Abstract



An Agent-Based Simulation of How Promotion Biases Impact Corporate Gender DiversityChibin ZhangAleria PBCPaolo GaudianoCity College of New YorkandAleria PBCCorresponding Author: Paolo Gaudiano, c/o Aleria PBC, 261 Madison Ave, 10th Fl, New York, NY 10016 USAEmail: paolo@aleria.techNote: A shorter version of this paper with partial, preliminary results was presented at the Future Technologies Conference in September of 2019, and appears in Zhang, C. & Gaudiano, P. (2019). An agent-based simulation of corporate gender biases. In K. Arai et al. (Eds.): Future Technologies Conference, AISC 1069: 90–106.AbstractDiversity & Inclusion (D&I) is a topic of increasing relevance across virtually all sectors of our society, with the potential for significant impact on corporations and more broadly on our economy and our society. In spite of the fact that human capital is typically the most valuable asset of every organization, Human Resources (HR) in general and D&I, in particular, are dominated by qualitative approaches. We introduce an agent-based simulation that can quantify the impact of certain aspects of D&I on corporate performance. We show that the simulation provides a parsimonious and compelling explanation of the impact of hiring and promotion biases on the resulting corporate gender balance. We show that varying just two parameters enables us to replicate real-world data about gender imbalances across multiple industry sectors. In addition, we show that the simulation can be used to predict the likely impact of different D&I interventions. Specifically, we show that once a company has become imbalanced, even removing all promotion biases is not sufficient to rectify the situation, and that it can take decades to undo the imbalances initially created by these biases. These and other results demonstrate that agent-based simulation is a powerful approach for managing D&I in corporate settings, and suggest that it has the potential to become an invaluable tool for both strategic and tactical management of human capital. Keywords: Diversity/Gender, Simulations and Agent-Based Modeling, Labor and Workforce Dynamics, Strategic Human Capital INTRODUCTIONIn spite of the growing body of evidence showing that companies with greater gender representation in leadership roles tend to outperform companies with fewer women (Dezso? et al., 2012; Flabbi et al., 2014; Hunt et al., 2018), many industries continue to exhibit a sharp gender imbalance, with senior and executive levels being dominated by men. These imbalances contribute to some of the severe problems we see across a variety of industries, ranging from gender pay gaps (Biagetti et al., 2011; Blau et al., 2007) and high churn rates (Becker-Blease et al., 2016; Shaffer et al., 2000) to discrimination lawsuits (Hirsh et al., 2018; Murphy, 2004). In turn, these problems lead to high costs and internal instabilities, and expose companies to significant reputational risk. Beyond the private sector, gender imbalances also impact academia and the public sector (Bain et al., 2000; Jokinen et al., 2017). Given the extensive studies showing that greater gender inclusion can lead to corporate, economic and societal benefits, given the tangible negative implications of gender imbalances, and given the ongoing efforts ranging from individual activism to legislation, why are there still such significant gender imbalances across virtually all industry sectors? We believe that the relative lack of progress is due primarily to the sheer complexity of the problem, and the lack of tools that can deal with this degree of complexity. Today, HR management is considered a “soft” skill; workforce analytics platforms rely on measurements and statistical analysis, but are unable to quantify the myriad activities, interactions, attitudes and subjective preferences of employees.The complexity that so challenges workforce analytics, we believe, is also the reason why certain D&I initiatives that seem to work within one organization, often fail to produce results – or even backfire – at other organizations: each organization is a unique “ecosystem” whose macroscopic behavior emerges from the complex web of interactions among its staff, leadership, customers, suppliers and partners. Borrowing a D&I initiative from another company and hoping that it will have a positive impact on our company, is analogous to copying a specific advertisement that was successful for another company in a different sector, and expecting it will sell our products.When you also consider that the impact of personnel initiatives can take months or years to be observed, and that missteps can be extremely costly, it’s no wonder that leaders are reluctant to take decisive action. What is needed is a quantitative approach that can capture and analyze the behavior of complex systems.We have successfully begun using agent-based simulation, one of the primary tools of Complexity Science, to replicate the complex behaviors of people within organizations. In this paper, we show the results of applying agent-based simulation to a particular aspect of corporate gender imbalance: by simulating the hiring and career advancement of employees at typical companies, we can analyze the impact of introducing gender biases.Under reasonable assumptions, we find that gender biases in promotion can yield the kinds of gender imbalances that are typical of many companies, with decreased representation of women at higher corporate ranks. We also find that by adjusting gender biases in hiring as well as promotions, it is possible to develop gender imbalances that match the patterns observed in different industries.Because they capture the causal relationships that link individual behaviors and interactions to the resulting system-level behaviors, agent-based simulations can be used to predict the outcome of different initiatives. Here we use our simulation to test the likely impact of removing all promotion biases in a company that is already gender-imbalanced. Under a variety of scenarios, we find that simply removing biases is not a very effective strategy, as it can take much longer to eliminate the gender biases than it took to establish them in the first place.Lastly, we use the simulation to explore how company-level biases lead to different individual day-to-day experiences for employees based on their personal characteristics, and discuss how these experiences can impact employee satisfaction and productivity.Our findings, in line with other studies, show that agent-based simulation is a powerful tool for workforce analytics, and that this approach holds great promise for theoretical and applied research into D&I – a topic of great current interest with significant economic and societal implications.After introducing some background materials, the remainder of this paper describes the simulation we have developed, and then presents several results we obtained with the simulation. The paper is brought to a close with some conclusions and suggestions for future opportunities to expand this line of work.BACKGROUND Gender biases in the workplace Although female labor force participation is increasing, women still are severely underrepresented at the top levels of organizations: according to the U.S. Department of Labor, women account for almost half of the total labor force in the U.S., and more than 40 percent of those have college degrees; however, in 2018, women only held 26.5% of executive and senior-level management positions, and only 5% of chief executive officer positions in S&P 500 companies (Catalyst, 2019). To understand the causes of these types of gender imbalances, Bielby et al. (1986) categorized the causes of the gender gap in upper management positions into supply-side and demand-side explanations. According to supply-side explanations, the divergence in employment outcomes between women and men is mainly due to differences in gender-specific preferences and productivity (Matsa et al., 