Power-Law and "Elite Club" in a Complex Supplier-Buyer Network: Flexible Specialization or Dual Economy?

W O R K I N G P A P E R S




Power-Law and “Elite Club” in a Complex Supplier-Buyer Network:
Flexible Specialization or Dual Economy?



May 2006

























Tsutomu Nakano

Associate Professor of Corporate Strategy and Organization Theory, Kwansei Gakuin Business School, Japan/

External Faculty Affiliate, Center on Organizational Innovation, ISERP, Columbia University

Email: tn70@columbia.edu








Douglas R. White

Professor of Anthropology, Institute of Mathematical Social Science, University of California, Irvine/

External Faculty, Santa Fe Institute
Email: Douglas.White@uci.edu























Center on Organizational Innovation

Columbia University in the City of
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The preferred citation for this paper is: Nakano, Tsutomu, and Douglas R. White. May
2006. “Power-Law and ‘Elite Club’ in a Complex Supplier-Buyer Network: Flexible


Specialization or Dual Economy?” Working Papers Series, Center on Organizational
Innovation, Columbia University. Available online at
http://www.coi.columbia.edu/pdf/nakano_white_de.pdf.

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Power-Law and “Elite Club” in a Complex Supplier-Buyer Network:
Flexible Specialization or Dual Economy?









Tsutomu Nakano

Associate Professor of Corporate Strategy and Organization Theory, Kwansei Gakuin Business School, Japan/
External Faculty Affiliate, Center on Organizational Innovation (ISERP), Columbia University
Email: tn70@columbia.edu


Douglas R. White

Professor of Anthropology, Institute for Mathematical Behavioral Sciences, University of California, Irvine/
External Faculty, Santa Fe Institute
Email: Douglas.White@uci.edu



April 2006



Copyright © Tsutomu Nakano & Douglas R. White

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Abstract


After the 1990s, original equipment manufacturers (OEM) as multinational conglomerates have
become more powerful than ever, exerting control over their suppliers, owing in part to the
advanced machining and information technologies. Is this a revival of the traditional Marxian
framework, or a “dual economy”? Conducting network analysis of supplier-prime buyer relations
among over 8,300 firms in an industrial district, we found not only structural properties of
“flexible specialization” as a division of labor among dedicated small- and medium-sized
suppliers but also an invisible “elite club” or cohesive core composed of extremely powerful
OEMs plus their elite suppliers, employing analyses of cohesion and assortative correlation in
the structural embedding. An overwhelming majority of the suppliers were not free from
dependency upon the core in order to gain access to and social endorsement from the consumers,
as substantiated by the overall power-law node links, against the claims of “flexible
specialization.” The present study suggests a “dual economy” not on the basis of firm size as
traditionally claimed, but of competition to be suppliers of prominent OEMs in the acyclically
hierarchical network, from the relational approach of network integration mechanisms, as a latent
but decisive explanatory variable.

Key Words: Complex systems; dual economy; flexible specialization; industrial districts;
network analysis; power-law; structural embedding
















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1. Introduction: “Dual Economy,” Industrial Districts, and Complex Networks

