Prejudice and racial matches in employment

Accepted Manuscript

Prejudice and Racial Matches in Employment Timothy N. Bond, Jee-Yeon K. Lehmann PII: DOI: Reference:

S0927-5371(17)30216-6 10.1016/j.labeco.2018.02.004 LABECO 1621

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Labour Economics

Received date: Revised date: Accepted date:

28 November 2016 6 February 2018 7 February 2018

Please cite this article as: Timothy N. Bond, Jee-Yeon K. Lehmann, Prejudice and Racial Matches in Employment, Labour Economics (2018), doi: 10.1016/j.labeco.2018.02.004

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Highlights • Propose model of taste-based discrimination with unobservable prejudice. • Workers observe race of a supervisor, which provides a signal of prejudice.

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• Uncertainty about prejudice induces lower reservation wages for blacks with white supervisors. • Construct data on geographic prejudice and supervisor race for set of workers.

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• Predictions on wages and job stability consistent with findings from data.

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Prejudice and Racial Matches in Employment✩ Timothy N. Bonda,∗, Jee-Yeon K. Lehmannb Department of Economics, Krannert School of Management, Purdue University, 403 W. State Street, West Lafayette, IN 47907, USA b Analysis Group, Inc., 111 Huntington Ave., 14th Floor, Boston, MA 02199, USA

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Abstract

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We develop a model in which some employers hold unobservable racial prejudice towards black workers. Workers, however, observe a signal of prejudice status – the presence of a black supervisor. Jobs in firms with black supervisors hold higher option value for black workers, because they are less likely to face prejudice-based termination. Hence, black workers are willing to accept employment with lower expected match quality from firms with black supervisors. We derive predictions on differences in wages and job stability across supervisor race and prejudice levels and find empirical support for them using unique longitudinal data on worker’s supervisor and state-level measures of prejudice. Keywords: prejudice; racial discrimination; supervisor race JEL: J71, J31

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We are grateful to Peter Arcidiacono, Katherine Eriksson, Cynthia Gramm, Kevin Lang, Steven Lehrer, David Neumark, Melinda Petre, Shannon Seitz, Anson Soderbery, and conference and seminar participants at Purdue University, Queen’s University, the University of California, Davis, the University of Kentucky, the Twentieth SOLE Meetings / Fourth SOLE/EALE World Conference, the 6th Annual European Search and Matching Network Annual Conference, the Spring 2016 Midwest Macro Meetings, the 91st Annual Western Economic Association International Conference, and the Fifteenth IZA/SOLE Transatlantic Meeting for their helpful comments; and the Bureau of Labor Statistics (BLS) and the General Social Survey (GSS) for providing us with the confidential data used in this project. Funding for this project was made possible in part by grant number 1H79AE000100-1 to the UC Davis Center for Poverty Research from the U.S. Department of Health and Human Services, Office of the Assistant Secretary for Planning and Analysis (ASPE), which was awarded by the Substance Abuse and Mental Health Services Administration (SAMHSA). The views expressed are those of the authors and do not necessarily reflect the official policies of the Department of Health and Human Services. Some of the data used are derived from Sensitive Data Files of the GSS, obtained under special contractual arrangements designed to protect the anonymity of the respondents. These data are not available from the authors. Persons interested in obtaining GSS Sensitive Data Files should contact the GSS at [email protected]. This research was conducted with restricted access to the BLS data. The views expressed here do not necessarily reflect the views of the BLS. The views presented are those of the authors and do not necessarily reflect those of Analysis Group, Inc. or its clients. We thank Paul Thomas, Mary Kate Batistich, and Jacob Elich for their excellent research assistance. Any mistakes are our own. ∗ Corresponding author Email addresses: [email protected] (Timothy N. Bond), [email protected] (Jee-Yeon K. Lehmann) Preprint submitted to Elsevier

February 12, 2018

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1. Introduction

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Despite the narrowing of the racial gap in many key labor market outcomes over the past fifty years, significant differences between black and white Americans remain. In the 2000s, year-round, full-time employed black men earned less than 80% of that earned by white men and faced more than double the rate of unemployment (Lang and Lehmann, 2012). Some of these differences can be attributed to persisting gaps in skill (Neal and Johnson, 1996). However, substantial differences in wages and employment remain even after accounting for observable differences in education and cognitive test scores (e.g., Carneiro et al., 2005; Dawkins et al., 2005; DellaVigna and Paserman, 2005; Black et al., 2006; Bjerk, 2007; Lang and Manove, 2011). At the same time, despite dramatic declines in measures of anti-black prejudice in national polls over the past fifty years, recent studies demonstrate the persistence of subtle and subconscious forms of prejudice and their impact on employer behavior (Bertrand et al., 2005; Ziegert and Hanges, 2005; Rooth, 2010). The rhetoric of the most recent presidential campaign and the current political and social discourse highlight the existence of both mild and extreme forms of racial prejudice in the contemporary U.S. In this study, we provide new insights into the observed black-white differences in wages and job stability in the U.S. through a model of job search that incorporates employer prejudice and imperfect information about who holds these prejudices.1 In our model, workers randomly match with firms and learn an initial productivity of the job. After a period of probationary employment, they receive a stochastic productivity increase and the job can transform into a permanent match. Prejudiced employers engage in taste-based discrimination by making job offers to black workers at lower rates, and also terminating black workers at higher rates following the probationary period.2 Under these conditions, the model predicts that black workers are willing to accept jobs with worse initial match quality from firms with black supervisors in return for lower termination risk, and in turn, the higher option value that these job offer them. From this intuitive result, we derive several novel predictions on black-white differentials in wage and job stability and their relation to supervisor’s race and local prejudice levels. Conditional on tenure, black workers have lower average wages in jobs with a black supervisor than in jobs with a white supervisor. However, black workers are compensated for their lower wages with 1 As in Lang and Lehmann (2012), we define prejudice as a “dislike” for black workers based on a “preconceived opinion that is not based on reason or actual experience.” Specifically, this distaste must be strong enough so as to induce employers to make employment decisions based on it. 2 There are many reasons why a black worker, who is offered a job, might face prejudice on the job, including the subconscious forms of prejudice already mentioned, differences in the identity of the hiring officer and the supervisor, the impact of affirmative action at the hiring stage (Lehmann, 2011), and prejudiced managers who derive utility from directly impeding black workers’ career progress (Charles, 2000).

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longer employment spells in these jobs. As the proportion of prejudiced employers increases in the local labor market, the expected termination risk from employers without black supervisors increases and the wage and job stability effects become magnified. Surprisingly, our model predicts that the gap between wages for black workers in jobs with black and white supervisors will widen as prejudice levels increase. In other words, as prejudice levels rise, black workers fare increasingly worse in terms of their average wage in jobs with black supervisors relative to jobs with white supervisors. We find empirical support for these predictions and others related to black and white wages and job stability using data on local prejudice levels from the General Social Survey (GSS) – similar to those used in Charles and Guryan (2008) – and information on workers’ wages, employment history, and the race of their supervisors in the National Longitudinal Survey of Youth 1997 (NLSY97). Our results demonstrate that despite the decline in reported prejudice levels in the U.S., remaining racial prejudice and uncertainty about which employers hold these sentiments can have significant negative effects on the labor market outcomes of black workers. Even when prejudice is not pervasive, the threat of prejudiced-based employment decisions and workers’ inability to perfectly identify prejudiced employers can cause black workers to select into worse job opportunities with unprejudiced employers they can identify. 1.1. Related Literature and Our Contributions

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Our work adopts the taste-based discrimination framework that dates to Becker (1971). While current economic literature has given greater attention to models of statistical discrimination that rely on imperfect information about workers’ productivity, several recent studies demonstrate that taste-based discrimination models with employer prejudice can generate predictions on black and white wage and/or employment differentials that are generally consistent with observed empirical regularities (e.g., Charles and Guryan, 2008; Lang and Lehmann, 2012; Nunley et al., 2015; Borowczyk-Martins et al., 2017). In Becker’s seminal work, prejudiced employers dislike hiring black workers, and to offset their utility loss, they are only willing to hire black workers at a lower wage than whites. These wage differentials are, however, short-lived in a perfectly competitive labor market. As noted by Arrow (1972), employment will be segregated, but entry by unprejudiced firms will eliminate wage differentials provided there are sufficient number of unprejudiced potential entrants. However, as originally demonstrated by Black (1995), when there are search frictions in the labor market, racial wage differentials from employer prejudice can persist. The existence of prejudiced employers who dislike hiring black workers reduces the arrival of job offers to black workers, which induces black workers to set a lower reservation wage for accepting employment than white workers, and thus results in lower average black wages. Because 4

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workers’ search behavior has a direct effect on wages, search models can arrive at large racial wage differences even when prejudice is scarce and frictions are low (Ros´en, 1997; Lang et al., 2005; Holden and Ros´en, 2014).3 In addition, the search framework can also facilitate predictions about black and white employment differentials, which can be substantially larger than wage differences (e.g., Stratton, 1993; Johnson and Neal, 1998; Ritter and Taylor, 2011; Lang and Lehmann, 2012). These wide, unexplained employment differentials demonstrate the critical need for researchers to better understand the factors that contribute to racially varying levels and types of search frictions in their effort to explain racial differences in labor market outcomes. We adopt a standard random search model similar to Black (1995) and Bowlus and Eckstein (2002) and incorporate (i) uncertainty about the prejudice of the employer and (ii) signaling of employer prejudice through the race of supervisors at the employer to generate unique predictions on racial differences in wages and job stability across employers and labor markets with varying levels of prejudice. In its structure, our model is closely related to a discrimination model with evolving uncertainty about job match quality as presented in Fryer et al. (2013b), which is a simplification of Jovanovic (1979). In contrast to Fryer et al. (2013b), our model assumes that some employers hold prejudicial beliefs that impact their hiring and retention behavior, rather than engage in statistical discrimination. Likely due to limited data, there are few empirical studies on the impact of prejudice levels on black labor market outcomes in the U.S. Closely related to our work is that of Charles and Guryan (2008) who test the empirical validity of the canonical Becker model of taste-based discrimination. Using measures of prejudice constructed from responses to race-related questions also from the GSS, Charles and Guryan find empirical support for the prediction that prejudice levels of the “marginally prejudiced” employer in the state (who are most likely to interact with black workers given the employment segregation predicted from Becker’s model) negatively impact black wages.4 Their estimates suggest that racial prejudice can account for as much as one-fourth of the black-white wage gap. Although we rely on similar measures of local prejudice, the structure of our model and the focus of our analyses differ from Charles and Guryan (2008) in several important aspects. First, our model is built on a random search framework rather than Becker’s frictionless model. With random search, workers cannot freely segregate, and thus it is the rate of 3 However, Moen (2003) demonstrates in an environment with heterogeneous productivity that it is possible for low-productivity workers to damage the outcomes of high-productivity when search frictions are low and match quality is important. 4 Charles and Guryan (2011) extend this analysis by showing that, despite decreases in the average level of prejudice in the U.S. over the past half-century, there has been little change in the level of prejudice held by the marginally prejudiced individual.

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prejudice overall, rather than the prejudice level of the “marginally prejudiced” employer that influences disparities. Second, our model and empirical analyses focus on the role of employer prejudice on black workers’ selection of jobs (and its implications on wages and job stability) as opposed to prejudice’s role in determining how workers are treated by employers. Several previous studies have suggested that the race of the hiring officer and manager can impact the hiring and careers of black workers. Turner (1997) finds that black owners hire blacks at higher rates than white owners, while Stoll et al. (2004) find additionally that at firms with a black hiring officer, black applicants make up a greater proportion of the applicant pool. More recently, Giuliano et al. (2009, 2011) exploit changes in the race of managers within establishments at a large U.S. retail firm, to show that black managers disproportionately hire blacks relative to managers of other races and black workers under black managers have better career trajectories. It is difficult to assess, however, whether these results are due to prejudice or hiring officers’ worse ability to evaluate candidates who are not of the same race. Fadlon (2015) uses the same data on supervisor’s race in the NLSY97 to test a model of statistical discrimination in which black employers observe black workers’ skill levels at the hiring stage with better accuracy than white employers. He finds that the correlation between wage and skill (as measured by scores from the Armed Forces Qualifying Test) is stronger for workers who have a same-race supervisor. Our study is focused on the job choice of the worker rather the hiring decisions of a firm. The presence of a black supervisor conveys information to black workers that other black workers have been successful in the firm, and that at least some managers do not possess prejudice.5 We generate predictions on how this influences equilibrium job selection, and consequently differences in wage and job stability across firms. The remainder of our paper is organized as follows. In Section 2, we introduce our model of employer prejudice and supervisor race and derive our testable predictions. We describe the data in Section 3. We present results from our empirical analysis of black and white wage and employment differentials in Section 4, including a discussion on how our results relate to theories of statistical discrimination and race-based job referral networks. Section 5 concludes. 2. Model of Search and Racial Matches in Employment In this section, we develop a tractable model of search and racial employment matches in the presence of imperfect information about employer prejudice to motivate our empirical 5

The race of the supervisor does not necessarily indicate the race of the hiring officer, and it is not clear that the reported supervisor has any input into the hiring process.

