The three articles in this issue are the result of a call for papers on the topic of 'Comparative and Transnational Corporate Networks: Clubs, Small Worlds, and Globalization'. The call made the following request:
Up until two and half decades ago, the United States dominated the statistics on foreign direct investment. The United Kingdom retained a prominence dating back to its colonial legacy, and smaller countries, such as Sweden, generated important multinational corporations given their national size. Globalization has shattered this dominance. There are now multinational corporations from many countries. Countries such as China are moving rapidly as location for foreign companies to a home of their own multinational corporations. Yet, amidst these changes, national corporate ties have remained remarkably persistent, and this persistence in the form of ownership networks and governance has been very robust to the in-roads made by globalization.
In the past years, our abilities to analyze these changes have grown remarkably. Thanks to the advances in the study of networks, new methods are able to explore robustness or change even though ties among firms are very sparse at a national and global level. These methods include methodologies of small worlds, of scale-free networks, and dynamic statistical and simulation models. We welcome submissions to this special issue that employ these new methods.
At the same time, the rhetoric of globalization reflects battles among clubs and cliques. This rhetoric is anchored in the fashioning of new governance codes as well in the polemics of economic patriotism. Articles on the politics and rhetorics that are conceptually tight and that rely upon historical, statistical, or innovative qualitative methods are actively sought for this special issue.
Two of the papers responded directly to this call by providing an analysis of the over-time changes in a comparative framework. The first article, by Jerry Davis, provides a broad perspective on the changes in ownership and governance in the United States. It frames very nicely the two articles that follow by providing an important historical sketch over the collapse of the bank-dominated finance network in the United States that has become replaced by a mutual fund domination. As continental Europe has historically been considered as bank dominated but is currently under going diverse transformations, the United States story presents a potential avenue of development.
The principal learning from the Davis article is that changes in the sources and vehicles of financial investment influence governance. In the seminal article with Mark Mizruchi (Davis and Mizruchi, 1999), Davis and Mizruchi found that the disintermediation of banks and the direct accessing of capital through issuing bonds lead to the disintermediation of banks. These changes in lending lead to a reduction of the centrality of banks as the providers of directors to executive boards. Thus, they found a direct link between ownership and board representation.
The article by Davis in this issue does not show this result. Whereas mutual funds have grown to be a primary owner of equity in the United States, the funds rarely put directors onto boards. In the case of Fidelity (which is dominantly owned by a family), it is the largest owner in the case of 490 firms and is not surprisingly central in the US ownership network. However, it plays a minor role on boards. Instead, it votes its shares, often in a way that reflects its interest in managing the corporate pension funds more than its shareholders of its individual funds. Davis doubts, consequently, that mutual funds are activists. Thus the control benefits of concentrated ownership are attenuated by the conflicts of interest, and liabilities, that confront financial institutions.
Gregory Jackson offers a comment on the Davis article that argues that the new financial capitalism is poorly understood by the conventional categories of dominant and concentrated owners. The multiplicity of ownership types (e.g. mutual funds, private equity, and insurance companies) results in a complex confluence of varying identities and objectives. He argues that governance is enacted through informal governance, because dominance by any one type is so rarely achieved. Despite the proliferation of governance codes, Jackson notes that share turnover is very high among the largest owners in the US, UK, and Germany, and thus exit is surely the most used form of shareholder pressure. In some ways, this observation reflects the belief of many financial economists that it is the market, either financial or product or more poignantly in their interaction, that offers the most effective governance.
This dialogue between Davis and Jackson echoes a commonly heard observation on network studies on owners and boards: data alone are not going to tell the story. The analysis of network statistics, for example, centrality, small world, or density, requires contextual knowledge. However, in a time of growing penetration of governance ideologies and capital, these network statistics can pick up the impact of the global economy on national firms and their governance. It is this type of analysis that is offered by the next two articles.
