Tsukuba Economics Working Papers
No. 2016-001

Is Racial Salary Discrimination Disappearing in the NBA?
Evidence from Data during 1985--2015
byHisahiro Naito
University of Tsukuba
and
Yu Takagi
University of Tsukuba
April 2016

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANIs Racial Salary Discrimination Disappearing in the
NBA? Evidence from Data during 1985–2015

Hisahiro Naito∗
Department of Economics
Graduate School of Humanities and Social Sciences
University of Tsukuba

Yu Takagi †College of International Studies
University of Tsukuba
April 22, 2016∗†

Address: Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8573; e-mail: naito@dpipe.tsukuba.ac.jp
Address: Tennodai 1-1-1, Tsukuba, Ibaraki 305-8573; e-mail: yu.baske.sumeo@gmail.com

Abstract
This study re-examines racial salary discrimination of National Basketball Association
players by constructing a long unbalanced panel covering the 1985–1986 to 2015–2016
seasons. Contrary to the results of previous studies, we find that non-white players
are paid equally to white players with similar characteristics in the 1980s and 1990s,
but that white players started to be paid 20 percent more than non-white players in
the last 10 years. Our results are robust in all specification checks such as the quantile
regressions, controlling the sample selection and controlling different contract types.
Non-parametrically estimated density of the counter-factual salary of non-white players
confirms our results. In addition, we find that neither the employers preference nor
income gap of white and black fans explain this increasing salary gap.
JEL Classification: C25
Keywords: racial discrimination, NBA, labor markets, salary discrimination

1

Introduction

The issue of whether discrimination in the labor market is disappearing has important
policy implications. Because various external factors, such as globalization, taxes, andcompetition with other product markets, affect the degree of wage discrimination, it isimportant to know how wage discrimination changes over time.
In the literature of discrimination in labor markets pioneered by Becker (1971),
researchers have used the data of professional sports athletes to analyze the issue of
discrimination because of the availability of information on each player’s productivity
in a large number of dimensions (Kahn, 2000). Among studies that used informationof professional sports athletes, studies that use information of players of the National
Basketball Association (NBA) provide an interesting case for several reasons. First,
in the previous studies that utilized the data in 1980s and 1990s, it is reported thatin the 1980s, there was a white premium of the NBA’s salary—the salary of a white
player is higher than that of a non-white player with the same productivity (Kahnand Sherer, 1988; Koch and Vander Hill, 1988; Wallace, 1988; Brown et al., 1991).1
However, several studies report that such a premium reduced or disappeared in the
1990s (Dey, 1997; Hamilton, 1997; Gius and Johnson, 1998; Bodvarsson and Brastow,
1998; Eschker et al., 2004; Hill, 2004; Groothuis and Hill, 2013).2 Some studies reportthat in the 2000s, there was even reverse discrimination against white players (Yang1

For example, Kahn and Sherer (1988) found a strong white (20 percent) premium controlling

productivity and other covariates using the salary data in the 1985–1986 season.
2
Hamilton (1997) found evidence of racial pay differences only at the upper end of the 1994–1995
season of salary distribution. Hill (2004) showed that the importance of controlling the height or
position. He argued that the white premium was the return of the height, not the racial gap. A study
most closely related to the current study is Groothuis and Hill (2013). They used unbalanced panel
data from 1990 to 2008 and controlled for the sample selection problem. They found that there wasno discrimination against black players in their dataset.

1and Lin, 2012; Groothuis and Hill, 2013). Thus, it is natural to examine whether
this trend continues in more recent years and whether salary discrimination eventuallydisappeared.
Second, there is discrepancy on anecdotal and empirical evidence regarding discrimination in the NBA. Although the previous literature suggests that salary discrimination is disappearing in the 1990s and might even be moving in the opposite direction(reserve discrimination against white) in the 2000s, there is opposite anecdotal andempirical evidence of racial discrimination against black players in the NBA. For example, in April 2014, the owner of Los Angeles Clippers was banned from the NBA
permanently and fined $2.5 million for his racial comments. Kanazawa and Funk (2001)
found that TV viewing is affected strongly by the ratio of white players in the team byexamining the viewing data in the 1996–1997 season. Price and Wolfers (2010) showedthat a referee prefers a player whose race is the same as that of the referee when he or
she makes a decision on fouls. Such anecdotal or empirical evidence warrants further
investigation of racial salary discrimination by using longer data.
Third, the NBA experienced important changes in the 2000s. First, the NBA experienced substantial globalization in the 2000s. In 2002, 2005, and 2006, the first pick inthe draft was an international player.3 The season’s MVP during the 2004–2005, 2005–
2006, and 2006–2007 seasons were international players.4 In addition, broadcasting theNBA’s games to countries outside the United States became common in those years.
In the literature of labor economics, there is increasing interest whether globalization
would lead to a decrease or increase of discrimination in the labor market (Berik etal., 2004; Black and Brainerd, 2004; Busse and Spielmann, 2006). The salary data
3

