Stefania VitalipersName, James B. GlattfelderpersName, Stefano BattistonpersName (2011date). “The Network of Global Corporate Control.” PLoS ONEtitle·j.
Object of study — the worldwide network of direct and indirect ownershipterm and controlterm among transnational corporationsterm
Research question — whether transnational corporationsterm are isolated, form separate coalitions, or form a globally connected core-periphery structure and how controlterm is concentrated
Contribution — the first global ownership-network investigation, a method correcting control overestimationterm in large cyclic networks, and a topology-plus-control characterization
Cross-disciplinary analysis
content-tags & facets:
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | concentration of corporate control, ownership-network topology, competition, and financial fragility — “A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporations (TNCs). However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert control over other firms via a web of direct and indirect ownership relations which extends over many countries. Therefore, a complex network analysis [1] is needed in order to uncover the structure of control and its implications. Recently, economic networks have attracted growing attention [2] , e.g., networks of trade [3] , products [4] , credit [5] , [6] , stock prices [7] and boards of directors [8] , [9] . This literature has also analyzed ownership networks [10] , [11] , but has neglected the structure of control at a global level. Even the corporate governance literature has only studied small national business groups [12] . Certainly, it is intuitive that every large corporation has a pyramid of subsidiaries below and a number of shareholders above. However, economic theory does not offer models that predict how TNCs globally connect to each other. Three alternative hypotheses can be formulated. TNCs may remain isolated, cluster in separated coalitions, or form a giant connected component, possibly with a core-periphery structure. So far, this issue has remained unaddressed, notwithstanding its important implications for policy making. Indeed, mutual ownership relations among firms within the same sector can, in some cases, jeopardize market competition [13] , [14] . Moreover, linkages among financial institutions have been recognized to have ambiguous effects on their financial fragility [15] , [16] . Verifying to what extent these implications hold true in the global economy is per se an unexplored field of research and is beyond the scope of this article. However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate control. This was never performed before and it is the aim of the present work.” | |
| claim-type | method — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | |
| method — evidence | — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | |
| object of study — evidence | — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | |
| research question — evidence | — “A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporations (TNCs). However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert control over other firms via a web of direct and indirect ownership relations which extends over many countries. Therefore, a complex network analysis [1] is needed in order to uncover the structure of control and its implications. Recently, economic networks have attracted growing attention [2] , e.g., networks of trade [3] , products [4] , credit [5] , [6] , stock prices [7] and boards of directors [8] , [9] . This literature has also analyzed ownership networks [10] , [11] , but has neglected the structure of control at a global level. Even the corporate governance literature has only studied small national business groups [12] . Certainly, it is intuitive that every large corporation has a pyramid of subsidiaries below and a number of shareholders above. However, economic theory does not offer models that predict how TNCs globally connect to each other. Three alternative hypotheses can be formulated. TNCs may remain isolated, cluster in separated coalitions, or form a giant connected component, possibly with a core-periphery structure. So far, this issue has remained unaddressed, notwithstanding its important implications for policy making. Indeed, mutual ownership relations among firms within the same sector can, in some cases, jeopardize market competition [13] , [14] . Moreover, linkages among financial institutions have been recognized to have ambiguous effects on their financial fragility [15] , [16] . Verifying to what extent these implications hold true in the global economy is per se an unexplored field of research and is beyond the scope of this article. However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate control. This was never performed before and it is the aim of the present work.” | |
| contribution — evidence | — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | |
| mechanism | directed weighted graph Firms become nodes and percentage ownership becomes directed weighted links. — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | mechanisms[0] |
| mechanism | indirect ownership paths Products and recursive paths propagate economic value beyond direct holdings. — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | mechanisms[1] |
| mechanism | threshold rule A majority shareholder receives full control while others receive none. — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | mechanisms[2] |
| mechanism | network control Directly controlled value is added to value influenced recursively through the network. — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | mechanisms[3] |
| mechanism | cycle correction The new method prevents recursive cross-shareholding paths from counting control repeatedly. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | mechanisms[4] |
| mechanism | recursive search A search discovers all ownership paths originating from or pointing to TNCs. — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | mechanisms[5] |
| mechanism | Lorenz-like curve Sorting holders and cumulating control measures how small a fraction holds a chosen total share. — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | mechanisms[6] |
| mechanism | topology plus control ranking Combining component location with influence identifies where powerful actors reside. — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | mechanisms[7] |
| builds-on | Previous work on large control networks — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | claim_relations[0] |
| contrasts-with | small national samples — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | claim_relations[1] |
| extends | rich-club phenomenon — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | claim_relations[2] |
| sense | ownership as a directed weighted relation rather than mere affiliation — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | senses[0] |
| sense | control as influence over strategy rather than legal ownership alone — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | senses[1] |
| sense | network control as economic value influenced through all ownership paths — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | senses[2] |
| sense | core as the one dominant strongly connected component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | senses[3] |
| sense | bow-tie as asymmetric global corporate topology — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | senses[4] |
| sense | concentration as cumulative control held by a small top fraction — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | senses[5] |
| sense | super-entity as an analytical description, not demonstrated coordinated action — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | senses[6] |
| sense | general method as scalar flow over directed weighted real-world networks — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | senses[7] |
| control | three control-estimation models — held — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” — rules out dependence of concentration on one ownership-to-control model — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | controls[0] |
| control | more conservative control models — held — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” — rules out dependence on assigning all control to the majority shareholder — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | controls[1] |
| note | Previous work on large control networks — The method explicitly builds on prior work while correcting its cycle problem. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | claim_relations[0] |
| weight | Previous work on large control networks — 0.95 — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | claim_relations[0] |
| note | small national samples — The global analysis addresses the limited scope of prior studies. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | claim_relations[1] |