Evis Sinani, Anna Stafsudd, Steen Thomsen, Christofer Edling, and Trond Randøy present a very thoughtful analysis of governance systems of three Scandinavian countries: Denmark, Norway, and Sweden. These three countries not only share many structural traits in common but also differ in many regards, especially regarding the composition of boards and owners. According to a strict interpretation of the financial legal theory of governance, capital market development is epiphenomal, that is, there is 'one best way' (see La Porta et al., 1998). Clearly, the Scandinavian countries have achieved advanced capital market development despite important differences; while belonging to the same legal family, they are not homogeneous in the identity of dominant owners (e.g. cooperatives in Denmark, or business groups in Sweden). Sinani et al. wish to know how similar levels of capital market development can be achieved despite these differences. They posit that the answer is to be found in the clubbiness of the governance systems. All of these countries evidence high small world statistics. They speculate that small worlds are helpful for the enforcement of control through reputation effects, as well as through information dissemination.
An interesting part of their analysis is the investigation of diversity (i.e. gender, nationality, and age). They find that firm size, industry, and country effects matter, but there is no effect of the Chair's ties on diversity. It would be nice to know if a local measure of clustering matters to determine if diversity is indeed an outcome of homophily (see Stafsudd, 2006, for an investigation along these lines).
In recent years, the empirical finance and economic literatures have developed the custom of testing for robustness of their results. Sinani et al. have done this in one regard. They show that the small world of Sweden is still found even if the Wallenberg and Handelsbanken ego networks are removed. This is an interesting finding to show that Sweden has a fractal-like quality in which small worlds features scale as expected over size distributions.
The article by Eelke Heemskerk and Gerhard Schnyder studies the important questions of 'distintegration' of corporate governance systems. Using a similar design as that of the Scandinavian article, they compare two small countries that are similar in many ways. Interestingly, they find that the ownership network (i.e. two firms are connected through a common owner) for their two country cases is not very revealing. In the Netherlands, the ownership network is almost entirely centered around a few financial institutions, which hold equity as an investment. Furthermore, in the Netherlands capital ownership does not imply control, as discussed by Heemskerk and Schnyder in their article. In Switzerland too, inter-company ownership has not played any significant role in corporate control throughout the 20th century. Pyramids are quasi inexistent (see La Porta et al., 1998); cross shareholdings amounted, at the beginning of the 1990s, to less than 1% of total market capitalization. Also, in both countries direct and indirect ownership ties are only in rare cases accompanied with board interlocks, as we now also mention. For these reasons, despite concentrated ownership, a network analysis of ownership ties (either direct or through common owners) does not reveal much.
Yet, the Netherlands and Switzerland have responded very differently in terms of corporate governance. Switzerland has unraveled its 'fortress' protection against foreign shareowners exercising voting power. The Netherlands has been slow to adopt greater shareholder voice. At the same time, the power of the banks in governance has declined in both countries in terms of the importance of bank lending as a source of capital. Still, the Swiss banks have moved closer to a US type of banking profile, whereas the Dutch banks relied heavily on commercial banking loans as the source of their profits.
The central finding of their paper is that the Swiss banking centrality in board networks disintegrated along the lines of the Davis and Mizruchi story, whereas the Dutch banks maintained their role. Clearly, the key difference is that the Dutch banks continued to rely heavily on commercial banks and thus did not face the conflict of interest of an investment bank which might be more motivated by fees collected through merger and acquisition advice than by lending. In particular, Dutch financial executives became far less important in the interlocking directorate network, even if individual Dutch supervisors (who were not financial executives) remained among the most connected directors.
No doubt, the study by Heemskerk and Schnyder is not without ambiguity. As much as they see change, one might argue that there is a still considerable robustness in the governance networks. After all, the networks remained very much clustered. As they include, the functional property of the networks appear to be more persistent than suggested by the individual structural measures. In all, though, the Davis and Mizruchi thesis that changes in lending leads to changes in bank centrality in interlocking directorates appears to hold up, even if the institutional details are quite different.
