The Core of the Global Corporate Network

Giglio, Ricardo; Lux, Thomas Article — Published Version The Core of the Global Corporate Network Networks and Spatial Economics Provided in Cooperation with: Springer Nature Suggested Citation: Giglio, Ricardo; Lux, Thomas (2021) : The Core of the Global Corporate Network, Networks and Spatial Economics, ISSN 1572-9427, Springer US, New York, NY, Vol. 21, Iss. 3, pp. 681-705, https://doi.org/10.1007/s11067-021-09527-8 This Version is available at: https://hdl.handle.net/10419/287078 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1007/s11067-021-09527-8 The Core of the Global Corporate Network Ricardo Giglio1·Thomas Lux2 Accepted: 2 March 2021 ©The Author(s) 2021 Abstract We investigate the network topology of a comprehensive data set of the worldwide population of corporate entities. In particular, we have extracted information on the boards of all companies listed in Bloomberg’s archive of company profiles in October, 2015, a total of almost 100,000 firms. We provide information on board membership overlaps at various levels, and, in particular, show that there exists a core of directors who accumulate a large number of seats and are highly connected among themselves both at the level of national networks and at the worldwide aggregated level. Keywords Board and director interlocks ·Network core ·Network formation 1 Introduction The structure and formation of corporate networks has intrigued researchers from diverse scientific fields and the public in general for a long time. Corporate governance structures can be cast into the format of a network due to the fact that often members of a corporate board are serving on the boards of two or more companies, thus generating a network of connections between different companies. This network has been characterized as belonging to the class of small world networks (see, Research funding by the European Union’s Seventh Framework Programme under grant agreement no. 612955 for part of this research is gratefully acknowledged. We are also very grateful for the helpful comments of an anonymous reviewer. Thomas Lux [email protected]kiel.de Ricardo Giglio [email protected] 1Department of Production and Systems Engineering, Federal University of Santa Catarina, 88040-900, Florian´ opolis, Brazil 2Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany / Published online: 10 July 2021 Networks and Spatial Economics (2021) 21:681–705 for instance, Battiston and Catanzaro 2004, or Sankowska and Siudak 2016). Consequently, only a few degrees of personal connections are necessary to transverse the whole network.1Some questions naturally arise: Are the network structures the result of purposeful creation of links by some influential elite? Or are they just unintended outcomes from multiple individual and isolated choices? Regardless of the academic discussion, there is also a growing public concern that a relatively small group of people have close personal inter-connections while managing/controlling together a large share of the world economy. The basic empirical question posed by these different viewpoints is whether there is something unexpected in the network structure of board interlocks, i.e. structural features that could not be explained by a simple null model of appointments of board members and that would require the development of more involved sociological and/or economic models of how firms choose their board members with an eye on their connections to other boards. The present paper contributes to the recently burgeoning literature on the structural features of corporate board interlocks. In particular, we revisit the network properties of corporate boards using a nearly comprehensive worldwide database, that also allows us to analyze interlocks across national borders besides domestic ones. Namely, we have gathered all board members listed in Bloomberg’s archive of company profiles. The number of companies for which board information is available, amounts to almost 100,000. This is more than twice the number of listed companies worldwide. Although it seems impossible to identify by what criteria their large data set has been constructed from the even larger universe of all corporate entities worldwide, it is likely that it covers completely all firms beyond a certain size in countries that are integrated in the world economy to a certain degree and that it might constitute a more incomplete sample of the lower end of the size distribution of firms. However, we are mainly interested in those companies whose boards have overlaps with other firms and are not completely isolated. Their number in the database is almost 82,000 and since these will be the more visible ones it seems likely that the data base covers this interesting subsample to a very large extent, if not almost completely. Following the approach of Milakovic¸etal.(2010), we confirm their results of a highly significant deviation from a random null model both for many of the countries included in our data base and for the aggregate worldwide board network as a whole. We also investigate this issue from a slightly different angle by studying the so-called “rich club” phenomenon. The “rich club” statistics quantifies the tendency of the dominant members of a network (in terms of their degree) to form tightly connected communities. Again, we find strong indication of the presence of this phenomenon in the international board network. Taken together, our results, thus, indicate that not only is the accumulation of multiple memberships a non-random event, but also that directors with a high number of seats are unexpectedly highly connected (i.e. have more joint appointments than expected by random assignments, even taking into 1Davis et al. (2003) illustrates the short distances within this network with the observation that a flu virus infecting the J.P. Morgan Chase board in January could spread to 80% of the Fortune 1000 by May through monthly board meetings alone. 