THE PATTERN OF KNOWLEDGE FLOWS BETWEENTECHNOLOGY FIELDSmeca_4073 364..397

Mauro Caminati and Arsenio Stabile*University of Siena

(April 2008; revised May 2009)

ABSTRACT

This paper exploits recent contributions to the notions of modularity and autocatalytic sets to identifythe functional and structural units that define the strongest systematic and self-sustaining channelsof knowledge transfer and accumulation within the network of knowledge flows between technologyfields. Our analysis reconstructs the architecture of the empirical knowledge pattern based on theUnited States Patent and Trademark Office (USPTO) patent citation data at the level of resolutionof three-digit technology classes, for the period 1975–99.

1. INTRODUCTION

1.1 Aims and scope

This paper uses patent citation data to recover the network of knowledgeflows between technology fields in the period 1975–99. At a very aggregatelevel, this network provides an approximate representation of the knowl-edge input–output structure supporting the production of new ideas.Through a structural analysis of knowledge flows, we seek to recover thedisciplinary-field composition of the main R&D communities in the lastquarter of the 20th century. In these years, the technological opportunities

* A preliminary version of this paper was presented at the Lucca Conference ‘The Institutionaland Social Dynamics of Growth and Distribution’, 10–12 December 2007. The present versionbenefits from detailed comments and constructive criticism by Andrea M. Lavezzi and twoanonymous referees. The usual caveats apply. Financial support from the Italian MIUR(research project: Economic Growth: Institutional and Social Dynamics) and Siena University isgratefully acknowledged.

Metroeconomica 61:2 (2010) 364–397doi: 10.1111/j.1467-999X.2009.04073.x

© 2009 The AuthorsJournal compilation © 2009 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford, OX42DQ, UK and 350 Main St, Malden, MA 02148, USA

marking the golden age of high total factor productivity (TFP) growth losttheir momentum; a reorientation of R&D in the USA and other leadingOECD countries was preparing the ground for a major revolution in theinformation and communication technologies (ICT) and other small-scalerevolutions, as in biotechnology. Towards the end of the period understudy, these revolutions also left their mark in the statistics of TFP growth,notably in the USA.

A number of research questions orient our study. How sparse, ormodular, is the architecture of the network? Is there a correspondencebetween the communities identified through the analysis of knowledgeflows and the prevailing trajectories in technological space? Was the promi-nent position of the ICT trajectory already evident in the pattern of knowl-edge transfer during the early phase of the period under study? Is theacceleration of this trajectory in the last phase signalled by structuralchanges in that pattern? What are the other prominent directions in thecirculation of new ideas?

To address these questions, the paper exploits recent contributions to thenotions of modularity and autocatalytic sets (ACSs). They suggest a means toidentify the functional and structural units of an empirical knowledge patternthat define the strongest systematic and self-sustaining mechanisms of knowl-edge transfer and accumulation within the network. A knowledge pattern ishere defined by the network of knowledge flows between technology fields.We follow the Newman and Girivan (2004) method of defining the commu-nity structure within a knowledge network based on their notion andmeasure of modularity. Beside the structural viewpoint of partitioning thenetwork of technology fields into modules, we also adopt a functional view-point. Through the separation of first-order from lower-order magnitudelinks and by exploiting the notion of ACSs, we identify the functional unitsthat define the strongest systematic and self-sustaining mechanisms of knowl-edge transfer and accumulation within the network. We expect that thedominant core groups of technology fields so identified correspond to theprevailing technological trajectories of the period. This prediction is corrobo-rated by the empirical analysis of section 3. This explores the architecture ofthe empirical knowledge pattern in the period 1975–99, as derived from theUnited States Patent and Trademark Office (USPTO) patent citation data(Hall et al., 2002) at the level of resolution of three-digit technology classes.

The paper is organized as follows. In the next subsection we examine therelation between our analysis and the existing literature. Section 2 introducesour formal description of a knowledge pattern and the precise notionsof modularity, ACS and core structures that will be used in the rest of thepaper. Section 3 exploits these notions to analyse the salient properties of the

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empirical knowledge pattern in the last quarter of the 20th century, and themain features of structural change between the first and last phase of thatperiod. Section 4 concludes.

1.2 Knowledge spillovers and technology representations

The premise that knowledge externalities are highly relevant to the pace oftechnological progress underlies the applied and theoretical literature vari-ously addressing the relation between R&D and economic growth. There is adifference in emphasis in this respect. In the highly stylized models of the newgrowth theory contemplating a variety of innovation goods produced byspecialized sectors, knowledge spillovers are treated as extending, either glo-bally across sectors, or within the boundary of each application domain. Thisdifference in treatment, global versus sector-specific spillovers, is often only amatter of analytical convenience.1 What has been so far completely disre-garded in the new growth literature is that knowledge flows span selectivelyacross the space of R&D domains, responding to technological, social andinstitutional constraints.

This has been a topic of extensive applied research aimed at quantifying thesize and scope of inter-sector spillovers. In this framework, a fundamentaldistinction has been made between rent spillovers and pure-knowledge spill-overs (Griliches, 1979, 1992). The former are carried by transactions ofinnovation goods2 and their estimation exploits R&D and patent data. Grili-ches et al. (1986) and Griliches (1990) discussed the gains and problemsoriginating from the use of patents as indicators of innovative activity. Aproblem arising from the use of R&D data is the difficulty of relating the lineof business in which the R&D effort originating the innovation is made,to the lines of business in which the innovation output finds its application.The first to address this problem was Schmookler (1966, chapter 8), whoproposed an input–output matrix of innovation flows, where rows areinnovation-source industries and columns innovation-using industries. Ter-lekyj (1974) combined R&D survey data with input–output statistics toestimate an innovation-flow matrix of the type proposed by Schmookler.These attempts gave rise to a literature on innovation-flow analysis through

1 Aghion and Howitt consider economy-wide (Aghion and Howitt, 1998, chapter 12) or sector-specific (Aghion and Howitt, 2005) spillovers, depending on the model at hand.2 The economic value of an innovation is only partially reflected in the price of the goodembodying it. The buyer of an innovation good can avail himself or herself of the services of theknowledge embodied in it, or even directly access that knowledge (through reverse engineeringand other means), without paying the full economic value of the innovation.

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input–output methods.3 An important step towards the estimation of moredisaggregated and precise innovation-flow matrices is Scherer (1982a, 1982b,1982c, 1984), which report a method for linking R&D survey and patentdata. The method identifies a concordance between a technology class in thepatent classification system and the industrial source and application sectorof the corresponding patent. Alternative methods of assigning patents toindustries are discussed in Kortum and Putnam (1997), Verspagen (1997),Johnson (2002) and Schmoch et al. (2003). Twenty years after his seminalcontributions, Scherer (2003) revisits the problems and methods of rent-spillover analysis through technology flows matrix estimation.

Contrary to rent spillovers, pure knowledge spillovers originate from thefact that a new idea, though possibly embodied in some specific good, istypically non-rival in its use, and can be (to some extent) communicated bymeans of a codified string of information. Printed communication in jour-nals, working papers and patent publications, in addition to conference andpersonal communication, are potential sources of knowledge spillovers.Jaffe et al. (2000) reported the results of a survey suggesting that althoughpatent citations carry a ‘fair amount of noise’ (p. 215), they are well ‘cor-related with significance or importance as perceived by the inventors them-selves’ (p. 218). The conclusion is that aggregate citation flows (aboutsectors, technology fields, geographic areas etc.) can be used as proxies forknowledge spillover intensity. Through patent citations we can recover thetechnology class source and destination of a spillover flow, where the des-tination domain may not correspond to, and be much wider than, theindustrial sectors in which the physical good embodying the innovation isused. Jaffe et al. (1993) made a seminal contribution to the analysis ofknowledge spillovers based on patent citations, followed by other contri-butions with different co-authors, that are now gathered in a importantbook (Jaffe and Trajtenberg, 2002). These contributions do not attempt toassign technology classes to industries by means of concordance tables.Examples of the attempt in question are Verspagen (2004) and Verspagenand de Loo (1999), which started from patent citation data to arrive at amatrix of inter-industry knowledge spillovers. The use of concordancetables in a patent citation-based analysis of knowledge spillovers involvesboth information gains and losses. The gain is obviously the ability to mapthe knowledge flows in the economic space of industries; the losses havelargely to do with the degree of arbitrariness that any such mapping

3 See Wolff and Nadiri (1993), Evinson and Johnson (1997) and Mohnen (1997), and theresearch there cited.

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contains.4 In this paper, we adopt a technology field (patent class), ratherthan a product space (Standard Industrial Classification, SIC), representa-tion; we do not use concordance tables and it must therefore be recalledthat the map from technology fields to industrial sectors is not everywhereone to one; simultaneously, R&D labs in the same industrial sector mayundertake research in a plurality of fields.