The last article in this issue is a project report on the Wissenschaftszentrum zu Berlin (WZB), or Social Science Research Center in Berlin, by Ariane Antal and the former President Juergen Kocka. Antal worked for many years with Meinolf Dierkes on an international project described in the text. Kocka is the leading business historian in Germany and the author of several books on the history of managers, working class, and corporate evolution. The Center has always loomed large in my professional memory. I knew it since graduate studies as a organized anarchy of disciplines and inter-disciplinary encounters, orchestrated at first across several buildings that reflected various aspects of historical German culture in various states of ruin and restitution before being re-assembled in the 'birthday cake' structure designed by James Sperling on the banks of a canal, not far from where Rosa Luxembourg and Karl Liebknecht were murdered. At that time, Karl Deutsch was the director of the unit on comparative social science, and a brilliant young researcher, Tom Cusack was starting his career working on Globus, a political and economic model of the world. This was social science thinking big.
Antal and Kocka relate briefly the history of this institute. They focus on a particular project, headed by Meinolf Dierkes, that compared organizational learning in different national environments. The project was important not only for its extension of comparative methodologies, but also as a regional broadening of the Center to non-European countries, such as China and Israel. The project was massive in its scale and involved many hundreds of organizations across three countries. In this project, the comparative advantage of a large social science center could be exploited, namely the possibility to launch large-scale research programs.
In between the lines of this article is the story of the tensions between an international research institute and the demands of the national institutions funding the organization. There is also the open question of the learning dynamic proposed by large projects and that proposed by the more prevalent model of smaller and more individual projects. The WZB is unique as a social science research institute in terms of its size and ambition. As a result, it has played an important role in the intellectual development of many researchers, both from Europe and from other regions. Its learning trajectory, one senses, hangs in between its successful integration into German universities and its larger objective to be an international research home. This positioning creates a certain amount of creative tension and spaces of institutional void to be filled, allowing for the type of entrepreneurial academics that is often missing in more 'disciplined' universities.
A note on bipartite networks
The two empirical articles on the Scandinavian and Dutch/Swiss comparisons relied upon standard network statistics first explored in the seminal article by Watts and Strogatz (1998); the derived SW Statistic was later defined in Kogut and Walker (2001). Since these publications, many articles have used these statistics, including Davis et al. (2003) and Baum et al. (2004). The small world statistics used in these articles are very useful in providing comparisons to these earlier works.
Recall that the small world statistics work by normalizing the clustering and path lengths by the values taken from an 'equivalent' random graph. By equivalent, we mean a graph that has the same number of nodes and links. If we assume that these links (or more exactly, degrees) are distributed as Poisson, we have exact formulas for the calculation of the clustering and path lengths derived from the fundamental work of Erdos and Renyi. It is these formulas that Watts and Strogatz used for the random graph normalization in their papers.
Let us remind ourselves why we need the random graph values (see also the discussion in Uzzi et al. (2007) in this journal). We do not know the distributional properties of clustering and path lengths. Thus when we compare networks (especially those of very difference sizes), it is hard to know what it means to have a large or small clustering value. What is the benchmark? For the calculation of statistical significance, we can often use the central limit result that the distribution of a mean asymptotically tends to the normal; for small samples, we use a Student-t approximation. Whereas we do not know exactly the distribution for the clustering and path length case, Watts and Strogatz showed that we can surely get a sense of large and small by comparing the empirical values against the random graph equivalents. We can now say that the clustering value is much bigger, or smaller, than the random value. And since the appropriate random value is calculated using the same number of nodes and links, we can compare graphs of very different sizes once we have normalized (i.e. divided) the empirical values by the random values. It is this division that Watts and Strogatz provided in their article. The SW Statistic simply then takes the ratio of these normalized values, as proposed in Kogut and Walker (2001).
Unfortunately, the random graph calculations for clustering and path length are not appropriate to a bipartite graph which characterizes board and ownership networks. A bipartite graph has two sets or types of nodes. Imagine that some nodes are blue, others red. The only links permitted are those that connect blue and red nodes; red-red and blue-blue are not allowed.1 The convention is to graph these networks by isolating the red and blue nodes, putting one set above the other, and then drawing lines between them (see Wasserman and Faust (1997) for their discussion of affiliation networks). We can then speak of the upper and lower set of nodes. For an ownership network, the sources could be owners and the targets could be firms. Such a graph is directed.
