Discrimination in Hiring: Evidence from Retail Sales∗

Alan Benson†, Simon Board‡, and Moritz Meyer-ter-Vehn�

July 30, 2019

Abstract

Using data on 36,949 newly-hired commission-based salespeople at a major U.S. retailer, we

�nd that white, black and Hispanic managers within the same store are more likely to hire

workers of their own race. This may be caused by managers' intrinsic taste for hiring same-race

applicants (taste-based discrimination), or by their greater ability to screen same-race applicants

(screening discrimination). We derive the testable implications of these models for the mean

and variance of productivity and show that white and Hispanic hiring is consistent with the

screening hypothesis. We �nd little evidence of complementarities between supervising (rather

than hiring) managers, or employee discrimination in this setting.

∗Keywords: Taste-based discrimination, statistical discrimination, screening discrimination, hiring; JEL codes:J71, M51.†University of Minnesota, https://carlsonschool.umn.edu/faculty/alan-benson‡UCLA, http://www.econ.ucla.edu/sboard/�UCLA, http://www.econ.ucla.edu/mtv/

1

1 Introduction

More than �fty years after the U.S. prohibited employers from using race as a factor in employment,

the persistence of racialized labor market outcomes�including segregation and pay gaps�remains

among the most striking features of the labor market. Controlling for education and experience,

black and Hispanic workers have signi�cantly lower employment rates and wages than white workers,

especially for less-educated workers (Altonji and Blank, 1999; Ritter and Taylor, 2011; Lang and

Lehmann, 2012). Understanding the causes of racial disparities is important for policymakers and

managers who wish to promote equality and enhance productivity.

Taste-based discrimination (Becker, 1957) is the simplest, and perhaps the presumptive, theory

of discrimination. If employers have an intrinsic taste for hiring same-race workers then they lower

the hiring bar for their own race, leading to labor market segregation and wage disparities (e.g. Black,

1995). Screening discrimination (Cornell and Welch, 1996), though less prominent in the literature,

poses an alternative theory of racialized labor market outcomes. This model adapts the classical

Phelps (1972) theory of statistical discrimination to allow employers to be better at screening same-

race applicants, and is also consistent with the observed tendency for managers hire their own race.1

This assumption is corroborated by evidence from psychology, linguistics, and legal scholarship

that �nds that people communicate more e�ectively with those who share the same background.

This �nding is especially relevant in the hiring context, where managers explicitly report di�culty

reading subtle and nonverbal cues to assess �t with the job when assessing candidates with di�erent

backgrounds. Although both taste and screening are consistent with a wide variety of empirical facts

(e.g. labor market segregation, pay gaps, and di�erences in employment rates), they call for radically

di�erent remedies. For example, if taste is the dominant factor in discrimination, racial quotas

will generally raise productivity as biased managers hire more quali�ed minorities; in contrast,

if screening is the dominant factor, quotas will lower productivity as uninformed managers hire

mismatched minorities. Conversely, algorithmic hiring tools will improve diversity and productivity

under screening discrimination, but not under taste-based discrimination.

This study aims to distinguish and test the di�erent predictions of the taste-based and screening

models of discrimination. In both models, managers observe a noisy signal of applicants' produc-

tivity and hire those whose expected productivity lies above a threshold. In the taste-based model,

managers adopt lower thresholds when evaluating same-race applicants. In the screening model,

managers use the same threshold for all races but observe a more precise signal when evaluating

same-race applicants.

We show that both taste and screening discrimination predict that managers will be more likely

1In Phelps (1972) there is a single recruiter who has more precise signals about majority applicants than minorityapplicants. Screening discrimination posits that there are di�erent races of recruiters who have more precise signalsabout same-race applicants.

2

to hire workers of the same race, though for di�erent reasons. With taste-based discrimination,

managers lower their standards for same-race candidates; with screening discrimination, managers

receive stronger signals of ability from same-race candidates. Both models also predict same-race

workers will have greater retention. With taste-based discrimination, managers treat same-race

workers more leniently; with screening discrimination, managers make fewer mistakes in hiring

same-race workers.

In contrast, the taste-based and screening models make di�erent predictions regarding the rel-

ative productivity of same-race and cross-race hires. Under taste-based discrimination, managers

lower the hiring threshold for same-race workers, meaning that the productivity of same-race hires

has a lower mean and higher variance. In contrast, under screening discrimination, managers can

screen same-race workers with greater accuracy, so the productivity distribution of same-race hires

has a higher mean and lower variance. As a corollary, the taste-based model implies that pro-

ductivity is submodular in the manager and worker race, while the screening model implies that

productivity is supermodular.2

Testing the con�icting predictions of the taste and screening models requires a direct measure of

productivity. Models of discrimination are often evaluated by using turnover, promotions, or wages

as a proxy for productivity; these measures are ill-suited to our context since they re�ect endogenous

decisions made by potentially biased managers. For instance, turnover among same-race workers

could be lower because managers don't want to �re same-race workers, or because they have precise

signals about same-race candidates and make few errors.

We evaluate the taste-based and screening models using longitudinal administrative data from

a large national retailer from 2009 to 2015. Each store typically employs several hiring managers

of di�erent races, allowing us to examine di�erence in their behavior after controlling for store and

job �xed e�ects. The data include the races of 621,231 white, black, and Hispanic newly-hired

workers and the races of their 31,767 hiring managers at 4,885 store locations.3 For a subset of

36,949 salespeople, the data further include sales versus targets, the performance measure used

to determine commissions. We use these data to examine how the mean and variance of sales

productivity depends on whether they were hired by a same-race manager.

First, we show that the probability that a hire is a given race is 2.3 percentage points higher

when the manager shares the same race, after controlling for store and job �xed e�ects. This gap

is positive and statistically signi�cant for all same-race pairs, and represents a particularly large

increase for minority workers since they account for a much smaller percentage of hires. Workers of

all three races also have the lowest turnover under same-race managers. These results are consistent

2If yij is the average productivity of race-i workers hired by race-j managers, then y is supermodular if yii+ yjj ≥yij + yji, and submodular if the inequality is reversed. We often talk of such di�-in-di� predictions since, unlikepairwise comparisons, they are robust to asymmetries in the mean ability of workers and managers of di�erent races.

3For linguistic simplicity, we refer to white, black, and Hispanic all as �races.�

3

with both taste-based and statistical discrimination.

Second, we use the productivity data to evaluate the two theories. We �nd that productivity

is signi�cantly supermodular, both in the �rst three months and in the longer term, for all races.

Additionally, same-race variance in productivity is lower among whites and Hispanics. These two

results are especially pronounced among Hispanics: Under Hispanic managers, mean productivity is

2.9% higher and the variance is 10.2% lower than under white managers. This e�ect is particularly

stark at the bottom of the distribution, where Hispanic workers hired by Hispanic managers are

about 15% more productive than those hired by white managers.

This pattern of results�a greater mean productivity and lesser productivity variance for same-

race hires�suggest that better same-race information plays an important role in explaining racial-

ized labor market outcomes in the low-skill market overall, and especially for Hispanics. We then

explore whether this information is likely to have come through formal channels (e.g. through the

job application process) or through informal channels (e.g. through social networks) by examin-

ing whether same-race hires tend to share other observable characteristics (age and gender), which

would suggest that they are also socially connected. We �nd little evidence that same-race hires

share these other demographic characteristics, suggesting that managers' superior ability to screen

in this setting comes from formal rather than informal channels.

The remainder of the paper explores alternative mechanisms that could account for some or

all of these results. The most obvious alternative explanation is that managers and workers of the

same race are productive complements (e.g. Lang, 1986).4 However, this alternative is di�cult to

reconcile with the evidence. First, simple models of complementarities are inconsistent with the

distribution of productivity for all races. Second, when workers move between managers, we �nd no

evidence of segregation, which we would expect if workers and managers were complementary and

maximizing productivity. Third, when a manager changes, the mean productivity of their workers

does not change; productivity thus appears to depend on the race of the hiring manager rather than

the race of the supervising manager.

We also explore the possibility that workers prefer to work for same-race managers. If workers

prefer to work for same-race managers regardless of their ability, this would yield segregation but

not supermodularity. Thus, to explain our supermodularity results, the preference for same-race

managers must be greater among high ability workers, which would also raise the variance of same-

race productivity. This is inconsistent with Hispanics, but may help explain black performance.

Other evidence is mixed. On the one hand, we present evidence that same-race turnover is lower,

after controlling for productivity. This seems particularly important for high-performing black

workers, helping to explain the high mean and variance of black managers. On the other hand, the

4By �complementarity production� we mean that workers are more productive when working with others of thesame race, so the most productive assignment is to match people with the same race. In contrast, acts of �favoritism�,like assigning better shifts to same-race workers, is zero sum.

4

lack of segregation among internal transfers suggests that same-race preference is not widespread.

At a macroeconomic level, taste-based and screening discrimination pose many of the same

symptoms, including minorities' longer job search durations, greater unemployment, and lower pay.

However, they have di�erent implications for the e�ect of racial quotas, centralized hiring, and

diverse hiring committees on segregation, unemployment, pay, and job matching. Our results show

that managers and policy makers need to take screening discrimination into account when designing

such policy reforms, and that the form of discrimination may not be cleanly symmetric across groups,

suggesting the e�ectiveness and appropriateness of interventions will also vary by minority group.

1.1 Literature

There is widespread evidence for discrimination in recruiting. For example, in an audit study,

Bertrand and Mullainathan (2004) �nd that applicants with white-sounding names receive a 50%

higher call-back rate as black-sounding names. While such studies have shown that discrimination

exists, these results could be explained by either taste-based or statistical discrimination.

Closer to our study, Giuliano, Leonard and Levine (2009, 2011) study hiring practices of man-

agers of di�erent races at a large chain of retail stores.5 They �nd that there is same-race bias in

hiring of black employees of similar magnitude to our data. They also �nd evidence of bias in His-

panic hiring when the store is heavily Hispanic.6 The major advantage of our data is that we have

an objective measure of productivity that helps identify the cause of the segregation. For example,

Giuliano et al. show black workers are more likely to turn over and less likely to be promoted under

white managers, but in the absence of productivity data, this could be due to lower performance or

to managerial bias in retention and promotion criteria.

Two closely related studies use matched employee-employer data to study the e�ect of ethnic

composition on hiring and wages. Dustmann, Glitz, Schönberg, and Brücker (2016) show that �rms

in Germany with more minorities employees hire more minority applicants and pay them slightly

higher wages. They argue that these results come from referrals that provide information about

match quality, which they interpret through a model of screening discrimination. Relatedly, Åslund,

Hensvik, and Skans (2014) show that immigrant managers in Sweden are more than twice as likely

to hire immigrants compared to native managers. Immigrants also are paid higher wages when

managers are also immigrants, which is mainly explained by individual worker e�ects, meaning

that immigrant managers hire higher quality immigrant recruits. Our study is complementary to

5Looking across �rms, Bates (1994), Turner (1997), Carrington and Troske (1998), and Stoll, Raphael, and Holzer(2004) show that blacks are employed at greater rates in establishments with black owners and managers. Of course,di�erences in hiring rates across �rms may re�ect more than just the race of the hiring manager.

6Our �rm has quite di�erent demographics, so one should not be surprised to see some di�erences (e.g. in theirdata, di�erences between white and Hispanic managers are smaller). Front-line workers in Giuliano et al. (2009,2011) are 70% female with an average age of 22. In contrast, our workers are 54% are female with a median age of35, and our commissioned salespeople are 39% female with a median age of 32.

5

these, having four main contributions. First, whereas wages are endogenous and may be higher

because of taste-based or screening discrimination, our productivity data allows us to tease apart

these explanations. Second, by looking at similar jobs within a single large employer, we are

less concerned about unobserved heterogeneity in hiring practices. Third, we look at the entire

distribution of productivity rather than just the mean, providing a richer picture of hiring practices.

Fourth, our study addresses the hiring of di�erent races in the U.S. rather than di�erent immigrant

groups in Europe.7

Other studies have sought to isolate and test individual types of discrimination. One strand of

literature has found evidence of taste-based discrimination and complementarities in production.

For instance, Hedegaard and Tyran (2018) �nd that Danish students discriminate in choosing co-

workers based on students' names, even after productivity information is disclosed. Looking at a

fruit picking farm, Bandiera, Barankay, and Rasul (2009) show that managers help out socially

connected workers at the expense of unconnected workers when paid a �xed wage, but not when

paid a performance bonus. Within a Kenyan �ower packing �rm, Hjort (2014) shows that workers

try to lower the performance of team members from di�erent tribes, even at a cost to themselves.

And in a study of a French grocery chain, Glover, Pallais, and Pariente (2017) show that minority

cashiers are as productive as non-minority cashiers on average, but become less productive when

working under managers who were deemed biased by an implicit association test.

A second strand of literature aims to isolate statistical discrimination. Agan and Starr (2017) use

audit methods to show that that �ban-the-box� laws that prohibit employers from asking about job

applicants' criminal histories can lead employers to reduce the call-back rate for black applicants.8

To test for statistical discrimination more broadly, Altonji and Pierret (2001) hypothesize that

wages will become more correlated with AFQT scores (a measure of intellectual ability not seen by

employers) and less correlated with race as workers grow older. Their evidence is mixed: the race

gap widens with experience, contradicting their model; however, adding AFQT scores reduces the

degree to which the race gap widens, consistent with the predictions. Oettinger (1996) observes

that increased wage gap may be explained by greater mismatch �rm-worker matching for blacks.

Lang and Manove (2011) also �nd that blacks obtain more education then whites, holding AFQT

constant, consistent with a model of statistical discrimination whereby blacks need to signal their

ability.9

7Fisman, Paravisini, and Vig (2017) uses a similar methodology as us to assess discrimination in Indian loandecisions They show that same-group borrowers can borrow more than cross-group borrowers (where a �group�corresponds to religion or caste). Consistent with screening discrimination, they �nd that same-group borrowers arealso less likely to default and the variation of same-group loan sizes are higher.

8See also Doleac and Hansen (2019). For further evidence on statistical discrimination with respect to job tests,credit checks and drug tests see Autor and Scarborough (2008), Bartik and Nelson (2017), Ballance, Cli�ord, andShoag (2017), and Wozniak (2015).

9There is also evidence of statistical discrimination against consumers in price negotiations. Ayres and Siegelman(1995) observe that black customers in car dealerships receive worse o�ers, no matter the race of the salesperson.

6

Screening discrimination�the theory that managers statistically discriminate and that same-

group managers get a better signal of workers' productivity�has received wide support in other

�elds. First, research in psychology and communication has long shown that di�erences in commu-

nication patterns and underlying experiences impairs communication across races. Erickson (1975)

evaluated videos of career counseling sessions at junior colleges, providing early evidence that people

in �gatekeeping� positions often have di�culty interpreting and relating to people who of di�erent

races, and especially when they are also separated by other dimensions of social background. In an

ethnographic study of 185 Chicago-area �rms, Neckerman and Kirschenman (1991) �nd evidence

that �interviewing well goes beyond interpersonal skills to common understandings of appropriate

interaction and conversational style�in short, shared culture.� Wolgast, Björklund, and Bäckström

(2018) �nd that professional interviewers in Sweden placed greater attention to cultural �t when

interviewing applicants with Arab-sounding names, and comparatively less attention to questions

related to job �t. Second, research in psychology and law has found that people are slow to update

beliefs around individual characteristics when that individual is a member of another race. Psy-

chologists largely attribute this e�ect to learned, accumulated expertise as we spend greater time

with people similar to us (Kelly et al., 2007; French, 1973; Erickson and Schultz, 1982). As a result,

people tend to think categorically about members of races with whom they have limited experience.

For example, studies have found that same-race eyewitnesses are much better at distinguishing

suspects than eyewitnesses of other races (Behrman and Davey, 2001; Chance and Goldstein, 1996).

While prior studies have largely aimed to provide evidence for individual theories of labor market

discrimination, the e�ect of di�erent policies depends on which theory is dominant. Our contribution

is to distinguish and test between the taste-based and screening models of discrimination using data

at a large US retailer, which o�ers productivity data on a large number of workers, and the race of

their hiring managers.

2 Theory

We �rst describe a general model based on Phelps (1972). We then specialize it to examine the

predictions that result from taste-based discrimination and screening discrimination. With taste-

based discrimination, a version of Proposition 1 was shown by Cornell and Welch (1996). With

screening discrimination, Propositions 5 and 6 are closely related to the analysis of Simon and

Warner (1992) and Dustmann, Glitz, Schönberg, and Brücker (2016). Our theoretical contribution

formalizes these results and puts them together in a single analytical framework. This analysis

forms the theoretical basis for our empirical analysis in the subsequent sections.

There is a population containing mass nA race-A workers and nB race-B workers; race-A workers

Similarly, List (2004) �nds that baseball card traders believe minority customers have a wider variance in willingness-to-pay for baseball cards, leading them to o�er minorities less favorable quotes.

7

are in the majority, so nA ≥ nB. Motivated by our data (see Figure B1 in Online Appendix B), we

assume the log of workers' sales is normally distributed, y ∼ N(µ, σ20) and refer to y as the worker's

productivity.

