Evolution and structure of technological systems - An ... · Evolution and structure of...

Evolution and structure of technological systems - Aninnovation output network ∗

Josef Taalbi 1

1Department of Economic History, Lund University.

November 19, 2018

Abstract

This study examines the network of supply and use of significant innovations across industriesin Sweden, 1970-2013. It is found that 30% of innovation patterns can be predicted by networkstimulus from backward and forward linkages. The network is hierarchical, characterized by hubsthat connect diverse industries in closely knitted communities. To explain the network structure, apreferential weight assignment process is proposed as an adaptation of the classical preferentialattachment process to weighted directed networks. The network structure is strongly predicted bythis process where historical technological linkages and proximities matter, while human capitalflows and economic input-output flows have conflicting effects on link formation. The results areconsistent with the idea that innovations emerge in closely connected communities, but suggest thatthe transformation of technological systems are shaped by technological requirements, imbalancesand opportunities that are not straightforwardly related to other proximities.

JEL: O31, D85, O33.Keywords: Innovation, Network evolution, Technological systems

1 Introduction

A fundamental issue in the study of complex net-works is to identify mechanisms that shape thestructure and evolution of biological, economicand social networks, such as the Internet, neuralnetworks and scientific citations and collabora-tions (Albert and Barabasi 2002, Dorogovtsevand Mendes 2002, Dorogovtsev et al 2000, New-man 2001, 2005). Innovation networks share

∗I gratefully acknowledge funding support from theJan Wallander and Tom Hedelius foundation (grant noW2015-0445:1) and Sweden’s governmental agency forinnovation systems, Vinnova (grant no 2014-06045). Partof this paper was written during a research visit at INETOxford. I gratefully acknowledge the hospitality of theComplexity Economics programme.

many often observed features of real networks,such as scale-free degree distributions and non-trivial clustering. Yet, the mechanisms responsi-ble for the structure and evolution of innovationnetworks are still not well understood. In thefield of innovation studies, scholars have for sometime theorized the mechanisms that drive thestructure and evolution of technological systems,i.e. networks of agents involved in the generationand use of technology, which in the presence ofradical innovation and momentum can becomesynergistic clusters (Carlsson and Stankiewicz1991). A large literature suggests the evolution ofsuch technological systems to be driven by inno-vational complementarities, knowledge spilloversand increased incentives to innovate owing to

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technological advances upstream (Acemoglu et al2016, Bresnahan and Trajtenberg 1995, David1990, Lipsey et al 2005, Romer 1986, Verspagen1997), or driven by the response of agents todemand and systemic imbalances downstream inthe technological system (Hughes 1987, Rosen-berg 1969). Notably, in a recent study, Ace-moglu et al (2016) found strong evidence for arole played by upstream network stimulus in theUS patent citation network.

So far, such empirical studies have made use ofR&D and patent flows, which does not necessar-ily capture innovation and, as noted by Acemogluet al (2016), might be understood as ’normal sci-ence’. Noting that the evolution of technologicalsystems and sociotechnical transitions are drivenby the development and diffusion of major orradical innovations (Carlsson and Stankiewicz1991, Geels 2002, 2005), there are open ques-tions regarding the role of network stimulus andthe mechanisms responsible for the structureand evolution of technological systems. This pa-per studies these problems through the lens ofinter-industrial networks of significant innova-tions, viz. commercialized inventions that havea non-incremental degree of novelty (comparePavitt 1984, Taalbi 2017a). Through analysisof such an innovation output network for Swe-den, 1970-2013, this study examines underlyingdynamics that shape innovation patterns overtime and the structure of supply and use of in-novations across industries. Previous studies onthis database (Taalbi 2017a,c) have found thatinnovation activity is typically the response toproblems and opportunities that have emergedelsewhere in the technological system and thatthese problems and opportunities focus innova-tion activity in distinct communities. However,no earlier attempt has been made to explainthe structure and evolution of the technologicalsystem through network analysis.

The present study suggests that network stim-ulus from industries upstream and downstreamexplains variations within and between indus-tries and that the evolution of the innovationnetwork is best described as a process whereprevious ties and proximities in the innovationnetwork largely determine the appearance of new

ties. The process is driven by hubs, key suppli-ers, that connect diverse user industries in stablecommunities. While there is moderate evidencefor a role played by underlying economic, skill orknowledge proximities, the results stress that thebulk of significant innovations are geared towardstechnological diversification rather than follow-ing existing industry interdependencies. Hence,the results are consistent with a view of innova-tion activity as a process of co-evolution betweenindustries, but emphasize that the formation oftechnological systems are shaped by technologi-cal requirements, imbalances and opportunitiesthat may not be squarely captured through eco-nomic or other proximities.

Section 2 discusses the theoretical frameworkfor network evolution. Section 3 discusses thedata sources and variables used. Section 4presents the results, followed by concluding re-marks.

2 Evolution of innovation

networks

2.1 Extrinsic and intrinsic mech-anisms

What mechanisms account for the structure andevolution of innovation networks? One maybroadly distinguish between mechanisms intrin-sic and extrinsic to a network under study. Draw-ing on seminal work (Albert and Barabasi 2002,Dorogovtsev et al 2000, Newman 2001, 2005),the literature on evolving networks offers a fewintrinsic candidate mechanisms.

Foundational insights stem from the notionthat different linkage formation mechanisms arereflected in qualitatively different degree distri-butions. Random graphs generated by the Erdos-Renyi model with homogenous probability, pre-dicts a binomial degree distribution. Many largereal world networks have however been shown tohave scale-free distribution in the node degreesk of the form

P (k) ∝ k−γ (1)

where in practice it is often found that 2 ≤ γ ≤ 3.

