Referral Hiring and Gender Segregation in the Workplace

Transcription

1 Referral Hiring and Gender Segregation in the Workplace Troy Tassier Department of Economics E 528 Dealy Fordham University Bronx, NY tassier@fordham.edu January 9, 2007 I thank Mary Beth Combs, Ross Hammond, George Neumann, Scott E. Page, and Cosma Shalizi for helpful comments. 1

2 Referral Hiring and Gender Segregation in the Workplace Abstract Segregation by type of work or discrimination are two common explanations for gender segregation in the workplace. Here, I discuss a third: gender segregation may occur because of referral hiring through segregated social networks. I examine data on the inter-firm gender segregation of employees at US colleges and universities. Using a combination of analytical modeling, empirical estimation, and agent based modeling techniques I find that plausible levels of referral hiring generate high levels of segregation that are consistent with the levels of segregation observed in the data. 2

3 1 Introduction The effect of gender segregation on inequality has received a large amount of attention. Researchers argue that gender segregation both within and across firms and across occupations may be one of the major causes of income inequality for women. 1 Several causes for gender segregation have been put forth by other researchers such as: gender segregation may occur as a result of discrimination (Becker 1971; Bergmann 1974), differences in training (or tastes) for specific types of work (Mincer and Polachek 1974), and referral hiring through segregated social networks (Marx and Leicht 1992; Mouw 1999). In this paper I concentrate on the least discussed of these listed items, referral hiring through segregated social networks. In this paper I consider referral hiring to be any means by which an employee learns of a job through a social contact (which may include familial contacts), or a firm learns of a potential applicant through an employee who is a social contact of the potential applicant. Thus I consider referral hiring to be any means of transferring job information that occurs at least in part through social contacts or social networks. The literature on referral hiring is vast. Researchers robustly find that around one-half of all jobs are filled through referral hiring (Granovetter 1995; Bewley 1999) with some occupations and firms having much higher rates. Since social networks are segregated by ethnicity and gender (Marsden 1988) information about jobs is likely to be segregated as well. Thus when employers rely on social channels to find workers their pool of applicants can be biased by the current ethnic or gender composition of the employer. Similarly, when workers use social channels to find employers their pool of potential employers can be biased toward the firms and industries of their social contacts. This bias of individuals referring like-individuals is defined as referral homophily (McPherson, Smith-Lovin, and Cook 2001). In this paper I investigate the potential of referral hiring to create inter-firm gender segregation. I use a model developed in Tassier (2005) coupled with data on staffing at US colleges and universities. I estimate parameters of the model empirically and then simulate the hiring process of the model to generate a distribution of workers across firms. I then compare the distribution generated by the model to the actual distribution. I find that reasonable levels of referral hiring can generate levels of segregation that closely match observed levels of segregation. before I begin, I want to make clear that I am not proposing that referral hiring is the only cause of gender segregation in the workplace or even that referral hiring is the primary cause. instead I am showing that observed levels of referral hiring are sufficient to generate very high levels of gender segregation. Further it is likely that discrimination and referral hiring produce feedback effects that reinforce each other as I discuss int he conclusion. 1.1 An Overview of Gender Segregation and Referral Hiring There are surprisingly few studies of inter-firm gender segregation. This is mostly due to data limitations. Most of the studies that have been done tie inter-firm gender segregation to the male-female wage gap. (McNulty 1967; Buckley 1971; Blau 1977; Groshen 1991; 1 See for instance Bergmann (1986) or Blau and Kahn (2000). 3