Recruiting is performed by managers. There are mA race-A managers mB race-B managers,

where mA ≥ mB. Each manager meets mass 1 of workers drawn randomly from the population,

obtains a signal of the workers' productivity, and recruits a worker if the signal is above a cuto�. A

manager's signal is given by y = y+ε, where the noise ε ∼ N(0, σ2ε ) is independent of y. Using Bayes'

rule, the expected productivity of the applicant given the signal y, the estimate, is a weighted sum

of the prior and the signal, where the weights re�ect the signal variance σ2ε and the cross-sectional

productivity variance σ20,

y = E[y|y] =σ20

σ20 + σ2εy +

σ2εσ20 + σ2ε

µ.

We will work with the estimate y since it is a su�cient statistic for the signal y. As usual in

Bayesian updating, it is important to distinguish between two variances. Ex-ante, the estimate y

is distributed normally with mean µ and estimator variance η2 := σ40

σ20+σ

2ε. Notably, the estimator

variance η2 falls in the signal variance σ2ε . For example, with a completely noisy signal, σ2ε =∞, all

workers have the same expected ability y, so the estimator variance η2 is zero. Ex-post, conditional

on y, the realized ability y is distributed normally with mean y and residual variance ρ2 := σ20σ

2ε

σ20+σ

2ε.

For example, with a completely noisy signal, σ2ε =∞, the residual variance equals the cross-sectional

variance of productivity σ20.

For ease of exposition, we assume that managers have log-utility so wish to hire a worker if the

expected log-sales y exceeds a cuto� y∗.10 We then consider two forms of discrimination. Under

taste-based discrimination, biased managers gain extra utility b > 0 when hiring a worker of their

own race. Managers then apply di�erent thresholds y∗s , y∗c to same-race and cross-race workers,

where y∗c = y∗s + b. Under screening discrimination, same-race applicants have lower signal variance

than cross-race applicants, σ2s < σ2c , and managers apply the same cuto� y∗ for both races of

workers.

Figure 1 illustrates the distribution of the estimate y and cuto�s y∗ under the two models. All

the proofs are in the Appendix.

2.1 Taste-based Discrimination

Under taste-based discrimination, managers are biased toward their own race, hiring an applicant

with estimated productivity above cuto�s y∗c = y∗s + b. The probability that an applicant of race

i ∈ {s, c} is hired is pi = Pr(y ≥ y∗i ). A race-A manager then hires mass NA = nAps+nBpc workers.

10In Section 2.3 we argue that our results continue to hold when agents maximize expected sales rather thanexpected log-sales.

8

(a) Taste-based Discrimination (b) Screening Discrimination

Same-race

managers

hire

All

managers

hire

Estimator

ys = yc

bias

µ y⇤s y⇤cy

All

managers

hire

Same-race

managers

hire

Same-race

estimator, ys

Cross-race

estimator, yc

µ y⇤y

1

Same-race

managers

hire

All

managers

hire

Estimator

ys = yc

bias

µ y⇤s y⇤cy

All

managers

hire

Same-race

managers

hire

Same-race

estimator, ys

Cross-race

estimator, yc

µ y⇤y

1

Figure 1: Distribution of the estimator, y.Notes: Under taste-based discrimination, same-race and cross-race applicants have the same estimator variance,

but managers apply di�erent hiring thresholds. Under screening discrimination, managers apply the same hiring

threshold across races, but same-race candidates have a larger estimator variance, η2s > η2c .

Of these, fraction rAA = nAps/NA are race-A workers, and rBA = nBpc/NA are race-B workers.

Proposition 1 (Hiring). In the taste-based model:

(a) Managers hire relatively more workers of their own race, i.e. rAA > rAB and rBB > rBA.

(b) Majority managers hire more workers than minority managers, NA ≥ NB.

Managers are biased toward workers of their own race, and so lower the required standard and

hire relatively more of them (see Figure 1a). Since majority managers apply this lower standard

to more applicants, they hire more workers. Or, equivalently, it takes less time for them to �ll any

open position.

We next turn to productivity. Given cuto� y∗i , the average productivity of recruits is yi :=

E[y|y ≥ y∗i ], and the productivity variance of recruits is vi := V ar(y|y ≥ y∗i ).

Proposition 2 (Productivity). In the taste-based model:

(a) Average productivity is lower for same-race hires than cross-race hires, ys < yc.

(b) Majority managers/workers have lower average productivity than minority managers/workers.

(c) Productivity variance is higher for same-race hires than cross-race hires, vs > vc.

Managers apply a lower standard to same-race workers, so their average productivity is lower

(see Figure 1a). Since majority managers apply this lower standard to more applicants, the average

productivity of their teams is lower. Similarly, majority workers are more likely to be hired by a

same-race manager, so their average productivity is lower. Finally, the lower same-race standard

y∗s < y∗c raises the productivity variance of same-race recruits as additional low-productivity workers

are hired. Speci�cally, by the law of total variance, we can decompose the productivity variance

of recruits into the sum of estimator variance V ar(y|y ≥ y∗i ) and residual variance V ar(y|y) = ρ2.

The estimator variance is higher for same-race recruits, V ar(y|y ≥ y∗s) > V ar(y|y ≥ y∗c ), while the

residual variance is equal for both races.

9

To illustrate these results, Figure 2(a) plots the di�erence between same-race and cross-race

productivity by quantile. That is, quantile 0 corresponds to the di�erence between the worst same-

race and cross-race recruits, while quantile 1 corresponds to the best recruits. One can see that

the same-race recruits are less productive; this gap shrinks as the recruits get better since the best

workers are hired no matter the race of the manager.

The di�erence in average productivity is critical for distinguishing taste-based and statistical

discrimination. However, the pairwise comparison in Proposition 2 relies on the assumption that the

underlying productivity of race-A and B workers is the same. To allow for possible heterogeneity in

across races, we decompose same and cross race hires and test the simple corollary that productivity

is submodular,

yAA + yBB < yAB + yBA (1)

where yAB is the average productivity of race-A workers hired by race-B managers.11

The submodularity test presented in (1) is distinct from the traditional Becker outcomes test,

which notes that the productivity of marginal hires among disfavored groups will be greater than

the productivity of marginal hires of favored groups (see Arnold, Dobbie, and Yang (2018), Benson,

Li, and Shue (2019) and Simoiu, Corbett-Davies, and Goel (2017) for applications to bail decisions,

promotions, and tra�c stops). In contrast, we compare the relative hiring of managers of di�erent

races. The submodularity test then �di�erences out� mean productivity gaps across races, allowing

us to identify the relative bias of race-A and race-B managers even if workers of di�erent races have

di�erent productivity distributions, as biased managers hire more marginally-quali�ed same-race

applicants. That is, the submodularity test examines whether the tendency of managers to hire

their same race is explained by relative bias; we do not estimate productivity at the margin and so

our results should not be interpreted as estimates of absolute bias.12

Finally, we consider turnover. Suppose the �rm eventually learns the actual productivity y and

�res a worker if it is more than ∆ below the cuto� y∗i . Turnover is thus qi := Pr(y ≤ y∗i −∆|y ≥ y∗i ).

Proposition 3 (Turnover). In the taste-based model:

(a) Turnover is lower for same-race hires than cross-race hires, qs < qc.

(b) Turnover is lower for majority managers/workers than minority managers/workers.

This result is somewhat counter-intuitive. Same-race recruits have lower average productivity

and higher variance, but lower turnover. The result follows since managers apply the same bias

11To verify submodularity with heterogeneous distributions, observe that if race-A managers have a lower cuto�for race-A workers than race-B managers, their recruits will be weaker, i.e. yAA < yAB . Similarly, if race-B managershave a lower cuto� for race-B workers than race-A managers, we have yBB < yBA. Summing yields inequality (1).Submodularity also obtains if managers adjust their standards so they hire the same number of workers in expectation.

12Asymmetry may also arise through di�erences in the level of bias, bi. For example, in the spirit of Bordalo etal. (2016), the majority group may have a (largely) false stereotype that the minority group had low productivity, sobA > bB . This does not a�ect Proposition 2 .

10

(a) Taste-based Discrimination (b) Screening Discrimination

90%

95%

100%

105%

110%

Sam

e− v

s C

ross

−ra

ce P

rodu

ctiv

ity G

ap

Quantile0.5 1

90%

95%

100%

105%

110%

Sam

e− v

s C

ross

−ra

ce P

rodu

ctiv

ity G

ap

Quantile0.5 1

Figure 2: Same-Race Productivity Gap by QuantileNotes: This picture shows the di�erence between same-race and cross-race productivity by quantile (the y-axis

shows the de-logged scale for ease of interpretation). These �gures assume ability has mean µ = −0.5 and variance

σ20 = 0.4, the signal variance is σ2

ε = 0.2 and cuto� is y∗ = −0.3; this generates a productivity distribution with

mean 0.046, median 0.028 and variance 0.21, similar to our data (see Figure B1 in the Online Appendix B). Under

taste-based discrimination, the bias is b = 0.1. Under screening discrimination, the same- and cross-race signals have

variance σ2s = 0.2 and σ2

c = 0.3.

b when �ring as when hiring. An agent is thus �red if the measurement error y − y exceeds the

�safety margin� y−y∗+ ∆. Both same- and cross-race recruits have the same residual variance, but

cross-race recruits have lower safety margins (in the likelihood ratio order). Indeed, in Figure 1a,

one can see that cross-race recruits are closer to the hiring threshold then same-race recruits.

2.2 Screening Discrimination

We now turn to screening discrimination, assuming same-race managers have more accurate signals

than cross-race managers, σ2s < σ2c . Managers are unbiased and thus apply the same threshold y∗

for both races of workers. We also assume that less than half the applicants are hired, i.e. y∗ > µ.

We �rst consider hiring:

Proposition 4 (Hiring). In the screening model:

(a) Managers hire relatively more workers of their own race, i.e. rAA > rAB and rBB > rBA.

(b) Majority managers hire more workers than minority managers, NA ≥ NB.

Managers have better signals about same-race applicants, so the estimator variance is higher and

candidates have a higher probability of passing the hiring threshold (see Figure 1b). Since majority

managers have accurate signals about more applicants, they hire more people. These predictions

are the same as with taste-based discrimination (Proposition 1). Thus, hiring data alone is not

enough to di�erentiate between the two models. To do this one needs productivity data, for which

the models generate opposite predictions.

11

Proposition 5 (Productivity). In the screening model:

(a) Average productivity is higher for same-race hires than cross-race hires, ys > yc.

(b) Majority managers/workers have higher expected productivity than minority managers/workers.

(c) Productivity variance is lower for same-race hires than cross-race hires, vs > vc.

Since managers have better signals about same-race applicants, the estimator variance is higher.

That is, there are many same-race candidates whose expected productivity y far exceeds the thresh-

old y∗. In comparison, the estimated productivity of most cross-race hires is relatively close to

y∗, and so same-race hires have higher expected productivity than cross-race hires (see Figure 1b).

Majority managers hire more same-race applicants, so the average productivity of their teams is

higher. Similarly, majority workers are more likely to be hired by a same-race manager, so their

average productivity is higher. Finally, the higher accuracy of the same-race signals means that the

productivity variance is lower for same-race hires. Intuitively, if managers screen on a very noisy

signal then the variance of realized productivity equals that of the prior; as the accuracy rises, more

unproductive workers are excluded, and the variance of realized productivity falls.

To illustrate these results, Figure 2(b) plots the di�erence between same-race and cross-race

productivity by quantile. One can see that the gap is initially positive, shrinks as the workers get

better, and eventually becomes negative. Intuitively, cross-race managers make some very bad hires

since their signal is imprecise, leading to a large gap at the lowest quantiles. The cross-race manager

also makes fewer hires overall (Proposition 4(a)), so the very best are also a larger percentage of

their hires, leading the gap to become negative at the highest quantiles.

As with taste-based discrimination, the pairwise comparison in Proposition 2 does not accommo-

date productivity heterogeneity across races, and so we test the simple corollary that productivity

is supermodular,

yAA + yBB > yAB + yBA. (2)

This is the opposite to the submodularity (1) predicted by taste-based discrimination.

Returning to turnover, suppose again that a worker is �red if his realized productivity y falls

below y∗ −∆.13

Proposition 6 (Turnover). In the screening model:

(a) Turnover is lower for same-race hires than cross-race hires, qs < qc.

(b) Turnover is lower for majority managers/workers than minority managers/workers.

Same-race recruits have higher mean productivity and lower residual productivity variance. Both

of these forces lower the chance of outliers, and thus turnover.13The ability to �re the agent may introduce di�erent cuto�s y∗ for the di�erent races. This can go in either

direction. If the managers cares most about long-run productivity, the ability to �re low-productivity workers meansmanagers would lower their standards for high-variance cross-race applicants. Conversely, if reversing one's hiringdecision is viewed as a bad signal by the store manager, managers would raise their standards for cross-race applicants.

12

Table 1: Summary of Theoretical Results

Is same-race or cross-race higher?

Taste-based discrimination Screening discrimination

Hiring Same-race Same-race

Productivity mean Cross-race Same-race

Productivity variance Same-race Cross-race

Turnover Cross-race Cross-race

Table 1 summarizes our results. Both the taste-based and the screening model predict more

same-race hiring and less same-race turnover. Data on allocations are therefore inadequate to

separate the models. In contrast, the models have opposite predictions for the mean and variance of

productivity, so our productivity data allow us to investigate the causes of discrimination in hiring.

2.3 Discussion

The model makes three assumptions of note. The �rst is that managers have log utility, which means

that they hire a worker if expected log-sales y exceeds a cuto�, y∗. Instead, suppose managers are

risk neutral and wish to maximize expected sales; they are then risk-loving with respect to log-

sales. Under taste-discrimination, managers still apply a higher threshold to cross-race hires than

same-race hires, and so none of our results change. Under screening discrimination, things become

a little more complicated since managers now apply a lower hiring threshold to cross-race hires

than same-race hires because of the higher residual variance of cross-race applicants. This new force

works against the bias for hiring same-race candidates, Proposition 4, but the result still holds if

the hiring threshold is su�ciently high. On the other hand, the lower threshold means the manager

hires more low-productivity cross-race workers, and thus reinforces Propositions 5-6. See Online

Appendix A.1 for details.

Second, we assume that majority and minority managers have the same hiring standard. This

means that majority managers hire more workers under both taste-based and screening discrimina-

tion (Propositions 1(b), 4(b)). Of course, if di�erences in team size are su�ciently large, minority

managers will search for longer or will lower their standards. Allowing for the latter possibility com-

plicates our analysis, but it is still the case that the two models have the same predictions for hiring

and opposite predictions for productivity. That is, productivity is submodular under taste-based

discrimination, and supermodular under screening discrimination.

Finally, in conceptualizing screening, we are agnostic as to whether managers' informational

advantages accrue before or after workers' formal job applications. For instance, managers may

13

be socially connected to workers of the same race and encourage high ability workers to apply, or

alternatively, managers may be better at discerning same-race high ability workers in the course of

the formal hiring process. In Section 4.5 we try to distinguish these hypotheses.

3 Empirical Setting

Our data come from the U.S. operations of a large national retailer from February 2009 to Jan-

uary 2016. Each establishment is led by a store manager and a team of associate store managers

(henceforth �managers�) who hire for their respective departments, among other duties. When a

department has a vacancy, they post an ad speci�c for that opening. Applicants to sales roles take

a screening test online or at a store location, which generally requires less than an hour to complete.

The test asks candidates about their background and experience, how they would respond under

hypothetical scenarios with customers or colleagues, and a personality test. These tests are scored

by an algorithm that provides a three-tier recommendation for whether to proceed with an inter-

view. Department managers observe these recommendations and select whom to interview, though

they are not obligated to follow the recommendation. These interviews can vary substantially, but

managers receive a guide for conducting behavioral interviews that further ask applicants how they

would respond to hypothetical scenarios. Consistent with this training, most employees report that

managers use behavior-based questions. For example, the applicant may be asked to describe a life

or work experience in which they overcame an obstacle, helped a stranger, or witnessed dishonesty.

Proponents of behavioral interview techniques assert that future behavior in a particular position is

best predicted by the past behaviors under similar positions, and that structured behavioral inter-

views can reduce bias (Bohnet, 2016). Critics argue that behavioral interviews are biased against

workers with limited experience related to the hypothetical scenario, and reward story-telling ability

rather than the ability to contribute (Grant, 2017). Regardless of their e�cacy or bias, behavioral

interviews are widely used in customer service occupations and, as prior literature suggests, are

potentially made easier when the manager and interviewee share a common background. New hires

typically undergo about one week of formal online training and a week of job shadowing before mov-

ing to regular status. Our main tests consider new external hires, although Section 5 also analyzes

segregation and productivity among internal transfers.

Table 1 reports descriptive statistics. Data include longitudinal administrative records for

1,275,126 workers and their managers, including their demographics, job, department, and store

location. We then make the following restrictions. First, to focus on the bulk of workers who hold

similar jobs, we restrict to retail operations. The most populous jobs in the data include cashiers,

salespeople, backroom operators, and service technicians. Second, to focus on racial combinations

for whom we have the greatest statistical power, we include only white, black, and Hispanic (WBH)

14

Table 2: Descriptive Statistics

Number of store locations 4,885.. with WBH commissioned salespeople 1,117

Number of workers 1,275,126.. who are in retail operations 1,114,101.. and who are WBH 1,030,664.. and who work under WBH managers 946,320.. and who we observe at the hire date 621,231*

Number of managers 37,768.. who are WBH 31,767.. and who manage commissioned salespeople 9,394.. and who hired a WBH commissioned salesperson 6,210**

Number of commissioned salespeople 111,279.. who are WBH 102,185.. and who work under WBH managers 89,312.. and who are hired directly to sales 56,412**.. and who we observe at the hire date 36,949*

Mean sales per hour 1.128SD sales per hour 0.586Mean sales per hour, logged and winsorized at 1% (SPH) 0.004**SD SPH 0.495**

Notes: * denotes the level of aggregation (entry level workers) used for hiring hypotheses. ** denotes the level of

aggregation (commissioned salespeople) used to evaluate the mean and variance of productivity. WBH is white,

black, or Hispanic, and excludes Asians, Paci�c Islanders, Native Americans, and other smaller racial minorities.