In the traditional Marxian framework of the so-called “dual economy” perspective, firm size
plays a decisive role in perpetuating the structural divide in the macro economy. This is due to
availability of and access to crucial resources, such as financial capital and human resource that
each of the manufacturing firms can mobilize. In effect, according to the theory, there are two
different sectors in the economy: The primary core comprised of large firms that enjoy efficiency,
productivity, security, social status, and high wages in good work conditions; and the peripheral
secondary, composed of small- and medium-sized enterprises (SME) that are denied access to the
affluence by the powerful large firms, being dependent upon and exploited by the latter (Averitt
1968; Edwards 1979). Accordingly, there are dual labor markets (Doeringer and Piore 1971).1
The vertical integration by large firms of the multidivisional form (M-form) was in fact a
dominant paradigm of the twentieth-century American capitalism until the 1970s (Fligstein 1985).
Transaction cost economics (TCE) (Williamson 1981) explained the advantage of the vertical
integration, focusing on the transaction cost of the firms such as for monitoring of opportunism
and information search under the bounded rationality (March and Simon 1958). Relying largely
upon the coordination skills of the divisional managers within the firms, through the direct
supervision of their own divisions as profit centers within the firm, the middle managers were
seen to fill a critical role. This was to maximize the organizational profit, as the “visible hand” for
the cognitively constrained CEOs who cannot monitor the entire organization directly from the
corporate headquarters (Chandler 1962). In addition, agency theorists (Fama 1980) also
accounted for an advantage of the M-form from financial perspectives, arguing that self-interest
of the divisional managers should lead to a maximization of shareholder values. Given the
appropriate incentive packages offered to those managers, firms are regarded simply as a “nexus
of contracts” and residual claims, disregarding the fact that they are indeed social entities where
people as stakeholders interact through a complex web.
A turning point from these rather under-socialized perspectives came with some empirical
studies of organizations from social network approaches in the 1970s, when Granovetter, in an
early first critique of TCE, argued that embedded relationships among trading partners is a better
governance mechanism for the firms than the M-form structure, creating peer pressure that should
discourage opportunism at the lower monitoring cost (1985), and generating more efficient
information search mechanisms through the networks (1982). Many studies followed or
rediscovered the importance of social capital (Coleman 1988; Dore 1983) as an articulation of
embedded relationships that can facilitate churning and fusion of information and tacit knowledge
within and across organizations (Eccles 1981; Nonaka 1994; Powell and Stuart 1996;
Stinchcombe 1959).
A theoretical framework that articulated the advantage of SMEs over the large firms, as
another critique of TCE, is “flexible specialization” theory (Piore & Sabel). From a network
perspective, the theory contends that, as the so-called “information age” has rapidly grown since
the 1980s, the speed of technological innovation has increased dramatically and markets have
become much more uncertain, unpredictable, and volatile, due to constantly changing customers’
tastes and demand for variations of quality products. In such relentlessly moving markets, nimble
and flexible manufacturing systems in industrial districts, which function on the foundations of
the division of labor among technologically specialized SMEs,2 have a competitive advantage
over the mass production system traditionally carried out by atomized, large firms with their M-
form structure (Goodman and Bamford 1989; Lazerson 1995; Locke 1995; Putnam 1993; Pyke,


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Becattini and Sengenberger 1990; Sabel and Zeitlin 1997; Uzzi 1997). 3 These network
perspectives offered drastically different images of SMEs embedded in their social capital as
creative and innovative, being part of the advanced and efficient economy.
The new digital technologies after the 1990s, however, appear to have made the OEMs leaner,
more efficient and more powerful than ever (Helper, MacDuffie and Sabel 2001), as they can
leverage the collaborative arrangements with their SME suppliers as for “mass customization” or
“diversified quality production” (Streeck 1992). The new manufacturing paradigm is distinct
from both the mass production by large, atomized firms as an extension of Tayler’s “scientific
management” (1947 (1911)) on the one hand, and the variety-based flexible manufacturing for
small volume production as conceptualized by “flexible specialization” on the other. In effect,
large OEMs can organize an efficient flexible production system simultaneously for both volume
and variety, formerly incompatible in terms of the production costs.
The notion of “transnational management,” introduced by (Bartlett and Ghoshal 2000), became
a popular term in the early 1990s in the management literature, presenting hopes and high
aspirations to the SMEs in regional economies for the possibilities of truly collaborative
arrangements with large conglomerates, on a global scale. The experience afterwards, nonetheless,
seems quite disappointing for many SMEs that have worked for multinational conglomerates,
because strategic decisions were confined in the hands of these headquarters as concerned a
variety of quality control know-hows, advanced machining technologies, and information
management systems rooted in the modern management science (Kristensen and Zeitlin 2005).
Thus, these recent developments in the regional manufacturing clusters have brought the old
issue back into question—Is the “dual economy” thesis, once denied and largely forgotten as
memories of the past with the widespread acceptance of network perspectives, including “flexible
specialization,” valid again in the age of the advanced manufacturing and information
technologies? Moreover, is this a kind of exploitation of the retarded secondary economy by the
efficient primary, or overwhelming advantage of the rich and powerful large firms at the expense
and de-skilling of craft workers contained in the SMEs?
While many researchers have endeavored to articulate mechanisms of “flexible specialization”
in various industrial districts and time periods, those studies had limitations. First, given the
conceptual framework as the division of labor among technologically specialized SMEs through
regional ties in rather cohesive networks, “flexible specialization” implicitly put focus on local
structure, or the smaller parts of whole networks. It was conceptually beyond the scope to discuss
global, or overall, integration mechanisms of complex networks.
Second, studies of regional interfirm networks relied mainly on qualitative research techniques
in order to depict the structural integration mechanisms, and these findings have evoked
considerable debate. Some insist that there are no universally applicable structural models of
industrial districts. Paniccia (1998), for instance, argued that even in Italy where the research
pioneers conceptualized and then empirically tested “flexible specialization” theory, there existed
many different patterns and forms of industrial clusters across space and time. While those
studies qualitatively provided rich details about the competitive advantage of the SMEs’ social
capital, they were not able to communicate systematically the structural mechanisms of interfirm
networks in industrial districts.
Lastly, existing empirical investigations mainly studied smaller-scale industrial districts where
either a single or relatively few industries were involved, leaving large-scale industrial districts
largely outside the research area. These are systems whose complexity goes well beyond the
egalitarian notion of “flexible specialization” to produce numerous parts, components, and


