What Happens When Employers are Free to Discriminate .../file/F3_bryson.pdf · Evidence from the English Barclays Premier Fantasy Football League Alex Bryson National Institute of

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What Happens When Employers are Free to Discriminate?

Evidence from the English Barclays Premier Fantasy Football League

Alex Bryson

National Institute of Economic and Social Research

Centre for Economic Performance, LSE

Arnaud Chevalier

Royal Holloway, University of London

Centre for the Economics of Education, LSE

and IZA

DRAFT: VERY PRELIMINARY

Version v1: June 2012

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ABSTRACT

Research on employers’ discrimination is limited by the unlawfulness of such activity. As

such, researchers have focused on the intention to hire, rather than hiring decisions and

wage settlements. Instead, we rely on a virtual labour market, the UK Fantasy Football

league, where employers can freely exercise their taste for racial discrimination in terms

of hiring, firing and market valuation . We find black players are valued more highly

than white players, but the difference disappears after controlling for on-field

performance and other observable characteristics. However, the market values player

performance differently according to race. There is a greater valuation of black player

performance relative to white player performance in the lower parts of the performance

distribution, whereas at high performance levels white player performance is valued more

highly than black player performance. There is also evidence that employers evaluate

player performance differently by race when making hiring and firing decisions.

Employer demand for players rises with their performance, but less so in the case of

black players. This finding is consistent with racial discrimination. However, there is no

racial differential in the weight employers attach to performance in the most recent game:

this has a large effect on employers' decision to hire players for the next game regardless

of race.

Key words: race; labour market discrimination; football

JEL: J15; J23; J24; J71; M51

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1. INTRODUCTION

In most advanced economies it is unlawful for employers to discriminate against

individuals either directly or indirectly on grounds of race, either in their recruitment

practices or once an individual has become an employee.1 Despite anti-discrimination

legislation numerous studies suggest that employers do discriminate on grounds of race.

One set of studies identifies discrimination by seeking to control for differences across

workers in wage regressions, treating remaining racial differences as evidence of

discrimination. Others use field experiment techniques to identify employer

discrimination in recruitment by assigning job applicants' attributes and submitting

curricula vitae to real job vacancies. Those studies identify a reduced likelihood of an

employer "call back" for black applicants relative to identical candidates whose race has

been assigned as "white". However, the first type of study is often limited by the lack of

individual level productivity measures, while the second type only identify possible

discrimination at one (early) stage of the hiring process.

This paper contributes to the literature because we are able to identify the value

employers attach to workers in an environment where discrimination is not unlawful

(information regarding the workers employed remains private to the firm), productivity

is measured at no cost by all employers and wages are observed. Moreover, firms are all

identical, only employers decide on labour matches and the labour market is non-

excludable: i.e. workers can be observed in more than one firm at the same time.

1 There are exceptions. Policies of "positive discrimination" and "affirmative action" may permit employers

to discriminate in favour of minority groups who are identified as particularly disadvantaged in the labour

market.

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We analyse data from the UK Barclays Premier League Fantasy Football. This is a

competition entered by 2.8 million individuals each season. The purpose is to be the best

performing team in the fantasy league, something that is achieved by accumulating points

related to the performance of professional footballers on the pitch. Seven features of this

setting mean that we can recover more precise estimates of racial discrimination in

relation to hiring and firing and workers' market value than is possible in other settings.

First, we are able to identify the effects of taste-based employer discrimination as

opposed to effects of customer, co-worker or statistical discrimination. There is no

possibility of customers’ discrimination - something that may influence employers via

crowd attendance at games - since employers do not have clients. There is no team

production: the absence of co-worker relations means there is no co-worker

discrimination. It also means that we can ignore the importance of productivity spill-over

across players which would complicate recruitment and retention decisions by bringing in

factors other than individual talent. Employers have access to very 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. They also know the skin colour of all workers in the population of

potential recruits. They are therefore able to account fully for the performance of

workers and their race in decisions concerning recruitment and retention. Thus, if there

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are any indications of racial bias, they are unlikely to reflect anything else but employer

discrimination.2

Second, the costs of discrimination to employers are lower in our setting than would

ordinarily be the case so that, other things equal, we would expect a greater likelihood of

discriminatory behaviour than might be the case in other settings. In our setting

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. Furthermore, the costs of dismissal are zero: employers are able to off-

load workers as they wish and without financial costs.

Third, the setting is a single occupation in a single industry, so workers are good

substitutes for one another, and the full productivity history of workers is available at no

cost. There is also no monitoring cost. Thus this study can overcome the problem that, in

many studies, it is difficult to compare "like-for-like" workers. Fourth, the firms are very

similar. All firms are identical in size and production function. In assembling the

workers required to run the firm the employer must fill particular job slots within the

firm. At the beginning of the year all employers face the same budget constraints, so their

ability to recruit a mix of more and less talented workers is identical at the outset,

although budgets vary with firm success in competing with others and in buying and

selling workers as the season progresses. Fifth, although firms are in competition with

2 In this sense, our study is unique. As Altonji and Blank (1999: 3195) state in their review of the sports

discrimination literature: "Studies that relate salaries directly to player specific performance measures

cannot distinguish between consumer discrimination, employee discrimination, or employer

discrimination".