2

In the context of growing networks, this hasbeen explained by the preferential attachmentof new nodes to nodes that are already well con-nected (Barabasi and Albert 1999). The prefer-ential attachment process is well in accordancewith the notion in innovation studies that broadtechnology shifts are characterized by path de-pendence, increasing returns and the emergenceof a persistent core-periphery structure wheregeneral-purpose technologies supply most of theinnovations across the board (Arthur et al 1987,David 1985, Lipsey et al 2005). Hence the evo-lution of innovation networks, like many othernetworks (Barabasi and Albert 1999, Newman2001), may be a process determined largely bynetwork topology.

Other mechanisms related to the networktopology have however been suggested to be ca-pable of explaining community structure in com-plex networks, notably based on the notions oftriadic closure and node similarity (Adamic andAdar 2003, Bianconi et al 2014, Liben-Nowell andKleinberg 2007). In general, the probability thattwo nodes will become connected may depend onthe respective number of neighbors or the indirectpaths between nodes. For instance, it is intuitivethat two scientists may be more likely to collabo-rate in the future if they have mutual connections.Along these lines, an important perspective isthat innovation flows are governed by a processof co-evolution across industries, in the sensethat innovations respond to opportunities andproblems that appear in closely knitted techno-logical sub-systems (Bresnahan and Trajtenberg1995, Carlsson and Stankiewicz 1991, Nelson1994, Taalbi 2017a). Co-evolution is stipulatedto take place in terms of opportunities providedupstream in the value-chain (Acemoglu et al2016, Bresnahan and Trajtenberg 1995, Lipseyet al 2005), but also through problems and imbal-ances downstream that focus innovation activity(Hughes 1987, Rosenberg 1969).

Innovation studies also advance several rea-sons why innovation flows could be expected toevolve due to mechanisms extrinsic to innova-tion processes. One hypothesis advanced is thatinnovation networks in general co-evolve withunderlying economic interdependencies and dif-

ferent kinds of proximities, e.g., cognitive, orga-nizational, social, institutional and geographical(Boschma 2005, Boschma and Frenken 2010). Itis for instance plausible that innovation flows fol-low existing input-output relationships betweenindustries of capital or intermediate goods (De-Bresson 1991, DeBresson and Hu 1996), in linewith accounts that stress the role of demandconditions in spurring innovation (von Hippel1988, Lundvall 1988, Schmookler 1966). Cogni-tive proximities are also likely to induce inno-vation, for instance in the sense that innovativeproblem solution requires a shared knowledgebase between the technology being developedand the user application. Similarly, users needcomplementary absorptive capacity to exploitinnovations from other industries (Cohen andLevinthal 1990, Nooteboom et al 2007).

The suggested importance of economic andcognitive proximities in innovation processes how-ever comes with caveats, as processes of radicaland incremental innovation are fundamentallydifferent phenomena. Firms often innovate inorder to branch into fields where they are not eco-nomically active, viz. through exploration anddiversification (March 1991). As it were, radicalinnovation may be associated with explorationand ventures into new markets, while more in-cremental innovations are more likely to followestablished paths such as production networks.Moreover, too high (e.g., cognitive) proximitiesbetween industries may be negatively associatedwith innovation. Indeed, previous comparisonsof innovation indicators and measures of relat-edness have suggested mixed relationships, andthat radical innovation is associated with unre-lated variety (Castaldi et al 2015).

2.2 Evolution of a weighted inno-vation network

Bringing these perspectives together, the forma-tion of network ties can be viewed as a process inwhich there are several potential mechanisms atplay: preferential attachment, triadic closure andunderlying economic, knowledge and technologi-cal proximities. The innovation dynamics can bemodelled on two levels. It is first important to

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understand to what extent the pre-existing net-work structure predict innovation performance.Following Acemoglu et al (2016), one may modelthe count of innovations by sector as predictedby network stimulus from backward and forwardlinkages in previous periods. The details of sucha model are described in connection with theempirical results in section 4.2.

Section 4.3 then analyzes the formation pro-cess of ties between industries and the structureof the network. To model network evolution,one may start by considering a straightforwardframework for link formation where the proba-bility of a new innovation between industry iand industry j depends on the cumulative flowof innovations wij. Intersectoral innovation net-works are weighted directed networks, with afixed number of nodes. Preferential attachmentin a setting where direction and weight matter,relates the probability of flows to the in- andout-strength of nodes, defined as sini =

∑j wji

and souti =∑

j wij . The process is defined by thenotion that the probability that an innovation is

supplied an industries i depends onsouti∑wij

, and

that is used by industry j depends onsinj∑wij

. The

probability of a new link from industry i to jcan then be expressed as the product of the two

terms Πw = αsouti sinj

(∑wij)

2 .

It is however advantageous to introduce nodeheterogeneity to the preferential attachment pro-cess. In this conceptualization, the probabilitythat innovations are supplied by industries i de-

pends onsouti∑wij

, but, given the industry of supply,

innovations are more likely to be used by indus-tries which are typical users of industry i, hencedepending on

wijsouti

. The product of these two

terms gives the probability of a link between iand j as

Πw ∝wij∑wij

(2)

Clearly, introducing node heterogeneity resultsin a process of preferential assignment of inno-vations to industry pairs (edges), rather thanto particular nodes. In the remainder of thisstudy, ”preferential attachment” is used to referto this type of process unless stated otherwise.

When conceptual separation from the classicalmodel is needed the perhaps more accurate label”preferential weight assignment” (PWA) will beused.