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modules for a variety of end products. The local SME suppliers should differentiate in the
division of labor under the leading roles of organizing prime buyers, in the tiers of subcontracting
networks that eventually lead to the top original equipment manufacturers (OEM) for the
assembling work as hubs.4
In effect, the complex webs in large industrial districts are understudied, as both the rarity of
such network datasets and the overwhelming complexities placed technical limitations on
researchers wanting to carry out quantitative analysis of the interfirm networks. There is today a
paucity of alternative theories available with which to explore and explain the network properties.
The objective of the present research, therefore, was to articulate, with the “dual economy”
thesis as a point of reference, the network integration mechanisms whereby OEMs organize their
suppliers as hubs by probing the complex web of supplier-prime buyer networks from the
approach of large-scale network analysis. The project was an attempt to analyze these structural
properties, full-fledgedly employing some of the recent innovations both in theory and analytical
techniques in the area of quantitative network analysis. While past and current examples abound
that are relevant to the study of complex interactive networks, still, for large-scale industrial
districts, only a very few network studies have yet been made.5
Accordingly, the initial study question was set to find how the complex systems of regional
interfirm networks function as structural mechanisms of large-scale “flexible specialization.”
How is the global structure of interfirm linkages in large-scale industrial districts—the overall
structure of supplier networks as trade relationships—organized on the foundations of local
structure? Can we find any clear structural cleavages in the regional economies when we test the
dualism from a relational approach of network analysis?
The remainder of the paper begins with a brief overview of previous network literature and
theoretical issues relevant to the study of industrial districts, followed by the research design and
methodological issues, including data, concepts, and analytical tools applied from the study of
social network analysis as a complex system. We end with a discussion of findings and their
implications.
As a note, the present discussion uses “suppliers” and “subcontractors” in industrial districts
rather interchangeably. It also employs such terms as “regional supplier networks,” “suppler-
prime buyer networks” and “subcontracting hierarchies” interchangeably to refer to hierarchical
interfirm networks in large-scale industrial districts where the SME suppliers work for or with
their prime buyers in various manufacturing activities executed in the regional economies. Pajek
(Batagelj and Mrvar 2005) was used both to calculate network analytical measures and to draw
graphs.

2. Data and Network Properties

2.1 Large-Scale Network and Regional Supplier-Prime Buyer Relationships
The study of complex systems has gained attention in many academic disciplines since the late
1990s. In the area of knowledge management, for instance, Powell and his colleagues (2005)
studied the recent co-evolution of cohesion and in recruitment of novelty in large-scale
collaboration networks among firms in the life sciences. Padgett, Doowan and Collier (2003)
simulate the co-evolution of firms in production and distribution markets, with firms as bundles
of skills transformed by goods passing through them. In anthropology, a large-scale and
diachronic analysis of marriage, sponsorship and elite networks in Mexico (White, Schnegg and
Brudner 1999) found co-evolution of a distinctive cultural heritage with a two-level “invisible
state” that bound together districts in a large geographic region.


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Among the alternative models for complex interactive networks, studies of small-world (Watts
1999) and scale-free networks (Barabási 2002) represent breakthrough achievements that have
drawn much recent attention. Many applications of the small-world model have been made
recently, including Newman’s study of scientific collaboration networks (2001), and
organizational studies in the areas of corporate interlocks and governance structure (Davis, Yoo
and Baker 2003; Kogut and Walker 2001; Robins and Alexander 2004), interfirm alliance
formation and joint ventures (Baum, Shipilov and Rowley 2003), and emergence of industries
(Uzzi and Spiro 2005).
While the study of complex networks has expanded rapidly and been fraught with debates over
models and applications, it offers a variety of both analytical and conceptual tools that can be
employed in order to unveil the structural properties in large-scale industrial districts.