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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 which, at least at the

outset, are identical. Sixth, workers have no say in the firms they join, so there is no

selection of workers into more (less) discriminating firms. Finally, employers are price

takers: the price of recruiting individual workers varies substantially but individual

employers are unable to influence these prices, so the price attached to workers is

exogenous to the firm, but relates very strongly to worker performance.

Our analyses focus on the relationship between race and two labour market outcomes.

First, we consider the price set for workers by the market which, as noted above, operates

beyond the control of particular firms. There is no bargaining. Instead, employers are

price takers. Nevertheless, it may be that the market-set wage is itself discriminatory if

market value is affected by race having accounted for individual worker performance.

Second, we examine what role, if any, workers' race plays in employers' decisions to

recruit and retain them, conditional on their productivity and other factors.

We find black players are valued more highly than white players, but the difference

disappears after controlling for on-field performance and other observable characteristics.

However, the market values player performance differently according to race. There is a

greater valuation of black player performance relative to white player performance in the

lower parts of the performance distribution, whereas at high performance levels white

player performance is valued more highly than black player performance. There is also

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evidence that employers evaluate player performance differently by race when making

hiring and firing decisions. Employer demand for players rises with their performance,

but less so in the case of black players. This finding is consistent with racial

discrimination. However, there is no racial differential in the weight employers attach to

performance in the most recent game: this has a large effect on employers' decision to

hire players for the next game regardless of race.

The remainder of the paper is set out as follows. Section Two reviews the previous

literature on racial discrimination in the labour market. 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

There are a variety of reasons as to why employers discriminate on grounds of race.

Profit maximising employers may exploit the labour market vulnerability of certain

groups of workers, such as illegal migrants, by offering them employment at lower wages

than other workers vying for the same positions, leading to an increased propensity to be

taken on but at a lower wage than might otherwise be the case. Alternatively, employers

may have a "taste" for employing individuals "like" themselves, in which case white

employers are engaged in what Becker (1957) termed "taste-based discrimination" when

they offer jobs to whites before non-whites regardless of their aptitude for the job. In such

circumstances, employers may pay a price for their taste-based discrimination if their

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recruitment or promotion procedures are based on skin colour rather than aptitude or

productivity. Alternatively, in the absence of information on prospective employees,

employers may judge the quality of applicants based on group characteristics, such as age

or race, resulting in what has been termed "statistical discrimination". The purpose of

legislation is to reduce employers' propensity to discriminate on grounds of race by

increasing the costs of doing so via penalties attached to discrimination. The deterrent

effect, as with legislation to deter crime, is a function of the size of the penalties and the

probability of detection (Becker, 1968).

In employment there are three possible sources of racial discrimination: the employer, co-

workers, and customers (Becker, 1957). As noted above, there is no interaction between

players chosen by the Fantasy Football employer and employers' hiring and firing

decisions are private information. This means both co-worker and customer effects are

not relevant, allowing us to focus exclusively on employers' taste-based discrimination.

Studies capturing perceptions of racial discrimination in the labour market suggest it

remains commonplace, a finding which is supported by depth interviews with employers

themselves (see Pager and Shepherd, 2008, for a review). In a laboratory experiment

Dovidio and Gaertner (2000) find employers discriminate on racial grounds, but only in

the case of applicants whose qualifications mean the hiring decision is a difficult one.

Reviewing audit studies which identify racial differentials in hiring rates, Altonji and

Blank (1999: 3194) conclude; "the studies to date generally suggest that hiring

discrimination continues to occur". More recently, Bertrand and Mullainathan (2004) find

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substantial racial discrimination in call-backs which is uniform across occupation,

industry and employer size. These field experiment studies are clean in the sense that they

are able to isolate the role of race on hiring through the manipulation of curricula vitae,

but they suffer from the fact that no actual hiring takes place. What they observe instead

are 'call-backs' or offers. In our data real hires occur.

Turning to the sports literature on racial discrimination, the consensus 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". Kahn (1999) suggests that the racial discrimination on compensation in

basketball found in early studies disappeared over time, although there is some evidence

of an unexplained black-white salary shortfall among elite players (Hamilton, 1997).

Further, 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".

There even appears to be some diminution in the degree of customer discrimination. An

early study identified racial discrimination in the value of baseball cards traded by

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individual collectors (Nardinelli and Simon, 1990). The price paid for black and Hispanic

retired baseball players is lower than that for whites conditional on career performance

statistics.3 However, a more recent paper finds no such price differential (Bodvarsson

and Brastow, 1999).

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) 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.

Most of the empirical studies of racial discrimination focus on North American labour

markets, especially the sports literature. However, there is one study that focuses directly

on racial discrimination in English professional soccer. Szymanski (2000) shows that

teams with a higher share of black players have higher performance controlling for

payroll expenditures, a finding which is consistent with racial discrimination. Whereas

Szymanski uses payroll expenditures to proxy for talent, we have direct match-by-match

time-varying data on individuals' on-field labour productivity, measured across a variety

of dimensions.

3 Unlike their study which captures customer discrimination, our private individuals are picking players in

order to win and they are in competition with others.

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3. DATA AND INSTITUTIONAL SETTING

We analyse the virtual market for professional footballers playing in the Barclays Premier

League which is the top flight of professional football in England. We do so using data

from the Barclays Premier Fantasy Football League. This league comprises nearly three

million individuals who sign up to play the game in the course of a season.