4 Carrington and Troske 1994). Overall the studies find that there are substantial levels of inter-firm gender segregation and that women tend to be sorted into low-paying firms. In addition, although it is not the focus of this paper, inter-firm racial segregation has also been found to be prevalent. For instance Becker (1980) finds most of the segregation of black and white workers... is segregation by place of work [85%] rather than stratification into different occupational categories [15%]. As mentioned above, discrimination and taste for different jobs are most often cited as the main cause of the observed levels of inter-firm segregation. Here I discuss another potential explanation: referral hiring. Several studies have found that a large percentage of jobs are found by using social contacts. In summary these surveys find that between one-third and two-thirds of workers find their jobs through friends, relatives, and other social contacts. (See Granovetter (1995), Ioannides and Datcher Loury (2004), and Bewley (1999) for an overview of this literature.) Because referrals play such a prominent role in the attainment of employment it has been argued that referral hiring may be a large cause of income inequality. This may be especially true of groups that have recently entered traditional labor markets such as women or recent immigrants, or groups that have traditionally faced open discrimination, such as African Americans. This line of research follows the idea that it s not what you know, but who you know (Montgomery 1991). These arguments look at both the structure of one s social network and the quality (in terms of providing access to jobs) of one s social network. While most of the work on the consequences of referral hiring have concentrated on income inequality there may be a second effect: workplace segregation. Just as one can think of a group of friends as a network, one can also think of firms or jobs as a network. If an individual knows about an open job because of the job he holds, those two jobs are connected. Thus firms and related positions in an industry or perhaps in geographic proximity form a job network. Individuals who are near each other in a social network may tend to work in jobs that are close to each other in a job network if referrals play a prominent role in the hiring process; social contacts may work in the same firm or industry or in jobs related in some other way. Thus workplace segregation may occur as a result of referral hiring since social networks are segregated. 2 Further, there exists evidence of racial and gender homophily in job referrals. For instance Fernandez and Sosa (2005) find a significant bias to like gendered referrals for both women and men in data from a call center at a large bank. There is some evidence that referral hiring may cause workplace segregation. Marx and Leicht (1992) find that referral hiring reduces female and minority representation in job types that most frequently hire by referral. Mouw (1999) finds that firms with small numbers of minorities who hire through referral are less likely to hire a minority worker compared to similar firms who hire through newspaper advertisements. While both offer evidence suggesting referral hiring could cause segregation, neither explicitly investigates a 2 Marsden (1988) finds that social networks tend to be most homogeneous in race and ethnicity. O Reagan and Quigley (1993) argue that segregation of social contacts occurs along lines of race, ethnicity, gender, and income. 4

5 model of referral hiring and segregation or attempts to estimate the amount of segregation that could be created by observed levels of referral hiring. In the following sections of this paper I use a model developed in Tassier (2005) to investigate the extent to which referral hiring can account for observed levels of gender segregation in staff data at US colleges and universities. The paper proceeds in three steps: First, I discuss briefly the analytical model to be used in the paper. 3 Second, after introducing the data, I complete an empirical estimate of various model parameters that will be used later in the paper. Third, I complete an agent-based simulation exercise aimed at investigating whether the level of segregation observed in the data can be generated by a model of referral hiring. In the end, I am able to show that the estimated model matches key parameters such as the level of referral hiring and that the model is able to create levels of gender segregation similar to the levels observed in the data. However, the model cannot fully explain all of the observed segregation. 2 A Model of Referral Hiring and Worker Distributions Consider a population of N workers of two types: w and m. Let the fraction of workers who are type w be given by γ. Type m workers make up the complement, 1 γ. Each type of worker is equally qualified to work; Firms are indifferent as to whether they employ a type w or a type m worker. There are F firms indexed by f that each employ θ f workers; note that θ f can differ across firms. Let F f=1 θ f < N such that there is some unemployment. Define the fraction of unemployed workers who are type w as U w. Let the state of firm f at time t be given as the number of workers of type w the firm employs at time t, Wf t. Each period a fraction λ of employed workers separate from their jobs and enter the unemployed pool. When a firm loses a worker it immediately hires a new worker from the unemployed pool. If the unemployed pool only contains workers of one type, U w = 0 or U w = 1, the firm chooses randomly among the unemployed workers with uniform probability. Now consider the case when U w (0, 1). Since all workers are equally qualified, the firm is equally satisfied with any worker it hires. I assume that there are two means by which firms hire workers, full search or referral hiring. If the firm hires by search the firm chooses a random worker from the unemployed pool. Thus the firm chooses a type w worker with probability U w (the fraction of type w workers in the unemployed pool.) Assume that s percent of hires are search hires. Alternatively, assume that (1 s) percent of hires are referral hires. When the firm hires through referral I assume that the likelihood of hiring a type i employee is equal to the fraction of type i workers currently employed by the firm. Thus with probability s the firm chooses with uniform probability over all workers in the unemployed pool; and with probability (1 s) the firm chooses a worker with a bias given according to the proportion of each type it currently employs. If firm f hires by referral it hires a type w worker with probability W t f θ f 1 and a type m worker with probability 1 W t f θ f 1. 3 A full description of the model and the resulting equilibrium properties of the model can be found in Tassier (2005). 5