We think of the disciplinary technological knowledge available in theeconomy as subdivided into different disciplinary fields. A field correspondsto a set of functional or ‘phenotypic’ traits, and may be defined by a specificapplication domain, or by the use of a technological device (possibly acrossmultiple domains).

To relate this technology field representation to the more usual productspace representation, it is worth recalling the distinction between radical andincremental innovation.5 The former, as opposed to the latter, causes arelevant discontinuity in knowledge. What counts as a relevant discontinuityis identified by the production of a new technological lineage (Mokyr, 1990);in this way, the distinction may not be invariant with respect to the level ofresolution at which technological lineages are defined. In the product spacerepresentation where a technology results from the integration of compo-nents in a product system (cf. Henderson and Clark, 1990), a radical inno-vation is a change in the core design concepts that are embodied in thecomponents. New components are thus produced, which are linked, togetherwith the unchanged components, to form a new architecture. Incrementalinnovation is an adaptive change within an existing lineage. It improves uponone or more established designs, leaving the core design concepts and thelinks between them fundamentally unchanged. The further notion of archi-tectural innovation (Henderson and Clark, 1990), identifies the reconfigura-tion of an established system, such that pre-existing components are linkedtogether in a new way. Studies in the dynamics of technological changehighlight the complementarity between radical and incremental innovations.Often a radical breakthrough, such as the introduction of screw propulsionin ship building (Rosenberg, 1982, p. 63), is enabled by the accumulation ofincremental improvement steps in some components (e.g. metal working)and an entirely new technological lineage (e.g. wireless communication) may

4 On this, see the results of an experiment reported in Scherer (1982c). The difficulty of assigningpatents to industry of production and sector of use is partly related to multiproduct firms.Moreover, to the extent that R&D in different industries tends to draw upon a larger variety ofdisciplinary fields, there is a greater overlapping between the field domains pertaining to differentindustries.5 A restatement of the basic definitions with reference to the literature is in Henderson and Clark(1990).

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simply result from the recombination of an unchanged set of core designconcepts to serve the needs of a new application domain (Levinthal, 1998).

On the assumption that the scope of a disciplinary-field definition is suffi-ciently narrow, a radical innovation in the product space representation givesrise to a change in the number and/or quality of technology fields; incremen-tal and architectural innovations in the former representation do not have thesame effect, but only affect the knowledge stock of some pre-existing field.In our technology field representation, we shall also refer to the notion ofnetwork innovation, defined as a change in the matrix [cij] describing theaverage frequency with which the learning interface (Pavitt, 1998) from fieldj to field i is activated by an incremental innovation in field j. A networkinnovation so defined leaves the number and quality of technology fieldspossibly unchanged. The value cij depends on the extent to which (i) knowl-edge produced in field j is on average relevant to R&D in i, and (ii) there aretighter or looser relations between the R&D labs operating in the two fields.Network innovations are those affecting the two circumstances (i) and (ii)above. It is worth observing that a radical innovation as defined here alsoalways carries with it a network innovation. To the extent that the formergives rise to a new field, it opens up a new set of potential cross-field learninginterfaces and specifies a new set of technological opportunities. The circum-stances (i) and (ii) are also partly shaped by the cumulative effect of thelearning processes leading to incremental innovations. Still, in the presenttheoretical framework we make the bold approximation that the accumula-tion of incremental innovations exerts only a slow effect on the matrix [cij]; inthis way, at any given date, the latter can be defined independently of theincremental-innovation flow at the same date.

2. KNOWLEDGE PATTERN, MODULARITY AND ACS

2.1 The connection matrix C

We consider an economy with a finite set S = {1, . . . , n} of known technol-ogy fields. The technological state of the economy is defined by {G(S, L, C),A}. Ai (i = 1, . . . , n) is the number of useful ideas cumulatively produced byR&D in field i. G(S, L, C) is a weighted directed graph, with a set S of nodesthat are here interpreted as technology fields, a set L of directed knowledgelinks between these nodes, and a connection matrix C of weights, or intensitycoefficients, attached to the links in question. Column j of C lists the linksdirected from j to the other fields.

The average number of incremental innovations per unit of time in a givenfield depends on two main factors: in the first place, the set of innovation

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opportunities available in that field, and in the second place, the innovationeffort in the same field. In this paper, we assume that innovation opportuni-ties are primarily determined by the local knowledge base. This consists ofthe subset of ideas that are known to R&D labs currently operating in thegiven field and that are potentially conducive to useful recombinations anddevelopments leading to new disciplinary knowledge. Under a recombinantinterpretation of knowledge growth (Reiter, 1992; Weitzman, 1998), theknowledge base can be regarded as the repertoire of recombination possibili-ties from which innovations will originate.

So defined, the local knowledge base partly consists of ideas originatedfrom past innovations in the same technology field, but will also partlyconsist of ideas originated from past innovations in other fields that are madeavailable to the field in question by the knowledge interfaces currently activeacross technologies. The knowledge pattern is the set of knowledge interfacesthat are active across fields, together with their degree of activation. Moreprecisely, the intensity cij of knowledge transfer from field j to field i is theaverage frequency with which one innovation in field j gives rise to ideas thatare relevant to one unit of effective R&D effort in field i.6 We may note, inpassing, that the same idea discovered in one field may be relevant to manyother fields; hence, there is no implication that the elements in the columns ofC add up to 1. Knowledge produced by past innovations in one field is alwaysrelevant to R&D activity in the same field; that is, cii > 0 (i = 1, . . . , n). Bydefinition, C satisfies the condition: cij = 0 if and only if the directed link( j → i) ∉ L. This justifies the following definition.

Definition 1: G(S, L) is the unweighted directed graph associated with theweighted directed graph G(S, L, C), or, more synthetically, with C.

The radical discovery that brings j into the set S of known technologiesalso brings the knowledge stock Aj to its lower bound Aj = 1; after that, Aj

grows as a result of the cumulative flow of incremental-innovation arrivals inthe technology field j. On the premise that radical innovations producing newtechnological lineages and fields of applications are relatively infrequent(Mokyr, 1990), in the theoretical framework of this paper the set S of tech-nology fields is taken as given. The analysis is focused on the way in whichdifferent structural characteristics of the matrix C of knowledge interfaces,

6 cij will not fully capture the occasional transfer of a radically new idea from j to i, unless wehave a reliable way of weighing the importance of ideas. The absence of such reliable weights ismade less dramatic by the fact that a radical innovation is normally followed by a swarm ofincremental innovations, so that the frequency cij of systematic knowledge transfer will at leastpartly reflect the importance of ideas.

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linking the existing fields, materialize into a different long-term compositionof the vector �A of incremental-innovation flows. On the assumption thateach incremental innovation gives rise to a standard quality improvement,knowledge production per unit of time in sector i is measured by theincremental-innovation flow �Ai. This depends on two main factors, theknowledge base of field i and the effective R&D effort in this field.The knowledge base of field i is the repertoire of available ideas that arethe ‘building blocks’ of one average R&D unit operating in this field. A largerknowledge base provides a larger repertoire of recombination possibilitiesyet, simultaneously, makes R&D activity more difficult because searchspaces are more complex. On this ground, we hold to Aghion and Howitt’s(2005) idea that when the effect of innovation activity on innovation outputis at stake, R&D activity in field i is best measured by effective R&D effortQi/Ai, where Q is unweighted R&D investment. The repertoire of recombi-nation possibilities of field i determines the innovation opportunities offeredto one unit of effective R&D in i. This repertoire corresponds to the knowl-edge flows SjcijAj received by i through the active interfaces described by theith row of C. More formally, Ai (i = 1, . . . n) evolves according to the differ-ential equation:

�AQA

c Aii

iij jj

n==∑σ

1 (1)

where s is a uniform productivity parameter. Let ai = Ai/SjAj. A companionpaper (Caminati and Sordi, 2008) studied the dynamics of the column vectora of share distributions ai (i = 1, . . . , n) resulting from equation (1) and fromthe further assumption that the relative R&D effort Qi/SiQi increases(decreases) in those fields where innovation opportunities are higher (lower)than average. In the long-run condition such that the effective R&D effortQi/Ai converges to a uniform value q, equation (1) expressed in matrix nota-tion reads

�A CA= σq (2)

If C is indecomposable and A* > 0 satisfies l*A* = C A*, where l* is themaximum eigenvalue7 of C, then �A A* * *= σ λq , and the maximum persistentgrowth rate of ideas is l*sq. The idea stocks are in balanced growth equi-librium at A*, and under the above assumptions, the idea-stock distributiona converges asymptotically8 to the stationary distribution at A*. If C is

7 l* is the Perron–Frobenius (maximum modulus) eigenvalue of C.8 The proof is given in Caminati and Sordi (2008) for low dimensional n. Simulations supportthe conjecture that the results holds for any finite n.