The first picks in the draft of 2002, 2005, and 2006 were Yao Ming (China), Andrew Bogut(Australia), and Andrea Bargnani (Germany), respectively.
4
The MVP of the 2004–2005 season, the 2006–2006 season, and the 2006–2007 season were SteveNash (South Africa), Steve Nash (South Africa), and Dirk Nowitzki (Germany), respectively.

2

of the NBA provides an interesting case for the study. Second, from the 2002–2003
season, the NBA introduced luxury tax to penalize the team whose total salary toplayers exceeds the upper limit determined by the NBA.5 The standard tax theory of
the public finance (Salanie, 2011) showed that even when the tax is imposed on theemployers (teams), some portion of the tax burden is shifted to the employees (players) through lower wage rates (salary). Thus, it is possible that the luxury tax could
affect the salary of players and thereby, affected white and black players differently.6
Interestingly, as we show later, we find that the white premium increased in the 2000s
and 2010s, although the causality is not clear.
This study revisits the issue of the white premium of the salary of NBA players
by making long unbalanced panel data of the salary and other indices of performance,
which covers the 1985–1986 season to the 2015–2016 season for annual salary and the
1984–1985 season to the 2014–2015 season for indices of performance. First, we findthat in the 1980s, non-white players were paid equally to white players.7 Second,consistent with the previous literature, which shows that racial salary discrimination
was disappearing in the 1990s, we find that during the 1980s and 1990s, there wasno white premium. However, in the 2000s, we find that the white premium becomes
about 9 percent (p < 0.05) and in the 2010s, it reached 26 percent (p < 0.01). Our
results show that the result of the previous literature that racial salary discrimination
5

Although the NBA introduced a salary cap from the 1985–1986 season, this salary cap was theso-called “soft cap” in the sense that there are lots of exceptions on the salary cap and that the team
could exceed the salary limit by using those caps. The luxury tax introduced from the 2002–2003
season was a hard cap. Thus, any team that exceeded the limit needs to pay the luxury tax.
6
In addition, the NBA started the official minor league (D-league). This could affect the wage rateof the black and white players differently.
7This result shows a sharp contrast to the results of early literature. We find that the lack of several
important variables in previous studies leads to the conclusion that there was salary discrimination
against black players in the 1980s. See the discussion of Subsection 2.5.

3

is disappearing is quite temporary, and in fact, it increased in the late 2000s and,especially, in the 2010s.
To confirm the robustness of our results, we conduct robustness checks by runningthe quantile regression at several quantiles, restricting the sample to players with morethan or equal to 5 years of experience, restricting the sample to US-born players,
controlling the performance at t-2 and t-3 instead of at t-1, controlling the sample
selection problem, and adding the team’s fixed effect interacted with year dummy. In
addition, we reconcile the difference of the results between our study and the previous
studies. We find that when we drop some control variables from our regression equation,
which are not included in the previous studies, the magnitude of the coefficient andstatistical significance becomes similar to the results of the previous studies. Thissuggests the importance of including those control variables.
In addition, to visually identify the counter-factual salary distribution, we nonparametrically estimate the density of the actual salary of white players and nonwhite players, the counter-factual density of the salary of non-white players by using
the method developed by DiNardo et al. (1996). We find that during 1985–1995,
the salary density of non-white players is located slightly to the right of the salarydensity of white players—on average, non-white players earn more than white players.
However, the difference of the two densities could be explained by the difference ofthe performance and other covariates between the white and non-white players. In
1995–2005, both salary density of white and non-white players becomes quite similar.
Even after adjusting the performance and other covariates, the salary density of whiteand non-white players is similar. However, in 2005–2015, the salary density of white
players is located slightly to the right of the salary density of non-white players—on
average, white players earn more than black players. This difference persists even if
we adjust the performance and other covariates between white and black players. This4