| weight | small national samples — 0.95 — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | claim_relations[1] |
| note | rich-club phenomenon — The authors conjecture that the dense control core generalizes a rich club. — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | claim_relations[2] |
| weight | rich-club phenomenon — 0.7 — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | claim_relations[2] |
| note | structure of the control network —causes→ global market competition — Flat but sign-unspecified effect claim. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[0] |
| relation | structure of the control network —causes→ global market competition — The control-network structure affects global market competition. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[0] |
| weight | structure of the control network —causes→ global market competition — 0.85 — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[0] |
| note | structure of the control network —causes→ financial stability — Flat but sign-unspecified effect claim. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[1] |
| relation | structure of the control network —causes→ financial stability — The control-network structure affects financial stability. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[1] |
| weight | structure of the control network —causes→ financial stability — 0.85 — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concept_edges[1] |
| audit | indirect links —causes→ shareholders becoming very powerful — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says indirect links CAN result in some shareholders becoming very powerful; hedged. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concept_edges[2] |
| effect direction | indirect links —causes→ shareholders becoming very powerful — increases — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concept_edges[2] |
| note | indirect links —causes→ shareholders becoming very powerful — Modal can-result statement. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concept_edges[2] |
| relation | indirect links —causes→ shareholders becoming very powerful — Indirect links can result in shareholders becoming very powerful. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concept_edges[2] |
| weight | indirect links —causes→ shareholders becoming very powerful — 0.7 — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concept_edges[2] |
| audit | TNC network —distinct-from→ listed companies in separate countries and their direct shareholders — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: 'this data set' = the TNC network (previous sentence). — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | concept_edges[3] |
| note | TNC network —distinct-from→ listed companies in separate countries and their direct shareholders — Explicit difference in coverage. — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | concept_edges[3] |
| relation | TNC network —distinct-from→ listed companies in separate countries and their direct shareholders — The global TNC data fundamentally differs from prior country-listed-company data. — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | concept_edges[3] |
| weight | TNC network —distinct-from→ listed companies in separate countries and their direct shareholders — 0.95 — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | concept_edges[3] |
| note | strongly connected component —part-of→ largest connect component — Explicit container-first containment; endpoint spelling follows the staged source. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[4] |
| relation | strongly connected component —part-of→ largest connect component — The largest connected component contains one dominant strongly connected component. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[4] |
| note | core —is-a→ tightly-knit group of corporations — Direct categorical restatement. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[5] |
| relation | core —is-a→ tightly-knit group of corporations — The core is a tightly-knit group of corporations holding one another's shares. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[5] |
| note | core —part-of→ bow-tie — Explicit container-first containment. — “Network topology. ( A ) A bow-tie consists of in-section (IN), out-section (OUT), strongly connected component or core (SCC), and tubes and tendrils (T&T). ( B ) Bow-tie structure of the largest connected component (LCC) and other connected components (OCC). Each section volume scales logarithmically with the share of its TNCs operating revenue. In parenthesis, percentage of operating revenue and number of TNCs, cfr. Table 1 . ( C ) SCC layout of the SCC (1318 nodes and 12191 links). Node size scales logarithmically with operation revenue, node color with network control (from yellow to red). Link color scales with weight. ( D ) Zoom on some major TNCs in the financial sector. Some cycles are highlighted.” | concept_edges[6] |
| relation | core —part-of→ bow-tie — A bow-tie consists of a strongly connected core plus IN, OUT, tubes, and tendrils. — “Network topology. ( A ) A bow-tie consists of in-section (IN), out-section (OUT), strongly connected component or core (SCC), and tubes and tendrils (T&T). ( B ) Bow-tie structure of the largest connected component (LCC) and other connected components (OCC). Each section volume scales logarithmically with the share of its TNCs operating revenue. In parenthesis, percentage of operating revenue and number of TNCs, cfr. Table 1 . ( C ) SCC layout of the SCC (1318 nodes and 12191 links). Node size scales logarithmically with operation revenue, node color with network control (from yellow to red). Link color scales with weight. ( D ) Zoom on some major TNCs in the financial sector. Some cycles are highlighted.” | concept_edges[6] |
| note | out-section —contrasted-with→ in-section — Direct size comparison. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[7] |
| relation | out-section —contrasted-with→ in-section — The out-section is significantly larger than the in-section. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[7] |
| weight | out-section —contrasted-with→ in-section — 0.95 — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concept_edges[7] |
| note | network control —contrasted-with→ wealth — Direct inequality comparison. — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | concept_edges[8] |
| relation | network control —contrasted-with→ wealth — Network control is much more unequally distributed than wealth. — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | concept_edges[8] |
| weight | network control —contrasted-with→ wealth — 0.95 — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | concept_edges[8] |
| outcome | control — held — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | controls[0] |
| outcome | control — held — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | controls[1] |
| relation | Ownership → directed weighted graph — Ownership corresponds to a directed weighted graph of firms and ties. — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | unhoused_relations[0] |
| relation | ownership share → control — Larger ownership shares are associated with larger control. — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | unhoused_relations[1] |
| weight | ownership share → control — 0.95 — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | unhoused_relations[1] |
| relation | cycles → control overestimation — Cycles and upstream positions cause the basic computation to overestimate control. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[2] |
| weight | cycles → control overestimation — 0.95 — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[2] |
| relation | new methodology → control overestimation — The new method overcomes control overestimation in large networks. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[3] |
| weight | new methodology → control overestimation — 0.95 — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[3] |
| relation | TNC network → bow-tie — The global TNC network has a bow-tie structure. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | unhoused_relations[4] |
| relation | core → super-entity — Top core holders can be thought of as an economic super-entity. — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | unhoused_relations[5] |
| weight | core → super-entity — 0.7 — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | unhoused_relations[5] |
| relation | ownership relations → financial network — Ownership relations are used conditionally as a proxy for undisclosed financial ties. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[6] |
| weight | ownership relations → financial network — 0.7 — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[6] |
| relation | financial network → systemic risk — A very densely connected financial network is prone to systemic risk. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[7] |
| weight | financial network → systemic risk — 0.7 — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[7] |