682 R. Giglio, T. Lux account the higher chances of overlaps for directors with multiple positions). Beside these key results the paper also provides some additional insights into the features of the worldwide board network in terms of the role of different countries and economic sectors. The paper proceeds as follows: The following section offers an overview over related previous research on board interlocks from a network perspective. Section 3 provides information on the data set used and some descriptive statistics. Section 4 defines the network statistics used in our analysis, and Section 5presents our empirical results on interlocks at the national and international level, and on the importance and degree of international integration of different countries and economic sectors in the worldwide board network. Section 6discusses potential explanations of our findings and Section 7concludes. 2 Related Literature Research on the topology and economic relevance of interlocks between corporate boards has been burgeoning over the last few decades and has benefited greatly from methodological advances in the broader area of network science that has established itself since the 1990s. The long legacy of research in corporate networks is exemplified by the seminal volume by Mizruchi (1982) who studies the close connections between a relatively small sample of 167 firms in the USA from 1904 to 1974 documenting that this sample of the most important firms constitutes what would in modern terminology be denoted a large connected component. The development of structural network models has spurred a large literature attempting to characterise board interlocks using the new formal approach to network analysis from the natural sciences. Evidence for small-world properties of this network has been reported by, among others, Davis et al. (2003), Conyon and Muldoon (2006) and Kogut (2012) for the U.S., Milakovic¸etal.(2010), (2015) and Raddant et al. (2017) for Germany, Battiston and Catanzaro (2004), Bellenzier and Grassi (2014) and Clemente et al. (2018) for Italy, Raddant and Takahashi (2019) for Japan and Biswas (2020) for India. These contributions find that board networks resemble small world networks and exhibit positive assortativity. Often the authors argue that the concentration of a multitude of board seats in the hand of few individuals constitutes a significant deviation from a null model in which board positions would be independent random draws assigning a fixed population of directors to a given number of board positions. Similar results are documented for networks of ownership by Kogut and Walker (2001) for German data and by Vitali et al. (2011) and Glattfelder and Battiston (2019), for a broad international data base. Several of the mentioned papers go beyond identifying structural characteristics and attempt to identify leading players within the network. Milakovic¸etal.(2010), (2015) and Raddant et al. (2017) show that there is a significantly non-random hierarchical structure in the German board network with a closely knit ”core” that remains structurally stable over time. Milakovic¸etal.(2015) also emphasize that this unlikely concentration of multiple 683The Core of the Global Corporate Network positions within a single subset of the largest companies survives over time, irrespective of the change of personnel and even the entry and exit of firms to and from the corporate core of the economy. In a similar vein, Vitali et al. find a “bow-tie” structure of the international ownership network in which transnational corporations constitute the closely connected core. The finding of significant clustering of interlocks now apperas to be a wellestablished empirical fact. Possible explanations of this phenomenon fall into various categories: (i) corporate social interlocks could be a result of favoritism and thus would reflect existing personal relationships in the elitistic circles of a society, (ii) joint board positions could be an effective way of learning about managerial practices or (iii) could be a reflection of material entanglement of interests between firms, such as a link with its corporate clients, or firms along a supply chain. Finally, (iv) board interlocks could just be the imprint of certain individuals with extraordinary capabilities as supervisors being in high demand so that they receive multiple offers to serve on corporate boards. Any of the more economically oriented explanations should, in principle, be testable by scrutinizing the hypothesis of a link between board overlaps and firm performance. An increasing body of research has indeed embarked on investigating whether board interlocks are an imprint of ‘crony’ capitalism or whether they are a valuable source of acquisition of information or expertise to a firm. However, empirical evidence on this issue is mixed. Some studies did rather find a negative effect of busy directors on performance criteria. Such a finding would be in line with decreasing returns to supervision but would demand a non-economic explanation for why interlocks exist in the first place despite the inefficiency of overburdened holders of multiple seats. Andres and Lehmann (2010), for instance, regress various measures of firm performance on centrality statistics computed for the members of the supervisory boards of German DAX30 companies. They find that higher centrality is associated with lower performance but higher compensation of board members, a result that is in line with the sociological hypothesis of an organisational elite that is not chosen according to economic performance criteria. The findings of Andres and Lehmann (2010) have been confirmed