implies that the difference in 2005–2015 mainly comes from other factors that cannot
be explained by the performance and other covariates.
Although we do not find the exact cause of the rise of salary discrimination, we
examine two possible causes. First, we examine whether the race of the owner or GMof the team affects the white premium. We find that even if we control the race ofowner and GM, the pattern of the white premium does not change at all. In addition,
we examine the effect of income distribution of white and black fans. Again, we findthat the pattern of the white premium does not change, even if we control the income
distribution of residents in the team’s state.
Our results have several implications. First, the disappearance of the white premium reported by previous studies (Bodvarsson and Brastow, 1998; Dey, 1997; Eschker
et al., 2004; Hamilton, 1997; Gius and Johnson, 1998) is temporary.
Second, although our result is not consistent with previous studies, that racial salary
discrimination is disappearing in the NBA, it is consistent with the broader literaturethat racial discrimination is persistent in different forms in the NBA (Kanazawa andFunk, 2001; Price and Wolfers, 2010).
The organization of the rest of our paper is as follows. In Subsection 2.1, we
discuss the data and how we construct the variables. In Subsection 2.2, we present our
main results. In the Subsection 2.3, we estimate the actual and counter-factual salary
distribution and examine how they changed over time. In Subsection 2.4, we discuss
why our results differ from the estimates of the previous literature. In Section 3, we
provide a brief conclusion.

5

2

Analysis

2.1

DatasetThis study obtains information on salaries and player productivity from several sources.
For information on the annual salaries of players, we obtain information of the annual
salaries from the ESPN salary-ranking website8 , NBA’s reference website9 , and fans’
website10 . We check the consistency of the salary information among three sources andfind that information on those three sources is consistent. For indices of performance,birthplace, nationality, height, weight, and birth year, we collected data from the
ESPN website11 and the reference website of NBA players12 . In addition, we checkthe consistency of indices from these two sources and find that the information isconsistent between these two sources. The salary data are available from the 1985–
1986 to the 2015–2016 seasons, except for the 1986–1987 and 1989–1990 seasons.13 The
information on performance is available from the 1984–1985 to 2014–2015 seasons. The
median income of black and white residents in each state and year is calculated fromthe CPS data available from the IPUMS CPS.14
Some players are posted on the waiver list during the season after the contract issigned. When another team makes a claim on this waived player within 48 hours after
he was posted on the waiver list, the contract is transferred to this new team and the
new team needs to take full responsibility for the contract, including payment of theremaining salary. In most cases, however, no team lodges a claim within 48 hours to8

http://espn.go.com/nba/salaries
http://www.basketball-reference.com/players/
10
https://www.eskimo.com/~pbender/11
http://espn.go.com/nba/statistics
12
http://www.basketball-reference.com/players/
13
For the 1989–1990 and 1989–1990 seasons, the NBA, player’s union, and individual teams refused9

to release salary information.
14
https://cps.ipums.org/cps/

6this posted player. In this case, the player obtains free agency. In this case, a newteam can make an offer to this player with the minimum salary that is determined by
the NBA. In our dataset, about 5 percent of observations experience these kinds oftransfers during the season. It is natural to assume that the characteristics of thosewaived players are different from non-waived players. Thus, we exclude those waived
players from our dataset. To check the sensitivity of our regression result due to the
exclusion of those waived players, we conduct robustness checks by including thoseplayers and re-estimating the equation. Our robustness checks show that the result
does not change, even if we include those players.
The number of players in our dataset is 1,856 and the number of observations is9,822. As we discuss in the next section, we use ordinary least squares (OLS) withclustering robust standard errors, instead of the random-effect model of the panel data.
For the indices of player performance, we use 16 indices listed in Table 2. In addition to
those 16 indices, we include the height and weight, current team dummy, year dummy,
and foreign player dummy as additional control variables. The foreign dummy is equal
to 1 if a player is born outside of the United States. For our regression, we do not put
the team’s average salary or attendance as a control variable. Instead, we put the teamdummy or team dummy and its interaction with year dummy to control time-invariant
and time-variant team’s effect
2.2

