Numbers and structural positions of women in a national director interlock network

Numbers and structural positions of women in a national director interlock network Alex Stivala (Università della Svizzera italiana [USI], Lugano, Switzerland), Peng Wang (Swinburne University of Technology, Australia & USI), Alessandro Lomi (USI) INSNA Sunbelt XLIII, Portland, OR and online, June 27 –July 1, 2023 Online presentation, Alex Stivala, June 28, 2023 1 Collaborators, funding, acknowledgements, disclosure. •Unpublished work: Alex Stivala, Peng Weng and Alessandro Lomi, 2023. •This work was funded by Swiss National Science Foundation (SNSF) grant 200778. •We used the high-performance computing cluster at the Institute of Computing, Università della Svizzera italiana, for all data processing and statistical computations. •Conflict of interest disclosure: I am a direct shareholder in several ASX listed companies, including some specifically mentioned in this work, and their competitor companies. I am also an indirect shareholder in ASX listed companies via the default superannuation fund for Australian university employees. 2 Outline and contributions •Substantive: •A director interlock network for all (over 2000) companies (rather than the top 200 or 300, as usual practice) listed on the ASX is constructed. •Descriptive statistics of the network, companies and directors. •Based on the theoretical framework of Kanter (1977) we examine the relative proportion of women and test a “token woman” hypothesis proposed by recent work including Evtushenko & Gastner (2020). •We move beyond simple counting (binomial distribution null model) and examine the structural position of women using network centrality measures, ERGM and ALAAM. •Methods innovations: •Open-source software for ERGM estimation, simulation and GoF for large bipartite networks is developed, and demonstrated on the ASX network, and a much larger (approx. 350 000 node) international director interlock network. •Open-source software for ALAAM estimation, simulation and GoF for large bipartite networks is developed, and used for testing the structural position of women in the ASX director interlock network. 3 A “token woman” hypothesis (Evtushenko & Gastner 2020) •“The probability that a woman joins the board has been shown to be negatively correlated with the number of women currently on the board and to increase when a woman departs the board [15]. The underlying assumption is that companies tend to recruit “token women” (i.e. exactly one per board) from a limited pool of female candidates [10,35].” •“In this hypothesis, a woman is only added when there is currently no other woman on the board [15,35]. With exactly one woman, the board satisfies a minimum criterion of diversity that reduces external pressure for greater female representation without seriously threatening the power of the “old-boys network”. If the token woman hypothesis is true, there would be a higher proportion of boards with exactly one female board member than in the null model.” 10. Dezső , C.L., Ross, D.G., Uribe, J.: Is there an implicit quota on women in top management? A large-sample statistical analysis. Strategic Manag. J. 37(1), 98–115 (2016) 15.Farrell, K.A., Hersch, P.L.: Additions to corporate boards: the effect of gender. J. Corp. Finance 11(1-2), 85–106 (2005) 35. Strydom, M., Yong, H.H.A.: The token woman. In: 25th Australasian Finance and Banking Conference (2012), available at http://dx.doi.org/10.2139/ssrn.2136737 4 Evtushenko, A., Gastner, M.T. (2020). Beyond Fortune 500: Women in a Global Network of Directors. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_47 “This implies that women are generally more clustered than expected if they were distributed randomly, contradicting the token woman hypothesis.” Data is from Financial Times database, Sept. 2016: 38. Thomson Reuters Corporation: Profiles and lists of directors of publicly traded companies. https://markets.ft.com/data/equities/results (2016), retrieved on 17 September 2016 5 Data source •Data on the directors of all ASX listed companies from the Connect 4 Boardroom database (14 Sept., 2022; accessed via Swinburne subscription by Peng Wang). •This is a Thomson Reuters commercial product, aggregating open source data from company annual reports, announcements to the ASX, etc. •It includes director country, gender and age. •I joined this with other open source data directly from the ASX (company directory [5 Oct. 2022], foreign entity report [Sept. 2022]) to get more company information: GICS industry group, listing date, market capitalization, foreign country incorporation. 