Does Competition Squeeze Out Taste-based
Discrimination? Evidence from a Virtual
Labour Market
Alex Bryson
University College London
Arnaud Chevalier
IZA - Bonn
October 2016
(Preliminary and incomplete – Do not Quote)

Bryson is also affiliated to NIESR (London), IZA (Bonn) and Rutgers (New Jersey) : [email protected]
Chevalier is also affiliated to Royal Holloway (London), Deutsche Sporthochschule (Koeln), SFI
(Copenhagen), and ROA (Maastricht): [email protected]

0
ABSTRACT
Using unique data on a virtual labour market with 3 million identical firms observed for
38 periods we test Becker's prediction that competition drives out taste-based
discrimination in the labour market. The setting allows us to isolate taste-based
discrimination since information about all workers’ productivity is available at no cost
and the employee- and consumer-based channels of discrimination are shut down. In a
context where workers are close substitutes we find some evidence of racial
discrimination in hiring decisions which increases over time. Discriminating employers
forfeit about 1% of production per week. Employers facing more competition do not
appear more likely to either change behaviour or disappear from the market.
Key words: race; labour market discrimination; dynamics, competition, football
JEL: J15; J23; J24; J71; M51
Acknowledgements
We thank Wiktor Piotrowski for research assistance and participants at the European
Association of Labour Economics in Ghent for valuable comments. Alex Bryson thanks
the Norwegian Research Council for funding (grant number 202647). Both authors thank
the Centre for Economic Performance for seed money for this research.
1
“Presumably, the amount of observable discrimination against
minorities in wages and employment depends not only on
tastes for discrimination but also on other variables, such as
the degree of competition [..]” (Becker, 1993, p387)
“Many behavioral anomalies disappear when traders are
experienced” (Al-Ubaydli and List, 2016)
1.
INTRODUCTION
Despite anti-discrimination legislation numerous studies suggest that employers
discriminate on grounds of race. Theoretically, discrimination in the labour market may
originate from employers' taste-based discrimination (Becker, 1957), whereby
discriminating employers behave as if workers from the discriminated group are more
expensive than they are. This additional cost-discriminating coefficient should vary with
the level of prejudice. As first pointed out by Arrow (1972) Becker’s model predicts that
in a competitive setting, discriminating employers will be driven out of the market since
they forfeit profits. While this is one of the main conclusions of Becker’s model, it has
not been tested empirically. Using novel data this is what we seek to do in this paper.
Our study analyses hiring in a virtual labour market created by the Fantasy
Premier League (FPL), an on-line competition based on the Premier League, the foremost
league of English football (soccer), entered by more than 3 million individuals
worldwide.1 The aim of FPL participants is to assemble and manage the best performing
team in the fantasy league, something that is achieved by accumulating points related to
the performance of professional footballers week by week on the pitch in the real world.
Participants behave like employers hiring their initial squad of players and subsequently
1
https://fantasy.premierleague.com/
2
buying and selling them in any game week during the 38 week season so as to maximise
points.
This virtual setting is ideal for establishing whether taste-based hiring
discrimination is driven out by competition between employers. Employers have perfect
information about the race and week-by-week on-field performance of every professional
football player in the whole sector so there are no grounds for statistical discrimination.
There are no customers and, in this virtual world, no co-worker relations, so that we can
rule these out as potential pressures on employers' decisions as to whether to
discriminate. Firms are identical in terms of their production functions and compete
directly with one another to win the FPL. Most also enter mini-leagues composed of
groups of employers (usually work colleagues or school friends) where the stakes are
high.
The FPL is a perfectly competitive labour market, where every week, participants
can buy and sell football players (workers), so as to alter the composition of their team.
Workers’ prices are set exogenously and posted, so that firms cannot bargain them down.
Since this is a virtual market each worker can potentially be bought by several firms so
that the supply of workers is large. In most other settings it is difficult to determine the
forgone profits of discriminating firms and it is not clear how much competitive pressure
firms face. In our set-up, on the other hand, post hoc we know the optimal team each
week and can measure how far from this optimal frontier a given firm is, such that we can
measure the forgone production of a discriminating firm. Finally, we have time-varying
information on the competition faced by each participant. As such, we can observe
dynamic discriminatory behaviour, and can compare employers with similar levels of
3
initial discrimination facing various level of competition. We test the hypothesis that, as
the football season unfolds, competitive pressures change such that the potential
performance penalties associated with racial discrimination in hires rises (falls) for those
nearer the top (bottom) of the league(s) they are competing in. Time-variance in
competition allows us to test the proposition that competition should squeeze out
discriminatory behaviours, at least for those still trying to win their league.
Using aggregate weekly data Bryson and Chevalier (2015) find little evidence of
racial discrimination in Fantasy Football hires and fires. Using new micro-data on each
individual firm's hires and fires we examine the role competition plays in a firm's
propensity to discriminate. If discrimination is statistical, it should diminish over time, as
employers discover more about the true productivity of workers, but this should be
independent of the competitive environment they face.2 The influence of competition on
employers’ discriminatory behaviour is specific to taste-based discrimination, and thus
allows us to test between competing sources of discrimination.
Our analyses examine what role, if any, workers' race plays in employers' choice
of their squad at the start of the season and their subsequent decisions to recruit and retain
footballers each week of the season, conditional on their productivity, price and other
factors. We find some evidence of racial discrimination in hiring decisions which
increases over time. Discriminating employers forfeit about 1% of production per week.
Employers facing more competition do not appear more likely to either change behaviour
or disappear from the market.
2
Caminade et al. (2016) present a theory and find evidence of a positive link between market power and
statistical price discrimination. However, this arises through imperfect market competition which does not
exist in our setting.
4
The remainder of the paper is set out as follows. Section Two reviews the
previous literature on racial discrimination in the labour market and other markets.
Section Three presents our data and the institutional setting for the empirical analysis.
Section Four outlines our empirical strategy. Section Five presents results and Section Six
concludes.
2.