| relation | ownership relations → blocs — Ownership connections could facilitate the formation of blocs. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[8] |
| weight | ownership relations → blocs — 0.7 — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[8] |
| relation | blocs → market competition — Potential blocs would hamper market competition. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[9] |
| weight | blocs → market competition — 0.7 — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[9] |
| relation | core → rich-club phenomenon — The dense control core could be a generalization of the rich-club phenomenon. — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | unhoused_relations[10] |
| weight | core → rich-club phenomenon — 0.7 — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | unhoused_relations[10] |
| no type for this | Ownership → directed weighted graph — Ownership corresponds to a directed weighted graph of firms and ties. — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | unhoused_relations[0] |
| no type for this | ownership share → control — Larger ownership shares are associated with larger control. — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | unhoused_relations[1] |
| no type for this | cycles → control overestimation — Cycles and upstream positions cause the basic computation to overestimate control. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[2] |
| no type for this | new methodology → control overestimation — The new method overcomes control overestimation in large networks. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | unhoused_relations[3] |
| no type for this | TNC network → bow-tie — The global TNC network has a bow-tie structure. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | unhoused_relations[4] |
| no type for this | core → super-entity — Top core holders can be thought of as an economic super-entity. — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | unhoused_relations[5] |
| no type for this | ownership relations → financial network — Ownership relations are used conditionally as a proxy for undisclosed financial ties. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[6] |
| no type for this | financial network → systemic risk — A very densely connected financial network is prone to systemic risk. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | unhoused_relations[7] |
| no type for this | ownership relations → blocs — Ownership connections could facilitate the formation of blocs. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[8] |
| no type for this | blocs → market competition — Potential blocs would hamper market competition. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | unhoused_relations[9] |
| no type for this | core → rich-club phenomenon — The dense control core could be a generalization of the rich-club phenomenon. — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | unhoused_relations[10] |
| limitation | The analysis does not test the consequences of global control structure for competition or financial fragility. — “A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporations (TNCs). However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert control over other firms via a web of direct and indirect ownership relations which extends over many countries. Therefore, a complex network analysis [1] is needed in order to uncover the structure of control and its implications. Recently, economic networks have attracted growing attention [2] , e.g., networks of trade [3] , products [4] , credit [5] , [6] , stock prices [7] and boards of directors [8] , [9] . This literature has also analyzed ownership networks [10] , [11] , but has neglected the structure of control at a global level. Even the corporate governance literature has only studied small national business groups [12] . Certainly, it is intuitive that every large corporation has a pyramid of subsidiaries below and a number of shareholders above. However, economic theory does not offer models that predict how TNCs globally connect to each other. Three alternative hypotheses can be formulated. TNCs may remain isolated, cluster in separated coalitions, or form a giant connected component, possibly with a core-periphery structure. So far, this issue has remained unaddressed, notwithstanding its important implications for policy making. Indeed, mutual ownership relations among firms within the same sector can, in some cases, jeopardize market competition [13] , [14] . Moreover, linkages among financial institutions have been recognized to have ambiguous effects on their financial fragility [15] , [16] . Verifying to what extent these implications hold true in the global economy is per se an unexplored field of research and is beyond the scope of this article. However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate control. This was never performed before and it is the aim of the present work.” | limitations[0] |
| limitation | Basic recursive network-control formulas severely overestimate actors inside or upstream of cycles. — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | limitations[1] |
| limitation | Earlier ownership data covered listed companies in separate countries rather than the true global network. — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | limitations[2] |
| limitation | Missing disclosure of financial contracts prevents direct reconstruction of the global financial network. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | limitations[3] |
| limitation | Ownership structure is only hypothesized to proxy financial-network structure. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | limitations[4] |
| limitation | The study neither demonstrates nor excludes coordinated bloc behavior by the corporate core. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | limitations[5] |
| limitation | Pooling ownership across countries may obscure differences in legal and institutional settings. — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | limitations[6] |
| limitation | Financial institutions may hold equity without intending to exercise control, and evidence is mixed. — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | limitations[7] |
| limitation | The appearance of similar bow-ties in other networks and the proposed rich-club interpretation remain conjectures. — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | limitations[8] |
Content tags
content-observations:
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Transnational corporations form a giant bow-tie and much control flows to a small tightly knit financial core. — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | content_tags.findings[0] |
| finding | The global ownership network contains 600,508 nodes and 1,006,987 ownership ties. — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | content_tags.findings[1] |
| finding | The largest connected component contains three quarters of nodes and 94.2 percent of TNC operating revenue. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.findings[2] |
| finding | The network contains one dominant strongly connected component of 1,347 nodes. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.findings[3] |
| finding | The core is small, dense, and internally retains about three quarters of its firms' ownership. — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.findings[4] |
| finding | Network control is substantially more unequal than wealth and top actors control far more than their wealth predicts. — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | content_tags.findings[5] |
| finding | Combining topology with control rankings shows that powerful actors tend to occupy the core. — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | content_tags.findings[6] |
| finding | The small core collectively holds a large fraction of total global TNC control and is dominated by financial intermediaries. — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | content_tags.findings[7] |
| finding | The existence of ownership ties correlates with financial ties in several countries, motivating a systemic-risk hypothesis. — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | content_tags.findings[8] |
| finding | No study establishes or excludes that the international core has acted as a competition-hampering bloc. — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | content_tags.findings[9] |
| finding | Control concentration is robust across three different ownership-to-control models. — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | content_tags.findings[10] |
| finding | The method generalizes to directed weighted networks carrying resources, energy, or another scalar quantity. — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | content_tags.findings[11] |
| quantity | 43060 — TNCs in the OECD-defined starting list — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | content_tags.quantities[0] |