Empirical Analysis

The main regression equation that we utilize in this study is as follows:
ln Sijt = β0 + γW hiteijt + β1 X1,ij,t−1 + β2 Xjt + γj + γt + εijt

(1)where i is an index of individual, t is the index of the season, and j is the index of thecurrent team. Sijt is the annual salary of the player i in the season t who belongs to the7team j. γj is the team’s fixed effect. γt is the time fixed effect; εijt is the error term.
Xi,t−1 is player i’s productivity in season t-1. It is possible that the player’s salaryis determined by the performance a few years before the season t, and we conduct arobustness check by replacing Xi,t−1 with Xi,t−k where k = 2 or 3.
Since we use panel data instead of cross-sectional data, εijt can be serially correlated
for the same i. We use the OLS with the assumption that the error term is clusteredat the player’s level. We do not use the random effect of the panel data. The random
effect model is more efficient than the OLS with the clustering robust standard error if
it is correctly specified. However, once misspecified, the random effect model generates
the inconsistent estimate of the coefficients and standard error. Thus, we use the OLS
with the clustering robust standard error for the robustness of the results.
Our main interest is β1 , which measures how much percent the annual salary increases when the race of a player is white, controlling the productivity of this player
and the characteristics of the team he belongs to.
Tables 1 provides the summary statistics of the variables used in our regression.
Among 9,822 observation, 24 percent of the observations is white, and 13 percent
are foreign players. We classify the positions of players into three categories—center,
guard, and forward. About 40 percent of the observations is guard, another 40 percent
is forward, and 20 percent is center. We control for age, age squared, experience, andexperience squared. Our robustness check shows that including the quadratic termof age and experience is important. The average age is 27 years and the averageexperience is 5.5 years. The previous study shows the importance of controlling theheight or position, as discussed in the literature section. The lower part of Table 1 lists
the 16 indices of performance variables used in our regressions.
Table 2 shows our main regression results. The row White displays the estimatedcoefficient of the white dummy in the regression equation. In the regression equation,8the dependent variable is the logarithm of the annual salary at year t. The explanatory
variables are the white dummy, foreign player dummy, performance indices listed inTable 1 at season t-1, age, age squared, experience, experience squared, two position
dummies, height, weight, and team dummy at season t. Our robustness check shows
the importance of the square of experience and age. For calculating the standard error,
we assume that the error term is clustered at the player’s level and apply the clusteringrobust standard error. The first block of Table 2 shows the results of OLS. The first,
second, third, fourth, and firth columns show the estimated coefficients of the whitedummy, numbers of observations, and R squared when all observations, observationsin the 1980s, observation in the 1990s, observations in the 2000s, and observations in
the 2010s are used for the estimation, respectively.
The first block of Table 2 shows that in the 1980s and 1990s, black players areas equally paid as white players with similar characteristics. The coefficient of thewhite player dummy is economically very small and statistically insignificant. In the
2000s and 2010s, however, the white premium becomes significant economically andstatistically. In the 2000s, the white premium becomes about 10 percent (p < 0.05).
In the 2010s, the white premium becomes more than 20 percent (p < 0.01).
In the first block, we estimate the white premium using OLS. However, in the NBA,
there are super stars in terms of salary. In addition, there is a minimum salary for
NBA players. In such a situation, running the quantile regression is a useful device
to detect racial discrimination, since OLS can be affected substantially by the outlier
and minimum cutoff line in the presence of the outlier and minimum salary. In thesecond block, we run the 50 percentile quantile regression. The dependent variable andexplanatory variables are the same as in the OLS case. The result of the 50 percentile
quantile regression result shows that even with the quantile regression, the patternof the white premium does not change—in the 1980s and 1990s, there was no white9