2011), therefore individual attributes determine the gender inequalities in the workplace (Olsen et al., 1983). For example, some believe that balancing work and family life lowers women’s promotion rate as women need to take on a larger share of domestic and parental responsibilities (Kossek et al., 2016); others hypothesize that women, in general, are less competitive than men so they may be reluctant to compete for promotion (Niederle et al., 2007). In contrast, demand-side explanations suggest that gender stratification in the workplace is primarily due to gender-specific barriers; demand-side explanations focus on the institutional constraints and managerial biases faced by women in climbing the career ladder. For example, a male-dominated board of directors may prefer to hire male executives (Matsa et al., 2011); women must meet higher performance standards for promotion than their male colleagues (Gjerde, 2002; Lyness et al., 2006); and stereotypes of leadership style differences favor men in advancing to leadership roles (Vinkenburg, et al., 2011). In this paper, we introduce a quantitative methodology that provides indirect but compelling evidence for a demand-side explanation. Specifically, we simulate the typical career advancement of employees in an organization, and test the hypothetical impact of introducing gender biases in the promotion process. We find that, under a range of simple and realistic assumptions, it is possible to replicate the levels of gender disparity that are observed in typical companies across a variety of industries, with increasing male dominance at increasingly senior levels. Hence, while we cannot conclusively prove that gender imbalances are due to gender-specific barriers, we demonstrate that the existence of gender-specific barriers yields the kinds of imbalances that are observed empirically. Another gender-specific barrier that we examined is bias in hiring. As suggested in a recent report by McKinsey & Company (Krivkovich et al., 2018), in some industries women may remain underrepresented at manager levels and above because they are less likely to be hired into entry-level jobs, in addition to being less likely to be promoted into manager-level positions. To test this hypothesis, we extended our simulation to capture a simple form of hiring bias, and found that by adjusting the hiring and promotion biases simultaneously we are able to replicate industry-specific gender balance patterns across various industry sectors, as reported in the McKinsey study. Simulating Corporate D&IA majority of the research on gender inequality in the workplace is conducted by applying statistical methodology on collected data. These statistical approaches have significant limitations, including the fact that they hide details about individuals and cannot capture dynamic interactions; in general, statistical approaches capture population-level outcomes but cannot capture the underlying causal relationships and time-dependent interactions that lead to those population-level outcomes.The human behaviors and interactions that drive the performance of an organization – including the impact of personal interactions that are influenced by D&I – are exactly the types of complex relationships that cannot be captured through statistical, population-based analyses. A more fruitful approach to analyzing the impact of D&I is to apply methodologies that are designed specifically to analyze complex systems. In this paper we draw from Complexity Science, a discipline that first took shape in the late 1960s with the seminal work of Thomas Schelling on the emergence of segregation (Schelling, 1969), and became a full-fledged area of academic inquiry in 1984 with the creation of the Santa Fe Institute. Complexity Science is a broad field that encompasses a variety of technologies for studying complex systems, i.e., systems whose behavior depends in complex and often unpredictable ways on the behaviors of many individuals interacting with one another and with their environment (Waldrop, 1992). One of the primary tools for the analysis of complex systems is agent-based simulation, a methodology that combines behavioral science and computer modeling (Bonabeau, 2002). Agent-based simulations capture the behaviors of individuals, as well as their interactions with other individuals and with their environment, to simulate the way in which the overall behavior of a system emerges from these complex chains of interactions. Agent-based simulations are ideally suited to analyze and predict the performance of human systems such as companies (Fioretti, 2013; Wall, 2016), because they capture the mutual relationship between individuals and the organization in which they belong: in the case of a company, the behaviors of individual employees combine to determine the success of an organization and, conversely, the environment created by the company influences the performance of the individual employees. This sort of “feedback loop” is part of what makes workforce management so complex, and it is exactly the type of problem that lends itself to analysis using agent-based simulation. In this light, agent-based simulation promises to be a valuable tool specifically to capture the impact of D&I on corporate environments: to the extent that a company influences people’s experiences differently based on personal traits, the company’s performance will in turn be impacted by how those people are treated. In fact, the connection between D&I and complexity science has been proposed by others (Page, 2017), and agent-based simulation has already been used to analyze issues related to corporate D&I. For example, the simulation developed by Bullinaria (2018) shows how ability differences and gender-based discriminations can lead to gender inequality at different hierarchical levels within an organization; Taka?cs et al. (2012) found that discrimination can emerge due to asymmetric information between employer and job applicants, even without hiring biases; Robison-Cox et al. (2007) used agent-based simulation to test the possible explanations of gender inequality at the top level of corporations, and found that giving men favorable performance evaluations significantly contributes to the gender stratification of top-level management.Our agent-based simulation takes a step further and simulates ongoing activities and transitions within a typical company, to show the dynamics of how corporate gender imbalances arise at each level of the hierarchy as a result of biases in hiring and promotion processes. Our simulation replicates the day-to-day operations of a typical company with men and women distributed across four levels: entry-level employees, managers, vice presidents (VPs) and executives. In a pilot project, we were able to simulate the impact of gender biases in the promotion process, which leads to the kinds of gender imbalances seen in real companies, with increasing representation of men in higher levels of the company (Zhang & Gaudiano, 2019). In this paper we report a more complete set of results and provide a direct comparison to industry data. In addition, we provide additional results showing that removing biases in a company that is already imbalanced is not a very effective strategy, as gender inequalities can persist for significant periods of time. Our findings are in line with those of Kalev et al. (2006), who found that programs targeting lower levels of management, such as diversity training and performance evaluations, do not help to increase diversity at higher corporate levels, and that imbalances persist after organizations adopt these diversity management programs. THE SIMULATION One of the most powerful aspects of agent-based simulation is that it captures the way real-world systems work in an intuitive, human-centric fashion. This means that anyone who has familiarity with the problem can contribute to the design of the simulation. In a sense, agent-based simulation democratizes