In Figure 1, we portray the bipartite graph for sources and targets; the edges are directed investments from sources to targets and there are no direct transactions (i.e. investment) among nodes of the same type. Therefore, a target can be uniquely identified as a network node that has only incoming links, while a source has only outgoing ties. Figure 1 shows that the directed connections from sources [ B,C,D,E] to targets [ 2,3,4] create unipartite ties among sources B,C,D, and E.
Consider now the problems posed by ignoring the bipartite structure and focusing on only the unipartite. The first loss of information results from the binary coding of ties. In Figure 1, for an ownership network, we see that owners B and C invest in target 2. We indicate the one mode projection onto the unipartite source graph by putting in a link between nodes B and C. Nodes C and D have invested in two common targets 3 and 4. We indicate these two ties by the two lines between them. However, in a one-mode projection, the binary adjacency matrix would indicate by a one the existence of a tie between them. We would lose consequently the weighted nature of their shared investments in two sources. In other words, the investments of C into 3 and C into 4 are redundant. In fact, we could remove target 3 and the adjacency matrix to the on-mode projection would not change. We would not be able to distinguish the case if nodes C and D invested in only a single target 3 or in two targets 3 and 4. This type of problem leads to a solution of 'weighted' graphs, which appears to be entirely ignored in the board interlock and ownership studies.
The second loss of information is more subtle and more important to the studies in this issue. The figure indicates that the degree of the nodes varies from 0 to 3. If we increase the degree of the investing source nodes, it is more probable that the unipartite graph will evidence more ties among the source firms. This increase in density, as discussed below, can be expected to increase the triangular closure among the nodes: that is, nodes B, C, D are more likely to be connected directly in the one-mode projection. In our figure, nodes B, C, and D compose a triangle (or cluster) in the unipartite case. If the degree of node C decreased to two, there is a one-third chance that C and B would no longer be connected. Clearly, the degree of the nodes evident in the bipartite graph conditions the expectation for clustering in the unipartite case. However, this conditioning is lost in the unipartite projection if no account is made of the bipartite graph. This seemingly innocuous implication poses an important consequence for the choice of the appropriate random graph by which to compare the empirical graph.
Bipartite graphs have not been frequently studied in the social network literature, with the important exception of the work on affiliation networks (Wasserman and Faust, 1997). Affiliation networks arise naturally since people are often members of associations, clubs, or other institutions. In the context of ownership networks, the bipartite structure is the result of investments by owners into targets. The language for describing bipartite networks is not adequately general, though a convenient terminology is to refer to each type of node as either top or bottom (Guillaume and Latapy, 2004).
In analyzing an affiliation network, the top or bottom set of nodes may attract most interest, while the other may be neglected. Implicitly, the previous treatments of many social networks assumed a preference by treating only the unipartite structure. Such a choice might make sense, such as with scientific collaboration networks where the focus is more on the scientists than the papers. In the case of ownership networks, it is theoretically more reasonable to consider the target firm network as primary.
However, while it seems largely a theoretical question which set of nodes to analyze, there are important methodological issues as well. As noted earlier, the normalization used in Watts and Strogatz, and by many empirical studies later, is not appropriate to bipartite graphs. Newman et al. (2001) were among the first to note that the Erdos–Renyi random graphs provide the wrong randomization for comparison to the empirical clustering and path length values. In the discussion of Figure 1, we have already noted that the degree distribution of one set of nodes will influence the network properties (i.e. clustering) of the other set of nodes. What appears as high clustering for the bottom set of nodes might be the expected outcome of a random assignment of ties to the top set of nodes. To derive correctly then the appropriate random comparison, the clustering value must be conditioned on the joint probability of the degree distributions from the top and bottom set of nodes.