premium, but in the 2000s, the white premium began to emerge and, in the 2010s, it
became more than 20 percent.
The third block of Table 2 shows the results of 25 percentile quantile regression. Itshows that the pattern of the estimated coefficient of the white dummy is the same as
the OLS case.
The fourth block of Table 2 shows the results of 75 percentile quantile regression.
It shows that the pattern of the white premium is slightly different from the pattern in
the OLS case. When 75 percentile quantile regression is applied, the white premium
becomes insignificant in the 2000s, but becomes 20 percent in the 2010s. This suggeststhat the rise of the white premium occurred initially at the middle to lower distribution
and expanded into higher quantiles.
In Table 3, we conduct several robustness checks. In the first block, we control thetype of the contract indirectly. As shown by Kahn and Shah (2005), the white premium
can be quite sensitive to the type of contract, as discussed in the introduction. Playerswith experience of more than 3–5 years (depending on the initial contract) can become
free agent players. On the other hand, the salaries of the drafted rookie players are
determined by the NBA’s rules. Thus, there is no room for racial discrimination forthe drafted rookie players. This implies that the inclusion of rookie players could affectthe white premium substantially, as demonstrated by Kahn and Shah (2005). In thefirst block of Table 3, we restrict the sample to players who have 5 years or more ofexperience. The dependent variable and explanatory variable are the same as in Table
2. The result of the first block shows that the result of OLS with all players continues
to hold even in the restricted sample. This suggests that the type of contract does notaffect the change of the white premium over time.
In the second block of Table 3, we restrict the sample to US-born players.15 Since15

In all the above regressions except the second block of Table 4, we include the foreign player dummy

10the NBA experienced a dramatic globalization in the 2000s, fully controlling for thebirthplace of players seems to be important. The result of the second block of Table 3
shows that controlling for foreign players fully does not affect the pattern of the whitepremium at all.
In the third block of Table 3, we control the sample selection problem. As discussed
by Groothuis and Hill (2013), given the performance at season t-1, having a contract atseason t is not random. If the team selectively has a contract with white players when
the potential salary of players is high, such behavior would generate a white premium.
To control such a sample selection issue, we apply Heckman’s two-step procedure.16
The third block of Table 3 shows that controlling the sample selection problem does
not affect the pattern of the white premium.
Table 4 shows additional robustness checks. In Table 2, we use the indices of theperformances of the previous season to control the productivity of players. However, it
is quite possible that the salary of the player at season t is affected by the performanceat t − 2 or t − 3. The first and second blocks of Table 5 show the coefficients of thewhite dummy when the indices of performance at season t − 2 or t − 3 are used as thecontrol variables and the dependent variable is the log of salary at season t. The firstand second blocks of Table 4 show that the pattern of the white premium does not
as an explanatory variable. Thus, we control the birthplace of players to some degree. However, we
do not make other variables interact fully with the foreign player dummy. Thus, we implicitly assume
that the coefficient of other explanatory variables is the same between US-born and foreign players.
If the effect of those control variables differ between foreign and US-born players, our estimate of
the coefficient of the white dummy can be biased. To solve this problem, we restrict our sample toUS-born players and apply the same regression equation, except for the foreign player dummy.
16
One of the important issues of implementing the Heckman two-step estimation method is tofind an excluded variable that enters the selection equation but is not included in the second-stage
equation. We use the performance variables at t-2 as excluded variables.

11

change from Table 2.
In the third block of Table 4, we control another sample selection issue. As discussed
in the data section, we exclude players posted during the season. This is because often
they are hired by the second team at the minimum salary. The third block of Table 4shows the results of the regression when we include those players in the sample. The
results of Table 4 show that the results of Table 2 do not change even if those waived
players are included.
In all the abovementioned regressions, we include the team dummy to control theteam’s fixed effect. For example, suppose that the team’s financial condition is timeinvariant and that teams located in big cities are financially more affluent and tend to
pay higher salaries, regardless of the race of players. In addition, suppose that teams
located in big cities tend to hire white players for some exogenous reasons. Then, thesalary regression exhibits a positive correlation between race and salary, even if there
is no salary discrimination within a team. To control such an effect, we need to include
the team’s fixed effect. However, if the team’s financial condition is time-variant, it
is not sufficient to include the team’s fixed effect. We need to include the interaction
term of the team dummy and the year dummy. In the fourth block of Table 4, we
include the interaction term of the team dummy and year dummy. The fourth blockof Table 4, however, shows that the pattern of the white premium is not affected atall, even if we include the interaction of the team dummy and year dummy.
2.3Counter-factual Salary Distribution

