), idea-based models of economic growth let an economy’s rate of knowledge growth vary with investments in knowledge production, most importantly with R&D. These models, however, treat the relationship between R&D and knowledge growth as an unexplained parameter, i.e. they are silent on the knowledge productivity of R&D. My theory covers this hiatus by indicating how the yield of knowledge investments varies with network-structural properties of the knowledge niche one invests in. Thus, it could be incorporated in idea-based growth models to derive more precise predictions of economic growth, and to estimate econometric models with greater accuracy. Clearly, to pursue this line of research one would need to shift the focus of analysis from the level of knowledge domains to the level of

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countries. For example, rather than the degree of specialization of a domain, one should calculate the degree of knowledge specialization of a nation. From a technical point of view this shift would require the analyses of 2-mode networks – i.e. networks represented by matrices of relationships containing countries in the rows and knowledge domains in the columns – rather than 1-mode networks such as the ones analyzed in this thesis – i.e. networks represented by domainby-domain matrices. Except for this technical adjustment, I believe my theory of knowledge growth can be straightforwardly applied to explaining why investments in R&D yield different knowledge outputs across countries. Importantly, the data necessary to carry out this line of research are widely accessible. Especially with regard to the OECD area, the World Wide Web stores a wealth of statistics pertaining to countries’ R&D investments and economic growth, while, to characterize countries’ knowledge niches, patent data seem a straightforward and valuable option. As a third line of promising future research, I would like to suggest that my theory of knowledge growth be applied to the level of the firm. In knowledgeintensive industries, firms do not only face the problem of effectively learning and applying existing knowledge. Rather, they are confronted with a context of Red Queen technological evolution (McKendrick and Barnett 2001) wherein they need to constantly develop new and better technologies to keep abreast with competitors. In light of this, it comes as no surprise that firms have become the locus of technological knowledge production of the knowledge economy (Chapter 1). To shed light on both the micro-processes of technological knowledge production and on the issue of competition, it is important to understand what determines knowledge growth at the level of the firm. I contend that the theory advanced in this thesis can here be fruitfully employed. Especially concerning large firms, this contention can easily be tested empirically. Numerous datasets report detailed firm-level statistics on knowledge investments, while patent data could be used as indicators of firms’ knowledge niches as well as of their knowledge production. On the basis of these data, my proposed theory could then be operationalized by a 2-mode firmby-domain network, making possible to investigate how the network configuration of firms’ knowledge stocks affect the productivity of firms’ knowledge investments.

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V. CONCLUSIONS The dynamics by which new ideas accumulate upon existing ones, thereby expanding the stock of human knowledge, can be formally modeled as an evolving network of domains interconnected through hybridizations. Based on the analysis of all technological knowledge patented in the United States between 1975 and 1999, this thesis demonstrated that the configuration of this network at a given point in time affects the subsequent process of knowledge growth in important and predictable ways. I have little doubt that other interesting aspects of the advancement of human knowledge can be explained within this network-analytic framework.

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SAMENVATTING Hoe komt het dat kennisdomeinen wat hun groei betreft sterk van elkaar verschillen? Dit proefschrift probeert deze vraag te beantwoorden door voort te bouwen op het bekende idee dat nieuwe ideeën voortkomen uit het op een nieuwe manier combineren van bestaande ideeën. Deze ideeënkruisingen ontwikkelen zich niet zozeer op grond van toeval zoals plantenvarianten in de vrije natuur, maar volgens padafhankelijke netwerkstructuren waarin kennisdomeinen met elkaar worden verbonden. Op basis van deze gedachte wordt kennisgroei in dit proefschrift netwerkanalytisch gemodelleerd. Met de netwerkbenadering worden theoriebouw en empirisch onderzoek gestuurd en aangescherpt. Gebaseerd op alle technologische kennis gepatenteerd in de Verenigde Staten van 1975 tot 1999 wordt vervolgens aangetoond dat de netwerkpositie waarin kennisdomeinen zijn ingebed hun groei op voorspelbare wijze beïnvloedt. Het proefschrift is op de volgende wijze opgebouwd. In hoofdstuk 1 wordt betoogd dat de groei van het reservoir van menselijke kennis goed gemodelleerd kan worden als een dynamisch netwerk van kennisdomeinen. Na een formalisering van het model volgt de centrale onderzoeksvraag. In hoofdstuk 2 wordt uitgelegd waarom en hoe het formele model kan worden getoetst met patentdata. Deze data zijn relevant omdat zij een belangrijk en omvangrijk deel van de technische kennis van onze kenniseconomie weergeven. Ze worden daarom ook veel gebruikt in econometrische studies als indicatoren van kennisdomeinen, kennisverbreiding en van kennisopbrengsten. In dit proefschrift worden ze voor alle drie gebruikt. Hoofdstuk 3 beschrijft de collectie van data, die informatie bevat over alle kennis gepatenteerd bij de grootste patent institutie wereldwijd, de US Patent and Trademark Office (USPTO), tussen 1975 en 1999. Na enkele beschrijvende statistieken worden mogelijke problemen van deze dataset voor de toepassing in dit onderzoek genoemd en worden oplossingen daarvoor aangedragen.