Newman et al. (2001) propose a solution based on a polynomial generating function to represent the degree distribution. From this expression, the clustering and path length measures can be calculated. For the bipartite case, it is necessary to work with the generating functions of the degree distribution of the top and bottom set of nodes. From these two functions, the cluster and path length values for the one-mode projection can be calculated, that is, equations 81 in the Newman, Strogatz, and Watts paper for clustering, and 72, 73, and 53 for the path length. Newman, Strogatz, and Watts applied their model to empirical data to see if real-world phenomena could be adequately represented by a random-graph with a prescribed degree distribution. With few exceptions, the empirical data sets were well approximated by the theoretical model. That is, they found that many empirical data sets were very close to the random values derived from an arbitrary degree distribution. Using data provided by Jerry Davis, they confirmed his earlier finding that the US board interlock data differed noticeably (note that we cannot say statistically significantly) from a random distribution conditioned on the bipartite structure.
Nevertheless, it was necessary to go back and review previous results. For example, the small world of Kogut and Walker clearly overestimated degree clustering, though they found later that the attenuated small world properties still held using a normalization derived from Poisson degree distribution for a bipartite graph (Kogut and Walker, 2003). In general, neglect of the degree distribution for both the top and bottom set of nodes tended to overstate clustering. Thus, Conyon and Muldoon (2006) rejected small worlds for their UK and German board data.
The arbitrary degree distributions proposed by Newman et al. rely upon polynomial generating functions, which are good candidates to produce the appropriate random graph benchmarks, though how good is not entirely obvious. An alternative is to work directly with the empirical bipartite graphs, fix the number of nodes and degrees, and then randomize the edges over many iterations. Robins and Alexander (2004) develop this bootstrap approach by starting from the observed graph of director and board affiliations, which automatically has the required constraints. The initial iterations (
15,000) operate by removing a randomly selected edge and adding a new edge between a previously untied director and company randomly selected, provided that the constraints are observed. The result is a graph that is random conditional on the infrastructure constraints and with the same number of edges as the observed graph. This graph serves as the starting point for the second simulation (400,000 iterations) from which data are collected. This method is a brute-force approach to randomization while respecting the constraints.
Robins and Alexander define clustering using the bipartite graph rather than the one-mode projection. Reasoning analogously to the transitivity definition of clustering, they propose to measure clustering as a complete bi-clique. Borgatti and Everett (1997) introduced an analogue of a network clique, a biclique, as a complete bipartite subgraph. The notation of a (p,q) biclique denotes a clique with p nodes of one type and q nodes of the other type. Robins and Alexander propose the (2, 2) biclique for the bipartite graph as an analogue of the triangle in a one-mode network, which is the simplest one-mode clique, with the exception of the degenerate single edge. A (2, 2) biclique occurs when two venture capital firms have investments in the same two targets.
For example, in Figure 1, the links from B to 2 and C to 2 and 3 form a three-path configuration. The links from C to 3 and 4 and D to 3 and 4 form a (2, 2) biclique. Clustering then is four times the number of bicliques over the number of three-paths configurations; this statistic is analogous to the triangular definition of clustering for the unipartite graph. A nice benefit of the randomization method is that the difference between the empirical census and the random census divided by the standard error results is a normal standard variate, thus permitting the possibility to accept or reject the null hypothesis of no difference between the two graphs.
Verifying the SW statistics
In order to verify the SW statistics given in the articles by Sinani et al. and by Heemskerk and Schnyder, we estimated the clustering and path lengths using the bipartite normalization. We used both the Newman–Strogatz–Watts (NSW) and the Robins–Alexander (Robins) normalizations, as there has not been a useful comparison between the two measures.
These results are given in the tables below. To put the networks into a comparative framework, we show the descriptive network statistics for their ownership and board interlock data in Tables 1, 2, 3 and 4. As Sinani et al. and Heemswerk and Schnyder note, their networks show very large giant components, that is, most of the nodes in their networks can reach one another by a path. The networks differ very much in sizes. This difference does matter for comparing such statistics as density. However, once statistics are normalized (as we will do for clustering and path length), then we will be able to compare them.