Since at the outset no edges have innovations,the process is appropriately modelled as a mixedprocess of preferential attachment and randomassignment of innovations to unused edges. Asensible generalization is to let the preferen-tial attachment process be potentially non-linearthrough a parameter λ, leading us to specify theprobability for an edge with weight w as

Πw = (1− α)δw,0 + αwλ∑wλNw

(3)

where δw,0 is 1 for w = 0, otherwise 0 and Nw isthe number of edges with weight w. For α = 1,the model reduces to a pure preferential attach-ment process.

The linear model, i.e. when λ = 1 is ourbaseline model. The distribution resulting fromequation 3 however depends on the parameter λand whether the number of edges of the networkare finite or growing (Bagrow et al 2008). In ourcase (section 3), the network size is fixed but thetime lapsed is smaller than the number of edges.In this scenario, the network can be treated asgrowing, with α as a historically observed pa-rameter. Appendix B derives and details therelevant weight distributions for linear and sub-linear attachment kernels. For the baseline linearcase λ = 1, weights follow a Pareto distributionP (w) ∝ w−1−1/α. For the sub-linear case λ < 1,weights follow a stretched exponential.1

Equation 3 describes our baseline model, usedto make predictions on weight distribution. How-ever, it is also desirable to test for the effectof exogenous networks zij capturing (possiblyevolving) proximities between industries however

1Notice that our model only contains a random processfor edges with weight zero. Compare the model set up byBagrow et al (2008) for fixed size networks, which includesa random homogeneous process for all nodes. Theyshow that with a fixed number of nodes A, the limitingdistribution of the process depends on the parameter αand the time lapsed. In the asymptotic limit, the systemhas two attractors. If α < 1

2 , the distribution approachesa Gaussian of width t

[1−2α]A . If α > 12 , the distribution

retains the power-law distribution in the tail.

4

measured. This gives a test equation

Πw = β0 + β1wij∑wij

+∑l

βlzij,l (4)

It is also desirable to test for other link forma-tion mechanisms, such as triadic closure and theeffect of indirect links, using node similarity met-rics Sij. These are tested using link predictionmethods in section 4.3.

3 Materials and methods

Innovation networks, in the sense of innovationflows between sectors, have been studied in alarge number of empirical works, using a vari-ety of measurements of innovation: patent data(Acemoglu et al 2016, van Meijl 1997, Nomalerand Verspagen 2008, 2012, Scherer 1982, Verspa-gen 1997), R & D flows (Hauknes and Knell2009, Leoncini and Montresor 2003, Leonciniet al 1996, Montresor and Marzetti 2008) and in-novation output data (DeBresson and Townsend1978, DeBresson et al 1996, Robson et al 1988).The innovation network used in this study stemsfrom a Swedish innovation output database (Sjooet al 2014, Taalbi 2017a), assembled through aliterature-based innovation output methodology(Kleinknecht and Bain 1993). 15 trade journals,covering the manufacturing and ICT service sec-tors, were screened for significantly improvedproducts, commercialized on a market. The in-novations collected were subject to a criterionof commercial status and novelty according toindependently edited journal articles. Hence,innovations are not incremental or mere inven-tions without economic or societal interest, butsignificant and novel to the industry.

The innovation network is constructed by map-ping the number of innovations flowing fromproduct groups to the sectors in which the inno-vation is used or explicitly intended to be used.This refers strictly to the commercial use of theinnovation, as distinguished from patent cita-tion networks that map knowledge flows betweentechnologies. The product innovations found inthe journal articles were categorized accordingto the Swedish Industrial Classification system

2002 (SNI 2002) corresponding to ISIC Rev. 3.For each innovation, user industries were likewiseassigned according to ISIC Rev. 3, at the lowestlevel of detail possible.

In practice, the innovation output networkused in this study is a weighted directed net-work with industries as nodes and innovationcounts as edges. The full detail innovation net-work is a 98 × 98 matrix, with 9,604 possibleentries per year. Since there is a selection on thesource industries of innovations, being in prac-tice limited to manufacturing and ICT services,regressions include flows from these sectors toothers, in practice 6370 network edges. Sinceany innovation may have several user industries,a weighting procedure was constructed so thateach innovation is only counted once. Hence aninnovation that has n user industries will haven linkages of weight 1/n. Innovations may bepartially for final consumption or have a general-purpose character. These user categories havenot been included in the network analysis. Outof 3685 innovations, the sum total of betweenindustry flows was 3248.2.

From this data, the yearly flows of innovations∆wij and the cumulative flow of innovations be-tween industries wij are constructed. To accountfor node proximities, this data is also used toconstruct a battery of similarity metrics. A firstset of measures aim to capture triadic closure: iftwo nodes i and j have links to a third node, theyare likely to obtain links too. These local metricsare based on the number of common neighborsof two nodes i and j∑

k∈Γ(i)∩Γ(j)

wik + wjk (5)

with Γ(i) being the set of neighboring nodes ofi, and k an index of neighboring nodes.

The Jaccard similarity metric normalizes theeffect of neighborhood size

∑k∈Γ(i)∩Γ(j)

wik + wjk∑l∈Γ(i)wil +

∑m∈Γ(i) wim

(6)

Since rare connections may be more indicativeof where new links emerge, the Adamic-Adar

5

metric (2003) normalizes the metric by letting acommon neighbor k be weighted by the rarity ofrelationships between other nodes and k∑

k∈Γ(i)∩Γ(j)

wik + wjk

log(

1 +∑

m∈Γ(k) wkm

) (7)

Global metrics are based on the overall net-work. In this study we use the Katz metric(1953), which is the sum of all walks that existbetween nodes, weighted by a parameter βl thatdecreases with path length l. In compact matrixnotation the metric is defined as

Skatz =∞∑l=1

βlWl = (I− βW)−1 − I (8)

with I the identity matrix, Skatz = ||Skatzij ||, W =

|| wij∑wij|| and 1/β being greater than the largest

eigenvalue of W. This metric has the advantagethat it can be decomposed into the matrix ofdirect links W and indirect (second and higherorder) links Skatz − βW.