6 Thus the likelihood that a worker of type w gets hired is: 0 if U w = 0 P r(w) = su w + (1 s) W f t θ f if U 1 w (0, 1) 1 if U w = 1 Recall that the state of a firm is defined by the number of type w workers at the firm. Each time a worker leaves a job and is replaced by a new worker the state of the firm can change in one of three ways: 1) The firm can move one state lower, from state x to state x 1, if the firm replaces a type w worker with a type m worker; 2) The firm can remain in the same state if it replaces a type m worker with another type m worker or if it replaces a type w worker with another type w worker; Or 3) the firm can move one state higher, state x to state x + 1, if the firm replaces a type m worker with a type w worker. The probability of each of these transitions occurring for a particular firm f depends on the number of type w workers currently employed at the firm, Wf t, the total number of employees at the firm, Θ f, the number of type w workers in the unemployed pool, U w, and the level of referral versus search hiring that takes place, s. For the moment suppose that each firm employs the same number of workers, Θ f = Θ for all f. Further suppose that there exists a steady state in the model such that U w is constant. 4 Then these transitions are linear functions of Wf t (the state of the firm), s, Θ, and U w. Note that only the state of the firm varies across the firms; s, Θ and U w are the same for each firm. Thus one can write a transition function for each firm state that is dependent on the firm s current state and the other homogeneous variables. There are Θ+1 of these functions; one for each state 0, 1,..., Θ. Define the transition function for each state W as T (W ). (Note that I am suppressing the notation of the homogeneous variables for simplicity.) Let the matrix of these transition functions be T. One also can define a distribution of workers across firms using the state of each firm in the population. Let d 0 be the number of firms with no workers of type w, d 1 be the number of firms with one type w worker etc... Let the distribution be given as D. Taking D together with T, one can solve for a steady state distribution of firm states. The steady state distribution is the distribution that solves DT = D. The details of solving for this steady state distribution with a homogeneous firm size are shown in Tassier (2005). Further, the distribution is unique since all the elements of the transition matrix are linear. Most importantly for this paper the level of segregation is monotonically decreasing in s. As referral hiring increases segregation increases. Unfortunately, the model cannot be solved analytically for heterogeneous sized firms. Thus I employ computational methods in this paper to estimate the steady state distribution. Note that if s = 1 the model is a pure random matching model. As s decreases referrals play an increasingly prominent role in hiring. And, in the limit as s 0 the model contains only referral hiring. Thus the model can account for any level of referral hiring; it is flexible in that for any level of referral hiring the model provides an expected worker distribution and level of segregation. Thus if we know the level of referral hiring we can use the model 4 This second assumption is proven to be true for the model in Tassier (2005). Further, the steady state is unique. 6 (1)

7 to predict segregation. Unfortunately I do not know of a publicly published data set that contains information on propensities to hire by referral and also includes the distribution of workers across firms. Thus I will need to work through a calibration exercise to estimate the level of referral hiring in the data and then use this estimate as a parameter in the model to generate an expected distribution of worker types across firms. To accomplish the parameter estimation I will need to look at changes in workforce composition across time. To do so, consider the following representation of the model. Given a separation rate λ, level of random matching s, and overall fraction of women in the work-force, γ, at time t, one can write the following difference equation for the expected fraction of women employed at firm f, in the next period, p t+1 wf : p t+1 wf = (1 λ)pt wf + λ[sγ + (1 s)p t wf] (2) Proportion (1 λ) of the employees retain their jobs while proportion λ are replaced with new workers. Of those new workers a fraction s are matched randomly from the unemployed pool and a fraction (1 s) are matched according to the current proportion of women at the firm. Write p wf = p t+1 wf pt wf. So, p wf = (1 λ)p t wf + λ(sγ + (1 s)p t wf) p t wf (3) Simplifying yields the following difference equation for firm trajectories of worker composition: p wf = (γ p t wf)λs (4) Note that this model of individual firm composition is the same model as I used above. Here I am simply considering how the composition of an individual firm s workforce is expected to change over time. For s (0, 1] there is a unique steady state for a firm, specifically p wf = γ. If γ > p t wf then the proportion of women employed should increase. If γ < pt wf then the proportion of women employed should decrease. If γ = p t wf then the proportion of women employed should remain constant. Firms should be moving toward the population mean at a trajectory that is a function of λs and how far from the mean the firm currently is. Firms with gender compositions that deviate strongly from the mean will move toward the mean at a faster rate. Note that if there is not any referral hiring, s = 1, the speed at which firms approach the mean is fastest. As referral hiring increases (s decreases) the rate of change in firm composition slows; there is more persistence in the gender composition of firms. In the following section of the paper I will use the model described above in conjunction with data from the National Center for Education Statistics. I will use Equation 4 to estimate the fraction of random search hiring, s, in the data. I use the estimated value for s in an agent-based simulation of the referral hiring model to create an expected distribution of female workers across firms. I then compare this expected distribution to the observed distribution to explore how well a referral hiring model matches the data. 7