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decomposable, it may be that the flows in C exclude a number of fields fromparticipating in the maximum self-sustaining growth rate of ideas; in this case,the relative share ai of such fields converges to zero asymptotically. The set offields participating in the maximum persistent growth of ideas is the set ofstrictly positive elements of the eigenvector A* associated with l*. (Usinga genericity argument, l* is assumed to have multiplicity 1; see section 2.3below.)

2.2 Modularity of C

Under the above interpretation, the exploitation by field i of a relevant inputidea discovered in field j requires meeting the constraints carried by the inputin question. To the extent that technological progress exploits an ever largervariety of input ideas, progress is likely to be faced with the solution of anever larger number of conflicting complementarity constraints,9 hence, withproblems of increasing difficulty (Page, 1996). Evolvability in the technologi-cal knowledge domain requires that complexity does not grow in proportionwith the inevitable growth in the scale of the system (Kauffman, 1993;Caminati, 2006). A way to slow down complexity growth is that the varietyof fields, which are the direct and indirect source of a field input ideas, growsmore slowly than variety in the technology system as a whole. The predictionis that the structure of C should reveal a selection for modularity in thepattern of knowledge interactions.

The power of modularization finds its limits in the fact that the price to payfor a simplification of the search space is a lower ability to attain globaloptima (Ethiraj and Levinthal, 2004; Marengo et al., 2005). Moreover, topreserve the ability of designing a radical change in the organization of atechnology system, it is necessary that some units preserve a global knowl-edge of the diverse disciplinary components that are involved (Brusoni et al.,2001; Prencipe, 2003). Far from questioning the relevance of modularity,these ideas challenge the identification of modularity with separability(Frenken, 2006), or even with near-decomposability (Simon, 1962). What isrequired is a notion that is weaker than Simon’s, in that strong interactionsbetween the modules are allowed (cf. Watson, 2006). This more general viewof modularity finds an operational definition and measure in the notion ofnetwork modularity recently proposed by Newman and Girivan (2004): intu-itively, the set of n fields can be partitioned into m < n disjoint groups such

9 See Kauffman et al. (2000); Fleming and Sorenson (2001) attempted an empirical investigationbased on patent citations.

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that, on average, and in ways that will be specified below, the within-grouplinks are stronger than they would be if the cross-field distribution of linkswere random.

2.3 Modularity, ACSs and core structures

The above intuitive and quite general idea of modularity of the connectionmatrix C admits a quantitative expression, based on recent contributionsin network theory and applications. Suppose that the set N = {1, . . . , n} oftechnology fields is partitioned into m disjoint subsets, or groups, so thatN = N1 � N2 � . . . � Nm, where Nh is the set of fields belonging to group h.The total intensity of an outward link from group h directed to itself or toother groups is âh = SjSicij (j ∈ Nh, i = 1, . . . , n). The corresponding totalintensity of an inward link to group h from itself or from other groups isa ch j i ij= Σ Σˇ (i ∈ Nh, j = 1, . . . , n). If the total intensity of links in C isT = SiSjcij (i, j = 1, . . . , n), then the average relative frequency with which anoutward link in C originates from, and arrives to, group h is êh = âh/T ande a Th h=ˇ ˇ , respectively. The modularity measure Qh of the links from and togroup h in the context of the given network C is then expressed by the extentto which the frequency of within-group links exceeds the frequency thatwould be expected from the hypothesis of a random wiring.

QT

c e eh ijj Ni N

h h

hh

= ⎡⎣⎢

⎤⎦⎥

−∈∈∑∑1

ˆ ˇ (3)

The modularity of C according to the partition {N1, . . . , Nm} is thenexpressed by the sum Q = ShQh, which may be negative if the partition isill-chosen. Indeed, the relative goodness of two alternative partitions of Nis evaluated by choosing the partition yielding a higher value of Q. In thisspirit, the modularity of C is defined by selecting the Q-maximizing partition(Newman and Girivan, 2004). Because the Q modularity of the null partition{N} is zero, and the Q-maximizing value of C is taken over all possiblepartitions of {N} (including the null partition), the Q modularity of C takesvalues in the interval [0, 1]. If C is diagonal, with cii > 0 (i = 1, . . . , n),Q(C) → 1 as n → +•. Given n, modularity is maximal when every field sendsspillovers only to itself and not to the other fields.

According to this view, modularity is a property that comes in continuousdegrees; it is not a discrete, yes or no, property. A system architecture mayexhibit a relevant degree of modularity in spite of the fact that its modules areneither completely separable, nor even nearly decomposable; there may be

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some isolated, but possibly strong, interactions between them. As will beargued, this more general view of modularity is well suited to the analysis of thepatterns of knowledge transfer between technology fields. Consistent with thisview, we need to identify a few benchmark values of the measure Q within therange [0, 1] that can be taken as a signal of low, moderate or high modularity.10

If we attach to a weighted directed network described by C the dynamicinterpretation of equation (1), a relevant notion of connection intensity isthat of closed-path connectivity, expressing the extent to which a circularflow within the network is self-sustaining. This is because our analysis isfocused on the structural characteristics of C that are able to sustain, in thelong run, persistent rates of incremental-innovation flow. In order that theprocess of knowledge production is self-sustaining, the provision of inputideas cannot be once and for all.11 A isolated radical innovation in one fieldwill not produce persistent progress, if it is not followed by a swarm ofincremental innovations, in the same and in other fields. The flow rate ofoutput ideas, from field i to the others, is limited in the long run by the rateat which input ideas flow to field i. R&D in field i will never run short of inputideas, if and only if node i is on a closed path12 within the knowledge networkdescribed by G(S, L, C). This is the idea formalized in the model of subsection2.1. The measure of closed-path connectivity of a subset of nodes in G(S, L,C) is a strictly increasing function of (i) the multiplicity of closed pathsconnecting every node in the subset to itself, and (ii) the connection weightson such paths. By way of example, within the network described in figure 1and corresponding to

C =

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

c c

c c c

c c

c

11 12

21 22 24

31 33

44

0 0

0

0 0

0 0 0

* *

* * *

* *

*

(4)

10 Our benchmark values of Q result from computation experiments with artificial C matrices.Because the lowest Q value corresponding to a block diagonal form of C is Q = 0.5, a matrix Cis modular if and only if Q(C) � 0.5. Modularity is moderately high if 0.5 < Q � 0.66, high if0.66 < Q � 0.75 and very high if Q > 0.75.11 Rosenberg stressed that however important the initial formulation of the steam-engine prin-ciple, the steam-engine trajectories in ship navigation or in factory motive power were fuelledand could maintain their momentum only through continuous improvements in steam-enginedesign, which drew upon further improvements in other fields, such as metallurgy or metalworking.12 The closed path in question may also be a self-loop, connecting i to itself.

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there are two closed paths connecting both node 1 and node 2 to themselves;there is only one closed path connecting node 4 to itself. For the sake of laterreference, we introduce the following definition.

Definition 2: The ACS of a directed graph G(S, L, C) is a connected sub-graph G(S′, L′, C′) ⊆ G(S, L, C) embedding a closed path, i.e. such thateach vertex in the subgraph has at least one incoming link from somevertex of the subgraph ((Jain and Krishna, 2003). A directed subgraphG(S′, L′, C′) is connected if there is at least one directed path connecting allthe nodes in S′.

The definition admits that the same ACS may embed disjoint closed paths,so that a smaller ACS may be embedded in a larger one. Different closedpaths within the same ACS may then reveal a different connectivity. Theclosed-path connectivity of an ACS is then defined by the highest connectiv-ity measure attained on the set of its closed paths. To make this definitionoperational, we extend to weighted directed networks the maximum (Perron–Frobenius) eigenvalue measure of closed-path connectivity discussed in Jainand Krishna (2003) for unweighted directed graphs.