analytics, because it does not require knowledge of advanced mathematical or computational techniques. Agent-based simulations allow domain experts to be closely involved both with the model design and with the analysis of the results (Gaudiano, 2017), a key departure from more traditional approaches to analytics, in which a data scientist analyzes large amounts of data using analytical tools to look for patterns, and the domain expert is relegated to making sense of the identified patterns. In fact, working closely with domain experts, our team has developed dozens of agent-based simulations to solve complex problems across many sectors, including consumer marketplaces (Gaudiano, 2016; Duzevik et al., 2007), energy consumption in commercial buildings (Gaudiano, 2013), manpower and personnel management for the U.S. Navy (Garagic et al., 2007), healthcare (Gaudiano et al., 2007) and computer security (Shargel et al., 2005). In all these examples, the simulations were developed by asking domain experts to describe individual behaviors and interactions, and translating them into software simulations. The knowledge of the domain experts is retained in the simulation, which makes the “structure” of the simulation intuitive to anyone using them. Running the simulation then replicates the complex interactions over time that are impossible to grasp intuitively or mathematically.This is one of the benefits of agent-based simulations: because they are literally trying to replicate the individual-level behaviors, they are intuitive to domain experts; but because they replicate the complex interactions over time that occur in real systems, they are able to reproduce the outcomes observed in the real world. We now show how we applied this methodology to the study of corporate D&I, and, more specifically, to corporate gender biases.Core Elements of Our SimulationThe simulation we developed for the present study is based on simple assumptions about the operations of a typical company. Because we are exploring gender biases, in our simulated company there are two types of employees, men and women. And because our aim is to study the impact of institutional barriers, our simulation assumes that men and women have identical abilities and that their performance is also identical. While many other details could easily be added, for the present study we wanted to focus exclusively on how gender biases in promotion and hiring impact the overall behavior of a company. REF _Ref37997040 \h \* MERGEFORMAT Figure 1 is a screenshot of the simulation, which was developed with the NetLogo simulation platform (Wilensky, 2015). Employees fall into one of four increasing ranks: entry-level employees, managers, VPs and executives. At each rank there are men (in blue – or darker shade if viewed in grayscale) and women (in yellow – lighter shade). Insert REF _Ref37997040 \h \* MERGEFORMAT Figure 1 about hereAt the start of each simulation “run,” employees are distributed across ranks in a way that mimics a typical company, with smaller numbers of employees at higher ranks. The company is assumed to grow over time, creating vacancies within each rank. In addition, employees may separate from the company, creating additional vacancies. Vacancies at the entry level are filled through hiring from a hypothetical external pool of candidates, while vacancies at all other ranks are filled by promoting individuals from the rank immediately below, which, in turn, creates additional vacancies at the rank from which someone was promoted. For this version of the simulation we do not simulate direct hiring into higher ranks, nor do we allow promotions to skip levels. However, these and other details could be added if we were interested in exploring the effects of such modifications.While the simulation runs, the employees move back-and-forth across the floor of their rank as time elapses. (This movement is not relevant to the results, but it helps to visualize the activities unfolding over time.) Employees who separate from the company rise just above the other employees, turn gray and gradually fade. Employees who are promoted are seen floating up to the next level. These movements help to visualize the main activities that take place during each simulation run.In addition, to help visualize the gender balance for each employee rank, the floor of each level of the simulation acts as a simple histogram, showing the percentage of men and women at that rank, while the two vertical bars on the left of the screen show the overall gender balance across the entire organization.The company’s overall gender balance is an emergent behavior that results from three main HR activities that take place as the company grows over time: hiring, promotion and separation. We now describe each of these processes.Simulating the Hiring Process When a vacancy occurs at the entry level, the simulation assumes that a new employee will be hired from a potentially infinite external candidate pool. By default, there is an equal chance of hiring a man or a woman. Gender biases in hiring can be simulated by setting a hiring-bias parameter, which changes the probability of men (or women) being hired. When an employee is hired, the simulation begins to track their seniority, i.e., amount of time they have been with the company. At the start of the simulation, employees are assigned a random rank and seniority level.Simulating the Promotion ProcessWhen a vacancy appears at any rank above the entry level, promotions are simulated by identifying a pool of “promotion candidates” from the rank immediately below, and then choosing randomly one employee from that pool. By default, the promotion pool is set as a percentage of the total number of employees at that rank, and is based on the “promotion score” of each employee, a normalized value based on the amount of time the employee has spent at the current rank (“rank seniority”), relative to the amount of time spent by the most senior employee at that rank. In other words, in the absence of a bias, promotions are based on rank seniority, with some randomness to reflect the fact that seniority is not an exact indicator of merit. It is worth noting that seniority has been widely used as a salient criterion for promotion in many industries, and it has been suggested that promoting the most senior employee instead of promoting the candidate with best performance or ability, can reduce possible psychological disturbances (Mills, 1985).When an employee is promoted, its seniority at the new rank is set to zero, while the simulation still tracks the total amount of time that the employee has been with the organization.Gender biases in the promotion process are simulated by adding a promotion-bias parameter, a value that is added to the rank seniority of each employee to calculate the promotion scores. The promotion-bias parameter can be positive or negative to simulate biases that favor men or women, respectively. The promotion-bias parameter is applied uniformly at all ranks.It is important to note that we are not suggesting how promotion biases come into play; we are simply interested in understanding how gender biases in the promotion process, if present, would impact the overall outcomes for the company, regardless of their source or nature.Simulating the Separation ProcessIn this simulation we do not distinguish between employees who quit and those who are fired, referring simply to “separation” as the act of an employee leaving the company. While it would be possible to capture the nuances of the different types of separations, for the purposes of this study the key value of separations is to create turnover at a rate comparable to what we see in real companies, so that the company’s employee pool is refreshed over time.We simulate separations by assuming a certain annual company turnover rate and apply that uniformly at each rank at each time step. This means that, in a given year, the absolute number of employees who