6 Descriptive statistics •Of the 9971 people, 1899 (19%) are women. •Of the 13452 positions, 2784 (21%) are occupied by women. •The proportion of companies with exactly one woman is 30%. •The proportion of companies with at least one woman is 66%. 7 Note degree in the bipartite network includes both modes (for people, number of boards they sit on, for companies, board size), so mean not meaningful. Negative assortativity indicates board size is negatively correlated with number of boards its members are on (large boards tend to have people who sit on few boards; small boards tend to have people who sit on many boards). This is the only time we consider one-mode projections; all network statistics and models use the original two-mode (bipartite) network. 8 Frequency and total market capitalization of GICS industry groups 9 Moving beyond counting •So far, we have just looked at counts (or proportions) of women in the network. •But what about their structural positions? •Are women more, or less, central in the network than men? •Do women tend to be associated with particular industries, or larger or smaller companies? •We will use some more advanced models to answer these questions. 16 Software for large bipartite ERGM and ALAAM •ERGM: https://github.com/stivalaa/EstimNetDirected •ALAAM: https://github.com/stivalaa/ALAAMEE 17 Mode A is people, mode B is companies. •Positive BipartiteContinuousActivityA age: Older directors tend to be on more boards. •Positive BipartiteActivityA notAustralia: Directors resident in countries other than Australia tend to be on more boards. •Positive BipartiteTwoPathMatchingA country: Directors on a board tend to be from the same country. •Positive BipartiteActivityB notAustralia: Foreign incorporated company boards tend to have more directors. •Positive BipartiteContinuousActivityB logMarket Cap: Larger market cap. Is associated with larger boards. •Positive Matching country: directors tend to be resident in the same country as the country of incorporation of the boards they sit on. •No significant effects for gender: •BipartiteTwoPathMatchingA gender --- gender homophily on boards --- is negative but not significant. •BinaryPairInteraction gender.F industryGroup.Materials --- women directors tendency to be on Materials industry group boards --- is negative but not 18 signif. •BinaryPairInteraction gender.F industryGroup.Banks --- women directors tendency to be on bank boards --- is positive but not signif. •BinaryPairInteraction gender.F notAustralia --- women directors tendency to be on foreign incorporated company boards --- is positive but not signif. 18 ERGM estimation for Evtushenko & Gastner data Parameter Estimate Std Error Edge -10.3903 0.2757 * BipartiteAltStarsB.5. 0.4660 0.0472 * IsolateEdges - 0.0864 0.2574 BipartiteAltStarsA.5. - 2.6763 0.2562 * BipartiteActivityA_female 0.0511 0.1069 BipartiteContinuousActivityA_age 0.0053 0.0025 * BipartiteActivityB_industry.Personal.Goods 0.2082 0.0938 * BipartiteActivityB_sector.Oil.and.Gas - 0.0118 0.0167 BinaryPairInteraction_gender.Male_industry.Personal.Goods - 0.3871 0.1560 * BinaryPairInteraction_gender.Female_sector.Oil.and.Gas - 0.1021 0.1221 TotalRuns 20 ConvergedRuns 20 num_Persons = 321869 num_Companies = 34769 Mode A is people, mode B is companies. •Positive BipartiteContinuousActivityA_age: older directors tend to be on more boards (just as for ASX data). •Positive BipartiteActivityB_industry.Personal.Goods: companies in Personal Goods industry tend to have larger boards. •Negative BinaryPairInteraction_gender.Male_industry.Personal.Goods: men are less likely to be on boards in Personal goods industry. •BinaryPairInteraction_gender.Female_sector.Oil.and.Gas (and its control BipartiteActivityB_sector.Oil.and.Gas) are both negative but not significant. (BipartiteActivityA_female is positive but not significant). 19 x--o--* *--o--* •Negative bipartiteAlterTwoStar2A suggests that there is a significant tendency against a board having two women; a tendency against “contagion” (multiple women on same board). In conjunction with positive bipartiteAlterTwoStar1A might be considered evidence for the “token woman” hypothesis: there is a tendency towards a board having a woman, but against having an additional woman. •Negative Ego age: women directors tend to be younger than male directors (just as in descriptive statistics). •Negative Alter industryGroup.Materials: Women directors less likely to be on boards in Materials industry group (note: includes mining). •Positive Alter industryGroup.Banks (only signif. In Model 1): Women directors more likely to be on bank boards. •Positive Alter logMarketCap: Women directors tend to be on boards of companies with larger market capitalization. •Positive Alter notAustralia: Women directors are more likely to be on boards of foreign incorporated companies. •Negative Mismatching country: Women directors tend not to be on boards with directors of a different nationality. 