PREVIOUS LITERATURE
Studies capturing perceptions of racial discrimination in the labour market suggest it
remains commonplace, a finding which is supported by in-depth interviews with
employers (see Pager and Shepherd (2008) for a review), and audit studies (see Bertrand
and Mullainathan (2004) for a prominent example). Charles and Guryan (2008) show that
in the United States a quarter of the racial wage gap is due to prejudice.
Taste-based discrimination occurs when employers offer jobs to applicants, or set
wages, based on race rather than aptitude for the job (Becker, 1957). Employers may pay
a price for taste-based discrimination if their recruitment or promotion procedures are
based on skin colour rather than aptitude. Becker argued that, in competitive markets, the
price of such discrimination is not sustainable in the long-run. Employers may also
engage in what has been termed "statistical discrimination" (Arrow, 1972, 1973; Phelps,
1972) whereby, in the absence of information on prospective employees' worth,
employers may judge the quality of applicants based on group characteristics such as
race, resulting in potentially discriminatory outcomes.
5
It is only recently that discrimination studies have sought to distinguish between
taste-based and statistical discrimination (Guryan and Charles, 2013). List (2004) shows
sports-card traders from minority groups receive lower initial and final offers than those
from majority groups.
In four complementary follow-up experiments exogenously
manipulating information on race he finds the observable differences in treatment are due
to statistical discrimination. Other field experiments manipulating the race of participants
in various markets conclude that discrimination is statistically-based.3
The consensus is the sports literature is that racial discrimination has declined
over time. Reviewing the wage discrimination literature for the United States, Rosen and
Sanderson (2001: F58) suggest that the discrimination which "was easily detected in the
initial studies of the 1960s and 1970s...had mostly disappeared by the 1990s...It is
difficult to find a negative coefficient on race in US data these days". Two studies on
hiring decisions for marginal workers suggest no racial bias against players or coaches in
basketball (Brown et al., 1991; Kahn, 2006). However, in their review of the sports
literature through to the late 1990s Altonji and Blank (1999: 3196) argue that there is
evidence of salary discrimination, especially in professional basketball, some customer
discrimination against minority players, and "some hiring discrimination, although these
results depend on the sport and position [of the player on the field]".
Racial discrimination may be less apparent than it used to be because black
players have been integrated into North American professional sports. Goff et al. (2002)
3
Zussman (2013) manipulates information on the race of online car buyers in Israel and combines it with
sellers’ interviews aimed at revealing the origin of racial prejudice. Doleac and Stein (2013) manipulate
pictures of online sellers of iPods in the United States. Both Zussman (2013) and Doleac and Stein (2013)
point to distrust across groups as the cause of such behaviour, which is also consistent with Pope and
Sydnor's (2011) evidence that black borrowers face higher interest rates in peer to peer lending.
6
treat the integration of black players into North American baseball and basketball as akin
to the diffusion of a productivity-enhancing technology. Consistent with this proposition
they show black players were more productive than white players during the quarter
century over which sports moved from a segregated to an integrated equilibrium. The
productivity differential dissipates post-diffusion.
3.
DATA AND INSTITUTIONAL SETTING
3.1 Institutional Set-up
We analyse the virtual market of the Fantasy Premier League (FPL), an on-line
game based on the Barclays Premier League, which is the top flight of professional
football in England. FPL is played by about 3 million individuals who sign up to play the
game in the course of a season. Participation in the FPL is free. On subscribing,
participants are given a fictional budget of £100 million from which they must purchase a
squad of fifteen professional footballers playing in the league.4 The price of players is set
by the FPL and reviewed every week. Like in a real firm, different positions must be
filled. A team must consist of two goalkeepers, five defenders, five midfielders and three
strikers. These players are real footballers playing professional football in the Barclays
Premier League; their actions on the pitch are rewarded in fantasy points. Participants in
the FPL are employers in the sense that they buy and sell the players they need in order to
produce points and win the FPL. The overall winner is the team with the most points at
the end of the season, or over a month for the monthly prizes. It is also possible to enter
teams in private leagues, so as to compete amongst friends. These competitions create
4
There are over 600 players to choose from in a given season. They cannot hire more than three footballers
playing for the same club in the Premier League.
7
incentives for FPL participants to maximize the number of points scored throughout the
season, even when an overall win is no longer possible. Information on these local
leagues will give us the amount of competition each individual faces.
As well as selecting their initial squad, employers are able to hire and fire new
workers after each game, subject to budget constraints. The cost of a hire is the value of
the incoming player plus the gap between the value of the outgoing player on the open
market and the value the employer recovers on sale (which is not the full market price).5
Employers are permitted one transfer per week which does not affect their accumulated
points total. Any additional transfers entail a deduction of four points, which must be
added to the financial cost of making a transfer. Once a year, FPL participants are
allowed to hire an unlimited number of footballers with no point penalty.
The points scoring system, i.e. the production function of our firms, is presented
in Appendix Table A1. Footballers score points for playing in that particular week, for
the time spent on the pitch, and for the actions they perform (positive points for goal
scoring, assists and the like, and negative points for own goals, and disciplinary offences
leading to red and yellow cards) and bonus points for overall performance. Bonus points
are awarded to the best three players in each game, again based on some pre-determined
metrics (see Table A1). Productivity is thus objectively measured for all workers.6
5
There is a gap between the buying and selling prices of players. This margin is half of the difference
between the current price and the price at which the player was bought; this can be thought as a tax on the
value added. As such, transferring players has a financial cost and leads to a reduction in the firms’ budget.
So firms may not always optimize their teams and may refrain from using their weekly transfer.
6
The productivity measure is largely independent of the referee – apart from disciplinary offences - so the
behaviour of players is unlikely to be directly affected by referees’ discrimination (Parsons, Sulaeman,
Yates and Hamermesh, 2011).
8
Demand for particular players reflects what is known about their on-field
performance, i.e. their productivity, as well as their cost to the employer – as determined
by the market value of the player set by FPL – and employers’ personal preferences.
