This Research Bulletin has been published in Global Networks, 8 (1), (2008), 94-115.
Please refer to the published version when quoting the paper.
A tendency in the globalization literature toward conceiving of the global economy as structured by networks among places has led researchers to focus on mapping such networks among world cities (Friedmann 1986; Castells 1996; Taylor 2001; Sassen 2001). Separately, organizational research has examined the role of networks among firms in structuring competition, collaboration, and cooperation (Pfeffer 1982; Uzzi 1996; Gulati and Gargiulo 1999; Polenske 2004). In the case of both inter-city and inter-firm networks, advantages accrue to cities and firms by virtue of their structural positions in their respective networks, which in turn generate hierarchies. Some cities are better places for doing business than others due to the access they provide to global markets through their connections to other cities. Similarly, some firms are better business partners due to the access they provide to strategic information through their relationships with other firms. Recognizing this, numerous rankings have been offered in attempts to identify the best (i.e. most advantaged or advantageous) cities and firms. While this is sometimes a useful task, it often obscures two deeper questions. First, concerning inequality, exactly how much better or structurally advantaged are the top cities or firms relative to those lower in the hierarchy? Second, comparatively, is the degree of inequality of structural advantage greater among cities or firms? Answering these questions is an important step toward understanding the differential roles these two entities play in structuring global economic activity.
In this paper, I answer these two questions by comparing the degree of inequality in city and firm hierarchies that are implied by the organization of the networks in which they are embedded. To define these two networks – one among 313 world cities, another among 100 advanced producer service (APS) firms – I offer a mathematical simplification and substantive extension of Taylor’s (2001) method for specifying the world city network that draws on Simmel’s ( 1955) and Breiger’s (1974) notions of duality. The results suggest that within each network the degree of inequality depends on the specific conception of structural advantage. However, comparing across the two networks, the distribution of structural advantages is generally more unequal among cities than firms. These differences may result from cities’ greater dependency on environmental and historical contexts than firms. Whatever their cause, they suggest that while advanced producer service firms are important in the global economy, cities are more critical sources of advantage (and disadvantage). That is, even under conditions of footloose global capitalism, place still matters.
To this end, I begin by reviewing the logic behind a world city network conception of globalization, and the use of centrality indices in this literature to measure three types of structural advantage. I then offer a parallel conception of the world firm network, and consider the same three types of structural advantage in this context. In the third section, I turn to a more general discussion of ‘dual’ networks. The fourth section describes the method used to define and analyze the dual city and firm networks, then presents the city and firm hierarchies of structural advantage with corresponding measures of inequality. These results are interpreted and discussed in the fifth section, and in the final section I offer some conclusions and directions for future inquiry.
WORLD CITY NETWORKS & HIERARCHIES
An economic agent who generates and distributes goods or services in global markets, a producer, might derive certain benefits or advantages from two key sources: site and service. First, where a producer is located may confer some benefits, as some cities, through their service infrastructures, may offer more opportunities to engage in global markets than others. Second, the service firms that facilitate a producer’s operations may confer benefits, as some may offer more opportunities to exploit new technology or benefit from other types of strategic information. Many of the site advantages that cities offer to producers derive from their position in the world city network, while many of the service advantages that firms offer derive from their position in the world firm network. In this and the following section, I review conceptions of these two sorts of networks, and how positions in each enable cities and firms to offer structural advantages to producers.
The World City Network
For nearly a century, there has been an interest in identifying and describing those great cities of the world where things get done (Geddes 1915; Hall 1966). While drawing on the insights of these earlier works, the current round of globalization research most clearly follows from Friedmann’s (1986) ‘world city hypothesis.’ More narrowly, it is the second of seven interrelated conjectures that has served as a touchstone for globalization theorists: “Key cities throughout the world are used by global capital as ‘basing points’ in the spatial organization and articulation of production and markets” (Friedmann 1986:71). That is, cities serve as layover stops for economic resources in constant global circulation. Castells (1996) reaffirmed the importance of networked places by identifying a shift from a world organized around ‘spaces of places’ toward one organized around ‘spaces of flows.’ In the former case, locations were significant because of the activities that take place within them, while in the latter they are significant because of the activities that take place between them, serving as conduits for coordinating activities in other locations. Cities, in their role as nodes in a global network, are therefore crucial to the global economy because they serve as liminal zones for placeless and mobile money and ideas.
While Friedmann (1986) and Castells (1996) offered heuristic and theoretical ideas about why globalization requires a networked conception of cities, by focusing on the interdependence of key cities and advanced producer service (APS) firms, Sassen (2001) and Taylor (2001) concretized conceptions of both the world city and the world city network. Sassen (2001) notes that despite the geographic dispersion of economic activity that is globalization’s namesake, there is at the same time a concentration of certain activities in certain cities. Specifically, while the ‘everyday’ work of production is pushed to the periphery by centrifugal forces of cheap land and labor, the APS firms that coordinate and control these activities are concentrated in cities by centripetal forces of place-bound infrastructures and human capital reserves. These APS firms, which include transnational banks, international law firms, and global accounting and marketing specialists, are particularly significant to producers with global aspirations because their specialized support services are essential to successfully conducting business amid the complexities and uncertainties of cross-border transactions. Thus, the interdependence of dominant places and cutting-edge firms serves as the foundation for her notion of world cities, which are key sites in the production of global economic control, but more narrowly serve as producers’ access points to the global economy.
Taylor (2001) adopted Sassen’s (2001) conception of world cities as hinging upon the interdependence of cities and APS firms, but then asked, “how can it be extended to account for [the] world city network?” (p. 183). He answered this question by observing that to effectively link producers to global markets in other cities, APS firms must offer seamless service to their clients through intra-firm networks among their branch locations in different cities. These intra-firm networks imply inter-city economic networks because a producer based in one city can most effectively conduct business in other cities when the APS firms that support its operations maintain branch locations in these other places. Consider several producers based in city A that receive specialized support from a bank with its only additional offices in cities B and C. These producers will enjoy seamless financial support, and thus more effective access, when transacting business in cities B and C, but not elsewhere. In this example, the branch office network of the bank metaphorically allows the producers to ‘speak the same language’ as their potential customers and business partners in other places. But more generally, it demonstrates that the breadth of an APS firm’s branch office network defines the breadth of global markets to which its producer clients have direct or effective access.