20 Note that Ego betweenness is positive and signif. In Model 1 (no structural effects), consistent with descriptive statistics (in hidden bonus slides) that mean betweenness centrality is higher for women than men; however in Model 4 (includes structural effects), is becomes negative and signif: once we control for these structures (including those just described suggesting support for “token woman” hypothesis) women are associated with less central positions (with betweenness centrality mesasure). For BiRank centrality, women are also associated with less central positions (Model 5, Ego.birank negative and signif.); this is also the case with simple descriptive statistics (median and mean are both lower for women than for men (p < 0.001 Wilcoxon rank sum test with continuity correction [hidden bonus slides]). ALAAM “outcome” binary variable is female on mode A (directors; mode B is companies). The values in parentheses are the estimated standard errors. Values in light gray are not statistically significant at the conventional 0.05 significance level. The models were estimated by stochastic approximation with the ALAAMEE software. Centrality measures were centered around their means and scaled by their standard deviations when used as nodal attributes in the ALAAM estimation. 20 Conclusions (1) •We constructed a director interlock network for all companies listed on the ASX, and examined descriptive statistics related to the distribution of women directors. •Using the binomial distribution null model, we find no evidence for the “token woman” hypothesis in Australian listed companies. •For boards of size six (the modal and median size) only, this model provides evidence against the hypothesis. •We estimated bipartite ERGM models for the Australian listed company director interlock network (2 087 companies, 9 971 directors), and the Evtushenko & Gastner (2020) international director interlock network (321 869 directors, 34 769 companies). •Most parameters related to gender were not statistically significant. •But in the international director network, men are less likely to be on boards in Personal goods industry. 21 Conclusions (2) •We estimated bipartite ALAAM models (dependent variable: female on director node) for the ASX director interlock network. •These models suggest there is a tendency towards a board having a woman, but against having an additional woman: evidence for the token woman hypothesis. •Also confirms several hypotheses about the structural positions of women in the Australian listed company director interlock network: •Female directors tend to be younger than male directors. •Female directors are less likely to be on boards in Materials industry group. •Female directors more likely to be on bank boards. •Female directors tend to be on boards of companies with larger market capitalization. •Female directors are more likely to be on boards of foreign incorporated companies. •Female directors are associated with less central positions in the director interlock network. 22 Slides and software availability •This is unpublished work (as of June 2023). •Some more details, and references, are in the “hidden bonus slides” after this one. •I will make these slides available on my website: •https://sites.google.com/site/alexdstivala/home/conferences •The software for large bipartite ERGM and ALAAM estimation is available from: •ERGM: https://github.com/stivalaa/EstimNetDirected •ALAAM: https://github.com/stivalaa/ALAAMEE •Unfortunately, data cannot be made publicly available as it contains data from a commercial Thomson-Reuters database. 23 Data cleaning and checking •I removed the ASX test company TES. •I verified that all companies have at least 3 directors, as required by the Corporations Act. •The Connect 4 Boardroom data codes director age as age (rather than year of birth). For 10 occurrences where this had clearly been coded incorrectly as year of birth (e.g., 1965), I subtracted it from 2022 to convert it to age. •There is a lot of missing data for age (75% missing), but no missing data for gender. •I selected two prominent companies in the top ten ASX companies (CSL and WBC), and 3 randomly selected companies (TAR, YRL, and SRJ) and manually checked the Connect 4 information against company websites and annual reports. •Consistent with the domination of the ASX by mining companies, 2 of these 3 randomly chosen companies are mining companies (and the 3rd is in in the oil & gas sector). 