Beyond Fortune 500: Women in a Global Network of Directors
BBeyond Fortune 500: Women in a GlobalNetwork of Directors
Anna Evtushenko and Michael T. Gastner Cornell University, Ithaca, NY 14853, USA, [email protected] , Yale-NUS College, 16 College Avenue West,
Abstract.
In many countries, the representation of women on corporateboards of directors has become a topic of intense political debate. Socialnetworking plays a crucial role in the appointment to a board so thatan informed debate requires knowing where women are located in thenetwork of directors. One way to quantify the network is by studying thelinks created by serving on the same board and by joint appointments onmultiple boards. We analyse a network of ≈
320 000 board members of36 000 companies traded on stock exchanges all over the world, focusingspecifically on the position of women in the network. Women only have ≈ −
13% of all seats, but they are not marginalised. Applying metricsfrom social network analysis, we find that their influence is close to thatof men. We do not find evidence to support previous claims that womenplay the role of “queen bees” that exclude other women from similarpositions.
Keywords: interlocking directorates, social networks, gender inequality
Females on boards of directors and board diversity more broadly are the topicof many studies [1,8,16]. Research has shown that female board representation is“positively related to accounting returns” [31]. The World Bank [36] estimatesthat 39% of the worldwide labour force in 2016 are women, but the percentageof women in leadership positions is much lower. Recent reports state that only24% of senior management positions [17] and 15% of corporate board seats [6]are held by women. The percentage of female CEOs among Fortune 500 firms iseven lower (6.4%) [27]. Women’s chances to become a CEO or a board memberdepend on multiple factors, such as “country wealth, gender egalitarianism andhumane orientation” [13]. Nevertheless, female board participation is slowly onthe rise globally. Shareholders and governments no longer regard it as a legitimatepractice to recruit directors from an exclusively male “old-boys network” [30,11].Various countries, for example Israel [23] and Norway [32], have enacted lawsthat favour the appointment of women [33]. As a consequence, there are signsthat, at least in some European countries, the “glass ceiling” that has keptwomen out of the boardrooms is beginning to crack [14]. a r X i v : . [ c s . S I] O c t Evtushenko and Gastner
Once appointed, female directors must navigate intricate networks of profes-sional relationships. A concrete manifestation of such a professional network are“interlocking directorates” [25] (i.e. the practice that some directors hold seatson more than one board). A recent survey by Credit Suisse [7] relates “over-boarding” (i.e. an excessive number of board seats held by an individual) tothe current trend towards increasing the number of female board members. Theprobability that a woman joins the board has been shown to be negatively cor-related with the number of women currently on the board and to increase whena woman departs the board [15]. The underlying assumption is that companiestend to recruit “token women” (i.e. exactly one per board) from a limited pool offemale candidates [10,35]. Some commentators compare women directors withmultiple seats to queen bees [37], implying that these women allegedly usurppower at the expense of female competitors. The purpose of this article is to testwhether such narratives stand up to quantitative scrutiny.Board interlocks can be inferred from a bipartite graph where every edgeis between one company and one director (Figure 1) [2]. Each director at oneend of an edge sits on the board of the company at the other end of this edge.The study of board interlock networks started already in the 1970s [34], but atthat time the role of the director’s gender was not yet in the limelight. Interestin the role of women on boards has intensified in recent years, see for exampleRef. [12] for a critical review. Still, relatively little is known about the role thatthe gender plays for the network formed by interlocking directorates.
Fig. 1.
Network representations of board interlock. (a) Bipartite graph where everyedge is between a company (large node) and a person (i.e. a director, small node). (b)In this article, we analyse the social network of directors that results from a one-modeprojection of the bipartite graph: directors are connected if and only if they sit togetheron a board.
A woman’s position in the social network certainly influences her chancesto be appointed to a board [3], but only few papers have analysed the realnetwork [39,20,32,26]. The most comprehensive quantitative network study todate is the PhD thesis by Hawarden [18], which looks at empirical data and builds omen on boards 3 a modelling framework called “Glass Network” theory. It posits the existence of“glass nets” that prevent women from assuming board seats, but those womenwho succeeded in crossing a glass net behave like queen bees. We further theexploration of this topic using network analysis applied to a large dataset, whichwe now describe.