To the extent that these producers must rely on this bank to support their cross-border (or, more accurately here, inter-city) economic transactions, the bulk of such transactions involving producers in A will be with others located in B and C. The branch network of the APS firm creates (the potential for) an economic linkage between producers in A and markets in B and C, or more abstractly between city A and cities B and C. These linkages, forged by the co-location of an APS firm’s branch offices in multiple cities, structure Taylor’s (2001) conception of the world city network. Specified in this way, the presence (or absence) of connections between cities in the world city network reflects producers’ opportunities for (and barriers to) direct, effective access to global markets. Of course, the opportunities a city offers its producers for access to global markets are not simply either present or absent, but rather are a matter of degree. While the preceding example presumed the existence of only one APS firm, it is more likely that any (potentially) world city will contain a range of such firms. Thus, for Taylor (2001), inter-city linkages are stronger or weaker depending on the extent of overlap in the composition of cities’ entire APS firm complexes. This recognizes that when two cities contain branch offices of many of the same APS firms, they offer proportionally greater opportunities for producers to conduct seamless, direct, and effective economic exchanges between them.
The World City Hierarchy
Also a matter of degree is the directness of these linkages, and the potential for economic exchanges they represent. In the example above, producers in city A have seamlessly supported access to markets in two other cities, but they may have indirect access to additional markets through middleman service providers in intermediary cities. A city’s position within the world city network structure defines the extent to which it offers producers the advantage of direct or indirect access to the global economy. Such differential structural advantages, deriving from cities’ different positions in the network, result in a world city hierarchy in which some places are better sites for producers than others.
There have been numerous attempts to define such hierarchies through the identification and ranking of world cities – Beaverstock, Taylor, and Smith (1999) review more than two dozen. Until very recently, many of these analyses have focused on various economic attributes of the cities themselves, including the presence of corporate headquarters (Cohen 1981) and APS firms (Sassen 2001). However, with the recent turn to thinking about globalization in terms of networks, Taylor (1997) observed that the world city hierarchy “can only be defined through…a network” (p. 325). While the presence of various economic entities within a city can indicate the city’s capacity to engage in certain activities, like production, they cannot indicate its capacity to support producers’ engagement in a key activity of the global economy: inter-city transactions. Understanding the hierarchy of world cities in their capacity to support their producers engagement in the global economy requires not an analysis of world cities per se, but rather of the relationships between them, that is, of their networks.
Empirical work adopting this approach has been slow to develop, in part due to a lack of relational data (Short et al. 1996). However, through the clever transformation of data from existing sources, a few researchers have constructed world city networks and used them to examine the world city hierarchy. Typically a city’s position in the hierarchy is taken to depend on its capacity to control economic exchange, and especially to offer producers an advantage in the global economy. In network terms, this is reflected in the extent to which a city is central in the world city network, where cities that are more central in the web of inter-city economic flows offer producers greater advantage. Just as there are several different ways that a city may offer producers an advantage, there are also different ways of conceptualizing centrality in a network. In the remainder of this section, I consider three specific notions of network centrality: degree, closeness, and betweenness (Freeman 1978/79).
The simplest way that a city might be an advantageous location for a producer in the global economy involves offering direct access to markets in many different places. A city containing APS firms that maintain branches worldwide is well-connected in the world city network (e.g. Chicago is directly connected to 55% of cities in the network), and thus offers its producers direct and effective access to diverse points in the global marketplace. Compare this to a city whose APS firms’ branches connect it (i.e. its producers) only to a few other cities (e.g. St. Louis is directly connected to only 2%, using the networks described below). The well-connected Chicago has more to offer producers than the more isolated St. Louis in terms of market access and opportunities to be involved in inter-city transactions. Counting the number of markets to which a city provides direct access – its number of direct connections in the world city network, or degree centrality – indicates its capacity for offering its producers direct involvement in the global economy. Because different cities offer different capacities for direct market access, cities’ level of degree centrality defines one hierarchy of world cities: a hierarchy of direct access.
Of course, cities will not always offer their producers direct access to foreign markets. A hierarchy of opportunities for direct access may inappropriately penalize cities that offer significant but indirect access. Consider a city, X, that contains APS firms, perhaps newly established, that maintain only a one additional branch location worldwide. Its producers would have only a single opportunity to engage in seamless inter-city transactions, and thus city X would appear to offer its producers only marginal opportunities for involvement in the global economy. However, suppose further that the ‘one additional branch location’ of these APS firms happens to be in New York. In virtue of their co-location in New York, there are opportunities for the APS firms serving X-based producers to form partnerships or bundle services with the multitude of other, better connected APS firms located in New York. Thus, while X-based producers enjoy seamless support only for transactions with New York, they can engage in transactions more globally through intermediate APS firms in New York. More generally, while seamless APS support in inter-city transactions is ideal, intermediate APS firms in intermediate cities can bridge gaps.
Nonetheless, there is advantage in near-seamless support. The fewer intermediate firms and cities on which an economic agent must rely for access, the more unconstrained and independent its action may be. This suggests a second sort of world city hierarchy deriving from advantages of structural position: a hierarchy of indirect access. The ability for a city to offer producers indirect market access is captured by the notion of closeness centrality, which indicates the inverse of the average number of intermediary steps necessary for a producer in one city to conduct transactions with another city. Cities that have high closeness centrality scores – that are removed from other cities in the network by only a few steps – offer producers both independence, and wide reaching, though indirect market access.
When inter-city transactions cannot be completed directly, but rather require intermediary cities, the intermediaries act as brokers or gatekeepers of access. Indeed, as Lyons and Salmon (1995) suggest, “the function of a global city may be to…’broker’ corporations located in cities throughout the nation” (p. 106). In the example above, New York plays a critical role because producers in city X depend on its APS firms for access to foreign markets. That is, New York lies between producers in city X and the rest of the global marketplace. Betweenness centrality captures the degree to which a city is in this type of position by counting the number of times it functions as the intermediary in inter-city connections. A city that is highly ‘between’ offers its producers a benefit that derives from its criticality as an intermediary. Because the city, and more specifically the APS firms within in, are essential for others’ access to global markets, all participants in the global economy have an interest in ensuring the health and stability of these broker cities’ economies. Producers located in cities that broker others access to markets, therefore, enjoy the goodwill of others toward its host city’s economy, perhaps in the form of deference or elevated status.