In unweighted directed networks, cij � 0 implies cij = 1. In this case, themaximum eigenvalue l* of C or of C′ ⊂ C is a measure of the largest

Figure 1. Network corresponding to the matrix C of expression (4). The identification of thedominant ACS in the text follows from the assumption c44 < l*(C).

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multiplicity of closed paths connecting a subset of nodes in C or C′, respec-tively13 (Jain and Krishna, 2003). In weighted directed graphs, l* is aweighted measure of closed-path connectivity: each closed path is weighted bythe strength of the links building the path.14

Definition 3: The dominant ACS of the graph G(S, L, C) is the largestsubgraph G(Sa, La, Ca) with the property that the associated connectionmatrix Ca satisfies l*(C) = l*(Ca). The set of nodes in Sa are identified by thestrictly positive elements in the right eigenvector of C associated with theeigenvalue l*(C).

In the light of the ideas growth equation (2), we interpret Sa as the set offields (nodes) participating in the maximum persistent growth rate of ideasthat can be fuelled by the weighted links in C.

Definition 4: On the generic assumption that the eigenvalues of C aredistinct, the core of the dominant ACS G(Sa, La, Ca) is the unique largestclosed path, namely a subgraph G(Sc, Lc, Cc), with the property thatl*(Cc) = l*(Ca) = l*(C). Here, Sc ⊆ Sa ⊆ S and Lc ⊆ La ⊆ L.

The core of an ACS is its largest subgraph such that the l* measure ofconnectivity, on the ACS and on the subgraph, is the same. Every node in thecore is linked to every other node in the ACS through a directed path. The setof nodes in the dominant ACS that are not in its core, together with theirmutual links, form the periphery. There are no directed paths starting atperiphery nodes and arriving at core nodes.

With the tools above we can now look at the graph G(S, L, C) of figure 1,which is interpreted here as a knowledge network. In this example, thedominant ACS of the graph consists of the nodes 1, 2, 3 and the links betweenthem. The reason is that node 4 does not receive links from the others; as aresult, to the extent that c44 is strictly lower than l*, input ideas cannotpersistently flow to node 4 at the same rate at which they flow, in the long run,to the other nodes. Node 4 is not in the position of participating to the highest

13 To the extent that a closed path may be a strict subgraph of another, this largest multiplicitymay not be expressed by an integer value of l*.14 To see that weights matter, consider the matrix C′ corresponding to the subgraph defined bythe nodes 1, 2 and 3 in figure 1, and the links between them. Under the unweighted graphrestriction, the largest multiplicity of closed paths connecting a subset of nodes in C or C′ is thesame. That is, l*(C) = l*(C′). If we now drop the unweighted graph restriction, so that cij � 0takes values in (0, 1], the same conclusion may not hold. It may now be the case thatl*(C) > l*(C′), provided that c44 in equation (4) is large compared with the elements of C′.

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persistent rate of knowledge production in the network. Mathematically, theformal counterpart to this is that the fourth component in the eigenvector ofC associated with l* is zero.

Node 3 has a peripheral position within the dominant ACS of ourexample because it receives, but does not send, links to nodes 1 and 2. Theoutcome is that node 3 is a sort of parasite within the dominant ACS. Itcannot contribute to the persistent rate l*. If we remove node 3 and itslinks from the dominant ACS, the highest persistent rate of knowledgetransfer carried out by nodes 1 and 2 is unchanged; it is still l*. Nodes 1and 2, and the links between them, are the core of the dominant ACS; node3 is the periphery.

The core of the dominant ACS of a knowledge pattern is the centre of thestrongest self-sustaining mechanisms of knowledge creation and transmis-sion within that pattern. In a relevant sense, the links connecting the core tothe other fields in the dominant ACS disseminate building blocks (Holland,1998), which are the aggregate outcome of the relations within the core.Heuristically, this form of aggregation reflects the combinatorial view ofknowledge creation adopted in this paper.

On the premise that the empirical pattern C can be recovered from theavailable data, we formulate the following conjecture.

Conjecture 1: The fields in an ACS of C can be meaningfully interpreted asthe fields which, taken together, identify a self-sustaining technological tra-jectory characterizing the historical period under investigation. We expectthat these fields have a high degree of technological proximity. The relativemeasure of closed-path connectivity of different ACSs, together with theirrelative dimension, gives us a way of evaluating the rate of progress along thedifferent trajectories, and their relative importance in terms of knowledgediffusion effects.

3. CONTINUITY AND CHANGE IN THE PATTERN OF KNOWLEDGETRANSFER: 1975–99

3.1 The data

The data source for our exercise is the National Bureau of EconomicResearch (NBER) Patent-Citations data file, as made available in Jaffe andTrajtenberg (2002). The main data set PAT63_99 contains all utility patents15

15 Utility patents constitute the overwhelming majority of patents, which include, in addition,design, reissue and plant patents (cf. Hall et al., 2002, p. 407, n. 4).

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granted by the US Patent and Trademark Office (PTO) between 1 January1963 and 30 December 1999. Among the variables that the PTO originallyassigned to each patent, the most relevant for us, in addition to the grantyear, is the main US patent class.16 The 417 patent classes in the USPTOclassification in use in 1999 are aggregated by the authors of the NBERfile into 36 technological subcategories, which are further aggregated intosix categories (‘Chemical’, ‘Computers and Communications’, ‘Drugs andMedical’, ‘Electrical and Electronic’, ‘Mechanical’ and ‘Others’). The dataset PAT63_99 can be usefully matched with a second data set, namelyCITE75_99, which contains all citations made to patents in PAT63_99 bypatents issued between 1 January 1975 and 30 December 1999.

The first aim of our exercise is to obtain from the citations data justdescribed a computationally viable description of the propensity of knowl-edge to flow across technology fields, where a field is here identified with aUSPTO three-digit class. Consistent with the definition of the C matrix inequation (1), we are interested in a measure of the average intensity withwhich one idea produced in a given field represents a relevant knowledgeinput to ideas production in the same or in other fields. To compute thismeasure, we studied how strongly patenting in a class xy in a time interval[t, t + z] was followed by citations to xy by patents issued in every other classin the time interval [t + s, t + z]. In this way, for each class xy, we obtaineda 417-dimensional vector of citations to xy. The corresponding vector ofrelative spillover intensity from xy to the other classes was obtained bydividing the citations vector by the number of patents issued in xy in theperiod [t, t + z]. Proceeding in this way for each xy in the set of 417 classes, wearrived at a matrix of spillover intensity, which is the empirical analogue ofthe matrix C in our model. Because we are most interested in detectingthe qualitative features of structural change, the time interval covered bythe citations data was divided into two subperiods of approximately equallength. For the sake of later reference, these intervals, namely [t + s,t + z] = [1975–86] and [t + s, t + z] = [1987–99], are referred to below as W1and W2, respectively. The corresponding connection matrices are C(W1) andC(W2).

This periodization was partly suggested by the need to preserve com-parability between C(W1) and C(W2). We had to make sure that the non-

16 The reason for the qualification ‘main’ is that the PTO assigns each patent a three-digitpatent class and a subclass, and also any number of ‘subsidiary’ classes and subclasses thatseem appropriate. Moreover, the system is continuously updated, with new classes beingadded and others being reclassified or discarded. In this case, the PTO retroactively assignspatents to patent classes, according to the most recent classification system (cf. Hall et al.,2002, p. 415).

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avoidable truncation effects related to backward and forward citation lags(Hall et al., 2002, pp. 421–4) introduce similar distortions on the two matri-ces. The backward (forward) citation lag is the lag between the grant orapplication year of the citing (cited) patent and that of the cited (citing)patent. For instance, all the citations made by patents issued in the first year(t + s = 1975) of W1 to patents issued before t = 1963 cannot be included inthe computation of C(W1), because they are not in the data set. To preservecomparability, a corresponding truncation effect is introduced on the cita-tions made by patents issued in the first year (1987) of W2. In other words,comparability between C(W1) and C(W2) is preserved by holding s constantbetween the subperiods (s = 12) and by allowing for negligible differences inz (z = 23 in W1, z = 24 in W2; the corresponding values for t are t = 1963 andt = 1975, respectively). The backward truncation Lb that is applied to thecitations made by the patents issued in the year t + s + i is Lb = s + i, wherei = 0, . . . , z - s; the inequality 12 � Lb � 24 defines the lower and upperbounds to the backward lags that are admitted by our periodization. Thecumulative distribution of backward citation lags reported in Hall et al.(2002, p. 422) shows that truncation at Lb = 12 (Lb = 24) includes on averagealmost 60 per cent (about 80 per cent) of the citations made.