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analysis. Prejudiced firms are biased at both hiring and retention: (i) they are less likely to make job offers to black workers and (ii) they are also less likely to retain black workers after hiring. The presence of prejudiced firms, therefore, decreases job arrival rates for black workers, which in turn, make them less selective in accepting employment opportunities. In addition, expectation of lower retention rates at prejudiced firms decreases the option value of jobs that are offered by firms that may be prejudiced.6 Although workers cannot identify which firms are prejudiced, they observe an informative signal that indicates that some firms are less likely to be prejudiced. In practice, this signal could take many forms; we focus on the presence of a black supervisor at the firm. Given that black workers face higher termination risk from prejudiced firms and that prejudiced firms are more likely to be without black supervisors, these jobs hold lower option value for black workers. Consequently, black workers are more selective in accepting jobs at firms without black supervisors. Below, we outline the theoretical model that formalizes this intuition. 2.1. Primitives

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We model a discrete-time economy with evolving uncertainty about job match quality similar in spirit to Fryer et al. (2013b). There are two types of infinitely-lived agents: workers and firms. All agents are risk neutral and discount future periods at common rate β. 2.1.1. Workers

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Workers differ in their race (black or white) but are otherwise identical. During each period of unemployment, a worker encounters a firm with probability δ. During the meeting, both firm and worker observe an initial productivity level ω, which is distributed uniformly over [0, ω] throughout all possible matches. If the firm makes the worker an offer and the worker accepts, he enters a stage of “probationary employment” in the following period; otherwise he moves into the next period unemployed. Probationary employment lasts one period, after which the worker’s productivity level receives a shock ξ, which is distributed uniformly over [0, ξ]. Hence, his new productivity becomes θ = ω + ξ. If the match is not terminated, the worker enters “permanent employment” and continues to produce θ until the match is terminated.7 At the end of each period 6

This option value comes from a stochastic productivity increase after one period of employment for people who retain their jobs. This provides a useful modeling technique and is closest to modeling evolving information about match quality. But, prejudice on the job can affect career trajectories in other important ways as well, such as receiving less training, being denied promotions, etc. Each of these are uncertain events that affect the value of future employment, and therefore, would affect the option value of a job at acceptance. 7 We will assume throughout that ω < ω ˜ , where ω ˜ solves ω ˜ = (1 − β)Qw and Qw is defined as in (6) below.

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(including after the probationary employment period), there is an exogenous probability α that the match is destroyed. Other than the expected value of future job offers, there are no benefits or costs associated with unemployment. 2.1.2. Firms

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Firms are either prejudiced or unprejudiced, with p representing the fraction of prejudiced firms in the economy. Prejudiced firms employ a biased hiring and retention process. With a common probability s, prejudiced firms will decline to make a job offer to an otherwise qualified black candidate and terminate the employment of an otherwise qualified black candidate after the probationary period. Workers do not observe whether a firm is prejudiced during the initial job offer, but they do observe the race of their potential supervisor. A fraction b of non-prejudiced firms employ black supervisors (i.e., “black supervisor firms”); for simplicity, we assume that prejudiced firms never employ black supervisors. Applying Bayes’ Rule, the probability that a white supervisor firm that makes a job offer to a black worker is prejudiced is p(1 − s) . p(1 − s) + (1 − p)(1 − b)

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White workers are treated the same by all firms. To simplify the analysis, we assume that once they pass the probationary period, black workers no longer face additional termination risk from prejudiced firms.8 Firms may freely enter and exit the economy, regardless of their type. Jovanovic (1979) shows that the following constitutes an equilibrium: all firms pay their workers their marginal product in each period with the implicit promise that they will also be paid their marginal product in all subsequent periods.9 While other equilibria exist, focusing on an equilibrium of this type has become common for this class of models (e.g., Fryer et al., 2013b) and has two important features for our context. First, wages do not signal prejudice status, and thus supervisor race is informative. Second, free entry does not force prejudiced firms out of the market; in fact any p can constitute an equilibrium. This implication is appropriate for our context as the geographical variation in the level of prejudice across the U.S. that we employ This assumption assures that the probability of a worker voluntarily leaving a job after the probationary period is always less than 1, which simplifies the mathematical exposition but has no other consequence. 8 Relaxing this assumption would induce black workers to be more selective on accepting permanent employment from white supervisor firms. This would raise their wages and increase their separation rates, which would reinforce our main results. 9 Our model has an additional complication relative to Jovanovic (1979) in that workers hold beliefs about whether the firm is prejudiced that could be influenced by wage offers. In this equilibrium, workers believe that any firm who deviates from this implicit contract is prejudiced with certainty. See the discussion in section 2.6

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to test our model appears to have primarily historical, rather than economic, underpinnings. 2.2. White Workers

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To solve the model, we work backwards from the worker’s decision heading into the permanent employment stage. First, consider white workers, who do not face prejudice, and thus do not differentiate firms by supervisor race. Suppose that such a worker has passed the probationary period and learns that they have a permanent productivity θ at their current employer. For the worker, her value of continued employment is then Jw (θ) = θ + β(1 − α)J(θ) + βαQw 1 [θ + βαQw ] , = 1 − β(1 − α)

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where the subscript w denotes the worker’s race (white), and Q denotes the value of unemployment. It then follows that a worker will accept permanent employment whenever her value of continued employment is greater than or equal to her value from returning to unemployment or Jw (θ) ≥ Qw . Setting (2) equal to Qw and solving for θ, we can derive a white worker’s reservation permanent wage as

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θw∗ = (1 − β)Qw .

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Now consider a white worker’s decision to accept an offer for a probationary period of employment with an initial match quality of ω. If she were to accept, she would receive ω in the probationary period and the expected discounted value of earnings in the next period:

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Vw (ω) = ω + β(1 − α)[1 − F (θw∗ |ω)][E(J(θ)|θ > θw∗ ) − Qw ] + βQw 2 β(1 − α) 1  =ω+ ω − (1 − β)Qw + ξ + βQw , 1 − β(1 − α) 2ξ

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where again the subscript w denotes the worker’s race (white), and F (·|ω) denotes the conditional CDF of permanent productivity. By applying the uniform distribution assumption on θ, we derive the final expression in (4). It again follows that the worker will accept probationary employment with a match quality of ω whenever Vw (ω) ≥ Qw , and thus, the worker’s reservation probationary wage is implicitly defined by ωw∗ = (1 − β)Qw −

2 β(1 − α) 1  ∗ ωw − (1 − β)Qw + ξ . 1 − β(1 − α) 2ξ

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Finally as unemployed workers receive no benefits and endure no search costs, we can 9

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express their value of unemployment as Qw = δβ[1 − G(ωw∗ )][E(Vw (ω)|ω ≥ ωw∗ ) − Qw ] + βQw ˆ δβ 1 ω Vw (ω) − Qw dω, = 1 − β ω ωw∗

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where G is the CDF of ω, and the final expression follows from applying the assumed uniform distribution. This expression is simply the expected discounted value of earnings given their optimal reservation strategy for accepting offers. 2.3. Black Workers

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We now turn to the strategy of black workers. First, by assumption, upon reaching the permanent employment stage, black workers no longer face a threat of prejudice. Thus, the value of a permanent job offer with productivity θ for a black worker is 1 [θ + βαQb ] , 1 − β(1 − α)

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θb∗ = (1 − β)Qb .

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and the reservation productivity is

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Note that these values differ from those of white workers only because blacks have a different value of unemployment, Qb . 2.3.1. Black Workers and Firms with a Black Supervisor

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Now consider a black worker’s decision at the probationary employment stage. As there is no threat of prejudice from a firm with a black supervisor, the value of a probationary employment offer from a firm with a black supervisor to a black worker is nearly equivalent to the value of offers received by white workers,

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where the subscript b, b indicates an offer to a black worker from a firm with a black supervisor. A black worker’s reservation wage for accepting probationary employment from a firm with a black supervisor is ∗ ωb,b = (1 − β)Qb −

2 β(1 − α) 1  ∗ ωb,b − (1 − β)Qb + ξ . 1 − β(1 − α) 2ξ

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2.3.2. Black Workers and Firms with a White Supervisor

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The value of probationary employment from a white supervisor firm differs from that of a black supervisor firm, because there is a probability π that the white supervisor firm is prejudiced. If the employer is prejudiced, the worker has an s probability of being involuntarily terminated after the probationary period. Thus, the value of accepting a job offer with match quality ω from a white supervisor firm is Vb,w (ω) = ω + β(1 − α)[(1 − π) + π(1 − s)][1 − F (θb∗ )][E(J(θ)|θ > θb∗ ) − Qb ] + βQb , (11)

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where the subscript b, w indicates an offer to a black worker from a firm with a white supervisor. Note that by increasing the probability of termination after the probationary period through s, the threat of prejudice reduces the future option value of white supervisor job offers to black workers. Equating (11) to Qb , we can derive the reservation probationary wage from white supervisor jobs for black workers, 2 β(1 − α)(1 − πs) 1  ∗ ωb,w − (1 − β)Qb + ξ . 1 − β(1 − α) 2ξ

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Finally, note that (1 − p)b fraction of unemployed black workers’ encounters will be with black supervisor firms, while s fraction of their encounters with prejudiced firms will not result in a job offer. Thus, the value of unemployment for black workers can be expressed as " # ˆ ˆ δβ (1 − p)b ω (1 − p)(1 − b) + p(1 − s) ω Qb = Vb,b (ω) − Qb dω + Vb,w (ω) − Qb dω , ∗ ∗ 1−β ω ω ωb,b ωb,w

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which is simply the expected discounted value of earnings given black workers’ optimal reservation strategy. 2.4. Comparative Statics: Supervisor Race

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Given these reservation strategies, we derive several predictions on differences in wages and employment duration. Below, we provide intuition for these propositions, while formal proofs are presented in Appendix A.1. Proposition 1. Conditional on tenure, the average wage of black workers with white supervisors is higher than for black workers with black supervisors. For black workers, the possibility of facing a prejudiced employer reduces the option value of employment offers from white supervisor firms. Therefore, black workers will be more selective in the job opportunities they accept from these firms. This strategy leads black 11

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workers to have a higher distribution of probationary wages in the jobs they accept from employers with white supervisors, which in turn, implies a higher distribution of permanent wages at these firms. Proposition 2. Conditional on tenure, the average wage of black workers with black supervisors decreases as prejudice increases.

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As the fraction of prejudiced firms increases in the labor market, the job arrival rate for black workers decreases, because prejudiced employers sometimes refuse to make job offers to black workers. The reduction in the job arrival rate decreases the value of unemployment for black workers, and hence, black workers lower their reservation wage for jobs with black supervisors.

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Proposition 3. Conditional on tenure, the gap between wages for black workers with black supervisors and black workers with white supervisors increases as prejudice increases.

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Proposition 3 is perhaps our model’s most surprising wage result. When the fraction of prejudiced firms increases in the labor market, the wage gap between black workers with black supervisors and black workers with white supervisors actually increases. The intuition is as follows. As prejudice increases, the value of unemployment decreases for black workers, which induces them to become less selective on the jobs they accept. As prejudice has no direct effect on the value of black supervisor jobs, this response simply requires a reduction ∗ in ωb,b . However, a growth in the number prejudiced firms also increases the probability that white supervisor firms are prejudiced, which increases the prejudiced-based termination risk ∗ and decreases the value of white supervisor jobs, even holding ωb,w constant. Thus, an equal reduction in reservation job value due to an increase in prejudice levels will involve a larger ∗ ∗ decrease in ωb,b than in ωb,w .

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Proposition 4. Black workers have longer job durations with black supervisors than white supervisors.

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Although black workers have a lower reservation match quality for accepting probationary employment with black supervisors, it is never sufficiently low so as to offset the termination risk posed from white supervisor jobs. At the equilibrium reservation wage, workers are indifferent between offers from white supervisor firms and black supervisor firms. Since the reservation white supervisor job has a higher wage than the reservation black supervisor job, it follows that the reservation black supervisor job must be more stable for the worker to be indifferent. Proposition 5. The duration of black worker matches decreases as prejudice increases, regardless of supervisor race. However, the duration of jobs with white supervisors decreases more than the duration of jobs with black supervisors. 12

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The first part of the proposition follows from Proposition 2. An increase in prejudice levels lowers black workers’ reservation match quality for probationary employment with black supervisor firms, leading to greater turnover. As shown in Proposition 3, an increase in prejudice leads to an increase in the gap between probationary wages for black supervisor and white supervisor jobs. Since workers are indifferent in equilibrium at the reservation match, it must be that the reservation match for white supervisor jobs becomes less stable, both relative to black supervisor jobs and in absolute terms (given the first part of the proposition). Proposition 6. The expected discounted lifetime value of an accepted job by a black worker with a black supervisor is higher than that for a white supervisor

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Proposition 6 follows despite the fact that, in expectation, white supervisor jobs are higher paying at every tenure level. This is because of the strong differences in stability. Permanent jobs are always higher paying than probationary jobs, and black workers are more likely to become permanently employed at black supervisor firms. The higher probability of advancement dominates, despite the fact that the workers who do advance with white supervisors earn higher wages.

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2.5. Comparative Statics: Worker Race Proposition 7. Conditional on tenure, black workers in jobs with black supervisors have lower wages than white workers.

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It is straightforward to see that black workers with black supervisors will be paid lower wages than whites, since the presence of prejudiced employers induces black workers to be less selective in accepting jobs from black supervisor firms. However, it is important to note that our model does not necessarily imply that black workers in white supervisor jobs will have lower wages than white workers. Prejudice induces black workers to be more selective with job opportunities at white supervisor firms, which will lead to a higher observed distribution of wages for some parameters.10

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Proposition 8. The duration of black worker matches are shorter than the duration of white worker matches, regardless of the race of the supervisor. The existence of prejudice causes black workers to accept lower quality job offers than white workers, which in turn leads to lower job stability. Even though it is possible to observe black workers with white supervisors earning higher wages than white workers, this is only because prejudice makes these jobs so unstable; the high match quality only partially offsets the higher prejudice-based termination risk. 10

We note however, that the expected lifetime discounted earnings for blacks are unambiguously lower than for whites.