Participation in the fantasy league is free. On subscribing employers are given a budget of

£100 million from which they must purchase a squad of fifteen players consisting of two

goalkeepers, five defenders, five midfielders and three strikers. These players are real

players playing professional football in the Barclays Premier League. The employer then

selects the 11 players who will score points for their fantasy team depending upon their

performance in real football games played that week. The points scoring system is

presented in Appendix Table A1. One can see, for example, that players score points for

playing 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). These individual

subscribers are employers in the sense that they buy and sell the players they need in

order to produce points and win the league. The overall winner is the team with more

points than other employers over the course of the season4.

Demand for particular players reflects what is known about their on-field performance,

the cost to the employer – as determined by the market value of the player set by Fantasy

4 There are also monthly prizes for the best scoring team. It is also possible to enter teams in private

leagues, so as to compete amongst friends. These create incentives for fantasy league players to maximize

the number of points scored throughout the season even when an overall win is no longer possible.

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Football staff – and employers’ personal preferences. Employers have excellent

information on each player’s on-field performance across the dimensions described in

Table A1 for each game over the course of the season, together with other information on

the player including injuries. The summary information presented on the first pop-up

page for the employer is a summary of the player’s position, team, the proportion of other

employers who have that player in their squad, his performance in recent matches, his

current market value, and upcoming fixtures. It also contains a colour photograph of the

player which allows the employer to identify his race clearly. This is illustrated in Figure

A1 for Emmanuel Adebayor.

We have match-by-match data on the 600 players in the squads of the 20 football teams

playing in the Premier League in the 2008/09 season.5 Each club plays 38 games in the

season. We have a total of 20,775 player-match observations but we confine our analyses

to those players who play at least once during the season. The estimation sample for

most of our multivariate analyses is 17,554 player-match observations based on 508

players.

Descriptive data for our dependent and independent variables are contained in Appendix

Table A2. Szymanski (2000: 597) notes that there were only 4 black players playing in

the 38 English professional football clubs in his data in 1974. By 1993 black players

were much more common, accounting for around 8 per cent of his sample. In our data

for the Premier League fifteen years later the figure is 38 per cent, well above the

percentage of black people in the English population as a whole. However, as in

5 We hope to add data from subsequent seasons in a revised version of the paper.

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Szymanski's case, there is substantial variance in the use of black players across teams:

21 per cent of appearances for Middlesborough were made by black players, but the

figure was three times higher (65 per cent) at Portsmouth.

The player performance data available to the employers described in Appendix Table A1

comes from Fantasy Football who run the league. Players' productivity is based on

rudimentary objectively verifiable data of their performance in a game, as explained

above. In addition, the Fantasy Football staff are able to allocate three, two or one

discretionary bonus points to the players they thought were the best players on the pitch

for each of the 10 games which occur on a particular match day. Individual points in a

given week range between -4 and +21 with a mean of 1.47. 67

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 productivity of players. If we assume top-flight professional football

played in England is racially integrated we would not expect productivity differences by

race, for reasons discussed by Goff et al. (2002) in their study of North American

basketball and baseball.8

Time on 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

6 On a few occasions during the seasons, teams actually play two games in a fantasy league week. When

this is the case, a player score is the sum of his performances at both games. Conversely, these teams will

have weeks where they do not play, and all their players will score zero on that week. This information is

available to fantasy league players. 7 Not all footballers play in a given week, so the mode score is actually zero.

8 However, there have recently been allegations of racial abuse by players.

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they are responding to customer preferences for white players, or because they are

indulging their own taste-based discrimination or statistical discrimination.

Player value is the price at which a player can be bought or sold. 9

These values, which

range between £3.8 million and £14.7 million (Christiano Ronaldo's value), are reviewed

after each match and, as we shall see, reflects a number of factors including player

performance, the type of player (position played, age, international status), club played

for and perhaps race if taste is a factor.

Employers are able to buy and sell after each game, subject to budget constraints and a 3-

player-per-team rule. The cost of a hire is therefore 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). Employers are permitted

one transfer per week which does not affect their accumulated points total. However,

additional transfers above that single “free” transfer entail a points deduction of four

points which must be added to the financial cost of making additional transfers. Our

measure of hires and fires is the net transfers for each player after each match in the

season, that is, the number of hires minus the number of "fires" or sales across all players.

The variable runs from a minimum of -279,518 to a maximum of 128,891 with a mean of

138.

9 There is a gap between the buying and selling prices of players. This margin depends on the player’s

value but is not available in our dataset. As such, transferring players has a financial costs and leads to a

reduction in the firms’ budget. As such, firms may not always optimize their teams and refrain from using

their weekly transfer.

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There are some shortcomings to our existing data which are worthy of mention. First, we

have no information on the employers, which means we are unable to account for

employer fixed effects in our analyses. Second, we do not observe employers' initial

squad choice, only the flow of players via net transfers, conditional on players being

hired in the first period. Thus, our analysis of racial discrimination in hiring will only

uncover any discrimination based on the transfer of players who have been hired at least

once. If racial discrimination is an important factor in who employers pick for the first

game of their season our results will underestimate total discrimination.

4. EMPIRICAL STRATEGY

We investigate two potential dimensions along which racial discrimination may occur.