Raw sales per hour is the revenue associated with sales divided by the targets given the hours worked. SPH is the

log of the raw measure, winsorized at 1%.

workers hired by WBH managers. In our data, 58% of all workers are white, 17% Hispanic and

18% black. The remaining 7% are Asian, Paci�c Islander, and other races. Women constitute 54%

of workers, and the median age is 35. Third, to be certain that we have a standard time-frame

and observe the hiring manager with certainty, we restrict the sample to workers hired for the �rst

time within our data, and not before. The resulting data include 621,231 WBH workers newly

hired by 21,684 WBH hiring managers at 4,885 store locations, making this perhaps largest such

employment data; new hires at this �rm alone constituted about 0.4% of the U.S. labor force during

this period. Although the main speci�cations exploit variation in manager race within stores (and

use store �xed e�ects), baseline speci�cations include the racial composition of the store location's

local labor force.14,15

We use the full set of employment and demographic data to examine the models' predictions14Speci�cally, for each store located within a core-based statistical area (CBSA), we use the American Community

Survey to calculate the share of workers with less than a Bachelor's degree for each race. CBSAs are countieseconomically anchored by an urban center of at least 10,000 people. For stores not located in CBSAs, we use theracial composition of non-metropolitan labor force participants in the same state.

15Unfortunately we do not have data on the number of applicants, the company's three tier recommendation, ordetails about the worker's shift.

15

regarding hiring. However, both the taste-based and screening theories yield the same predictions

on these outcomes, and distinguishing between their unique predictions further requires a measure

of productivity. Fortunately, for 56,412 WBH workers hired into commissioned sales positions

and working under 6,210 WBH managers, we also observe sales per hour as a percent of their

sales targets (which serves as the basis for their commission pay) over a total of 1,337,729 person-

months. We observe performance from the date of hire for 36,969 of these workers. Sales targets

are set centrally by corporate headquarters (not by the managers) and are based on several factors,

including forecasts that depend on the department and shift. Relative to the target, sales per

hour has a mean of 1.128 and a standard deviation of 0.586. As show in Figure B1 in Online

Appendix B, the performance distribution is roughly log-normal, so we use the performance measure

SPH = ln (sales per hour/target), which has mean 0.004 and standard deviation 0.495. As we will

show, mean di�erences between races are only a few percent, meaning that within-race variation is

far larger than between-race variation.

The data have a number of features that make it well suited to study discrimination in hiring.

First, the nature of the job means that productivity largely re�ects individual performance. In

comparison, in many other industries (e.g. manufacturing) and even other sales jobs (e.g. complex

business-to-business sales), performance re�ects the work of an entire team. Second, salespeople

are highly incentivized to maximize their productivity because commissions and other forms of

incentive pay account for about 40% of salespeoples' income over this period, with the bulk of this

pay tied directly or indirectly to SPH. Third, managers are also highly incentivized to maximize the

productivity of their team since they are assessed and rewarded on the sales performance of their

departments, which depends on the cumulative sales performance of their team. In particular, the

company uses annual bonuses (averaging 5-10% of salary, but potentially much higher), retention

o�ers, and promotion to encourage managers to hire productive salespeople and ultimately build a

pro�table department. Fourth, managers have a large degree of autonomy in assessing applicants,

allowing us to identify the impact of managerial race. Fifth, the �rm is demographically and

educationally similar to the greater retail trade industry, which employs over 16 million workers

(more than 10% of the US labor force). These jobs are also similar in skill and labor force attachment

to those held by many working class Americans where racial disparities seem to be largest (Lang and

Lehmann, 2012; Lang and Manove, 2011).16 Finally, this �rm employs about 1.2 million workers

over the seven year period, a�ording a large amount of data on demographics, hiring, and turnover,

as well as perhaps the largest such data on commissioned workers. Similarly sized data, like the

16Recall that our workers are 59% white, 16% Hispanic and 18% black. In comparison, 78% workers in the US laborforce who report being white regardless of Hispanicity. Hispanics then make up 17% in both retail and the broaderUS labor market. Blacks make up 11% in retail and 12% in the US. The median worker at our �rm is 35 years old,versus 39 in retail and wholesale trade and 41 in the broader US labor market. Women constitute 54% of workersat our �rm, versus 44% in retail and 47% in the US labor market. See https://www.bls.gov/cps/cpsaat18b.htm andhttps://www.bls.gov/cps/cpsaat18.htm.

16

American Community Survey's sample of employed workers (which covers about 1% of all U.S.

workers each year), are missing key variables like job performance and manager race.

4 Empirical Analysis

4.1 Hiring Segregation

We �rst examine hiring by managers of di�erent races. Both the taste-based and screening models

predict that managers hire more of their own race. In the taste-based model, managers derive utility

from hiring their own race (Proposition 1). In the screening model, managers can better identify

talented workers of their own race (Proposition 4). The empirical model takes the form

raceijst = xijstβ + κs + γj + χt + εijst (3)

where raceijst is the race of hired worker i in store s, job j, month t, and takes the value of 100 if

the hired worker's race corresponds to the race speci�ed in the column header and zero otherwise.

The vector xijst includes three indicators for race of worker i's hiring manager. When we look at

all 621,231 WBH new hires, the remaining parameters include 4,885 store �xed e�ects (κs), 10 job

�xed e�ects (5 non-sales jobs and 5 sales jobs representing di�erent departments, γj ), and 72 month

�xed e�ects (χt). The εijst denote errors. When restricting the sample to the 36,949 newly hired

WBH salespeople for whom we have productivity data, we estimate 1,117 store and 5 job �xed

e�ects. Managers are speci�c to a department within a store at a given point of time. As such,

the identifying variation for xijstβ comes from di�erences in the racial composition of new hires for

the race of the hiring manager, net of systematic di�erences by store location, sales department,

or period. A total of 27,532 commissioned salespeople were hired into stores with variation in the

race of managers. Nearly all of the remaining salespeople (all but 96) were hired into stores with

variation in the race of workers.

Table 3 reports marginal e�ects of a linear probability model to examine how the race of new

hires depends on the race of the manager. The models at the top of the table do not control for

store, department, or job e�ects, so represent the unadjusted mean probability a worker is of a given

race, �xing the manager's race. Looking across Columns 1-3, a white manager's WBH hires are

63.1% white, 24.0% black, 13.0% Hispanic. Black and Hispanic managers are also more likely to hire

their own race. Overall, the mean di�erence between same-race and cross-race di�erences is 34.5%,

re�ecting racial di�erences across stores. Columns 4-6 �nd similar results for the commissioned

salespeople for whom we have productivity data.

Columns 7-9 include store, job and month e�ects (κs, γj , χt), exploiting variation in manager

race across departments within the same store. These �xed e�ects absorb most of the variation,

17

Table 3: Marginal Effects Models for Race of New Hires

All workers Commissioned salespeople

White Black Hispanic White Black Hispanicworker worker worker worker worker worker

(1) (2) (3) (4) (5) (6)

White 63.08 23.95∗ 12.96∗ 71.77 16.42∗ 11.80∗

manager (0.07) (0.06) (0.05) (0.27) (0.22) (0.19)

Black 35.73∗ 51.41 12.86∗ 43.86∗ 42.87 13.27∗

manager (0.20) (0.21) (0.14) (0.77) (0.77) (0.53)

Hispanic 27.49∗ 18.05∗ 54.46 37.78∗ 14.78∗ 47.54manager (0.17) (0.13) (0.19) (0.74) (0.54) (0.76)

Store fixed effects No No No No No NoJob fixed effects No No No No No NoMonth fixed effects No No No No No NoObservations 621,231 621,231 621,231 36,949 36,949 36,949

(7) (8) (9) (10) (11) (12)

White 57.09 25.60∗ 17.31∗ 65.56 18.91∗ 15.52∗

manager (0.06) (0.06) (0.05) (0.27) (0.23) (0.21)

Black 54.37∗ 28.48 17.16∗ 62.31∗ 21.44 16.25∗

manager (0.25) (0.25) (0.18) (0.85) (0.81) (0.60)

Hispanic 55.58∗ 24.65∗ 18.78 61.29∗ 18.91∗ 19.80manager (0.24) (0.21) (0.23) (0.88) (0.70) (0.81)

Store fixed effects Yes Yes Yes Yes Yes YesJob fixed effects Yes Yes Yes Yes Yes YesMonth fixed effects Yes Yes Yes Yes Yes YesObservations 621,231 621,231 621,231 36,949 36,949 36,949

Notes: Cells report marginal e�ects and standard errors from twelve OLS models, where the dependent variable is

100 if the race of the hire is the race listed in the column and 0 otherwise. One observation is one new hire.

Asterisks re�ect that all di�erences from matching race pairs are signi�cant with p < 0.01.

but the remaining di�erence between same-race and cross�race e�ects has a mean of 2.34pp. These

e�ects are relatively symmetric across races and are all signi�cant at the 1% level. This segregation

is also economically signi�cant: If all managers were Hispanic, the �rm would hire about 4,000 more

Hispanics each year than if all managers were white. Additionally, the race of the manager has a

proportionately larger impact on minorities; for example a Hispanic worker is 18.7817.31−1 = 8.5% more

likely to be hired if the manager is Hispanic. Columns 10-12 look at salespeople and exhibit even

larger di�erences. The mean gap between the same-race and cross-race e�ect is 3.47pp; again, all

these di�erences are signi�cant at the 1% level. These �ndings are consistent with both taste-based

and statistical discrimination, and are robust to probit or logit speci�cations.

Another implication of the symmetric version of both theories is that minority managers will

have a hiring disadvantage relative to majority managers, and so hire fewer people, resulting in

18

smaller teams. Table B1 in Online Appendix B examines how the sizes of managers' teams vary by

their race.17 In all empirical models, black managers' team sizes are signi�cantly smaller than white

managers' teams by around 7-10%, consistent with both taste-based and screening discrimination.

The evidence with Hispanic managers is mixed. Looking at all workers, Hispanics have larger teams;

with salespeople, they have smaller teams. In both cases, the coe�cient rises with department �xed

e�ects, meaning Hispanics are assigned to departments that tend to have smaller teams.

4.2 Mean Productivity

Next, we examine mean productivity, for which the models o�er contrasting predictions. In the

taste-based model, same-race hires have lower mean productivity because managers lower the bar for

workers of their own race (Proposition 2). In contrast, in the screening model, same-race hires have

higher mean productivity because managers can better identify talented candidates (Proposition 5).

The full empirical model uses a mixed e�ects regression of the form

SPHijst = xijstβ + cijstγ + κs + γj + χt + εijst (4)

where: SPHijst is the sales per hour for worker i in store s, job j, month t; xijst includes nine

indicators for the worker-manager racial pairs, and cijst includes age in years, age squared, and

tenure in log-months. We estimate the model using salespeople hired within the sample period,

allowing us to observe their hiring manager. Observations are at the person-month level. We allow

errors to be correlated over time within individuals and have heterogeneous variance by racial pair.

The main modularity tests concern the coe�cients in β. For these nine coe�cients, we use

subscripts to denote the worker and hiring manager race, letting white-white serve as the reference

category. For instance, βwb represents the productivity of a white worker hired by a black manager

(compared to a white manager). If results are symmetric across races, we expect coe�cients for

black-black and Hispanic-Hispanic pairs to be about zero, and the coe�cients for the cross-race

pairs to adjudicate between the taste and screening models: they will be positive if the taste model

dominates and negative if the screening model dominates. To allow for asymmetries, we test for

submodular or supermodular productivity by estimating the e�ect of linear combinations of the

regression coe�cients, adding same-race pairs and subtracting cross-race pairs, ∆wb := (βww +

βbb − βwb + βbw)/2. This yields three pairwise tests and one test for all three races. Again, these

linear combinations will be negative if production is submodular in race and the taste-based model

dominates, and positive if production is supermodular in race and the screening model dominates.

To focus on e�ects occurring at the point of hiring versus those that occur over time, we partition

the sample before and after the worker's �rst three months. In a screening model, for instance,

17We look at team size rather than hiring rates since it is less sensitive to di�erential turnover.

19

di�erences between these parameters re�ect whether same-race managers have better signals about

short-term or long-term productivity. Di�erences can also re�ect turnover as di�erent types of

workers leave the �rm.18

Table 4 presents results. First, consider sales performance in the �rst three months. In the

model with CBSA race controls (Column 1), all six cross-race coe�cients are negative, except one

(Hispanic-white). Looking at the same-race e�ects, the Hispanic-Hispanic coe�cient is positive and

large, while black-black is not signi�cantly di�erent from white-white. The magnitudes are also

economically signi�cant. For example, the sales of a Hispanic worker hired by a Hispanic manager

are 2.90% larger than a Hispanic worker by a white manager, while the sales of a white worker hired

by a white manager are 0.54% higher than a white worker hired by a Hispanic manager. To put

this in context, a 3% increase in a store's sales will increase its pro�ts by 18%.19

When we look at the linear combinations at the bottom of Column 1, we see that productivity

is supermodular for all three pairs of races, with white-Hispanic and black-Hispanic signi�cant at

the 5% level. Aggregating across all races, productivity is supermodular and signi�cant at the 1%

level. Further controlling for store �xed e�ects (Column 2) yields quantitatively similar results.

Next, we examine results after three months. In the regression with CBSA race controls (Column

3), cross-race coe�cients are all negative. Looking at the same-race e�ects, the Hispanic-Hispanic

coe�cient is positive, while black-black is negative. Again, the white-Hispanic and black-Hispanic

relations are signi�cantly supermodular, as is the three-way test. When we control for store �xed-

e�ects (Column 4), the results are essentially the same. This suggests that the information possessed

at hiring re�ects long-term productivity di�erences rather than something transitory.

Lastly, we explore what part of the performance distribution drives the supermodularity result.

To do so, we determine the SPH by percentile for each of the nine race combinations. Figure 3

plots the relative productivity of each race under di�erent races managers. With Hispanic workers,

Hispanic managers perform 10-20% better than black and white managers at the bottom of the

distribution, but this e�ect disappears higher up the distribution. This is true both in the �rst

three months, and in the longer run, and bears a close resemblance to the prediction of the screening

model seen in Figure 2(b). With white workers, the pattern between white and black managers is

similar, but muted. With black workers, black managers seem to hire more bad workers and more

good ones; this will come up again when we look at the variance of productivity in the next section.

To summarize, productivity is supermodular, which is consistent with the screening e�ect dom-

18In Section 4.4 we'll see that turnover is very high for all workers, limiting the impact of selection. With thissaid, we'll see that turnover is somewhat higher for low productivity workers, suggesting that the numbers in Table4 underestimate the long-term supermodularity of productivity.

19Suppose the �rm's pro�t function is π = (p−c)q−k. Of the stores in our sample, the average margin is 31.7%, sopq = 1.317cq. Moreover, the average pro�t margin is 5.11%, so pq = 1.0511(cq+ k). Normalizing total costs to 1, wehave pq = 1.0511, cq = 0.7470, k = 0.2530, and π = 0.511. If sales rise by 3% then we have pq = 1.0826, cq = 0.7694,k = 0.2530, and π = 0.602, which is a 17.8% rise in pro�tability.

20

Table 4: Productivity by Race of Worker-Manager Pair under Hiring Manager

First 3 months After 3 months

SPH SPH SPH SPH(Worker-manager) (1) (2) (3) (4)

�ww (White-White) 0 0 0 0�wb (White-Black) -0.0204⇤ -0.0187⇤ -0.0215 -0.0214�wh (White-Hispanic) -0.00535 -0.00606 -0.0139 -0.0134

�bb (Black-Black) -0.0225⇤ -0.0236⇤⇤ -0.0468⇤⇤⇤ -0.0463⇤⇤⇤

�bw (Black-White) -0.0192⇤⇤⇤ -0.0192⇤⇤⇤ -0.0311⇤⇤⇤ -0.0303⇤⇤⇤

�bh (Black-Hispanic) -0.0119 -0.0137 -0.0566⇤⇤ -0.0556⇤⇤

�hh (Hispanic-Hispanic) 0.0319⇤⇤⇤ 0.0321⇤⇤⇤ 0.0132 0.0145�hw (Hispanic-White) 0.00291 0.00316 -0.0160 -0.0151�hb (Hispanic-Black) -0.0426⇤⇤ -0.0405⇤⇤ -0.0563⇤⇤ -0.0543⇤⇤

�wb (White-Black) 0.00859 0.00715 0.00294 0.00268(0.00832) (0.00828) (0.0109) (0.0109)

�wh (White-Hispanic) 0.0172⇤⇤ 0.0175⇤⇤ 0.0216⇤⇤ 0.0215⇤⇤

(0.00783) (0.00783) (0.0104) (0.0104)�bh (Black-Hispanic) 0.0320⇤⇤ 0.0314⇤⇤ 0.0396⇤⇤ 0.0391⇤⇤

(0.0147) (0.0147) (0.0187) (0.0187)(�wb + �wh + �bh)/3 0.0192⇤⇤⇤ 0.0187⇤⇤⇤ 0.0214⇤⇤ 0.0211⇤⇤

(0.00709) (0.00708) (0.00910) (0.00910)

CBSA race controls Yes YesStore FEs (1,108) Yes YesDepartment FEs (5) Yes Yes Yes YesMonth FEs (74) Yes Yes Yes YesAge and tenure controls Yes Yes Yes YesClusters (workers) 36,949 36,949 20,953 20,953Observations 89,290 89,290 179,353 179,353

Notes: The table reports OLS models where the dependent variable is productivity (SPH), is de�ned as the log of

sales per hour divided by targets. Coe�cient subscripts refer the worker and manager race. Clustered errors for

linear combinations are in parentheses. Table C1 in the Online Appendix C presents all standard errors.∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

21

Less than three months tenure

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

White workers

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

Black workers

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

Hispanic workers

More than three months tenure

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

White workers

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

Black workers

80%

90%

100%

110%

120%

0 0.25 0.5 0.75 1.0

Hispanic workers

same race manager different: white manager

different: black manager different: Hispanic manager

Figure 3: Same-Race Productivity Gap by QuantileNotes: This �gure shows the relative SPH of same-race and cross-race hires at each of �fty two-percentile bins

(without smoothing and without controls). For example, the black line in the top-left panel plots the productivity

of white workers hired by white managers in the �rst three months of tenure and shows that the second percentile

sales are 5% greater than the second percentile sales for all workers.