Employers have excellent information on each footballer’s performance across the
dimensions described in Table A1, both in previous years when the season starts and in
the past games as the season progresses. As such, information about the productivity of
each potential worker improves over time, and is available to all firms. The summary
information presented for each footballer contains a colour picture, as well as his
position, team, the proportion of other employers who have that player in their squad, his
performance in recent matches, his current market value, upcoming fixtures, the number
of games the player is scheduled to play this week (usually one, but occasionally zero or
two) and an injuries update. It also includes a colour picture of the player (see Figure
A1). These pictures were used to determine the race of each footballer via face
recognition software, using a dichotomous categorisation: white, non-white.7
Eight features of this setting mean that we can recover more precise estimates of
racial discrimination in relation to hiring than is possible in other settings. First, we are
able to identify the effects of taste-based employer discrimination, as opposed to the
effects of customer, co-worker or statistical discrimination. There is no possibility of
customer discrimination since employers do not have clients. 8 Team production is simply
additive in individual workers' production; the absence of co-worker relations means
there is no co-worker discrimination. It also means that we can ignore productivity spill-
7
There are few players defined as other races – for the analysis they have been grouped with black players.
When ambiguities arose the ethnicity variable was defined by three individuals and a simple majority rule.
8
In a real world setting customer discrimination can affect team selection via crowd attendance at games
(Bryson et al., 2014).
9
over across workers, which would complicate recruitment and retention decisions by
bringing in factors other than individual talent. Employers have access to comprehensive
weekly data on the productivity histories of all workers in the industry, together with their
market prices, so their information set regarding worker value is much richer than would
ordinarily be the case. Since the productivity of every worker in the industry (not only the
employer’s own employees) is perfectly known, at least as the season progresses, there is
no scope for statistical discrimination. Employers also know the skin colour of all
workers in the population of potential recruits: it is not just proxied by name as in many
field experiments (Bertrand et al, Mulainathan, 2004, for example).9 They are therefore
able to account fully for the performance of workers and their race in decisions
concerning recruitment and retention. Thus, if there are any indications of racial bias,
they are unlikely to reflect anything but employer taste-based discrimination.
Second, employers are free to discriminate in their hiring and firing behaviour. In
this sense we are "turning back the clock" to a time when employers faced no legal
impediments to discrimination. Therefore the costs of discrimination are low and we can
thus identify an unbiased taste for discrimination.
Third, the setting is a single occupation in a single industry, so workers are
perfectly substitutable for one another (within a position on the field), and the full
productivity history of workers is available at no cost; i.e. there is no monitoring cost.
Thus, this study can overcome the problem that, in many observational studies, it is
difficult to compare "like-for-like" workers. There could still be an issue that black and
9
In Germany it is relatively common for job applicants to attach a photograph of themselves to their
applications. Recent correspondence studies in Germany confirm applicants are much less likely to receive
a call back if their photograph indicates they are from an ethnic minority (eg. Weichselbaumer, 2016).
10
white players are not perfect substitutes if there is discrimination on the pitch: i.e.
coaches are less likely to select black players or leave them on the pitch for shorter
periods of time. We will demonstrate below that this is not the case.
Fourth, as in a laboratory experiment, the firms are identical in size, technology
and initial budget. In assembling the workers required by the firm, employers must fill
identical job slots within the firm. At the beginning of the year all employers face the
same budget constraint, so their ability to recruit a mix of more and less talented workers
is identical at the outset, although budgets vary as the season progresses due to value
added (destroyed) when selling workers.
Fifth, although firms are in competition with one another, workers are able to
work at more than one firm simultaneously so that firms are not in direct competition
with one another for worker talent. Thus, in principle, all workers are available for hire,
subject to firms' budget constraints.
Sixth, workers have no say in the firms they join and can only exit if fired, so
there is no selection of workers into more (less) discriminating firms.10
Seventh, employers are price takers: the price of recruiting individual workers, i.e.
a sign-on fee, varies substantially but individual employers are unable to influence these
prices. Prices attached to workers are exogenous to the firm, but relate very strongly to
worker performance, as we shall see. As such, firms cannot exploit minority workers by
offering them lower sign on fees. Once signed, there are no wages in our set up.
10
Worker selection based on perceptions of discriminatory tendencies in particular occupations or among
certain employers may contribute to wage discrimination. For example, Plug et al. (2014) find gays and
lesbians in Australia shy away from more prejudiced occupations.
11
Finally, ours is a dynamic setting with a large number of employers engaged in
many transactions over 38 periods. We are therefore able to estimate influences on
employer hiring and firing decisions over time, including the role of change in the
competitive environment.
One might question whether employers would express their discriminatory
preferences in a set-up like the FPL since there is no physical interaction between
employers and employees.11 However, it is not always the case that in large firms most of
the individuals involved in the hiring decision will have to meet an employee later on.
But, perhaps more importantly, psychologists have shown that pictures of unknown outof-group individuals trigger more activity in the amygdala, a subcortical structure of the
brain involved in emotional learning and in particular danger, than pictures of unknown
in-group members (Hart et al., 2000). This activity was positively correlated with other
measures of unconscious racial bias, such as the Implicit Association Tests, or eyeblink
startle, but not to the modern racism scale (Phelps et al., 2000). This indicates that
discriminatory behaviour is controlled unconsciously - what Kahneman (2011) calls
"system 1" - and does not require physical contact.
One might also question whether FPL employers will spend the time and effort to
optimise in what seems to be a low-stakes game. In fact, participants spend a
considerable amount of time thinking about their team picks and adjusting their squad.
Furthermore, part of the motivation comes from competition against work colleagues or
friends in mini-leagues where winners’ “bragging rights” are highly prized. 12
11
Alternatively, one could argue that the absence of interaction makes it easier to discriminate.
A 2008 survey of fantasy league participants in the United States revealed that the three main reasons to
participate were enjoyment, competition with others and pressure from peers (Baerg, 2009).