2.2 Ohta Industrial District
The present research studied a web of supplier-prime buyer relationships among manufacturing
firms linked to Ohta, which is one of 23 wards in Tokyo, as one of the two largest industrial
districts in Japan. Over 7,000 SMEs were engaged in a variety of manufacturing processing
activities, parts, components, and modules production, and assembling work to compose a
complex web of regional interfirm linkages. A majority of the SMEs had the size of a typical
family household, or even smaller, in terms of the number of employees. The industrial district
has been well known as a so-called machine-tools industry where the SMEs functioned as
suppliers for leading Japanese OEMs in other applied industries.
At the time of the survey, in 1994-95, among over 7,000 manufacturing firms in the industrial
district, a majority of firms were specialized in their own areas of processing activities. In
particular, many firms were engaged in various metal-cutting processes. At the same time, a
minority were suppliers of parts and components in areas such as automobile production,
aerospace technologies, computer-related products, electrical and electronic equipment and
devices, general industrial and precision machinery, jigs and tools, and shipbuilding, among other
areas. Roughly only 10%-20% of suppliers that specialized in certain areas of processing and
parts and components production had product lines of their own brands (Seki and Kato 1990).
To conduct the present network analysis, name-generating data from Akusesu Data (Ohta-ku
Sangyo Shinko Kyokai 1997a; Ohta-ku Sangyo Shinko Kyokai 1997b) were used. The dataset
encompasses approximately 70% of all manufacturing establishments in operation in Ohta-ward
during the years of 1994-95. The questionnaire employed asked each of the roughly 7,000 SMEs
located in Ohta-ward to list up to three names of their prime buyers. To be specific, among the
5,111 firms in Ohta from the dataset, 2,710 firms (53%) listed a total pool of 4,077 other firms as
their prime buyers. Another 2,401 firms (47%) listed no prime buyers. Of the 5,111 SMEs that
responded, 501 firms (9.8%) listed only one prime buyer; 530 firms (10.4%) only two; and 1,679
firms (32.9%) listed three names as their prime buyers. Of the 4,077 listed prime buyers, 841
were supplier-prime buyers located in Ohta, which were named by peer SME suppliers in Ohta,
and 3,236 were prime buyers outside Ohta. The total number of firms in the dataset and included
in the network was 8,347.6

2.3 Distribution of Node Links
Node centrality has been a key analytical concept in social network analysis (Freeman 2004). The
in-degree centrality score of a firm was determined by the aggregate number of times the 5,111
SME suppliers listed a given firm as one of their three prime buyers. Overall, no single firm


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constituted a hub that dominated the large-scale regional web, but some were marginally so.
Toshiba was the most popular prime buyer, and 112 suppliers in Ohta listed Toshiba as one of
their three prime buyers, while 53 listed NEC, 45 listed Hitachi, and so forth. There are many
hubs along a gradient, not just one.
The “pecking order” for in-degree, including the frequency of ties to powerful OEMs, is
consistent with the kind of power law that Barabási (2002) uses to characterize preferential
attachments of ties to hubs proportional to degree in a scale-free network. The distribution of in-
degree for all firms is plotted in Figure 1 on a double-logarithmic scale, and the slope (α ~ 2.3) of
the straight line that approximates the distribution (y = 1539.4x-2.2862 and R2 = 0.8537) is within
the range of values (α ~ 1.8 to 2.5) for scale-free preferential attachment networks of size 4-8,000
(White and Johansen 2005, p. 17).7 Furthermore, the various indices of graph centralization for
the largest component proposed by Freeman (1979)—degree, betweenness, and closeness
centralization—are all extremely low, showing again no single dominant node to which most
other nodes are directly connected.
A scale-free model of hub centralities rather than a single hub with spokes might be applicable
as a model of a centralized network in Ohta, except for the fact that it is linkages from central
nodes and not attachments to them that organize the network (author publication 2006 to be
inserted after review). For example, in the subcontracting hierarchies in industrial districts,
typically firms at high levels as hubs recruit and control their suppliers, and most suppliers
largely follow their lead. Barabási overgeneralizes when he infers preferential attachment from
fitting the slope of a degree distribution of this sort to a power law.

4
3
2
1
f
i
rms
0
number of
log of -1
-.5
0.0
.5
1.0
1.5
2.0
2.5
Log of indegree


Figure 1 A Power Law in Ohta.
Data was created from Ohta-ku Akusesu Deta 1 & 2 (Ohta-ku Sangyo Shinko Kyokai 1997a; 1997b).

2.4 OEMs’ Hierarchical Group Networks
How can we identify subgroups of core firms, as local structures, embedded in a large-scale
complex network? Egocentric networks give us a first approximation. The “competitive
cooperation” conceptualized by “flexible specialization” as the division of labor among SMEs in
regional networks in Ohta is illustrated, to a certain degree, by Figure 2. NEC’s hierarchically
organized “double hub-and-spoke” network structure extends to include 124 supplier firms at
Tiers-1, -2 and -3. Ranked second in terms of in-degree from its 53 Tier-1 suppliers, as a leading
OEM in Ohta, NEC uses local-core Tier-1 firms as assemblers or organizers of parts and
components production. While the Tier-1 suppliers did not supply one another, each lower tier


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also uses independent subordinates as Tier-2 or lower in order to organize the division of labor
among dedicated SME suppliers to work in various specialized areas. Similarly, to a certain
degree, the supplier group networks of other large OEMs operate on the foundations of this kind
of division of labor among specialized SME suppliers in their areas of technological competence,
engineering knowledge, and workers’ skills.