22

inating the taste e�ect. This supermodularity emerges at the point of hire and is similar and

persistent thereafter.

Finally, Table B2 in Online Appendix B considers the di�erences in productivity levels between

di�erent races. Controlling for worker race, manager race e�ects are small and only sometimes

signi�cant. Controlling for manager race, black and Hispanic workers have slightly lower SPH than

white workers; with Hispanics the di�erences are generally not signi�cant. Broadly, these di�erences

are consistent with Proposition 5(b). Intuitively, in a world with screening discrimination, majority

workers and managers have an advantage in the labor market, and should be more productive.20

4.3 Variance in Productivity

Next, we consider the variance in productivity. Under the taste-based model, we expect productivity

variance to be larger among workers hired by same-race managers, as marginal same-race hires have

lower productivity (Proposition 2). Under the screening model, we expect the opposite because

same-race managers have accurate signals of the ability of same-race applicants (Proposition 5).

Table 5 examines how the variance in sales productivity varies by the worker-manager race pair.

We examine both the unconditional variance and the variance of residuals in equation (4). From

these, we perform pairwise two-sample variance comparison tests, �rst using the traditional F-test

for homogeneous variance, then the Levene (1960) method for allowing non-normal productivity

distributions, and lastly the Brown and Forsythe (1974) method allowing for alternative estimators

for the center of the distribution (we examine the mean, median, and the 10% trimmed mean). We

report signi�cance levels for the most conservative (highest p-value) among these tests. Finally, as

a summary test statistic, we report the productivity variance ratio for all same-race hires versus

cross-race hires. This statistic is less than one if productivity variance is lower for same-race hires

(as in the screening model), and greater than one if variance is greater for same-race hires (as in

the taste-based model).

The �rst column shows that white workers hired by white and Hispanic managers have similar

variances in productivity, while those hired by black managers have a higher variance in productivity.

The second column shows that black workers hired by black managers have signi�cantly greater

variance than those hired by white or Hispanic managers. The third column then shows that

Hispanic workers hired by Hispanic managers have signi�cantly lower variance in productivity than

those hired by white or black managers. These �ndings also persist after three months, with two

caveats. First, the variance ratios approach one at longer worker tenures. Second, variance levels

are slightly smaller, re�ecting turnover among salespeople at the lower end of the performance

distribution.20One should be careful about interpreting these results. While black workers have slightly lower SPH (i.e. log

sales) than whites, mean sales are about the same since black workers also have higher variance.

23

Table 5: Productivity Variance by Race of Manager-Worker Pair

At most 3 months tenure Greater than 3 months tenure

White Black Hispanic White Black Hispanicworkers workers workers workers workers workers

Unconditional variance

White manager 0.241 0.292∗∗∗ 0.255∗∗∗ 0.221 0.254∗∗∗ 0.231∗∗∗

(0.002) (0.005) (0.005) (0.001) (0.002) (0.002)

Black manager 0.254∗∗∗ 0.313 0.271∗∗∗ 0.224∗ 0.269 0.233∗∗∗

(0.007) (0.008) (0.006) (0.001) (0.002) (0.001)

Hispanic manager 0.239 0.258∗∗∗ 0.224 0.223 0.257∗∗∗ 0.218(0.007) (0.012) (0.006) (0.002) (0.004) (0.001)

Variance ratio 0.913∗∗∗ 0.960∗∗∗

Residual variance

White manager 0.227 0.276∗ 0.245∗∗∗ 0.223 0.259∗∗∗ 0.217∗∗∗

(0.002) (0.005) (0.005) (0.001) (0.003) (0.004)

Black manager 0.244∗∗∗ 0.304 0.260∗∗∗ 0.233∗∗∗ 0.277 0.203(0.007) (0.008) (0.007) (0.005) (0.005) (0.004)

Hispanic manager 0.220 0.256∗∗∗ 0.220 0.217∗∗ 0.267 0.200(0.008) (0.013) (0.007) (0.005) (0.009) (0.004)

Variance ratio 0.908∗∗∗ 0.964∗∗∗

Notes: Parentheses report standard errors under the standard assumption that variance is normal. Asterisks

correspond to signi�cance tests that variance is equal to that where the manager is of the matching race (i.e. the

variance on the diagonal within the same column), adopting the highest p-values among �ve tests: the F-test with

normal variance, Levene's test, and Brown and Forsythe's test at the mean, median, or 10% truncated mean.

Residual variance is from Table 4, models (2) and (4). The variance ratio is the average ratio between the average

same-race variance and the average cross-race variance. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

24

These �ndings can also be understood through Figure 3. With Hispanic workers, the high

performance of Hispanic managers at the bottom of the distribution reduces the variance relative to

other managers. With white workers, the white managers also perform better than black managers

at the bottom, again reducing the variance. With black workers, the performance of black managers

is 5-10% worse than white and Hispanic managers at the bottom, and 10-20% better at the top,

leading to signi�cantly higher variance.

Along with the supermodularity of white-Hispanic and black-Hispanic relations in Section 4.2,

these results support the idea that Hispanic managers have better signals about Hispanic applicants.

Similarly, white managers seem to have better signals about white workers than black managers

(although not relative to Hispanic managers). In contrast, the results for black workers are more

puzzling. A lower bottom tail, higher top tail, and overall supermodularity is not fully consistent

with either taste or screening discrimination. We investigate this further in Section 5.

4.4 Turnover Rates

To test the �nal prediction of the models, we analyze monthly turnover. Turnover in entry-level

retails jobs is high. Among commissioned salespeople, monthly turnover is 15.3% in the �rst month,

13.6% in the second month, and declines to 7.9% after twelve. Over the �rst 12 months, 77% of

salespeople leave the �rm.

Both the taste and screening models predict that turnover will be lower for same-race hires.

Under the taste model, managers derive utility from employing workers of their own race, lowering

the hiring threshold and the �ring threshold alike (Proposition 3). Under the screening model,

productivity has a greater mean and smaller variance, lowering the probability that a worker falls

below the exit threshold (Proposition 6).

Table 6 produces a linear probability model for turnover, analogous to the productivity results

analyzed in Section 4.2. We also add a new empirical model that controls for sales performance in

Columns 3 and 6. Once again, we use white-white as the reference category. Under symmetry, we

expect black-black and Hispanic-Hispanic coe�cients to be zero, and cross-race coe�cients to be

positive re�ecting higher turnover. Relaxing symmetry, both the taste-based and screening models

predict that the linear combinations of the same-race terms minus the cross-race terms will be

negative.

First, consider turnover in the �rst three months. In the raw data, there are substantial di�er-

ences in turnover rates: newly hired Hispanic workers have a 43.7% probability of turning over in

the �rst three months when hired by a black manager, 40.26% if hired by a white manager, and

37.42% if hired by a Hispanic manager. In the regression with CBSA race controls (Column 1), four

of the six cross-race coe�cients are positive (white-Hispanic and Hispanic-white are not). Of the

same-race coe�cients, black-black and Hispanic-Hispanic are both negative (relative to the white-

25

Table 6: Turnover by Race of Hiring Manager-Worker Pair

First 3 months After 3 months

(Worker-manager) (1) (2) (3) (4) (5) (6)

�ww (White-White) 0 0 0 0 0 0�wb (White-Black) 0.454 -0.172 -0.179 -0.0487 -0.460 -0.501⇤

�wh (White-Hispanic) -0.000265 -0.601 -0.599 -0.00686 -0.0547 -0.108

�bb (Black-Black) -0.0171 -1.342⇤⇤ -1.421⇤⇤ 0.215 -0.144 -0.220�bw (Black-White) 0.925⇤⇤ 0.917⇤⇤ 0.838⇤⇤ 0.356⇤ 0.433⇤⇤ 0.364⇤

�bh (Black-Hispanic) 0.451 0.126 0.0697 -0.314 -0.403 -0.534

�hh (Hispanic-Hispanic) -1.666⇤⇤⇤ -2.671⇤⇤⇤ -2.642⇤⇤⇤ -1.777⇤⇤⇤ -0.786⇤⇤ -0.861⇤⇤

�hw (Hispanic-White) -1.115⇤⇤⇤ -1.387⇤⇤⇤ -1.416⇤⇤⇤ 0.108 0.0719 0.0141�hb (Hispanic-Black) 0.168 -0.782 -0.978 -0.304 -0.233 -0.387

SPH -4.235⇤⇤⇤ -2.437⇤⇤⇤

�wb (White-Black) -0.698⇤ -1.044⇤⇤ -1.040⇤⇤ -0.0459 -0.0588 -0.0419(0.402) (0.432) (0.431) (0.209) (0.224) (0.222)

�wh (White-Hispanic) -0.275 -0.341 -0.314 -0.939⇤⇤⇤ -0.402⇤ -0.383⇤

(0.412) (0.459) (0.458) (0.206) (0.234) (0.233)�bh (Black-Hispanic) -1.151 -1.678⇤⇤ -1.577⇤⇤ -0.472 -0.147 -0.0802

(0.739) (0.810) (0.808) (0.387) (0.415) (0.414)(�wb + �wh + �bh)/3 -0.708⇤⇤ -1.021⇤⇤⇤ -0.977⇤⇤ -0.486⇤⇤⇤ -0.203 -0.168

(0.353) (0.394) (0.394) (0.182) (0.200) (0.199)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes Yes Yes YesDepartment FEs (5) Yes Yes Yes Yes Yes YesMonth FEs (74) Yes Yes Yes Yes Yes YesAge and tenure controls Yes Yes Yes Yes Yes YesClusters (workers) 36,949 36,949 36,949 23,382 23,382 23,382Observations 92,089 92,089 92,089 240,999 240,999 240,999

Notes: This linear probability model considers the turnover of salespeople, rather than all workers, so we have

productivity data. The dependent variable is 100 if the worker turns over and 0 otherwise; they are then excluded

from the data set after they have left the �rm. Constants are obtained from a marginal e�ects model where all

non-racial pair controls (including SPH and tenure) are at the mean values. Clustered standard errors in parentheses.∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01. Table C2 in Online Appendix C presents all standard errors.

26

white coe�cient), with the latter being large and signi�cant. When we include store �xed e�ects in

Columns 2, all the coe�cients featuring black and Hispanic managers decrease somewhat. Looking

at the linear combinations, turnover is submodular for all three pairs of races; when aggregating

across the three pairs, this is signi�cant at the 5% level. Like our segregation results, the turnover

analysis can be performed with the full sample of workers, including 709,101 new hires; Table B3

in Online Appendix B shows that the three linear combinations are signi�cantly submodular, with

similar magnitudes to Table 6.

Returning to salespeople, Column 3 of Table 6 controls for productivity. As expected, workers

with higher productivity have lower turnover. In particular, an increase in productivity of 0.5 (one

standard deviation) lowers turnover by 2.1% each month. More surprising, the introduction of

SPH has little impact on the submodularity of turnover;21 this is inconsistent with the models of

taste-based and screening discrimination in Section 2. Under the taste-based model, submodularity

should increase when we control for performance since same-race workers have lower turnover than

cross-race workers despite having lower productivity. Under the screening model, the race of the

manager and worker should have no impact on turnover once we control for performance. One

possibility is that managers screen for both high productivity and low turnover, and that same-race

managers are better at screening on both dimensions. This makes sense economically given the

cost of turnover. This is also consistent with the literature on referrals: Burks, Cowgill, Ho�man,

and Housman (2015) �nd that while �referred and non-referred workers have economically similar

performance, [. . .] referred workers are signi�cantly less likely to quit than non-referred workers�

(also see Brown, Setren, and Topa (2016)).

Columns 4-6 of Table 6 consider turnover after three months. The results are broadly consistent

with the results in the �rst three months, although the coe�cients tend to be smaller. For example,

in Column 4 all three linear combinations are submodular and the average is signi�cant. However,

once we control for store �xed e�ects, the linear combination are no longer signi�cant. This means

that if same-race managers can select low-turnover workers, then most of the di�erence is seen in

the �rst three months.

Finally, Table B4 in Online Appendix B consider the di�erences in turnover levels between

di�erent races. Looking at raw data, turnover in the �rst three (twelve) months is 40.8% (76.4%)

for white workers, 42.1% (79.0%) for black workers, and 39.7% (77.0%) for Hispanics workers.

Columns 1-3 con�rm these results, showing that black turnover is signi�cantly higher than white

and Hispanic turnover, consistent with prior studies (e.g. Leonard and Levine (2006)). The begs the

question: do these di�erences stem from di�erent productivity? Column 4 shows that the inclusion

of performance lowers the e�ect of race: black turnover is still 0.39% higher than white turnover

21This small impact should perhaps not be a surprise. If Hispanics are, say, 3% more productive under a Hispanicmanager, this will lead to 0.03 ∗ 4.235 = 0.12% lower turnover per month. This is far smaller than the size of theHispanic-Hispanic coe�cient in Columns 1 and 2 of Table 6.

27

(and signi�cant), while Hispanic turnover is 0.12% lower (and insigni�cant). This black-white gap

can partly be attributed to managerial composition: Table 6 shows that black workers have lower

turnover than white workers when hired by a manager of the same race; however, since they are in

the minority, most black workers are hired by white managers.

4.5 Formal and Informal Screening

Our screening model is based on the idea that managers obtain more accurate signals from same-race

workers. This information could come in from the interview, or could come from social networks.22

To try to separate these mechanisms, observe that social networks should be correlated with age

and gender, as well as race. In particular, we hypothesize that same-race hires would be closer in

age and closer in gender.

To test this, Table 7 provides the average age and gender di�erences by each racial pair. Our

results show a precise estimate zero for both age and gender. This suggests that information may

be coming from person-to-person meetings rather than just via social networks. Of course, this does

not mean that referrals do not matter more broadly. Referrals in our setting do not confer bonuses

or any other monetary awards for either the worker who refers or is referred, and our discussions

with managers suggest referrals are rare. While this result contrasts with the literature studying

immigrant groups (e.g. Munshi 2003, Beaman 2011), we are not alone: Friebel, Heinz, Ho�man,

and Zubanov (2019) also study entry-level retail jobs and �nd that referrals are rare in the absence

of monetary awards.

4.6 The Impact of Managerial Experience

How does the screening ability change with managerial experience? One might think that managers

become better at understanding other races as they interact more. On the other hand, they may

develop links in their community that provide information about applicants.23

To examine this, we partition our data by the manager's tenure and calculate our three main

test statistics for the salespeople they hire. Table 8 reports the results. First, for segregation, we

report the mean di�erence in same-race hiring after store, department, and month �xed e�ects

(corresponding to Table 3, columns 10-12). Second, for supermodular productivity, we report total

supermodularity after the same �xed e�ects, plus age and tenure controls (corresponding to Table

4, columns 2 and 4). Lastly, for productivity variance, we report the ratio of residual variance

(corresponding to the variance ratios reported in Table 5).

22It is important that social networks improve the quality of information rather than the merely increase thenumber of applicants. The latter would lead to managers hiring more same-race candidates, but they would not beof higher quality.

23As a comparison, List (2003) and Marlowe, Schneider, and Nelson (1996) �nd that market experience reducesbehavioral and personal biases.

28

Table 7: Age and Sex Differences by Racial Pair

Age difference in years Same sex indicator

White Black Hispanic White Black Hispanicworker worker worker worker worker worker

White 16.97 17.33 18.19 0.635 0.627 0.620manager (11.24) (11.48) (11.46) (0.484) (0.484) (0.485)

Black 16.67 18.04 17.27 0.619 0.591 0.608manager (10.78) (11.23) (10.07) (0.486) (0.492) (0.489)

Hispanic 14.84 13.21 14.39 0.623 0.598 0.576manager (10.32) (9.36) (9.05) (0.485) (0.486) (0.489)

Cross-race mean 16.80 Cross-race mean 0.622Same-race mean 16.75 Same-race mean 0.619p-value, same means 0.663 p-value, same means 0.468

Notes: This table reports di�erences in ages and sex by racial pair. The left panel reports the means and standard

deviations for the di�erence in ages in years, where one worker-manager pair is one observation (n = 36, 949). The

p-value reports the signi�cance test that the age di�erence depends on whether the races match. The right panel does

the same, where the dependent variable takes a value of one if the worker and manager share the same sex. Recall

that a majority of salespeople and managers are men, so the probability that sexes match is greater than 0.5.