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2.6. Model Robustness

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Our model relied on a strong set of uniform distributional assumptions. In Appendix A.2 we explore to what extent our results hold for general distributions. The key takeaways are as follows. The intuition behind our results are not distribution-dependent. The threat of prejudice always decreases the option value of employment offers from white supervisor firms, which induces black workers to be more selective, and thus, they have lower reservation probationary wages in their employment opportunities with white supervisors than black supervisors. In some cases, such as Propositions 1 and 2, this implies differences in wages for any distribution. For others, such as Propositions 3 and 4, the differences will depend on the shape of the job offer distribution; in particular, whether there is relatively more mass near the white supervisor reservation wage or the black supervisor reservation wage. For example, black workers will always lower their reservation wage for black supervisors more than white supervisors in response to an increase in prejudice. However, if there are very few jobs in the area where they have lowered their reservation black supervisor wage and many jobs in the area where they have lowered their reservation white supervisor wage, the average wages may actually decrease more for white supervisors. While our predictions are derived from one specific – but commonly focused on – equilibrium in which all firms pay workers their marginal product in each period, other equilibria exist. A natural question is then whether our predictions would hold in other equilibria. A key factor to consider in answering this question is whether the equilibrium wages in these other equilibria would signal the prejudice status of the employer. For example, suppose there exists an equilibrium in which firms offer wages below marginal product to black workers, because the presence of prejudice reduces their value of unemployment. If these pay differences were identical across all (i.e., prejudiced and non-prejudiced) firms, black workers would still use supervisor’s race to infer prejudice status, and our main results will still hold. However, suppose an equilibrium existed in which non-prejudiced firms with white supervisors offered black workers a contract with wages initially above marginal productivity, but below marginal productivity at some point in the future. Such an equilibrium would reveal their prejudice status to black workers. Although this wage structure would be illegal, it would remove the information value of supervisor’s race, and thus, may lead to scenarios in which our predictions would not hold.11 A further consideration is the impact of alternative wage equilibria on entry. In Jovanovic (1979)’s equilibrium, wages are equal to marginal product, and thus there is no incentive 11

We note, however, that our results may still hold in this situation simply because the firm’s prejudice status and the likelihood of a white supervisor are correlated.

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for additional non-prejudiced firms or firms with black supervisors to enter. When wages are below marginal product, firms should enter, and especially non-prejudiced firms since they would be more profitable overall.12 To approximate our results in this environment, we would need two additional factors. First, there is a cost of entry for non-prejudiced firms that is a function of the amount of prejudice in the local population. This ensures that there is some relationship between the geographic prejudice measures we will use in our empirical section and the equilibrium rate of prejudice among employers. Second, employing a black supervisor is more costly than employing a white supervisor. This ensures that some nonprejudiced firms will be willing to trade-off missing out on some black workers to fear of prejudice for a lower supervisor cost. Both of these assumptions seem plausible. There will be few non-prejudiced individuals in highly prejudiced areas, meaning that at some point further entry of non-prejudiced employers will require a migration cost. Black supervisors might be more costly to acquire through labor market competition, but also higher search costs for finding a qualified supervisor given the large black-white skill differences in the U.S. economy. 3. Data: NLSY97 and GSS

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We test these predictions from our model using data from the National Longitudinal Survey of Youth 1997 (NLSY97) and the General Social Survey (GSS).

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3.1. National Longitudinal Survey of Youth 1997

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The NLSY97 surveys a sample of individuals in the United States who were aged 12 to 17 in 1997 annually on a wide array of topics including scholastic aptitude, family characteristics, and labor market outcomes. Of most interest to us are the annual job surveys. In each year, the NLSY97 tracks all jobs in which the respondent worked in the previous year and allows these jobs to be linked across survey years. Importantly for our purposes, the NLSY97 also includes of information on the race of the individual’s supervisor (self-reported) for each job until the 2009 wave of the survey. This variable allows us to test our predictions on the relationship between supervisor race, wages, and job stability. 3.2. General Social Survey The GSS is a survey of social attitudes conducted on a nationally representative sample in the United States. The survey was conducted every year from 1972 to 1994 (except in 1979, 1981, and 1992). Since then, it has been conducted biannually. Included in this survey 12

Non-prejudiced firms would earn higher profits because they terminate qualified black workers at lower rates when entering permanent employment.

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are various questions assessing individuals’ racial attitudes with which we can measure local levels of prejudice. We combine cross-sectional samples from the 1996-2010 waves of the GSS and calculate the fraction of white individuals who hold certain race-associated beliefs at the state-level. 3.3. Measure of Prejudice

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mjk = αj pk + jk .

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In our model, prejudice is defined as the fraction of employers in a state who hold a strong enough distaste for blacks so as to induce them to make employment decisions on the basis of race. While no question in the GSS addresses this directly, we can construct a measure that uses the information from all the questions that are available using factor analysis.13 Define pk as the rate of employment prejudice in state k and mjk , j ∈ {1, ..J} as J measures of prejudice in the GSS, then we can relate these measures by (14)

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Under the assumptions that E[jk lk ] = 0, ∀j 6= l and E[pk jk ] = 0, factor analysis can estimate pk up to a positive scalar. We restrict our attention to questions that measure purely racial animus rather than political sentiments, were asked in each year of the GSS from 1996-2010, and were measured on a dichotomous or close to dichotomous scale.14 We are thus left with four questions for mj : 1) whether they believe racial disparities are due to blacks’ “lack of will,” 2) whether they believe racial disparities are not due to discrimination, 3) whether they would be opposed to a close family member marrying a black individual, and 4) whether they believe racial disparities are due to “inborn disability.”15 In practice, the choice of questions is of little consequence to our results. In Appendix C.3 we show our results are robust to a large set of alternative measures of prejudice from the GSS. There is substantial variation across states in the propensity to respond positively to each of these questions; when we estimate a regression of individual responses to each question on a set of state of residence indicators, we can strongly reject the equality of the coefficients on these indicators in every case. We calculate the fraction of prejudiced responses by whites for each question at the state13

Factor analysis is an increasingly common tool used to estimate latent variable models in economics. It has been used, for example, to estimate college quality (Black and Smith, 2006), the skill content of jobs (Bacolod et al., 2009), parental investment (Aizer and Cunha, 2012), and the prevalence of crack cocaine (Fryer et al., 2013a). 14 For example, we did not consider a question on whether a racist book should be removed from a library, as this may elicit one’s attitude towards free speech. We also excluded from our analysis a question on how “lazy” blacks are on a scale of 1 to 7 given the numerous problems with interpreting such a scale (see for example, Bond and Lang, 2014), though we do use this as part of a robustness check in the appendix. 15 For a detailed description of these questions, see Appendix B.

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level. While it would be ideal to look at variation in finer geographic levels, sample sizes in the GSS do not permit this. We exclude a small number of states for which we do not have at least 30 respondents on each question. This exclusion leaves us with measures of prejudice for 43 states, calculated off of an average of 208 individuals in each state. To avoid confounding our measures with time trends in prejudice, we adjust each state’s yearly prejudice rates using a common national time trend.16 We then use these measures to estimate the factor model.17 Following convention, we normalize our prejudice measure to have mean 0 and standard deviation 1 across states. We note several shortcomings to this approach. First, our model is interested in studying the impact of prejudice among employers, while the GSS surveys a nationally representative sample of individuals in the U.S. If the relationship between prejudice among employers and prejudice among the population at large differs in way that is correlated with local labor market conditions, our results may be biased. While sample sizes in the GSS do not allow us to estimate our prejudice measure among only employers or managers, we estimated the relationship between income and the probability of giving a prejudiced response at the individual level, and reassuringly found little evidence that it differed across states for any measure. Second, while it has become conventional to use the GSS to measure differences in prejudicial tastes (e.g., Charles and Guryan, 2008; Mas and Moretti, 2009; Lang and Lehmann, 2012), survey responses in the GSS may capture other factors ranging from differences in the human capital of black workers to differences in the demographic characteristics of whites. The use of factor analysis should partially alleviate the first concern. If three of our measures are strongly driven by prejudice and one is strongly driven by another factor (that is uncorrelated with prejudice), the latter question will receive little weight in our measure.18 In Table 1, we present estimates from a regression model of our prejudice measure on several state-level demographic and economic variables. The two columns present estimates with and without census division fixed effects, respectively. Without census division fixed effects, there is a particularly strong correlation between higher prejudice and the fraction of blacks in the state. However, this correlation appears to be driven by regional differences. Once one accounts for census division fixed effects, we cannot reject the joint test that all coefficients are zero, suggesting that our measure of prejudice is not highly confounded by demographic 16

We first calculate the fraction in each state who respond affirmatively to each question in each wave of the survey. We than estimate a linear time-trend in these data, and subtract the trend from each state-year estimate before combining the years to create one state measure. 17 The factor loadings are lack of will (.92), no discrimination (.78), oppose marriage of close family member (.84), and inborn differences (.55). 18 In contrast, if three of our measures are driven by another factor and only one is driven by prejudice, the question actually measuring prejudice will receive little weight.

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Table 1: Conditional Correlations between Prejudice Measure and State Demographics

(2) -0.006 (0.014) -0.637 (1.336) 0.147 (0.205) 0.347* (0.170) -0.003 (0.029) Yes 43 1.395

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(1) Obama Vote Share -0.020 (0.015) State Fraction Black 5.403*** (1.218) Black-White Education Gap 0.038 (0.230) State Unemployment Rate 0.106 (0.129) State Real Per Capita Income (in 1000s) -0.048* (0.024) Census Division FE No Observations 43 F -statistic 8.354***

Notes - State unemployment rates and real per capita income are averaged values from 1997-2008. F -statistic is a joint test of the null that all coefficients are equal to zero. * p < .1, ** p < .05, *** p < .01 Source - GSS (1996-2010), 2000 U.S. Federal Decennial Census, Bureau of Labor Statistics, Federal Reserve Economic Data, Atlas of U.S. Presidential Elections.

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differences across regions. We will directly control for these variables in our empirical model below. In Table 2, we report (un-weighted) averages of these racial attitudes and our prejudice measure by census division.19 Prejudice appears to be highest in the South (divisions 5-7), particularly in the East South Central (division 6) which consists of Alabama, Kentucky, Mississippi, and Tennessee. The New England (division 1), Mountain (division 8), and Pacific (division 9) regions appear to have the least prejudice, although the ordering depends on the question. Our prejudice measure reflects the conclusion that one would draw from examining patterns in the individual responses: the highest prejudice levels are found in the South and the lowest prejudice levels are found in New England and the West. We also observe substantial variation in prejudice levels within census divisions; the standard deviation of state-level prejudice is less than 0.5 in only two of the nine divisions. To interpret the magnitudes of these differences, consider that a one standard deviation increase in our prejudice measure corresponds roughly to moving from the Mountain states (Arizona, Colorado, Idaho, New Mexico, Montana, Utah, Nevada, and Wyoming) to the East North Central (Indiana, Illinois, Michigan, Ohio, and Wisconsin). 19

The number of states in a census division ranges from 3 (Division 2) to 8 (Division 5). For confidentiality reasons, we are not permitted to display descriptive statistics at a level that is less aggregated than 3 states.

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Table 2: White Prejudice by Census Division

Census Division

Lack Will No Discrimination Oppose Marriage Inborn Differences Prejudice Observations

1 0.38 0.59 0.12 0.07 -1.08 (0.63) 393

Midwest

2 0.46 0.65 0.19 0.14 -0.11 (0.52) 1023

3 0.51 0.69 0.21 0.11 0.20 (0.38) 1412

4 0.40 0.64 0.19 0.08 -0.67 (0.76) 619

South 5 0.55 0.73 0.27 0.10 0.69 (0.76) 1355

6 0.63 0.79 0.44 0.11 1.75 (0.45) 501

West 7 0.57 0.77 0.32 0.11 1.06 (0.76) 736

8 0.41 0.61 0.15 0.06 -0.82 (0.50) 622

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Northeast

9 0.40 0.65 0.11 0.07 -0.87 (0.19) 988

Notes - Average of de-trended fraction of individuals in each state by census division who reported each belief. Prejudice is

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the first factor from a principal factor analysis, normalized to be mean 0 and standard deviation 1 across states. Standard deviations in parenthesis. See Appendix B for details of the data construction. Source - GSS (1996-2010)

3.4. Supervisor Race, Wages, and Job Spells

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We use the geocode files to match these prejudice measures with the individuals in the NSLY97 to create a panel of jobs, supervisor race, and levels of prejudice for the state in which the worker lives. An ideal dataset would contain detailed information about the composition of the management team at the worker’s establishment. The NLSY97, however, does not provide such information about employers as we are only able to observe the worker’s self-reported race of one immediate supervisor in each year of the spell. In order to better capture the racial composition of management at the firm, we classify a job spell as having a black supervisor if the worker ever reports having a black supervisor during that spell. We note that this categorization will still be subject to error. First, even in a firm with many black managers, a given worker may never report to a black supervisor simply by chance. However, we expect this probability is likely to be small for black workers given the substantial workplace segregation in the United States (e.g., Carrington and Troske, 1998; Hellerstein and Neumark, 2008). Second, there is a chance that the worker may report to a black supervisor later in their job spell even though none were present when the worker accepted the job. On their own, such misclassifications should simply attenuate our results. However, to the extent that remaining measurement error is correlated with the length of a job spell, there may be additional bias. In Appendix C.2, we present results from two robustness exercises to address this concern. To focus only on the black-white wage and employment gap, we drop all non-black, 19