Examining the rank ordering of cities in these hierarchies may help to contextualize otherwise abstract ideas about the world city network, and lend face validity to the types of structural advantage they are meant to capture. However, such lists also conceal the degree of inequality in the hierarchies. They obscure the differences between each position in the hierarchy and create the potentially misleading impression that each higher ranked city is merely an additively more advantageous location for producers. By directly considering the degree of inequality in these hierarchies, it is possible to better understand their significance. For example, position in a hierarchy marked by little inequality – where there is little difference between each rank position – is much less significant than position in a highly skewed hierarchy. Thus, when selecting a headquarters site, producers may do better to distinguish potential host cities on the bases of more consequential, skewed hierarchies. Additionally, focusing on the broad distributional properties of these hierarchies rather than on their particularities facilitates comparisons with hierarchies that emerge from the world firm network, which is one central goal of this paper.
Formulating hypotheses concerning the world city hierarchies and their levels of inequality is challenging because each of the few studies that have adopted a rigorous network approach have relied upon different data and conceptions of the world city network. Nonetheless, it is possible to draw some exploratory conjectures from three exemplar studies: (1) Smith and Timberlake’s (2001) 100-city network based on flows of airline passengers; (2) Taylor, Catalano, and Walker’s (2002) 315-city network based on APS firm locations; and (3) Alderson and Beckfield’s (2004) 3,639-city network based on Fortune 500 headquarter-subsidiary locations. First, regardless of the specific conception of centrality used to define the hierarchy, each study finds that London, New York, Paris, and Tokyo are at or near the top, but that below the apex there are differences. Thus, it is expected that all three hierarchies will be similar at the top but otherwise will show differences that reflect the different types of structural advantage. Second, although they do not explicitly quantify it, each study notes a level of inequality inherent in hierarchies that are based on measures closely corresponding to degree centrality (eigenvalue, global connectivity, and outdegree, respectively). Thus, it is expected that the degree centrality-based hierarchy will show a significant level of inequality. Finally, though based on very different data from that employed in the analyses below, it may also be instructive to note that among the cities for which Alderson and Beckfield report values, closeness centrality exhibits a striking pattern of equality, while betweenness centrality exhibits just the opposite.
World cities are places that bring together place-bound resources with firm-bound specializations to serve as sites of global economic control, and as points of access to the global economy for producers located within them. In the world city network, as conceived by Taylor (2001), two world cities are linked to the extent that they both contain branch locations of the same advanced producer service (APS) firms. Linkages in this network indicate opportunities for producers located in one city have direct access to markets in another. The more central a city is in this network, the more it is an advantageous location for a producer seeking to exploit global markets, thus situating it higher in a world city hierarchy. Three specific forms of network centrality define hierarchies of cities vis-à-vis their provision of three structural advantages. Degree centrality identifies those cities that provide many opportunities for direct access to global markets. Closeness centrality identifies cities that offer indirect access to a wide range of global markets, through a few intermediaries. Finally, betweenness centrality highlights cities that serve as brokers in inter-city transactions, and thus which offer benefits of economic stability and prestige.
WORLD FIRM NETWORKS & HIERARCHIES
The World Firm Network
Clearly, cities’ position in a world city network enables them to offer different types of structural advantages to producers located within them. Moreover, the uneven distribution of these structural advantages across cities implies a world city hierarchy, that is, a hierarchy of good places to do global business. While Sassen (2001) and Taylor’s (2001) image of network globalization is compelling, I argue that it is incomplete. APS firms are acknowledged for their importance in supporting inter-city transactions, but once their intra-firm branch networks are used to identify inter-city linkages, they largely vanish from the model and the focus remains on cities as the key organizing unit and source of advantage. Conceiving of globalization as structured by a network of cities linked by APS firms neglects an alternative conception of globalization as structured by a network of firms linked by cities. On this latter conception, APS firms’ position in a world firm network enables them to offer different types of structural advantage to their producer clients. An uneven distribution of these structural advantages across firms implies a world firm hierarchy, that is, a hierarchy of good firms on whom to depend for specialized support for global operations. Whereas the previous section laid out the logic for globalization structured by a world city network, I turn now to consider the logic of a world firm network.
Both Fernandez and Su (2004) and Freeman and Audia (2006), in their reviews of organizational sociology, suggest that research would benefit from an increased recognition of the continuing importance of spatial communities in organizational interactions, in contrast to placeless considerations of market communities alone. Elements of this literature support conceptualizing a world firm network in which firms are linked by their co-location in cities, similar to Taylor’s (2001) world city network discussed above where cities are linked by co-located firms. When two APS firms maintain a branch location in the same city, they operate within the same resource, normative, and social environment. The more cities in which two APS firms both maintain branch locations – that is, the more their intra-firm branch networks overlap geographically – the greater the extent to which they operate in shared environments. These shared environmental conditions create opportunities for linkages between firms through the exchange of information, both directly through employees and alliances, and indirectly through competition and modeling. When aggregated, such informational exchange linkages define a world firm network.
When two APS firms share operating environments, there are at least two key resource pools they also share: labor and clients. In the case of labor, they recruit from the same local labor pool of managerial elites (Castells 1996), and thus may trade employees who carry institutional knowledge with them. For example, the experienced employees in one accountancy firm’s office are prime recruitment targets for another accountancy firm operating an office across the street, and if recruited bring knowledge of their former employer’s strengths and weaknesses. Even if employees do not switch firms, they are nonetheless likely to know and interact with one another, and thus share information, due to tendencies toward homophily in personal social networks (McPherson, Smith-Lovin, and Cook 2001). That is, for example, because the IT professionals in a city’s APS firms likely have similar educational, economic, and social backgrounds, they are likely to live in the same neighborhoods, dine in the same restaurants, and work out in the same gyms – all opportunities for informal information exchange. Finally, with increasing degrees of professionalization among APS employees in the form of educational credentialing and professional societies, we are likely to see “professional networks that span organizations and across which new models diffuse rapidly” (DiMaggio and Powell 1983:152). These three mechanisms – inter-firm hiring, socializing, and professional networking – highlight some ways that information might flow directly between APS firms that maintain same-city branch locations.
Information might also flow between APS firms, more indirectly, when they share the same pool of potential local clients. In the case of competition for clients, firms will seek to obtain information about one another’s core technologies and strategies in an attempt to differentiate themselves and secure a competitive advantage. In the alternative case of cooperation, firms will seek to create strategic alliances, possibly by offering bundled services to a client. Thus, whether APS firms respond to demand scarcity with competition or cooperation, both strategies imply opportunities for information exchange between them.