To measure underlying economic proximities,the Leontief inverse is used, constructed fromInput-Output tables 1995-2011 (OECD). Thisis calculated from the accounting identity (inmatrix notation) Ax + y = x, with A an N byN input coefficient matrix, and x, y are 1×Noutput and value added vectors respectively. TheLeontief inverse matrix is defined as the marginaleffect of a change in value added of an industryon the demand for goods, in compact matrixform:

L = (I−A)−1 (9)

We also follow earlier studies (Leoncini et al1996, Montresor and Marzetti 2009) and usethe R&D expenditure embodied in direct andindirect economic good requirements betweensectors as a measure of knowledge flows, viz.knowledge proximities between industries. Thismeasure assumes that innovation is embodiedin the exchange of intermediate goods, calculat-ing a network R from the intra-sectoral R&Dexpenditures and Leontief inverse

R = rq−1 (I−A)−1 y (10)

where r, q and y are diagonalized vectors ofR&D expenditure, output and final demand re-spectively.

As an additional measure of economic prox-imities this study also employs the ”Los index”(Los 2000), which departs from the idea thatthe relatedness between industries is expressedthrough the similarity of the input goods used.The technological relatedness is then measuredas the cosine similarity between a pair of inputcoefficient vectors aik and ajk according to

ωij =

∑nk=1 aik · ajk√∑n

k=1 a2ik ·∑n

k=1 a2jk

(11)

with i, j, k ∈ {1, ..., n} as sector indices.To measure knowledge-base proximities, a skill-

relatedness measure is used, constructed by Nef-fke et al (2011). This measure is based on humancapital flows between industries at the 4-digitlevel for Sweden, constructed for the years 2004-2007. In addition, the model estimations alsouse value added 1970-2013 as a control variablefor ”gravity” between industry i and j,

Fij = gmimj

m2(12)

where mi, mj is the value added of industry iand j respectively, m is total value added and gis a parameter.

4 Results

4.1 Network structure

The network of supply and use of innovation ob-jects reveals several structural properties of inter-est: stability, hierarchy and asymmetry. Overallthe network is very stable over time: Pearsoncorrelations between 5-year periods range be-tween 0.46 and 0.62 (see Table A.1). FiguresA.1-A.3 in Appendix A highlight the heterogene-ity and asymmetric character of innovation flowsbetween 29 aggregate sectors. Some industries,mainly machinery, ICTs and software, tend tobe major suppliers, supplying to a broad rangeof industries, while others (e.g., construction andtransport services) are almost exclusively users of

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innovation. Figure 1 shows an exponential weightdistribution in the total out- and in-strength ofindustries. The weight distribution (Figure 2),lies closer to a power-law predicted by a linearpreferential attachment process, but is betterfitted as a stretched exponential, as predicted bya sub-linear rate of attachment (see Table 2 andAppendix B).

Figure 2: Cumulative distribution of innovationflows wij (log-log), 1970-2013 and theoreticallypredicted distributions obtained by using valuesof the fitted parameters (see Tables 2, model 1,4a and Appendix B)

100 101 102

10−4

10−3

10−2

10−1

w

P(w′ ij>w

)

P (w′ij > w)Linear

Sub-linear

Secondly, it is possible to observe that thenetwork is hierarchical and has a significant com-munity structure within the network (see alsoTaalbi 2017a). The network has a modular struc-ture similar to the hierarchical model suggestedby Ravasz and Barabasi (2003). The overallprobability that two neighbors of a node arethemselves neighbors is a sizeable 0.608. More-over, the local clustering coefficient C, measuringthe average probability that two neighbors of anode are neighbors, scales like C ∼ k−1 in thetail (Figure 4). This indicates a hierarchy inwhich low degree nodes belong generally to wellinterconnected communities (high clustering co-efficient), while hubs connect many nodes thatare not directly connected (low clustering coeffi-cient) (Ravasz and Barabasi 2003). In our case,major innovation suppliers such as ICTs act ashubs that connect user industries in a more orless star-like structure (compare Taalbi 2017b).

More specifically, the interdependencies in theSwedish network of innovations can be describedin terms of ten subgroups (Figure 3) centered onpulp and paper, foodstuff, ICTs, automotive vehi-cles and land transportation, medical equipmentand healthcare, forestry, construction, militarydefense and military suppliers, electricity andtextiles (see Taalbi 2017a and Taalbi 2017b forfurther discussion).

Figure 4: Local clustering coefficients. ICT in-dustries in blue. Dashed line k−1

101 102

10−0.6

10−0.4

10−0.2

100

Node degree k

Clu

ster

ing

coeffi

cien

tC

(k)

4.2 Network stimulus effects

Let us first turn to what role the network struc-ture has for innovation performance over time.To construct predicted innovations in a five-yearperiod from forward and backward flows, we com-bine the pre-existing network with the numberof innovations that were launched in the previ-ous five-year period. Let Xi,T be the numberof innovations in industry i in period T . Ex-pected innovation counts from forward linkagesare calculated as

Xfi,T =

∑j

wjisoutj

Xj,T−1 (13)

and expected innovations from backward linkagesas

Xbi,T =

∑j

wijsinj

Xj,T−1 (14)

7

Figure 1: Out- and in-strength distribution, 1970-2013

(a) Out-strength

100 101 102

10−2

10−1

100

souti

P(s′out

i>sout

i)

(b) In-strength

100 101 102

10−2

10−1

100

sini

P(s′ini

>sin i)

Figure 3: Community structure of the networkof innovations, 1970-2013.