First, there may be discrimination in the way the market sets the price, or value, of black

players. This may arise if the market systematically understates the performance of black

players versus white players, or if the market price setters simply undervalue black

players irrespective of their perceived performance. Second, there may also be

discrimination in the labour market, irrespective of the player's value if, conditional on

performance, employers are simply less likely to purchase black players at a given

price/value. Racial differences in value and hires will arise through taste-based

discrimination in much the same way as Becker envisaged (see Altonji and Blank, 1999:

3170) except we have no production function based on joint output of black and white

workers interacting because ours is strictly additive performance of players in our team.

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There are no wages in our set up. Instead, employers pay a signing on fee which is

exogenously given and employer decides whether to recruit or not on that basis.

As Kahn (1999: 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 zero dismissal costs.

First we identify whether there are any racial differences in the valuation of players at the

start of the season and, if so, whether they can be accounted for by performance in the

previous season. Second, we examine the determinants of players' value throughout the

season as a whole estimating models for the value of the player each week, conditional on

his performance earlier in the season and in the match that has just been played, plus

other controls. We log players' value so that it conforms more to a normal distribution.

We isolate race-related differences with a dummy variable identifying black players

where 1=black and 0=white10

, together with interactions between the black dummy

variable and player performance. Third, we investigate determinants of employers' net

demand for players, that is, the difference between the number of hires and the number of

fires a player is subject to after each match.

10

There are few players defined as other races – for the analysis they have been aggregated to the black

players. This ethnicity variable was defined by the authors.

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Because our data are repeat observations on players for different matches during the

season we cluster standard errors for players to account for the non-independence of

those observations and deploy a robust estimator to account for heteroskedsatic error

terms.

5. RESULTS

5.1 Does the Fantasy Football League Function like a normal labour market?

Before we investigate the racial differences in player value and hires we need to establish

whether the Fantasy Football league functions like a normal labour market. Evidence to

this effect is presented in Figure 1. Panel A shows better performing players are valued

more highly. Panel B shows that the demand for players, as measured by the net

difference between hires and fires, rises fairly monotonically with player performance in

the previous game. Although net employer demand rises sharply at around 17-18 points,

there are fewer than 10 observations in this part of the points distribution. Panel C

suggests that the net demand for players does not vary much with the value of players

throughout most of the distribution of value. Panel D records the amount of activity in

the transfer market over the course of the season. There is a great deal of variance over

the course of the season, though activity begins to fall away in the last third of the

season.11

[INSERT FIGURE 1 ABOUT HERE]

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In the Premier League employers can only buy and sell players in the closed season and the January

transfer window. This stricture does not apply to the Fantasy Football employers.

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5.2 The Market Valuation of Black and White Players

Figure 2 shows the distribution of player value by race over the whole season. The

distributions are similar, but we can see that black players are valued more highly than

their white counterparts, as indicated by the fact that the black dotted line lies to the right

of the black solid line. However, it is also notable that the maximum value for a black

player is £11.2 million (Emanuel Adeybayor) whereas there are four white players valued

more highly (Gerrard, Torres, Lampard, and Ronaldo).

[INSERT FIGURE 2]

One possible reason for a race differential in the valuation of professional football players

is that black players are more likely than white players to be forwards who attack the goal

and score goals. Conversely, they are less likely to be defenders, midfielders and

goalkeepers.12

The market valuation of black and white players by position does differ a

little, with black forwards’ valuation tending to lie below that for whites, but the

differences do not seem large (Figure 3). Another possible reason for the average greater

value of black players is positive migration selection. Non-UK players who get contracts

to play in the UK are likely to be of greater ability than the average UK born player.13

[INSERT FIGURE 3]

12

Thirty percent of black players are forwards compared to 12 percent of whites. 13

Forty five percent of players in the league are non-UK citizen. Twenty seven percent of UK players are

black and 46% of non-UK players are black.

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Our first test of whether there is any potential racial discrimination in the market for

professional footballers is to establish whether there is a racial differential in the market

valuation of the productivity of on-field performance. We begin with the initial valuation

of players at the beginning of the season. Black players had a higher valuation than white

players at the start of the season, the difference being around 5 percent (Table 1, column

1). Although this differential persists when one accounts for on-field performance in the

previous season (column 2) the black coefficient turns negative and statistically non-

significant when one accounts for additional controls such as the player's position on the

field, age, nationality, international status and club (column 3). The performance of

players enters the initial valuation equations in a non-linear fashion, with the valuation of

higher points rising at the top end of the points distribution. We therefore interact race

with points and points squared. Once controls are added there appears to be a greater

valuation of black player performance relative to white player performance in the lower

parts of the performance distribution, but the effect flips around at high performance

values such that white player performance is valued more highly than black player

performance. However the effects are not quantitatively large: each additional point

awarded for the previous season's performance translates into a 0.01 percent increase in

player value.14

[INSERT TABLE 1]

14

Points scored by players in the 2007/08 season ranged from zero to 283 with a mean of 46 and standard

deviation of 52,

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Turning to the valuation of players through the course of the season, Figure 4 suggests

that there might be a racial difference in the valuation of player performance, but only

among players with the highest productivity levels. The figure shows the market

valuation of a player following his performance in a game the previous week. The solid

lines represent white players, while the dotted line represents black players. In both cases

the central line is the mean relationship and the lines either side of it give the 95 per cent

confidence interval. Across most of the distribution in player on-field productivity the

lines are indistinguishable. There is a suggestion that whites’ performance is more highly

valued among the top performers, but the small sample sizes mean that the difference is

imprecisely estimated.