We emphasize that the qualitative results of the following analysisare robust to a one-year perturbation of the separation date between the firstand second period, provided that the symmetry of truncation effects ispreserved.

A second problem faced by the computation of C is that there is a risingtrend, largely common across categories, in the mean number of citations perpatent. This trend reflects, to a large extent, an increasing propensity to citeby PTO officers, as a result of the easier access to larger data sources broughtabout by computerization of the PTO during the 1980s. Although the risingcitations trend may not be entirely a pure artefact of the changed PTOpractices, in the absence of a better alternative, the construction of C(W2)was carried out using discounted citations data. In particular, the number ofcitations made by patents issued in class xy in period W2 was discounted bythe xy growth rate of citations made per patent between W1 and W2.

There is a third potentially distorting characteristic in the data set, namelythe rising trend in the yearly number of patents issued since 1983. This featurehas received different explanations. Conventional wisdom relates it to the1982 change in US patent legislation; Kortum and Lerner (1999) rejected thishypothesis and relate the surge in patenting to ‘an increase in US innovationspurred by changes in the management of research’ (p. 1). Be it as it may, ourcomputation procedure takes care of the rising trend because the empiricalconnection coefficient cij is here defined by the average number of citations

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made by the patents in class i to one patent in class j.17 Computation of theempirical coefficient cij conforms to the definition of the corresponding theo-retical coefficient in the ideas growth model of section 2.

3.2 Modularity, communities of knowledge and technology domains

To identify meaningful technological communities, we generated endog-enous partitions of S. After theoretical evaluation and effective implementa-tion of alternative partition methods,18 we finally followed the approachrecently suggested by Newman and Girivan (2004) and Newman (2004).These authors proposed that the appropriateness of any two community-structure partitions of a given network are evaluated using their proposedmeasure of modularity Q that was described in section 2 above. In this spirit,they proposed that the best community structure identification in a givennetwork is the Q-maximizing partition.

The matrices19 C(W1) and C(W2) are generated by the Q-maximizingpartitions and corresponding class reordering. To generate this network-community structure, we followed the algorithm suggested in a still morerecent contribution by Newman (2006), which was adapted to our purpose ofdealing with weighted directed networks. One year after this adaptation wascompleted and the relevant computations carried out, a similar adaptationappeared in Leicht and Newman (2008). The MATLAB routine carrying outthe computation is in itself an output of the present research.20 The routineidentifies n = 31 technological communities in period W1, and n = 44 com-munities in period W2; in both cases, n is endogenously determined.

These endogenously determined groups correspond to interaction modules:a class is assigned to a group only on the grounds that its within-groupinteractions are on average stronger than its between-group interactions. This

17 More precisely, the number of citations made by class xy patents issued in period [t + s, t + z],to class hk patents issued in [t, t + z], is divided by the number of hk patents granted in [t, t + z].18 In particular, we obtained a 32-group partition of the 418 classes, and a correspondingpermutation of C, using the algorithm CONCOR (Breiger et al., 1975), which partitions itera-tively the set of technology classes into two groups, such that the inward and outward connec-tions of two classes in the same (opposite) group are positively (negatively) correlated. Thismethod was finally left aside, on grounds that the mathematical underpinnings of the algorithmCONCOR are questionable (Brandes and Erlebach, 2005, pp. 270–1) and that the number ofblocks had to be fixed exogenously.19 Visual representations of these matrices are readable only in a colour format. They can beobtained on request from the authors.20 It was produced with the programming assistance of Emiliano Sparacino, currently a PhDstudent at the Department of Information Engineering of Siena University. The routine is freelyavailable upon request.

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definition does not meet the strong requirements (low order of magnitude ofall between-module interactions) imposed by Simon’s tighter notion of near-decomposability (Simon and Ando, 1961; Simon, 1973).

The Newman–Girivan Q measure signals a meaningful degree of modu-larity in both periods. The Q measure falls from 0.68 in period W1 to 0.63 inperiod W2. These values are just above and just below (respectively) thethreshold value (0.66) separating moderately high from high modularitymeasures.21 Before commenting upon the distribution of modularity and itschange across the network subsystems, more needs to be said about thetechnology domain composition of the knowledge communities.

3.2.1 Newman modules and their technology domain

Tables 1 and 2 specify the size of the main Newman groups and their per-centage composition by NBER technological category. The percentageassigned to each category depends on the number of classes belonging to it.The tables signal three types of findings.

First, the large categories Mechanical and Others participate in mostNewman groups; smaller categories, such as Computer and Communicationsor Drugs and Medical (Health), are highly concentrated in a restrictednumber of groups. Second, there are areas of meaningful intersectionbetween knowledge communities and technology domains. In particular, theICT knowledge community is identified by group 31 in period W1, by groups1 + 44 in period W2, and results from the tight mutual wiring connecting thelarge majority of classes in Computer and Communications, among them-selves, and with a relevant subset of classes in Electrical and Electronic (e.g.semiconductors). Third, there are a number of modules in which a relativelylarge variety of technology domains (categories) participate in the process ofknowledge exchange: they are identified by a modal participation share,which is lower than 50 per cent. This finding is representative of the tendencytowards the inter-disciplinarity of knowledge flows, which is now well docu-mented in field studies on innovation (Pavitt, 2003).

Further considerations on the pattern of knowledge flows are suggested bythe group contributions to modularity, weighted by the number of groupmembers, which is reported in figure 2. What is most relevant there is that, inboth periods, the maximum per-class contribution to modularity comes fromthe ICT community, which in both series corresponds to the last plottedvalue.

21 See footnote 10.

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Among the communities endogenously identified, it is precisely the ICTcore group that shows a much higher than average tendency to receiveknowledge spillovers from, and to send knowledge spillovers to, the classesbelonging to the same community.

3.2.2 Disaggregating modularity change

The 7 per cent fall of the aggregate Q modularity measure between W1 andW2 is the outcome of a ‘spreading out’ of the knowledge links, which takesplace in a relative large number of technology domains. This finding is notwell represented by the Newman group disaggregation offered in figure 2,as a result of the endogenously changing number and composition of theNewman groups. To avoid this problem, figure 3 reports the unweightedmodularity profiles corresponding to the partition of S into 32 NBER

Table 1. Technological communities of period W1

Newmangroup Size Q % Ch % H % C&C % E % M % O

4 27 0.00175 7 37 0 0 19 375 32 0.00144 3 0 0 0 75 228 17 0.00155 0 0 0 100 0 09 36 0.00165 14 0 0 17 22 47

11 19 0.00133 0 0 5 0 16 7916 39 0.00164 87 0 0 0 3 1017 22 0.00191 86 5 0 0 0 923 30 0.00117 3 0 0 3 40 5424 17 0.00116 0 0 0 0 82 1829 27 0.00156 26 0 4 26 18 2630 24 0.00183 13 4 17 37 25 431: ICT 43 0.00244 0 0 67 19 7 7C(W1) 418 0.68 18.7 3.3 8.4 12.4 28 29.2

Notes: To make the presentation of the results less cumbersome, column 1 reports the labels ofthe ‘main Newman groups’ and the ‘aggregate’ group C. A main Newman group contains 17 ormore classes; in period W1 the set of the main Newman groups covers 80 per cent of the classesin C. The qualitative nature of our findings is unaffected by a less restrictive definition of a ‘mainNewman group’, or if we refer to the complete population of groups. Size = number of classesin the group; Q = group contribution to modularity; Ch = Chemical; H = Drugs and Medical;C&C = Computer and Communications; E = Electrical and Electronic; M = Mechanical;O = Others.

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Table 2. Technological communities of period W2

Newmangroup Size Q % Ch % H % C&C % E % M % O

1 23 0.00187 0 0 39 57 4 04 45 0.00151 20 0 0 44 25 119 35 0.00149 3 29 0 6 26 36

10 24 0.00132 0 0 0 0 79 2113 21 0.00145 5 0 0 10 61 2414 21 0.00134 0 0 0 0 24 7621 47 0.00134 88 4 0 0 2 625 19 0.00130 53 0 0 5 5 3740 18 0.00141 11 0 0 11 45 3344 28 0.00287 0 0 78 7 4 111 + 44: ICT 51 0.00240 0 0 60.5 29.5 4 6C(W2) 418 0.63 18.7 3.3 8.4 12.4 28 29.2

Notes: Legend as in table 1. In period W2 the set of the main Newman groups covers 67 per centof the classes in C; the ICT group is the sum of the Newman groups 1 and 44.