| quantity | about 30 million — economic actors in Orbis 2007 — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | content_tags.quantities[1] |
| quantity | 600508 — nodes in the resulting TNC network — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | content_tags.quantities[2] |
| quantity | 1006987 — ownership ties in the resulting network — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | content_tags.quantities[3] |
| quantity | 3/4 — share of all nodes in the largest connected component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.quantities[4] |
| quantity | 94.2% — share of total TNC operating revenue in the largest component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.quantities[5] |
| quantity | 1347 nodes — size of the dominant strongly connected core — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.quantities[6] |
| variable | ownership share (direct edge weight and basis for control) — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | content_tags.variables[0] |
| variable | operating revenue (firm economic value aggregated by network control) — “The topological analysis carried out so far does not consider the diverse economic value of firms. We thus compute the network control that economic actors (including TNCs) gain over the TNCs' value (operating revenue) and we address the question of how much this control is concentrated and who are the top control holders. See Figure S3 in Appendix S1 for the distribution of control and operating revenue.” | content_tags.variables[1] |
| variable | network control (actor importance and concentration outcome) — “The topological analysis carried out so far does not consider the diverse economic value of firms. We thus compute the network control that economic actors (including TNCs) gain over the TNCs' value (operating revenue) and we address the question of how much this control is concentrated and who are the top control holders. See Figure S3 in Appendix S1 for the distribution of control and operating revenue.” | content_tags.variables[2] |
| variable | network topology (location and connectivity dimension combined with control ranking) — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | content_tags.variables[3] |
| variable | models used to estimate control (robustness dimension) — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | content_tags.variables[4] |
| variable | investor protection (country-level determinant statistically associated with ownership) — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | content_tags.variables[5] |
| definition | ownership — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | content_tags.definitions[0] |
| definition | ownership network — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | content_tags.definitions[1] |
| definition | control — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | content_tags.definitions[2] |
| definition | network control — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | content_tags.definitions[3] |
| definition | strongly connected component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.definitions[4] |
| definition | bow-tie — “Network topology. ( A ) A bow-tie consists of in-section (IN), out-section (OUT), strongly connected component or core (SCC), and tubes and tendrils (T&T). ( B ) Bow-tie structure of the largest connected component (LCC) and other connected components (OCC). Each section volume scales logarithmically with the share of its TNCs operating revenue. In parenthesis, percentage of operating revenue and number of TNCs, cfr. Table 1 . ( C ) SCC layout of the SCC (1318 nodes and 12191 links). Node size scales logarithmically with operation revenue, node color with network control (from yellow to red). Link color scales with weight. ( D ) Zoom on some major TNCs in the financial sector. Some cycles are highlighted.” | content_tags.definitions[5] |
| definition | core — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | content_tags.definitions[6] |
| definition | concentration — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | content_tags.definitions[7] |
| definition | super-entity — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | content_tags.definitions[8] |
Concepts
terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.
| concept | structure of the control network — not defined in this paper's own words; global corporate-control architecture — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concepts[0] |
| concept | global market competition — not defined in this paper's own words; market outcome potentially affected by control structure — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concepts[1] |
| concept | financial stability — not defined in this paper's own words; system outcome potentially affected by control structure — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concepts[2] |
| concept | transnational corporations — not defined in this paper's own words; globally operating corporations in the ownership network — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concepts[3] |
| concept | ownership network — not defined in this paper's own words; directed weighted network of firms and shareholding ties — “A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporations (TNCs). However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert control over other firms via a web of direct and indirect ownership relations which extends over many countries. Therefore, a complex network analysis [1] is needed in order to uncover the structure of control and its implications. Recently, economic networks have attracted growing attention [2] , e.g., networks of trade [3] , products [4] , credit [5] , [6] , stock prices [7] and boards of directors [8] , [9] . This literature has also analyzed ownership networks [10] , [11] , but has neglected the structure of control at a global level. Even the corporate governance literature has only studied small national business groups [12] . Certainly, it is intuitive that every large corporation has a pyramid of subsidiaries below and a number of shareholders above. However, economic theory does not offer models that predict how TNCs globally connect to each other. Three alternative hypotheses can be formulated. TNCs may remain isolated, cluster in separated coalitions, or form a giant connected component, possibly with a core-periphery structure. So far, this issue has remained unaddressed, notwithstanding its important implications for policy making. Indeed, mutual ownership relations among firms within the same sector can, in some cases, jeopardize market competition [13] , [14] . Moreover, linkages among financial institutions have been recognized to have ambiguous effects on their financial fragility [15] , [16] . Verifying to what extent these implications hold true in the global economy is per se an unexplored field of research and is beyond the scope of this article. However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate control. This was never performed before and it is the aim of the present work.” | concepts[4] |
| concept | Ownership — not defined in this paper's own words; direct and partial firm holding represented as graph links — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | concepts[5] |
| concept | directed weighted graph — not defined in this paper's own words; graph representation of ownership — “Ownership refers to a person or a firm owning another firm entirely or partially. Let denote the ownership matrix, where the component is the percentage of ownership that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graph with firms represented as nodes and ownership ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownership of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownership . If we now consider the economic value of firms (e.g., operating revenue in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2” | concepts[6] |
| concept | ownership share — not defined in this paper's own words; percentage holding in a firm — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | concepts[7] |
| concept | control — not defined in this paper's own words; influence over firm strategy — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | concepts[8] |
| concept | threshold rule — not defined in this paper's own words; majority-based control assignment — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | concepts[9] |
| concept | network control — not defined in this paper's own words; total direct and indirect economic value influenced — “Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership share in a firm, the larger is the associated control over it, denoted as . Intuitively, control corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Control is usually computed from ownership with a simple threshold rule: the majority shareholder has full control. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some control (see Appendix S1 , Section 3.1). In analogy to ownership, the extension to a generic graph is the notion of network control : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network control of . Thus, network control has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).” | concepts[10] |