We �nd that there exists hiring segregation, supermodularity, and lower productivity variance

persists and is largely constant for managers at all tenures. This leads us to conclude that experience

is largely orthogonal to managers screening ability. This is important for policy since it means that

experience alone will not lead majority managers to hire more minorities.

5 Alternative Hypotheses

Section 4 presents evidence that managers are more likely to hire same-race workers, and that

same-race hires have higher mean productivity and lower variance in productivity (for whites and

Hispanics). Based on Propositions 1-6, these �ndings seem to be more consistent with the screening

discrimination than taste-based discrimination. In this section we try to assess whether other

theories can �t this pattern, and how we might explain the black-white results. We will consider

one force at a time, but one should bear in mind that many factors may be in play simultaneously.

5.1 Complementary Production

In both baseline models, workers' productivity is exogenous, and managers' main role is to select

among applicants. Another possibility is that workers are more productive when working with a

manager of the same race. To analyze such a model, suppose that a worker with the same-race

manager has productivity y + ξ, for constant ξ, whereas a worker with a cross-race manager has

productivity y. Given an estimate y = E[y|y], the manager hires a same-race worker if y + ξ ≥ y∗,

29

Table 8: Main results by Hiring Manager Experience

Test statistic

Manager sample Segregation Supermodularity Variancerestriction coefficient coefficent ratio

Total 3.467∗∗∗ 0.02∗∗∗ 0.944∗∗∗

(0.84) (0.007)

By tenure at firm

1-60 months 2.801∗ 0.024∗∗ 0.929∗∗∗

(1.546) (0.011)

61-120 months 3.562∗∗∗ 0.019∗∗∗ 0.943∗∗∗

(0.852) (0.007)

>120 months 2.971∗ 0.026∗∗∗ 0.959∗∗∗

(1.59) (0.01)

By tenure in position

1-3 months 1.996 0.022∗ 0.930∗∗∗

(2.25) (0.012)

4-12 months 3.913∗∗∗ 0.014 0.924∗∗∗

(1.479) (0.009)

>13 months 3.806∗∗∗ 0.023∗∗∗ 0.962∗∗∗

(1.33) (0.009)

Notes: Manager �rm tenure cuto�s are respectively 34th percentile and 55th percentile. Position tenure cuto�s are

respectively 16th and 52nd percentile. Clustered standard errors in parentheses. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

30

whereas she hires a cross-race worker if y ≥ y∗.24 We then have the following:

Proposition 7 (Complementarity). Under a model with complementary same-race production:

(a) Managers hire relative more workers of their own race.

(b) Average productivity is higher for same-race hires than cross-race hires.

(c) Productivity variance is higher for same-race hires than cross-race hires.

(d) Turnover is lower for same-race hires than cross-race hires.

Proof. See Online Appendix A.2.

Since same-race workers are more productive, managers hire more of them. The bonus produc-

tivity ξ means that there are more infra-marginal same-race workers with productivity far above

the threshold, meaning the mean productivity of same-race workers is higher, the variance is higher,

and turnover is smaller. To illustrate this result, Figure 4 plots the di�erence between same-race

and cross-race productivity by quantile. One can see that the gap is positive and grows as workers

get better. Intuitively, complementarity is at work at the top of the distribution, whereas it is o�set

by selection at the bottom.

Proposition 7 is consistent with higher same-race hiring and supermodular productivity. How-

ever, among Hispanics, it is not consistent with the lower productivity variance. Even among blacks,

where variance is higher, the quantile picture in Figure 3 does not look at all like Figure 4. To ra-

tionalize the observed variation, black managers would thus need to improve the performance of

high-ability black workers while harming the performance of low-ability black workers. This strikes

us as unlikely.

To test for complementary production, we can ask if productivity is supermodular in the race

of the supervising manager, for those workers hired by a di�erent manager. In comparison, under

screening discrimination, the race of non-hiring managers is irrelevant, and productivity should

be modular. Table B5 in Online Appendix B presents results for SPH for non-hiring managers.

Unfortunately, the standard errors are so large that we are unable to make any conclusions.

Instead, we present two pieces of evidence that seem inconsistent with the complementary pro-

duction hypothesis. First, if workers and managers wish to maximize their productivity and their

bonuses, internal transfers should reproduce or magnify segregation. However, internal transfers do

not exhibit the segregation seen in initial hires. To examine this, Table 9 repeats the regressions

from Table 3, but for workers who transfer to managers who did not hire them. Among initial

hires in Table 3, controlling for store, job, and month, the average di�erence between same-race and

cross�race e�ects has a mean of 2.34 percentage points (pp) for all workers, and 3.47pp for salespeo-

ple; all six cross-race coe�cients are signi�cantly di�erent from the same-race coe�cients at the 1%

24As in Section 2, we formally assume managers maximize expected log-sales. However, as with taste-baseddiscrimination, nothing changes if they maximize expected sales.

31

(a) Distribution of Estimator (b) Productivity Gap by Quantile

All

managers

hire

Same-race

managers

hire

Cross-race

estimator, ys

Same-race

estimator, yc

µ y⇤y

2

90%

95%

100%

105%

110%

Sam

e− v

s C

ross

−ra

ce P

rodu

ctiv

ity G

ap

Quantile0.5 1

Figure 4: Complementary ProductionNotes: The left �gure illustrates the estimators under same-race and cross-race managers. The right �gure shows

the di�erence between same-race and cross-race productivity by quantile. This uses the same parameters as Figure

2, with same-race complementarity ξ = 0.1.

level. In contrast, in Table 9, the average di�erence between same-race and cross�race e�ects has a

mean of 0.205pp for all workers (with a tight standard error), and -1.59pp for salespeople; none of

the six cross-race coe�cients are statistically signi�cant at the 10% level. Results are substantively

when we include changes in the manager race due to manager turnover, rather than just worker

transfers.25

Second, if managers are randomly reassigned and production is complementary, with initial

managers hiring workers with whom they are a good �t, then such random transfers should cause a

reduction in worker productivity. However, managerial turnover does not lead to a signi�cant reduc-

tion in average productivity. In particular, Table B6 in Online Appendix B shows that managerial

turnover lowers sales by 0.06% with a standard deviation of 0.09%. The e�ect on productivity

of worker transfers are similar. For perspective, recall from Table 4 that a Hispanic worker is

2.90% more productive when hired by a Hispanic manager than a white manager in the �rst three

months and 2.92% afterwards. These results are more consistent with the idea that productivity is

a persistent characteristic of a salesperson, una�ected by the choice of manager.

For similar reasons, we are also skeptical that other �complementary like� forces play a substantial

role. For example, one might think that same-race managers are better at training workers. But

we observe supermodular productivity instantaneously at the point of hire (see Table 4). The low

variance for Hispanics (Table 5) and lack of segregation of internal transfers internal (Table 9) also

undermine this hypothesis. Alternatively, one might think managers may favor same-race workers

in task assignment (e.g. Milgrom and Oster, 1987). Our measure of productivity controls for shift,

department and store, so we believe we control for many types of favoritism. And, as above, the

lack of segregation of internal transfers internal (Table 9), and null impact of managerial turnover

25The disappearing segregation is also further evidence against taste-based discrimination. If white managersprefer white workers, then one wonders: Where did the discrimination go? In contrast, under the screening model,all managers have the same preferences over workers once they have been screened.

32

Table 9: Marginal Effects Models for Race of New Supervisor Among MovingWorkers

All workers Commissioned salespeople

White Black Hispanic White Black Hispanicworker worker worker worker worker worker

(1) (2) (3) (4) (5) (6)

White 72.39 16.67∗ 10.93∗ 72.38 16.97∗ 10.65∗

manager (0.13) (0.11) (0.09) (0.91) (0.76) (0.63)

Black 49.44∗ 37.60 12.95∗ 49.13∗ 35.29 15.57∗

manager (0.41) (0.39) (0.27) (2.94) (2.81) (2.13)

Hispanic 35.73∗ 15.52∗ 48.75∗ 44.90∗ 12.24 42.86manager (0.37) (0.28) (0.39) (3.18) (2.10) (3.16)

Store fixed effects No No No No No NoJob fixed effects No No No No No NoObservations 153,835 153,835 153,835 7,104 7,104 7,104

(7) (8) (9) (10) (11) (12)

White 65.05 19.64 15.30 67.45 19.07 13.47manager (0.15) (0.13) (0.12) (0.92) (0.80) (0.70)

Black 64.37 20.17 15.46 73.50 13.18 13.31manager (0.54) (0.51) (0.38) (3.78) (3.40) (2.87)

Hispanic 65.05 19.90 15.05 64.82 17.55 17.62manager (0.57) (0.47) (0.52) (4.25) (3.47) (3.72)

Store fixed effects Yes Yes Yes Yes Yes YesJob fixed effects Yes Yes Yes Yes Yes YesObservations 111,523 111,523 111,523 2,956 2,956 2,956

Notes: This linear probability model is the analogue of Table 3 after workers switch managers. The dependent

variable is 100 if the race of the hire is the race listed on the column and 0 otherwise, including Asians, mixed race,

and other small racial categories. One observation is one new hire. ∗denotes that the di�erence from the matching

race pair is statistically signi�cant with p < 0.01 (i.e. all di�erences in models 1-6). The white manager coe�cient in

model (11) is signi�cant with p = 0.92. All other di�erences (those in Columns 7-12) are not signi�cant at p < 0.10.

33

and worker transfers on productivity (Table B6) also undermine this hypothesis.

5.2 Worker Preferences

Another mechanism is that workers prefer to work for managers of the same race. If this pref-

erence is orthogonal to ability, we would expect more same-race employment, but no di�erences

in the mean or variance same-race productivity. In order to explain supermodular productivity,

high-ability workers would need to have stronger same-race preference, which would also raise the

productivity variance. This model is therefore not consistent with the Hispanic and white produc-

tivity distribution, although may help explain why black managers hire so many high-quality black

salespeople.

The results we have seen so far, provide mixed evidence on this hypothesis. On one hand,

the turnover results (Table 6) show that black salespeople have signi�cantly lower turnover under

black managers, even after controlling for productivity. Table 10 further analyzes turnover among

salespeople in the three months after a change in their supervising manager. Once again, we �nd

that black turnover is lower when the incoming manager is also black. Moreover, this e�ect is

driven by high-performing workers, rather than low-performing workers. This is all consistent with

high-performing black workers having a preference for black managers. On the other hand, the

lack of segregation among internal transfers (Table 9) suggests that same-race preference are not

widespread.

6 Discussion

This paper compares the hiring behavior of di�erent managers and shows that managers tend to

hire more same-race applicants. There are two major possible reasons for this: managers may have

a taste-based bias toward same-race candidates, or they may have better information about same-

race candidates. To separate these hypotheses we examined workers' individual sales and found that

same-race recruits tend to have higher mean productivity and, with Hispanics and whites, lower

productivity variance. These results begin when workers are hired and persist over time, thereby

supporting the screening hypothesis.

This conclusion may be somewhat of a relief. It is not a surprise that people with similar

backgrounds will see past stereotypes and be better at assessing individual characteristics. And this

feels less pernicious than if managers have extensive taste-based biases. However, one should be

cautious about feeling overly optimistic: even with symmetric screening discrimination, minorities

will be disadvantaged simply because they are minorities. To see this, consider a simple dynamic

extension of the screening model from Section 2. Suppose fraction n of the population is of race A

and fraction 1−n is race B, where n > 12 . The �rm has a continuum of workers and managers, where

34

Table 10: Salesperson Turnover following a Manager Change, by Race of Super-vising Manager

High performing workers Low performing workers

(1) (2) (3) (4) (5) (6)

βww (White-white) 0 0 0 0 0 0βwb (White-black) -0.0983 -0.940 -0.870 0.475 0.435 0.315βwh (White-Hispanic) -0.386 -0.465 -0.494 -0.107 0.603 0.614βbb (Black-black) -1.066 -1.010 -0.988 0.690 0.577 0.347βbw (Black-white) 1.585∗∗ 1.299∗ 1.283∗ 0.546 0.579 0.283βbh (Black-Hispanic) 0.0588 1.385 1.328 0.927 0.336 -0.0259βhh (Hispanic-Hispanic) -0.447 -0.116 -0.0913 -2.615∗∗∗ -2.190∗ -2.353∗

βhw (Hispanic-white) -0.714 -0.717 -0.726 0.0743 -0.215 -0.513βhb (Hispanic-black) 0.826 0.932 1.057 0.0693 -0.256 -0.296

SPH 3.522∗∗∗ -8.445∗∗∗

∆wb (White-Black) -1.277 -0.685 -0.701 -0.165 -0.218 -0.125(0.637 (0.729) (0.728) (0.754) (0.880) (0.883)

∆wh (White-Hispanic) 0.326 0.533 0.564 -1.291 -1.289 -1.228(0.647) (0.766) (0.767) (0.700) (0.815) (0.812)

∆bh (Black-Hispanic) -1.199 -1.722 -1.732 -1.460 -0.847 -0.842(1.258) (1.398) (1.400) (1.324) (1.514) (1.510)

(∆wb + ∆wh + ∆bh)/3 -0.716 -0.625 -0.623 -0.972 -0.785 -0.732(0.583) (0.668) (0.667) (0.633) (0.731) (0.732)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes Yes Yes YesDepartment FEs (5) Yes Yes Yes Yes Yes YesMonth FEs (74) Yes Yes Yes Yes Yes YesAge and tenure controls Yes Yes Yes Yes Yes YesClusters (workers) 10,474 10,474 10,474 10,713 10,713 10,713Observations 22,109 22,109 22,109 20,881 20,881 20,881

Notes: We restrict the sample to workers in the three months following the receipt of a new incoming supervising

manager. The linear probability model relates the probability of turnover to the race of salespeople and the race of

their incoming manager. One observation is one worker in one month, for the sample of workers who receive a new

incoming supervising manager (but who do not change positions themselves). The dependent variable is 100 if the

worker turns over in that month and zero otherwise. Age and tenure coe�cients and all standard errors are in Table

C3 in Online Appendix C. Clustered standard errors in parentheses. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

35

workers leave at rate ψe, while managers leave at rate ψm. As before, managers search sequentially,

hiring the �rst applicant with an expected productivity above a threshold y∗. We assume that

managers have more accurate signals of same-race applicants than cross-race applicants, while the

underlying talent distribution is the same. Since minority managers hire fewer applicants from

a �xed pool (Proposition 4(b)), we assume they search for longer, so all managers hire the same

expected number of workers. Finally, we assume that when a manager leaves, a random worker is

promoted into the vacancy.

Suppose there are initially fraction N0 workers of race A and M0 managers of race A. Over

time the process {Mt, Nt} evolves as managers hire workers, and workers are promoted to become

managers.

Proposition 8. Starting from any initial condition {M0, N0}, the system converges to a unique

steady state {M∗, N∗}. Workers and managers have the same composition of races, and the majority

population is over-represented, M∗ = N∗ > n.

Proof. See Online Appendix A.3.

That is, minorities are at a disadvantage simply because they are minorities. Intuitively, the

problem is that most minorities are hired by majority managers who are not good at evaluating

their application. For example, if 1 − n = ε ≈ 0 of both the population and managers are race-B

then only (pc/ps)ε of the workers will be race-B in steady state, where ps and pc are the probabilities

of hiring a same-race and cross-race applicants. Even though each race-B manager hires relatively

more race-B workers, the race-A managers interview the vast majority of the race-B applicants, and

they hire race-B workers at a lower rate.

This �institutional bias� can be mitigated if the �rm promoted more minority managers.26 This

is especially useful as a way to get to steady state. However, it is harder to use such a policy to

shift an inequitable steady state. First, minorities tend to have lower productivity (Proposition

5b) so, if anything, the �rm might want to promote fewer of them. Second, minority managers'

teams tend to have lower productivity (Proposition 5b), meaning this strategy is costly for the �rm.

Third, the �rm might need to promote an infeasibly high number of minorities to achieve equality.

Appendix A.3 shows that as the number of race-B's vanish, the number of race-B managers would

have to equal pc/(pc + ps) to achieve equitable recruitment, meaning the ratio of race-B managers

to workers grows without bound.

A di�erent strategy is to centralize recruitment and take away the job of hiring from the day-

to-day manager. For example, one scheme would match the candidate with the interviewer best

equipped to interview them on a variety of characteristics (e.g. race, age, school, gender). One

26For example, Miller (2017) �nds that a�rmative action boosts the share of black employees over time, and thatthis persists even after the policy ends.

36

can then evaluate the interviewer based on their acceptance rate and the subsequent productivity

of their hires. This is somewhat related to Google's human resource policy whereby a team of

managers interview each candidate and are evaluated ex-post (Bock, 2015).

7 Conclusion

We hope our �ndings are of interest to economists of all stripes. For policy analysts interested in

racial discrimination, our results point to the importance of screening discrimination in the work-

place. As discussed in Section 6, this may be just as detrimental to the employment opportunities

of minorities as taste-based discrimination, though the solutions are quite di�erent. Racial hiring

quotas, which could improve productivity if managers are biased, could be detrimental to produc-

tivity and yield mismatch if managers are instead better at screening their own race. Instead, �rms

should encourage diversity among hiring managers to ensure that the backgrounds of their hiring

managers re�ect the workers they want to screen, and invest in technology and skills training that

helps managers screen other races.