separate is greatest at the entry level, and decreases with increasing rank. This ensures that the ratios of the number of employees across ranks remains consistent (subject to small fluctuations due to the timing of terminations and promotions) as the company grows over time. Notice that this also means that the average “tenure” of employees is directly proportional to rank: if there are twice as many entry-level employees than VPs, then, on average, the tenure of a VP will be about twice as long as that of an entry-level employee.To determine which employees separate at each rank, at each time step we determine the number of employees who are likely to separate, and then we randomly select these employees from a “separation pool,” a portion of the employees with the lowest promotion score at that rank; in other words, the decision to terminate is influenced both by seniority (or lack thereof) and gender. Applying the same gender bias for separations as well as for promotions reflects two assumptions: first, that the sources of bias that drive promotion decisions are also behind termination decisions. This seems reasonable, given that typically the same manager is in charge of both decisions. Second, if bias causes women to be held back, they are more likely to get frustrated, which may increase the probability that they will separate voluntarily (i.e., quit). In preliminary studies we have tried other separation processes, such as purely random selection. Including gender bias in separation heightens and accelerates some of the results we report, but does not alter our overall findings.Simulation setup Simulation Time Step and DurationThe simulation is time-based, meaning that we simulate the passage of time, with each time step equal to one week of operations. The software is designed to allow any level of temporal resolution, but we found that a weekly time step gives the best balance between capturing typical fluctuations and being able to simulate sufficiently long operating periods to see meaningful results. For all results reported below, we ran the simulations for the equivalent of either 10 or 40 years (520 or 2,080 time steps, respectively). Using a standard laptop, we can simulate four decades of company operations in a few seconds. We have tested reducing the time step to one day or even hours, and found no significant differences – other than taking proportionately longer to run. All time-dependent variables described herein are specified as annual rates, and then scaled automatically to the time-step size to ensure consistent behavior.RandomnessAt each time step, the simulation includes several operations that invoke a random-number generator, which results in variance across simulations (e.g., in selecting promotion and separation candidates). To ensure reproducibility of individual simulation runs, we have the ability to select the seed for the random-number generator. Unless otherwise specified, each of the results reported here was obtained by averaging the results from ten runs with different random seeds at each parameter setting, and includes error bars corresponding to one standard deviation. We found that results do not vary significantly as we increase the number of simulations beyond pany Size and Employee DistributionsFor all results reported here, the company begins with a total of 300 employees, 150 women and 150 men. The employees are distributed across the four levels in a way that roughly simulates a typical company: 40% at the entry level, 30% at the manager level, 20% at the VP level and 10% at the executive level. We have tested the simulation with other settings and found that the overall company size and exact distribution across levels has no significant impact on the results. However, the smaller the company, the more fluctuations will be seen across simulation runs with different random pany Growth and Separation RatesAs mentioned earlier, the simulation time step is set to correspond to a seven-day period. At each time step, random numbers are drawn to determine whether separations, hires or promotions need to take place. The frequencies of each of these occurrences are set so that, over the course of a simulated year, the overall growth and churn rates are within a range that would be consistent with a “generic” company: the company grows by 10% each year (linearly, meaning that it will double in size in ten years, and triple in size in 20 years), while we target an annual churn rate of 20%, which is in line with national average separation rates (Mercer, 2020).Promotion and Separation PoolsFor promotions, we set a candidate pool size of 15%: in other words, when someone needs to be promoted to a higher rank, we select the 15% of employees with the highest promotion scores, and then randomly choose one of them to be promoted. For separations, we set the candidate pool size to 50%, meaning that someone is selected randomly from half of the employees at each rank with the lowest promotion scores. We have tested different size candidate pools and found that the results do not change significantly as these parameters are changed.Employee Characteristics and VariablesOur simulation treats each employee as an “agent” with certain characteristics and variables. For this study, at the start of each run every agent is assigned a gender value that remains unchanged during the simulation. Each employee is also randomly assigned to an initial rank based on the distributions given above, and is given a start date that is set randomly (proportional to the starting rank). The start date is used to calculate the seniority of each employee. All other agent properties are variables, such as seniority and promotion score, that are used to track the state of each agent over time and to make decisions about promotions and separations. REF _Ref37997114 \h Table 1 describes all the agent characteristics and variables we used.Insert REF _Ref37997114 \h Table 1 about hereScenario-Testing ParametersTo test the impact of gender biases, we varied certain parameters systematically to explore scenarios of interest. Specifically, all of the scenarios reported here manipulated one or more of the following three parameters:Hiring Bias: this parameter determines the proportion of men and women that are hired when vacancies occur at the entry level. A positive bias means men are favored, and a negative bias means women are favored.Promotion Bias: this parameter is added to the seniority of each simulated employee to influence the probability that the employee will be included in the candidate pool when a promotion takes place. A positive bias means men are favored, and a negative bias means women are favored. The bias is expressed as a number between 0.0 and 1.0 that is added directly to the employee’s rank seniority.Promotion Bias Duration: for some of the scenarios we tested, the Promotion Bias was set to zero after a certain amount of time (typically 10 years) to simulate the removal of all gender biases in promotions and separations.A complete list of parameter settings used for all simulations (except as noted) is provided in REF _Ref37999515 \h Table 2.Insert REF _Ref38789930 \h Table 2 about hereResultsExperiment 1: the Impact of Gender Biases in Promotion In the first set of experiments we wanted to establish a baseline and then test the impact of systematically increasing the degree of gender bias in the promotion process. In all these simulations, the hiring bias is set to zero. REF _Ref38789991 \h Figure 2 shows the gender balance at each rank during a 40-year simulation when there is no promotion bias or hiring bias. The figure shows that, in the absence of biases, the gender balance stays at 50-50 throughout the simulation, with only small oscillations due to the inherent randomness of the simulations. Insert REF _Ref38789991 \h Figure 2 about hereNext, we tested the impact of increasing the promotion bias to 0.1, 0.3 and 0.5. As mentioned earlier, in the absence