| concept | indirect links — not defined in this paper's own words; ownership paths propagating control upstream — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[11] |
| concept | shareholders becoming very powerful — not defined in this paper's own words; upstream accumulation outcome — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[12] |
| concept | cycles — not defined in this paper's own words; recursive cross-shareholding structures — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[13] |
| concept | control overestimation — not defined in this paper's own words; bias caused by recursive paths — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[14] |
| concept | new methodology — not defined in this paper's own words; large-network cycle-corrected control computation — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[15] |
| concept | TNC network — not defined in this paper's own words; global network discovered from Orbis — “We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownership pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC network includes 600508 nodes and 1006987 ownership ties.” | concepts[16] |
| concept | listed companies in separate countries and their direct shareholders — not defined in this paper's own words; scope of the prior datasets — “Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholders). Here we are interested in the true global ownership network and many TNCs are not listed companies (see also Appendix S1 , Section 2).” | concepts[17] |
| concept | largest connect component — not defined in this paper's own words; dominant global ownership component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[18] |
| concept | strongly connected component — not defined in this paper's own words; mutually reachable ownership group — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[19] |
| concept | core — not defined in this paper's own words; dominant SCC in the bow-tie — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[20] |
| concept | tightly-knit group of corporations — not defined in this paper's own words; dense mutually owning core — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[21] |
| concept | bow-tie — not defined in this paper's own words; IN/OUT/core/tube/tendril topology — “Network topology. ( A ) A bow-tie consists of in-section (IN), out-section (OUT), strongly connected component or core (SCC), and tubes and tendrils (T&T). ( B ) Bow-tie structure of the largest connected component (LCC) and other connected components (OCC). Each section volume scales logarithmically with the share of its TNCs operating revenue. In parenthesis, percentage of operating revenue and number of TNCs, cfr. Table 1 . ( C ) SCC layout of the SCC (1318 nodes and 12191 links). Node size scales logarithmically with operation revenue, node color with network control (from yellow to red). Link color scales with weight. ( D ) Zoom on some major TNCs in the financial sector. Some cycles are highlighted.” | concepts[22] |
| concept | out-section — not defined in this paper's own words; downstream bow-tie component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[23] |
| concept | in-section — not defined in this paper's own words; upstream bow-tie component — “The computation of control requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenue ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cycles of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected component (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competition [13] , [14] . The second characteristics is that the largest connect component contains only one dominant strongly connected component (1347 nodes). Thus, similar to the WWW, the TNC network has a bow-tie structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected component, or core , is very small compared to the other sections of the bow-tie, and that the out-section is significantly larger than the in-section and the tubes and tendrils ( Figure 2 B and Table 1 ). The core is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownership of firms in the core remains in the hands of firms of the core itself. In other words, this is a tightly-knit group of corporations that cumulatively hold the majority share of each other.” | concepts[24] |
| concept | wealth — not defined in this paper's own words; comparison distribution for network control — “It should be noticed that, although scholars have long measured the concentration of wealth and income [22] , there is no prior quantitative estimation for control. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holders holding cumulatively of the total network control. Thus, the smaller this fraction, the higher the concentration. In principle, one could expect inequality of control to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holders accumulate of the control over the value of all TNCs (see also the list of the top holders in Table S1 of Appendix S1 ). The corresponding level of concentration is , to be compared with for operating revenue. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network control is much more unequally distributed than wealth. In particular, the top ranked actors hold a control ten times bigger than what could be expected based on their wealth. The results are robust with respect to the models used to estimate control, see Figure 3 and Tables S2 and S3 in Appendix S1 .” | concepts[25] |
| concept | top holders — not defined in this paper's own words; actors ranked highest by control — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | concepts[26] |
| concept | super-entity — not defined in this paper's own words; dense core of mutually connected top holders — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | concepts[27] |
| concept | financial intermediaries — not defined in this paper's own words; dominant sector in the core — “The fact that control is highly concentrated in the hands of few top holders does not determine if and how they are interconnected. It is only by combining topology with control ranking that we obtain a full characterization of the structure of control. A first question we are now able to answer is where the top actors are located in the bow-tie. As the reader may by now suspect, powerful actors tend to belong to the core. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the core has about chance of also being among the top holders, compared to, e.g., for the in-section (Table S4 in Appendix S1 ). A second question concerns what share of total control each component of the bow-tie holds. We find that, despite its small size, the core holds collectively a large fraction of the total network control. In detail, nearly of the control over the economic value of TNCs in the world is held, via a complicated web of ownership relations, by a group of TNCs in the core, which has almost full control over itself. The top holders within the core can thus be thought of as an economic “super-entity” in the global network of corporations. A relevant additional fact at this point is that of the core are financial intermediaries. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire core.” | concepts[28] |
| concept | financial network — not defined in this paper's own words; contract network hypothesized from ownership ties — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | concepts[29] |
| concept | systemic risk — not defined in this paper's own words; fragility of densely connected finance — “This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stability? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relations [23] . Thus, in the hypothesis that the structure of the ownership network is a good proxy for that of the financial network, this implies that the global financial network is also very intricate. Recent works have shown that when a financial network is very densely connected it is prone to systemic risk [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.” | concepts[30] |
| concept | ownership relations — not defined in this paper's own words; links that may facilitate blocs — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | concepts[31] |
| concept | blocs — not defined in this paper's own words; potential coordinated groups — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | concepts[32] |
| concept | market competition — not defined in this paper's own words; outcome potentially hampered by blocs — “Secondly, what are the implications for market competition? Since many TNCs in the core have overlapping domains of activity, the fact that they are connected by ownership relations could facilitate the formation of blocs, which would hamper market competition [14] . Remarkably, the existence of such a core in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entity” has ever acted as a bloc. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competition in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownership structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.” | concepts[33] |