Modularity by Newman group

0.003

0.0025

0.002

0.0015

Wei

ghte

d Qi

0.001

0.0005

01 3 5 7 9 1113151719212325272931333537394143

Newman group i

1975–861987–99

Figure 2. Contribution (weighted by community size) to the Newman–Girivan measure ofmodularity of each Newman community for the periods W1 and W2. In each period, the ICTcommunity (label 31 in W1 and label 44 in W2) ranks highest. In period W2, the value of label 1is missing; the data of the original groups 1 and 44 have been aggregated to form a single ICTgroup, corresponding to label 44 in this figure.

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technological subcategories;22 modularity falls in 19 of these subcategories,showing that the change is quite widespread across the network. Among themost notable exceptions to this behaviour are the NBER subcategories 21(Communications), 22 (Computer Hardware and Software), 46 (SemiconductorDevices). This suggests that the ‘spreading out’ of knowledge interactionstakes place mainly outside the ICT group.23 A slight aggregation of thecontributions to modularity, by NBER category, reveals that the percentagemodularity fall is most pronounced in Chemical (-21 per cent), and is average(-7 per cent) in Mechanical and in Others; Computer and Communications (+6per cent) and, to a lower extent, Electrical and Electronic (+1 per cent)represent the only outliers with respect to the prevailing direction of change.

In the concluding section of this paper the composite pattern of changedescribed above will be interpreted in the light of other results of the follow-ing analysis: the dominant position of the ICT group throughout the period1975–99, and the sharp increase in the rate of ICT knowledge circulation anddiffusion in the second phase of that period.

22 We may note, in passing, that the cardinality measure of the Newman group set and of thesubcategory set is in the same order of magnitude.23 Notice that in the Newman group representation of the modularity profiles (figure 2), the ICTcontribution is nearly unchanged between W1 and W2.

Modularity by subcategoryM

odul

arity

0.035

0.03

0.025

0.02

0.015

0.01

11 13 15 21 23 31 33 41 43 45 49 52 54

Subcategory

59 62 64

1975–861987–99

66 68

0.005

0

Figure 3. Contribution to the Newman–Girivan measure of modularity of each NBERtechnological subcategory in periods W1 and W2. 11 - 19 = Chemical; 21 - 24 = Computerand communications; 31 - 39 = Drugs and Medical; 41 - 49 = Electrical and Electronic;51 - 59 = Mechanical; 61 - 69 = Others.

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3.2.3 Was ICT knowledge general purpose?

Apparently, our finding concerning the highest level and time persistence ofthe modularity score of the ICT group is in sharp contrast with the finding inHall et al. (2002), based on the Herfindahl concentration of the class distri-butions of patent citations made (input) and received (output). Hall et al.(2002) find that, on average and throughout the period 1975–99, patentsin the Computer and Communications category have the lowest concentrationindexes of the input and output patent citations by class. This means that, onaverage, a patent issued in the Computer and Communications category sendsknowledge connections to, and receives knowledge connections from, a setof technology classes, which is wider than the corresponding set referring tothe average patent issued in each of the other categories. On this account,they argue that patents in Computer and Communications are most ‘original’because they creatively exploit knowledge from a wider set of technologyclasses, and produce also the most ‘general’ knowledge because knowledgecreated by them disseminates to a wider set of classes. According to Hall et al.(2002), the highest generality score makes the label ‘general purpose tech-nologies’ most appropriate for the classes belonging to the Computer andCommunications category.

We maintain that the ICT ideas produced and diffused in 1975–99 can beappropriately labelled ‘general purpose’, but the claim does not and cannotrest upon the evidence brought by Hall et al. (2002) concerning the Herfind-ahl index for the class24 distribution of patent citations. The modularityresults show that the relatively wider set of technology classes that have (onaverage) knowledge interactions with an ICT patent is composed, to a rela-tively larger extent, by classes belonging to the same ICT group. The endog-enous identification of the ICT community through the Newman procedurereveals the mixed composition of this community, integrating computer,communications and a non-negligible subset of electronic classes (tables 1and 2). We conclude that the corroboration of the general purpose propertyof ICT ideas requires a more elaborate analysis of some structural propertiesof the connection matrices, focused on the notions of modules and ACSs. Itis to this analysis that we now turn.

24 We computed the Herfindahl concentration indexes concerning the NBER subcategory dis-tribution (rather than class distribution) of the absolute number of inward and outward cita-tions, for the periods W1 and W2. The findings (which can be obtained upon request) show thatpatents in Computer and Communications occupy an intermediate position in the rank list ofconcentration indexes.

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3.3 Closed-path connectivity and other core properties ofthe knowledge network

The empirical knowledge patterns defined by the matrices C(W1) and C(W2)have been shown to be significantly modular. This finding must be coupledwith the further observation that these networks reveal a far reaching wiringstructure provided by weak links, which contribute to endow these networkswith relatively strong connectivity properties. If the links of every order areconsidered, no matter how weak, the dominant ACS in both of these net-works includes all the nodes, and most significantly, the core of the dominantACS includes over 90 per cent of the nodes. We observe, following thesuggestion of Simon and Ando (1961), that the viewpoint that takes intoaccount the effects coming from the very weak links, amounts to consideringthe long-run connectivity property of the network. If we hold to this perspec-tive, we conclude that the property of closed-path connectivity is widespread:the large majority of fields contribute, in the very long run, to the self-sustaining property of knowledge production.

However informative, the long-run perspective is not useful for discrimi-nating different functional units within the network, and to assess theirrelative importance. For instance, how is one to assess the relative general-purpose property of ideas produced in different disciplinary fields, if mostlikely (as a result of the very large core of the dominant ACS of C) the ideaproduced in any field has, in the long run, a potential direct or indirect effecton every other field? To gain additional information, it is worth ranking thelinks according to their order of magnitude, separating those of higher orderfrom those of lower order.

To this end, we produced dichotomized connection matrices CA(W1),CA(W2) with the defining property that all connection links of the originalmatrix, which are larger than or equal to 0.1, are set equal to 1 and all ofthe others are set to 0. In this and the next subsection, we discuss thequalitative information drawn from this exercise. A sensitivity analysiswas carried out to check that the qualitative nature of the results that willbe presented is robust to perturbations of the split parameter s around thevalue s = 0.1.25

25 Alternative dichotomizations of the matrices C(W1) and C(W2) were produced by selectingthe value of the split parameter s within the interval 0.075 � s � 0.125. As expected, the absolutesize # of the dominant ACS1 (and of the other leading ACSs) is inversely related with the valueof s. Likewise, the ratio r = #Core/#ACS1 tends to decrease when s increases. Most important forthe present analysis is that the structural change, from period W1 to period W2, concerningthe different composition between core and periphery of the dominant ACS1, is very robust

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3.3.1 The ACSs of CA

Simon’s idea of separating first-order magnitude from lower-order magni-tude links brings to the fore interesting functional and structural propertiesof the connection matrix C. A close scrutiny of the dichotomized matrixCA shows that, in both periods, there are three principal and separate,self-sustaining flows of knowledge circulation within the network. Theycorrespond to different ACS of the matrix CA, labelled ACS1, ACS2, ACS3.The fourth column (% core) of table 3 shows that their core units are char-acterized by technology domains that are stable across the two periods.They correspond to the ICT classes, the health-care technologies (e.g. sur-gery),26 and a subset of specialized chemical technology classes (syntheticresins, coating, adhesive bonding etc.), respectively. Most relevant amongthem is the dominant ACS1, on the grounds of its much larger size, itstechnological characterization and the much higher measure of closed-pathconnectivity.

perturbations of s. At each value of s, the ratio r is systematically lower in W1 than in W2. In theformer, r takes values in the interval [0.18, 0.58]; in the latter r ranges in the interval [0.74, 0.91].Notably, the two intervals are disjoint.26 With reference to the USA, previous studies emphasized the relatively high rate of innovation(patenting) activity in the ICT and health-care technologies (cf. Hicks et al., 2001). Here theemphasis is on the ability to achieve a self-sustaining flow of knowledge spillovers.