For organizational economists, we show that the identity of hiring managers has an important

impact on the types of workers hired and on their productivity. While we focus on race as the

identifying feature, one would imagine that other background variables a�ect the ability to screen

applicants (e.g. age, national origin, gender, or educational background). This raises questions

of how to structure hiring to most e�ectively use the information within the �rm. It also raises

questions of how �rms invest in their recruiting skill by hiring people who are good at recruiting

(e.g. Montgomery, 1991; Board, Meyer-ter-Vehn, and Sadzik, 2017).

The paper is also of interest to macro labor economists seeking to understand why minorities

have lower wages, higher turnover, higher unemployment duration and higher unemployment rates.

For example, Lang and Lehmann's (2012) survey observes that blacks have 10-15% lower wages

after controlling for AFQT, at least 30% higher turnover, 30% higher unemployment duration, and

double the unemployment rate. Our results suggest that the vast majority of these di�erence come

from across-�rm variation rather than within-�rm variation. First, the expected sales of blacks is

about the same as whites.27 Second, Table B4 implies that black turnover is only 4-8% higher than

white turnover, depending on the controls. Third, Table 3 implies that black applicants have 11%

larger probability of being hired when the hiring manager is black; since most managers are white,

one might expect unemployment durations to be similarly longer. Putting this together, the higher

turnover and lower retention would suggest that if white unemployment is 5%, black unemployment

27The expected SPH (i.e. log sales) of black workers are lower than that of whites, but blacks also have highervariance which matters since expected sales are E[exp(y)] = exp(µ+ σ2/2). In particular, Columns 2 and 4 of TableB2 in Online Appendix B show that µw − µb is 0.016 in the �rst three months and 0.0234 after 3 months, while the�rst row of Table 5 says that (σ2

w − σ2w)/2 is -0.026 in the �rst three months and -0.017 after three months.

37

should still be less than 6%.28 These �ndings are hard to reconcile with the models that Lang

and Lehmann calibrate in which either all �rms are homogeneous, or some �rms taste-discriminate.

Instead, one should look to models where black workers end up at �rms that consistently pay lower

wages and have higher turnover.

Labor market discrimination has attracted considerable attention across the social sciences be-

cause the persistence of racialized labor market outcomes remains one of the most pressing issues

of our time. Our results suggest that screening discrimination potentially plays an important role

in explaining these phenomena, meriting consideration of a di�erent set of solutions.

28Suppose workers leave unemployment at Poisson rate ζ and enter it at rate λ, then steady state implies ζu =λ(1 − u). Using ζw = 1.11ζb and λb = 1.04λw and uw = 0.05, we obtain ub = 0.057. Similarly, if we use λb = 1.08λwthen ub = 0.059.

38

Appendix

Proofs for Section 2

Useful properties of the normal distribution: First, recall the convenient expressions for

expectation and variance of a truncated normal y ∼ N(µ, η2),29

E[y|y ≥ y∗] = µ+ λ(α)η (5)

V ar(y|y ≥ y∗) = η2(1 + αλ(α)− λ(α)2) (6)

where α := (y∗ − µ)/η is the cuto� corresponding to y∗ for standard normal ζ ∼ N(0, 1), with

density φ, cdf Φ, and hazard rate λ = φ/(1− Φ).

Recall that the density φ(α) = exp(−α2/2)/√

2π is log-concave since (log φ)′′ = −1, and write

δ = y − y∗ ≥ 0 for the excess productivity, i.e. the random variable that measures the amount by

which expected productivity y exceeds the hiring threshold y∗.

Lemma 1. The distribution of excess productivity δ decreases in the cuto� y∗ and increases in the

variance η2 in the likelihood ratio order.

Proof. The density of δ is given by

g(δ) = g(δ; y∗, η2) := φ

(y∗ + δ − µ

η

)/

(1− Φ

(y∗ − µη

)).

Thus, δ decreases in the cuto� y∗ in the likelihood ratio order if

g(δ; y∗, η2)g(δ; y∗, η2)

≤ g(δ; y∗, η2)g(δ; y∗, η2)

for all δ < δ and y∗ ≤ y∗. Rearranging, we obtain

log g(δ; y∗, η2) + log g(δ; y∗, η2) ≤ log g(δ; y∗, η2) + log g(δ; y∗, η2),

which is to say that the density is log-submodular in δ and y∗. Di�erentiating,

∂2(log g)

∂y∗∂δ=

∂2

∂y∗∂δlog φ(

y∗ + δ − µη

) =1

η2(log φ(δ))′′ < 0

as required.

To see that δ increases in the variance η2, we wish to show that the density is log-supermodular

in δ and η2. We write ψ(δ, η) = y∗+δ−µη , note the derivatives ∂ψ

∂δ > 0, ∂ψ∂η < 0, ∂2ψ

∂η∂δ < 0, and then

29E.g., https://en.wikipedia.org/wiki/Truncated_normal_distribution

39

compute

∂2(log g)

∂η∂δ=

∂2

∂η∂δlog φ(ψ(δ, η)) =

∂ψ

∂δ· ∂ψ∂η· [log φ(ψ(δ, η))]′ +

∂2ψ

∂η∂δ· [log φ(ψ(δ, η))]′′ > 0

as required.

Finally, we claim that

αλ′(α) < λ(α). (7)

To see this, �rst note that λ(α) = E[ζ|ζ ≥ α] = α +∫∞δ=0 δg(δ)dδ > α. Clearly, λ(α) increases in

the cuto� α, but at rate less than one since the integral decreases in the cuto� α by Lemma 1.

Proof of Proposition 1: The hiring probability p = Pr(y > y∗) = 1−Φ((y∗ − µ)/η) decreases in

y∗. Since y∗s < y∗c , we have ps > pc. Part (a) then follows by

rAA =mAps

mAps +mBpc=

1

1 +mBpc/mAps>

1

1 +mBps/mApc=

mApcmApc +mBps

= rAB

since ps > pc. Part (b) follows by

MA = mAps +mBpc = mApc +mBps + (mA −mB)(ps − pc) ≥ mApc +mBps = MB

since ps > pc and mA ≥ mB. �

Proof of Proposition 2: For part (a), expected productivity y = E[y|y ≥ y∗] clearly increases in

the threshold y∗. Since y∗s < y∗c we have xs > xc.

For part (b), writing yA, yB for the expected productivity of a race-A,B manager, we have

yA =xsmAps + xcmBpcmAps +mBpc

<xcmApc + xsmBpsmApc +mBps

= yB

since ys > yc and ps > pc. A similar argument applies to the expected productivity of a race-A,B

worker.

For part (c) we apply the law of total variance, observe that the residual variance ρ2 = σ20σ

2ε

σ20+σ

2εis

independent of expected productivity y, and apply (6) for the variance of the truncated normal to

obtain

v = E[V ar(y|y)|y ≥ y∗] + V ar(E[y|y]|y ≥ y∗) = V ar(y|y) + V ar(y|y ≥ y∗)

= ρ2 + η2(1 + αλ(α)− λ(α)2). (8)

Recalling the de�nition of α = (y∗ − µ)/η and (7), we have ddy∗ v = η2(αλ′(α) − λ(α)) < 0. Since

y∗s < y∗c , we have vs > vc. �

40

Proof of Proposition 3: Part (a) follows from y∗s < y∗c and the fact that q increases in y∗. To

see this last claim, let ε := y − y be the di�erence between estimated and actual productivity, and

recall the excess productivity δ := y − y∗ ≥ 0 from Lemma 1. Substituting and rearranging, the

�ring probability becomes

q = Pr(ε ≥ δ + ∆|δ ≥ 0) =

∫δ≥0

Pr(ε ≥ δ + ∆)g(δ; y∗, η2)dδ. (9)

The excess productivity δ falls in y∗ by Lemma 1, and the integrand Pr(ε ≥ δ + ∆) falls in δ; thus,

the �ring probability q rises.

Part (b) follows by the same argument as part (b) of Proposition 2, with turnover qs < qc

replacing productivity xs < xc. �

Proof of Proposition 4: Given that y∗ > µ, the hiring probability p = 1−Φ((y∗−µ)/η), increases

in η. Since the estimator variance η2 = σ40/(σ20 + σ2ε ) decreases in σ

2ε , and σ

2s < σ2c , it follows that

ps > pc. Both part (a) and (b) then follow as in Proposition 1. �

Proof of Proposition 5: For part (a),

y = E[y|y ≥ y∗] = y∗ +

∫ ∞0

δg(δ; y∗, η2)dδ

which increases in the η by Lemma 1. Since the estimator variance η2 decreases in σ2ε , and σ2s < σ2c

it follows that ys > yc. Part (b) follows as in Proposition 2(b) with the reversed inequality, ys > yc.

For part (c), we rearrange (8) to get v = σ20 + η2(αλ(α) − λ(α)2). Recalling α = (y∗ − µ)/η,

di�erentiating by η, rearranging, and recalling (7), we get ddηv = η(αλ′(α)− λ(α))(2λ(α)− α) < 0.

Since the estimator variance η2 decreases in σ2ε , and σ2s < σ2c , it follows that vs < vc. �

Proof of Proposition 6: For part (a), the �ring probability q is given by equation (9). An

increase in signal variance σ2ε has two e�ects that both raise q. First, it raises the residual variance

ρ2 = σ20σ2ε /(σ

20 +σ2ε ) of ε and, since δ+∆ > 0, it directly raises the integrand Pr(ε ≥ δ+∆). Second,

the increase in σ2ε lowers the estimator variance η2 which raises excess productivity δ by Lemma 1.

Since the integrand Pr(ε ≥ δ + ∆) decreases in δ, this e�ect is also positive. Thus, σ2s < σ2c implies

qs < qc. Part (b) follows by the same argument as part (b) of Proposition 3. �

41

References

Agan, A., and S. Starr (2017): �Ban the Box, Criminal Records, and Racial Discrimination: A Field

Experiment,� Quarterly Journal of Economics, 133(1), 191�235.

Altonji, J. G., and R. M. Blank (1999): �Race and Gender in the Labor Market,� Handbook of Labor

Economics, 3, 3143�3259.

Altonji, J. G., and C. R. Pierret (2001): �Employer Learning and Statistical Discrimination,� Quarterly

Journal of Economics, 116(1), 313�350.

Arnold, D., W. Dobbie, and C. Yang (2018): �Racial Bias in Bail Decisions,� Quarterly Journal of

Economics, 133(4), 1885�1932.

Åslund, O., L. Hensvik, and O. N. Skans (2014): �Seeking Similarity: How Immigrants and Natives

Manage in the Labor Market,� Journal of Labor Economics, 32(3), 405�441.

Autor, D. H., and D. Scarborough (2008): �Does Job Testing Harm Minority Workers? Evidence from

Retail Establishments,� Quarterly Journal of Economics, 123(1), 219�277.

Ayres, I., and P. Siegelman (1995): �Race and Gender Discrimination in Bargaining for a New Car,�

American Economic Review, pp. 304�321.

Ballance, J., R. Clifford, and D. Shoag (2017): � �No More Credit Score� Employer Credit Check

Bans and Signal Substitution,� Working paper, Harvard.

Bandiera, O., I. Barankay, and I. Rasul (2009): �Social Connections and Incentives in the Workplace:

Evidence from Personnel Data,� Econometrica, 77(4), 1047�1094.

Bartik, A. W., and S. T. Nelson (2017): �Credit Reports as Resumes: The Incidence of Pre-Employment

Credit Screening,� Working paper, MIT.

Bates, T. (1994): �Utilization of Minority Employees in Small Business: A Comparison of Nonminority

and Black-owned Urban Enterprises,� The Review of Black Political Economy, 23(1), 113�121.

Beaman, L. A. (2011): �Social Networks and the Dynamics of Labour Market Outcomes: Evidence from

Refugees Resettled in the US,� Review of Economic Studies, 79(1), 128�161.

Becker, G. S. (1957): The Economics of Discrimination. University of Chicago press.

Behrman, B. W., and S. L. Davey (2001): �Eyewitness Identi�cation in Actual Criminal Cases: An

Archival Analysis,� Law and Human Behavior, 25(5), 475�491.

Benson, A., D. Li, and K. Shue (2019): �Promotions and the Peter Principle,� Quarterly Journal of

Economics, forthcoming.

Bertrand, M., and S. Mullainathan (2004): �Are Emily and Greg More Employable than Lakisha

and Jamal? A Field Experiment on Labor Market Discrimination,� American Economic Review, 94(4),

991�1013.

42

Black, D. A. (1995): �Discrimination in an Equilibrium Search Model,� Journal of Labor Economics, 13(2),

309�334.

Board, S., M. Meyer-ter-Vehn, and T. Sadzik (2017): �Recruiting Talent,� Working paper, UCLA.

Bock, L. (2015): Work Rules!: Insights from Inside Google That Will Transform How You Live and Lead.

Twelve, New York.

Bohnet, I. (2016): �How to Take the Bias Out of Behavioral Interviews,� Harvard Business Review.

Bordalo, P., K. Coffman, N. Gennaioli, and A. Shleifer (2016): �Stereotypes,� Quarterly Journal

of Economics, 131(4), 1753�1794.

Brown, M., E. Setren, and G. Topa (2016): �Do Informal Referrals Lead to Better Matches? Evidence

from a Firm's Employee Referral System,� Journal of Labor Economics, 34(1), 161�209.

Brown, M. B., and A. B. Forsythe (1974): �Robust Tests for the Equality of Variances,� Journal of the

American Statistical Association, 69(346), 364�367.

Burks, S. V., B. Cowgill, M. Hoffman, and M. Housman (2015): �The Value of Hiring through

Employee Referrals,� Quarterly Journal of Economics, 130(2), 805�839.

Carrington, W. J., and K. R. Troske (1998): �Inter�rm Segregation and the Black/White Wage Gap,�

Journal of Labor Economics, 16(2), 231�260.

Chance, J. E., and A. G. Goldstein (1996): �The Other-Race E�ect and Eyewitness Identi�cation,� in

Psychological Issues in Eyewitness Identi�cation, ed. by . G. K. S. L. Sporer, R. S. Malpass, pp. 153�176.

Lawrence Erlbaum Associates, Inc.

Cornell, B., and I. Welch (1996): �Culture, Information, and Screening Discrimination,� Journal of

Political Economy, 104(3), 542�571.

Doleac, J. L., and B. Hansen (2019): �The Unintended Consequences of �Ban the Box�: Statistical

Discrimination and Employment Outcomes when Criminal Histories are Hidden,� Journal of Labor Eco-

nomics, forthcoming.

Dustmann, C., A. Glitz, U. Schönberg, and H. Brücker (2016): �Referral-Based Job Search Net-

works,� Review of Economic Studies, 83(2), 514�546.

Erickson, F. (1975): �Gatekeeping and the Melting Pot: Interaction in Counseling Encounters,� Harvard

Educational Review, 45(1), 44�70.

Erickson, F., and J. Schultz (1982): The Counselor as Gatekeeper. Academic press.

Fisman, R., D. Paravisini, and V. Vig (2017): �Cultural Proximity and Loan Outcomes,� American

Economic Review, 107(2), 457�492.

French, P. (1973): �Kinesics in Communication: Black and White,� Language Sciences, 28, 13�16.

Friebel, G., M. Heinz, M. Hoffman, and N. Zubanov (2019): �What Do Employee Referrals Do?,�

NBER Working Paper 25920.

43

Giuliano, L., D. I. Levine, and J. Leonard (2009): �Manager Race and the Race of New Hires,� Journal

of Labor Economics, 27(4), 589�631.

(2011): �Racial Bias in the Manager-Employee Relationship An Analysis of Quits, Dismissals, and

Promotions at a Large Retail Firm,� Journal of Human Resources, 46(1), 26�52.

Glover, D., A. Pallais, and W. Pariente (2017): �Discrimination as a Self-ful�lling Prophecy: Evidence

from French Grocery Stores,� Quarterly Journal of Economics, pp. 1219�1260.

Grant, A. (2017): �Question 2, August 2017,� Wondering Blog, https://www.adamgrant.net/wondering-

archives.

Hedegaard, M. S., and J.-R. Tyran (2018): �The Price of Prejudice,� American Economic Journal:

Applied Economics, 10(1), 40�63.

Hjort, J. (2014): �Ethnic Divisions and Production in Firms,� Quarterly Journal of Economics, 129(4),

1899�1946.

Kelly, D. J., P. C. Quinn, A. M. Slater, K. Lee, L. Ge, and O. Pascalis (2007): �The Other-

Race E�ect Develops During Infancy: Evidence of Perceptual Narrowing,� Psychological Science, 18(12),

1084�1089.

Lang, K. (1986): �A Language Theory of Discrimination,� Quarterly Journal of Economics, 101(2), 363�382.

Lang, K., and J.-Y. Lehmann (2012): �Racial Discrimination in the Labor Market: Theory and Empirics,�

Journal of Economic Literature, 50(4), 1�48.

Lang, K., and M. Manove (2011): �Education and Labor Market Discrimination,� American Economic

Review, 101(4), 1467�1496.

Leonard, J. S., and D. I. Levine (2006): �The E�ect of Diversity on Turnover: A Large Case Study,�

ILR Review, 59(4), 547�572.

Levene, H. (1960): �Robust Tests for Equality of Variances,� Contributions to Probability and Statistics, 1,

278�292.

List, J. A. (2003): �Does Market Experience Eliminate Market Anomalies?,� Quarterly Journal of Eco-

nomics, 118(1), 41�71.