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non-white workers. Further, the NLSY97 ceased asking the supervisor race question with the 2009 survey, so we exclude all observations after 2008. This yields an initial sample of 86,572 job-years. Of these, 30,945 are pre-market jobs which we exclude. We then drop all job-years with reported wages less than $1 per hour or above $100 per hour (833), job-years with less than 30 hours or more than 80 hours of work per week (16,555), and job-years from individuals who report less than 9 years of education (1,886). Finally, we drop all observations from job spells where we observe non-white, non-black supervisors in each year, and job spells for which we never observe supervisor’s race (8,726 job-years). These restrictions yield a final sample with 27,627 job-year observations, 27,185 of which are in states where we have a measure of prejudice. The first three columns of Table 3 show descriptive statistics of our sample broken down by race. To avoid over-weighting jobs with very short spells, we weight each observation by the number of days the worker was employed in that position in the previous year.20 Thus, we can view our results as representative of the average job a worker worked in a given year. Consistent with previous research, blacks earn lower wages, have lower average education, have shorter job durations, score in lower percentiles on the Armed Services Vocational Aptitude and Battery (ASVAB), and have a higher implied female labor force participation rate. Consistent with previous studies (e.g., Turner, 1997; Carrington and Troske, 1998; Giuliano et al., 2009), there is a startling amount of implied segregation by supervisor race. Only 8% of white workers work at an establishment in which they will encounter a black supervisor, compared to 53% of black workers. Black workers live, on average, in areas with higher rates of prejudice.21 While the difference in responses on each individual question is small, it amounts to a 0.47 standard deviation difference in overall prejudice, which is roughly equivalent to the difference between the East North Central and the South Atlantic (Delaware, District of Columbia, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, and West Virginia). In columns (4) and (5) of Table 3, we break down our sample by supervisor race. Black supervisors’ workers earn lower wages, are less educated, and score in lower percentiles of the ASVAB than those who work for white supervisors. However, this is likely because 20

Because the NLSY97 is a panel, we use the interview dates to calculate the number of days of employment at a firm. We weight all jobs that were worked for more than 365 days between surveys (either due to the survey being not quite annual or the worker did not respond in a previous survey year) as if they were worked for exactly 365 days. Our results are not sensitive to this modification and are robust to weighting all jobs equally. 21 As workers may sometimes switch states of residence during a job spell, we measure prejudice only through the state they resided in when they first report the spell. This is primarily a concern during the final year of the spell, where the job may have ended because the worker moved to a new location.

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Table 3: Descriptive Statistics

Worker Race

Supervisor Race Black (5) 7.11 (0.43) 13.05 (2.26) 0.50 (0.50) 4.22 (2.76) 2.15 (1.78) 0.35 (0.27) 0.77 (0.42)

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All White Black White (1) (2) (3) (4) Log Wage 7.17 7.23 7.07 7.19 (0.44) (0.44) (0.40) (0.44) Education 13.26 13.40 12.99 13.33 (2.32) (2.36) (2.21) (2.34) Female 0.46 0.44 0.50 0.45 (0.50) (0.50) (0.50) (0.50) Potential Experience 3.96 3.79 4.32 3.89 (2.73) (2.67) (2.80) (2.71) Tenure 2.01 2.09 1.86 1.97 (1.72) (1.77) (1.61) (1.70) ASVAB 0.46 0.54 0.30 0.50 (0.28) (0.27) (0.23) (0.27) Black Worker 0.33 0.20 (0.47) (0.40) Black Supervisor 0.23 0.08 0.53 (0.42) (0.27) (0.50) Lack Will 0.50 0.48 0.53 0.49 (0.08) (0.08) (0.08) (0.08) No Discrimination 0.69 0.67 0.72 0.68 (0.07) (0.07) (0.08) (0.07) Against Marriage 0.24 0.22 0.27 0.23 (0.09) (0.09) (0.10) (0.23) Inborn Differences 0.10 0.10 0.10 0.10 (0.03) (0.03) (0.03) (0.03) Prejudice 0.19 0.04 0.51 0.10 (0.82) (0.78) (0.80) (0.80) Observations 27627 18230 9397 21483

0.53 (0.08) 0.72 (0.08) 0.27 (0.27) 0.10 (0.03) 0.52 (0.81) 6144

Notes - Columns 2 and 3 present descriptive statistics by worker race, while columns 4 and 5 are by supervisor race. Each observation is a job-year. Standard deviations in parenthesis. Observations are weighted by days that were worked in that year. See Appendix B for description of prejudice measures. Source - NLSY79 (1997-2008) and GSS (1996-2010) combined dataset.

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black workers account for 77% of black supervisor job-years, compared to just 20% of white supervisor job-years. Similar to black workers, the average worker in a job spell with a black supervisor lives in a state with a 0.42 standard deviation higher level of prejudice. 4. Empirical Results 4.1. Identification Strategy

4.2. Wage Effects

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Testing the predictions from our model requires access to data on a large number of employment relationships across different employers and across geographies with varying levels of prejudice. The NLSY97 is well-suited for such a task. However, the available information on firms in the NLSY97 is less than ideal. We are unable to observe multiple workers working at the same firm and have only limited data on employer characteristics. Thus, we require a strong identifying assumption that any unobserved employer characteristic affects individuals of both races equally, and therefore, the effect of supervisor race and prejudice on white workers can account for the impact of any unobservable firm characteristics on wages. We are thus ignoring, for example, how highly productive and less productive firms may differ in dimensions such as hierarchy selection, job assignment, etc. which may differentially affect workers with different skills. Likewise, our assumption would be violated if, for whatever reasons, blacks received a lower proportion of their output than whites across all firms. In light of this, our results should be best interpreted as strongly suggestive of a mechanism, rather than establishing a causal link between prejudice and differential job selection by black workers.

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We first test our predictions on wages. Our main specification estimates (15)

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where Xit is a vector of time-varying controls, bw i is an indicator equal to one if the worker e is black, bit is an indicator equal to one if the employer is a black supervisor establishment, ωi is a worker fixed effect, and εi is the econometric error term.22 Importantly, as our main theoretical results only hold conditional on tenure, Xit includes a quadratic in days of job tenure in each specification.23 The coefficient γ1 represents the conditional difference 22

We report results using pooled cross-sections in Appendix C.1. We prefer the worker fixed effect regressions since they make less stringent assumptions on the selection of workers into firms. 23 Our results are robust to alternatively controlling for a quartic in tenure or using yearly categorical variables. Proposition 6 predicts that, unconditional on tenure, in the long run blacks will earn higher wages with black supervisors than white supervisors because the former jobs having higher probabilities of

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in wages between workers with black supervisors and white supervisors for white workers. The coefficient γ2 represents the conditional difference in the wages for black workers with black supervisors and black workers with white supervisors workers relative to that same difference for whites. The worker fixed effect accounts for any time-invariant differences in ability across workers. We then identify γ2 off the difference in wage changes experienced by black workers when they move to an employer with a different race relative to white workers. Proposition 1 predicts that γ2 < 0. Table 4: Racial Employment Matches and Wages: Worker FE Estimates

Dependent Variable: Log Wage Black Supervisor (γ1 )

(3) 0.016 (0.020) -0.041* (0.024) Yes Yes Yes Yes Yes Yes Yes 27089

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Worker Characteristics Employer Characteristics Occupation FE Industry FE State Characteristics State FE Year FE Observations

(2) 0.030 (0.022) -0.049* (0.026) Yes No No No Yes Yes Yes 27583

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Black × Black Supervisor (γ2 )

(1) 0.032 (0.022) -0.051* (0.026) Yes No No No No No No 27627

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Notes - Robust standard errors in parenthesis clustered at the individual level. All regressions include worker fixed effects and quadratic terms in potential experience and tenure. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics include controls for the yearly unemployment rate and real per capita income. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002)

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SOC codes. * p < .1, ** p < .05, *** p < .01 Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

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We report these results in Table 4.24 In column (1) we include only controls for experience and tenure. Our estimate of γ1 is positive, which suggests that having a black supervisor may be correlated with other positive firm characteristics, although the coefficient is not statistically significant. However, consistent with our model, we find a larger, negative, and becoming permanent, and permanent jobs pay higher wages. Interestingly, we do not find evidence for these composition effects when we remove the tenure control, but this is likely due to the youth of our sample. 24 All wage regressions apply the yearly duration weights discussed in the previous section. Removing these weights has no impact on the results. As there are likely common shocks to individual wages, we cluster our standard errors at the individual level. This formulation allows errors to be correlated within a job spell, the unit of variation of our main variable of interest.

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statistically significant coefficient on γ2 . Rather than gains, black workers experience wage decreases when working at black supervisor firms. To account for geographic wage differences, in column (2) we include state fixed effects, as well as time-varying state economic characteristics and year fixed effects.25 Our results are largely unchanged. In column (3) we present our preferred specification which accounts for unobserved employer heterogeneity by including industry and occupation fixed effects, as well as controls for the log of establishment size, and indicators for whether the worker receives any job benefits, whether he is a member of a union, and whether he has employer sponsored health insurance.26 Employer characteristics explain almost half of the wage benefit whites see when they work at a firm with a black supervisor, but have far less explanatory power on the negative effect for blacks. The coefficient γ2 remains negative and statistically significant. Given our identifying assumptions, our preferred estimate finds that the black workers earn 4.1 percentage points less at black supervisor establishments than white supervisor establishments. Our model also made predictions on how these wage differences vary with levels of local prejudice. To test these we estimate (16)

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where ps is the prejudice level in state s. As prejudice is normalized to be mean zero, γ1 , and γ2 the same statistics as in (15) for the mean state. The coefficient γ3 represents the rate at which white workers wages with white supervisors changes with a one standard deviation increase the fraction of prejudiced individuals in a worker’s state, while γ4 represents how black workers with white supervisors’ wages change with prejudice relative to white workers with white supervisors. The parameter γ5 represents the rate at which white workers’ wages with black supervisors change relative to white workers with white supervisors as prejudice increases, while similarly γ6 estimates how the gap in wages between black workers with black supervisors and black workers with white supervisors changes with prejudice relative to that same gap for white workers. The combined effect γ4 + γ6 then tells us the total effect of an increase in prejudice on black workers with black supervisors relative to white workers with black supervisors; i.e under our identifying assumption the effect of prejudice on the 25

We use fixed effects and characteristics for the state in which the individual was living when they first reported the job. This is to avoid, for example, recording a job which was terminated due to a move as being in the state in which the worker recently moved to. 26 Industry fixed effects are 2-digit (2002) NAICS codes, while occupation fixed effects are 2-digit (2002) SOC codes. We convert the census industry and occupation codes provided by the NLSY into NAICS and SOC codes using the crosswalk provided by the Census.

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wages of black workers with black supervisors. As we include worker fixed effects, γ3 and γ4 are identified off of workers who move to a different state, while γ5 and γ6 are identified off of variations in the magnitude of the change in wages when switching from a white supervisor establishment to a black supervisor establishment across states with different measured prejudice. Proposition 2 predicts γ4 + γ6 < 0 while Proposition 3 predicts γ6 < 0.

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Table 5: Racial Employment Matches, Prejudice, and Wages: Worker FE Estimates

Dependent Variable: Log Wage (2) 0.008 (0.025) -0.025 (0.038) -0.003 (0.027) -0.040 (0.032) 0.065** (0.028) -0.072* (0.039) -0.112** Yes No No No Yes Yes Yes 27154

(3) -0.003 (0.024) -0.014 (0.033) -0.007 (0.022) -0.016 (0.030) 0.051** (0.023) -0.068** (0.032) -0.0838* Yes Yes Yes Yes Yes Yes Yes 26672

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(1) Black Supervisor (γ1 ) 0.012 (0.025) Black × Black Supervisor (γ2 ) -0.028 (0.038) Prejudice (γ3 ) -0.007 (0.017) Prejudice × Black (γ4 ) -0.049 (0.034) Prejudice × Black Supervisor (γ5 ) 0.062** (0.028) Prejudice × Black × Black Supervisor (γ6 ) -0.068* (0.039) γ4 + γ6 -0.117*** Worker Characteristics Yes Employer Characteristics No Occupation FE No Industry FE No State Characteristics No Census Division FE No Year FE No Observations 27154

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Notes - Robust standard errors in parenthesis clustered at the state level. All regressions include worker fixed effects and quadratic terms in potential experience and tenure. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics include yearly unemployment rate and real per capita income, as well as the vote share for Barack Obama in the 2008 election, and the fraction of the population

that is black and the black-white education gap in the 2000 Census. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002) SOC codes. Significance stars on γ4 + γ6 represent p-level on test of γ4 + γ6 = 0. * p < .1, ** p < .05, *** p < .01 Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

We estimate (16) in Table 5.27 While our model is ambiguous with respect to the impact 27

To allow for errors to be correlated within states, we cluster our standard errors at the state level, which

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of prejudice on equilibrium black worker-white supervisor wages, we estimate γ4 is negative, though statistically insignificant. We find a strong positive effect for γ5 , which suggests that the correlation between firm productivity and having a black supervisor is stronger in states with a higher degree of prejudice. Despite this, we find an even larger negative and statistically significant estimate for γ6 . Black workers do not see an increased benefit from having a black supervisor in high prejudice areas, instead the “supervisor race” wage gap rises. We also see a strong negative and statistically significant estimate for γ4 + γ6 , indicating that relative to similar workers in low prejudice areas, black workers with black supervisors in high prejudice areas earn lower wages. Because prejudice is measured at the state level, we cannot include state fixed effects in these specifications. Instead, in column (5) we include census division fixed effects, as well as a set of state economic and social characteristics.28 Our results are largely unchanged. In column (6) we present our preferred specification with industry and occupation fixed effects, and our employer characteristic controls. While observable employer differences have some explanatory power, both γ6 and γ4 + γ6 remain statistically significant, confirming the main predictions of our model. Our estimates suggest that a one standard deviation increase in prejudice, which is roughly the difference in prejudice between the Mountain states and the East North Central, lowers the wages of black workers with black supervisors by 8.4% and raises the supervisor race wage gap by 6.8 percentage points.