The source of our data is the Financial Times [38], an international English-language newspaper specialising in business and economics. Its website is asource of up-to-date information on financial markets and companies tradedas equities. The website has data on the performance and structure of roughly36 000 companies from 54 countries. The resulting data base is, to the best ofour knowledge, the largest that has so far been used in the literature on boardinterlocks. The Financial Times (FT) receives their information from the mediacompany Thomson Reuters, which in principle has data on yet more firms. How-ever, we decided to use the FT data because this subset is more representativeof companies that make up the business world.The specific fields that we obtained for each company were name, uniquecode, sector, industry (i.e. subsector), country, revenue for the past 12 months,number of employees, date incorporated, and a list of directors, each if avail-able. For each director, we recorded his or her name, gender, and age, each ifincluded in the FT database. People were then identified as the same individ-ual and assigned a unique ID if their three fields matched (for example, thenames and genders were the same, and ages were blank) because we assumethat the underlying Thomson Reuters database would have identical entries oneach individual in all his or her companies. There were a total of 35 927 compa-nies and 321 967 directors. Here we make no distinction between executive andnon-executive directors.In terms of missing data, 273 companies have zero directors listed. Amongthe fields relevant to the analysis, for 5732 companies (15.95%) we have no in-formation about the country, for 4461 (12.41%) no sector, and for 5020 (13.97%)no industry. 96 751 directors (30.1%) are listed without gender. For 126 092 di-rectors (39.2%), the database contains no information about their age. We showsummary statistics of the network and the subgraphs consisting of only male oronly female nodes in Table 1.
The proportion of female directors in the FT data is 9.43% of all nodes and13.49% among people with confirmed gender. This percentage is comparable tovalues stated in previous studies of international data. For example, Dawson etal. [6] found that women hold 14.7% of seats in the CS Gender 3000 data base;
Evtushenko and Gastner
Table 1.
Statistics of the full network and the subgraphs consisting of only male or onlyfemale nodes. We calculate the average path length with the harmonic mean formulaby Newman [28] to handle disconnected components. nodes all male female edges 2809623 1092004 44666diameter 24 29 40average path length 13.90 22.90 517.79density 5 . × − . × − . × − components 9404 12393 12355% of nodes in the largest component 74.7 74.8 79.4% of edges in the largest component 85.5 85.1 89.6 Deloitte [9] puts this number at 15% for data from nearly 7000 companies. Bothof these reports emphasise that there can conceivably be a difference betweenthe proportion of female directors and the proportion of female seats becauseof overboarding. On the boards of S&P500 companies, overboarding is moreprevalent among women [7]. However, in the more comprehensive FT data, wefind that, at the international level, the proportions of seats and directors aresimilar: the percentage of female seats is 9.73% and thus only 0.29% larger thanthe percentage of female directors. The underlying reason is that overboardinghardly differs between genders: 14.7% of women and 14.8% of men are multipledirectors. Overall, taking into account ungendered nodes, 14.06% of directorsare multiple directors. 4.22% of directors are on more than 2 boards, 1.76% onmore than 3, and 0.40% on more than 5.It is interesting to see whether the ratio of female seats to all seats differs bycountry, sector or industry. We can easily compute these numbers because foreach company we know its country, sector, and industry, as well as the numberof all directors and the number of female directors.Figure 2 plots the proportion by sector and then subdivides each sector by in-dustry, with industries following their sectors in descending order. We note thatwomen are more represented in Financials, Consumer Services and Telecommu-nications than in Technology and Basic Materials. These findings are consistentwith the report by Credit Suisse [6].We find greater discrepancy between our data and Credit Suisse when we splitour data by country (Figure 3) instead of sector or industry. While we agree thatScandinavian countries generally rank highly, we find lower percentages of femaleseats than those reported by both Credit Suisse and Deloitte [9]. For example,we find the percentage of female seats in Sweden to be 21.52%, whereas CreditSuisse reports 33.6% and Deloitte 31.7%. We believe that the difference is dueto our larger sample size. The FT data base includes 465 Swedish companiescompared to only 125 in Deloitte’s data.The top-ranked country in our data is Ukraine (22.6%). We have not foundprevious reports on female directors in Ukraine so that we cannot rule out thatits top rank is owed to a relatively small sample size of only 19 Ukrainian compa-nies. Another surprisingly highly ranked country is Thailand (19.5%). Although omen on boards 5
