It has been more than a decade since the Supreme Court ruled on the case of Citizens United v. Federal Election Commission, which upheld the principle that independent campaign financing is protected as a form of free speech. As Temple law professor David Kairys describes, what made the decision so contentious was that not only was money equated with speech, but that the protections afforded under the umbrella of free speech were explicitly extended to the case of corporate personhood, thereby limiting lawmakers’ ability to restrict the flow of money from corporations to candidates. Part of what makes the prospect of unchecked corporate influence so frightening is the potential for coordination among corporate elites, who are bound together through various types of social networks, including interlocking directorates.
In my previous post, I introduced the concept of interlocking directorates in the context of a discussion regarding the organizational connections between railroad corporations in the late nineteenth century. The general idea behind the notion of interlocking directorates is that corporations are tied to one another through common board members. These types of ties not only linked railroad corporations to one another, but to corporations in adjacent sectors of the economy such as banking, insurance, finance, and industry. The emergence of the anti-trust movement was a direct response to the consolidation of corporate control over the course of the late nineteenth century, eventually coming to a head in the Progressive Era. In the presidential election of 1912, Democratic candidate Woodrow Wilson successfully ran on a platform that called for, among other things, legislation preventing the formation of interlocking directorates. This vision was at least partially realized with the passage of the Clayton Act of 1914, which prohibited large companies from forming interlocking directorates with would-be competitors. Though the magnitude of the effect is somewhat unclear, the Clayton Act is said to have tempered the prevalence of interlocking directorates in the United States.
Given their historical importance, it is not surprising that questions regarding the nature of interlocking directorates came to occupy a central place in economic and political sociology. This led to two interrelated lines of work, one of which focused on the transformation of corporate control, and the other of which focused on the relational foundations of corporate political action. Research on interlocking directorates thrived as a result of concomitant developments in the area of network analysis, which contributed to a tight coupling between theory and method. These new techniques could be readily applied to earlier time periods due to the availability of historical information included in financial manuals such as Moody’s, Poor’s, and the Manual of Statistics. Using data originally compiled by David Bunting, I want to use the remainder of this post to examine a single question: did the relationships between America’s corporate elite in the late nineteenth and early twentieth centuries constitute a small world?
Work on the small-world problem is often traced back to the work of psychologist Stanley Milgram, who asked each member of a set of randomly selected research participants to help get a message to a distant stranger by sending the message to an individual with whom they were on a first name basis. Once the messages were sent on, the process was repeated until they reached their intended target. Milgram found that people were able to transmit the messages relatively efficiently, as evidenced by the number of intermediaries required to get the message from one of the original randomly selected participants to the intended target. In the end, it took anywhere from two to ten intermediaries to get the message across the country, with a median value of just five intermediaries. As Watts and Strogatz (1998) argue, however, the small-world phenomenon is defined not only by the fact that people tend to be relatively close to one another, but the fact that tend to be relatively close to one another in a network otherwise characterized by high levels of clustering.
To what extent does this characterization apply to the world of corporate elites? To help fix ideas, we will start by looking at the network of interlocking directorates from 1905 and then zoom out to look at trends across the broader period. For the purpose of comparing results over time, I focus specifically on interlocking directorates among railroads, banks, and insurance corporations. Interlocking directorates are a classic example of a two-mode network in which ties are formed between two distinct types of entities, as seen in the figure below. The number of firms represented in the graph is a reflection of the data collection strategy used by Bunting, who focused specifically on the 25 largest railroads, 20 largest banks, and 10 largest insurance corporations. These 55 firms were held together by a total of 860 directors. The average firm had 20.5 directors on its board, while the average director sat on 1.31 boards. There were some directors, however, who sat on as many nine boards at the same time. Roughly 12 percent of directors sat on boards in more than one industry. In the absence of interlocks, we would expect to observe a separate component for each firm. Yet with the exception of five isolated firms, all of the corporations were bound together as part of a single coherent network making up the main component of the graph. From here on out, we will focus exclusively on the main component.
In order to quantify the degree of small-worldness in this network, we first need to measure (a) the proximity between the nodes and (b) the amount clustering in the underlying graph. While we can calculate separate distance measures for individuals and corporations, we will focus on the original two-mode graph. In general, the distance between any given pair of nodes can be measured in terms of the geodesic distance, which is defined as the length of the shortest path from one node to the other. Taking the average shortest path length gives us a measure of overall proximity for the graph as a whole. In this case, the average shortest path is equal to 5.42 steps. Calculating the degree of clustering is complicated by the fact that we have two-mode data. When working with one-mode data, the global clustering coefficient measures the propensity for triadic closure. As Opsahl (2013) shows, this approach can be meaningfully extended to the case of two-mode data. In this case, the two-mode clustering coefficient is equal to 0.18.
At this point, you should be asking yourself whether the measures that we just calculated are large or small. To figure this out, we can compare these measures to what we would get if ties were generated at random. This can be done using simulation. The key is generating graphs that share the same basic properties as the observed data. More specifically, this means generating graphs with the same number of nodes of each type, as well as the same number of total edges. Following the example of Robins and Alexander (2004), the simulation process is constrained to ensure that every node has at least one tie, as we would expect when looking at interlocking directorates. If the corporate network from 1905 were a small world, we would expect (a) the observed value of the average shortest path length to be comparable to the mean of the average shortest path length across simulated datasets and (b) the observed value of the two-mode clustering coefficient to be well above the mean of the two-mode clustering coefficient across simulated datasets. Both of the expectations bear out. The observed value of the average shortest path length is just 0.69 standard deviations above the mean of the simulated distribution, as compared to the observed value of the two-mode clustering coefficient, which is 332 standard deviations above the mean of the simulated distribution! Altogether, this provides support for the claim that the network of corporations and corporate elites in 1905 can be described as a small world.
By way of conclusion, I want to briefly consider how things changed over time in the century between 1836 and 1935. In the context of a blog post, it isn’t reasonable to start simulating random graphs for every year. We can, however, look at variation in the observed statistics to get a sense of how things compared to 1905. The results are shown in the figure below. We observe a notable shift around 1891 in both the average shortest path and the two-mode clustering coefficient. Whereas the length of the average shortest path begins to decline, the magnitude of the two-mode clustering coefficient begins to increase. These began to shift back following the turn of the century. In the case of the average shortest path length, we see a noticeable upward shift starting in 1912, which coincides with the presidential election described above. In the case of the clustering coefficient, on the other hand, we start to see a downward shift starting in 1904. This latter shift coincides with the Supreme Court’s intervention in the railroad industry as part of the Northern Securities case, which prevented a massive three-way merger between the Northern Pacific, Great Northern, and Chicago, Burlington, and Quincy corporations.