| concept | investor protection — not defined in this paper's own words; country determinant of ownership relations — “Two issues are worth being addressed here. One may question the idea of putting together data of ownership across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relations in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protection is statistically relevant [27] . In any case, it is remarkable that our results on concentration are robust with respect to three very different models used to infer control from ownership. The second issue concerns the control that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert control. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holders are at least in the position to exert considerable control, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.” | concepts[34] |
| concept | scalar quantity — not defined in this paper's own words; resource or energy flowing on a directed network — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | concepts[35] |
| concept | rich-club phenomenon — not defined in this paper's own words; dense association among high-degree nodes — “Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantity (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tie structure with a very small and influential core is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tie). However, the fact that the core is so densely connected could be seen as a generalization of the “rich-club phenomenon” with control in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing control in a “fitness model” [29] of network evolution.” | concepts[36] |
| concept | small national samples — not defined in this paper's own words; limited scope of previous investigations — “The structure of the control network of transnational corporations affects global market competition and financial stability. So far, only small national samples were studied and there was no appropriate methodology to assess control globally. We present the first investigation of the architecture of the international ownership network, along with the computation of the control held by each global player. We find that transnational corporations form a giant bow-tie structure and that a large portion of control flows to a small tightly-knit core of financial institutions. This core can be seen as an economic “super-entity” that raises new important issues both for researchers and policy makers.” | concepts[37] |
| concept | Previous work on large control networks — not defined in this paper's own words; methodological predecessor — “Because of indirect links, control flows upstream from many firms and can result in some shareholders becoming very powerful. However, especially in graphs with many cycles (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the control assigned to actors in two cases: firms that are part of cycles (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networks used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodology to overcome the problem of control overestimation, which can be employed to compute control in large networks.” | concepts[38] |
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The Network of Global Corporate Controlterm Abstract The structure of the control networkterm of transnational corporationsterm affects global market competitionterm and financial stabilityterm. So far, only small national samplesterm were studied and there was no appropriate methodology to assess controlterm globally. We present the first investigation of the architecture of the international ownership networkterm, along with the computation of the controlterm held by each global player. We find that transnational corporationsterm form a giant bow-tieterm structure and that a large portion of controlterm flows to a small tightly-knit coreterm of financial institutions. This coreterm can be seen as an economic “super-entityterm” that raises new important issues both for researchers and policy makers.
Introduction A common intuition among scholars and in the media sees the global economy as being dominated by a handful of powerful transnational corporationsterm (TNCs). However, this has not been confirmed or rejected with explicit numbers. A quantitative investigation is not a trivial task because firms may exert controlterm over other firms via a web of direct and indirect ownership relationsterm which extends over many countries. Therefore, a complex network analysisterm·mth [1] is needed in order to uncover the structure of controlterm and its implications. Recently, economic networks have attracted growing attention [2] , e.g., networks of trade [3] , products [4] , credit [5] , [6] , stock prices [7] and boards of directors [8] , [9] . This literature has also analyzed ownership networksterm [10] , [11] , but has neglected the structure of controlterm at a global level. Even the corporate governance literature has only studied small national business groups [12] . Certainly, it is intuitive that every large corporation has a pyramid of subsidiaries below and a number of shareholders above. However, economic theory does not offer models that predict how TNCs globally connect to each other. Three alternative hypotheses can be formulated. TNCs may remain isolated, cluster in separated coalitions, or form a giant connected component, possibly with a core-periphery structure. So far, this issue has remained unaddressed, notwithstanding its important implications for policy making. Indeed, mutual ownership relationsterm among firms within the same sector can, in some cases, jeopardize market competitionterm [13] , [14] . Moreover, linkages among financial institutions have been recognized to have ambiguous effects on their financial fragility [15] , [16] . Verifying to what extent these implications hold true in the global economy is per se an unexplored field of research and is beyond the scope of this article. However, a necessary precondition to such investigations is to uncover the worldwide structure of corporate controlterm. This was never performed before and it is the aim of the present work.
Methods Ownershipterm refers to a person or a firm owning another firm entirely or partially. Let denote the ownershipterm matrix, where the component is the percentage of ownershipterm that the owner (or shareholder ) holds in firm . This corresponds to a directed weighted graphterm with firms represented as nodes and ownershipterm ties as links. If, in turn, firm owns shares of firm , then firm has an indirect ownershipterm of firm ( Figure 1 A ). In the simplest case, this amounts trivially to the product of the shares of direct ownershipterm . If we now consider the economic value of firms (e.g., operating revenueterm·var in USD), an amount is associated to in the direct case, and in the indirect case. This computation can be extended to a generic graph, with some important caveats [17] , Appendix S1 , Sections 3.1 and 3.2 Ownershipterm and Controlterm. ( A&B ) Direct and indirect ownershipterm. (A) Firm has percent of direct ownershipterm in firm . Through , it has also an indirect ownershipterm in and . (B) With cyclesterm one has to take into account the recursive paths, see Appendix S1 , Section 3.1. ( C&D ) Threshold model. (C) Percentages of ownershipterm are indicated along the links. (D) If a shareholder has ownershipterm exceeding a threshold (e.g. ), it has full controlterm (100%) and the others have none (0%). More conservative model of controlterm are also considered see Appendix S1 , Section 3.1.
Each shareholder has the right to a fraction of the firm revenue (dividend) and to a voice in the decision making process (e.g., voting rights at the shareholder meetings). Thus the larger the ownership shareterm in a firm, the larger is the associated controlterm over it, denoted as . Intuitively, controlterm corresponds to the chances of seeing one's own interest prevailing in the business strategy of the firm. Controlterm is usually computed from ownershipterm with a simple threshold ruleterm: the majority shareholder has full controlterm. In the example of Figure 1 C, D , this yields in the direct case and in the indirect case. As a robustness check, we tested also more conservative models where minorities keep some controlterm (see Appendix S1 , Section 3.1). In analogy to ownershipterm, the extension to a generic graph is the notion of network controlterm : . This sums up the value controlled by through its shares in , plus the value controlled indirectly via the network controlterm of . Thus, network controlterm has the meaning of the total amount of economic value over which has an influence (e.g. in Figure 1 D ).