(2004): �The Nature and Extent of Discrimination in the Marketplace: Evidence from the Field,�

Quarterly Journal of Economics, 119(1), 49�89.

Marlowe, C. M., S. L. Schneider, and C. E. Nelson (1996): �Gender and Attractiveness Biases in

Hiring Decisions: Are More Experienced Managers Less Biased?,� Journal of Applied Psychology, 81(1),

11.

Milgrom, P., and S. Oster (1987): �Job Discrimination, Market Forces, and the Invisibility Hypothesis,�

Quarterly Journal of Economics, 102(3), 453�476.

44

Miller, C. (2017): �The Persistent E�ect of Temporary A�rmative Action,� American Economic Journal:

Applied Economics, 9(3), 152�190.

Montgomery, J. D. (1991): �Social Networks and Labor-Market Outcomes: Toward an Economic Analy-

sis,� American Economic Review, 81(5), 1408�1418.

Munshi, K. (2003): �Networks in the Modern Economy: Mexican Migrants in the US Labor Market,�

Quarterly Journal of Economics, 118(2), 549�599.

Neckerman, K. M., and J. Kirschenman (1991): �Hiring Strategies, Racial Bias, and Inner-City Work-

ers,� Social Problems, 38(4), 433�447.

Oettinger, G. S. (1996): �Statistical Discrimination and the Early Career Evolution of the Black-White

Wage Gap,� Journal of Labor Economics, 14(1), 52�78.

Phelps, E. S. (1972): �The Statistical Theory of Racism and Sexism,� American Economic Eeview, 62(4),

659�661.

Ritter, J. A., and L. J. Taylor (2011): �Racial Disparity in Unemployment,� Review of Economics and

Statistics, 93(1), 30�42.

Simoiu, C., S. Corbett-Davies, and S. Goel (2017): �The Problem of Infra-Marginality in Outcome

Tests for Discrimination,� Annals of Applied Statistics, 11(3), 1193�1216.

Simon, C. J., and J. T. Warner (1992): �Matchmaker, Matchmaker: The E�ect of Old Boy Networks

on Job Match Quality, Earnings, and Tenure,� Journal of Labor Economics, 10(3), 306�330.

Stoll, M. A., S. Raphael, and H. J. Holzer (2004): �Black Job Applicants and the Hiring O�cer's

Race,� ILR Review, 57(2), 267�287.

Turner, S. C. (1997): �Barriers to a better break: Employer discrimination and spatial mismatch in

metropolitan Detroit,� Journal of Urban A�airs, 19(2), 123�141.

Wolgast, S., F. Björklund, and M. Bäckström (2018): �Applicant Ethnicity A�ects Which Questions

Are Asked in a Job Interview,� Journal of Personnel Psychology.

Wozniak, A. (2015): �Discrimination and the E�ects of Drug Testing on Black Employment,� Review of

Economics and Statistics, 97(3), 548�566.

45

Online Appendix

A Omitted Proofs

A.1 Maximizing Expected Sales

In this appendix we analyze the model variant in which managers maximize expected sales, as

discussed in Section 2.3. Let Y be a worker's sales, and assume a manager wishes to hire workers

with Y ≥ Y ∗. As in the main text, let y = E[y|y] be expected log-sales, with mean µ, estimator

variance η2 = σ40/(σ20 +σ2ε ), and estimation error y− y with residual variance ρ2 := σ20σ

2ε /(σ

20 +σ2ε ).

The manager's expected utility from a worker given estimate y is thus

E[Y |y] = E[ey|y] = eyE[ey−y|y] = ey+ρ2/2.

The manager thus wishes to hire a workers with estimate y ≥ y∗ := log Y ∗ − ρ2/2. Intuitively,

managers lower their standard, y∗ < log Y ∗, since they are risk-loving with respect to uncertainty

in log-productivity.

Under taste-based discrimination, biased managers gain extra utility from same-race candidates.

Suppose they gain utility Y from a cross-race candidate, and Y B from a same-race candidate, where

B > 1 is the same-race bias. Taking logs, the cross-race cuto� y∗c = log Y ∗ − ρ2/2 thus exceeds the

same-race cuto� y∗s = log Y ∗−b−ρ2/2 by the bias b = logB. The analysis of hiring is thus identical

to that in Section 2.1, and thus the proofs of Propositions 1�2 carry over unchanged. When it comes

to turnover, suppose that the manager �res the worker if their realized productivity y drops more

than ∆ below the cuto� y∗i . Thus the turnover rate for i ∈ {c, s} is

qi := Pr(y ≤ y∗i − ∆|y ≥ y∗i ) = Pr(y ≤ y∗i −∆|y ≥ y∗i ).

where ∆ := ∆− ρ2/2. This is the same as in Section 2.1, and Proposition 3 immediately applies.

Under screening discrimination, the signal variance σ2ε is lower for same-race applicants than

for cross-race applicants, σ2s ≤ σ2c . This implies that cross-race hires have more residual variance

than same-race hires, ρ2s ≤ ρ2c . Thus, managers set a lower threshold for cross-race hires, y∗c =

log Y ∗ − ρ2c/2 < log Y ∗ − ρ2s/2 = y∗s . Intuitively, managers are risk-loving with respect to the log-

productivity, and thus likes cross-race candidates because of their high residual variance. We �rst

verify that managers still hire more same-race workers.

Proposition 4′ (Hiring). Assume log Y ∗ > µ+ σ20. In the screening model:

(a) Managers hire relatively more workers of their own race, i.e. rAA > rAB and rBB > rBA.

(b) Majority managers hire more workers than minority managers, NA ≥ NB.

46

Proof. For part (a), let Φ and φ be the cdf and pdf of the standard normal distribution. Write the

precision of the prior as h0 := 1/σ20 and the precision of the raw signal as hε = 1/σ2ε . The estimator

variance and residual variance are then η2 = hε/((h0 + hε)h0) and ρ2 = 1/(h0 + hε). Now, the

acceptance rate can be written as a function of the signal precision

p(hε) : = Pr

(y ≥ log Y ∗ − ρ2

2

)= 1− Φ

(log Y ∗ − µ− ρ2

2

η

)=

= 1− Φ

√(h0 + hε)h0hε

(log Y ∗ − µ)− 1

2

√h0

(h0 + hε)hε

Simple computations show that the derivative equals

p′(hε) = −φ(·)×√h0

(− h0

2hε

√1

hε(h0 + hε)(log Y ∗ − µ) +

1

4

(1

hε+

1

h0 + hε

)√1

(h0 + hε)hε

)

= φ(·)× 1

2

√h0

(h0 + hε)hε

h0hε

((log Y ∗ − µ)− 1

2

1

h0

(1 +

hεh0 + hε

))Given that hε/(h0+hε) ≤ 1, this last term is positive if log Y ∗ ≥ µ+σ20. Since same-race candidates

have greater signal precision hε, they have a higher the acceptance rate, and so managers hire

relatively more same-race workers. The compositional e�ects in Proposition 1(b) follow from part

(a) as before.

Turning to productivity, Proposition 5 is una�ected by the change in objective function. The

proof of Proposition 5(a) and (c) shows that productivity of cross-race hires has lower mean and

greater variance when using the same bar, y∗c = y∗s . When risk-neutral managers lower the bar for

cross-race recruits, this further lowers their expected productivity and raises productivity variance.

The compositional e�ects in Proposition 5(b) follow from part (a) as before.

Finally, when we consider turnover, Proposition 6 is also una�ected. The proof of Proposition

6(a) shows that cross-race hires have higher turnover when using the same bar, y∗c = y∗s . When we

lower the bar for cross-race recruits, this further raises their turnover. The compositional e�ects in

Proposition 6(b) follow from part (a) as before.

A.2 Proof of Proposition 7

As with taste-based discrimination, a manager compares the estimate y to a cuto� y∗c = y∗ for

cross-race workers, and y∗s = y∗ − ξ for same-race workers. The comparison of hiring and �ring

probabilities in parts (a) and (d) follows by identical arguments as Proposition 1(a) and 3(a) in

the taste-based model, with the bonus productivity ξ substituting for the bias b. Similarly, the

comparison of productivity variance in part (c) follows by identical arguments as Proposition 2(c),

47

M

N

N = 0

M = 0

(0, 0)

(1, 1)

Figure 1: The dynamics of the population of the managers and workers

1

Figure A1: Population Dynamics of Managers and Workers

since the only di�erence is that the productivity distribution of same-race workers shifts up by ξ,

which does not a�ect its variance.

For part (b), the expected productivity of a same-race worker equals

y = E[y + ξ|y ≥ y∗ − ξ] = y∗ + E[y − (y∗ − ξ)|y ≥ y∗ − ξ] (10)

which rises in ξ, since by Lemma 1 the distribution of excess productivity δ := y − (y∗ − ξ) falls inthe cuto� y∗ − ξ, and hence rises in ξ. Hence, (10) rises in ξ, which concludes the proof since the

expected productivity of cross-race workers is given by (10) with ξ = 0.

A.3 Proof of Proposition 8

Let ps and pc be the probability same-race and cross-race candidates are hired. Let Mt ∈ [0, 1] and

Nt ∈ [0, 1] be the number of A managers and workers at a �rm, and consider the dynamics (Mt, Nt)

in (M,N) space (see Figure A1).

First, consider the dynamics of workers, given the the number of managers. Let ψ be the rate

at which workers leave; this could be due to exit or promotion. A race-A manager hires race-A

workers over race-B workers in the ratio psn/pc(1 − n). Hence the number of of race-A workers

evolves according to

N = ψ

[(1−M)

(pcn

pcn+ ps(1− n)

)+M

(psn

psn+ pc(1− n)

)−N

]. (11)

One can verify that ddM N ∈ (0, ψ) and d

dN N = −ψ. Thus, in (M,N) space, N = 0 is a straight line

from ( pcnpcn+ps(1−n) , 0) to ( psn

psn+pc(1−n) , 1), with slope exceeding one.

Next, consider the dynamics of managers, given the number of workers. Managers retire at rate

ψm and replacements are chosen randomly from the population of workers, so M = ψm(N −M).

Thus, M = 0 along the diagonal where N = M .

48

Figure A1 illustrates the dynamics of (M,N). It is evident that there is a unique steady state

where M = 0 and N = 0, and that the system converges to this steady state from any initial

condition. When N = M = n, then

N = ψ

[(1− n)

(pcn

pcn+ ps(1− n)

)− n

(pc(1− n)

psn+ pc(1− n)

)]sgn= (ps − pc)(2n− 1) > 0

if n > 1/2. Thus the steady state must satisfy N∗ = M∗ > n.

Finally, we consider how many managers of a particular race are required to obtain equitable

hiring. Rearranging (11), if we have N = 0 when N = n, then M must solve

M

((p2s − p2c)n(1− n)

(psn+ pc(1− n)) (pcn+ ps(1− n))

)=

(ps − pc)(1− n)n

pcn+ ps(1− n).

Letting 1− n = ε ≈ 0, we obtain

M

(p2s − p2cpspc

)ε ≈ (ps − pc)

pcε,

so that the number of race-B managers is 1−M ≈ pc/(ps + pc).

49

B Other Empirical Results

Less than three months tenure

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

White workers

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

Black workers

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

Hispanic workers

More than three months tenure

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

White workers

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

Black workers

0.00

0.02

0.04

0.06

-1.0 -0.5 0 0.5 1.0

Hispanic workers

same race manager different: white manager

different: black manager different: Hispanic manager

Figure B1: Histograms of SPH by Manager Race, Worker Race, and TenureNotes: The top-left hand �gure shows the distribution of productivity for white workers in the �rst three months;

the black line is productivity under white managers, the green line is productivity under black managers, and the

blue line productivity under Hispanic managers. The statistical power of the data a�ord us the ability to plot the

frequency distributions for every combination of racial pair at 5%-wide intervals of SPH without the use of kernel

densities or other smoothing.

50

Table B1: Team Size by Manager Race

All workers All workers Sales only Sales only(1) (2) (3) (4)

White

Black -1.707∗∗∗ -0.894∗∗ -0.866∗∗∗ -0.509∗∗∗

(0.610) (0.444) (0.213) (0.139)

Hispanic 0.660 1.011∗∗ -0.674∗∗∗ -0.0519(0.686) (0.505) (0.206) (0.137)

Constant 23.39∗∗∗ 15.49∗∗∗ 8.976∗∗∗ 6.798∗∗∗

(0.194) (0.366) (0.0689) (0.126)

Stores FEs Yes Yes Yes YesManager gender Yes YesManager tenure Yes YesDepartment FEs Yes YesMonth FEs Yes YesClusters (managers) 8,961 7,690 8,961 7,690Observations 14,5271 138,784 145,271 138,784

Notes: In this OLS regression, the dependent variable in the �rst pair of columns is the count of all workers under

a manager. In the second pair of columns, the dependent variable is the count of salespeople. For each of these

dependent variables, the �rst column controls for store �xed e�ects. The second column adds a variety of other

controls; the latter regression has slightly fewer observations because of left-censoring when measuring job tenure for

some long-tenured managers, but results remain substantively the same when we impute tenures.

51

Table B2: Productivity by Race of Manager and Worker

First 3 months After 3 months

(1) (2) (3) (4)

Black manager -0.0175∗∗ -0.00774 -0.0223∗∗ -0.0211∗∗

(0.00740) (0.00882) (0.00892) (0.00926)

Hispanic manager 0.0101 0.00498 0.0228∗∗∗ 0.00151(0.00706) (0.00884) (0.00831) (0.00878)

Black worker -0.0142∗∗ -0.0155∗∗ -0.0291∗∗∗ -0.0234∗∗∗

(0.00620) (0.00680) (0.00793) (0.00841)

Hispanic worker 0.00867 -0.00945 -0.0117 -0.0268∗∗∗

(0.00655) (0.00726) (0.00841) (0.00906)

Age 0.00539∗∗∗ 0.00601∗∗∗ 0.00630∗∗∗ 0.00648∗∗∗

(0.00107) (0.00106) (0.00141) (0.00131)

Age-squared (x0.001) -0.0923∗∗∗ -0.0959∗∗∗ -0.0761∗∗∗ -0.0714∗∗∗

(0.0138) (0.0137) (0.0178) (0.0164)

Log-tenure 0.0173∗∗∗ 0.0198∗∗∗ -0.00806∗∗ -0.00611∗∗

(0.00419) (0.00408) (0.00346) (0.00301)CBSA race controls (5) Yes YesStoreFEs (1,108) Yes YesDepartment FEs (5) Yes Yes Yes YesMonthFEs (74) Yes Yes Yes YesClusters (workers) 36,949 36,949 20,836 20,836Observations 89,035 89,035 175,568 175,568

Notes: In this OLS model, the reference categories are white managers and white workers. Clustered standard errors

in parentheses. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

52

Table B3: Turnover Regressions, All Workers

First 3 months After 3 months

(Worker-manager) (1) (2) (3) (4)

�ww (White-White) 0 0 0 0

�wb (White-Black) 0.449⇤⇤⇤ 0.702⇤⇤⇤ 0.226⇤⇤⇤ 0.440⇤⇤⇤

(0.127) (0.148) (0.0691) (0.0802)

�wh (White-Hispanic) 0.351⇤⇤⇤ 0.487⇤⇤⇤ -0.0157 0.264⇤⇤⇤

(0.135) (0.151) (0.0712) (0.0806)

�bb (Black-Black) 0.914⇤⇤⇤ 1.463⇤⇤⇤ 0.647⇤⇤⇤ 1.084⇤⇤⇤

(0.113) (0.144) (0.0703) (0.0870)

�bw (Black-White) 2.044⇤⇤⇤ 2.074⇤⇤⇤ 1.395⇤⇤⇤ 1.394⇤⇤⇤

(0.0647) (0.0721) (0.0424) (0.0465)

�bh (Black-Hispanic) 1.902⇤⇤⇤ 2.056⇤⇤⇤ 0.809⇤⇤⇤ 1.387⇤⇤⇤

(0.169) (0.186) (0.109) (0.118)

�hh (Hispanic-Hispanic) -1.457⇤⇤⇤ -0.614⇤⇤⇤ -1.845⇤⇤⇤ 0.00715(0.0940) (0.149) (0.0452) (0.0806)

�hw (Hispanic-White) -0.0879 0.0682 0.00227 0.330⇤⇤⇤

(0.0782) (0.0840) (0.0463) (0.0505)

�hb (Hispanic-Black) -0.870⇤⇤⇤ 0.332 -0.372⇤⇤⇤ 0.363⇤⇤⇤

(0.191) (0.209) (0.109) (0.120)

Age 0.263⇤⇤⇤ 0.360⇤⇤⇤ -0.205⇤⇤⇤ -0.157⇤⇤⇤

(0.0109) (0.0109) (0.00546) (0.00561)

Age squared (x 0.001) -3.449⇤⇤⇤ -4.587⇤⇤⇤ 1.371⇤⇤⇤ 0.735⇤⇤⇤

(0.150) (0.148) (0.0685) (0.0702)

Log-tenure 14.74⇤⇤⇤ 14.98⇤⇤⇤ -2.958⇤⇤⇤ -2.563⇤⇤⇤

(0.0434) (0.0423) (0.0175) (0.0169)

�wb (White-Black) -0.790⇤⇤⇤ -0.656⇤⇤⇤ -0.487⇤⇤⇤ -0.375⇤⇤⇤

(0.0865) (0.0917) (0.0513) (0.0546)�wh (White-Hispanic) -0.860⇤⇤⇤ -0.585⇤⇤⇤ -0.916⇤⇤⇤ -0.294⇤⇤⇤