When APS firms share operating environments, they share not only the associated resource pools, but also the uncertainty and complexity that follows from environmental instabilities. Institutional theory suggests that under conditions of environmental uncertainty, APS firms will model the practices of other firms in similar situations, that is, of other APS firms operating in the same city or cities (DiMaggio and Powell 1983). This modeling process implies the indirect transfer, intentionally or not, of information about operating practices from one firm to another. Both resource dependency theory (Pfeffer 1982) and recent versions of transaction cost theory (Powell 1990) also suggest that inter-firm networks result from environmental uncertainty or instability. The former theory predicts that when resources are scarce firms will seek to cooperate in order to weather bad times through the exploitation of economies of scale and resource complementarities. The latter predicts that firms will seek to establish alliances, partnerships, and networks when resource instability elevates transactions costs beyond a market-based solution, but not to the point of requiring complete vertical integration. In short, as Gulati and Gargiulo (1999) found, “organizations enter ties with other organizations in response to the challenges posed by the interdependencies that shape their common environment” (p. 1443).
These ideas about the inter-firm exchange of information depend on several different mechanisms. However, they all suggest that inter-firm exchanges of information will be greater among firms operating in the same environment(s). Therefore, it is appropriate to conceive of a world firm network which defines two firms as linked to the extent that they share operating environments, that is, to the extent that the maintain branch locations in the same set of cities. The network linkages, then, indicate information sharing opportunities among APS firms. Being the client of a well-networked APS firm has several advantages for a producer. For example, Uzzi (1996) has found that networked firms have higher survival chances than other firms, suggesting that networked APS firms can provide more stable service to their clients. Barley, Freeman, and Hybels (1992) argue that technical innovations are more efficiently obtained by networked firms, suggesting that networked APS firms can provide more sophisticated services to their clients. However, just as with the advantages cities offer to producers, the advantages APS firms offer to producers depend on the firms’ position in the network. Some positions hold greater structural advantages than others, generating a hierarchy of APS firms in terms of their capacity to offer advantages to producer clients.
The World Firm Hierarchy
Above I considered how three different conceptions of network centrality correspond to three types of structural advantage that cities might offer to producers. In the context of the world firm network, these same three versions of centrality correspond to similar types of structural advantage that APS firms can offer their producer clients. First, producers benefit from receiving services from APS firms that have direct connections to many other firms. Such degree-central APS firms exchange information directly with many other firms, and therefore exchange information rapidly and accurately. In turn, these firms are maximally able to offer their producer clients services utilizing the most cutting edge technology and research (Barley, Freeman, and Hybels 1992). In addition to these informational benefits, APS firms that are central in this way also offer their producer clients more opportunities for strategic alliances among their service providers. For example, while a producer’s APS firm may only provide support in European markets, a well-connected firm will have opportunities to ally with other APS firms which can extend the producer’s reach into other markets. Thus, on this first notion of network centrality, the more direct network connections an APS firm has, the more information and alliance opportunities it has, and the higher the quality of service it can provide.
To provide high quality service, based on the most recent technologies, an APS firm must be aware of new innovations in its field, whether marketing, finance, or law. However, an APS firm does not need to exchange information directly with the source of the new technology since such information diffuses (passively) through networks. Instead, what is necessary is that an APS firm be connected to many different parts of the firm network, either directly or indirectly. Consider, for example, an APS firm operating exclusively in North America, and a service innovation pioneered by a firm operating exclusively in Asia. These two firms do not maintain locations in any of the same cities, and thus lack opportunities to directly exchange information. Nonetheless, if a third firm operates in both North America and Asia, exchanging information with each of the first two firms, then it creates a channel through which the innovation can flow. The fewer such intermediate firms, acting as diffusion channels, that are necessary to link two firms together, the faster the information will diffuse (Valente 1995). Put another way, the closer two firms are in the network (i.e. closeness centrality), the less dependent one is on intermediary channels of diffusion for learning of innovations pioneered by the other. Thus, APS firms with high closeness centrality can provide their producer clients with more independent and rapid access to information from wider ranges of sources.
APS firms that serve as diffusion channels offer a third set of advantages to their clients in virtue of the brokering power associated with such a network position (i.e. betweenness centrality). Firms that mediate the exchange of information between others learn about innovations sooner. In the example above, the third firm learns of the new technology before it diffuses to other firms. These ‘between’ firms can also use their network position to stop or slow certain innovations from diffusing in an attempt to gain a partial monopoly on their use (Barley, Freeman, and Hybels 1992). Finally, such firms can leverage other firms’ access to diffusing innovations in attempts to secure more favorable terms in situations of competition or cooperation. In sum, the producer clients of these tertius gaudens (Burt 1992) firms benefit in three ways: they enjoy faster access to new service innovations, they have access to innovations which producers serviced by other firms may not, and they enjoy the upper hand in competitive and cooperative arrangements. Thus, on this final notion of centrality, the more an APS firm serves as a channel of diffusion between other firms, the greater power it has over information diffusion in the system, which translates into improved access to information for its producer clients.
Because APS firms occupy different positions relative to one another in the world firm network, the extent to which each firm can offer its clients these structural advantages differs. The unequal distribution of centrality, and the associated capacity to offer benefits to clients, across APS firms defines a world firm hierarchy – a hierarchy of service firms on whom it is good for producers to depend. While researchers have used firm attributes to predict firm centrality in a network (e.g. Barley, Freeman, and Hybels 1992), or used firm centrality to predict economic outcomes (e.g. Uzzi 1996), unlike cities, there has been relatively little attention paid to centrality hierarchies among firms. One finding that is consistently borne out is the high centrality of banks in inter-firm networks (e.g. Mariolis 1975, Mintz and Schwartz 1985). But as with city rankings, the inequalities among firms in such hierarchies remain obscured, and this study must proceed in an exploratory fashion.
The role of networks among firms in structuring the global economic hierarchies is no less important that the role of networks among cities. In the conception of the world firm network proposed above, two APS firms are linked to the extent that they maintain branch locations in the same set of cities. Linkages in this network indicate opportunities for APS firms to exchange information with one another. The more central a firm is in this network, the more it is an advantageous source for producers requiring specialized services, thus situating it higher in a world firm hierarchy. Three specific forms of network centrality define hierarchies of firms vis-à-vis their provision of three structural advantages. Degree centrality identifies firms that have direct access to strategic information, which they can pass to producer clients in the form of enhanced service quality. Closeness centrality identifies firms that have relatively independent, albeit indirect, access to information from a wide range of sources throughout the network. Finally, betweenness centrality highlights firms that are able to broker or control the flow of information through the system, and thus which may offer their producer clients with negotiating power and monopolistic information access.