Deloitte estimates the percentage to be only 11.7%, it is plausible that the truenumber is higher because Thailand is among the countries with the largest pro-portion (37%) of women in senior management [17]. Near the bottom of theranking is Japan (1.2%) where our number is even lower than previous esti-mates (Credit Suisse: 3.5%, Deloitte: 4.1%).Similar to the worldwide trend mentioned above, the proportion of female directors by country hardly differs from the proportion of female seats (i.e. thedata shown in Figure 3). We have inferred the country of a person as the mostcommon country of her or his companies. Based on this assumption, we havecalculated the countrywide proportion of female directors. In every country in-cluded in the FT database, it differs by less than 0.022% from the proportionof female seats so that the conclusions do not depend on whether we use femaleseats or female directors as the basis of our analysis.Another measure for comparing female representation across countries is theproportion of companies with at least one woman on their boards. Worldwide,we find that 50.3% of companies have at least one director who FT identifiesas female. Because FT does not include gender information for 30.1% of thedirectors (see section 2), the true percentage of companies with women on theirboards is likely to be higher. Lee et al. [24] estimate 73.5% for the smallerMSCI data base. The country rankings, shown in Figure 4 (grey bars in theplot), are similar to those for the proportion of female directors by country inFigure 3. Ukraine drops to the ninth position, but the Scandinavian countriesand Thailand maintain their high rankings. Oman, Japan, Pakistan, and Qatarremain at the bottom.It is instructive to compare the observed percentage of companies with womenon their boards with the expected values from a simple probabilistic null model.We assume that the probability of a seat being held by a woman is equal tothe observed fraction p of female seats in a given country. In the null model, weassume that the assignment of women to seats is independent of the gender ofthe other seats. Suppose the size of a board is s . For each of the s seats, we flip abiased coin which shows heads with probability p and tails with probability 1 − p .When the coin shows heads, the seat is, in this model, given to a woman. Theprobability that the company’s board has at least one woman equals 1 − (1 − p ) s .If the fraction of boards with s seats is f s , then the expected fraction of boardswith women is (cid:80) s f s [1 − (1 − p ) s ].The alternative hypothesis is that companies tend to have a single tokenwoman on their boards. In this hypothesis, a woman is only added when thereis currently no other woman on the board [15,35]. With exactly one woman, theboard satisfies a minimum criterion of diversity that reduces external pressurefor greater female representation without seriously threatening the power of the“old-boys network”. If the token woman hypothesis is true, there would be ahigher proportion of boards with exactly one female board member than in thenull model.We calculated the null model’s expectation value for the global data andthe predicted proportion of single-woman boards for each country. Worldwide, Evtushenko and Gastner
ChemicalsIndustrial MetalsMiningForestry & Paper
Basic Materials
Technology Hardware & EquipmentSoftware & Computer Services
Technology
Industrial EngineeringElectronic & Electrical EquipmentConstruction & MaterialsIndustrial TransportationGeneral IndustrialsAerospace & DefenseSupport Services
Industrials
Alternative EnergyOil & Gas ProducersOil Equipment Services & Distribution
Oil & Gas
Automobiles & PartsLeisure GoodsFood ProducersHousehold GoodsBeveragesPersonal GoodsTobacco
Consumer Goods
ElectricityGas Water & Multi−utilities
Utilities
Pharmaceuticals & BiotechnologyHealth Care Equipment & Services
Health Care
Mobile TelecommunicationsFixed Line Telecommunications
Telecommunications
Travel & LeisureMediaFood & Drug RetailersGeneral Retailers
Consumer Services
Financial ServicesBanksReal Estate Investment & ServicesNonlife InsuranceLife InsuranceGeneral Financial
Financials
Proportion of female seats S e c t o r o r I ndu s t r y Type
Sector
Industry
Fig. 2.
Proportion of female seats by sector (darker colour) and industry (i.e. subsector,lighter colour).omen on boards 7
QatarJapanOmanPakistanTaiwanMoroccoHungaryArgentinaIndiaMexicoChileSri LankaTurkeyCzech RepublicAustriaBrazilSwitzerlandPortugalGermanyMalaysiaChinaCanadaItalyBulgariaSloveniaLithuaniaNetherlandsRussiaAustraliaRomaniaBelgiumNigeriaUnited KingdomIrelandIndonesiaGreeceFrancePolandUnited StatesSingaporeEstoniaDenmarkHong KongIsraelPhilippinesNew ZealandIcelandKenyaSouth AfricaFinlandThailandNorwaySwedenUkraine0.00 0.05 0.10 0.15 0.20
Proportion of female seats C oun t r y Fig. 3.
Proportion of female seats by country. Evtushenko and Gastner
QatarPakistanJapanOmanHungaryMoroccoTaiwanArgentinaIndiaBulgariaCzech RepublicGermanyTurkeyPortugalCanadaAustraliaChileNetherlandsSri LankaBrazilAustriaMexicoUnited KingdomRomaniaSwitzerlandLithuaniaMalaysiaIcelandBelgiumSloveniaFranceEstoniaIrelandItalyChinaPolandNigeriaIndonesiaDenmarkNew ZealandRussiaKenyaUnited StatesGreeceSingaporeUkraineIsraelSouth AfricaHong KongPhilippinesSwedenNorwayThailandFinland 0 0.25 0.5 0.75 1
Proportion of companies C oun t r y Fig. 4.