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4.3. Job Stability

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To investigate the relationship between job stability and supervisor race, we calculate the total duration of each job-worker match, to create a sample of jobs rather than job-years. Our model predicts that, as jobs with black supervisors offer black workers less exposure to prejudice than jobs with white supervisors, these jobs will have longer durations (Proposition 4). However, it is important to note that our model predicts these differences in stability occur only during the probationary period of employment. Once all the uncertainty of the model is resolved, there is no predicted difference in the hazard rate. It would thus be inappropriate to test our model using, for example, a proportional hazard model. is the level of variation for prejudice. This approach generally produces more conservative estimates than clustering at the individual level. 28 The state controls are the fraction of the vote for Barack Obama in 2008, the fraction of the population that was black and the black-white education gap in the 2000 Census, and yearly unemployment and real per capita income. As an additional robustness check, we estimated all of our main results excluding workers in the South which has, by far, the highest levels of prejudice. The magnitudes of our results are nearly universally stronger, although they are estimated with less precision.

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Figure 1: Supervisor Race Gap in Survival Rates for Black Workers

Notes - Plot of point estimates for γ3N for all N from months 1 to 48. Confidence intervals derived from robust standard errors clustered at the individual level. Regressions included controls for gender; education; start year; industry and occupation

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fixed effects; whether the employer offered health insurance; whether the employer offered any benefits; union membership; unemployment rate, real per capita income, and a state fixed effect for the worker’s state of residence at the beginning of the job; a quadratic term in starting potential experience; and a quartic in ASVAB percentile score. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

We instead estimate a series of linear probability models, (17)

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e w e ZiN = βXi + γ1N bw i + γ2N bi + γ3N bi bi + εiN

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where Xi is a vector of job- and worker-specific controls defined at the beginning of the employment relationship, ZiN is an indicator for whether job i lasted more than N months, and N is every monthly interval between 1 and 48 months.29 We are thus able to estimate a different survival function for each job type with minimal parametric assumptions, subject to the caveat that we only allow the survival rates to change at monthly intervals. Under the same identifying assumption as before, our model predicts γ3N > 0.30 29

We define a month as 30.5 days. We adopt the pooled cross-sectional approach here since our data is right-censored at 2009, which can have unpredictable effects on the fixed effect estimate. See Van den Berg (2001) for a review of duration models with censorship and individual heterogeneity. 30 Note that in addition to account for unobservable differences in firm heterogeneity, γ2N will also partially account for any arbitrary correlations between job duration and supervisor’s race due to the forward-looking nature of our supervisor race variable.

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We display the result of this estimation in Figure 1. Consistent with the predictions of the model, black supervisor jobs quickly separate themselves in survival rates. Black workers are 5.4% more likely to last at least a year in a job with a black supervisor than a white supervisor. Survival rates begin to converge particularly after 2 years, and the difference falls to 2.6% after four years. We can strongly reject the joint test that the survival patterns are independent of supervisor race.31 One final prediction of our model is that prejudice negatively influences the job stability of all black worker matches, but more so for white supervisor matches than black (Proposition 5). Following the same strategy as before, we estimate, e w e w e w e ZiN = βXi + γ1N bw i + γ2N bi + γ3N bi bi + γ4N ps + γ5N bi ps + γ6N bi ps + γ7N bi bi ps + εiN , (18)

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where our predictions are γ5N < 0, γ7N < 0, γ5N + γ7N < 0. Panel A of Figure 2 plots estimates for γ5N + γ7N . Particularly for shorter durations, we find support for the theory. After 6 months of employment, the estimated effect is consistently negative. A one standard deviation increase in prejudice is associated with a 4.8 percentage point decrease in the probability of lasting at least one year at a job with a black supervisor, though this effect fades to a 1.3 percentage point decrease for four years.32 We can reject that prejudice does not affect the survival function at the 1% level. The results for white supervisors in Panel B, however, do not support the model. Prejudice consistently increases the stability of jobs for black workers who never encounter a black supervisor, despite our model predicting both a decrease in stability absolutely and relatively to jobs with black supervisors. We note that while our model does predict that black workers should become more selective in the types of white supervisor jobs they accept as prejudice increases, they should never do so in a way that counteracts the actual decrease in job stability caused by an increase in prejudice among employers. The explanation must come from outside the model.33 4.4. Discussion: Statistical Discrimination and Job Referrals

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Two important and related factors not considered in our model are the impact of statistical discrimination and race-based job referral networks. Statistical discrimination models 31

It is possible that the lower job stability we observe for black workers at white supervisor firms is in fact a positive if, for instance, these firms provide better networks and workers are able to quickly find higher wage opportunities outside the firm. However, we find no impact of supervisor race on the wages of the next job a worker accepts, suggesting this is not the case. 32 The strong effects for short durations are not trivial given the youth of our sample. The median job spell for black workers was only 329 days. 33 One explanation may be that, since prejudice increases the difference in wages between accepted white supervisor and black supervisor jobs, black workers with white supervisors are less vulnerable to poaching.

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Figure 2: Effect of Prejudice on Black Worker Job Survival Rates by Supervisor Race

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(a) Black Supervisor

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(b) White Supervisor

Notes - Panel A plots point estimates for γ5N + γ7N for all N from months 1 to 48, while Panel B does the same for γ5N . Confidence intervals derived from robust standard errors clustered at the state level. Regressions included controls for gender; education; start year; industry and occupation fixed effects; whether the employer offered health insurance; whether the employer offered any benefits; union membership; fraction of the vote share for Barack Obama in the 2008 U.S. President Election, fraction of the population which is black and the black-white education gap in the 2000 U.S. Census, state unemployment rate, state real per capita income, and census division fixed effects for the worker’s residence at the beginning of the job; a quadratic term in starting potential experience; and a quartic in ASVAB percentile score. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

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(e.g., Cornell and Welch, 1996; Fadlon, 2015) suggest that black managers should be better at evaluating black workers than white managers. Referral networks theory suggests that firms with many black workers will receive better information on future black applicants through the private information of employees in these applicants’ social sphere (e.g., Dustmann et al., 2015). It is straightforward to see that both of these factors should work in favor of our predictions on job stability and against our predictions on wages. Black workers are willing to accept lower match quality jobs with black supervisors because, due to lower rates of involuntary termination, they have higher option value than comparable white supervisor jobs. If black workers also receive additional information on the future match quality of a job with a black supervisor (e.g. learning ξ before acceptance), the option value of bad jobs in an absolute sense decreases. Black workers become less likely to accept these matches, raising wages and job stability. Whether our results hold then depends on whether the strength of prejudice in reducing reservation job value is sufficient to offset the strength of information asymmetries/networks in reducing the option value of low wage employment. In other words, our results suggest either that prejudice against black workers is pervasive, black social networks are poor, or both. As further evidence to this point, Figure 3 plots the distribution of ASVAB scores for black workers by the race of their supervisor. If job referral networks were strong, we would expect a positive sorting of black workers into firms with black supervisor. However, we see no evidence that this is the case. Black workers with white supervisors actually have higher ASVAB scores than black workers with black supervisors. There is no difference in the variance across supervisor race and little difference in the shape. These results are also not surprising given that racial disparities in the quality of job referral networks have been documented in both economics and sociology (e.g., Holzer, 1987; Smith, 2005; Tenev, 2017). Further, similar equilibrium effects may also occur in other minority communities. While Hensvik (2014) and Dustmann et al. (2015) find evidence for positive sorting into minority managed firms for women and German ethnic minorities, respectively, (˚ Aslund et al., 2014) find no wage effects for immigrants in Sweden hired by immigrant managers. 5. Conclusion In this paper, we develop a search model where some employers hold prejudices that are unobservable to workers. Workers instead observe a signal of an employer’s prejudice status, the presence of a black supervisor. Since prejudiced employers have a biased retention policy, 30

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Figure 3: Distribution of Black Worker ASVAB Percentile Scores by Supervisor Race

Notes - Kernel density estimates of ASVAB percentile scores for black workers by supervisor race.

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Source - NLSY97 (1997-2008)

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these jobs present less option value to black workers. Thus, they have lower reservation wages for employment when they can observe a black supervisor. This effect leads to lower wages overall and less job stability, but blacks still have relatively more stable matches when employed at a firm with a black supervisor. Increasing the level of prejudice decreases the value of search for black workers. This leads black workers to adopt lower reservation wages for jobs with black supervisors, causing these matches to have both lower wages and less job stability. It also decreases the value of employment with white supervisors, leading black workers to be more selective on the types of white supervisor jobs they accept. Thus, while white supervisor jobs become less stable as prejudice increases, the accepted wages actually increase relative to the wages accepted by workers with black supervisors. We found support for the main predictions of our model using longitudinal data on job spells with information on supervisor race, matched with data on levels of local prejudice. Our results show that asymmetric information regarding employer prejudice can have important labor market consequences, which suggests that firms that are not prejudiced should be willing to invest in communicating this information to prospective black employees. Because of data limitations, we were only able to look at one possible signal, which we assumed was exogenous. The optimal adoption of signals, such as affirmative action in

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promotion and hiring, remains an open question. Developing models of firm organizational practices under asymmetric information about prejudice and identifying data which could test these models presents an important direction for future research. Although measured racial prejudice in the United States has declined substantially over the last few decades, our paper demonstrates that the remaining prejudice and uncertainty about which firms hold these racial prejudices, can still have significant negative effects on black employment outcomes. Even when prejudice is not pervasive, the threat of prejudice, and the inability to identify employers who possess it, causes black workers to select into worse job opportunities with the unprejudiced employers they can identify.

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Ziegert, J. C., Hanges, P. J., 2005. Employment discrimination: the role of implicit attitudes, motivation, and a climate for racial bias. Journal of Applied Psychology 90 (3), 553.

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A. Theoretical Appendix A.1. Proofs of Main Results Proof of Proposition 1. Comparing (10) to (12), 2 β(1 − α) 1  ∗ ωb,b − (1 − β)Qb + ξ 1 − β(1 − α) 2ξ 2 β(1 − α)[(1 − π) + (1 − πs)] 1  ∗ − ωb,w − (1 − β)Qb + ξ . 1 − β(1 − α) 2ξ

(A.1)

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∗ ∗ ωb,w − ωb,b =

∗ Note that the squared term in both expressions is an increasing function of ωi,j , while the coefficient on ∗ ∗ the first squared term is strictly larger than the coefficient on the second. Thus, if ωb,b > ωb,w , the left-

hand side of (A.1) is negative while the right-hand side is positive which is a contradiction. Thus, the distribution of probationary job wages for blacks with white supervisors is drawn from a higher distribution than the distribution for black supervisor jobs. Since the distribution of permanent job wages is a truncated

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distribution with the same truncation point, but the distribution of white supervisor jobs is higher, this proves the proposition.

Proof of Proposition 2. Taking the derivative of (10) with respect to p

∂Q (1 − β) ∂p

(A.2) (A.3)

(A.4) (A.5)

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=

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  ∗ ∗  ∂ωb,b ∂ωb,b ∂Qb β(1 − α) 1  ∗ ∂Qb = (1 − β) − − (1 − β) ω − (1 − β)Qb + ξ ∂p ∂p 1 − β(1 − α) ξ b,b ∂p ∂p " !#−1 ∗ ωb,b − (1 − β)Qb + ξ β(1 − α) = 1+ 1 − β(1 − α) ξ !#−1 " ∗ ωb,b − (1 − β)Qb + ξ ∂Qb β(1 − α) × (1 − β) 1 + ∂p 1 − β(1 − α) ξ

Taking the derivative of (13),

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" # ˆ ω ˆ ω ∂Qb δβ 1 = (b − s) Vb,w (ω) − Qb dω − b Vb,b (ω) − Qb dω ∗ ∗ ∂p 1−β ω ωb,w ωb,b ˆ δβ b(1 − p) ω ∂Vb,b (ω) ∂Qb ∂Qb + − dω ∗ 1−β ω ∂Q ∂p ∂p b ωb,b ˆ δβ (1 − p)(1 − b) + p(1 − s) ω ∂Vb,w (ω) ∂Vb,w (ω) ∂Qb ∂Qb + + − dω. ∗ 1−β ω ∂p ∂Q ∂p ∂p b ωb,w

(A.6)

Define "

K1 ≡ (b − s)

ˆ

ω

∗ ωb,w

Vb,w (ω) − Qb dω − b

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ˆ

ω

∗ ωb,b

#

Vb,b (ω) − Qb dω ,

(A.7)

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∗ ∗ which is strictly negative because Vb,b (ω) > Vb,w (ω) and ωb,w > ωb,b . Rearranging terms,

" # ˆ ω ∂Vb,w (ω) δβ ∂Qb K1 + [(1 − p)(1 − b) + p(1 − s)] = dω ∗ ∂p (1 − β)ω ∂p ωb,w " !#−1 ˆ ˆ b(1 − p) ω ∂Vb,b (ω) ∂Vb,w (ω) (1 − p)(1 − b) + p(1 − s) ω 1− 1− × 1 + δβ dω + dω . ∗ ∗ (1 − β)ω ωb,b ∂Qb (1 − β)ω ∂Qb ωb,w

It then follows that since K1 < 0 and

∂Vb,w ∂p

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(A.8) < 0 that the numerator of (A.8) is negative. For the denominator,

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  ∂Vb,b (ω) (1 − α)(1 − β) 1 [ω − (1 − β)Qb + ξ] =β 1− ∂Qb 1 − β(1 − α) ξ   ∂Vb,w (ω) (1 − α)[(1 − π) + π(1 − s)](1 − β) 1 [ω − (1 − β)Qb + ξ] , =β 1− ∂Qb 1 − β(1 − α) ξ

(A.9) (A.10)

each of which is bounded between zero and one for ω above the reservation wage.34 Proof of Proposition 3. Taking the derivative of (12) with respect to p

(A.11)

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∗ ∂ωb,w ∂Qb β(1 − α)s 1 ∗ (1 − b)(1 − s) 1 = (1 − β) + [ω − (1 − β)Qb + ξ] , ∂p ∂p 1 − β(1 − α) 2ξ b,w [p(1 − s) + (1 − p)(1 − b)]2 K2

where

β(1 − α)(1 − πs) 1 ∗ [ω + (1 − β)Qb + ξ]. 1 − β(1 − α) ξ b,w

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K2 = 1 +

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It is straightforward to see that this is strictly greater than

∗ ∂ωb,b ∂p .