12
12
3.2: Player Data Description
Each week, the FPL participants select the 11 players from their 15 man squad
who will score points for their fantasy team depending upon their performance in real
football games played that week, as well as a captain whose productivity will be doubled.
The data available to us contains the weekly team composition of every single participant
for the full period of the league. As such, we can identify which player got hired/fired, as
well as the allocation of captaincy and allocation to the bench (the four non-scoring
players of that week).13 As in most audit studies, we have limited knowledge on the
characteristics of the participants, we only know their self-reported country of
residency14, previous experience of playing the FPL and past performance.
To these data we have added the characteristics (age, gender, nationality),
including race, of the 670 footballers registered in one of the 20 football teams playing in
the Premier League in the season of interest. 30% of footballers in the league are black,
however the share varies considerably by position from 1% for goalkeepers to 39% for
forwards. Each club plays 38 games in the season, we thus have an unbalance panel of
22910 observations on point tally, price and transfer on the FPL market of each footballer
on a game to game basis. The player performance data available to all employers comes
from FPL, which runs the fantasy league. Players' productivity is based on rudimentary
objectively verifiable data of their performance in a game, as explained above and in
13
Players on the bench will automatically be included as point scoring players if one of the selected point
scoring players did not play. As such, we observe the allocation to the bench with some measurement error.
14
While based on the English Premier League, the FPL is open to anybody (the website now lists 6
different languages). 55% of participants listed the UK as their country of residence, with an additional
25% residing in the West.
13
Appendix Table A1. Individual points in a given week range between -4 and +24 with a
mean of 1.3.15 Points scored by players is of interest in its own right since we can
establish to what extent there are any racial differences in the distribution of productivity
between white and black footballers. Figure 1A reports a large overlap in the distribution
of the (log) total number of points scored over the season by race but the distribution for
white players is shifted to the right. The average total point accumulated by footballers is
actually significantly different between race (26.4 vs 22.8), so black and white players
appear to be close but not perfect substitutes, with the superstar footballers being
disproportionally white.16 The racial difference in performance seems to be mostly driven
by footballers playing in the midfield position (Figure 1B-1D). We find little evidence of
differences in productivity between players of different races, consistent with Goff et al.'s
(2002) contention that top-flight professional sports are racially integrated (see below)
[FIGURE 1 A-D]
Time on the pitch enters our performance metric. But this could itself be a
function, in part, of racial discrimination among "real world" Premiership coaches if their
decisions regarding who to play and how long to play them for are racially biased, either
because they are responding to customer preferences for white players, or because they
are indulging their own taste-based discrimination or statistical discrimination. There is
some evidence of racial differences in playing times; blacks are marginally less likely to
play (45.4% vs 41.4%) and conditional on playing, play for five minutes less. The
differences in playing time disappear when controlling for position, and thus mostly
reflect the differences in the distribution of position between races.
15
16
Not all footballers play in a given week, so the mode score is actually zero.
This differs from the data used in Bryson and Chevalier (2015) which refers to different seasons.
14
The second main determinant of demand for a player is price. Prices are set by the
FPL and appear to be a function of performance and net demand (see below). After the
initial valuation, players’ prices are reviewed on a weekly basis. In any week, 80% of
prices remain the same, and weekly price adjustments are in general small. Over the
season, price ranges between £3.8 million and £14 million (van Persie) and, on average,
the distribution of prices between races largely overlap (Figure 2A), although the
performance distribution had a longer tail for white players. When separating by position,
some racial differences in the price distribution appear (Figure 2B-2D). Those are mostly
in line with the differences in productivity: white midfielders are more productive and
their price distribution is shifted to the right. For defenders, the price distributions largely
overlap but for forwards the price distribution of black players is of different shape
(bimodal) and shifted to the right. Below we investigate these differences further to
assess whether the FPL sets players’ prices fairly.
[Figure 2A-D]
3.3 Does the FPL function like a labour market?
Before we investigate the racial differences in team composition we need to
establish whether the FPL functions like a labour market. Evidence to this effect is
presented in Figure 3. Panel A and B shows that better performing players in the previous
week are in net demand and show an increase in their price. These effects are particularly
steep for players scoring more than 10 points in a given week, which is a rare event (12%
of observations). This is consistent with a market for superstars, as originally conceived
by Rosen (1981). Unsurprisingly, price variation and net demand (Panel C) are highly
correlated, especially over the price change region [-0.2,0.1] which includes 98% of
15
observations. Overall, the FPL appears to behave like a labour market, where more
productive workers are in higher demand and command higher fees. These relationship
do not appear to differ by race
[FIGURE 3 A-C]
3.4 Local leagues and competition
Eighty-two percent of FPL participants join at least one local league, usually
consisting of family, friends and work colleagues. One can reasonably expect to do well
in these leagues because most are small (Figure 4). Because competitors are known there
are likely strong incentives to win associated with “bragging rights”. We use one’s rank
position in local leagues and the points distance between one’s own team and the teams
above and below to construct the relative performance measures that capture competitive
pressures (see Section Four).
[FIGURE 4]
4.
EMPIRICAL STRATEGY
We first investigate the overall team composition at the onset of the season and
over time as the season progressed and information about players’ productivity and the
overall team performance becomes more precise. To do so, we define the racial
composition of the team based on the proportion of non-whites in different positions
within the team. We construct a discrimination index based solely on outfield players
which sums the proportion of non-whites in different playing positions thus:
(1)
16
From this we construct dummy variables identifying employers who discriminate
against black players and those discriminating against white players. A randomly picked
team would be 30.2% non-white. We define an employer as discriminating against black
players when the fraction of black players in the team is at least one standard deviation
away from the mean (B0=26.7) :
(2)
Similarly an employer is deemed to discriminate against white players when the
fraction black is more than 33.7%.
(3)
First we estimate the probability of discriminating at the beginning of the season
when the employer first picks a squad as in equation (4):
(4)
Xi includes the few observable characteristics we have regarding participants
(region of origin, past participation to the FPL, performance in past participation (last
year and best ever), and numbers of private leagues entered as a proxy for interest in the
game).