Observed and predicted proportions of companies with at least one womanon their boards by country. The observed proportion is shown in grey. The predictedproportion is the combination of the grey and the blue bar. The prediction is calculatedunder the assumption that seats are taken by both genders independently given theobserved proportion of female seats in each country (see text). The prediction is higherthan the observed proportion in all cases except Slovenia, where the prediction is onlyslightly lower.omen on boards 9 we find that the prediction is higher than the observation (0 .
604 vs. 0 . . χ -test for normality ( p -values < − ) because they areslightly skewed towards higher age. However, the deviations from normality aresufficiently small to justify using Welch’s two-sample t -test. The null hypothesisof an equal mean for men and women is strongly rejected ( p -value < − ). Ourresult is consistent with earlier studies of French [24] and Singaporean data [40]where female directors were found to be on average 5–10 years younger. llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l ll age f r equen cy gender l malefemale Fig. 5.
The age distribution of directors by gender. Both distributions are well approx-imated by Gaussian functions (black solid curves), but with different means (dashedlines): the mean age of male directors is 55 . . While the attributes discussed in the previous section already give us some in-sight into gender differences, we can only truly assess the role of women whenconsidering their positions in the network. As we explained in the introduction,our data can be viewed as a bipartite network where edges run between direc-tors and boards (Figure 1a). In this network, there are 2 809 623 edges connecting321 967 directors to 35 927 boards. The average board size (of those available) is11.02. The mean size of a board without women is 8.88, whereas boards with atleast one woman have on average 13.10 seats. Some care needs to be taken wheninterpreting these numbers. Even in our earlier null model, where we assumedthat seats are independently taken by men and women, the mean size of a boardwith a woman is larger than the mean size without a woman. The reason isthat, in this model, the probability of at least one woman on a board of size s is1 − (1 − p ) s and thus increases with s . The mean board size conditioned on thepresence of at least one woman is µ null ≡ E [board size | woman] = (cid:80) ∞ s =1 sf s [1 − (1 − p ) s ] (cid:80) ∞ s =1 f s [1 − (1 − p ) s ] , where f s is, as before, the fraction of boards with s seats. We find µ null = 12 . p -value < − ). This result confirms previous observations that larger boardstend to have a higher probability of recruiting women [4,5,29].Larger boards tend to be in the largest component of the bipartite network.In the one-mode projection that only contains the directors as nodes (Figure 1b),the largest component consists of 74.7% of the nodes and 85.5% of the edges.Given that women are more likely to be on larger boards, it is not surprisingthat the proportion of women in the largest component (79.4%) exceeds thefraction of nodes belonging to that component. We confirm with the χ -testproposed by Hawarden & Marsland [19] that the proportion of women in thelargest component is significantly higher than that of men ( p -value < − ). Wetherefore agree with their previous result that, although women are a minority,they are not marginalised by being confined to unconnected, and hence lessinfluential, components.In terms of degree and betweenness centrality statistics, women are doingmarginally better than men (Table 2). The distributions of degree and between-ness centrality by gender are not normal but instead seem to follow power laws.We normalise them by log-transforming the data and restricting our sample tothe largest component and nodes with the parameter of interest >
0. The two-sample t -test for degree concludes that the marginal difference between men andwomen is statistically significant (p-value < . p -value 0.068). omen on boards 11 Table 2.
Summary statistics of the network with all nodes (i.e. nodes identified asmale, female, and those with missing gender information) and all edges. Larger valuesare highlighted in bold. “Like degree” is the degree between nodes of the same gender.We calculate the closeness centrality with the harmonic mean formula by Newman [28]to handle disconnected components. nodes all male female % of all 100 maximum degree average degree average “like degree” 11.21 degree in largest componentmaximum betweenness centrality . × . × . × average betweenness centrality . × . × . × average betweenness centrality . × . × . × in largest componentmaximum closeness centrality closeness centrality .
071 0 . average closeness centrality clustering coefficient clustering coefficient average clustering coefficient in largest component2 Evtushenko and Gastner In this paper we have analysed a new dataset which allows us to better un-derstand interlocking directorates. In particular, it has allowed us to show thedifferences of female representation by country and industry. Overall, there arestill many fewer women than men on boards, but our analysis contradicts the to-ken woman hypothesis whereby companies recruit exactly one woman to escapeaccusations of discrimination. A limitation of our dataset is that it only indicatespresence or absence of a link, but not its strength, which has been hypothesisedto depend on gender [21,22]. Our binary data, however, do not show evidencethat women are marginalised.
Acknowledgements:
We would like to thank Adrian Roellin for introducing usto the study of interlocks and to the Financial Times Equities database. M. T. G.was supported by the Singapore Ministry of Education and a Yale-NUS Collegestart-up grant (R-607-263-043-121).