of biases, each simulated employee’s promotion score is simply its seniority relative to the most senior employee at that level (rank seniority). Hence all the promotion scores prior to the application of a gender bias are between 0.0 and 1.0.Adding a promotion bias of 0.1 thus means that while women’s scores will still be in the range [0.0,1.0], men’s promotion scores will be in the range [0.1,1.1]. Similarly, at the highest level of bias reported here (0.5), men’s promotion scores will be in the range [0.5,1.5], while women’s promotion scores will stay in the range [0.0,1.0]. Insert REF _Ref38000163 \h Figure 3 about hereAs can be seen in REF _Ref38000163 \h Figure 3, a bias of 0.1 in promotions begins to show an interesting pattern: while the entry and manager levels continue to stay roughly at 50- 50, the VP level (dashed line with no symbols) is starting to show an imbalance in favor of men, and men now make up roughly 60% of the executive level (solid line with diamond symbols). The pattern becomes much more evident in REF _Ref38000404 \h Figure 4 and REF _Ref38790761 \h Figure 5, which show the gender balance at each company level when the promotion bias is set to 0.3 and 0.5, respectively. Several interesting phenomena are worth pointing out.Insert REF _Ref38000404 \h Figure 4 and REF _Ref38790761 \h Figure 5 about hereFirst, we see that, even though the promotion bias is a single parameter that works uniformly at each level, the successive promotions compound the effect, so that the gender imbalance is greatest at the executive level: after several simulated years, the executive level shows an imbalance of approximately 80% men when the bias is at 0.3, and exceeds 90% men when the bias is at 0.5. Second, increasing the bias has the effect of increasing the degree of imbalance, but also the speed with which the imbalance spreads through the organization: notice that with a bias of 0.3, the imbalance at the executive level builds gradually over a span of nearly 20 years; but when the bias is 0.5, the proportion of men at the executive level crosses the 80% mark in less than five years, and has essentially leveled off by year 10. Third, there is a surprising effect at the entry level: the percentage of female employees goes up as the promotion bias increases, even though there is no hiring bias, and even though women are being terminated more often than men because the promotion score influences separations. We can see in REF _Ref38000404 \h Figure 4 and REF _Ref38790761 \h Figure 5 that women make up an increasing percentage of the entry-level population, reaching 60% when the bias is 0.5. The reason for this “reverse imbalance” is that men are being promoted at a much higher rate than women, so that women are being left behind. In reality, this is not uncommon in the real world: many industries have large numbers of women in entry-level positions, and women often describe the negative experience of being “stuck” while their male colleagues get promoted (e.g., Chamorro-Premuzic, 2019).This last observation illustrates another great aspect of agent-based simulations: unlike typical “black-box” models, with an agent-based simulation it is possible to dig into the detailed activities to understand the origin of observed macroscopic phenomena, i.e., emergent behaviors. Overall, the results of the first experiment show that, starting with very simple assumptions, we can capture some qualitative phenomena that match our observations of real-world companies: the presence of gender biases in promotions leads to increasing gender imbalance at higher levels, and women being stuck in lower levels.In the next section, we show how, by manipulating both hiring and promotion biases, we can accurately replicate real-world data on gender imbalance observed for specific industries. Experiment 2: Combining Promotion and Hiring Biases to Match Industry-Specific Imbalances While the patterns shown in Experiment 1 qualitatively look remarkably like those we observe in real companies, we wanted to see whether, using a minimal set of assumptions, we could match real-world data on gender imbalances for more specific cases. To this end, we used our simulation to match data from McKinsey’s and LeanIn’s Women in the Workplace report (Krivkovich et al., 2018).We ran simulations for ten years, and measured the gender (im)balance at each rank. In all simulations we modified two parameters from the baseline case: the promotion bias and the hiring bias. In general, as mentioned earlier, higher promotion biases create larger imbalances at higher ranks, and can lead to reverse-imbalance at the entry level. In other words, if we think of the company’s gender balance as having the shape of a funnel going from the entry level up toward the executive level, that funnel is straight in the absence of biases, it becomes a bit narrower at higher ranks when promotion bias is low, and becomes dramatically narrower when promotion bias is high. In contrast, the hiring bias has a direct impact on the number of women at the entry level, which will have a uniform impact on all subsequent ranks; hence we expect that increasing the hiring bias will make the overall funnel narrower.In REF _Ref38002155 \h Figure 6, we show the comparison of ten-year gender balance data from our simulation and from the McKinsey report. The McKinsey report uses six levels (entry, manager, director, VP, SVP and C-Suite), so we selected the four levels that match the ranks used in our simulation: entry, manager, VP and Executive (C-Suite).Insert REF _Ref38002155 \h Figure 6 about hereStarting with REF _Ref38002155 \h Figure 6(A), we see that setting the promotion bias to 0.3 and high hiring bias of 0.4 results in only one third of women at the entry level, and less than 20% women in the top ranks. This shape closely matches the gender imbalances observed in the Engineering and Industrial Manufacturing sector in the McKinsey study. In REF _Ref38002155 \h Figure 6(B), the promotion bias remains at 0.3, but hiring bias is lowered to -0.1 so that recruitment at entry level favors women. As expected, the bias favoring hiring of women widens the base of the “funnel,” leading to approximately 60% women at entry level; however, the high promotion bias narrows the funnel, leading to only 20% women in the top ranks. These results match closely the gender data reported by McKinsey for the Insurance sector. In REF _Ref38002155 \h Figure 6(C), the promotion bias is lowered to 0.2. with the absence of hiring bias, women make up more than half of the entry level, while the somewhat lower promotion bias leaves nearly 25% of women in the top ranks. These results closely match the gender data reported by McKinsey for the Banking and Consumer Finance sector. Finally, REF _Ref38002155 \h Figure 6(D) shows a pattern that resembles the gender imbalances observed in the Retail sector, which tends to be dominated by women at the entry level, but with only a modest female representation at the top ranks. We obtained this graph by keeping the promotion bias to 0.2, but setting the hiring bias to -0.2 so that women receive favorable treatment when hiring into the entry level. Accuracy of the Industry SimulationsTo test the accuracy of our simulations of industry gender imbalances, we calculated the root-mean-squared deviation (RMSD) between each simulation and the data provided from the McKinsey study, given by the formula:RMSDi =(LOD-LOS)2+(L1D-L1S)2+(L2D-L2S)2+(L3D-L3S)24Where RMSDi is the RMSD for a given industry i; each squared term captures the difference between the gender balance data (subscript D) and the simulation (subscript S) at a given level Ln (with n representing rank, from 0 for the entry level to 3 for the executive level); and the division by 4 represents the fact that we are averaging the result across the four levels. Insert REF _Ref38002956 \h Table 3 about hereThe analysis of the accuracy of the simulations shown in REF _Ref38002155 \h Figure 6 is