30 Definition of “director” in this work •The data is from the Connect 4 Boardroom database (Thomson Reuters). •The definition of “director” in this data, is not necessarily the same as the legal definition. •It includes company secretaries, and certain key management personnel. •People who are legally company directors and secretaries, plus those whose appointments are significant enough that they must be reported to the stock exchange and in annual reports. •I claim that this more inclusive definition is more useful for work involving power and influence in the corporate interlock network, as it includes for example CEOs, CFOs, etc. – who may or may not be actual directors (so would in many cases be excluded if only actual directors are included), but who are inarguably powerful and/or influential. •Company secretary is more arguable, but under the Corporations Act they are company officers responsible for ensuring the company’s legal obligations are met. Company secretaries are responsible for organizing board meetings and liasing with regulators, so it is an important role. •This data also means the information is legally required and consistently defined, not relying on statements from company representatives or executives… Note potential problem with including company secretaries: there are firms that provide corporate governance services, such as providing company secretaries, and so a company secretary from such a firm can end up being the secretary for many firms, and therefore being very central in the network. But as noted, is an important role. See e.g. Robertson 2018 “THE ROLE OFTHE COMPANY SECRETARY: INFLUENCE, IMPACT AND INTEGRITY” AICD https://www.aicd.com.au/content/dam/aicd/pdf/toolsresources/bookstore/previews/Role-of-Company-Secretary-preview.pdf 31 Example: TAR https://www2.asx.com.au/markets/company/tar [accessed 22 Oct. 2022] Example of company secretary issue: Dan Smith works for (in fact is “Commercial Director” of) a firm called Minerva Corporate, which provides company secretarial and other listed company compliance services (https://www.minervacorporate.com.au/). According to his LinkedIn profile (https://au.linkedin.com/in/dan-smith-60a1b930, accessed 29 Nov. 2022), Dan Smith is the secretary of 8 companies and a director of 9 (some of these also secretary). (Note these companies are not all necessarily listed on the ASX). He is a director or secretary of 11 companies in the Connect 4 Boardroom data. TAR is smaller than a “small cap”, perhaps rather a “microcap” or even “nanocap” (or more derogatory, “penny stock”) – market cap. approx. $17 million (5 Oct. 2022). Other things to note: This board is all-male, the CEO is not listed as a director, and there is no Chair identified (under the Corporations Act a board meeting must have a Chair, who must be a director –there need not necessarily be an ongoing elected Chair, the Chair can be elected for a meeting, see s. 248E [replacable rule] Corporations Act (2001) Cth). 32 Note there is a lot of missing data for age (75% missing). Importantly, however, there is no missing data for gender. 33 Listing year distribution The oldest company is BHP (1885). The second oldest is SOL, Washington H Soul Pattinson (1903), originally a Sydney pharmacy, now an investment company. 34 Evtushenko & Gastner (2020) find that: “In terms of degree and betweenness centrality statistics, women are doing marginally better than men (Table 2). The distributions of degree and betweenness 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 to the largest component and nodes with the parameter of interest > 0. The twosample t-test for degree concludes that the marginal difference between men and women is statistically significant (p-value < 0.0001). The difference in the betweenness centrality is not statistically significant at a significance level of 0.05 (p-value 0.068).” 35 36 Note (top left graph) log market cap is linearly positively correlated with board size (degree of company nodes in bipartite network, i.e. degree centrality). 37 •This is what happens if we just use the overall relative frequency of women (0.21) for all board sizes, instead of the relative frequency conditional on each board size. •The fit is good for board size 7, where the relative frequency is close to the overall relative frequency. •But the fit is worse the further we get from this (lower relative frequencies for smaller boards, higher for larger). 38 •For completeness, this is what happens if, instead of using the observed relative frequency of women (the MLE for p), we assume it is 0.5 •Now (unsurprisingly, given the observed p = 0.21), the fit is bad •And for all board sizes except 3 (obs < expected) and 11 (n.s.), the observed relative frequency of boards with exactly one women is significantly higher than expected. 