We observe dynamics in team selection over 38 periods. As such we can estimate
whether the racial composition of a team changes as the season progresses, and
employers learn about the costs of discriminating arising from competition, as captured
by the team’s relative performance. We measure relative performance in terms of an
employer’s rank position in the mini-leagues and the points distance between the team
and those teams directly above and below the team in the mini-leagues.
17
We can run static versions of this model as in equation (5):
(5)
We also run dynamic models where we interact our competition measure with
time as in equation (6):
(6)
The equivalents of the above models are also run for the dummy variables
capturing discrimination against black players and white players respectively.
There are three reasons to suspect that discriminatory behaviour of employers
may diminish over the course of the season. First, as Antonovic et al. (2005: 923) note in
the context of The Weakest Link TV show, "the implicit cost of taste-based discrimination
rises as the game progresses (because one's probability of winning the game is higher in
later rounds) discriminatory outcomes due to taste-based discrimination should diminish
over time". Similarly, the cost of discrimination may become clearer over time. As such,
we would expect discriminatory behaviour to decrease over time in the FPL.
Second, whereas at the start of the season employers must rely on player
performance information from the previous season, employer information about player
performance is continually up-dated throughout the season such that, if there is any
uncertainty regarding productivity at the outset that could induce some statistical
discrimination, this dissipates over time as employers observe player’s "form", including
that of footballers they have not selected such that the information on productivity is
perfect and covers the full set of employees and potential employees.
18
Third, there may be non-random attrition such that the employers remaining
active in the league later on may not be representative of those who began the season.
For example, it may be those who are most committed to winning, or have the greatest
chance of winning, who continue to hire and fire to the end of the season. Figure A2
displays the fraction of active participants in the FPL, where active is defined as having
traded a player at least once in the last three weeks. It is apparent that market activity
declines over the course of the season, perhaps reflecting falling effort as most employers
find they are unable to win, or growing employer perceptions that they have optimised in
the face of budget constraints. The decline in participation is linear; and by the last week
of the season only 40% of initial participants are still actively playing the game. If we
assume that discriminatory behaviour is costlier for these employers still playing towards
the end of the season (since under-performance via discrimination is most keenly felt by
these employers) differential attrition should mean discrimination declines over the
season (see below).
As Kahn (2009: 14-15) notes, identification of racial bias in hiring and firing
decisions is best investigated using performance differences of marginal workers, as
opposed to the average worker because only the former is informative about the margin
where the hiring/firing decision is made. This is precisely what we observe in our data
since all players are available for hire by all employers at any point in time, and can be
dismissed with the low dismissal costs described in Section Three. We thus estimate the
probability of a team member to be fired, and whether at a given level of recent
performance, race matters. Similarly, we can investigate the hiring decision, on a weekly
basis. Another unique attribute of our dataset, is that we can focus on another set of
19
marginal player, the team captains. Each week, participants nominate one of their player
as the team captain, the points accrue to this player in that week are doubled.17 The costs
of discriminating on captaincy are thus twice as large as on any other players.
For all these decisions on marginal players, we estimate the following model,
where H can be hiring, firing or captaincy. The subscript p refers to a footballer. Xit and
Xpt are team and player’s characteristics.
(7)
5.
RESULTS
5.1
Racial mix
Figure 5 presents the distribution of team racial mix at the beginning of the
season, after 15 weeks and 30 weeks. The horizontal axis is the discrimination index
where zero corresponds to no discrimination, the red bar to the left identifies the point at
which black discrimination occurs and the red bar to the right identifies the point as
which white discrimination occurs, as per the definitions presented in Section Four.
[FIGURE 5]
There is a large dispersion in racial mix, with the distribution skewed to the left
indicating the average employer has fewer black players than if they had been chosen
randomly. In week one 20.6% of employers deviate by more than one standard deviation
17
The participant also nominates a vice-captain. If the nominated captain ends up not entering the pitch on
that week, the vice-captain points tally is doubled. If neither the captain nor vice-captain play, no player
gets his points doubled.
20
to the left, indicating discrimination against black players, while 12.2% are more than one
standard deviation to the right and thus discriminating against white players.
It is also apparent that the distribution shifts to the left over time, indicating
increasing discrimination against black players.
The same results are illustrated in Figure 6 using log number of picks by race in
weeks 1 and 30.
[FIGURE 6]
Table 1 presents the determinants of discrimination in period 1. The models are
not able to explain much of the overall variance in discriminating behaviour when
employers pick their first team of the season. It is notable that those employers who had
performed better in the previous season were less likely to discriminate. However, there
is no clear evidence of a role for competition as indicated by the number of local leagues
the employer’s team are entered in. Not playing in a local league is positively associated
with discriminating, but only against white players: not being in a local league is actually
associated with a lower likelihood of discriminating against black players in picking
one’s first team of the season.
[TABLE 1]
Table 2 runs similar estimates but this time focuses on discrimination against
black players and distinguishes between player position to look at employer choices
among clearly substitutable players. There are no co-variates with coefficients that are
stable across player type.
[TABLE 2]
21
5.2
Marginal workers
Table 3 presents estimates of employers’ propensity to discriminate across all 38 periods
using panel data with employer fixed effects. The coefficients therefore capture withinperson influences on FPL participants’ propensity to discriminate over time. Worse
relative performance – captured by the team’s rank in the local league – reduces the
propensity to discriminate against black players in the next period, but increases the
likelihood of discriminating against white players. The points distance between a team
and its nearest rivals is only statistically significant in the case of discrimination against
white players: one’s distance from near competitors increases discriminatory behaviour,
as Becker would have predicted.
[TABLE 3]
5.3
Local Competition and Discrimination over time
Figure 7 shows the effects of competition over time on the propensity to
discriminate using the discrimination index. The estimates presented are from OLS
regressions of racial mix with interactions between weeks and the variables representing
local competition. The role of team rank in the propensity to discriminate is rising over
time, with FPL participants reacting more strongly to their immediate competitors above,
particularly in the last third of the season. A similar pattern emerges using the alternative
black discrimination dummy as the dependent variables (Figure 8).