summarized in REF _Ref38002956 \h Table 3. In all cases, the RMSD was below 3%.Take together, the results shown in REF _Ref38002155 \h Figure 6 and REF _Ref38002956 \h Table 3 show that, by changing just two parameters – promotion bias and hiring bias – our simulation is able to replicate real industry data with high accuracy.Experiment 3: The Impact of Removing All BiasesMany companies nowadays have implemented diversity management policies in an attempt to create an inclusive environment for women and members of underrepresented minorities. One of the most important policies targeted at lowering managerial bias in promotion is diversity training. However, most of the research that examines the efficacy of diversity training such as seminars and workshops reveals that implementing diversity training as a single initiative will not lead to a more diverse organization, at least not in the short run (Cavaleros, Van Vuuren, & Visser 2002; Kalev, Dobbin, & Kelly, 2006). Some studies show that bias awareness training could even cause bias to be strengthened after the training (Duguid & Thomas-Hunt, 2015). We wanted to test what would happen in our simulation if we completely removed all biases (hiring and promotion) for a company that was already showing significant gender imbalance. In other words, we wanted to see whether creating equal hiring and promotion opportunities by eliminating all bias is sufficient to undo the gender imbalances originally caused by the biases. To test this, we repeated two of the same scenarios we tested in Experiment 1, but we set the promotion bias to zero after 10 years of operations. Once the promotion bias drops to zero, the promotion score is solely based on an employee’s seniority, meaning that advancement depends only on how long an employee has been at a given rank, and not on gender.The scenarios we chose for this Experiment used the same parameters from Table 2 that were used to generate REF _Ref38000404 \h Figure 4 (promotion bias of 0.3) and REF _Ref38790761 \h Figure 5 (promotion bias of 0.5) REF _Ref38006132 \h Figure 7 and REF _Ref38006138 \h Figure 8 show that even if all biases could be removed, it can take a very long time to “undo” the damage done, especially at the upper levels. Insert REF _Ref38006132 \h Figure 7 about hereSpecifically, we can see in REF _Ref38006132 \h Figure 7 that, after ten years of operations with a gender bias of 0.3, men occupy 80% of positions at the executive level, 75% at the VP level, 60% at the manager level and 45% at the entry level. (As we mentioned earlier, the reason why there are more women than men at the entry level is because more women are left behind as men have a higher chance of being promoted to the manager level.)When all biases are removed after ten years, we see that the entry level and the manager level return to 50-50 within three years, as women are quickly promoted from entry level to manager level. However, it takes nearly ten years for the VP level to return to approximately a 50-50 level. As to the executive level, we see a gradual decline over the two decades following bias removal, but even after a full 30 years, men still maintain a 60-40 majority over women.Insert REF _Ref38006138 \h Figure 8 about hereThe results are similar when the promotion bias is initially set to 0.5: as shown in REF _Ref38006138 \h Figure 8, after ten years the representation of men across the four levels is about 40% (entry-level), 70% (manager), 85% (VP) and 90% (executive). As in the previous example, the two lower levels return to 50-50 gender balance within about three years, the VP level reaches parity in just under ten years, while the executive level takes about 12 years to drop from 90% to 70%, but then declines only very gradually, and is still around 60% after three full decades without bias.These results are relatively easy to understand when we think about the compounding effects of two different factors. First, as explained in an earlier section – and as is generally the case in real companies –?the average tenure of employees is related to their rank, with employees at higher rank staying longer than employees at lower ranks. Hence it simply takes longer to “flush out” the imbalances at the higher ranks. Second, simply removing promotion biases does not cancel the existing disparities; consider for example what happens at the manager level in REF _Ref38006138 \h Figure 8: just when the biases are turned off in year ten, 70% of managers are male. If employees are promoted “fairly,” then for every ten managers promoted to VP level, seven of them will be men, which will continue to support gender disparity at the VP level. In fact, in our simulation, the women in this scenario will get a temporary “boost,” because all of the women managers who were more senior than their male peers but were not being promoted, will suddenly find themselves to be the most senior managers, and will be much more likely to be promoted in the first few months after the biases are turned off, a condition unlikely to occur in a real company.This experiment leads us to a general conclusion about corporate gender biases, namely, that simply removing biases is not an effective way to create equality. Put another way, when systemic biases have created disparities, equal opportunity is not an adequate remedy. Our results suggest strongly that some sort of affirmative action that favors the placement of women into higher ranks – whether through more aggressive promotion or through external hiring – is needed, if balance is to be restored.Experiment 4: The Impact of Promotion Biases on Individual EmployeesOne of the great benefits of agent-based simulations is that they make it possible to analyze at the same time the experiences of individuals and the overall company-level outcomes. This is perhaps the most powerful argument for using agent-based simulation as a core tool in managing talent in general: especially in the context of D&I, we tend to hear anecdotes about individual experiences, but most of the data reported is based on statistics measured at the company level, which hides the details of individual experiences. With agent-based simulation we can do both: we can calculate population-level data just as we would in the real world, without losing any of the information about individual experiences. This makes it possible to explore the causal relationships that link individual experiences with company-level, emergent outcomes.To illustrate this point, we conducted one final experiment to highlight how a company-wide promotion bias manifests itself in terms of the lived experiences of individual employees. In particular, while running simulations we noticed – not surprisingly –?that women were often stuck at each rank, while men with less seniority were getting promoted ahead of them. Anecdotally, this is an experience that is often reported by women.To quantify this phenomenon, we tracked how many times each simulated employee is passed over for promotion, and how much time it spends at a given rank. Specifically, each time an employee is promoted from a certain level, all other employees who are more senior increment a counter that tracks how many times they have been passed over for promotion. When an employee is promoted, we record the total amount of time it had spent at that rank (its “tenure-in-rank”) and the number of times it was passed over, and then we reset the counter to zero before heading to the higher rank. Note that, because there is no promotion beyond the executive level, this analysis can only be done for the first three ranks (entry level, manager, VP).Because the number of employees differs at different ranks, and because the simulation tracks every promotion, entry-level employees were being passed over many more times than managers, who in turn were being passed over more times than VPs. To correct this unrealistic situation, we normalized the data by dividing the number of times passed over by the