by B¨ ohler et al. (2010) showing also that only foreign investors are sensitive to this negative effect of high connectivity while domestic investors in Germany appear rather to assign value to it. Results for other countries are somewhat more muted: Biswas (2020) finds that in the Indian corporate board network companies which via joint appointments act as a bridge between otherwise unconnected communities enjoy a positive effect of these interlocks on performance. Faia et al. (2020) present evidence that supports the economic view of value creation through communication. They analyse the effects of a change in corporate regulations on the value of Italian listed companies. In 2011, a law has come into effect prohibiting multiple board positions in insurance and finance companies. As Faia et al. show companies whose centrality in the network had been reduced by this regulation suffered from losses in the stock market. Hence, this provides evidence of the stock market assigning a positive value to higher centrality. An even broader, closely connected literature studies the effects of connections between directors via social networks. For instance, Hwang and Kim (2009)findthat 684 R. Giglio, T. Lux the compensation of CEOs is higher if they are socially connected to some directors of the same company. Nguyen (2012) shows that accountability of CEOs is lower if they are socially connected with directors of the same firm. Souther (2018) finds that closer social proximity within a board is correlated to lower market valuation and higher director compensation. Since our analysis uses data on corporate boards only, we are unable to shed light on the relationship between board interlocks and economic performance. However, we will provide evidence that board interlocks across national borders show similar hierarchical tendencies like national ones. 3 Data Description Data was collected from the Bloomberg website in October 2015. More specifically, board membership information both from public and private companies was collected from specific pages such as http://www.bloomberg.com/markets/api/management/ board/DBK:GR for Deutsche Bank, as an example. Other company specific information (such as address and sector classifications) were collected from pages such as http://www.bloomberg.com/markets/api/quote-page/DBK:GR, again for Deutsche Bank as an example. Board members of all companies listed were extracted and links between boards via common members have been established. The complete list of companies is available in the http://www.bloomberg.com/robots.txt web file. For a similar approach of information retrieval through web crawling of a large data base see Fire and Puzis (2004). Board membership information was represented by means of incidence matrices, which allow for the calculation of network measures. Two directors are said to be connected if they hold seats in the same company, and two companies are said to be connected if at least one common director serves on their boards. This network can be analyzed in its bipartite form, and it can be transformed into a unipartite network of overlaps considering either directors or companies as nodes. In both cases, the incidence matrix Mis the same, and the respective adjacency matrices can be computed by the projections D=MMTand C=MTM. A particular feature of the network of board affiliations Dis the existence of node communities by construction (the boards), resulting in complete subgraphs in which all nodes (the board members) are connected to each other. This feature has an impact on some specific network properties: the existence of such communities produces trivially high average clustering coefficients, for example. In addition, the degree of a board member depends on the size of the boards in which she/he has a position. Hence, two members in equally connected but differently sized boards would have different degrees. To alleviate this particular feature, we restricted attention to the more interesting cases of directors who serve in at least two boards. With this restriction, all the trivial links within the same board are removed, and only connections between directors are counted as links that extend beyond one single board. As a consequence, the degree of each director now counts his contacts to other directors who have at least two board positions, and is not inflated by the number of single-seat colleagues in the same board (which actually is to some extend an idiosyncratic number for different 685The Core of the Global Corporate Network firms and not of major interest for our analysis). The subgraph formed by the network of board members holding at least b=2 positions (referred to as D2) keeps all important information with regard to overlaps in the entire network, but removes the influence of different board sizes. Thus, here only the network of members holding multiple (at least two) positions is considered. It is worthwhile to note that this definition of b-core (bfor board positions) is different from that of k-core (kfor degree). A k-core (or k-degenerate graph) is the (unique) maximal induced subgraph with nodes of a minimum degree of at least k. Alternatively, the k-core is the (unique) result of iteratively deleting nodes that have degree less than k, in any order. The total number of companies in Bloomberg’s database is 1,832,936 of which 66,375 (3.6%) are publicly listed, representing 99% of the world’s market capitalization. However, there is no board information for the majority of non-listed companies, neither for some of the listed companies. The total number of companies with board management information is 98,658 of which 60,631 (61.4%) are public and 38,027 (38.6%) are private. The number of not completely isolated companies amounts to 71,562 in total, divided into 51,256 (71.6%) public