[FIGURES 7 AND 8]
5.4
Discrimination and Productivity
22
Table 4 estimates the productivity loss (normalized as a percentage of the maximum)
arising from discrimination. There is a weak relationship between racial mix and
performance, with whiter teams having a lower loss. Lower competition from below
tends to increase loss, perhaps due to a reduction in effort.
[TABLE 4]
The productivity loss associated with racial mix in presented graphically in Figure 9. The
loss is defined as the gap from the weekly production frontier. There appear to be slight
gains from having a whiter team and large losses from having a very black team.
[FIGURE 9]
Finally in Figure 10 we look at the dynamic effects of competition on the loss function. It
would appear that the effect of team racial mix on production losses is fairly stable over
the season.
[FIGURE 10]
6.
CONCLUSIONS
In a perfectly competitive market, where employers can indulge in their taste for
discrimination, we find that a large fraction of them assemble teams of workers whose
racial composition is not representative of the workers’ racial mix. However, the costs of
discrimination, in term of lost productivity appear low. In our context where workers are
close substitutes we find some evidence of racial discrimination in hiring decisions which
increases over time. Discriminating employers forfeit about 1% of production per week.
Employers facing more competition do not appear more likely to either change behaviour
or disappear from the market.
23
References
Altonji, J. G. and Blank, R. M. (1999) "Race and gender in the labor market", Chapter
48, Handbook of Labor Economics, vol. 3, 3143-3259
Al-Ubaydli, O. and List, J. A. (2016) “Field Experiments in Markets”, NBER Working
Paper No. 22113
Antonovics, K., Arcidiacono, P. and Walsh, R. (2005) "Games and Discrimination:
Lessons from The Weakest Link", The Journal of Human Resources, XL, 4: 918947
Arrow, K. J. (1972) "Models of job discrimination" in A. H. Pascal (ed.) Discrimination
in Economic Life, pp. 83-102, Lexington, MA: Lexington Books
Arrow, K. J. (1973) "The Theory of Discrimination" in O. Ashenfelter and A. Rees
(eds.) Discrimination in Labor Markets, pp. 3-33, Princeton, NJ, Princeton
University Press
Baerg, A. (2009) “Just a Fantasy? Exploring Fantasy Sports”. Electronic Journal of
Communication, 19, 3.
Becker, G. S. (1957) The Economics of Discrimination, Chicago: Chicago University
Press
Bendick, M., Jr. (2007) "Situation Testing for Employment Discrimination in the United
States of America", Horizons Strategiques, 3(5): 17-39
Bertrand, M. and Mullainathan, S. (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
Bodvarsson, O. B. and Brastow, R. T. (1999) "A Test of Employer Discrimination in the
NBA", Contemporary Economic Policy, 17, 2: 243-244
24
Brown, E, Spiro, R. and Keenan, D. (1991) "Wage and Nonwage Discrimination in
Professional Basketball: Do Fans Affect It?", American Journal of Economics
and Sociology, 50, 3: 333-345
Bryson, A., Rossi, G. and Simmons, R. (2014) "The Migrant Wage Premium in
Professional Football: A Superstar Effect?", Kyklos, 67, 1: 12-28
Caminade, J., List, J. A., Livingston, J. A., and Picel, J. (2016) “When the Weak
Become Weaker: The Effect of Market Power on Third Degree Price
Discrimination”, University of Chicago mimeo
Charles, K. and Guryan, J. (2008) "Prejudice and the Economics of Discrimination",
Journal of Political Economy, 116(5): 773-809.
Charness, G. and Kuhn, P. J. (2010) "Lab Labor: What Can Labor Economists Learn
from the Lab?", NBER Working Paper No. 15913
Doleac, J. L. and Stein, L. C. D. (2013) "The Visible Hand: Race and Online Market
Outcomes", The Economic Journal, 123, F469-F492
Dovidio J. F, and Gaertner, S.L (2000) "Aversive racism and selection decisions",
Psychological Science, 11(4):315–19
Feld, J., Salamanca, N. and Hamermesh, D. S. (2013) "Endophilia or Exophobia:
Beyond Discrimination", NBER Working Paper No. 19471
Goff, B. L., McCormick, R. E., and Tollison, R. D. (2002) “Racial Integration as an
Innovation: Empirical Evidence from Sports Leagues”, The American Economic
Review, 92, 1: 16-26
Goldin, C. and Rouse, C. (2000) "Orchestrating impartiality: the impact of 'blind'
auditions on female musicians", American Economic Review, 90, 4: 715-741
25
Guryan, J. and Charles, K. K. (2013) “Taste-based or Statistical Discrimination: The
Economics of Discrimination Returns to Its Roots”, The Economic Journal, 123,
F417-F432
Hamilton, B. H. (1997) "Racial Discrimination and Professional Basketball Salaries in
the 1990s", Applied Economics, 29, 3: 287-296
Hart, A., P. Whalen, L. Shin, S. McInerney, H. Fischer and Rauch S. (2000) Differential
response in the human amygdala to racisal outgroup vs ingroup face stimuli.
Neuroreport, 11, 2351-2354
Kahn, L. M. (2006) “Race, Performance, Pay, and Retention Among National
Basketball Association Head Coaches”, Journal of Sports Economics, 7: 119149
Kahn, L. M. (2009) "The Economics of Discrimination: Evidence from Baseball", IZA
Discussion Paper No. 3987
Kahneman D. (2011) Thinking, Fast and Slow. Farrar, Straus and Giroux.