number of people at that rank, and multiplying by ten. This roughly corresponds to assuming that, at each rank, employees are only comparing themselves to a group of ten “peers.” We also normalized the passed-over data by the average number of years that employees spend at each rank, to obtain an average annual figure, which made comparison across ranks more meaningful. REF _Ref38603899 \h Figure 9 shows the results of this analysis. The top row shows data for VPs, the middle row for managers, and bottom row for entry-level. Within each row, the left chart shows the average number of times passed-over in one year, while the right chart shows the average tenure-in-rank in years. Within each chart, there are four pairs of bars, representing, from left to right, the level of promotion bias (0.0, 0.1, 0.3, 0.5); each pair of bars represents data for men (dark grey) and women (light gray). As with all other experiments, each data point was obtained by running the simulation ten times with different random seeds, and error bars show one standard deviation of the mean.Insert REF _Ref38603899 \h Figure 9 about hereSeveral things are worth noting. First, when there is no promotion bias (the leftmost pair of bars in each plot), we see that the results for men and women are very similar, as expected. Note also that, because promoted individuals are selected randomly from a promotion pool (as described in the section REF _Ref38604743 \h \* MERGEFORMAT Simulating the Promotion Process), even in the absence of biases there will always be some employees that are passed over, which is why the leftmost bars at all three ranks are non-zero.Focusing now on each rank, we see consistent patterns both in the passed-over data and in the time-in-rank data. First, as the bias increases, all simulations show that women are passed over more times per year than their male peers, as expected. Second, we see that the average tenure-in-rank increases for women, while staying flat or even decreasing for men.If we now compare the passed-over results across ranks, we notice another important trend: while at the entry level the average number of times passed-over for women seems to grow in a roughly linear proportion with the amount of promotion bias, for higher ranks this relationship seems to grow more geometrically: at the entry level, raising the bias from 0.1 to 0.5 increases the number of times passed-over for women from 0.63 to 1.91– a ratio of 3.0; at the manager level, this ratio increases to 6.2 (from 0.5 to 3.1); at the VP level, the ratio further increases to 15.1 (from 0.32 to 4.83). This, in retrospect, makes sense, because being passed over is compounded by the increasing proportion of men at higher ranks: the promotion bias gives each individual man an increasing chance of being promoted over a female peer, and there are a lot more men in each woman’s peer group – which means that even in the absence of biases, more men than women would be promoted.If we now focus on the tenure-in-rank data (the charts in the right column of REF _Ref38603899 \h Figure 9), we notice that the average time spent at each rank increases for women with increasing promotion bias, but this increase is fairly consistent across ranks. What is more interesting about the tenure-in-rank data is to observe that, especially at the lower ranks, the average tenure-in-rank of men decreases while that of women increases. This result, while not entirely surprising, further quantifies the differences in individual experiences of men and women that result when gender biases exist in the promotion process.There is one aspect of our simulations that is unrealistic, and which makes it difficult to compare our quantitative results to real-world data. Namely, in our current simulation employees only separate from the company at random times. In contrast, being passed over repeatedly in real life would likely cause a decrease in satisfaction, which would in turn lead to higher turnover rates for women than for men (Stamarski & Hing, 2015). Hence the idea that women will remain stuck at a level for a much longer time than men is somewhat unrealistic, because in real life, women in those situations would be more likely to quit.We are currently developing a version of this simulation in which each agent has an internal “satisfaction” variable that is impacted by being passed over for promotion, and which, in turn, increases the probability that an employee will voluntarily leave the company. In this case, we expect to see lower retention rates for women and immediate changes in the organization’s turnover rate (Holtom, Mitchell, Lee, & Inderrieden, 2005) – phenomena that are common across male-dominated industries. We leave this additional analysis to future work, and simply point out another advantage of agent-based simulation, viz, the ability to add details to the simulation without compromising or invalidating the results obtained with a simpler simulation.DISCUSSION We have introduced an agent-based simulation that captures, albeit in simplified form, some of the gender imbalances that are observed across a variety of industries, supporting a demand-side explanation of observed corporate gender biases (Bielby & Baron, 1986). What is perhaps most striking about our findings is that we are able to capture several phenomena through very simple assumptions, and by varying only a small number of parameters.Of course, the fact that our model is able to reproduce some of the observed phenomena does not mean that we are accurately capturing the true causes of these phenomena: it is possible that the mechanisms we hypothesized are not representative of real-world corporate functions, and that the similarity between our results and real-world observations are purely coincidental. However, what we have been able to show is that if a company has gender biases in the way it promotes its employees, then, over time, the company will exhibit growing levels of gender imbalance, and that this imbalance will be increasingly pronounced at higher ranks within the organization. Because our model is capturing the causal links between the behaviors of individuals and the emergent behaviors of a company, and because our model is very parsimonious in its assumptions, we are therefore confident that our model, while certainly simplistic, is capturing fundamental aspects of corporate function that reflect real-world contexts. There is another way in which our simulation offers indirect but strong support for a demand-side explanation of corporate gender biases: as we discussed in our description of Experiment 2, our simulation shows that reducing the number of women that are hired at the entry level (which could result from a smaller supply of women or from hiring biases) would results in an overall reduction in the representation of women that is consistent at all ranks. In other words, if we start the simulation assuming that only 40% of applicants are women, over time there will be 40% women at every rank. A supply-side hypothesis would have to explain the progressive reduction in representation at higher ranks, and why this progressive reduction is observed so consistently across every industry. Any single proposed factors, such as child-bearing or competitiveness, would be unable to explain the observed results.The Nature of Gender BiasesOur simulation treats gender bias as a single parameter. We are not making any claims about what is actually causing this bias, or whether the bias results from a single factor or from multiple factors. Rather, we believe that each company has a combination of individual biases and structural biases that jointly impact the probability that women will be selected for promotion.At the individual level, studies have shown that managers often fall victim to a range of unconscious biases, such as implicit prejudice based on stereotypes, group favoritism, or overclaiming credit for their own achievements (Banaji , Bazerman, & Chugh, 