and 20,306 (28.4%) private companies. When considering only the largest connected component of Cthere are 58,352 companies, of which 42,026 (72%) are public and 16,326 (28%) are private. In total, there are 311,939 board members holding 586,382 board positions, yielding an average number of board positions of 1.87. If completely isolated directors are excluded (that is, members of a disconnected board), 299,982 directors with at least one connection remain. If considering only those directors holding at least two board positions (these are responsible for the links between companies), 102,901 directors remain. In addition to these restrictions, when only the largest connected component (LCC)ofD2is considered, 85,046 directors remain. These raw numbers show that engaging in board interlocks is not an activity of public companies only, but rather that there is a strong interaction between them and the private companies. Available records cover companies from 156 countries, but with a high degree of concentration of companies among a small set of them. For instance, more than 90% of the companies are from only 23 countries. The five countries hosting most companies are (in order of their number of companies) the United States, Canada, United Kingdom, Japan, and China. In the following, we provide some basic network statistics for the overall network and those of some selected countries. Table 1displays information on the number of nodes and links in the network of companies, the average degree (i.e., number of connections of nodes) , the average shortest path length, the diameter, radius, density, number of triangles and average clustering coefficients. The diameter and the radius are the maximum and the minimum over all nodes of the so-called eccentricity, i.e., the maximum distance between a node and any other. The density gives the number of observed links as a fraction of all possible connections. The number of triangles simply counts the number of triples of nodes that have connections arranged in a circular manner, and the clustering coefficient is defined as the fraction of such observed triangles among the neighbors of a node averaged over all nodes. As Table 1shows, all our networks, national or global, feature the most common indicators of small-worldness: communities, short diameters and average shortest 686 R. Giglio, T. Lux Table 1 Number of nodes and edges, average degree and shortest path length ( ¯ L), diameter, radius, density, number of triangles and average clustering coefficient ( ¯ C)fortheLCC of the network of companies C, and for the networks of companies from selected countries Network LCC(C) US UK DE FR BR RU IN CN nodes 58,352 22,423 8,739 2,189 3,274 874 1,005 3,335 6,733 edges 454,352 121,227 44,507 14,916 25,958 5,273 6,410 14,090 29,776 ¯ deg 15.57 10.81 10.19 13.63 15.86 12.07 12.76 8.45 8.84 ¯ L7.17 6.34 7.43 5.64 5.07 5.07 5.16 5.11 6.83 Diam.26 2631171812131523 Rad. 14 14 16 9 9 7 7 8 12 Dens. 0.0003 0.0005 0.0012 0.0062 0.0048 0.0138 0.0127 0.0025 0.0013 Triang. 5,953,893 956,952 394,665 237,042 386,451 58,263 81,21 104,436 237,501 ¯ C0.55 0.48 0.54 0.61 0.64 0.72 0.67 0.45 0.51 path lengths. In Table 2we compare the empirical statistics to those of an Erd˝ osR´ enyi random network ER(N,M) with the same number of nodes N and edges M as the LCC of C, showing that the empirical number of triangles is several orders of magnitude higher than what one would expect if edges were created randomly between existing nodes. Hence, local clustering (i.e. interlocks) is a pervasive feature of this network (recall that we have at this stage already removed the built-in clustering of the board structures). 4 Measures of Concentration We are mostly interested in this paper in exploring various dimensions of concentration of links in the global corporate board network that our data identifies. One obvious avenue is to quantify the influence of different countries and different sectors of the economy within this global network. We analyze the relative position of countries and sectors using two different types of statistics: One is the concept of centrality which identifies the relative importance of a node within a network. Here we Table 2 Comparison between an ER(N,M) random network with the same number of nodes and edges as the LCC of the company network C Global (LCC of C)ER(N,M) Nodes 58,352 58,352 Edges 454,352 454,352 Average degree 15.57 15.57 Density 0.0003 0.0003 Triangles 5,953,893 1,968 Average clustering coefficient 0.55 1.40e-4 687The Core of the Global Corporate Network apply the concept of eigenvector centrality which assigns higher weights to the links between nodes with high centrality scores. The eigenvector centrality of an adjacency matrix A=(aij )between a set of nodes is then defined by the equation Ax =λx (1) in which λis the largest eigenvalue which exists and is positive given that A is a matrix with non-negative entries. Note that non-negativity of all elements of the eigenvector is only guaranteed for the one associated to the largest eigenvalue, so that we can only define a non-negative measure of centrality for this eigenvalue (cf. Newman 2008). The k-th element of the eigenvector νassociated with the largest eigenvalue then provides us with the measure of centrality for node k. Another aspect of interest is in how far the interlocks of a country or sector with other countries or sectors are diversified or not. We measure diversification using the Shannon entropy applied to interlocks of corporate boards: H(X) = −N n=1P(x i)log(P (xi)) log(N) (2) In our application, Nis the number of countries (sectors), and P(x i)are the relative frequencies of interlocks of a country (sector) with all other countries i= 1,..,N. It ranges from 0 (when all interlocks are with only one specific foreign country (sector)) to 1 (when all connections are evenly distributed across all other countries (sectors)). Moving on to the specific structure of the overall global network and its subsets, we are interested in whether we can confirm previous results for national board interlocks that have found statistical support for a non-random concentration of economic power in a network “core”. We follow Milakovic¸etal.