THE DUALITY OF WORLD CITIES AND FIRMS
From Simmel to Breiger
The concept of dualism has a long history in the social sciences, and plays an especially central role in Simmel’s theorizing. Simmel’s dualism is most explicit in his essay, The Web of Group-Affiliations ( 1955), where he axiomatically argues that “society arises from the individual and that the individual arises out of association” (p. 163). In the latter case, the uniqueness of individuals derives from their membership in a specific set of groups, while in the former case, the uniqueness of groups (i.e. society) derives from their specific sets of members. In a sense, individuals are the ties that bind groups together, while groups dually are the ties that bind individuals together. Thus, as Wolff (1959) summarizes, “the fact of sociation puts the individual into the dual position…that he is both a link in the organism of sociation,” connecting groups to one another through co-group membership, “and an autonomous organic whole,” himself linked to other organically whole individuals through group co-membership. (p. 350).
Breiger (1974) formalized this notion of duality by placing it in an algebraic and graph-theoretic (i.e. network) context. In his formulation, “the value of a tie between any two individuals is defined as the number of groups of which they are both members. The value of a tie between any two groups is defined conversely as the number of persons who belong to both” (p. 181–2). This conception of two dual networks, where the nodes and ties are reversible, has found expression in a variety of contexts, including studies of interlocking directorates (e.g. Mintz and Schwartz 1985), social movements (Diani 2000), and research collaboration (e.g. Newman 2001).
Using Breiger’s (1974) approach to define two one-mode networks from a single set of two-mode data offers a number of benefits generally, but is particularly useful in the case of world city and firm networks. First, it allows networks to be defined using readily available attribute data (e.g. APS firm locations), rather than requiring scarce relational data. Second, it makes the substantive meaning of network ties explicit and intuitive (e.g. firms link cities together, cities link firms together). Third, it provides two different ways of thinking about the structure of a social or economic system that, although derived from a common source, have distinct structural properties that are not simply mirror images of one another (Burris 2004). Fourth, it permits the application of well-known social network analytic tools (e.g. centrality, blockmodeling, etc.), rather than requiring more obscure methods designed specifically for two-mode data analysis (Robins and Alexander 2004). A final benefit, which I present in the following section, is the mathematical simplicity with which the derivation of these dual networks can be stated.
A Nascent Dualism
The notion of dual networks of globalization – one among cities, another among firms – is not entirely novel, but rather has been lurking just below the surface for some years. Indeed, in the initial formal specification of his world city network model, Taylor (2001) noted that “there is a parallel argument for [a network among] firms to that which can be presented for cities” (p. 187). This line of work was pursued slightly further in a subsequent paper in which the total service values of firms, across 316 cities, were computed ( Taylor, Catalano, and Walker 2002). However, because in both cases the focus had been the world city network, analysis stopped short of computing linkages among firms.
These nascent ideas about dualism were again brought to the fore by an exchange between Taylor (2006) and Beckfield and Alderson (2006), which appeared while this paper was under review. In defending their earlier (2004) analysis, Alderson and Beckfield note how Breiger’s (1974) conception of duality might be used to yield dual city and firm networks. The key point they seek to make is that the role of firms, which are the underlying agents of globalization, are present in both networks, and therefore in neither case are cities inappropriately reified. That is, the duality approach to defining these networks makes explicit a central tenet of the Friedmann-Castells-Sassen model of globalization, namely, that “world cities are not independent of the firms that create them” (Beckfield and Alderson 2006:897–8). Still, the discussion of the duality of cities and firms in globalization networks has remained at the theoretical level, and measuring and analyzing dual city and firm networks a mere hypothetical possibility – it is this gap that I aim to empirically close, and to which I now turn.
DEFINING DUAL NETWORKS
Taylor’s (2001) approach to quantitatively specifying the world city network using data on the location of APS firms has received widespread, though not unqualified (Beckfield and Alderson 2006), support and has since formed the basis for numerous empirical studies conducted through the Globalization and World Cities Study Group and Network (GaWC). It begins with a ‘service value matrix’, V, in which each cell contains a value that reflects the importance of firm j’s branch location in city i. This rectangular matrix is transformed into a square ‘elemental relational matrix’, E, where the value of each cell Epq is defined by:
These values indicate the degree to which the firm profiles of cities p and q overlap, and thus the strength of the connection between these two cities in the world city network.
Breiger (1974) used the same equation to transform a rectangular matrix indicating individuals’ memberships in groups into a square matrix indicating individuals’ relationships to one another, relying on Simmel’s ( 1955) notion of intersecting social circles. However, he also noted two important properties of this type of transformation. First, equation (1), and thus the relationship between matrices V and E can be more simply stated as:
Second, by reversing the order of the multiplier and multiplicand in equation (2), an alternative square matrix is defined, in Breiger’s (1974) case indicating the relationships of social groups to one another.
Combining Taylor’s (2001) substantive conception of the world city network and his method for defining it, with Breiger’s (1974) mathematical insights above, it is possible to define two matrices using a single ‘service value matrix’:
The first, E(c), contains measures of the strength of relationships between pairs of cities in the world city network, while the second, E(f), contains measures of the strength of relationships between pairs of firms in the world firm network. These two matrices, and the networks they represent, offer two complementary or dual pictures of the same global economic state of affairs, but each captures a unique perspective. In the former, cities are linked to one another by APS firms’ branches (i.e. facilitators of inter-city transactions), while in the latter, APS firms are linked to one another by cities (i.e. shared operating environments). These two matrices make it possible to consider and compare the role of cities as nodes in a global network with that of firms.