2003). At the structural level, a company may consider “face time” or other performance metrics that implicitly favor men as part of their promotion criteria. The idea behind our use of a single parameter is to show that, taken together, these kinds of biases combine to shape the experiences of individual employees in a way that differs for men and women. And although it is likely that, on one hand, certain forms of bias are wide-spread, and on the other hand, each company may have unique forms of biases, the fact that different industries exhibit different levels of imbalances suggests that certain types of biases may be endemic to specific industries.In the future, we hope that companies will be able to use agent-based simulations such as the one we have used here to estimate the level of gender biases that are likely to exist in their organizations, and then use that information as guidance to identify –?and remove – specific sources of bias that impact their employees.Benefits of Agent-Based Simulation as a Management ToolIt is worth noting that most research on gender inequality in the workplace is conducted by applying statistical methods to observed data. This common approach has a number of limitations, including the fact that it is only capturing present conditions, it removes any information about dynamics, it hides details about individual interactions, and, most importantly, it tends to identify correlations that may or may not be due to causal relationships. As we highlighted in Experiment 4, our agent-based simulation preserves the individual experiences, and makes it possible to explore the causal relationships that link individual behaviors to the emergent behaviors observed at the company level. This is one of the greatest benefits of using agent-based simulation to study corporate workforce management in general, and D&I in particular.Another significant benefit of agent-based simulation as a management tool is that, because it captures causal relationships rather than correlations, agent-based simulation can also be used to explore the likely impact of different initiatives. In other words, agent-based simulation can serve both as an explanatory tool and as a predictive modeling tool. For example, in this paper we used the simulation to estimate the likely impact of removing all promotion biases. In fact, we believe that the inability of corporations to predict the likely impact of different D&I initiatives, and the risks that D&I missteps can create, are some of the main reasons why, almost half a century after the passage of equal opportunity, corporate D&I across most industries has made little, if any, noticeable progress (Newkirk, 2019).Future Research DirectionsWe see this project as the beginning of a systematic study of the impact of D&I on corporate performance. For instance, while the simulation we used in this paper focused only on advancement, we can use a similar approach to simulate other aspects of workforce management, including retention or recruitment. In fact, a former graduate student of one of the authors, for his Masters thesis, developed an agent-based simulation that shows how job candidates are influenced by the perceived level of inclusion and diversity of a company, and how this will impact the talent pool available to any company and influence the cost of hiring (Naghdi Tam, 2017). We have also begun to simulate the impact of many other facets of D&I that impact the day-to-day experience of individual employees, how these experiences impact the satisfaction and productivity of individuals, and how this in turn impacts overall performance of the company across a variety of performance indicators.Even within the promotion model itself, there are many ways in which we could increase the fidelity of the model to explore the impact of different assumptions and of different initiatives. We already mentioned our plans to extend the simulation to track employee satisfaction and its impact on retention and productivity. Similarly, we could also simulate how the presence of managers of a different gender impacts satisfaction and career advancement, or we could test alternative hiring practices, such as hiring people directly into higher ranks. In other words, this model can serve as the basis to explore a large number of hypotheses about the sources of gender disparities, and to test the likely impact of different interventions. Finally, although in this paper we have focused on gender, and we treated gender only as a binary (male/female) variable, it is possible to capture a more nuanced and realistic representation of gender identity and to represent other personal characteristics that impact an employee’s experience, such as ethnicity, race, religious beliefs, sexual orientation, physical and cognitive abilities, and any other characteristic that may impact an individual’s experience within an organization. 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Table SEQ Table \* ARABIC 1List of employee agent variables tracked in the simulationVariable nameVariable DescriptionrankThe level within the organizationstart-dateThe date when the joined the companystart-date-in-rankThe date when they first reached a certain ranktenure-in-rankHow much time they have been at a certain rankseniorityA normalized variable [0-1.0] that reflects how long the employee has been at this rank, relative to all employees at the same rankpromotion-scoreA score that combines seniority and promotion gender biasestimes-passed-overThe number of times someone else from the same level with lower seniority was promotedhr-eventsA list of HR-related events such as being hired or promotedTable SEQ Table \* ARABIC 2Parameter settings for our promotion bias Experiments 1 and 3Simulation duration (in years)40 Number of repetitions of each simulation10Initial company size300Initial gender balance (male-female)50-50Promotion Bias level0, 0.1, 0.3, 0.5Promotion Bias DurationN/A (exp. 1), 10 (exp. 3)Hiring Bias0Promotion pool size 15%Termination pool size 50%Table SEQ Table \* ARABIC 3Bias parameters and simulation accuracy for the four industries simulated in Experiment 2Promotion biasHiring biasIndustry simulatedVariability score0.30.4Engineering and industrial manufacturing0.0070.3-0.1Insurance0.0240.20Banking and consumer finance0.0170.2-0.2Retail0.015Figure SEQ Figure \* ARABIC 1Screenshot of the simulationFigure SEQ Figure \* ARABIC 2Fluctuations in gender balance across all four levels during a 40-year simulation. For this figure the promotion and hiring biases are set to zeroFigure SEQ Figure \* ARABIC 3Fluctuations in gender balance across all four levels during a 40-year simulation when the promotion bias is 0.1Figure SEQ Figure \* ARABIC 4Fluctuations in gender balance across all four levels during a 40-year simulation when the promotion bias is 0.3Figure SEQ Figure \* ARABIC 5Fluctuations in gender balance across all four levels during a 40-year simulation when the promotion bias is 0.5Figure SEQ Figure \* ARABIC 6Simulating the gender imbalances of different industries by adjusting both promotion and hiring biases.(A) Promotion Bias 0.3, Hiring Bias 0.4(B) Promotion Bias 0.3, Hiring Bias -0.1(C) Promotion Bias 0.2, Hiring Bias 0.0(D) Promotion Bias 0.2, Hiring Bias -0.2 Figure SEQ Figure \* ARABIC 7Gender balance across all four levels during a 40-year simulation that starts with a promotion bias of 0.3, which drops to 0.0 after 10 years1221377143691BIASNO BIAS0BIASNO BIASFigure SEQ Figure \* ARABIC 8Gender balance across all four levels during a 40-year simulation that starts with a promotion bias of 0.5, which drops to 0.0 after 10 years1221377143691BIASNO BIAS0BIASNO BIASFigure SEQ Figure \* ARABIC 9Average number of times passed-over (left column) and average number of years in rank (right column) for VP (top row), Manager (middle row) and Entry (bottom row) levelsVP levelManager levelEntry level ................
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