Figure 2 NEC’s Supplier Network in Ohta: A Local Structure.
Graph produced from data in Ohta-ku Akusesu Deta 1 & 2 (Ohta-ku Sangyo Shinko Kyokai 1997a; 1997b). Colors
by in-degree.

3. Network Integration Mechanisms in Ohta

3.1 Oriented Network and Components
To introduce network analytical concepts, the links nominated by suppliers as to their prime
buyers constitute a digraph, or directed graph, in which the directionalities of the links do not
prevent links from being reciprocated. In fact, however, not a single pair of firms named one
another as prime buyers. Hence, the network of firms constitutes an oriented digraph (Harary
1969: 10), or digraph in which no symmetric pair of directed links exists. Thus, the term oriented
network can be used to describe this property of the subcontracting supplier-prime buyer network.
A component is a maximal connected sub-graph in which all the nodes are connected to one
another through one or more non-directed paths. As any exchange of goods through directional
ties is most likely to involve at least some communication, or two-way information exchange
between the two partners (Freeman 1979; Hanneman 2001), weakly-connected components still
bear social meanings even if they disregard the directions of ties. In the case of the Ohta’s
supplier networks, components should be composed of ties among connected suppliers, suppliers-
prime buyers, and prime buyers.
To relate the above concepts to the analysis of the interfirm networks in industrial clusters,
there are deep and extensive implications of the advancement in machining technologies after the
1990s on the network integration mechanisms in industrial districts. First, as the SMEs lack


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financial capital to invest in the very expensive high-tech equipments and advanced machining
technologies, these SMEs as dedicated suppliers need to depend upon the controlling, powerful
OEMs more than ever, belonging to the efficient but hierarchical production systems in order to
get access to the advanced management science techniques and information technologies, such as
concurrent engineering, just-in-time (JIT) inventory control, supply-chain management, and total
quality control, among others.
Second, an emergent role structure in the production network appears to be institutionalized on
the basis of the complex value-chain. Two kinds of division of labor should be embedded in the
complex network as the enmeshed role structures: A horizontal configuration among suppliers
organized by prime buyers or hubs, as suggested by “flexible specialization” theory; and vertical
as linked flows of manufacturing processes, marketing and sales, and distribution stages. A series
of horizontal division of labor among suppliers organized by hubs should be vertically linked or
oriented as entangled chains of production flows towards the assembly work by OEMs,8 as the
emergence of a production hierarchy where the subsequent marketing and sales and delivery
stages follow. While the consumer stands outside the set of linked manufacturing processes, the
marketing and distribution stages by reputable large firms involve a redefinition of the categories
and statuses of agents in exchange with their brand equity.
Thus, as each of the large-scale industrial districts is an extremely complex regional cluster of
firms, a complex web of suppliers and prime buyers should form a large component that contains
hierarchical properties. Therefore, the first hypothesis to test is as follows:

Hypothesis 1: In each of large-scale industrial districts, there should be a large component in
existence where SMEs interact in order to form a division of labor under the lead of many OEMs
or hubs

Consistent with this hypothesis, the largest component of 4,500 firms was identified. The
operation created a simpler and somewhat reduced network, by excluding 3,847 firms
disconnected from the component.

Hypothesis 2: The supplier-buyer relations within this component are hierarchical, due to the
nature of the network as regional subcontracting system.

This second hypothesis is explored in the next section.

3.2 Acyclic Depth Partition and DAG Structure in Ohta
Why did the complex web of regional supplier networks generate such a giant component of
4,500 firms? How was it hierarchically organized through commodity chains and other network
structures or processes? The Ohta supplier-prime buyer network has no reciprocated or
symmetric links. In a separate paper (author publication 2006 to be inserted after review), we
argued that the one-way directedness of supplier-prime buyer links is one of the fundamental
characteristics of complex hierarchical subcontracting relationships as large sparse networks
(LSN), with statistical evidence that these networks should generally take the form of directed
acyclic graph (DAG), based on our empirical study of the Ohta industrial district and
comparative observations on modern industrial districts.9
To elaborate on some of the global properties, an acyclic network is a special kind of oriented
network that contains no directed cycles. If we start a path from any node in the network and


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