The GaWC DataSet 11, assembled by Taylor and Catalano (2000) and described in detail by Taylor, Catalano, and Walker (2002), is a service value matrix containing information about the importance of 100 advanced producer service firms in 313 cities 1. Representative firms were included from the advanced producer service sectors of accountancy (e.g. Arthur Anderson), advertising (e.g. Young & Rubicam), banking/finance (e.g. Barclays), insurance (e.g. Lloyd’s), law (Baker & McKenzie), and management consultancy (e.g. Deloitte & Touche). For each city-firm pair, a score ranging from 0 to 5 was assigned, where 0 indicates no firm presence and 5 indicates the location of the firm’s headquarters. Applying equations (3) and (4) to this data yields two relational matrices: E(c) is a 313 ´ 313 matrix describing relationships among cities, and E(f) is a 100 ´ 100 matrix describing relationships among firms.
Because most network methods are designed for the analysis of binary data, relationships were recoded as present only if they were at least 15% as strong as the strongest relationship in the network, leaving networks of 118 cities and 81 firms. This threshold was selected because it balances inclusiveness against comparability in network sizes, and represents a midpoint in the range of reasonable threshold values. UCINET (Borgatti, Everett, and Freeman 2002) was then used to compute normalized degree, closeness, and betweenness centrality indices for each city and firm, which specify the city and firm hierarchies. The Gini coefficient is used as a measure of inequality within each of these hierarchies.
Table 1 presents the top 20 cities and firms in each hierarchy with their centrality scores and the associated Gini coefficient. A series of seven post-hoc comparisons, with Bonferroni corrections, examine the differences among these Gini coefficients. Within the city network, the level of inequality in the degree centrality hierarchy is significantly greater than that in the closeness hierarchy (z = 16.60, p < .01) and significantly smaller than that in the betweenness hierarchy (z = - 9.98, p < .01). A similar pattern is evident within the firm network (closeness vs. degree: z = 5.57, p < .01; degree vs. betweenness: z = -11.40, p < .01). Comparing across the two networks, the level of inequality is significantly larger for the city than firm hierarchy with respect to degree (z = 7.57, p < .01) and betweenness centrality (z = 4.97, p < .01). For closeness centrality, while there is statistically significantly greater inequality among firms than cities (z = -3.60, p < .01), the magnitude of the difference is practically insignificant.
To be sure, dichotomizing the networks to conduct these analyses does involve the loss of data, but as Hanneman and Riddle (2005) note, “very often, the additional power and simplicity of analysis of binary data is ‘worth’ the cost in information loss.” Still, to verify that the results were not distorted by the arbitrary selection of a dichotomizing threshold the analysis was repeated at thresholds of 1%, 5%, 10%, 20%, and 25% 2. Each higher threshold represents an increasingly restrictive understanding of the boundaries of the world city and world firm systems, and thus for obvious reasons the specific members and ordering of the hierarchy exhibit slight changes. However, the focus here is not on the specific rank ordering but on inequality, and in nearly all cases, the direction and significance of the difference of Gini coefficients measuring inequality remained the same. The closeness centrality hierarchy is the only exception: at low thresholds, inequality in the closeness centrality hierarchy is greater among cities, while at higher thresholds it is greater among firms. But, because at all thresholds the absolute magnitudes of Gini coefficients for closeness hierarchies are small, any difference between the two regardless of direction is not practically significant. Finally, although degree centrality can be computed using valued (i.e. non-binary) data, it is reported in table 1 using binary data for comparability with the other measures of centrality. A further sensitivity analysis confirmed that the results for degree centrality remain unchanged when valued data is used.
HIERARCHY AND INEQUALITY IN DUAL NETWORKS
Comparing Hierarchy and Inequality Within City and Firm Networks
The top-20 lists in Table 1 serve to contextualize the findings and lend some concreteness to the results. Within the three city hierarchies, there is strikingly little variation in the rank ordering at the top of the hierarchy, but this is consistent with the widespread agreement in the extant literature on the composition of the world city hierarchy’s apex. Still, there are a few discrepancies when comparing these hierarchies to more conventional conceptions of world cities based on attributional, rather than network, data (e.g. Friedmann 1986, Sassen 2001). For example, Paris ranks above Tokyo and Chicago ranks above Sydney or Mexico City. These differences reflect the importance of not merely being the site of numerous APS firms, but being the site of APS firms that are globally structurally significant on account of their branch locations (Taylor, Catalano, and Walker 2002). Within the three firm hierarchies, there is similarly little variation in the rank ordering. Notably, while banking and accounting firms compose 41% of the total world firm network, they constitute approximately 85% of the top-20 firms in each hierarchy, consistent with prior findings (Mariolis 1975, Mintz and Schwartz 1985). Thus, the method employed to construct the dual world city and world firm networks appears to yield hierarchies that are consistent with earlier studies.
The uniformity in these simple rankings, however, obscures variations in the levels of inequality within each of the hierarchies. Thus, it is more useful to consider patterns within the hierarchies than the simple rank orderings themselves. Within the city network, the levels of inequality among the three hierarchies are consistent with earlier findings by Taylor, Catalano, and Walker (2002) and Alderson and Beckfield (2004): there is inequality in the degree centrality hierarchy, bounded on each side by a fairly equal closeness hierarchy and a highly unequal betweenness hierarchy. The extent to which cities might offer their producers access to a wide range of global markets through a few intermediaries as measured by closeness centrality – a sort of transactional independence – is relatively uniform across all cities. This is intuitive because indirect access to global markets is the barest minimum for world city status and one that all cities, to the extent that they are properly included in this dataset, ought to attain. In contrast, the extent to which cities might offer their producers direct access to global markets, as measured by degree centrality, is significantly more unequal. That is, some cities offer much more direct market access than others. In fact, while the top two cities offer direct access to about 94% of the rest of the network, the third city offers direct access to only about 60%. This is even more the case for the extent to which cities offer the benefit of having their economies subject to the economic and political goodwill of other global economic participants, as measured by betweenness centrality. Only the top two cities are truly critical nodal points, each serving as intermediaries more than 30% of inter-city connections, which is reflected in the dramatically larger associated Gini coefficient.
This same relative pattern of inequality is also apparent within the firm network. All firms are able to offer their producer clients wide, though indirect access to strategic information and a consequently elevated quality of service, as implied by closeness centrality. Having such multiple channels of access, providing access to multiple parts of the network through only a few intermediaries is essential to firm independence, which in turn is a minimum threshold for status as a holder and producer of global economic control (i.e. a world firm). Many fewer firms offer the degree centrality benefits of direct access to strategic information from other firms, namely, fast and accurate access to diffusing innovations. And still fewer firms have the potential to offer control over when and where new information diffuses, or the upper hand in negotiations that comes with lying ‘between’ other firms.