(0.0865) (0.0958) (0.0456) (0.0518)�bh (Black-Hispanic) -0.788⇤⇤⇤ -0.769⇤⇤⇤ -0.818⇤⇤⇤ -0.330⇤⇤⇤

(0.142) (0.151) (0.0849) (0.0907)(�wb + �wh + �bh)/3 -0.812⇤⇤⇤ -0.670⇤⇤⇤ -0.740⇤⇤⇤ -0.333⇤⇤⇤

(0.0706) (0.0774) (0.0410) (0.0451)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes Yes YesDepartment FEs (5) Yes Yes Yes YesMonth FEs (74) Yes Yes Yes YesClusters (workers) 666,124 709,101 434,423 464,558Observations 1,820,922 1,933,752 4,710,242 5,159,371

Notes: This recreates Table 6 with all workers, rather than just salespeople. The dependent variable is 100 if the

worker turns over and 0 otherwise. Includes all workers, not just commissioned salespeople. Clustered standard errors

in parentheses. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

53

Table B4: Turnover by Race and Performance

(1) (2) (3) (4)

Black 0.830∗∗∗ 0.680∗∗∗ 0.476∗∗∗ 0.391∗∗

(0.174) (0.175) (0.169) (0.182)

Hispanic -0.269 -0.219 -0.437∗∗ -0.128(0.171) (0.171) (0.187) (0.205)

3 month SPH -2.897∗∗∗ -2.962∗∗∗

(0.168) (0.159)

Age 0.0171 -0.0327(0.0231) (0.0245)

Age squared (x 0.001) -1.18∗∗∗ -0.729∗∗

(0.281) (0.296)

Log-tenure -2.047∗∗∗ -1.314∗∗∗

(0.0490) (0.0617)

Stores FEs (1,108) Yes YesDepartment FEs (5) Yes YesMonth FEs (74) Yes YesClusters (workers) 36,949 26,332 36,949 26,332Observations 326,964 259,227 326,964 259,227

Notes: This linear probability model considers the turnover of salespeople. The dependent variable is 100 if the

worker turns over and 0 otherwise. Constants are obtained from a marginal e�ects model where all non-racial

pair controls (including SPH and tenure) are at the mean values. Clustered standard errors in parentheses. ∗p <

0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

54

Table B5: Productivity by Race of Manager-Worker Pair, for Non-hiring Man-agers

First 3 months After 3 months

SPH SPH SPH SPH

�ww (White-White) 0 0 0 0�bw (Black-White) -0.0338 -0.0363 -0.0221 -0.0222�hw (Hispanic-White) 0.0247 0.0321 0.00661 0.00688�bb (Black-Black) -0.0117 -0.00913 -0.0402⇤ -0.0406⇤

�wb (White-Black) -0.0152 -0.0139 -0.0380⇤⇤⇤ -0.0380⇤⇤⇤

�hb (Hispanic-Black) 0.000963 0.00558 -0.038 -0.0365�hh (Hispanic-Hispanic) 0.0454⇤ 0.0479⇤ 0.0196 0.0208�wh (White-Hispanic) -0.0274 -0.0289 -0.0188 -0.0195�bh (Black-Hispanic) 0.0867 0.0853 0.0122 0.0116Log-tenure 0.014 0.0201⇤ -0.0222⇤⇤⇤ -0.0252⇤⇤⇤

Constant -0.0052 -0.0078 0.0444⇤⇤⇤ 0.0510⇤⇤⇤

�ww (White-Black) 0.0374 0.041 0.0199 0.0196(0.0554) (0.0552) (0.029) (0.0289)

�wh (White-Hispanic) 0.0481 0.0447 0.0319 0.0334(0.0459) (0.0455) (0.0276) (0.0277)

�bh (Black-Hispanic) -0.0539 -0.0521 0.00513 0.00506(0.102) (0.102) (0.0516) (0.0517)

(�wb + �wh + �bh)/3 0.0315 0.0336 0.0569 0.0581(0.142) (0.141) (0.0761) (0.0763)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes YesDepartment FEs (5) Yes Yes Yes YesMonth FEs (74) Yes Yes Yes YesClusters (workers) 3,731 3,731 8,598 8,598Observations 9,408 9,408 113,628 113,628

Notes: These OLS models are the analogue to Table 4, under non-hiring managers. The dependent variable is

productivity (SPH). Clustered errors for linear combinations are in parentheses.

55

Table B6: Productivity under Non-hiring Managers (vs. Hiring Manager)

Extended sample Main sample

SPH SPH SPH SPH(1) (2) (3) (4)

Worker transfered under manager 0.00151 -0.0000816(0.00122) (0.00205)

Manager transfered above worker -0.000598 -0.00000115(0.000902) (0.00199)

Age -0.0129∗∗∗ -0.0128∗∗∗ -0.0472∗∗∗ -0.0472∗∗∗

(0.00260) (0.00260) (0.00589) (0.00589)

Age-squared (x 0.001) -119.3∗∗∗ -119.3∗∗∗ 365.8∗∗∗ 365.8∗∗∗

(30.38) (30.36) (70.08) (70.07)

Log-tenure -0.0143∗∗∗ -0.0143∗∗∗ -0.00569∗∗∗ -0.00569∗∗∗

(0.000947) (0.000952) (0.00164) (0.00167)

Worker FEs Yes Yes Yes YesMonth FEs (74) Yes Yes Yes YesClusters (workers) 99,317 99,317 36,949 36,949Observations 1,337,729 1,337,729 333,088 333,088

Notes: In this OLS model, the dependent variable is productivity (SPH), where the reference category is the

productivity of workers under hiring managers. Clustered standard errors are in parentheses. The extended sample

(columns 1 and 2) does not restrict to new hires, but uses an available �date in position� �eld to infer whether the

manager or worker moved. We do not use the extended sample in the main analysis because we do not observe the

race of the manager who hired the worker unless the manager's date in position predates that of the worker, and

then, we do not observe productivity at the start date. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

56

C Tables with Standard Errors

Table C1: Productivity Regressions from Table 4, with Standard Errors

First 3 months After 3 months

SPH SPH SPH SPH(Worker-manager) (1) (2) (3) (4)

βww (White-White)

βwb (White-Black) -0.0204∗ -0.0187∗ -0.0215 -0.0214(0.0104) (0.0104) (0.0145) (0.0145)

βwh (White-Hispanic) -0.00535 -0.00606 -0.0139 -0.0134(0.0106) (0.0106) (0.0148) (0.0147)

βbb (Black-Black) -0.0225∗ -0.0236∗∗ -0.0468∗∗∗ -0.0463∗∗∗

(0.0115) (0.0115) (0.0145) (0.0145)

βbw (Black-White) -0.0192∗∗∗ -0.0192∗∗∗ -0.0311∗∗∗ -0.0303∗∗∗

(0.00725) (0.00725) (0.00918) (0.00918)

βbh (Black-Hispanic) -0.0119 -0.0137 -0.0566∗∗ -0.0556∗∗

(0.0175) (0.0175) (0.0229) (0.0229)

βhh (Hispanic-Hispanic) 0.0319∗∗∗ 0.0321∗∗∗ 0.0132 0.0145(0.00937) (0.00944) (0.0121) (0.0121)

βhw (Hispanic-White) 0.00291 0.00316 -0.0160 -0.0151(0.00795) (0.00795) (0.0103) (0.0103)

βhb (Hispanic-Black) -0.0426∗∗ -0.0405∗∗ -0.0563∗∗ -0.0543∗∗

(0.0193) (0.0193) (0.0241) (0.0241)

Age 0.00521∗∗∗ 0.0054∗∗∗ 0.00631∗∗∗ 0.00641∗∗∗

(0.00107) (0.00107) (0.00140) (0.00140)

Age-squared (x 0.001) -0.0904∗∗∗ -0.0927∗∗∗ -0.0767∗∗∗ -0.0772∗∗∗

(0.0138) (0.0138) (0.0176) (0.0176)

Log-tenure 0.0176∗∗∗ 0.0168∗∗∗ -0.0111∗∗∗ -0.0107∗∗∗

(0.00403) (0.00423) (0.00307) (0.00360)

∆wb (White-Black) 0.00859 0.00715 0.00294 0.00268(0.00832) (0.00828) (0.0109) (0.0109)

∆wh (White-Hispanic) 0.0172∗∗ 0.0175∗∗ 0.0216∗∗ 0.0215∗∗

(0.00783) (0.00783) (0.0104) (0.0104)∆bh (Black-Hispanic) 0.0320∗∗ 0.0314∗∗ 0.0396∗∗ 0.0391∗∗

(0.0147) (0.0147) (0.0187) (0.0187)(∆wb + ∆wh + ∆bh)/3 0.0192∗∗∗ 0.0187∗∗∗ 0.0214∗∗ 0.0211∗∗

(0.00709) (0.00708) (0.00910) (0.00910)

CBSA race controls Yes YesStore FEs (1,108) Yes YesDepartment FEs (5) Yes Yes Yes YesMonth FEs (74) Yes Yes Yes YesClusters (workers) 36,949 36,949 20,953 20,953Observations 89,290 89,290 179,353 179,353

Notes: The dependent variable is productivity (SPH). Coe�cient subscripts refer the worker and manager race; e.g.

βbw refers to black workers hired by white managers. Clustered errors for linear combinations are in parentheses.∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

57

Table C2: Turnover Regressions from Table 6, with Standard Errors

First 3 months After 3 months

(Worker-manager) (1) (2) (3) (4) (5) (6)

�ww (White-White) 0 0 0 0 0 0

�wb (White-Black) 0.454 -0.172 -0.179 -0.0487 -0.460 -0.501⇤

(0.543) (0.608) (0.604) (0.260) (0.303) (0.302)

�wh (White-Hispanic) -0.000265 -0.601 -0.599 -0.00686 -0.0547 -0.108(0.585) (0.649) (0.646) (0.290) (0.320) (0.320)

�bb (Black-Black) -0.0171 -1.342⇤⇤ -1.421⇤⇤ 0.215 -0.144 -0.220(0.550) (0.683) (0.682) (0.300) (0.358) (0.356)

�bw (Black-White) 0.925⇤⇤ 0.917⇤⇤ 0.838⇤⇤ 0.356⇤ 0.433⇤⇤ 0.364⇤

(0.366) (0.404) (0.402) (0.197) (0.211) (0.210)

�bh (Black-Hispanic) 0.451 0.126 0.0697 -0.314 -0.403 -0.534(0.920) (1.014) (1.011) (0.469) (0.506) (0.505)

�hh (Hispanic-Hispanic) -1.666⇤⇤⇤ -2.671⇤⇤⇤ -2.642⇤⇤⇤ -1.777⇤⇤⇤ -0.786⇤⇤ -0.861⇤⇤

(0.510) (0.736) (0.735) (0.234) (0.369) (0.369)

�hw (Hispanic-White) -1.115⇤⇤⇤ -1.387⇤⇤⇤ -1.416⇤⇤⇤ 0.108 0.0719 0.0141(0.403) (0.438) (0.438) (0.229) (0.248) (0.247)

�hb (Hispanic-Black) 0.168 -0.782 -0.978 -0.304 -0.233 -0.387(0.968) (1.059) (1.054) (0.527) (0.575) (0.571)

SPH -4.235⇤⇤⇤ -2.437⇤⇤⇤

(0.262) (0.145)

Age 0.176⇤⇤⇤ 0.183⇤⇤⇤ 0.209⇤⇤⇤ -0.0767⇤⇤⇤ -0.0577⇤⇤ -0.0375(0.0519) (0.0537) (0.0535) (0.0233) (0.0246) (0.0246)

Age-squared (x0.001) -2.919⇤⇤⇤ -2.895⇤⇤⇤ -3.314⇤⇤⇤ -0.166 -0.453 -0.669⇤⇤

(0.667) (0.688) (0.685) (0.277) (0.296) (0.296)

Log-tenure -1.476⇤⇤⇤ -1.242⇤⇤⇤ -1.158⇤⇤⇤ -1.450⇤⇤⇤ -1.125⇤⇤⇤ -1.137⇤⇤⇤

(0.274) (0.275) (0.275) (0.0651) (0.0663) (0.0663)

�wb (White-Black) -0.698⇤ -1.044⇤⇤ -1.040⇤⇤ -0.0459 -0.0588 -0.0419(0.402) (0.432) (0.431) (0.209) (0.224) (0.222)

�wh (White-Hispanic) -0.275 -0.341 -0.314 -0.939⇤⇤⇤ -0.402⇤ -0.383⇤

(0.412) (0.459) (0.458) (0.206) (0.234) (0.233)�bh (Black-Hispanic) -1.151 -1.678⇤⇤ -1.577⇤⇤ -0.472 -0.147 -0.0802

(0.739) (0.810) (0.808) (0.387) (0.415) (0.414)(�wb + �wh + �bh)/3 -0.708⇤⇤ -1.021⇤⇤⇤ -0.977⇤⇤ -0.486⇤⇤⇤ -0.203 -0.168

(0.353) (0.394) (0.394) (0.182) (0.200) (0.199)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes Yes Yes YesDepartment FEs (5) Yes Yes Yes Yes Yes YesMonth FEs (74) Yes Yes Yes Yes Yes YesAge and tenure controls Yes Yes Yes Yes Yes YesClusters (workers) 36,949 36,949 36,949 23,382 23,382 23,382Observations 92,089 92,089 92,089 240,999 240,999 240,999

Notes: The dependent variable is 100 if the worker turns over and 0 otherwise. Clustered standard errors in

parentheses. ∗p < 0.10, ∗∗p < 0.05,∗∗∗ p < 0.01.

58

Table C3: Turnover Regressions from Table 10, with Standard Errors

High performing workers Low performing workers

(1) (2) (3) (4) (5) (6)

�ww (White-White) 0 0 0 0 0 0

�wb (White-Black) -0.0983 -0.940 -0.870 0.475 0.435 0.315(0.800) (1.019) (1.021) (0.984) (1.205) (1.199)

�wh (White-Hispanic) -0.386 -0.465 -0.494 -0.107 0.603 0.614(0.886) (1.071) (1.073) (0.986) (1.210) (1.200)

�bb (Black-Black) -1.066 -1.010 -0.988 0.690 0.577 0.347(0.886) (1.140) (1.138) (1.062) (1.372) (1.385)

�bw (Black-White) 1.585⇤⇤ 1.299⇤ 1.283⇤ 0.546 0.579 0.283(0.628) (0.705) (0.705) (0.662) (0.791) (0.788)

�bh (Black-Hispanic) 0.0588 1.385 1.328 0.927 0.336 -0.0259(1.558) (1.687) (1.696) (1.634) (1.860) (1.848)

�hh (Hispanic-Hispanic) -0.447 -0.116 -0.0913 -2.615⇤⇤⇤ -2.190⇤ -2.353⇤

(0.852) (1.238) (1.235) (0.843) (1.226) (1.223)

�hw (Hispanic-White) -0.714 -0.717 -0.726 0.0743 -0.215 -0.513(0.638) (0.743) (0.745) (0.765) (0.874) (0.868)

�hb (Hispanic-Black) 0.826 0.932 1.057 0.0693 -0.256 -0.296(1.683) (1.933) (1.933) (1.743) (2.132) (2.124)

Age -0.0645 0.00845 0.00984 0.0727 0.0807 0.0827(0.0706) (0.0792) (0.0793) (0.0817) (0.0905) (0.0904)

Age-squared (x0.001) -0.223 -1.065 -1.076 -1.818⇤ -2.058⇤ -2.030⇤

(0.838) (0.953) (0.954) (0.967) (1.078) (1.076)

Log-tenure -1.461⇤⇤⇤ -0.965⇤⇤⇤ -0.949⇤⇤⇤ -2.684⇤⇤⇤ -2.261⇤⇤⇤ -2.266⇤⇤⇤

(0.222) (0.230) (0.230) (0.257) (0.273) (0.272)

SPH 3.522⇤⇤⇤ -8.445⇤⇤⇤

(0.731) (0.732)

�wb (White-Black) -1.277 -0.685 -0.701 -0.165 -0.218 -0.125(0.637 (0.729) (0.728) (0.754) (0.880) (0.883)

�wh (White-Hispanic) 0.326 0.533 0.564 -1.291 -1.289 -1.228(0.647) (0.766) (0.767) (0.700) (0.815) (0.812)

�bh (Black-Hispanic) -1.199 -1.722 -1.732 -1.460 -0.847 -0.842(1.258) (1.398) (1.400) (1.324) (1.514) (1.510)

(�wb + �wh + �bh)/3 -0.716 -0.625 -0.623 -0.972 -0.785 -0.732(0.583) (0.668) (0.667) (0.633) (0.731) (0.732)

CBSA race controls (5) Yes YesStore FEs (1,108) Yes Yes Yes YesDepartment FEs (5) Yes Yes Yes Yes Yes YesMonth FEs (74) Yes Yes Yes Yes Yes YesAge and tenure controls Yes Yes Yes Yes Yes YesClusters (workers) 10,474 10,474 10,474 10,713 10,713 10,713Observations 22,109 22,109 22,109 20,881 20,881 20,881

Notes: The dependent variable is 100 if the worker turns over and 0 otherwise. Clustered standard errors in

parentheses. ∗p < 0.10, ∗∗p < 0.05, ∗∗∗p < 0.01.

59