(2010) in testing whether this degree of concentration of positions is statistically significantly different from what one would get under random assignment of director positions to the pool of individuals (which by construction would mean that with Xdirectors assigned to Y board positions and X<Y, a certain number of persons had to end up with multiple positions). This setting suggests as null model the Binomial probability of observing multiple board memberships in an independent sequence of kBernoulli trials with probability p. The probabilities for observing B=b(b=1,2,...,B)board memberships of a person is given under the random null model by Eq. 3. In this equation the parameters of the Binomial distribution are the mindependent Bernoulli draws for the “excess” in board positions, i.e. mis the overall number of board positions minus the number of directors in the data base, m=Y−X,andpthe success probability which is simply the inverse of the number of directors p=1 X: P(B =b) =m bpb(1−p)m−b.(3) We support this analysis by a related one which approaches the same phenomena from a somewhat different angle: the so-called rich club coefficient. The rich club phenomenon refers to the tendency of the dominant elements of the system to form tightly interconnected communities (Colizza et al. 2004). Considering the core of corporate networks, the existence of the rich club phenomenon might indicate the 688 R. Giglio, T. Lux False japan cote divoire cayman islands azerbaijan cambodia hungary taiwan cyprus barbados tanzania united republic of lithuania mongolia united kingdom puerto rico argentina norway sierra leone bahrain australia zambia french polynesia georgia belgium kazakhstan netherlands falkland islands malvinas denmark philippines latvia namibia switzerland guinea bulgaria jamaica greenland lebanon malaysia mozambique reunion niger canada qatar curacao sudan kuwait panama sweden luxembourg venezuela united arab emirates madagascar sri lanka china thailand belize ukraine trinidad and tobago oman finland saint pierre and miquelon mauritius jersey pakistan romania czech republic myanmar egypt guam papua new guinea united states austria congo colombia new zealand turkey saudi arabia estonia france bahamas slovakia gibraltar peru nigeria ecuador israel ireland san marino tajikistan togo jordan chile south korea spain isle of man virgin islands british morocco virgin islands us gabon mali russian federation hong kong ghana no-data portugal mexico greece india svalbard and jan mayen lesotho south sudan botswana italy south africa malta bermuda brazil singapore faroe islands korea south macau sar germany macedonia republic of poland indonesia liechtenstein guernsey monaco Fig. 6 Country level aggregation of international interlocks. The weighted connection between two countries is defined by the number of directors holding simultaneous positions in companies from both countries. Directors whose positions are all in companies of the same country are discarded. Nodes are sized and colored by eigenvector centrality Table 4presents a different perspective, not based on centrality, but rather on the relation between national and international interlocks. The first column shows the fraction of foreign interlocks over all multiple board positions of directors on the board of any country, while the second shows the normalized Shannon entropy of Eq. 2of the distribution of connections as a measure of how diversified or globalized a country is in its interlocks with other countries. Note that Hranges from 0 (when all connections have the same country as an end-point) to 1 (when the connections are equally distributed among all countries). In order to avoid that very small countries (such as Myanmar, Gabon, and Oman) dominate the top of the list (sorted by ratio between foreign and domestic interlocks) only because they have very few companies, we have arbitrarily removed all countries with less than 400 personal interlocks. 695The Core of the Global Corporate Network Table 4 Top and bottom ten and additional selected countries ordered by the ratio between the number of foreign and domestic interlocks, shown in the first column, while the second presents the entropy of the distribution of connections as a measure of how globalized a country is in contrast to strong local connections to only a few other countries Country Ratio Entropy Belgium 1.856 0.640 Luxembourg 1.850 0.676 Netherlands 1.811 0.641 Switzerland 1.712 0.627 Portugal 1.679 0.733 Poland 1.664 0.744 Cyprus 1.607 0.685 France 1.583 0.606 Finland 1.515 0.603 Denmark 1.502 0.620 ... ... ... Germany 1.317 0.593 Italy 1.317 0.611 United Kingdom 1.127 0.532 ... ... ... Israel 0.818 0.480 Thailand 0.813 0.540 Australia 0.796 0.474 China 0.737 0.433 United States 0.696 0.435 India 0.679 0.463 Canada 0.676 0.401 Taiwan 0.543 0.415 South Korea 0.481 0.462 Japan 0.380 0.371 The highest fraction of interlocks is observed for smaller European countries: Luxembourg, the Netherlands, Switzerland, and Belgium. However, also larger European countries like Germany, France and Italy are characterized by a relatively high degree of international interconnectedness of their business elite whereas the lower half of the spectrum is exclusively populated by the large Asian countries, the U.S. and Canada. While we would expect a size effect to play a large role in the U.S., the differences between the roughly similar size spectrum of Asian and European countries