[INSERT FIGURE 4]

To test this more formally we run the OLS estimates presented in Table 2. Black players

are more highly valued than white players, by 3-4 log points, a difference which is on the

margins of statistical significance and remains so when controlling for player

performance in the previous game. However the black coefficient becomes negative and

statistically non-significant with the addition of further controls and interactions between

race and points and points squared are statistically non-significant (column 4). If one

enters players' values at the start of the season it is very strongly correlated with value

later in the season, indicating strong persistence in the valuation of players. Its

introduction in columns 5 and 6 substantially increases the models' ability to account for

variance in player value during the season. Although the black coefficient turns positive

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it is far from statistically significant and the interactions with points and points squared

remain non-significant.15

[INSERT TABLE 2]

The picture looks different running the same models with random effects (Table 3). In

these models the valuation of black and white players differs with their performance in

the previous game. The black*points interaction is positive and significant whereas the

black*points squared coefficient is negative and significant, even when one controls for

player value at the start of the season. However, the size of the effects is not large and the

pattern of results is difficult to reconcile with a simple story regarding discriminatory

pricing of black versus white talent.

[INSERT TABLE 3]

So far we have treated player performance as if it was measured without error or racial

bias. But, as Altonji and Blank (1999) note, variables often treated as independent of

racial outcomes may be subject to bias themselves. One potential source for such a bias

is the black-white differential in the number of bonus points offered to players. These

bonus points are awarded at the discretion of the Fantasy Football staff based on

subjective assessments of who has been the best player in a game. Although black players

are just as likely to receive bonus points as white players, and although bonus points

15

We obtain similar results if we replace the linear and quadratic performance terms with a four-category

performance variable picking out very low, low, medium and high performance.

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awarded in the previous game affect player valuations after the game, Table 4 indicates

that the impact of those bonus points on player valuation is significantly lower if the

player is black (Table 4 column 4). However, the effect is not robust to the inclusion of

the player's valuation at the start of the season (column 6).

[INSERT TABLE 4]

5.3 Net employer demand for players

To establish whether employers discriminate on grounds of race in their hiring and firing

decisions we examine net employer demand for players after each game of the season.

Net demand is measured in terms of the difference between the number of hires and fires

for each player that take place in each match week: high positive (negative) numbers

indicate more (fewer) hires than fires. The mean net employer demand is 138, ranging

from the lowest value of -279,518 to the highest value of 128,891. Outlier values for

transfers (the top and bottom 1 per cent) are excluded when estimating the models.

[INSERT TABLE 5]

Panel A in Table 5 shows the demand for black players is lower than it is for white

players. This differential is statistically significant in column 1 without controls and in

column 2 when controlling for players' points tally through to the game before last. But

when race is interacted with the points tally in column 3 the main effect of being black is

positive and on the margins of statistical significance, whereas the interaction term is

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negative and statistically significant. The black*points tally interaction remains negative

and statistically significant when controls are added in columns 5 and 7. However the

effects are not large.

Panel B introduces player performance in the last game. This is strongly positively

correlated with employer demand for players and its introduction substantially increases

the variance in hiring and firing behaviour accounted for by the model. The black*points

in last game interaction is not statistically significant, indicating that there is no

indication of discrimination in terms of the way employers react to player performance in

the last game. However, the black*points tally in all preceding games this season remains

negative and statistically significant, consistent with racial discrimination in terms of the

way employers weigh up player performance over the course of a season.

[INSERT TABLE 6]

Table 6 repeats the analysis in Table 5 but with random effects models instead of OLS.

The results are robust to this alternative estimation procedure.

[INSERT TABLE 7]

Finally, in Table 7 we introduce performance in the last game as a non-linear term to

establish whether employers respond particularly strongly to a very good performance.

We find that they do: demand for players is much greater for the top 5 per cent of

24

performers, that is, those scoring 7 or more points in the last game. There is no racial

difference in the demand for players based on their performance in the previous game,

except among those with the highest points in the previous game. Among these very high

performing players demand for black players outstrips that for white players, as indicated

by the positive significant black* very high interaction effect (column 4). It is possible

that employers recognise the undervaluation of the best performing black players

indicated in Table 3. However, the differential demand for black players at the top of the

performance distribution remains apparent even when we control for players' value at the

start of the season (column 6).

6. CONCLUSIONS

Research on employers’ discrimination is limited by the unlawfulness of such activity. As

such, researchers have focused on the intention to hire, rather than hiring decisions and

wage settlements. Instead, we rely on a virtual labour market, the UK Fantasy Football

league, where employers can freely exercise their taste for racial discrimination in terms

of hiring, firing and market valuation . We find black players are valued more highly

than white players, but the difference disappears after controlling for on-field

performance and other observable characteristics. However, the market values player

performance differently according to race. There is a greater valuation of black player

performance relative to white player performance in the lower parts of the performance

distribution, whereas at high performance levels white player performance is valued more

highly than black player performance. There is also evidence that employers evaluate

player performance differently by race when making hiring and firing decisions.