Lang, K. and Lehmann, J. K. (2011) "Racial Discrimination in the Labor Market:
Theory and Empirics", NBER Working Paper Number 17450
Levitt, S (2004) “Testing Theories of Discrimination: Evidence from The Weakest
Link.” Journal of Law and Economics, 47(2): 431–52
List, J. A. (2004) "The Nature and Extent of Discrimination in the Marketplace:
Evidence from the Field", The Quarterly Journal of Economics, 119, 1: 49-89
Nardinelli, C. and Simon, C. (1990) "Customer racial discrimination in the market for
memorabilia: the case of baseball", The Quarterly Journal of Economics, 105, 3:
575-595
26
Pager, D. and Shepherd, H. (2008) "The Sociology of Discrimination: Racial
Discrimination in Employment, Housing, Credit and Consumer Markets",
Annual Review of Sociology, 1, 34: 181-209
Parsons, C., Sulaeman, J., Yates, M. and Hamermesh, D. (2011) Strike Three:
Discrimination, Incentives and Evaluation. American Economic Review, 101,
1410-1435
Phelps, E., K. O’Connor, W. Cunnignham, E. Funayama, C. Gatenby. J. Gore and
Banaji, M. (2000) Performance on Indirect Measures of Race Evaluation Predict
Amygdala Activation. Journal of Cognitive Neuroscience, 12, 729-738
Plug, E., Webbink, D. and Martin, N. (2014) "Sexual Orientation, Prejudice and
Segregation", Journal of Labor Economics, 32, 1: 123-159
Phelps, E. (1972) “The Statistical Theory of Racism and Sexism”, American Economic
Review, 62, 4:659-661
Pope, D., and Sydnor, J. (2011) “What’s in a picture? Evidence of Discrimination from
Prosper.com”, Journal of Human Resources, 46, 1: 53-92
Rosen, S. (1981) "The economics of superstars", American Economic Review. 71; 845–
858
Rosen, S. and Sanderson, A. (2001) "Labour Markets in Professional Sports", The
Economic Journal, 111, F47-F68
Weichselbaumer, D. (2016) “Discrimination against female migrants wearing
headscarves”, IZA Discussion Paper No. 10217
Zussman, A. (2013) "Ethnic Discrimination: Lessons from the Israeli Online Market for
Used Cars", The Economic Journal, 123, F433-F468
27
.4
.5
.2
C] Midfielders
2
4
6
Log Total points
.3
Black
.1
White
.2
0
kdensity ltpoints
0
.1
kdensity ltpoints
.3
.4
Figure 1 : Distribution of (log) total number of points by race
A] All players
0
B] Defenders
.4
0
2
4
6
Log Total points
Black
White
4
Black
5
.2
.15
2
3
Log Total points
.1
1
.05
0
kdensity ltpoints
.1
.25
.3
.2
D] Forward
0
kdensity ltpoints
.3
White
0
2
4
Log Total points
White
28
Black
6
Figure2: Distribution of (log) price by race
C] Midfielders
2
1.5
1
kdensity lprice
1.5
1
0
0
.5
.5
kdensity lprice
2
A] All Players
1
1.5
2
log price
White
2.5
3
1.4
1.6
1.8
2
2.2
2.4
lprice
Black
White
B] Defenders
Black
1
kdensity lprice
1.5
1
.5
.5
0
0
kdensity lprice
1.5
2
2
2.5
D] Forwards
1.4
1.6
1.8
2
lprice
White
1.5
2
2.5
lprice
Black
White
29
Black
3
Figure 3: Does FPL function like a labour market?
100000
0
50000
Weekly net transfer
150000
A] Lagged player performance and net demand
0
10
lagged performance
White
20
30
Black
.15
.1
.05
0
Weekly Price variation
.2
.25
B] Player lagged performance and weekly price change
0
10
lagged performance
White
20
30
Black
.1
0
-.1
-.2
Weekly Price variation
.2
.3
C] Weekly price change and net demand
-200000
-100000
0
100000
Weekly net transfer
White
200000
Black
0
300000
6.0e+04
4.0e+04
0
2.0e+04
Frequency
8.0e+04
Figure 4: Local League Size
0
10
20
30
Number of participants in league
1
40
Figure 5: Distribution of team racial composition over time
2
2
1.5
1
.5
0
kdensity lingame
Figure 6: Log Player’s Pick By Race, in Week 1 and 30
9
9.5
10
Ln Nbr of picks
week 1- black
week 1- white
10.5
week 30- black
week 30- white
3
11
60
40
0
20
Lag rank Estimates
80
100
Figure 7: Estimates of the Effect of Competition Over-Time – version 1Competition Index
A- Local League Rank
0
10
20
Week
30
40
15
10
5
0
Lag % to above competitor Estimates
20
B- % deficit to participant above
0
10
20
Week
30
40
5
0
-5
-10
-15
Lag % to below competitor Estimates
10
C- % advantage over participant below
0
10
20
Week
30
40
Note: Estimates from OLS regression of racial mix with interactions between weeks and the variables
representing local competition.
0
0
-10
10
20
Week
30
40
-8
-6
-4
-2
0
B- % deficit to participant above
0
10
20
Week
30
40
10
20
30
C- % advantage over participant below
0
Lag rank Estimates
-20
-30
-40
0
-10
Lag % to below competitor Estimates
Figure 8: Estimates of the Effect of Competition Over-Time – version 2- Black
discriminator dummy
A- Local League Rank
0
10
20
Week
30
1
40
Note: Estimates from OLS regression of racial mix with interactions between weeks and the variables
representing local competition.
0
.2
.4
.6
.8
Figure 9: Racial Discrimination and Production Loss
-2
0
2
4
Normalised share of non white in team
2
6
2
0
-2
Estimates on Loss
4
Figure 10: Estimates of team composition on loss function over time
0
10
20
Week
Black discrimination
30
40
White discrimination
Note: Estimates from a fixed effect model of the interactions between week, black/white
discrimination and discrimination index on the weekly loss function.