Table 3. Leading ACSs of period W1 and W2

# % # # core % core Newm gr. Reach l*

C(W1) 418 100 31 418 3.583ACS1(W1) 45 10.8 8 100 ICT 9 182 3.560ACS2(W1) 5 1.2 4 100 H 2 60 2.883ACS3(W1) 14 3.3 10 70 Ch. 5 145 2.508C(W2) 418 100 44 418 6.649ACS1(W1) 52 12.4 42 81 ICT 11 187 6.644ACS2(W1) 23 5.5 6 100 H 5 116 3.405ACS3(W1) 19 4.5 9 100 Ch. 4 120 3.318

Note: # = absolute size (number of classes); % # = (#_/# C) ¥ 100; # core = size of core; %core = fraction of classes in the most representative technology domain (H = Drugs and Medical,Ch. = Chemical); Newm. gr. = number of Newman groups that are represented, with one ormore classes; Reach = total number of classes in the Newman groups that are represented;l* = (Perron–Frobenius) eigenvalue measure of closed path connectivity.

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3.3.2 The general purpose property of ICT knowledge

Although well characterized in terms of technology class composition, thedifferent ACSs participate in different Newman communities; the number ofsuch communities increases with the size of the ACS. Because the members ofa Newman community are mutually relatively well connected, an ACS par-ticipating in a Newman module comes to be indirectly but relatively tightlyconnected with most of the classes in this module. Column 7 (reach size) oftable 3 specifies the total number of classes that are indirectly reached by anACS in this way.

The table shows that, in both periods, the size (in terms of class participa-tion) of ACS1 is at least twice larger than the size of ACS2 and ACS3. ACS1

comprises over 10 per cent of the overall number of nodes in the network. Inview of its size, the dominant ACS participates in a network subset compris-ing most large Newman modules, and including over 25 per cent of their totalnumber. In this way it is indirectly, but tightly, connected to an even larger setof technology classes (reach size), comprising, in both periods, over 43 percent of technology fields. These findings provide, in our view, a convincingcrucial integration to the results concerning the group contributions tomodularity and the Herfindahl concentration of the class distribution ofpatent citations. The new findings support the conclusion that the ideasproduced in the group of ICT fields were relatively general purpose, if com-pared with the ideas produced in the other field groups, during the periodunder study.

3.3.3 Comparing self-sustaining rates of knowledge flow

Further support of the conclusion that the knowledge spillovers in the ICTgroup had a prominent role throughout the period 1975–99 comes from acomparative evaluation of the connectivity measures l* for the differentACSs and for the entire networks C(W1) and C(W2).

The comparison was carried out as follows. From the weighted directedgraph G(S, L, C), corresponding to the empirical connection matrix C, weextract the subgraph G(Si, Li, Ci) where Si is the set of nodes in ACSi, Li ⊂ Lis the subset of links connecting the nodes in Si, and Ci is the connectionmatrix specifying the intensity of the links in Li, as reported in C. Our modelsuggests that the relative degree of participation of a subset Si of nodes to thelong-term self-sustaining mechanisms of knowledge creation and transmis-sion within C can be evaluated by comparing the Perron–Frobenius eigen-value of the connection matrix Ci of the subgraph G(Si, Li, Ci) with the

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dominant eigenvalue of C. The results of this exercise, summarized in the lastcolumn of table 3, lend support to the following conclusions:

(i) Among the prominent, self-sustaining flows of knowledge spillover thatcan be identified within the network, the flow generated by the group ofICT fields predominates in both periods. This conclusion holds not onlywith respect to the measure of knowledge transfer, but also with respectto the number of fields that are reached by the knowledge flow in theshort run (because the fields belong to the periphery or to the core of theACS) and in the medium run (because the fields belong to the modulesthat are directly reached by the ACS).

(ii) In the long run, i.e. when the links of every magnitude exert theireffect, the highest persistent flow rate that can be sustained in the knowl-edge network as a whole can be entirely traced to the flows generatedwithin the group of ICT fields. Again, this property holds in bothperiods.

(iii) In the period 1987–99 there is a general increase of knowledge transferwithin the network at large and in each of its leading ACSs. The change,as measured by the percentage increase of l* between W1 and W2, is 87per cent for the dominant ACS1, against 18 per cent for ACS2 and 32 percent for ACS3. The corresponding increase (85 per cent) of l* for theentire network C closely approximates the value obtained for ACS1.

Conclusions (i) and (ii) underline some elements of continuity between W1and W2. The ICT fields already had a primacy in the circulation of novelideas in the years 1975–86, shortly after the inception of slow productivitygrowth in the USA and the G7 countries. Among the leading flows ofknowledge circulation in this period, what best distinguishes the ICT flowfrom the others is its wider scope more than its faster rate. The early leadingposition of the information technologies in the process of knowledge pro-duction during the last decades of the 20th century is also partly mirroredin the growth statistics. With reference to the USA, Jorgenson (2001, 2005)finds that in the period 1973–89, information technologies provided thelargest contribution to TFP growth.

Conclusion (iii) brings to the fore that the acceleration of ideas productionand diffusion that takes place in the knowledge network as a whole duringthe last decade of the 20th century is largely explained by the accelerationtaking place in the ICT fields. The fact that acceleration is not uniform acrossfields is of special importance. It suggests that the measured accelerationis not an illusion possibly produced (in spite of our data treatment) by thepost-1983 general rise in US patents and patent citations.

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3.3.4 A closer look at ICT: core and periphery

The composition between core and periphery in the dominant ACS of thedichotomized matrix CA changes dramatically between W1 and W2 (seetable 4).

The absolute size of the dominant ACS1(W2) is only marginally larger(15.5 per cent) than the corresponding size of ACS1(W1): 52 classes in theformer against 45 in the latter. It is the relative composition of the dominantACS between core and periphery to change dramatically from period W1to W2. The ratio between the size of core and periphery is reversed: #Core/#Periphery is 0.216 in W1 and 4.2 in W2. The qualitative nature of theseresults is highly robust to a perturbation of the dichotomization value used togenerate CA.

In 1975–86, the eight core classes all belong to the NBER category Com-puter and Communications. Five of them (709, 710, 711, 712, 713) correspondto hardware innovations concerned with computer processing systems,architecture and memory; two classes (705, 707) correspond to applica-tion-oriented software innovations; and one class (714) is concerned withmechanisms for error detection/correction.

The fact that the semiconductor fields are not in the core of ACS1(W1), butonly in its periphery (257: Active solid state devices—transistors; 438: Semi-conductor device manufacturing—process) is somewhat surprising. Semicon-ductor technology is an input to computer technology and progress in theformer is considered a fundamental determinant of the improvement incomputer capacity and reduction in computer prices, which is the largestcomponent of the IT contribution to TFP growth in 1973–89 and later

Table 4. Dominant ACS of C

##

# ACS C&C E M O

W1A : ACS1 45 1 56 33 4 7coreACS1 8 0.18 100 0 0 0periphACS1 37 0.82 46 41 5 8W2A : ACS1 52 1 54 23 23 0coreACS1 42 0.81 67 14 19 0periphACS1 10 0.19 0 60 40 0

Notes: The columns in this table show the absolute size # (number of classes), the fraction ofACS size, and the NBER category percentage composition of the core and periphery of thedominant ACS1 corresponding to the ICT group in periods W1 and W2. C&C = Computer andCommunications; E = Electrical and Electronic; M = Mechanical; O = Others.

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(Jorgenson, 2005). A possible explanation is that spillovers from semiconduc-tors to the other ICT fields may be closer to rent spillovers (cf. Griliches, 1992)than to pure knowledge spillovers. If this were the case, they would beconveyed by flow-inputs of goods more than ideas. Only the latter are a focusof this paper. An alternative explanation is that knowledge spillovers fromsemiconductors to computer fields may be under-represented in our data ofperiod W1 as a result of the relatively low fraction of patentable semiconduc-tor innovations that were patented in that period. Cohen et al. (2000) reportedthat the rapid pace of technological change and the short product life cycle(typical of semiconductors) induce managers to conclude that lead-time,secrecy and manufacturing or design capability are more effective than patentsin preventing the copying of innovations. They find that, in the early 1990s, i.e.after the 1980s surge in patenting had already started, the mean percentage ofinnovations for which patents are considered an effective protection is defi-nitely below average for semiconductors compared with the other manufac-turing firms. The ratio between patentable innovations and patents must havebeen particularly low in the semiconductor fields during the interval 1975–86.This period mostly precedes the surge in ICT patenting (cf. Kortum andLerner, 1999) and the relative increase in the propensity to patent of semicon-ductor firms (cf. Hall and Ziedonis, 2001), which took place only after 1983.