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In hoofdstuk 4 wordt het netwerkmodel op de USPTO data losgelaten en worden de data daarmee geanalyseerd. Het kennisnetwerk blijkt sterk verbonden te zijn, een eigenschap die gedurende de observatieperiode nog verder versterkt. Het leeuwendeel van deze verbondenheid komt echter door relatief zwakke schakels. Het netwerk heeft daarnaast ook een ruggengraat van sterke schakels, die op zijn beurt uit een aantal gesegregeerde kenniskernen blijkt te bestaan. Het netwerk heeft tevens een kleine wereld topologie, die gedurende de observatieperiode geleidelijk overging in een toevalsstructuur. Hoofdstuk 5 begint met een weergave van een interessant verschijnsel: tussen 1975 en 1999 was vooruitgang in termen van groei verhoudingsgewijs zeer sterk geconcentreerd in grote domeinen. In een poging dit verschijnsel te verklaren wordt eerst aangetoond dat domeinen niet naar een zogenaamde “dikke staart” verdeling convergeren en ook niet naar een normale verdeling. Er is namelijk een diversiteit van domeinspecifieke dynamische evenwichtsgroottes. Vervolgens wordt ter verklaring de volgende hypothese geformuleerd, die na toetsing blijkt te worden onderbouwd. Een endogene dynamiek van kennisgroei – zelfbestuiving – versterkt systematisch het inherente groeipotentieel van kennisdomeinen, wat van domein tot domein verschilt. Doordat grote domeinen doorgaans over een groter potentieel beschikken en meer aan zelfbestuiving doen worden grootte verschillen nog verder versterkt, met als resultaat een disproportionele concentratie van groei onder de grootste domeinen. Hoofdstuk 6 legt de fundamenten van een dynamische theorie van kennisgroei, waarin een verklaring voor groei wordt gegeven in termen van een dialectische relatie tussen kennisspecialisatie en kennisondernemerschap. Het hoofdstuk begint met het operationaliseren van deze twee concepten in termen van respectievelijk het ontbreken of het hebben van “structurele gaten”. Hoe meer een domein ideeën kruist van op hun beurt onderling verbonden domeinen, dus hoe minder structurele gaten er overbrugd worden, des te hoger is de mate van kennisspecialisatie. Omgekeerd, hoe meer een domein ideeën kruist van onderling niet-verbonden domeinen, dus hoe meer structurele gaten worden overbrugd, des te hoger is de mate van kennisondernemerschap. Nadat deze twee concepten netwerkanalytisch zijn geformaliseerd en op een noemer gebracht wordt betoogd dat kennisspecialisatie een efficiënte wijze van

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kennisgroei mogelijk maakt, terwijl kennisondernemerschap nieuwe mogelijkheden voor kennisgroei biedt. Vanuit deze simpele stellingen worden drie hypothesen afgeleid over de effecten van kennis-specialisatie en ondernemerschap op de kennisgroei van domeinen. Ten eerste, hoe meer een domein zich in een gegeven tijdsinterval specialiseert, hoe efficiënter het groeipotentieel in zijn niche wordt benut en dus hoe sneller het domein groeit. Ten tweede, hoe hoger de mate van specialisatie op een bepaald moment, hoe lager het potentieel van verdere ideeënkruisingen die in de niche dan nog over is, en dus des te geringer de verdere groei. Ten derde, hoe hoger de mate van specialisatie van een domein, hoe lager de marginale productiviteit van mogelijke ideeënkruisingen die nog in zijn niche overblijft, dus des te geringer het effect van nog verdergaande specialisering. Alle drie de hypothesen worden bevestigd. In hoofdstuk 7 wordt op de theorie voortgebouwd met vier nader kwalificerende hypothesen, die ieder op hun beurt eveneens door de data blijken te worden gesteund. Ten eerste, de in het vorige hoofdstuk gestelde effecten van specialisatie en ondernemerschap gelden ook op langere termijn. Ten tweede, de theorie verklaart bovendien de rangorde in grootte van domeinen, op grond van de geschetste mechanismen. Ten derde, kennis-specialisatie en ondernemerschap hebben voorspelbare en significante effecten op de variantie van kennisproductiviteit, waarbij ondernemersschap een veel hoger risico bij zich draagt. En ten vierde, de productiviteit die in structurele gaten in de niche van een domein potentieel aanwezig is, neemt af naarmate meer andere domeinen met de gegeven niche een overlap hebben, of naarmate van een gegeven aantal domeinen de overlap hoger wordt. Hoofdstuk 8 vat de resultaten van de voorgaande hoofdstukken samen en bespreekt mogelijke implicaties voor wetenschap en beleid. De gepresenteerde theorie van kennisgroei heeft de empirische toetsen tot dusverre doorstaan en nieuwe toetsen zouden zinvol en mogelijk zijn met gebruik van data op andere aggregatieniveaus, bijvoorbeeld het niveau van individuele organisaties, en op andere gebieden, bijvoorbeeld wetenschap.