appears as the most striking outcome of this analysis. Smaller European countries are all characterized by a higher ratio of international than domestic interlocks, which along with a high entropy value (as a measure of diversification of connections), indicates the later are the most open countries as concerns the internationalization of their 696 R. Giglio, T. Lux business elite. Even the larger European countries (France, Germany, Italy, UK) are characterized by a ratio of foreign to domestic interlocks above unity. In contrast, the United States, China, India and the industrial countries of the Far East all are characterized by values below one and smaller numbers of their entropy statistics than the European Union members. A closely related interesting aspect is the average profile of the firms engaging in international interlocks. Assortativity is the preference of nodes to attach to others that are similar with regard to some attribute (Newman 2002). The classic example is the degree assortativity, given by the Pearson correlation coefficient between the degrees of nodes at either end of the edges. As a correlation coefficient, it ranges from -1 (perfect dissortativity) to 1 (perfect assortativity). Here we consider connectivity wih respect to the country of origin of a board. Since most interlocks often happen within countries, we generally observe positive assortativity with respect to this characteristic. Figure 7presents the overall country assortativity of the network of companies for varying thresholds of minimum degree, that is, for each degree kthe country assortativity is calculated considering only those nodes with degree higher than k. A consistent decrease in assortativity for growing values of kis observed indicating that the higher the number of connections, the higher the chances of engaging in international interlocks. Hence, the more interconnected a board is, the higher the chance that some of its directors will serve on boards in more than one country. Fig. 7 Country assortativity of the network of companies for varying thresholds of minimum degree, that is, for each degree kthe country assortativity is calculated considering only those nodes with degree higher than k. The higher the number of connections, the higher the fraction of international interlocks 697The Core of the Global Corporate Network 5.4 Sector Connectivity Countries are just one category that could be used to aggregate the entries of our universe of worldwide corporate boards. Another interesting aspect is to differentiate between firms by sectors of economic activity. Table 5presents the number of positions, directors, and companies by sectors of economic activity. The last two columns show the average number of board positions per director and the average board size. It can be seen that both the banking and the insurance industries are characterized by an average board size significantly higher than the others. There is vast literature supporting the prominent role of financial institutions in the networks formed by interlocking directorates (e.g., Davis et al. 2003). According to Kroszner and Strahan (2001), financial institutions depend more on the business scan than other companies, so for them it should be more necessary to maintain a large number of board connections. Table 6presents the eigenvector centrality (first column) and the diversity of connections (second column) by sector of economic activity. While the eigenvector centrality shows which are the most central sectors of activity in the network, the diversity of its connections indicates whether the sector is characterized by interlocks only with a few other related sectors or a large part of the network. The diversity of the connections is again defined as the normalized Shannon entropy of the weighted connections. As we can see, the entropy ranges from close to 0 when the sector basically connects to one or just a few other sectors (like Metals & Mining, for example), to close to 1 if the sector connects more or less equally to all other sectors (like Banking, for example). The analysis of the role of sectors in the worldwide board network reveals some interesting features: First, the most central sectors are Utilities,Banking and Oil, Gas & Coal, with quite some difference of their eigenvector centrality to the bulk of remaining sectors. In terms of diversity of linkages, we find that most sectors are connected via board overlaps to many other sectors. The pertinent entropy values are hovering around 0.8 −0.9 in the wide majority of the cases. The only extreme outlier is Utilities, the sector with the highest eigenvector centrality whose entropy is a low 0.226. This is explained by the relatively small sector size compared to the large number of conections it has, both within and between sectors. The last two columns of Table 5show that theUtilities sector exhibits both the highest average board size and the highest average accumulation of positions by directors among all sectors. In addition, approximately 20% of all linkages in the network of sectors are within the Utilities sector (self-loops), followed by Metals & Mining with 5% and Oil, Gas & Coal with 2%. Utilities also has the highest share of interlocks when self-loops are excluded (3.8%, followed by Banking and Oil, Gas & Coal with 3.1% each). The central position of the Banking sector is, of course, as expected as the financial industry should have connections to all other sectors due to its service function. Note, however, that its entropy does not appear unusual which speaks against the popular perception that this sector operates as the tacit control center of modern capitalist economies. Drawing on 100 large US industrial corporations between 1969 and 1979, Fligstein and Brantley (1992) hypothesize that interlocks with banks should be