25

Employer demand for players rises with their performance, but less so in the case of

black players. This finding is consistent with racial discrimination. However, there is no

racial differential in the weight employers attach to performance in the most recent game:

this has a large effect on employers' decision to hire players for the next game regardless

of race.

26

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27

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30

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gender wage gap", Journal of Economic Surveys, vol.19, 479-511.

31

Figure 1: Does Fantasy League function like a market?

A: Value and Productivity:

B: Productivity and net employer demand

C: Value and net employer demand

D: market activity per week

46

81

01

2

va

lue

-5 0 5 10 15 20points

-200

00

0

200

00

400

00

600

00

800

00

net tr

an

sfe

rs

-5 0 5 10 15 20points

-200

0

0

200

04

00

06

00

08

00

0

net tr

an

sfe

rs

4 6 8 10 12 14value

400

00

06

00

00

08

00

00

01

00

00

00

120

00

00

Tota

l n

br

of (n

et)

tra

nsfe

rs

0 10 20 30 40game week

0

Figure 2: Distribution of value by race

0.2

.4.6

Den

sity

4 6 8 10 12 14Value

White Non-white

1

Figure 3: Value by position and race

0.2

.4.6

0.2

.4.6

5 10 15 5 10 15

Defender Forward

Goalkeeper Midfielder

White Non-white

kd

en

sity v

alu

e

Value

Graphs by Position

2

Figure 4: relation performance value by race

51

01

52

0

Va

lue

-5 0 5 10 15 20Performance

White

Non-white

3

Table 1: Initial log(valuation) of players

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

Black 0.051 0.054 -0.011 0.042 -0.027

(2.83)** (3.84)** (1.15) (1.67) (1.65)

Points last

season

0.002 0.001 0.002 0.001

(5.43)** (4.02)** (4.02)** (2.52)*

Points last

season squared

0.001 0.001 0.001 0.001

(3.45)** (6.07)** (3.75)** (6.17)**

Not in FL last

season

0.069 0.052 0.063 0.048

(4.09)** (4.46)** (2.98)** (3.29)**

Black*points 0.001 0.001

(1.03) (1.72)

Black*points

squared

-0.001 -0.001

(1.42) (2.00)*

Black*not in

FL last season

0.024 0.016

(0.67) (0.70)

Controls? N N Y N Y

Constant 1.638 1.501 1.585 1.502 1.595

(139.90)** (116.38)** (53.11)** (97.87)** (52.52)**

Observations 594 594 594 594 594

R-squared 0.01 0.42 0.82 0.42 0.82

Note:

The sample is all players who began the season, minus those with missing data, regardless of whether they

went on to play in the 2008/09season

Models are estimated by OLS. t-stats are in parentheses.

Value is measured in million pounds in the first week the player appears in the Fantasy League (FL).

Black is a dummy variable indicating a non-white player.

Additional controls are dummies for position in the field, age cohort, British player, British International,

Other International, and club.

4

Table 2: Log(value) over the season

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

Black 0.034 0.037 -0.020 -0.020 0.005 0.003

(1.69) (1.92) (1.59) (1.55) (1.12) (0.68)

Points last

game

0.027 0.019 0.018 0.009 0.008

(7.43)** (8.96)** (6.16)** (9.68)** (7.47)**

Points

squared last

game

-0.000 -0.001 -0.000 -0.001 -0.001

(1.38) (2.40)* (0.94) (7.46)** (5.34)**

Value at start

of season

0.140 0.140

(29.80)** (30.08)**


(0.67) (0.63)

Black*points

squared

-0.001 0.000

(1.44) (0.27)

Controls N N Y Y Y Y

Constant 1.650 1.607 1.665 1.665 0.878 0.879

(122.88)** (133.69)** (39.44)** (39.44)** (29.33)** (29.48)**

Observations 17554 17554 17554 17554 17554 17554

R-squared 0.01 0.07 0.67 0.67 0.95 0.95

Note:

The sample is all players who played at least once during the season, minus those with missing data

(N=508 players)

Models are estimated by OLS. t-stats are in parentheses. Standard errors are clustered by player.

Value is measured in million pounds in each game played during the season. Points are points acquired in

the previous game.




5

Table 3: Log(value) over the season, random effects models

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

Black 0.034 0.034 -0.015 -0.016 0.001 0.001

(1.73) (1.74) (0.93) (0.97) (0.30) (0.15)

Points last

game

0.001 0.001 0.001 0.001 0.001

(3.40)** (3.62)** (1.51) (3.63)** (1.60)

Points

squared last

game

-0.000 -0.000 -0.000 -0.000 -0.000

(3.19)** (2.98)** (0.84) (3.10)** (0.96)

Value at start

of season

0.142 0.142

(35.24)** (35.20)**


(2.03)* (1.94)

Black*points

squared

-0.000 -0.000

(2.46)* (2.42)*


Constant 1.644 1.643 1.576 1.576 0.876 0.877

(126.89)** (126.93)** (46.10)** (46.15)** (36.39)** (36.36)**

Observations 17554 17554 17554 17554 17554 17554

Number of id 508 508 508 508 508 508

Note:


(N=508 players)

Models are estimated by random effects. z-stats are in parentheses. Standard errors are clustered by player.


the previous game.