(A.12)

Finally note that since ω and ξ are uniform,

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the probationary wage gap will be

m m ωb,w − ωb,b =

1 ∗ ∗ (ω − ωb,b ), 2 b,w

(A.13)

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where the superscript m denotes the mean. The permanent wage gap will be

m θb,w

−

m θb,b

=

ˆ

ω

∗ ωb,b

=

    ˆ ω 1 ω + ξ − (1 − β)Qb 1 ω + ξ − (1 − β)Qb dω − dω ∗ ∗ ∗ 2 ω − ωb,b 2 ω − ωb,w ωb,w

1 ∗ ∗ (ω − ωb,b ). 4 b,w

(A.14) (A.15)

Both of these expressions are strictly increasing functions of the gap in reservations wages.

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To see this, note that

ω−(1−β)Qb +ξ ξ

is simply the probability that ω + ξ is above the reservation wage.

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Proof of Proposition 4. Conditional on advancing to and accepting permanent employment, both types of jobs have a constant hazard rate of δ. Thus, we need only check the hazard of moving from probationary to permanent employment. Turning to the reservation match, the probability of advancing to permanent employment with a black ∗ ∗ supervisor is rb,b ≡ (1 − α)(1 − F [(1 − β)Qb − ωb,b ] = (1 − α)

∗ ξ+ωb,b −(1−β)Qb

ξ

∗ ∗ jobs rb,w ≡ (1 − πs)(1 − α)(1 − F [(1 − β)Qb − ωb,w ]) = (1 − πs)(1 − α)

, while for white supervisor

∗ ξ+ωb,w −(1−β)Qb

ξ

. Now, note that

∗ ∗ ∗ ∗ Vb,b (ωb,b ) = Vb,w (ωb,w ) = Qb . As ωb,b < ωb,w , both the probationary wage and the expected wage conditional

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on reaching permanent status are higher with white supervisors. Thus, for this equality to hold, it must be ∗ ∗ that rb,b > rb,w .

To find the average hazard rate of all accepted probationary jobs, we can simply integrate over the the m distribution of matches. Denoting rb,b as the average equilibrium probability of a black worker advancing to

permanent position with a black supervisor, 1−α 1 ∗ ξ ω − ωb,b

ˆ

ω

∗ ωb,b

ξ + ω − (1 − β)Qb dω

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m rb,b =

∗  rb,b (1 − α)  = + ω + ξ − (1 − β)Qb 2 2ξ

while for black workers with white supervisor,

1 (1 − α)(1 − πs) = ∗ ω − ωb,w ξ

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m rb,w

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ξ + ω − (1 − β)Qb dω

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∗   rb,w (1 − α) + (1 − πs) ω + ξ − (1 − β)Qb = 2 2ξ

Taking the difference,

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m m rb,w − rb,b =

(A.16)

 
(1 − α) 1 ∗ ∗ rb,w − rb,b − πs ω + ξ − [1 − β]Qb , 2 2ξ

(A.17)

(A.18)

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which is strictly negative.

Proof of Proposition 5. The hazard rate of permanent jobs is unaffected by prejudice. Turning to probationary jobs with black supervisors, the probability of advancing to permanent employment is an increasing

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∗ function of ωb,b which is a decreasing function of p (see proof of Proposition 4). ∗ ∗ For jobs with white supervisors, consider the reservation match. First note that as V (ωb,b ) = V (ωb,w ) at

the equilibrium, it must also be that

∗ ∂V (ωb,b ) ∂p

=

∗ ∂V (ωb,w ) ∂p

along the equilibrium path. As the reservation wage

and average permanent wage for white supervisors increases relative to that for black supervisors, this can only be the case if the probability of advancing to a permanent position decreases relative to jobs with black supervisors. Since jobs with black supervisors durations decrease absolutely, jobs with white supervisors must as well.

Proof of Proposition 6. The expected present discounted value of an accepted match with a black super-

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visor is ∗ E[Vb,b (ω)|ω ≥ ωb,b ]=

1 ∗ ω − ωb,b

ˆ

ω

ω+

∗ ωb,w

2 β(1 − α) 1  ω − (1 − β)Qb + ξ + βQb dω, 1 − β(1 − α) 2ξ

(A.19)

while for jobs with white supervisors, 1 ∗ ω − ωb,w

ˆ

ω

ω+

∗ ωb,w

2 β(1 − α)(1 − πs) 1  ω − (1 − β)Qb + ξ + βQb dω. 1 − β(1 − α) 2ξ

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∗ E[Vb,w (ω)|ω ≥ ωb,w ]=

(A.20)

∗ ∗ ∗ ∗ From Proposition 1 we know that ωb,w > ωb,b , but Vb,b (ωb,b ) = Vb,w (ωb,w ). Now, consider the value for

jobs that are accepted with probationary wages ∆ higher than the reservation wage. For black supervisor jobs, this value would be 2 β(1 − α) 1  ∗ ωb,b + ∆ − (1 − β)Qb + ξ + βQb , 1 − β(1 − α) 2ξ

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∗ ∗ Vb,b (ωb,b + ∆) = ωb,b +∆+

while for white supervisor jobs, ∗ ∗ Vb,w (ωb,w + ∆) = ωb,w +∆+

2 β(1 − α)(1 − πs) 1  ∗ ω + ∆ − (1 − β)Qb + ξ + βQb . 1 − β(1 − α) 2ξ b,w

(A.21)

(A.22)



   1 ∗ 1 ∗ ωb,b + ∆ − (1 − β)Qb + ξ − (1 − πs) ωb,w + ∆ − (1 − β)Qb + ξ ξ ξ

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where

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which simplifies to

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β(1 − α) 1 − β(1 − α)

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Taking the difference of (A.21) and (A.22), and differentiating with respect to ∆,

β(1 − α) 1 − β(1 − α)

K3 =

  1 K3 + πs∆ ξ

∗ ∗ rb,b − rb,w . (1 − α)

(A.23)

(A.24)

(A.25)

From Proposition 5, we know that K3 > 0 and thus (A.24) is positive.

In words, this means that as we increase probationary wages above the respective reservation levels for both black supervisors and white supervisors by equal amounts, the present discounted value of black supervisor offers increases relative to white supervisor offers. Given that the values are equal at the reservation wages, any equidistant increase in probationary wages from each reservation wage will lead the black

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∗ supervisor job to have a higher value than the white supervisor job. Thus, if we set ∆ = ω − ωb,w ,

1 ∗ ω − ωb,w

ˆ

∗ ∗ ωb,b +ω−ωb,w

Vb,b (ω)dω >

∗ ωb,b

1 ∗ ω − ωb,w

ˆ

ω

∗ ωb,w

Vb,w (ω)dω,

(A.26)

∗ where the right-hand side is E[Vb,w (ω)|ω ≥ ωb,w ]. Finally note that the left hand side is strictly less than

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∗ E[Vb,b (ω)|ω ≥ ωb,b ] which proves the proposition.

Proof of Proposition 7. This result is directly implied by Proposition 2. Black wages with black supervisors decrease as prejudice increases, and white wages are equal to black wages with black supervisors when p = 0.

Proof of Proposition 8. Note that the problem for whites is equivalent to the problem for blacks when p = 0. Thus, this result is directly implied by Proposition 5.

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A.2. Relaxing Uniform Assumption

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In this appendix, we relax the uniform distributional assumption. Instead we assume that ω follows some continuous, twice-differentiable distribution F over the interval [0, ω], that ξ follows some continuous, twice-differentiable distribution G over the interval [0, ξ], and that G and F are independent. At no point is the boundedness important, and the same arguments would follow if the distributions were unbounded. Note that this does not affect θb∗ or J(θ) since these values are realized after all the uncertainty is resolved. Under these assumptions, it then follows that equation (9) becomes

while equation (11) becomes

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β(1 − α) Vb,b (ω) = ω + 1 − β(1 − α)

ˆ

(1−β)Qb −ω

ˆ

ξ

β(1 − α) 1 − β(1 − α)

ˆ

β(1 − α)(1 − πs) Vb,w (ω) = ω + 1 − β(1 − α)

PT

ξ

ω + ξ − (1 − β)Qb dG(ξ) + βQb ,

(1−β)Qb −ω

ω + ξ − (1 − β)Qb dG(ξ) + βQb .

(A.27)

(A.28)

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The reservation probationary wages become

AC

∗ ωb,b = (1 − β)Qb −

∗ ωb,w = (1 − β)Qb −

ξ

(1−β)Qb −ω

β(1 − α)(1 − πs) 1 − β(1 − α)

ˆ

ω + ξ − (1 − β)Qb dG(ξ)

(A.29)

ξ

(1−β)Qb −ω

ω + ξ − (1 − β)Qb dG(ξ)

(A.30)

Finally, given (A.27) and (A.28), " # ˆ ω ˆ ω δβ Qb = (1 − p)b Vb,b (ω) − Qb dF (ω) + [(1 − p)(1 − b) + p(1 − s)] Vb,w (ω) − Qb dF (ω) ∗ ∗ 1−β ωb,b ωb,w

(A.31)

Proposition 9. Conditional on tenure, the average wage of black workers with white supervisors is higher than for black workers with black supervisors.

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∗ ∗ Proof. At equilibrium Vb,w (ωb,w ) = Vb,b (ωb,b ). By inspection of equations (A.28) and (A.27), Vb,w (ω) < ∗ ∗ Vb,b (ω) and Vb,w (ω) is strictly increasing in ω. Therefore, it must be the case that ωb,b < ωb,w . Since both

job offers are drawn from the same distribution, the distribution of probationary wages at white supervisors firms is simply a higher truncated version of the distribution of probationary wages at black supervisor firms. Thus the average probationary wage at white supervisor firms is higher. ˜ b,j (θ) as the distribution of permanent Now, consider the wage distribution of permanent jobs. Denote G

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wage offers for black workers at jobs with a supervisor of race j (i.e. the distribution of ω + ξ given the ˜ b,w (θ) reservation wage strategy of probationary employment). As ξ and ω are independent, it follows that G ˜ b,b (θ). Finally, as the distribution of accepted job offers is simply the truncation of these distributions FOSD G at the same point (θb∗ ), the distribution of accepted permanent job offers for white supervisor jobs also dominates that for black supervisor jobs, and thus the mean is higher.

Proposition 10. Conditional on tenure, the average wage of black workers with black supervisors decreases as prejudice increases ∗ Proof. We first prove that ωb,b is decreasing in p. Suppose not, and that there is some p0 > p such that

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∗ ∗ ∗ ωb,b (p0 ) > ωb,b (p). Since Vb,b (ωb,b ) = Qb in equilibrium and Vb,b (ω) is increasing in ω, this then implies that ´ω 0 ∗ ∗ Qb (p ) > Qb (p). However, given that Vb,b (ω) > Vb,w (ω), ωb,b < ωb,w and ω∗ Vb,b (ω) − Qb dF (ω) is strictly b,b

∗ ∗ ∗ decreasing ωb,b , this can only be the case if ωb,w (p) < ωb,w (p0 ). But then it must be the case that either at

∗ ∗ ∗ ∗ p0 , Vb,w (ωb,w ) < Vb,b (ωb,b ), or at p, Vb,w (ωb,w ) > Vb,b (ωb,b ) which is a contradiction. ∗ ∗ Finally since ωb,b is decreasing in p, E[ω|ω > ωb,b ] is also decreasing in p, which in turn implies that ∗ E[θ|θ > θb∗ , ωb,b ] is decreasing in p by the same argument as in Proposition 9.