39 46 Limitations and Future work •An updated “token women” hypothesis for the Australian context: •Given the corporate governance target of 30%, at least for the ASX300, •Rather than testing for an over-representation of boards with exactly one woman, instead test for over-representation of boards with only 30% women •As this is the minimum amount necessary to reduce external pressure to have more women in Australia. •[continued next slide…] Note for the updated (30%) hypothesis, we can already see from the graphs for the binomial null model that there is no evidence for this using this method (just by checking the observed and expected for ceil(0.3 * boardsize) in each plot, rather than just 1) 47 •We have information about whether a person is a Chair of a board, or an executive or non-executive director. We should use this (but have not yet). Based on previous work (some shown here) I hypothesize that: •Women are less likely than men to be Chair •Women are less likely than men to be executive directors •This work only examines the proportion and position of women in the interlock network --- it is does not consider effects e.g. on earnings quality, etc. •It would also be of interest to also include data about which committees (remuneration, audit, risk, etc.) a board member is on. (Suggested by Helen Bird). This data does not seem readily available, however (without a lot of work manually coding it –which for the existing data was done commercially by Thomson Reuters). •[continued next slide…] 48 More limitations and potential future work •We only have the director interlock network of ASX listed companies. But the closed social networks from which directors are recruited also often overlap with non-commercial directorships, such as non-profits (“prestigious” private schools, charities, foundations, etc.) and government boards. This data is not apparently easily available to us, however. •…[continues next slide] 49 These closed social networks also include, for example, as well as the stereotypical “old boys network”, family and social connections for example through “exclusive” club memberships: We can see this anecdotally as well. ANZ chairman David Gonski is a mentor to ex-AMP chairwoman Catherine Brenner. Gonski was also chairman of Coca-Cola Amatil when Brenner was appointed to the board in 2008. Meanwhile Brenner’s sister-in-law, Maxine Brenner, sits on the boards of Orica Ltd, Origin Ltd and Qantas Airways. … My research found that the social identity of candidates is a significant criterion in the selection of Australian company boards. Closed social networks are the primary means of identifying new board members. Smith, S. (2018). Company Boards Are Stacked with Friends of Friends so How Can We Expect Change?. The Conversation. https://theconversation.com/company-boards-arestacked-with-friends-of-friends-so-how-can-we-expect-change-95790 In the past, particularly in Melbourne, directors were part of old boy networks and were often on many boards together. Companies like Pacific Dunlop, BHP, ANZ would have interlocking boards where there were mutual advantages across businesses that is banks lending to companies with reputations of board members driving the due diligence procedures. Often board members were members of the same clubs such as the Melbourne Club, Australian Club and Athenaeum Club. (Male Participant 11) Smith, S. (2018). Beyond board capital: probing inside the black box of Australian board recruitment and dynamics (Doctoral dissertation, RMIT University), p. 124 50 I think in Australia it’s messier than in America or in Britain… clubs are relevant, I’m a member of the Australian Club. I know that the people that are members there go through a very elaborate screening process and so if I were choosing a director and one of the candidates was a member of the Australian Club I would say almost certainly honest, cooperative, easy to mix with and so on. There are lots and lots of different circles, there’s not a single tight network in Australia. There are scores, hundreds perhaps of little networks, things that will provide people that know about those networks with confidence in other people. (Male Participant 5: 40 years+ experience on various types of boards) Smith, S. (2018). Beyond board capital: probing inside the black box of Australian board recruitment and dynamics (Doctoral dissertation, RMIT University), p 139 Again, information such as club membership is not readily available in a systematic way, requiring (as in this thesis) case studies, interviews, qualitative methods. There are also other kinds of diversity (beyond gender diversity, and age) that are not considered here, and which we do not have data for, e.g., ethnic identification and socioeconomic class (for example whether someone attended a ‘prestigious’ private school) 51 References 52 B. Aronson and K.