The relative low size and restricted disciplinary-field composition of theICT core in 1975–86 signals that in this period knowledge circulation withinthe ICT group is still mostly one-way: from the deep source fields of thetechnology to the peripheral, application-oriented fields. This considerationcan only receive further support from the suggested indication that thedirected links from semiconductors to the other ICT classes are presumablyunderstated in our matrix C(W1).

In 1987–99, the situation is reversed. The core of the dominantACS1(W2A) contains 42 member classes, of which 28 belong to Computer andCommunications, eight in Mechanical and six in Electrical and Electronic. Theadditional Computer and Communications classes that are now represented inthe core correspond to innovations in communication devices, codingsystems, image analysis/storage/retrieval and computer graphics, genericcontrol or application-oriented data processing, symbolic information print-ing.27 Semiconductors now belong to the core (digital logic circuitry) togetherwith other Electrical and Electronic classes28 concerned with electrical devices

27 The Computer and Communications classes belonging to the core of ACS1(W2) are: 347, 455,379, 375, 370, 340, 380, 341, 382, 365, 369, 360, 358, 345, 395, 700, 701, 702, 705, 706, 707, 708,709, 710, 711, 712, 713, 714.28 The Electrical and Electronic classes belonging to the core are: 318, 324, 326, 327, 348, 386.

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and television. The fact that eight Mechanical classes (innovations in motorvehicles, power-stop and engine control, brake and gear transmissionsystems, photography and typewriting)29 are also present in the core ofACS1(W2A) gives further evidence that in the period 1987–99, innovation inICT reached not only a higher rate of activity and diffusion in the knowledgenetwork, but also a mutual tighter integration between the original sourcefields of the technology and the application oriented fields. The latter, not lessthan the former, gives now a fundamental contribution to the self-sustainingproperty of ICT knowledge production. In our view, the sharp absolute andrelative increase in the number of core members, and the more differentiatedtechnology-field composition of the core in W2, marks a decisive steptowards the completion of the ICT revolution.30

The above structural change in the relative size of core and periphery is notaccompanied by a comparable growth in the absolute size of ACS1. More-over, stability in absolute size of ACS1 is highly robust to perturbations of thedichotomization parameter. These features, in addition to the data treatmentdiscussed at the beginning of this section, support the conclusion that thestructural change in question is not a spurious effect of the aggregate trend inpatenting.

4. CONCLUSIONS

The construction of an empirical analogue to the connection matrix definedin section 2 required bold assumptions an time-consuming data treatment.The approximate nature of the empirical construct does not elicit rigorouspoint estimations of quantitative results. The analysis was more focused onthe qualitative properties of the phenomena under study: relative magnitudesat one point in time, and directions of change through time. With thisimportant proviso, the results presented in this paper shed some light on anumber of issues: (i) the tendency to an increasing interdisciplinary variety ofresearch areas of innovation activity, (ii) the depth, scope and timing of theICT revolution in R&D, and (iii) the structural change in the prevalentdirection of knowledge flows during a technological revolution. In whatfollows, we briefly address these issues in turn.

As expected, the broad spectrum of disciplinary fields can be divided intomore homogeneous groups, such that the within-group knowledge relations

29 The Mechanical classes belonging to the core are: 180, 192, 325, 303, 399, 400, 475, 477.30 The greater reach size of the ICT revolution in the second period is also signalled by the factthat semiconductors (through classes 257 and 438) are now present in the periphery of each ofthe three leading ACSs of C (W2A).

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are on average significantly stronger than the between-group relations. Sig-nificance is here measured by the Newman–Girivan Q modularity, which ishigh or moderately high throughout the period under study. There is in facta 7 per cent fall in the aggregate measure of modularity between the first andlater phase of the period. The fall of modularity is mostly concentratedoutside the ICT group, or at least outside its source technology fields such asComputer Hardware and Software and Semiconductor. For the Newman ICTgroup as a whole, the change of modularity, weighted by the size of groupmembers, is a modest -1.6 per cent. With these important qualifications, thedirection of change is quite widespread across the network, affecting nearly60 per cent of subcategories.

Different developments may contribute to the observed mild fall of modu-larity. One line of explanation conjectures a widespread long-run tendency toan increasing variety in the disciplinary-field composition of the knowledgebase of R&D labs (Pavitt, 2003). The tendency in question received qualifiedsupport by selected industry-based studies. For a data set on USPTO patentsand patent citations based on a sample of firms in the computer, electronicsand chemical industries, Fung and Chow (2002) found that the proportion ofpatents cited by at least two firms in the same industry is moderately increas-ing or stable between 1983 and 1987. Since then, the index has systematicallydeclined in each of the three industries during the decade 1987–97. Theauthors argued that ‘the falling trend indicates that firms are becoming morediversified in their research areas’.

A more diversified research area may or may not exit the boundary of agiven technology group. What our results on modularity change suggest isthat the spreading outside the boundaries of the given group did actually takeplace in many domains of R&D.

It can be conjectured that the greater and farther reaching knowledgeinteractions received an important impulse from the very diffusion of ICT,which had reached a greater stage of maturity in the second phase of theperiod under study. Informatization of research procedures and of commu-nication channels fostered the activation of new learning interfaces betweenpreviously separated research domains. This leaves the question of why thespreading out of knowledge links did not affect crucial fields in the ICTgroup, and scarcely at all the ICT group as a whole. On a closer scrutiny,this outcome is far from surprising, on the ground of the very broad over-lapping between the Newman ICT group and the dominant ACS of thenetwork describing the strong knowledge interactions. In synthesis, thespreading of knowledge links outside the boundaries of the group tookplace also in ICT, not less than in other domains; the difference is thatin ICT the process was largely compensated by the relatively stronger

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increase, between W1 and W2, of the connection coefficients linking thefields belonging to the group.

Salient features of our results concerning the dominant position of theICT group are elicited by the theoretical and analytical framework adoptedin this paper. The model outlined in section 2 suggests the possibility andpotential gains from applying the notions of ACS and of closed-path, self-sustaining connectivity to the analysis of technology knowledge transfer. Inthis way, we can show that throughout the period under study, the groupof ICT fields is dominant in the knowledge network, and ICT ideas aregeneral purpose. Throughout 1975–99, the rate of self-sustaining knowl-edge transfer in the network at large is explained by the rate concerningthe ICT group alone; the acceleration in the former between 1975–86 and1987–99 is likewise explained by the acceleration in the latter. In fact, thedifference in ideas circulation between the ICT and the other leadinggroups was much less sharp in 1975–86 than it was thereafter, suggestingthat the completion of the ICT revolution in the circulation of ideas islargely a 1990s outcome.

Restricting our focus to the strong knowledge interactions, we find that in1975–86, the dominant ACS corresponding to the ICT group has a small coreand a large periphery. The small core consists of source fields of the infor-mation technology.31 Application-oriented fields belong to the periphery.This means that during the early phase of the information revolution intechnological knowledge, the strong flows of ICT ideas are one-way: from thesource to the application fields. The prevalent direction of such strong knowl-edge spillovers corresponds in this phase to the direction of the rent spilloversembodied in ICT goods transactions. This structural property of knowledgeflows ceases to hold in the later phase, 1987–99. The relative size of the coreand periphery of the dominant ACS is now reversed. Within the dominantICT group the strong flows of ideas are now mostly self-sustaining, notone-way; the directions of rent and pure knowledge spillovers may nowdiverge. These findings are consistent with ideas about the importance ofstrong complementarities between the application-oriented and base compo-nents of a general purpose technology (David, 1990; Helpman, 1998) such asICT. Progress towards the completion of the ICT revolution is marked byinnovation solutions to such complementarities based on strong and mutualknowledge interactions between the different application-oriented and basecomponents of the technology.

31 We recall that the absence of the four semiconductors fields from the core during the earlyphase is presumably explained by the under-representation of semiconductor patents in our dataset.

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Mauro CaminatiDepartment of Economic Policy,Finance and DevelopmentPiazza San Francesco 7Siena,I-53100ItalyE-mail: caminati@unisi.it

Arsenio StabileFaculty of EconomicsPiazza San Francesco 7Siena,I-53100ItalyE-mail: stabilear@unisi.it

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