3
Table 1: Determinants of Discrimination in Period 1
Discriminate Discriminate
Index
Black
Points in FF last
-0.007
-0.003
(1.30)
(1.35)
Season (normalized)
Nbr Local Leagues I
-0.009
0.001
Nbr past participation
Played in FF last season
Best ever rank in FF
West
Rest of the world
Unknown
Nbr participants in local
league
Not playing in a Local
League
Constant
(2.13)*
Discriminate
neither
0.007
(2.67)**
-0.004
0.003
(1.06)
(5.41)**
(2.83)**
-0.017
0.006
-0.002
-0.004
(3.23)**
(2.84)**
(1.15)
(1.70)
(4.10)**
Nbr Local Leagues II
Discriminate
White
-0.004
0.003
-0.001
0.001
0.001
(1.23)
(1.23)
(0.82)
(0.51)
-0.040
-0.007
-0.015
0.022
(1.16)
(0.53)
(1.34)
(1.40)
0.000
-0.000
0.000
0.000
(9.71)**
(7.51)**
(6.92)**
(1.81)
-0.042
0.024
0.004
-0.027
(0.97)
(1.34)
(0.27)
(1.37)
-0.029
-0.008
0.017
0.012
(0.18)
(0.98)
(0.90)
(1.50)
0.033
0.003
0.023
-0.027
(0.55)
(0.14)
(1.23)
(0.99)
-0.000
0.000
-0.000
-0.000
(1.06)
(1.45)
(0.94)
(0.62)
0.044
-0.009
0.011
-0.002
(4.58)**
(2.42)*
(3.65)**
(0.41)
0.141
0.251
0.095
0.654
(3.14)**
(13.94)**
(6.68)**
(32.04)**
R2
0.01
0.00
0.01
0.00
Note: Model estimated by OLS. Number of observations 98,351. T-stat reported in parentheses.
4
Table 2: Determinants of Discrimination against black player in Period 1 – by
player’s position
Discriminate Discriminate
Discriminate
Defender
Mid-fielder
Forward
Points in FF last
0.002
0.012
-0.014
(1.06)
(5.57)**
(7.31)**
Season (normalized)
Nbr Local Leagues I
0.003
0.004
-0.005
(3.19)**
Nbr Local Leagues II
Nbr past participation
Played in FF last season
Best ever rank in FF
West
Rest of the world
Unknown
Nbr participants in local
league
Not playing in a Local
League
Constant
(4.86)**
(5.91)**
0.008
0.006
-0.005
(3.75)**
(3.09)**
(2.72)**
-0.004
0.002
0.000
(3.80)**
(2.05)*
(0.06)
0.008
0.089
-0.091
(0.55)
(6.55)**
(7.33)**
-0.000
-0.000
0.000
(8.23)**
(5.29)**
(3.32)**
0.000
0.024
0.003
(0.01)
(1.41)
(0.21)
-0.014
0.027
-0.001
(0.81)
(1.57)
(0.08)
-0.027
0.024
0.002
(1.12)
(1.00)
(0.10)
0.000
0.000
-0.000
(0.33)
(4.11)**
(1.85)
-0.013
-0.005
-0.004
(3.20)**
(1.31)
(1.03)
0.315
0.215
0.175
(17.10)**
(12.05)**
(10.78)**
R2
0.01
0.01
0.01
Note: Model estimated by OLS. Number of observations 98,351. T-stat reported in
parentheses.
31
Table 3: Determinants of Discrimination in all Periods – Individual Fixed Effect
Model
Discrimination
Discriminate Discriminate Discriminate
index
Black
White
neither
Points last week (norm)
-0.005
0.002
-0.001
-0.001
(13.30)**
(7.76)**
(9.05)**
(2.99)**
Lag Total points (norm)
0.024
-0.012
0.001
0.011
(30.79)**
(26.63)**
(4.31)**
(22.60)**
Lag Local League rank
0.571
(22.68)**
Lag % point to
competitor above
(1.46)
Lag % point to
competitor below
(0.91)
Constant
0.002
0.008
-0.017
-0.190
(13.59)**
0.100
(14.35)**
0.090
(5.93)**
-0.001
(0.85)
0.001
(2.37)*
-0.000
(0.31)
0.009
(1.89)
0.011
(4.80)**
-0.020
(3.96)**
0.311
0.076
0.613
(898.80)**
(442.47)** (1,635.71)**
Note: Number of individuals 98,351, Number of observations 3,638,987. T-stat reported
in parentheses.
(27.79)**
32
Table 4: Productivity loss (Normalised as % of maximum)
Normalised loss Normalised
loss
OLS
FE
Index<=0 * Index
0.030
0.002
(31.78)**
Index>0 * index
Lag Local League rank
(9.27)**
0.004
-0.001
(4.50)**
(7.53)**
0.264
-0.198
(15.51)**
(5.23)**
Lag % point to
competitor above
0.006
0.000
(2.22)*
(0.10)
Lag % point to
competitor below
(20.20)**
Constant
0.212
0.164
(13.10)**
-0.152
-0.012
(10.64)**
(8.50)**
Note: Number of individuals 98,351, Number of observations 3,638,987. T-stat reported
in parentheses. Clustered at the week level
33
34
APPENDIX
TABLE A1: POINTS SYSTEM IN FANTASY FOOTBALL
ACTION
Playing up to 60 minutes
Playing 60 minutes or more
For each goal scored by a goalkeeper or defender
For each goal scored by a midfielder
For each goal scored by a forward
For each goal assist
Clean sheet by a goalkeeper or defender
Clean sheet by a midfielder
For every 3 shot saves by a goalkeeper
For each penalty save
For each penalty miss -
POINTS
1
2
6
5
4
3
4
1
1
5
-2
For every 2 goals conceded by a goalkeeper or defender
For each yellow card
For each red card
For each own goal
Bonus points for the best players in a match
-1
-1
-3
-2
1/3
BONUS POINTS:
The three best performing players in each match according to the Bonus Points System
will receive additional bonus points. 3 points will be awarded to the highest scoring
player, 2 to the second best and 1 to the third. The Bonus Points System is based on
statistics on various dimensions of the player’s performance collected by OPTA
(http://www.optasports.com/).
35
APPENDIX FIGURE A1
36
Figure A2: Participant Attrition Over Time
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
Note: Active participants are defined as participants who have traded at least once in the
last three weeks.
37