8 3 Estimating Workplace Segregation Using a Referral Hiring Model 3.1 Data I use data from the 2001 and 2003 National Center for Education Statistics, Integrated Postsecondary Education Data System (IPEDS). The data summarizes the gender composition of the staff of individual postsecondary institutions in the United States. Thus I am able to compare the distribution of woman and men employees across schools (firms) to the distribution generated by the model of referral hiring discussed in the previous section. In my study I use information on all full-time non-faculty employees of colleges and universities across the United States. I use all schools that appear in both years of the data that have more than 100 full-time non-faculty employees. 5 This amounts to 1,916 schools. In these schools there are 1,314,777 workers in 2001 and 1,326,787 workers in The data in both years contains approximately 60% female workers. The analysis of segregation in the paper will use the 2003 data but I will use the 2001 data to help estimate the parameter s in the referral hiring model. To begin the analysis of the data I calculate the percentage of female workers at each firm in the sample. This frequency distribution is given in Figure 1 for the 2003 data. To better understand the data I first compare the observed data to a model that assumes random matching of workers at firms without regard to type. This random matching model is the same as my model with s = 1. Note that the observed distribution has thicker tails than the distribution predicted by a model of random matching; there is more gender segregation than would be implied by the random matching model. We can quantify the level of segregation by using standard measures. One common measure of segregation is the dissimilarity index created by Duncan and Duncan (1955). Their measure is defined as: ψ d = 1 2 F f=1 W f Nγ θ f W f N(1 γ) (5) Note that ψ d [0, 1]. The observed level of segregation in the data is and the level of segregation predicted by random matching is The observed level of segregation in the data is approximately four times the level that would be predicted by a random matching model. Thus it should be clear that a random matching model is a poor predictor of the level of segregation in the data. 5 There are some very small schools in the data sample. For example, one school employs only two nonfaculty workers. Since I am working with gender composition in terms of percentages I am concerned about small schools biasing my results. For instance the two employees of the school mentioned above are both women. Thus, this school is fully segregated. But a fully segregated school of two is far different than a fully segregated school of hundreds or thousands. To avoid these idiosyncrasies, I am only going to consider fairly large schools in my analysis. 8

9 Number of Firms Data s= Percent Women Figure 1: Observed 2003 frequency data on percent female workers across firms (labeled Data ) compared to a model of random placement of female workers across firms (labeled s = 1 ). 9

10 Table 1: Esimation of the Amount of Referral Hiring Coefficient Std Error s Estimating the Amount of Referral Hiring The goal of this paper is to examine how much of the observed excess segregation can be explained by the referral hiring model described above. To begin the analysis I need to estimate the level of referral versus search hiring in the data. To do so I calculate the difference between the percentage of female workers at each school in 2003 and 2001 and define that as p wf. The IPEDS data also contain the number of new hires at each school in each year of the data. I use the ratio of new hires to total employees of each school as an estimate of one year labor turnover at the school. If I extrapolate this one-year level of turnover to two years I have a level of λ to use for each school in the data sample. I then perform an OLS regression of Equation 4 above using 0.60 for γ (the observed percentage of female workers at schools across the entire sample) and the observed percentage of female workers at each school in 2001 for p t wf. The coefficient on this regression will give me an estimate of s, the amount of search (non-referral) hiring in the data. For the data sample, the coefficient in the regression is 0.56 (Table 6). Recall that this implies that s = 0.56; the implied level of search hiring is 56% and the implied level of referral hiring is 44%. I will use this level of s in the simulation exercise described in the next sub-section. Note the importance of the estimate of s for the model employed here. First, it is possible that the observed distribution of workers across firms occurs for a reason independent of referral hiring. Perhaps some firms consciously choose to hire a number of women that is different than the population average. If this was true, then we would expect each individual firm to remain at their current level of gender makeup. This would imply that s = 0. But because s 0, we see that the workforce composition of the firm is changing as long as they are not at the individual firm steady state. Second, the firms are changing their workforce composition in a way that is consistent with the model. Since the estimate of s is positive we know that firms are moving in the expected direction. If a school employs more women than average the school tends to decrease the number of women employed. If the school has fewer women than average, the school tends to increase the number of women employed. 3.3 Referral Hiring and Segregation In this section I use the model described above to explore how much of the observed deviations from random matching can be explained by the implied level of referral hiring in the data. In the model above it is not possible to solve analytically for the distribution of worker types across firms for heterogeneously sized firms. Instead of solving the model analytically, I use a series of agent-based experiments to generate the steady state distribution computationally. I use the exact distribution of firm sizes and the percentage of women employed in aggregate 10