Because of indirect linksterm, controlterm flows upstream from many firms and can result in some shareholders becoming very powerfulterm. However, especially in graphs with many cyclesterm (see Figures 1 B and S4 in Appendix S1 ), the computation of , in the basic formulation detailed above, severely overestimates the controlterm assigned to actors in two cases: firms that are part of cyclesterm (or cross-shareholding structures), and shareholders that are upstream of these structures. An illustration of the problem on a simple network example, together with the details of the method are provided in Appendix S1 , Sections 3.2–3.4. A partial solution for small networks was provided in [18] . Previous work on large control networksterm used a different network construction method and neglected this issue entirely [11] , Appendix S1 , Sections 2 and 3.5. In this paper, by building on [11] , we develop a new methodologyterm to overcome the problem of control overestimationterm, which can be employed to compute controlterm in large networks.
Results We start from a list of 43060 TNCs identified according to the OECD definition, taken from a sample of about 30 million economic actors contained in the Orbis 2007 database (see Appendix S1 , Section 2). We then apply a recursive search (Figure S1 and Section 2 in Appendix S1 ) which singles out, for the first time to our knowledge, the network of all the ownershipterm pathways originating from and pointing to TNCs (Figure S2 in Appendix S1 ). The resulting TNC networkterm includes 600508 nodes and 1006987 ownershipterm ties.
Notice that this data set fundamentally differs from the ones analyzed in [11] (which considered only listed companies in separate countries and their direct shareholdersterm). Here we are interested in the true global ownership networkterm and many TNCs are not listed companies (see also Appendix S1 , Section 2).
Network Topologyterm·var The computation of controlterm requires a prior analysis of the topology. In terms of connectivity, the network consists of many small connected components, but the largest one (3/4 of all nodes) contains all the top TNCs by economic value, accounting for 94.2% of the total TNC operating revenueterm·var ( Table 1 ). Besides the usual network statistics (Figures S5 and S6 in Appendix S1 ), two topological properties are the most relevant to the focus of this work. The first is the abundance of cyclesterm of length two (mutual cross-shareholdings) or greater (Figure S7 and Section 7 in Appendix S1 ), which are well studied motifs in corporate governance [19] . A generalization is a strongly connected componentterm (SCC), i.e., a set of firms in which every member owns directly and/or indirectly shares in every other member. This kind of structures, so far observed only in small samples, has explanations such as anti-takeover strategies, reduction of transaction costs, risk sharing, increasing trust and groups of interest [20] . No matter its origin, however, it weakens market competitionterm [13] , [14] . The second characteristics is that the largest connect componentterm contains only one dominant strongly connected componentterm (1347 nodes). Thus, similar to the WWW, the TNC networkterm has a bow-tieterm structure [21] (see Figure 2 A and Appendix S1 , Section 6). Its peculiarity is that the strongly connected componentterm, or coreterm , is very small compared to the other sections of the bow-tieterm, and that the out-sectionterm is significantly larger than the in-sectionterm and the tubes and tendrils ( Figure 2 B and Table 1 ). The coreterm is also very densely connected, with members having, on average, ties to 20 other members ( Figure 2 C, D ). As a result, about 3/4 of the ownershipterm of firms in the coreterm remains in the hands of firms of the coreterm itself. In other words, this is a tightly-knit group of corporationsterm that cumulatively hold the majority share of each other.
Network topologyterm·var. ( A ) A bow-tieterm consists of in-sectionterm (IN), out-sectionterm (OUT), strongly connected componentterm or coreterm (SCC), and tubes and tendrils (T&T). ( B ) Bow-tieterm structure of the largest connected component (LCC) and other connected components (OCC). Each section volume scales logarithmically with the share of its TNCs operating revenueterm·var. In parenthesis, percentage of operating revenueterm·var and number of TNCs, cfr. Table 1 . ( C ) SCC layout of the SCC (1318 nodes and 12191 links). Node size scales logarithmically with operation revenue, node color with network controlterm (from yellow to red). Link color scales with weight. ( D ) Zoom on some major TNCs in the financial sector. Some cyclesterm are highlighted.
Bow-tieterm statistics.
Notice that the cross-country analysis of [11] found that only a few of the national ownership networksterm are bow-tiesterm, and, importantly, for the Anglo-Saxon countries, the main strongly connected componentsterm are big compared to the network size.
Concentrationterm·def of Controlterm The topological analysis carried out so far does not consider the diverse economic value of firms. We thus compute the network controlterm that economic actors (including TNCs) gain over the TNCs' value (operating revenueterm·var) and we address the question of how much this controlterm is concentrated and who are the top controlterm holders. See Figure S3 in Appendix S1 for the distribution of controlterm and operating revenueterm·var.
It should be noticed that, although scholars have long measured the concentrationterm·def of wealthterm and income [22] , there is no prior quantitative estimation for controlterm. Constructing a Lorenz-like curve ( Figure 3 ) allows one to identify the fraction of top holdersterm holding cumulatively of the total network controlterm. Thus, the smaller this fraction, the higher the concentrationterm·def. In principle, one could expect inequality of controlterm to be comparable to inequality of income across households and firms, since shares of most corporations are publicly accessible in stock markets. In contrast, we find that only top holdersterm accumulate of the controlterm over the value of all TNCs (see also the list of the top holdersterm in Table S1 of Appendix S1 ). The corresponding level of concentrationterm·def is , to be compared with for operating revenueterm·var. Other sensible comparisons include: income distribution in developed countries with [22] and corporate revenue in Fortune1000 ( in 2009). This means that network controlterm is much more unequally distributed than wealthterm. In particular, the top ranked actors hold a controlterm ten times bigger than what could be expected based on their wealthterm. The results are robust with respect to the models used to estimate controlterm·var, see Figure 3 and Tables S2 and S3 in Appendix S1 .