The picture that emerges from examining these networks separately is something of a hierarchy of hierarchies. The wide, indirect access implied by closeness centrality is a baseline standard for both cities and firms to be real members of the global economic network. The direct access implied by degree centrality is somewhat less equally distributed, but still held by many of the nodes to varying degrees. As such, it is an ideal measure of world-cityness, as Alderson and Beckfield (2004) suggest. Finally, the extreme levels of concentration of control and criticality implicit in betweenness centrality cast it as a way to identify which nodes in a global economic network, if any, serve as keystones or linchpins.
Comparing Hierarchy and Inequality Across City and Firm Networks
Although cities and firms are similar in this way, an important difference in their capacities as sources of producer advantage also emerges from Table 1. Specifically, city hierarchies tend to be marked by greater levels of inequality than corresponding firm hierarchies. In the case of the closeness hierarchies, to be sure, the inequality among firms is statistically significantly greater than that among cities, but the small absolute magnitude of the difference suggests that it is not practically significant. This simply reflects that, of the cities and firms under consideration, they each meet the minimum threshold of world status set by closeness centrality. However, turning to the other hierarchies, the differences between city and firm inequalities are both statistically and practically significant. Capacity to offer advantages to producers is concentrated in a few top cities, while it is spread more evenly among firms. As a result, producers receiving support from different APS firms are on more equal competitive footing, deriving similar amounts of advantage from their firms’ structural position, than producers located in different cities.
Consider, for example, a producer whose operations require the services of a specialized accounting firm. It makes some difference whether this producer receives service from KPMG or PKF, respectively the most and least central of the top accountancy firms, because these two firms have differing capacities to offer their clients certain advantages. However, it makes significantly more difference whether the producer is located in London or Mexico City, respectively the most and least central of the top cities, because these two cities are more widely divergent in their capacities to offer advantages. Therefore, in considerations of securing maximal competitive advantage, where a producer is located has more impact than who provides specialized support services. To be sure, because firms are unequal in their capacities to provide certain advantages to their clients, a world firm hierarchy has real implications, but place still matters more. Furthermore, these differences exist not simply when comparing the top and bottom of the hierarchy, but even when comparing cities and firms at the very top. The choice between the second and third most central firms is negligible, but the choice between the second and third most central cities is quite dramatic. If the world city hierarchy is composed of distinct strata (e.g. core vs. periphery), the upper stratum may be even smaller than previously suggested.
While these results suggest that place matters more for producers, they also suggest that place matters more for the organization and vulnerability of global capital generally. Highly centralized networks, like the world city network, are at greater risk of fragmentation because many of the organizational and structural properties of the system depend on just a few nodes. For example, removing London or New York from the world city network would cripple inter-city transactions because it is essential as a linking intermediary. In contrast, removing KPMG from the world firm network would hinder some transactions, but other similarly central firms could easily pick up the slack. Thus, these results also suggest that urban social or economic instability or place-oriented terrorism, would have far greater consequences for the global economic network than the collapse of a multinational APS firm.
Two Difficult Questions
These data, unfortunately, leave two difficult questions unanswered: Why do we observe these differing patterns of inequality between cities and firms, and what are their implications for the way producers, cities (i.e. their leaders), and firms behave?
One possible explanation for these patterns is that firms are more nimble in their adaptability to changing economic conditions, allowing them greater flexibility in competition and networking, whereas cities are confronted with certain barriers. For an APS firm to be linked to other firms, it must be perceived as a valuable source of information or strategic alliances, which it turn require that it remain competent and competitive in its respective field. For a city to be linked to other cities, it must cultivate a diverse mix of well connected APS firms that open foreign markets to its producers. However, firms and cities differ in their flexibility to achieve these ends and thus to establish their centrality in their respective networks. For example, an accountancy firm can more easily adopt the latest accounting practices and thus remain competitive, than a city can offer new natural amenities (e.g. mountains and lakes) to attract the elite labor that staff APS firms (Florida 2005). That is, cities, as spatial entities, have a greater dependency on their environments, which decreases their range of adaptive options. If firms are more flexible in jockeying for structural position than cities, then the distribution of advantageous structural positions among them is likely to remain more balanced through the equilibrating forces of competition.
A second potential explanation may recognize that the world city system and distributions of power among cities within it predate the development of a world firm system. Cities have been cultivating and consolidating their bases of competitive advantage for centuries, over which time concentrations and inequalities of advantage have built up and become entrenched (Chase-Dunn 1985). For example, London, as the one-time capital of an empire on which the sun never set, held a favorable structural position in the world city system long before the rise of modern global capitalism. In contrast, because many of the APS firms under consideration are relatively young and of similar age, there has been less opportunity for the entrenchment and multiplication of inequalities among them.
Whatever the explanation for these patterns, they surely have implications for the three key players addressed in this paper: producers, firms, and cities. Their implications for producers are relatively clear: when considering expansion into new cities or new partnerships with advanced producer service providers, the former consideration ought to carry more weight. For firms, these results suggest that network position and the advantages it confers do little to differentiate firms from one another. As a result, while they are surely important, APS firms may have to look beyond the much-touted advantages of inter-organizational networks and look to more traditional paths of differentiation (e.g. product innovations, more specialized or more expansive service offerings, etc.).
Finally, the implications for cities are somewhat more difficult to pin down because such a discussion runs the risk of reifying cities. Both Taylor (2006) and Beckfield and Alderson (2006) are clear that their respective approaches recognize firms as the sources of economic agency, and treat cities as containers. Still, to the extent that cities have some form of agency, through their political and business leaders and directed as Logan (1978) suggested toward territorial differentiation and dominance, it may not be a mistake to talk of, for example, cities being “sought out by other cities, [to] have ties directed to them, and [to be] chosen over others” (Alderson and Beckfield 2004:824). In this conception of the world city network, seeking out connections to other cities involves attracting branch locations of globally significant APS firms, perhaps directly through tax incentives or indirectly through the development of a more cosmopolitan amenity-filled environment (Florida 2005). But, for cities looking to elevate their status in the world city hierarchy, the best strategy may not be to seek ties to top cities, which may yield one new link but many redundant indirect linkages. Instead, the key lies in forging ties with other cities whose connections are different from their own, thereby closing or at least bridging structural holes (Burt 1992). A stronger tie between Mexico City and New York would elevate the former’s status somewhat, but forging a new tie between Mexico City and, say, Zurich would have much deeper consequences for the way global capital is organized.