Tables 5, 6, 7, 8, 9, 10, 11 and 12 explore the small world statistics. We provide the results on each step of the analysis so as to give the reader full clarity as to the calculations. It is clear that the Robins and NSW estimates are not the same, though all of them show that the empirical values differ from the arbitrary degree distributions. It is unfortunate, since it would be convenient to find agreement and thus the formulas of NSW could be used instead of the brute-force simulation approach of Robins and Alexander. We have a preference for the Robins–Alexander statistics because they are derived using the full network (NSW rely upon the distributions of the first two steps) and because they give a useful bipartite census (not used in this introduction but see Robins and Alexander, 2004).
By and large, the unipartite values given in Sinani et al. and Heemskerk and Schnyder are over-estimates of the bipartite corrected values, but their fundamental conclusions are the same. All the networks are small worlds, as claimed in the articles published in this review.
The most insightful results are Figures 2 and 3 that map countries into the space defined by the coordinates of standardized clustering and standardized average path length. As all the countries lie above the line, it is clear that their interlocking networks and ownership networks are all small worlds. (The only exception is the case of the Netherlands in the panel on the left in Figure 3, which reflects the claim that ownership in the Netherlands is very dispersed.) By and large, the results shown in the right hand panel indicate weaker small world effects, consistent with the overall claim on the deterioration in the 1990s of national networks. However, the effects are still very much present, including Germany which we include to provide a well-studied benchmark to these results. The Swedish ownership network is especially marked as a small world.
Figure 2.
Interlocking boards and the SW statistics normalized by (a) Robins method, (b) Newman–Strogatz–Watts. These figures plot the components to the small world statistic (see Kogut and Walker, 2001) using the three normalizations and both panels for the interlocking board networks. The SW statistic is simply the empirical values of the average path length (APL) and clustering coefficient (CC) divided by the normalizing value calculated by the three methods described in the text and in the above tables. The abbreviations indicate the country: DE (Germany), CH (Switzerland), NL (Netherlands), DK (Denmark), NO (Norway), and SE (Sweden). Since the Robins and NSW statistics are derived from a bipartite graph that matches our data, we do not show the calculations for the Erdos–Renyi normalized values. The line with an intercept of 0.4 indicates the lower-bound to the SW effect. All values above this line have a standardized clustering value greater than 1. As apparent, all SW statistics indicate small worlds for these six countries. The cases of Germany and Switzerland show higher values using either measure. Both figures indicate that the second panel values are lower, suggesting that small worlds were reduced during the 1990s. Germany is the country that most consistently evidences a small world.
Full figure and legend (72K)Figure 3.
Ownership ties and the SW statistics normalized by (a) Robins method, (b) Newman–Strogatz–Watts. The SW estimates for the ownership data indicate rather robust finding of small worlds, except for the Netherlands in the year 2000 using the Robins method. Sweden has the clearest evidence for small worlds. The NSW suggest a deterioration in small worlds during the 1990s. However, the German case, where there is a small world effect, shows an increasing clustering to path length during the 1990s. At least during this period, small worlds did not deteriorate.
Full figure and legend (72K)While these methods have been discovered only in the past years, they were anticipated in the final chapter of the excellent volume by Stokman et al. (1985). They note that there is the possibility that the national networks they studied are simply random realizations, citing the random graph papers of Erdos and Renyi. The standardized statistics for small world detection incorporates this concern. We can conclude, given these results, that national governance networks studied in these articles are small worlds, though deteriorated by structural changes during the 1990s.
Notes
1 Guillaume and Latapy, 2004 develop a more general approach based on cliques that permits ties within the sets. Such an approach is often appropriate to ownership data, where owners can be also be firms. For a nice application, see Latapy, Magnien, and del Vecchio, 2008.
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Acknowledgements
We would like to express our gratitude to Jordi Colomer for his computational assistance and to Center for Globalization and Strategy at IESE Business School for the financial contribution to the broader research project from which this introduction is taken.