positively associated with corporate performance and debt/equity ratios. However, 698 R. Giglio, T. Lux their findings revealed a negative association between bank interlocks and most measures of profitability. In this sense, Mintz and Schwartz (1986) speak about financial hegemony: banks would play a central role in unifying the network of corporations Table 5 Number of positions, directors, and companies by sectors of economic activity. The last two columns show the average number of board positions per director and the average board size in number of positions Sector Positions (1) Directors (2) Companies (3) (1)/(2) (1)/(3) Metals & Mining 32411 12073 6089 2.68 5.32 Asset Management 18728 14219 4864 1.32 3.85 Oil, Gas & Coal 27825 12189 4455 2.28 6.25 Consumer Products 27220 16837 4423 1.62 6.15 Software 19685 13323 4227 1.48 4.66 Banking 38766 26726 4059 1.45 9.55 Real Estate 24635 14961 3845 1.65 6.41 Commercial Services 15660 13038 3832 1.20 4.09 Media 20938 13161 3817 1.59 5.49 Biotech & Pharma 22535 11806 3568 1.91 6.32 Retail - Discretionary 16240 10576 3126 1.54 5.20 Engineering & Construction Svcs 16180 11515 3068 1.41 5.27 Hardware 17042 11504 2823 1.48 6.04 Specialty Finance 13728 10532 2526 1.30 5.43 Utilities 24311 8986 2497 2.71 9.74 Chemicals 16223 11101 2436 1.46 6.66 Transportation & Logistics 13767 8577 2340 1.61 5.88 Machinery 12226 8690 2194 1.41 5.57 Electrical Equipment 12656 9071 2128 1.40 5.95 Health Care Facilities & Svcs 11549 8719 2112 1.32 5.47 Medical Equipment & Devices 10833 6321 1875 1.71 5.78 Home & Office Products 9864 7374 1819 1.34 5.42 Apparel & Textile Products 10672 7972 1808 1.34 5.90 Consumer Services 7633 6910 1779 1.10 4.29 Automotive 10944 6545 1589 1.67 6.89 Insurance 12506 7471 1574 1.67 7.95 Technology Services 8971 6157 1571 1.46 5.71 Gaming, Lodging & Restaurants 9614 6007 1510 1.60 6.37 Iron & Steel 9615 5712 1440 1.68 6.68 Telecom 9190 4259 1289 2.16 7.13 Institutional Financial Svcs 7444 4956 1189 1.50 6.26 Semiconductors 7896 4965 1173 1.59 6.73 Manufactured Goods 6211 4956 1135 1.25 5.47 Renewable Energy 6104 4135 1114 1.48 5.48 699The Core of the Global Corporate Network Table 5 (continued) Sector Positions (1) Directors (2) Companies (3) (1)/(2) (1)/(3) Construction Materials 7292 4676 1088 1.56 6.70 Distributors - Discretionary 4658 3811 1034 1.22 4.50 Retail - Consumer Staples 6667 3380 982 1.97 6.79 Recreation Facilities & Svcs 4654 3700 910 1.26 5.11 Waste & Environ Svcs & Equip 4119 3034 814 1.36 5.06 Containers & Packaging 4217 3055 682 1.38 6.18 Distributors - Consumer Staples 3095 2353 587 1.32 5.27 Passenger Transportation 4695 2260 528 2.08 8.89 Aerospace & Defense 3599 2003 489 1.80 7.36 Forest & Paper Products 2726 1770 444 1.54 6.14 Leisure Products 2350 1789 414 1.31 5.68 Transportation Equipment 2822 1547 396 1.82 7.13 Industrial Services 2371 1573 389 1.51 6.10 linked through shared directors. In their view, the inner circle of directors with multiple and diverse affiliations, would maximize overall profits, rather than acting in the interest of particular companies. From a different perspective, Ratcliff (1980) points out that no evidence of performance gains by interlocks with the financial sector has been found. Thus, it is argued that the financial institutions are not necessarily central, but different: banks are just special by their very nature in the sense they are holders and distributors of capital. 6 Discussion The present paper has contributed to the recently burgeoning literature on the network structure of corporate board interlocks. A number of previous studies have already demonstrated that corporate board and director networks exhibit assortative mixing, proximity to a small-world structure and a high concentration of multiple board memberships that would be highly unlikely to occur by chance under sensible null models for the formation of links in the board network. Here we have confirmed this finding using a large international data base. As we have demonstrated in Section 5.1 above, the deviation of the relative frequencies of multiple board positions from a Binomial null model holds not only for a broad range of countries (some of these not covered in previous literature), but it also applies to the worldwide network as a whole. It has also be shown that the subset of directors with large numbers of simultaneous positions exhibits the “rich-club” phenomenon, i.e. they are more closely connected among themselves than other members of the network. Again, this result could be shown to be a highly significant deviation from a random null model, i.e. , even taking into account that a director with multiple positions would by the nature of such 700 R. Giglio, T. Lux Table 6 Eigenvector centrality (first column) and connections diversity (second column) by sector of economic activity Sector Eigenvector Entropy Utilities 0.421 0.226 Banking 0.360 0.819 Oil, Gas & Coal 0.345 0.678 Consumer Products 0.226 0.855 Real Estate 0.223 0.813 Metals & Mining 0.214 0.400 Asset Management 0.206 0.865 Media 0.186 0.797 Insurance 0.183 0.849 Telecom 0.179 0.826 Chemicals 0.169 0.854 Retail - Discretionary 0.141 0.862 Biotech & Pharma 0.134 0.623 Gaming, Lodging & Restaurants 0.134 0.836 Engineering & Construction Svcs 0.130 0.875 Transportation & Logistics 0.130 0.824 Software 0.126 0.724 Retail - Consumer Staples 0.122 0.837 Specialty Finance 0.108 0.894 Hardware 0.107 0.852 Iron and Steel 0.107 0.842 Commercial Services 0.106 0.907 Electrical Equipment 0.099 0.914 Automotive 0.096 0.869 Technology Services 0.088 0.888 Institutional Financial Svcs 0.084 0.871 Medical Equipment & Devices 0.080 0.683 Machinery 0.076 0.896 Passenger Transportation 0.076 0.860 Renewable Energy 0.070 0.820 Apparel and Textile Products 0.068 0.865 Health Care Facilities and Svcs 0.067 0.862 Construction Materials 