ED

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Proposition 3 necessarily only holds at the reservation match. The problematic case here would be ∗ ∗ ∗ where the distribution of F (ω) is dense around ωb,w but not ωb,b , and ωb,w decreases in p. In this case, black workers begin accepting a large number of relatively low wage jobs from white supervisors, but accept very few new low wage jobs from black supervisors, which may raise the mean black supervisor wage relative to the white supervisor wage. Proposition 11. The gap between reservation wages for black workers with black supervisors and black workers with white supervisors increases as prejudice increases

PT

Proof. The proof is nearly identical to the proof of Proposition 3. Implicitly differentiating (A.29) and

AC

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(A.30) with respect to p

∗ ∂ωb,b ∂Qb = (1 − β) ∂p ∂p ∗ ∂ωb,w ∂Qb K4 = (1 − β) + ∂p ∂p K5

(A.32) (A.33)

where

K4 =

β(1 − α)s ∂π 1 − β(1 − α) ∂p

ˆ

ξ

∗ (1−β)Qb −ωb,w

β(1 − α)(1 − πs) K5 = 1 + 1 − β(1 − α)

ˆ

∗ ωb,w + ξ − (1 − β)Qb dG(ξ)

(A.34)

ξ

dG(ξ)

∗ (1−β)Qb −ωb,w

which are both positive.

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Propositon 4 also only necessarily holds at the reservation match. The problematic case would be ∗ ∗ situations where F (ω) has a large density between ωb,b and ωb,w . Thus although the reservation white supervisor job has a lower expected duration, and every white supervisor job has a lower expected duration conditional on ω, the average white supervisor duration may be higher because black workers avoid accepting a very high number of unstable jobs that they are willing to accept with black supervisors. Proposition 12. Black workers have longer job durations at the reservation black supervisor match than the reservation white supervisor match

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Proof. Suppose not, and that the reservation white supervisor match has a higher probability of becoming ∗ ∗ permanent than the average white supervisor match. Proposition 9 shows that ωb,w > ωb,b , and that that ∗ implies that the average permanent wages are also higher at the reservation wage. Thus Vb,w (ωb,w ) > ∗ Vb,b (ωb,b ) which is a contradiction.

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Proposition 5 holds for black supervisor jobs, but not necessarily for white supervisor jobs. The problem ∗ ∗ here are cases where ωb,w increases in p, and the area around ωb,w has a high density. Thus, while the new reservation white supervisor match is less stable than the old, black workers reject a large number of unstable white supervisor matches they previously accepted, potentially raising the average stability of accepted matches. Proposition 13. The average duration of black worker matches with black supervisors decreases as prejudice increases ∗ Proof. This follows directly from Proposition 10. Since ωb,b decreases in p, and job stability is an increasing

M

function of ω, the average stability of an accepted black supervisor job decreases.

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Proposition 14. The probability of the reservation match of a black worker with a white supervisor becoming permanent decreases as prejudice increases Proof. The same argument from the proof of Proposition 5 holds. Proposition 11 shows that

∗ ∂ωb,b ∂p

<

∗ ∂ωb,w ∂p

which implies that both the expected probationary wages and expected permanent wages increase for white

PT

supervisor jobs relative to black supervisor jobs. As

∗ ∂Vb,b (ωb,b ) ∂p

=

∗ ∂Vb,w (ωb,w ) ∂p

along the equilibrium path (i.e.

accounting for the equilibrium response of reservation wages to changes in p), it must be that the probability of advancing to the probationary period for white supervisor jobs has decreased relative to black supervisor

CE

jobs. Proposition 13 shows that job stability at black supervisor jobs decreases absolutely in p.

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Note that we cannot prove an analogous result in this environment to Proposition 6. A necessary condition for black supervisor jobs to have higher lifetime wages than white supervisor jobs is that white supervisor jobs have lower equilibrium probabilities of advancement to permanency. While this is true at the reservation matches, whether it holds for the distribution of accepted matches depends on the distribution of ω and θ. By definition, the expected lifetime earnings of the reservation matches are equal across supervisor race. Finally, note that white workers in our model are simply black workers with p = 0. Thus the results of Proposition 10, 13, and 14, also apply to Propositions 7 and 8.

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B. Data Appendix B.1. GSS Prejudice Measures Here we list the exact wording and coding of the questions we used to measure prejudice in the General Social Survey.

Lack Will

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The variable RACDIF4 asks, “On the average African Americans have worse jobs, income, and housing than white people. Do you think these differences are because most African Americans just don’t have the motivation or willpower to pull themselves up out of poverty?” Respondents could choose ‘Yes’ or ‘No.’ We coded ‘Yes’ answers as prejudiced responses. The question was asked in every survey from 1996-2010.

No Discrimination

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The variable RACDIF1 asks, “On the average African Americans have worse jobs, income, and housing than white people. Do you think these differences are mainly due to discrimination?” Respondents could choose ‘Yes’ or ‘No.’ We coded ‘Yes’ answers as prejudiced responses. This question was asked in every survey from 1996-2010.

Oppose Marriage

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The variable MARBLK asks, “How about having a close relative or family member marry a black person? Would you be very in favor of it happening, somewhat in favor, neither in favor nor opposed to it happening, somewhat opposed or very opposed to it happening?” Respondents could choose ‘Strongly Favor,’ ‘Favor,’ ‘Neither favor nor oppose,’ ‘Oppose,’ or ‘Strongly Oppose.’ We coded ’Strongly Oppose’ answers as prejudiced responses. The question was asked in every survey from 1996-2010.

Inborn Differences

PT

Against Housing Laws

ED

The variable RACDIF2 asks, “On the average African Americans have worse jobs, income, and housing than white people. Do you think these differences are because most African Americans have less in-born ability to learn?” Respondents could choose ‘Yes’ or ‘No.’ We coded ‘Yes’ answers as prejudiced responses. The question was asked in each survey from 1996-2010.

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The variable RACOPEN asks, “Suppose there is a community-wide vote on the general housing issue. There are two possible laws to vote on. One law says that a homeowner can decide for himself whom to sell his house to, even if he prefers not to sell to African Americans. The second law says that a homeowner cannot refuse to sell to someone because of their race or color. Which law would you vote for?” Respondents could choose ‘A homeowner can decide for himself whom to sell his house to, even if he prefers not to sell to African Americans,’ ‘A homeowner cannot refuse to sell to someone because of their race or color,’ or ‘Neither.’ We coded the first response as prejudiced. This question was asked in the 1996 survey, and again from 2004-2010.

Lazy

The variable WORKBLKS asks, “I’m going to show you a seven-point scale on which the characteristics of [Blacks] can be rated... A score of 1 means that you think almost all of the people in the group are [hard-working]. A score of 7 means that you think almost everyone in the group are [lazy]. A score of 4 means that you think that the group is not towards one end or another, and of course you may choose any number in between that comes closest to where you think people in the group stand.” Respondents can choose a number between 1-7. We coded answers of 6 or greater as prejudiced responses. This question was asked in every survey from 1996-2010.

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Favor Anti-Miscegenation Laws The variable RACMAR asks, “Do you think there should be laws against marriages between AfricanAmericans and whites?” Respondents could choose ‘Yes’ or ‘No.’ We coded ‘Yes’ answers as prejudiced responses. This question was asked in each survey from 1996-2002.

Against Black President

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The variable RACPRES asks, “If your party nominated an African-American for President, would you vote for him if he were qualified for the job?” Respondents could choose ‘Yes’ or ‘No.’ We coded ‘No’ responses as prejudiced responses. The question was asked in the 1996, 2008, and 2010 surveys.

Smart

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The variable INTLBLKS asks, “I’m going to show you a seven-point scale on which the characteristics of [Blacks] can be rated... A score of 1 means that you think almost all of the people in the group are [unintelligent]. A score of 7 means that you think almost everyone in the group are [intelligent]. A score of 4 means that you think that the group is not towards one end or another, and of course you may choose any number in between that comes closest to where you think people in the group stand.” Respondents could choose a number between 1-7. We coded answers of 2 or less as prejudiced responses. This question was asked in every survey from 1996-2010.

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C. Empirical Appendix C.1. Pooled Cross-Section Results

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In this section, we re-estimate our main results using a pooled cross-section specification. While this specification induces bias from the unobservable factors which would cause selection of individuals into firms with different raced supervisors, it provides an advantage in that observations from all workers can be used for identification, rather than the 1,278 black workers and 777 white workers who had both a black supervisor and white supervisor job spell. In the first four columns of Table C1, we estimate e log Wi = βXi + γ1 bei + γ2 bw i bi + ε i ,

(C.1)

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where Xi now additionally includes an indicator for race. Columns (1)-(3) are analogous to columns (1)-(3) of Table 4. The point estimates across these specifications are nearly identical in magnitude and statistically significant. In column (4), we attempt to further control for individual heterogeneity by including a quartic in the worker’s ASVAB percentile score. In doing so, we lose 4,731 observations from individuals who did not take the test in the NLSY97, which reduces our precision. While this estimate is not statistically significant, it maintains the same sign and is only slightly smaller in magnitude than our preferred estimate in column (3) of Table 4. Columns (5)-(8) estimate e w e w e log Wis = βXis + γ1 bei + γ2 bw i bi + γ3 ps + γ4 bi ps + γ5 bi ps + γ6 bi bi ps + εis .

(C.2)

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While we continue to see support across specifications (5)-(7) for Proposition 2, which are analogous to (1)(3) in Table 5, the point estimates are smaller in magnitude than in the fixed effect results. The estimates of γ6 are also not statistically significant. We lose statistical significance on γ4 + γ6 when we include ASVAB controls in column (8), and the point estimate of γ6 goes to 0. However, this appears to be entirely due to an idiosyncratic difference in sample between the aforementioned ASVAB takers and non-takers. When re-estimating columns (5)-(8) on just the sample of respondents with a valid ASVAB score, we consistently estimate a 0 coefficient for γ6 . Further the inclusion of the ASVAB itself as a control for this sample does not change the estimate. Given that the worker fixed effect does at least as good of a job as the ASVAB test score at controlling for worker heterogeneity, there seems to be little reason for preferring this estimate.35 One difference between the pooled cross-sections and our worker fixed effect results presented in the main text, is that the fixed effect regressions are identified off of only workers who move to a different state or work under jobs with supervisors of different races. Thus, a concern is that the differences are driven by a change in sample, rather than the improved ability of our worker fixed effects to account for individual heterogeneity. However, this does not appear to be the case. Estimating the pooled cross-sectional model on the sample of workers who move states or work jobs with supervisors of different races yields nearly identical results to those presented here.

C.2. Supervisor Race and Job Stability Correlation In constructing our measure of supervisor race, we used all available observations of each job spell. In general, this reduces measurement error, since we have more observations to observe and correctly categorize 35

We also estimated our main worker fixed effect regressions on only the sample of ASVAB takers. This produced estimates smaller in magnitude than those in Table 4 but still economically significant, though not always statistically significant due to the reduced sample size. These results are available upon request. It is unclear why the sample change has such an impact, but ASVAB participation was voluntary for the NLSY97, so it is prone to selection issues.

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C.3. Alternative Measures of Prejudice

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a spell as having a strong black presence. However, it creates a negative correlation between job spell length and the degree of measurement error, which can have difficult to predict effects. In Table C2 we test the sensitivity of our wage and job stability results to specifications that address this issue. In columns (1) and (2), we control for the total length of the job spell in a regression on wages. While this should eliminate the concerns about the bias of our supervisor race measure, it is an over-control in the sense that well matched jobs will necessarily be both high wage and more stable. Nonetheless, all of our model’s predictions hold under these specifications. As a second test, we estimate wage regressions which use only the race of the first reported supervisor of the job spell to classify the establishment’s supervisor race. This will reduce measurement error that comes from observing a supervisor later in a job spell who was not present when the worker accepted employment, but increases measurement error from missing black supervisors and managers who were present but not initially reported by the worker. Our strong belief is that the latter is likely to be more important than the former, so we would expect these estimates to be attenuated relative to Tables 4 and 5. Importantly, though there will be no correlation between measurement error in supervisor race and job spell length. We display these estimates in columns (3) and (4) of Table C2. Consistent with this specification being prone to more measurement error, our coefficients of interest are smaller in magnitude and not statistically significant. However, in each case they maintain the correct sign. In Figures C1 and C2 we repeat our analysis from the main text on job stability using the first supervisor race definition. We would expect that if the correlation between measurement error and duration were important it would matter most here, since it directly effects measurement of the left-hand side variable. However, these results look very similar to those presented in the main text.

AC

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Our constructed measure of prejudice provides an interval-scaled measure of employer prejudice provided that the fraction of individuals who give a prejudiced response to each of the questions we use is linearly related to the fraction of prejudiced employers in a state.36 We could alternatively measure prejudice using only a single question which would be correct under the weaker assumption that that question is linearly related to the fraction of prejudiced employers. However, the measurement error problem will be more severe, suggesting that the results will be further attenuated. To test the sensitivity of our results to different prejudice measures, in the first four columns of Table C3 we estimate (16) using the individual components directly. The columns use, in order: believe that blacks lag whites due to lack of will, do not believe blacks lag whites due to discrimination, oppose the marriage of a close relative to a black individual, and believe that blacks lag whites due to inborn disability. The responses are scaled to be mean 0, standard deviation 1 across states, to ease comparison with the factor analysis results. Reassuringly, the choice of question does not appear to be of great importance for our result. Black worker-black supervisor wages are decreasing in prejudice for all of the questions we use to construct our measure, and significantly so for two out of the four questions. The “supervisor race wage gap” for black workers is increasing in prejudice for every question as well, and statistically significant for all but the “no discrimination” question. In columns (5) through (9) we measure prejudice through five additional questions we did not use due to not being asked every year, difficulty in interpreting the question, or difficulty in interpreting the scale: opposition to open housing laws, belief that blacks are lazy, support for anti-miscegenation laws, refusal to vote for black presidential candidates, and a belief that blacks are not intelligent. These questions yield similar conclusions. Our result on the supervisor race wage gap is significant for 2 out of these 5 variables, while our result for black supervisor-black worker wages is statistically significant for four. In Table C4, we repeat this exercise, estimating (17) for 12, 24, and 36 month durations. The patterns mimic those seen in Figure 2 with the strongest negative effect seen at 12 months and declining thereafter. Only for refusal to vote for black presidential candidates and belief that blacks are not intelligent do we 36

We note that having an interval-scaled measure of prejudice is important, as it is nearly impossible to make cross-group comparisons with ordinal data (Bond and Lang, 2013, 2014).