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Plastic

Basic_metals

Measuring_instruments

Computer_and_related_services

Other_business_acitvities

Lifting_and_handling_equipment

Other_general.purpose_machinery

Other_special_purpose_machinery

Computers

Layout by communities, applying the fast greedycommunity detection algorithm (Clauset et al 2004).For further discussion, see Taalbi (2017a).

where wij is, as before, the cumulative flow ofinnovations from industry i to industry j andsinj and soutj are in- and out-strength of nodej. Expected innovations from forward flows arethus specified by combining the innovations inthe previous five-year period with pre-existingforward flows. Expected innovations from back-ward flows are similarly specified by combininginnovation in the previous five-year period withthe pre-existing backward flows.

These formulations assume that the extent towhich innovations respond to opportunities up-stream or problems and demands downstreamis related to the number of innovations in theprevious five-year period. This is motivated fromthe point of view that industries with many in-novations will engender new opportunities (Ace-moglu et al 2016, Bresnahan and Trajtenberg1995, Lipsey et al 2005), while also drawing at-tention to technological imbalances and criticalproblems that appear in the process of techno-logical change (cf. Hughes 1987, Rosenberg 1969,Taalbi 2017c).

Our results (Table 1a-1b) are in line with bothnotions. The analysis focuses on 44 industriesthat have launched at least one innovation bian-nually and 29 that launched at least one innova-tion per year. In a pooled regression (models 1-2),30% of the variation in innovation is explainedby forward linkages and backward linkages inthe previous five-year period. The coefficientsindicate that an increase in the predicted innova-

8

tions of 1% increases the number of innovationswith 0.38% and 0.34%. Since these results mayto some degree reflect common innovation trendsor persistence of innovation counts across indus-tries, a fixed-effects regression is also specified.In a fixed effects model, backward linkages ontheir own explain 6.4% of variations within indus-tries, while including time dummies and forwardlinkages account for 20.7% of within-industryvariations. Using the 29 most innovative indus-tries our models explain 25% of variations ininnovation launches overall. Backward linkagesaccount for 12.8% in a fixed effects formulation.

These results are only somewhat less strikingthan the results from USPTO patent citationnetworks, reporting network stimulus to accountfor 55% in a pooled model and 14% in a fixed-effects model (Acemoglu et al 2016). Importantlyhowever, in our case, there is also evidence for arole played by backward linkages in predictingthe locus of innovation activity, and in particularin predicting within-industry variations.

4.3 Drivers of network evolution

Next we turn to explain the inter-industry tieformation process. The previous results suggestsomething in between a stretched exponentialand a power-law distribution of the innovationflows wij and out- and in-strength (Figures 1-2).These results are consistent with a preferentialattachment mechanism.

To give a first intuition, Figure 5 plots theestimated probability of receiving a new linkagainst the number of previous innovations (cfNewman 2001), calculated as the average shareof innovations for industry pairs with a numberw of previous innovations for the period. Thereis clearly a dependence of the linkage formationprocess on previous ties.

Figure 5: The probability of an innovation be-tween industries by previous innovations wij = w,1970-2013.

10−1 100 101 102

10−4

10−3

10−2

10−1

Previous innovations (weights) w

Pro

bab

ilit

yof

new

inn

ovat

ion

In order to construct empirical models, we notethat the (expected) number of new innovationscan be linked to equation 3 through

∆wij = ∆wΠw (15)

where innovations arrive at a rate ∆w per calen-dar year. To carry out formal tests, equations3 and 15 are combined, leading to the linearbaseline model

∆wij∆w

= β0 + β1wij∑ij wij

+∑l

βlzij,l + εij (16)

where zij,l are measures of underlying proximities,and Greek lower case letters are estimated pa-rameters. In inter-industrial innovation networks,one would suspect that the formation of strongties is in part driven by industrial structure andunderlying proximities, but also by previous ties.

Table 2 reports results from a linear model.The models report robust standard errors. Thefirst estimation is a pooled regression, showinga statistically significant coefficient α for wijof 0.645. The theoretically predicted cumula-tive distribution is P (w′ij > w) ∝ w−1/α, in ourcase, w−1.6, shown in Figure 2. In this model,cumulative innovations explain 15% of the vari-ation in innovation flows. Columns 2-3 reportresults from including skill-relatedness, input-output proximities and the ”gravity” of produc-tion volumes. Skill-relatedness and production

9

Table 1: Regression analysis of network stimulus effects.

(a) 44 industries with at least 1 innovation biannually.

(1) (2) (3) (4)VARIABLES Pooled Clustered standard errors Fixed effects Year and fixed effects

Forward linkages 0.383*** 0.383*** 0.216***(0.0384) (0.0493) (0.0627)

Backward linkages 0.344*** 0.344*** 0.164*** 0.146***(0.0316) (0.0487) (0.0550) (0.0501)

Time dummies No No No YesConstant 0.809*** 0.809*** 1.469*** 1.841***

(0.105) (0.140) (0.130) (0.174)

Observations 319 319 321 319R-squared 0.300 0.300 0.064 0.207

Robust standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1

(b) 29 industries with at least 1 innovation per year.

(1) (2) (3) (4)VARIABLES Pooled Clustered standard errors Fixed effects Year and fixed effects

Forward linkages 0.211*** 0.211*** 0.187***(0.0473) (0.0563) (0.0594)

Backward linkages 0.288*** 0.288*** 0.240*** 0.161**(0.0392) (0.0575) (0.0699) (0.0664)

Time dummies No No No YesConstant 1.296*** 1.296*** 1.600*** 2.054***

(0.144) (0.182) (0.172) (0.262)

Observations 218 218 220 218R-squared 0.251 0.251 0.128 0.279


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Table 2: Regression results. Dependent variable: relative innovation flows.