-C. Yang. birankr: Ranking Nodes in Bipartite and Weighted Networks, 2020. URL https://CRAN.Rproject.org/package=birankr. R package version 1.0.1. A. Borisenko, M. Byshkin, and A. Lomi. A simple algorithm for scalable Monte Carlo inference. arXiv preprint arXiv:1901.00533v4, 2020. U. Brandes. A faster algorithm for betweenness centrality. J Math Sociol, 25(2):163–177, 2001. Z. Burgess and P. Tharenou. Women board directors: Characteristics of the few. J Bus Ethics, 37:39–49, 2002. M. Byshkin, A. Stivala, A. Mira, R. Krause, G. Robins, and A. Lomi. Auxiliary parameter MCMC for exponential random graph models. J Stat Phys, 165(4):740–754, 2016. M. Byshkin, A. Stivala, A. Mira, G. Robins, and A. Lomi. Fast maximum likelihood estimation via equilibrium expectation for large network data. Sci Rep, 8:11509, 2018. A. Clauset, C. R. Shalizi, and M. E. Newman. Power-law distributions in empirical data. SIAM Rev, 51(4):661–703, 2009. G. Csárdi and T. Nepusz. The igraph software package for complex network research. InterJournal, Complex Systems:1695, 2006. URL https://igraph.org. D. B. Dahl, D. Scott, C. Roosen, A. Magnusson, and J. Swinton. xtable: Export Tables to LaTeX or HTML, 2019. URL https://CRAN.R-project.org/package=xtable. R package version 1.8-4. C. L. Dezső, D. G. Ross, and J. Uribe. Is there an implicit quota on women in top management? A large-sample statistical analysis. Strateg Manag J, 37(1):98–115, 2016. T. Diviák, J. A. Coutinho, and A. D. Stivala. A man’s world? Comparing the structural positions of men and women in an organized criminal network. Crime, Law and Social Change, 74:547–569, 2020. 53 A. Evtushenko and M. T. Gastner. Beyond Fortune 500: Women in a global network of directors. In H. Cherifi, S. Gaito, J. F. Mendes, E. Moro, and L. M. Rocha, editors, Complex Networks and Their Applications VIII, pages 586–598, Cham, 2020. Springer International Publishing. A. Farrell and P. L. Hersch. Additions to corporate boards: The effect of gender. J Corp Finance, 11(1-2):85–106, 2005. L. C. Freeman. A set of measures of centrality based on betweenness. Sociometry, pages 35–41, 1977. L. C. Freeman. Centrality in social networks: Conceptual clarification. Soc Networks, 1(3):215–239, 1978. E. R. Gansner, Y. Koren, and S. North. Graph drawing by stress majorization. In International Symposium on Graph Drawing, pages 239–250. Springer, 2004. C. S. Gillespie. Fitting heavy tailed distributions: The poweRlaw package. J Stat Softw, 64(2), 2015. X. He, M. Gao, M.-Y. Kan, and D. Wang. BiRank: Towards ranking on bipartite graphs. IEEE Trans Knowl Data Eng, 29(1):57– 71, 2017. M. Hlavac. stargazer: Well-Formatted Regression and Summary Statistics Tables. Central European Labour Studies Institute (CELSI), Bratislava, Slovakia, 2018. URL https://CRAN.R-project.org/package=stargazer. R package version 5.2.2. J. Joecks, K. Pull, and K. Vetter. Gender diversity in the boardroom and firm performance: What exactly constitutes a “critical mass?”. J Bus Ethics, 118:61–72, 2013. R. M. Kanter. Some effects of proportions on group life: Skewed sex ratios and responses to token women. Am J Sociol, 82(5):965–990, 1977. 54 J. Koskinen and C. Edling. Modelling the evolution of a bipartite network—peer referral in interlocking directorates. Soc Networks, 34(3):309–322, 2012. M. Marchiori and V. Latora. Harmony in the small-world. Physica A, 285(3-4):539–546, 2000. T. Opsahl. Structure and Evolution of Weighted Networks. University of London (Queen Mary College), London, UK, 2009. URL http://toreopsahl.com/publications/thesis/. T. Opsahl. Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Soc Networks, 35(2):159–167, 2013. A. Parker, F. Pallotti, and A. Lomi. New network models for the analysis of social contagion in organizations: an introduction to autologistic actor attribute models. Organizational Research Methods, 25(3):513–540, 2022. J. Robertson. The role of the company secretary: Influence, impact and integrity. Australian Institute of Company Directors, Sydney, NSW, 2018. G. Robins and M. Alexander. Small worlds among interlocking directors: Network structure and distance in bipartite graphs. Computational & Mathematical Organization Theory, 10(1):69–94, 2004. D. Schoch. graphlayouts: Additional Layout Algorithms for Network Visualizations, 2020. URL https://CRAN.Rproject.org/package=graphlayouts. R package version 0.7.1. S. Smith. Beyond board capital: Probing inside the black box of Australian board recruitment and dynamics. PhD thesis, RMIT University, 2018. URL https://researchrepository.rmit.edu.au/esploro/outputs/9921864268201341. 55