11 across all schools (60%) from the observed data as parameters in the model. I also use a level of s = 0.56 as a parameter of the model. I then compare the observed distribution of women and men across firms to the distribution predicted by the model. More specifically let F be the number of firms in the sample of data. Initially each firm employs 0 workers. Let θ f be the number of employees each individual firm f will employee at the end of the experiment. As above, let γ be the proportion of type w agents (the percentage of women in the data) in the population of workers. I take the distribution of θ f and the level of γ directly from the observed data. Given the distribution of θ f, the percentage of women in the worker population, γ, and a level of referral hiring, 1 s, I create an expected distribution of worker types across firms in the following manner: I choose firms in a random order with replacement and allow the firm to hire one worker. If the chosen firm has not received its first worker I draw a random worker from the unemployed population. Each time a worker leaves the unemployed pool I adjust the fraction of type w workers in the remaining unemployed population, U w, accordingly. If a firm already employs one or more workers but does not yet employ its maximum level of θ f workers the firm hires a new worker using either referral or non-referral hiring as described by Equation 1. I repeat this process until all firms employ their full set of workers. Once this process is complete I have an experimentally generated mix of women and men at each of the F firms in the data for a specified level of s. Let p wf = W f /θ f be the proportion of workers employed at firm f that are type w. I then bin the firms by p wf at increments of Let the number of firms with p wf [0, 0.05) be F s (0), let the number of firms with p wf [0.05, 0.10) be F s (1) etc... This yields a frequency distribution of the proportion of women employed across firms in the experiment. I generate a set of 50 frequency distributions in the manner described above. I then find the average number of firms in each bin over the set of the 50 experiments. This procedure allows me to compare the expected distribution of worker types predicted by the model to the observed distribution of worker types across firms. I also perform a second set of experiments as a robustness check on my implied level of s. I generate a set of 50 frequency distributions for each level of s between 0.01 and 1.00 at increments of I use these experiments to find the value of s that best fits the distribution data using the standard Chi-squared goodness of fit test. Specifically I find the amount of referral hiring, 1 s, that minimizes the following: Min s D(s) = 20 x=0 [F ob (x) F s (x)] 2 F s (x) where x is the bin, F ob (x) is the observed frequency over the set of firms in the data, and F s (x) is the average frequency generated by the model for a given value of s. Note that if s = 1 the distribution of worker types is a binomial distribution; and in the limit as s 0 the model will yield complete segregation of types (Tassier 2005). As referral hiring increases segregation increases. In the next subsection I show that plausible levels of referral hiring are consistent with much of the observed levels of gender segregation in staff data at postsecondary schools in the United States. I discuss the results for s = 0.56 and for the set of simulations that best 11 (6)