(1) (2) (3) (4) (5)Proximities Cumulative Base model 1995-2011

VARIABLES Base model 1995-2011 1995-2011 fixed effects fixed effects

Pref. Att. 0.625*** 0.693*** 0.604*** 0.682***(0.0276) (0.0573) (0.0296) (0.0616)

Los index -0.000178*** -2.54e-05 -4.07e-05(2.92e-05) (2.45e-05) (2.78e-05)

Skill-relatedness 2.54e-06*** 3.16e-07 7.57e-07(9.62e-07) (9.21e-07) (9.20e-07)

Gravity 0.172*** 0.0277 -0.0439(0.0284) (0.0237) (0.0369)

Leontief 9.40e-05 -5.44e-05 3.62e-05(0.000109) (0.000109) (0.000146)

R&D flows 3.59e-07** 3.04e-07** 4.53e-07***(1.51e-07) (1.28e-07) (1.34e-07)

Constant 4.02e-05*** 0.000173*** 2.09e-05 4.05e-05 -7.41e-05*(3.50e-06) (1.49e-05) (1.41e-05) (3.32e-05) (4.21e-05)

Observations 273,910 71,370 71,370 273,910 71,370R-squared 0.150 0.003 0.155 0.155 0.168


Table 3: Logit regression (log odds). Dependent variable: edge (Y/N)



Pref. Att. 0.274*** 0.352*** 0.490*** 0.617***(0.00875) (0.0148) (0.0140) (0.0230)

Los index 0.341*** 0.586*** -0.0303(0.0948) (0.102) (0.152)

Skill-relatedness 0.0149*** 0.0121*** 0.00822**(0.00160) (0.00266) (0.00355)

Gravity 502.7*** 215.2*** -36.16(33.87) (39.99) (110.3)

R&D flows 0.00124*** 0.00134*** 0.000443**(0.000138) (0.000164) (0.000180)

Leontief 1.410*** 1.646*** -1.503***(0.188) (0.540) (0.381)

Constant 0.102 -3.777*** 0.394*** -0.483 0.695(0.0707) (0.0507) (0.128) (0.389) (0.514)



11

Table 4: Regression results, non-linear models.

(a) Two-step estimation of the parameters of a general preferentialattachment process (equation 3)

VARIABLES Step 1 Step 2

λ 0.649***(0.00827)

α 0.855***(0.0044)

Constant -1.707*** 4.54e-06***(0.0171) (2.63e-06)

Observations 5,861 273,910R-squared 0.512 0.121

Standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1

(b) Log-log estimations. Dependent variable: relative innovationflows (logs)



Pref. Att. 0.675*** 0.641*** 0.120*** 0.0878***(0.00712) (0.0166) (0.0136) (0.0243)

Los index -2.634*** -1.162*** 0.0581(0.153) (0.132) (0.132)

Skill-relatedness -0.00712** -0.00424* -0.000609(0.00299) (0.00235) (0.00255)

Gravity 700.4*** -0.517 -146.1(71.77) (75.74) (109.7)

Leontief -1.403 -1.827** 0.700(0.971) (0.806) (0.559)

R&D flows -0.00111*** -0.00108*** -0.000103(0.000378) (0.000263) (0.000194)

Constant -1.156*** -5.006*** -0.512*** -3.564*** -4.047***(0.0556) (0.104) (0.117) (0.242) (0.585)



12

volumes have significant coefficients but littleexplanatory power. Columns 4-5 include timedummies and fixed effects for nodes i (sender)and j (receiver).

This simple approach can be further analyzedin two separate regressions: one for the merepresence of ties and a regression that allows anon-linear dependence of innovation flows onprevious ties. Table 3 reports results from a lo-gistic regression where the dependent variable isa binary variable whether there is an innovationbetween i and j. Underlying proximities herehave positive and significant effects on the likeli-hood of an edge between two industries, whichis in line with expectations. These proximitiesseem to mostly capture between-effects. Whenincluding fixed effects for nodes i (sender) andj (receiver) only skill-relatedness and embodiedknowledge flows have a positive impact.

The most general specification allows for anon-linear attachment rate depending on theparameter λ. Our model estimated in a two-step regression. First λ is estimated usinglog ∆wij = β0 + λ logwij. Then relative inno-

vation flows∆wij∆w

are regressed onwλij∑wλij

The

coefficients are shown in Table 4a and the theo-retically predicted weight distribution is shownin Figure 2. There is clearly a better fit, thanassuming a linear model with λ = 1. Since otherregressors should be taken into account however,a log-log regression between the relative innova-tion flows and relative cumulative flows is morepractical. Table 4b reports the results. Previousinnovation flows have a large predictive power of56.5% of the variation in the size of innovationflows. A one percent increase in previous tiesincreases the number of innovations with 0.675%.Meanwhile, underlying proximities have negativeeffects on the (log) size of network ties, explain-ing together 15.3% of the variation between andwithin industries. This result lies in line with thenotion that radical innovation activity is likely tobe associated with unrelated variety, explorationand diversification. When fixed effects are usedfor sender and receiver nodes, such underlyingproximities however explain little of temporalvariation. Comparing results between Tables 3

and 4 motivates the interpretation that underly-ing proximities are positively associated with thepresence of innovation ties between industries,while smaller innovation flows are more commonbetween related industries as measured throughskill-relatedness and input-output flows.