Concentrationterm·def of network controlterm and operating revenueterm·var. Economic actors (TNCs and shareholders) are sorted by descending importance, as given by . A data point located at ( ) corresponds to a fraction of top economic actors cumulatively holding the fraction of network controlterm, value or operating revenueterm·var. The different curves refer to network controlterm computed with three models (LM, TM, RM), see Appendix S1 , Section 3.1, and operating revenueterm·var. The horizontal line denotes a value of equal to . The level of concentrationterm·def is determined by the value of the intersection between each curve and the horizontal line. The scale is semi-log.
Discussion The fact that controlterm is highly concentrated in the hands of few top holdersterm does not determine if and how they are interconnected. It is only by combining topology with controlterm ranking that we obtain a full characterization of the structure of controlterm. A first question we are now able to answer is where the top actors are located in the bow-tieterm. As the reader may by now suspect, powerful actors tend to belong to the coreterm. In fact, the location of a TNC in the network does matter. For instance, a randomly chosen TNC in the coreterm has about chance of also being among the top holdersterm, compared to, e.g., for the in-sectionterm (Table S4 in Appendix S1 ). A second question concerns what share of total controlterm each component of the bow-tieterm holds. We find that, despite its small size, the coreterm holds collectively a large fraction of the total network controlterm. In detail, nearly of the controlterm over the economic value of TNCs in the world is held, via a complicated web of ownership relationsterm, by a group of TNCs in the coreterm, which has almost full controlterm over itself. The top holdersterm within the coreterm can thus be thought of as an economic “super-entityterm” in the global network of corporations. A relevant additional fact at this point is that of the coreterm are financial intermediariesterm. Figure 2 D shows a small subset of well-known financial players and their links, providing an idea of the level of entanglement of the entire coreterm.
This remarkable finding raises at least two questions that are fundamental to the understanding of the functioning of the global economy. Firstly, what are the implication for global financial stabilityterm? It is known that financial institutions establish financial contracts, such as lending or credit derivatives, with several other institutions. This allows them to diversify risk, but, at the same time, it also exposes them to contagion [15] . Unfortunately, information on these contracts is usually not disclosed due to strategic reasons. However, in various countries, the existence of such financial ties is correlated with the existence of ownership relationsterm [23] . Thus, in the hypothesis that the structure of the ownership networkterm is a good proxy for that of the financial networkterm, this implies that the global financial networkterm is also very intricate. Recent works have shown that when a financial networkterm is very densely connected it is prone to systemic riskterm [16] , [24] . Indeed, while in good times the network is seemingly robust, in bad times firms go into distress simultaneously. This knife-edge property [25] , [26] was witnessed during the recent financial turmoil.
Secondly, what are the implications for market competitionterm? Since many TNCs in the coreterm have overlapping domains of activity, the fact that they are connected by ownership relationsterm could facilitate the formation of blocsterm, which would hamper market competitionterm [14] . Remarkably, the existence of such a coreterm in the global market was never documented before and thus, so far, no scientific study demonstrates or excludes that this international “super-entityterm” has ever acted as a blocterm. However, some examples suggest that this is not an unlikely scenario. For instance, previous studies have shown how even small cross-shareholding structures, at a national level, can affect market competitionterm in sectors such as airline, automobile and steel, as well as the financial one [13] , [14] . At the same time, antitrust institutions around the world (e.g., the UK Office of Fair Trade) closely monitor complex ownershipterm structures within their national borders. The fact that international data sets as well as methods to handle large networks became available only very recently, may explain how this finding could go unnoticed for so long.
Two issues are worth being addressed here. One may question the idea of putting together data of ownershipterm across countries with diverse legal settings. However, previous empirical work shows that of all possible determinants affecting ownership relationsterm in different countries (e.g., tax rules, level of corruption, institutional settings, etc.), only the level of investor protectionterm is statistically relevant [27] . In any case, it is remarkable that our results on concentrationterm·def are robust with respect to three very different models used to infer controlterm from ownershipterm. The second issue concerns the controlterm that financial institutions effectively exert. According to some theoretical arguments, in general, financial institutions do not invest in equity shares in order to exert controlterm. However, there is also empirical evidence of the opposite [23] , Appendix S1 , Section 8.1. Our results show that, globally, top holdersterm are at least in the position to exert considerable controlterm, either formally (e.g., voting in shareholder and board meetings) or via informal negotiations.
Beyond the relevance of these results for economics and policy making, our methodology can be applied to identify key nodes in any real-world network in which a scalar quantityterm (e.g., resources or energy) flows along directed weighted links. From an empirical point of view, a bow-tieterm structure with a very small and influential coreterm is a new observation in the study of complex networks. We conjecture that it may be present in other types of networks where “rich-get-richer” mechanisms are at work (although a degree preferential-attachment [1] alone does not produce a bow-tieterm). However, the fact that the coreterm is so densely connected could be seen as a generalization of the “rich-club phenomenonterm” with controlterm in the role of degree [3] , [28] , Appendix S1 , Section 8.2. These related open issues could be possibly understood by introducing controlterm in a “fitness model” [29] of network evolution.
Supporting Information Supporting material: Acronyms and abbreviations, Data and TNC Networkterm Detection, Network Controlterm, Degree and Strength Distribution Analysis, Connected Components Analysis, Bow-Tieterm Component Size, Strongly Connected Componentterm Analysis, Network Controlterm Concentrationterm·def, Additional Tables.
(PDF) Click here for additional data file.