0.066 0.882 Home & Office Products 0.054 0.906 Industrial Services 0.048 0.780 Semiconductors 0.045 0.791 Aerospace & Defense 0.045 0.912 Transportation Equipment 0.044 0.814 Consumer Services 0.041 0.916 701The Core of the Global Corporate Network Table 6 (continued) Sector Eigenvector Entropy Containers & Packaging 0.039 0.918 Recreation Facilities & Svcs 0.033 0.888 Manufactured Goods 0.031 0.902 Distributors - Discretionary 0.028 0.918 Forest & Paper Products 0.027 0.858 Waste & Environ Svcs & Equip 0.024 0.896 Distributors - Consumer Staples 0.017 0.871 Leisure Products 0.011 0.904 Design, Mfg & Distribution 0.008 0.839 appointments be more connected to other directors than a board member with a single position, the high connectivity within the group of high-degree directors is still highly significant. This confirms previous findings for the German board network by Milakovic¸etal.(2010) and provides a more rigorous underpinning of their graphical analysis. Since our analysis is of phenomenological nature, the interpretation of the results in terms of the factors governing board appointments is still open. What we can infer from our results is that there are intrinsic forces in the appointment process that work in favor of a certain concentration of positions in few hands as well as strong connections within the group of directors with multiple memberships. Potential explanatory factors for these tendencies could be economic mechanisms that via signaling of skills make the appointment to another board more likely if a director had already served in one or more positions (Williamson and Cable 2003). Note that this would imply benefits from multiple appointments that overcompensate for the incurred costs of reduced marginal productivity of directors in multiple positions. Besides individual skill, joint board positions could be the result of companies trying to preserve personal relationships along their supply chains or with their main provider of capital and credit in the financial sector. The analysis of the nature of multiple positions in the German economy by Milakovic¸etal.(2010) lends very little support to the former hypothesis and somewhat more to the latter. In contrast to “economic” hypotheses focusing on comparative advantages of busy directors as individuals or advantages in keeping directors busy to secure direct links to important business partners, “sociological” hypotheses would see board interlocks as the consequence of the formation and reproduction of a business elite irrespective of direct economic concerns (e.g. Mizruchi 2000). Evaluations of the influence on economic success of having directors with multiple positions on a company board do not provide convincing arguments for the “economic” viewpoint (c.f. Andres and Lehmann 2010). Some studies indeed provide results supporting the “sociological” view: for instance, Hwang and Kim (2009) show that CEO compensation is higher if there exist social connections between CEO’s and board directors (outside their professional environment), while Nguyen (2012) finds less accountability of 702 R. Giglio, T. Lux the directors if social connections exist. Fracassi and Tate (2012), in addition, document that social connections favor appointment decisions and reduce the monitoring efficiency of the board. A causal analyses of the factors determining the appointment of directors would require an approach different from the present one. First, a necessary precondition for such a study would be the availability of network data at different points in time. Using dynamic models of network formation (Lusher et al. 2013; Snijders 1996;2001), one could then attempt to disentangle various factors, from individual determinants (skill), over bilateral characteristics (social ties between incumbent directors and new candidates) to structural characteristics (ensuring interlocks with certain business partners). An example of a study using such a framework is Gygax et al. (2017) who investigate whether board interlocks have an influence on leverage decisions of firms. They find that board overlaps make leverage policies more similar, while existing similarities in leverage strategies are not a determinant of board appointments. Unfortunately, our data are neither of the required dynamic nature, nor do they come with sufficient exogenous information on board members of companies. Nevertheless, moving from the current phenomenological analysis to a causal framework should be high on the agenda of this research area. 7 Conclusion We have established a number of stylized facts for a large dataset extracted from Bloomberg’s archive of company profiles that should cover to a large extent the segment of large and medium-sized companies of all countries that are integrated sufficiently into the global economy. Our findings confirm previous evidence for national board networks that find a closely connected core around a small set of board members with a relatively large number of positions. Practically the same deviation from a random benchmark is observed for a variety of countries as well as for the entire aggregated network. This supports the view of Milakovic¸etal.(2015)ofaparticular type of self-organization of the board network into a distinctly non-random structure. Since we have confined ourselves to a data-analytical study here, we cannot provide an explanation of this seemingly very robust phenomenon. Given the strong evidence that exists by now on the formation of a closely connected core in board network structures, the analysis of potential generating mechanisms for this emergent feature should be an important task for future research. Funding Open Access funding enabled and organized by Projekt DEAL. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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