FUTURE DIRECTIONS AND CONCLUSION
The newness of the duality approach to defining world city and firm networks, and the exploratory nature of the analyses, mean that this study has raised more questions than it answers and identifies a number of potential directions for future work in this area. Additional work is clearly necessary to understand the two unanswered questions addressed above concerning the causes and effects of the observed patterns. More directly, however, the results of these analyses should be used to inform hypotheses that can now be tested in a more confirmatory framework. For example, because city hierarchies of advantage are more unequal than corresponding firm hierarchies, there ought to be greater variation between producers in different cities than between producers relying on different APS firms. Similarly, a change of headquarters location ought to have more consequences for producer performance than a change in how specialized services like banking and accounting are obtained.
This last point raises an important scope condition for this study that future work may seek to relax. A change in how a producer obtains specialized services may involve a shift from one APS firm to another, but may also involve the internalization of such services. Indeed, many of the very largest producers internalize even the most complex specialized service functions. They also maintain multiple global locations, thereby internalizing their direct economic access to foreign markets. Because such mega-producers need not rely on APS firms for access to the global marketplace, they are significantly less impacted by the advantages (and disadvantages) conferred by cities and firms. Thus, the conception of global advantage through city and firm networks that I have offered applies primarily to those smaller producers who cannot participate in the global economy without external supports. These smaller producers are worthy of study as they vastly outnumber, and frequently interact with, the larger ones. However, the recent calls to look beyond only APS and multinational firms as constituting the world city/firm network offer one way to draw producers of all size back in. Taylor (2005), for example, has recently included data on cultural, political, and social entities to derive a more comprehensive world city network. If even large producers depend on advantages derived from these other sorts of entities, this approach may offer one way of expanding the scope.
Another possible extension includes examining other structural patterns in the city and firm networks beyond hierarchies and inequalities. Derudder and Taylor (2005) have begun to explore the geographic cliqueishness of world cities, finding that network connections between cities tend to be regionally concentrated, thus identifying an additional way that place remains important in global economics. Considering cliqueishness in world firm networks, future studies may benefit from considering whether network connections between firms tend to be within-sector or between-sector. If the firm network is marked by sectoral cliques, then firms may experience greater information sharing benefits, while cross-sectoral cliques may indicate greater opportunities for strategic alliances in the form of service bundling.
Considering the rapidness with which the global economy changes, it will also be important to examine changes in these networks over time. At the nodal level of analysis, futures studies may explore rises and falls of cities and firms in their respective hierarchies. Formerly second tier cities (e.g. Chicago and Sao Paulo) and newly capitalist cities (e.g. Moscow and Shanghai) are likely to rise, potentially at the expense of top cities, creating a flatter world city hierarchy that more closely resembles that of firms. Mergers among APS firms will have particular significance in the longitudinal examinations of these networks. For example, at the time of writing it appears likely that Barclays will acquire ABN AMRO, which may have opposite effects on the world city and firm hierarchies. Because formerly unconnected pairs of cities in which one contained a branch of ABN AMRO and the other a branch of Barclays would become connected by the joining of these two intra-firm branch office networks, such a merger would bring cities closer together in the network and thus equalize their status in the hierarchy. But, at the same time, firms would become more stratified in their hierarchy as the dominant firm in a merger would capture some of the former centrality of the subordinate firm. Shifting to the dyadic level, longitudinal studies might also explore changes in the strength of ties between specific pairs of cities or firms, asking whether immigration flows or sister city arrangements for cities, and strategic alliances for firms, have short-term or long-term effects.
Finally, the tools available for analyzing network data are progressing at least as rapidly as the global economy, and future studies should look to these for new approaches to exploring the data. To illustrate an application of the dual network technique, Breiger (1974) described a way to remove ‘noise’ from the data and reveal the more interesting underlying structures. Though somewhat older, this underused approach may be especially helpful in the context of Taylor-style interlocking world city networks where meaningful patterns are often obscured by the fact that some APS firms maintain locations in (nearly) every city. More recently, Robins and Alexander (2004) describe some innovative methods for drawing conclusions about differences between dual networks through direct analysis of the original two-mode (i.e. city by firm) data, comparing it for inferential statistical purposes to simulated random graphs.
Clearly, there are many new directions that this paper has opened up. But, it has permitted a few interesting conclusions to be drawn as well. Both cities and firms play important roles in structuring global economic activity by offering certain advantages to producers. Many of the advantages they have to offer derive from their structural position within global networks, which can be used to define city and firm hierarchies. Although the networks and hierarchies among cities, and those among firms, have received significant attention, they tend to be addressed separately. In this paper, I have examined the two networks together as constituting dual versions of the same economic web, comparing their hierarchies of capacity to offer structural advantages to producers. The results suggest, first, that there is a hierarchy of hierarchies wherein most cities and firms offer wide, indirect access to markets and information (respectively), while few offer direct access, and fewer still offer advantages connected to control over that access. Second, the level of inequality among cities in offering these advantages is significantly greater than that among firms, suggesting that location trumps service in producers’ search for competitive advantages. Most broadly, therefore, in the networked global economy of footloose capital, and even at the top of recognized hierarchies, while advanced producer services matter, even more important is location, location, location.
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1. The original data contains 315 cities. However, two of these – Pyongyang, North Korea and Lucknow, India – are missing values for all 100 firms. Thus, they have been dropped from all subsequent analyses.
2. Higher thresholds yield networks that are not fully connected and reduce the sample size below what is necessary for stable estimates of the Gini standard error.
Table 1: Centrality and Hierarchy in the World City & Firm Networks
a Key to firms and sectors: KPMG (accounting); PriceWater, PriceWaterhouse Coopers (accounting); HLB (accounting); Deutsche, Deutsche Bank (banking); RSM (accounting); Citibank (banking); HSBC (banking); Moores Row., Moores Rowland (accounting); McCann Erik., McCann Erikson WorldGroup (advertising); Barclays (banking), McKinsey (consulting); Art. And., Arthur Anderson (accounting); Winterthur (insurance); BBDO (Advertising); AGN (accounting); PKF (accounting); J. Walt. Thos., J. Walter Thompson (Advertising); ABM AMRO (banking); Horwath (accounting); Chase (banking).
Edited and posted on the web on 27th June 2007
Note: This Research Bulletin has been published in Global Networks, 8 (1), (2008), 94-115