6

Table 4: Log(value) of Player and the Role of Bonus Points

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

Black 0.034 0.037 -0.020 -0.018 0.005 0.003

(1.69) (1.92) (1.58) (1.39) (1.12) (0.71)

Bonus points 0.041 0.017 0.023 0.000 -0.001

(5.27)** (4.63)** (4.29)** (0.11) (0.45)

Non-bonus

points

0.021 0.014 0.014 0.004 0.004

(9.08)** (10.67)** (7.60)** (8.83)** (6.01)**

Value at start

of season

0.140 0.140

(29.10)** (29.31)**

Black*bonus

points

-0.015 0.002

(2.14)* (0.85)

Black*non-

bonus points

-0.000 0.001

(0.13) (0.88)


Constant 1.650 1.611 1.668 1.667 0.880 0.881

(122.88)** (137.35)** (39.41)** (39.35)** (28.48)** (28.50)**

Observations 17554 17554 17554 17554 17554 17554

R-squared 0.01 0.08 0.67 0.67 0.95 0.95

Note:


(N=508 players)



the previous game. Bonus points run from zero to three and are awarded by FF staff to those they believe to

have played best in the game.




7

Table 5: net employer demand for players (1) (2) (3) (4) (5) (6) (7)

Panel A: excluding points in last game

Black -188.123 -182.296 180.155 -182.786 165.179 -184.353 163.321

(2.00)* (2.02)* (1.68) (1.90) (1.43) (1.99)* (1.43)

Points in

season exc.

last game

9.406 14.061 8.288 12.787 8.463 13.047

(3.79)** (4.22)** (2.79)** (3.47)** (2.65)** (3.38)**

Black*points

in season

exc. last

game

-13.132 -13.181 -13.197

(2.89)** (2.94)** (2.95)**

Value at start

of season

-10.527 -15.286

(0.11) (0.17)

Controls N N N Y Y Y Y

Constant 176.734 -86.649 -216.992 -529.543 -647.535 -470.827 -562.416

(2.61)** (1.45) (3.09)** (2.02)* (2.54)* (0.82) (1.01)

Observations 17202 17202 17202 17202 17202 17202 17202

R-squared 0.00 0.01 0.01 0.01 0.01 0.01 0.01

Panel B: including points in the last game

Black -188.123 -114.242 87.518 -129.390 74.045 -161.778 47.442

(2.00)* (1.27) (0.66) (1.40) (0.57) (1.81) (0.36)

Points last

game

664.712 632.815 704.504 673.043 712.370 681.297

(19.77)** (15.54)** (20.31)** (16.18)** (20.54)** (16.44)**

Points in

season exc.

last game

-5.743 -1.366 -11.442 -7.080 -7.968 -3.497

(2.45)* (0.43) (3.99)** (2.01)* (2.55)* (0.93)

Black*points

in season exc.

last game

-11.861 -12.231 -12.418

(2.74)** (2.86)** (2.91)**

Black*points

in last game

78.566 77.925 77.098

(1.11) (1.09) (1.08)

Value at start

of season

-221.542 -224.425

(2.38)* (2.47)*

Controls N N Y Y Y Y Y

Constant 176.734 -772.220 -841.537 -1,757.018 -1,822.727 -535.008 -586.871

(2.61)** (10.96)** (9.54)** (6.20)** (6.56)** (0.92) (1.02)

Observations 17202 17202 17202 17202 17202 17202 17202

R-squared 0.00 0.14 0.14 0.15 0.15 0.15 0.15

Note:



Net employer demand is measured by the difference in the number of hires and fires for a player. The top

and bottom 1% of transfer values are excluded from estimation.

8




9

Table 6: net employer demand for players, random effects models (1) (2) (3) (4) (5) (6) (7)

Panel A: excluding points in last game

Black -203.227 -199.720 172.688 -219.604 149.570 -225.836 143.841

(2.07)* (2.11)* (1.19) (2.12)* (1.01) (2.26)* (0.99)

Points in

season exc.

last game

6.520 11.337 2.522 7.278 2.807 7.640

(2.47)* (3.26)** (0.77) (1.85) (0.78) (1.80)

Black*points

in season

exc. last

game

-13.517 -14.026 -14.079

(2.69)** (2.80)** (2.80)**

Value at start

of season

-33.832 -39.016

(0.32) (0.39)

Controls N N Y Y Y Y Y

Constant 200.135 17.187 -116.755 -449.674 -578.261 -258.572 -358.702

(2.81)** (0.22) (1.30) (1.61) (2.12)* (0.41) (0.59)

Observations 17202 17202 17202 17202 17202 17202 17202

Number of id 508 508 508 508 508 508 508

Panel B: including points in last game

Black -203.227 -128.749 46.804 -154.919 31.900 -209.513 -14.422

(2.07)* (1.34) (0.29) (1.61) (0.20) (2.23)* (0.09)

Points last

game

688.456 652.494 710.375 675.512 719.286 684.879

(20.17)** (15.91)** (20.26)** (16.10)** (20.37)** (16.28)**

Points in

season exc.

last game

-1.360 2.695 -8.774 -4.700 -4.609 -0.437

(0.54) (0.81) (2.75)** (1.23) (1.32) (0.11)

Black*points

in season

exc. last

game

-11.461 -12.109 -12.351

(2.42)* (2.57)* (2.63)**

Black*points

last game

87.967 86.465 85.387

(1.22) (1.19) (1.17)

Value at start

of season

-340.227 -338.722

(3.19)** (3.25)**

Controls N N N Y Y Y Y

Constant 200.135 -908.356 -961.878 -1,677.88 -1,741.55 210.620 135.818

(2.81)** (10.74)** (9.37)** (5.61)** (5.97)** (0.33) (0.21)

Observations 17202 17202 17202 17202 17202 17202 17202

Number of id 508 508 508 508 508 508 508

Note:


Models are estimated by Random effects. z-stats are in parentheses. Standard errors are clustered by player.