Similarity metrics and link predic-tion

Alternative hypotheses to the preferential at-tachment mechanism departs from the notion oftriadic closure and a role played by global net-work topology taking into account indirect pathsbetween nodes. Table A.3 compares the relative

share of innovations∆wij∆w

with different similar-

ity measures. It is clear that the best performingmeasures are the preferential weight assignmentprocess and the Katz metric (coefficient β = 20),taking into account indirect ties. Local metrics(Jaccard and Adamic-Adar) have low correlation.A complementary approach is to evaluate thepredictors by using the N highest ranked pairsof nodes according to each predictor, letting Nbe equal to the number of innovations in a givencalendar year. This analysis is evaluated in termsof measures of accuracy and precision. Accuracyis defined as the share of true positives (TP) andtrue negatives (TN) in the total number of pos-

sible edges: accuracy =TP + TN

TP + TN + FP + FN.

Precision is defined as the ratio of true positivesto all edges predicted by the similarity metric

(false and true positives): precision =TP

FP + TP.

Figures 6a and 6b summarize the performanceof similarity metrics for the years 1971-2013. Itis clear that preferential weight assignment andthe Katz measure perform better than other po-tential link formation models.

The Katz metric is further analyzed in Table5. The Katz metric adds some information tothe pure preferential attachment process in thelogistic and log-log estimations (Tables 3 and4). When separating out indirect ties, equivalent

to Skatzij − β wij∑

wij, from direct ties

wij∑wij

, the

elasticities of Model 4 suggest that indirect ties

13

Figure 6: Boxplots of link prediction diagnostics

(a) Accuracy of node similarity metrics, 1971-2013

●

●

Pref. W.A. Katz Pref. Att. Adamic−Adar Jaccard

0.94

0.95

0.96

0.97

0.98

0.99

(b) Precision of node similarity metrics, 1971-2013

●

●

●

●

●

Pref. W.A. Katz Pref. Att. Adamic−Adar Jaccard

0.0

0.1

0.2

0.3

0.4

Table 5: Regressions with Katz metric

(1) (2) (3) (4) (5)Fixed effects

VARIABLES Base model Logit Log-log Separate (log-log) Separate

Katz β = 20 0.0275*** 0.290*** 0.722***(0.00143) (0.00914) (0.00747)

Katz, indirect ties 0.0434*** 0.0266***(0.00849) (0.00967)

Direct ties 0.648*** 0.114***(0.00885) (0.0138)

Constant 3.40e-05*** -0.697*** -3.121*** -1.070*** -3.350***(4.60e-06) (0.0453) (0.0359) (0.0593) (0.264)



14

play a significant but smaller role. For a onepercent change in indirect ties relative innovationflows increase with 0.04% while a one percentincrease in direct ties produces an increase of0.65%.

5 Conclusions

The dynamic evolution of innovation systems is aprocess that arises from a non-trivial interactionof societal, economic and technological incentives,demands and opportunities. Understanding howtechnologies co-evolve and provide downstreamand upstream stimulus for innovation elsewherein the technological system requires quantita-tive and qualitative evidence. This study askedwhether network stimulus matter in a quanti-tative sense for the significant innovations, andwhat factors determine the evolution of networksof significant innovations.

This study finds evidence that significant in-novations are afflicted by network stimulus, bothfrom forward and backward linkages, in line withthe received literature from innovation studies.Innovation network stimulus hence have a size-able explanatory power of innovation patterns.Our results differ from those reported by Ace-moglu et al (2016) since backward linkages havea pronounced role. This result is significant,since it is consistent with the view (Rosenberg1969) that innovations upstream in technologicalsystems target problems and imbalances down-stream, also documented in earlier research onthis database (Taalbi 2017a,b). One must notehowever that the network stimulus is based on adomestic flow, which is likely to underrate therole of supply of new opportunities.

Previous research on this database has givenqualitative evidence from innovation biographiesof a dynamics where innovations are developedas a creative response to opportunities upstreamor problems or imbalances downstream in thetechnological system in closely connected commu-nities. The Swedish innovation network clearlysuggests that the linkage formation of innova-tion networks is primarily shaped by historicalnetwork topology. The innovation network has

a hierarchical structure with strong persistenceand stability in network ties, forming througha preferential weight assignment process. Mainsupplier industries act as hubs, connecting di-verse industries in the network. Our results hencespeak in favor of the presence of key industries,some of which based on general-purpose technolo-gies, creating a persistent and locally star-likecommunity structure. In fact, most of these keyindustries are found in ICTs (compare Taalbi2017b). The evidence for exogenous factors wasless compelling. While gravitational pull fromimportant industries have consistent explanatorypower, economic and skill relatedness displayeda weaker and more complex relationship to inno-vation flows.

These results have corollaries for our under-standing of how technology shifts take place.First, our findings support the notions of networkstimulus, preferential assignment and historicalproximities as important mechanisms in the evo-lution of innovation systems and the formationof community structure. Our results, togetherwith earlier research, should be taken to suggestthat policy makers should monitor subsystems,centered on hubs and in driven by the opportu-nities upstream or imbalances downstream thatfocus innovation activity in the evolution of tech-nological systems.

Secondly, the results of this study suggest that,in terms of network link formation, networks ofsignificant innovations appear to be a markedlydifferent story from networks of regular inventionactivity. The mixed or negative association withconventional measures of economic, knowledgeand skill proximities suggests that networks ofradical innovations are driven by technologicaldiversification, and only to a lesser extent cor-related with inter-industrial proximities. Henceour study raises the question whether variousproxies of innovation networks and technologi-cal interdependencies, e.g., constructed throughimputed R&D flows or patent citation networks,can be taken to reflect all types of innovationactivity. While so, disruptive innovations thatdrive technological systems are not unpredictableas previous innovation ties between industriesare strong predictors of future ties. Hence, under-

15

standing the evolution of technological systemshence requires the continued collection and anal-ysis of direct measurements of innovation flows orpatent network data that differentiate betweenradical and incremental innovation.