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AC

CE

PT

ED

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see any evidence for a reversal in the direction of the duration relationship. Note that two-thirds of the responses for the black presidential candidate question came during Barack Obama’s presidential campaign and presidency, which may hamper its reliability as a measure of pure prejudice. Taken together, the results of Tables C3 and C4 suggest that our theory would likely be confirmed by a precise measure of state-wide rates of employment prejudice if such a measure existed. Moreover, nearly any way in which we construct a measure of prejudice from the General Social Survey will yield results supportive of our model.

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Figure C1: Supervisor Race Gap in Survival Rates for Black Workers (First Supervisor)

Notes - Plot of point estimates for γ3N for all N from months 1 to 48. Confidence intervals derived from robust standard errors clustered at the individual level. Regressions included controls for gender; education; start year; industry and occupation

AC

CE

fixed effects; whether the employer offered health insurance; whether the employer offered any benefits; union membership; unemployment rate, real per capita income, and a state fixed effect for the worker’s state of residence at the beginning of the job; a quadratic term in starting potential experience; and a quartic in ASVAB percentile score. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

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Figure C2: Effect of Prejudice on Black Worker Job Survival Rates by Supervisor Race (First Supervisor)

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(a) Black Supervisor

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(b) White Supervisor

Notes - Panel A plots point estimates for γ5N + γ7N for all N from months 1 to 48, while Panel B does the same for γ5N . Confidence intervals derived from robust standard errors clustered at the state level. Regressions included controls for gender; education; start year; industry and occupation fixed effects; whether the employer offered health insurance; whether the employer offered any benefits; union membership; fraction of the vote share for Barack Obama in the 2008 U.S. President Election, fraction of the population which is black and the black-white education gap in the 2000 U.S. Census, state unemployment rate, state real per capita income, and census division fixed effects for the worker’s residence at the beginning of the job; a quadratic term in starting potential experience; and a quartic in ASVAB percentile score. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

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51 Yes No No No No No No No No 27627

Yes No No No No Yes Yes No Yes 27583

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(3) (4) (5) -0.086*** -0.049*** -0.090*** (0.011) (0.012) (0.021) 0.017 0.007 0.032 (0.019) (0.022) (0.021) -0.044* -0.039 -0.036 (0.023) (0.026) (0.030) -0.049*** (0.015) -0.033 (0.024) 0.018 (0.027) -0.024 (0.040) -0.0571* Yes Yes Yes No Yes No Yes Yes No Yes Yes No Yes Yes No Yes Yes No Yes Yes No No No No Yes Yes No 27089 22423 27154

(6) (7) (8) -0.102*** -0.081*** -0.037* (0.020) (0.017) (0.019) 0.014 0.008 0.003 (0.020) (0.018) (0.021) -0.032 -0.028 -0.033 (0.024) (0.023) (0.026) -0.001 -0.006 -0.007 (0.016) (0.015) (0.015) -0.023 -0.024 -0.036 (0.023) (0.020) (0.022) 0.034 0.016 -0.000 (0.025) (0.021) (0.022) -0.031 -0.023 0.006 (0.031) (0.029) (0.030) -0.0539** -0.0472** -0.0306 Yes Yes Yes No No Yes No Yes Yes No Yes Yes No Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes Yes 27154 26672 22106

yearly unemployment rate and real per capita income, as well as the vote share for Barack Obama in the 2008 election, and the fraction of the population that is black and the black-white education gap in the 2000 Census. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002) SOC codes. Significance stars on γ4 + γ6 represent p-level on test of γ4 + γ6 = 0. * p < .1, ** p < .05, *** p < .01 Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

Notes - Robust standard errors in parenthesis clustered at the individual level in columns (1)-(4) and at the state level in columns (5)-(8). Worker characteristics include education, a gender dummy, and quadratic terms in potential experience and tenure. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics in columns (2)-(4) include controls for the yearly unemployment rate and real per capita income. State characteristics in columns (6)-(8) include

γ4 + γ6 Worker Characteristics ASVAB Quartic Employer Characteristics Occupation FE Industry FE State Characteristics State FE Census Division FE Year FE Observations

(2) -0.107*** (0.012) 0.028 (0.023) -0.050* (0.026)

M

(1) -0.119*** (0.012) 0.026 (0.023) -0.049* (0.027)

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Prejudice × Black × Black Supervisor (γ6 )

Prejudice × Black Supervisor (γ5 )

Prejudice × Black (γ4 )

Prejudice (γ3 )

PT

CE

Black × Black Supervisor (γ2 )

Black Supervisor (γ1 )

Black

AC Dependent Variable: Log Wage

Table C1: Racial Employment Matches, Prejudice, and Wages: Pooled Cross-Section Estimates

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52 Yes Yes Yes Yes Yes No Yes 27118

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(4) -0.011 (0.027) -0.012 (0.037) -0.004 (0.022) -0.027 (0.031) 0.039 (0.030) -0.051 (0.037) -0.0779 Yes Yes Yes Yes No Yes Yes 25896

First Supervisor

(2) (3) -0.009 0.001 (0.023) (0.024) -0.017 -0.030 (0.032) (0.028) -0.006 (0.021) -0.019 (0.030) 0.047** (0.022) -0.060* (0.030) -0.0797* Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes Yes 26700 26295

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(1) 0.009 (0.020) -0.041* (0.024)

Duration Control

Dependent Variable: Log Wage

the black-white education gap in the 2000 Census. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002) SOC codes. Significance stars on γ4 + γ6 represent p-level on test of γ4 + γ6 = 0. * p < .1, ** p < .05, *** p < .01 Source - NLSY97 (1997-2008) and GSS (1994-2010) combined dataset

for a quartic in total job duration. Columns (3) and (4) define a job spell as having a black supervisor only if the first reported supervisor is black. All regressions include worker fixed effects and quadratic terms in potential experience and tenure. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics in columns (1) and (3) include controls for the yearly unemployment rate and real per capita income. State characteristics in columns (2) and (4) include yearly unemployment rate and real per capita income, as well as the vote share for Barack Obama in the 2008 election, and the fraction of the population that is black and

Notes - Robust standard errors in parenthesis clustered at the individual level in columns (1) and (3), and at the state level in columns (2) and (4). Columns (1) and (2) control

γ4 + γ6 Employer Characteristics Occupation FE Industry FE State Characteristics State FE Census Division FE Year FE Observations

Prejudice × Black × Black Supervisor (γ6 )

Prejudice × Black Supervisor (γ5 )

Prejudice × Black (γ4 )

Prejudice (γ3 )

Black × Black Supervisor (γ2 )

PT

Black Supervisor (γ1 )

AC

Table C2: Racial Employment Matches, Prejudice, and Wages: Supervisor Race Robustness, Worker FE Estimates

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Lack Will

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No Open

Are Lazy

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Inborn Diff

AN US

No Marr

(2) (3) (4) (5) (6) 0.009 -0.001 -0.006 0.006 -0.005 (0.023) (0.024) (0.018) (0.024) (0.024) -0.033 -0.018 -0.027 -0.025 -0.022 (0.031) (0.032) (0.024) (0.031) (0.032) 0.013 -0.018 -0.008 0.018 0.017 (0.020) (0.025) (0.017) (0.018) (0.018) -0.039 -0.021 0.021 -0.041 -0.001 (0.029) (0.030) (0.021) (0.025) (0.023) 0.003 0.041** 0.057*** 0.034 0.043 (0.023) (0.019) (0.015) (0.026) (0.028) -0.011 -0.060** -0.047* -0.060* -0.046 (0.027) (0.027) (0.024) (0.035) (0.034) -0.0498 -0.0813** -0.0254 -0.102** -0.0469 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 26700 26700 26700 24227 26700

No Disc

Misceg Laws

Black Pres

marriage of a close relative to a black individual, (4) Believe blacks lag whites due to inborn disability, (5) Oppose open housing laws, (6) Believe that blacks are lazy, (7) In favor of anti-miscegenation laws, (8) Would not vote for a black presidential candidate, (9) Believe that blacks are not intelligent. All regressions include worker fixed effects and quadratic terms in potential experience and tenure. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics include controls for the yearly unemployment rate and real per capita income, as well as the vote share for Barack Obama in the 2008 election, and the fraction of the population that is black and the black-white education gap in the 2000 Census. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002) SOC codes. Significance

stars on γ4 + γ6 represent p-level on test of γ4 + γ6 = 0. * p < .1, ** p < .05, *** p < .01. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

Not Smart

(7) (8) (9) 0.003 -0.005 0.009 (0.021) (0.024) (0.020) -0.025 -0.017 -0.040 (0.028) (0.033) (0.029) 0.018 0.025* 0.023 (0.024) (0.013) (0.015) -0.016 -0.061*** -0.039** (0.032) (0.020) (0.018) 0.043** 0.040** 0.033 (0.016) (0.019) (0.022) -0.067*** -0.033 -0.027 (0.024) (0.031) (0.030) -0.0835** -0.0939** -0.0660** Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 26249 22496 26700

Dependent Variable: Log Wage

Notes - Standard errors clustered at the state-level in parenthesis. Each column represents prejudice being measured as the fraction in the state who report the prejudiced belief listed on the top. These are as follows: (1) Believe blacks lag whites due to lack of will, (2) Do not believe blacks lag whites due to discrimination, (3) Oppose the

Black Supervisor (γ1 )

(1) -0.004 (0.024) Black × Black Supervisor (γ2 ) -0.017 (0.033) Prejudice (γ3 ) -0.005 (0.017) Prejudice × Black (γ4 ) -0.008 (0.028) Prejudice × Black Supervisor (γ5 ) 0.058** (0.027) Prejudice × Black × Black Supervisor (γ6 ) -0.071* (0.037) γ4 + γ6 -0.0796* Employer Characteristics Yes Occupation FE Yes Industry FE Yes State Characteristics Yes Census Division FE Yes Year FE Yes Observations 26700

AC

Table C3: Robustness of Wages to Different Prejudice Measures: Worker FE Estimates

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AC PT

54

ED

(4) -0.022 (0.025) -0.009 (0.035) -0.003 (0.033) Yes Yes Yes Yes Yes Yes Yes Yes 10362

(5)

No Open (7)

Misceg Laws

-0.046 -0.037 (0.033) (0.026) -0.026 -0.023 (0.020) (0.019) -0.011 -0.002 (0.23) (0.017) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 11392 11208

(6)

Are Lazy

CR IP T

AN US

(3)

Inborn Diff

-0.045 -0.051* -0.023 (0.028) (0.027) (0.028) -0.026 -0.022 -0.004 (0.017) (0.018) (0.016) -0.025 -0.011 -0.004 (0.023) (0.018) (0.018) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 11392 11392 11392

M

-0.038 (0.040) -0.002 (0.024) -0.006 (0.028) Yes Yes Yes Yes Yes Yes Yes Yes 11392

(2)

(1)

No Marr

(9)

Not Smart

-0.017 -0.020 (0.025) (0.026) 0.020 -0.013 (0.008) (0.018) 0.056*** 0.024 (0.019) (0.017) Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes 9653 11392

(8)

Black Pres

worker was a union member, whether the employer offered health insurance, and whether the employer offered any benefits. State characteristics include controls for the yearly unemployment rate and real per capita income, as well as the vote share for Barack Obama in the 2008 election, and the fraction of the population that is black and the black-white education gap in the 2000 Census. Industry FE are 2-digit (2002) NAICS codes. Occupation FE are 2-digit (2002) SOC codes. * p < .1, ** p < .05, *** p < .01. Source - NLSY97 (1997-2008) and GSS (1996-2010) combined dataset

belief listed on the top. These are as follows: (1) Believe blacks lag whites due to lack of will, (2) Do not believe blacks lag whites due to discrimination, (3) Oppose the marriage of a close relative to a black individual, (4) Believe blacks lag whites due to inborn disability, (5) Oppose open housing laws, (6) Believe that blacks are lazy, (7) In favor of anti-miscegenation laws, (8) Would not vote for a black presidential candidate, (9) Believe that blacks are not intelligent. Each row represents the coefficient on the interaction between prejudice, and an indicator for being a black worker with a black supervisor for a different duration. All columns additionally control for supervisor race, and the interaction between race and supervisor race. Worker characteristics include controls for education, a gender dummy, and a quadratic term in potential experience at the beginning of the job. Employer characteristics include controls for log establishment size, a dummy for if this variable was top-coded, and indicators for whether the

Notes - Standard errors clustered at the state-level in parenthesis. Each column represents prejudice being measured as the fraction in the state who report the prejudiced

Worker Characteristics ASVAB Quartic Employer Characteristics State Characteristics Occupation FE Industry FE Census Division FE Year FE Observations

36 Months

24 Months

Prejudice × Black × Black Supervisor (γ4 + γ6 ) 12 Months

CE No Disc

Lack Will

Dependent Variable: Job Duration

Table C4: Robustness of Job Duration to Different Prejudice Measures: Pooled Cross-Section Estimates

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