10

Net employer demand is measured by the difference in the number of hires and fires for a player. The top

and bottom 1% of transfer values are excluded from estimation.




11

Table 7: Net employer demand for players, non-linear points in last game (1) (2) (3) (4) (5) (6)

Black -130.583 38.063 -17.465 -320.035 -140.488 -428.361

(0.99) (0.29) (0.12) (1.21) (1.05) (1.67)

Points (ref:

low)

Medium 379.247 543.574 631.246 738.617 814.948

(2.53)* (3.44)** (3.27)** (4.39)** (4.06)**

High 3,123.060 3,468.700 3,174.266 3,766.518 3,487.306

(11.87)** (11.70)** (9.32)** (11.51)** (9.67)**

Very high 12,052.095 12,477.359 10,630.445 13,079.901 11,270.761

(11.66)** (11.66)** (10.13)** (11.55)** (10.24)**

Black*medium -177.272 -163.582

(0.58) (0.55)

Black*high 768.582 706.742

(1.32) (1.21)

Black* very

high

5,224.971 5,074.005

(2.14)* (2.06)*

Value at start of

season

-706.373 -687.805

(4.07)** (3.88)**


Constant 188.967 -1,130.703 -2,036.693 -1,888.134 1,793.584 1,837.633

(1.92) (8.21)** (4.12)** (3.69)** (1.87) (1.82)

Observations 17554 17554 17554 17554 17554 17554

R-squared 0.00 0.10 0.11 0.11 0.11 0.12

Note:


(N=508 players)


Net employer demand is measured by the difference in the number of hires and fires for a player. Points are

points acquired in the previous game where low=-4 to zero (54% of observations); medium=1-2 (28% of

observations); high=3-6 (13% of observations); very high=7-21 (5% of observations).




12

APPENDIX

TABLE A1: POINTS SYSTEM IN FANTASY FOOTBALL

FOR PLAYING UP TO 60 MINUTES 1

FOR PLAYING 60 MINUTES OR MORE 2

FOR EACH GOAL SCORED BY A GOALKEEPER OR DEFENDER 6

FOR EACH GOAL SCORED BY A MIDFIELDER 5

FOR EACH GOAL SCORED BY A FORWARD 4

FOR EACH GOAL ASSIST 3

FOR A CLEAN SHEET BY A GOALKEEPER OR DEFENDER 4

FOR A CLEAN SHEET BY A MIDFIELDER 1

FOR EVERY 3 SHOT SAVES BY A GOALKEEPER 1

FOR EACH PENALTY SAVE 5

FOR EACH PENALTY MISS -2

BONUS POINTS FOR THE BEST PLAYERS IN A MATCH 1-3

FOR EVERY 2 GOALS CONCEDED BY A GOALKEEPER OR DEFENDER -

1

FOR EACH YELLOW CARD -1

FOR EACH RED CARD -3

FOR EACH OWN GOAL -2

13

APPENDIX TABLE A2

Mean (SD) Min Max

Market value 5.42 (1.42) 3.8 14.7

Log(value) 1.66 (0.22) 1.34 2.69

Net transfers 137.5 (8839.3) -279518 128891

Value at end 2007/8 4.18 (2.92) 0 12

Points in 2007/8 49.26 (52.37) 0 283

Not in league in

2007/8

0.28 (0.45) 0 1

Points in last game 1.69 (2.55) -4 21

Points squared last

game

9.34 (25.13) 0 441

Bonus points 0.13 (0.53) 0 3

Points, categorical:

Low

Medium

High

Very high

46.62

32.77

15.18

5.43

0

0

0

0

1

1

1

1

Points tally exc.

points in last game

28.49 (31.81) -1 221

Position:

Goalkeeper

Defender

Midfielder

Forward

7.67

34.13

37.67

20.53

0

0

0

0

1

1

1

1

Birth cohort:

1969-76

1977-79

1980-82

1983-85

1986-88

1989-92

8.89

19.17

26.38

19.21

18.38

7.97

0

0

0

0

0

0

1

1

1

1

1

1

England

international

0.13 (0.34) 0 1

International, other

country

0.52 (0.50) 0 1

Week in season 19.72 (10.63) 1 37

Two games in week 0.04 (0.19) 0 1

Black 0.38 (0.49) 0 1

14

APPENDIX FIGURE A1

15

Figure A2: Distribution of performance by race

Figure A3: Points per race and position

0.1

.2.3

kd

en

sity p

oin

ts

-5 0 5 10 15 20points

White Non-white

0.1

.2.3

0.1

.2.3

0 10 20 0 10 20

Defender Forward

Goalkeeper Midfielder

White Non-white

kd

en

sity p

oin

ts

points

Graphs by Position

16

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