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A Supplementary figures and tables

Figure A.1: Innovation network 1970-2013. Relative flows between 29 sectors.

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21

Table A.1: Correlation structure of network, five-year period and previous period

Period Pearson corr.1975-1979 0.62

(0.00)1980-1984 0.60

(0.00)1985-1989 0.60

(0.00)1990-1994 0.48

(0.00)1995-1999 0.50

(0.00)2000-2004 0.58

(0.00)2005-2009 0.62

(0.00)2010-2013 0.46

(0.00)

Table A.2: Cross-correlation. Independent variables

Variables Cum. flows Los Skill-rel. Gravity Leontief R&DCumulative flows 1.0000

Los index -0.0282 1.0000(0.0000)

Skill-rel. 0.0202 0.0711 1.0000(0.0000) (0.0000)

Gravity 0.0867 0.2565 -0.0030 1.0000(0.0000) (0.0000) (0.4230)

Leontief 0.0176 0.0493 -0.0004 0.0589 1.0000(0.0000) (0.0000) (0.9108) (0.0000)

R&D flows 0.0175 0.2217 0.1699 0.1444 0.0709 1.0000(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)

Table A.3: Cross-correlation table. Relative innovation flows and similarity metrics (lagged).

Variables Relative Jaccard Adamic-Adar Katz PWA PARelative 1.0000

Jaccard 0.0262 1.0000(0.0000)

Adamic-Adar 0.0318 0.8044 1.0000(0.0000) (0.0000)

Katz β = 20 0.3828 0.0556 0.0897 1.0000(0.0000) (0.0000) (0.0000)

Pref. W.A. 0.3897 0.0527 0.0824 0.9801 1.0000(0.0000) (0.0000) (0.0000) (0.0000)

Pref. Att. 0.2133 0.0833 0.1628 0.5340 0.4650 1.0000(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)

22

B Weight distribution

The network studied in this paper can be formal-ized as a network where one innovation is addedat each point in time t, such that the sum totalof innovations is t. It is also the case that thenumber of edges actually used is only a fractionof the total possible. With this in mind, it ispossible to specify a model in which time t issmaller than the (fixed) number of edges A outof which N have non-zero weight. In general,following Krapivsky and Redner (2001), with anattachment kernel aw that governs the flow ofinnovations between industries, a rate of weightassignment to unused edges β and an appropriatenormalization factor M =

∑w awNw, with Nw

being the number of edges with w innovations,the master equation is

∂Nw

∂t= βP (w) =

aw−1

MNw−1 −

awMNw (B.1)

which can be rearranged into

P (w) =aw−1

µβ + awP (w − 1) (B.2)

where µ = M/N and P (w) = Nw/N . Substitut-ing P (w − 1) recursively, it follows that

P (w) =1

aw

w∏j=1

(βµ

aj+ 1

)−1

(B.3)

A model of preferential attachment with het-erogeneity specifies that the probability of aninnovation flowing between industry i and j isrelated to weight of the edge wij/

∑wij . In prac-

tice, it is possible to model the evolution of theinnovation network as a mixed process or ran-dom and preferential attachment to edges. Withprobability α, innovations flow between industry

pairs i, j proportional towλ∑

w wλNw

. Innovations

also appear randomly in new industry pairs i, jwith probability 1 − α. Hence, the probabilityof an innovation to be added to an (ordered)industry pair with previous weight w is writtenas

Πw = (1− α)δw,0 + αwλ∑

w wλNw

(B.4)

For the empirical case where the number ofedges is fixed, this equation can be motivatedas an average over a process where edges withweight zero have probability (1− α) = N/A.

Using the master equation, and P (w) = Nw/Nand ∂N/∂t = m(1− α), where m is the numberof links (user industries) each innovation has,

P (w) =1

wλ

w∏j=1

jλ

(1− α)mµ

α+ jλ

(B.5)

For λ = 1, one may use the Gamma functionΓ(x+ 1) = x! to derive

P (w) ∝ w−1 Γ(w + 1)

Γ((1− α)mµ

α+ w + 1)

∼ w−1−1/α (B.6)

since for λ = 1, µ =∑

w wP (w) =t

(1− α)mt=

1

(1− α)m.

For λ < 1, the product in equation B.3 is writ-ten as the exponential of a sum. Using the series

representation of ln

((1− α)mµ(λ)

αw−λ + 1

)and integrating over w yields

P (w) ∝

w−λ exp−∞∑n=1

(−1)n

n

((1− α)mµ(λ)

α

)nw1−λn

1− λn(B.7)

which for1

2≤ λ < 1 is

P (w) ∝ w−λ exp−(

(1− α)mµ(λ)

α

)w1−λ

1− λ(B.8)

The cumulative weight distributions in the linearand sub-linear cases (Figure 2) are obtained byintegrating equations B.6 and B.8∫

w−1−1/αdw = w−1/α (B.9)

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and

∫w−λ exp−

((1− α)mµ(λ)

α

)w1−λ

1− λdw

∝ exp−(

(1− α)mµ(λ)

α

)w1−λ

1− λ(B.10)

The parameters of the linear model are given byestimating Model 1 in Table 2. The non-linear,in practice sub-linear, model is estimated in twosteps in Table 4. λ is estimated to 0.65. Using thefact that every innovation on average has m =

2.44 user industries,(1− α)

αµ is estimated to

0.596 in simulations. The resulting distributionis shown in Figure 2.

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