12 fit the distribution data below. For the 2003 data the calibration exercise described above yields s = 0.52 as the value that minimizes Equation 6 for the schools in the sample; In other words a level of 48% referral hiring is most consistent with the distribution data. As a comparison, the Chisquared statistic for s = 0.52 (the best fit) is 46.6, and for s = 0.56 (the level implied from turnover data) the statistic is Both of the referral hiring models match the data far better than the random matching model which has a Chi-squared statistic of 27,908. In other words, the model with just under 50% referral hiring fits the distribution data far better than a pure random matching model. 6 I next perform a visual comparison of the predicted frequency distribution with s = 0.52 (the best distribution fit), s = 0.56 (the level implied from the turnover data), and s = 1.0 (the benchmark random placement model) to the observed frequency distribution. Figure 2 compares the first two models to the data and the random placement model is compared to the data in Figure 1. Including referral hiring fits the observed data much better than a pure random matching model. As an additional, comparison Figure 3 shows the cumulative frequency of the data, the random matching model, and the two referral hiring models. Again, one can see the improvement of fit provided from the referral hiring models. Also, note the consistency of the two methods of finding the level of referral hiring employed in the paper. The first is an empirical estimation of changes in workforce composition across time. It yields a rate of 44% referral hiring. The second empirical exercise attempts to fit a worker distribution at a particular point in time. This exercise yields a very similar level of referral hiring, 48%. Thus both estimation exercises yield very similar results. Further if we return to the regression exercise and examine the standard error, one should note that you cannot reject the hypothesis that the true level of s is 52%. Thus the estimate of s in the two methods is not statistically distinguishable at standard levels of confidence. Finally, one should note that even though the referral hiring model fits the data far better than the random matching model, differences still exist between the best fit model and the data. In fact one would still statistically reject that the observed data comes from the best fit referral model. But, recall that the primary purpose of this paper is to examine the extent to which observed levels of gender segregation can be explained by referral hiring. I have demonstrated that a model with plausible levels of referral hiring can generate a large amount of segregation. But referral hiring cannot explain all of the observed level of segregation. There are several other factors which can potentially effect the observed distribution. Some reasons were mentioned earlier such as discrimination, worker tastes for specific occupations that differ by gender, or gender norms for specific occupations. Others may be less obvious such as the idea that some firms may attempt to comprise a balanced worker composition which influences their hiring decisions. For instance if a firm strays too far 6 I also note that the fit of the model to the distribution data is smooth. As you increase s from 0, the Chisquared statistic monotonically decreases, and as you increase s beyond s = 0.52 the statistic monotonically increases. Thus there are no local minima other than the global minimum. Thus one could use an iterative process to find the minimum. 12

13 Number of Firms Data s=.52 s= Percent Women Figure 2: Observed 2003 frequency data on percent female workers across firms compared to a model with 51% workers hired by referral and 49% hired by non-referral methods and to a model with pure random matching, s = 1. 13

14 Cumulative Distribution Numebr of Firms Data s=1.0 s=.52 s= Percent Women Figure 3: Cumulative frequency of the observed 2003 gender data, the purely random model, and the referral hiring model. 14

15 from employing an equal number of women and men they may start giving preference to the under-represented group in order to appear fair in their hiring practices. Any of these items may affect the worker distribution in any industry. Then there are other factors specific to the data studied here that may affect the distribution. For instance all-female schools may have more female workers than mixed gender schools if women are more comfortable than men in working in a mostly female setting. There are ways that each of these factors could be incorporated into the model. For instance one could assume that each school or firm has some inclination to prefer women (or men) and adjust each firms hiring propensity in Equation 1. Firms with a strong preference for one gender would be discriminating firms. Or one could account for the possibility of firms trying to balance their work-force by increasing the propensity to hire women of firms that employ few women. Each of these assumptions would add new parameters to the model and thus would allow one to better fit the data. However the goal of this paper is to examine how referral hiring alone impacts the distribution of workers across firms. And I have found that rates of referral hiring similar to those observed in other studies match the data closely, although not perfectly. 4 Conclusion This paper attempts to describe and measure the effect of referral hiring on inter-firm workplace segregation. The results suggest that a large amount of the observed levels of workplace segregation is consistent with plausible levels of referral hiring in the data studied here. Further, changes in the gender composition of firms across time also yield results suggestive of an effect of referral hiring on workplace segregation. The results do not rule out hiring discrimination as a cause of gender segregation in the data. But they do offer strong evidence that referral hiring is a complementary cause. Further, the two effects may accentuate each other. Suppose that a firm discriminates by giving hiring preference to type i applicants. Employing more type i workers then increases the likelihood that more type i referrals are generated. Thus one can envision referral hiring acting to reinforce discriminatory hiring practices. Further, even if the firm in the example stopped discriminating, the effects of referral hiring would perpetuate the effects of past discrimination. Future research will focus on the interconnectedness of discrimination and referral hiring. The results and discussion in this paper add to the list of possible effects of referral hiring. Previously most attention with regard to referral hiring focused on income inequality. However the two topics are clearly linked. A segregated workplace that hires by referral will limit the jobs available to groups with low rates of employment in given industries or firms. This paper also offers an example of the methodological complementarities between analytical theory, empirical estimation, and agent-based modeling techniques. The paper begins with an analytical model that can be solved for the case of a homogeneous firm size but not for the case of heterogeneous firm sizes. Thus in order to match the model to data one needs to employ computational methods. But in order to do so, one needs to first empirically estimate the parameters to be included in the computational model. Thus this paper demonstrates a clear example of the complementarities between each methodology for 15

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