The previous analysis consistently shows that in the in 2000s and 2010s, the racialsalary gap increased in the NBA in terms of mean and several quantiles. A natural
question is how the overall salary distributions of black and white groups have changedin the last 30 years, controlling the characteristics of performance and other covariates,
12

such as height and weight. In this subsection, we estimate the counter-factual salary
distribution of black players—hypothetical salary distribution of a black player treatedin the same way as a white player with a similar characteristic.
To be more accurate, let x be the attributes that characterize players, except therace of players. The attributes x include the performance of players at t-1, height,
weight, year dummy, and the team that he belongs to. Let s be the log of the annual
salary. Let fwhite (s|x) be the conditional salary density of a white player given x. Let
fnon−white (s|x) be the conditional salary density of a non-white player given x. Let
G(x|white) be the distribution function of x for a white player and let G(x|non-white)
be the distribution function of x of a non-white player. The salary density of white
players isZfwhite (s|x)dG(x|white)(2)

The salary density of non-white players isZfnon-white (s|x)dG(x|non-white)(3)

The counter-factual salary density of the black players—the density of the salary of
non-white players if the attributes of non-white players were rewarded in the same way
as the attributes of white players—is defined as follows:Z
fwhite (s|x)dG(x|non-white)(4)

In a very important study in labor economics, DiNardo et al. (1996) show that (4)can be calculated by non-parametric density estimation by reweighing. We calculate
actual unconditional salary distribution of white and non-white players and counterfactual distribution of the salary density of non-white players. Since we do not haveso many observations in the 1980s and 2010s, we divide the whole periods into 1985–
1994, 1995–2004, and 2005–2015. We generate the actual density and counter-factual13

density in those periods and check how they change over time. Figure 1 shows that
there is no discrimination against non-white players. In fact, the actual salary densityof the non-white players is located slightly to the right of the counter-factual salarydensity of white players. However, the counter-factual salary density of non-whites
is located slightly to the right of the salary density of white players. This implies
that the difference of the actual salary density of white and non-white players can be
explained by the difference of the attributes. In 1995–2005, the actual density of the
non-white and white players is similar. In addition, the counter-factual salary densityof the non-white and actual salary density of the white players becomes quite similar.
However, in 2005–2010, the actual salary density of the white players is located slightly
to the right of the actual salary density of the non-white players. On the other hand,the counter-factual salary density of the non-white players becomes very similar to
the actual density of the white players. This implies that the difference of the actual
salary density of white and non-white players does not derive from the difference of
the attributes but from racial salary discrimination.
2.4

Reconciling with Previous Results

One might ask the source of the difference between our results and those of previous
studies. Several studies report the presence of a white premium in the 1980s. In
addition, previous studies that use data in the 2000s show that the white premium
does not exist (Groothuis and Hill, 2013). To check for consistency, we run a regressionthat generates Table 2 separately for each year and plots the coefficient of the whitedummy. Figure A1 in the appendix shows the estimated coefficient of the white dummywhen the equation used in Table 3 is applied separately. Figure A1 shows that in the
1985–1986 season, the coefficient of the white dummy is positive but keeps declining
and becomes almost 0 for a while. In the late 2000s, it starts to increase. Thus, the14pattern in the 1980s and 1990s in Figure A1 is consistent with the previous studies.17
In addition, Figure A1 shows the main source of the difference between Groothuis andHill (2013) and ours. In Groothuis and Hill (2013), the year covered in their analysis isfrom between 1990 and 2008. However, as Figure A1 shows, the estimated coefficientof the white premium starts to be higher from 2005 when it is estimated for each year.
Thus, there would be no surprise that when the data are pooled from 1990 to 2008,
Groothuis and Hill (2013) did not find the white premium overall. Simply, the whitepremium started to rise from 2005 and the data from 1990 to 2008 are not sufficient
to detect such a trend.

3

Effects of Race of Owner, GM, and Income Gap on White Premium

One natural question is why the racial salary gap increased in the 2000s and 2010s.
Although we find that the exact cause of this rising salary discrimination is beyond
the scope of this study, we could exclude some possibilities. First, we have examined
whether the race of the owner or GM of the team affects the white premium. We
find that even if we control the race of the owner and GM, the pattern of the whitepremium does not change at all. More specifically, we estimate equation (1) with theinteraction term of the white dummy and race dummy of the owner of GM. The idea of
this regression is that the coefficient of the white dummy becomes bigger in the team17

The estimated coefficient of the white dummy in our regression that uses the data of the 1985–

1986 season alone is about 9 percent and is statistically insignificant (t=1.3). When we drop several
explanatory variables (age squared, experience squared, height, and weight) from our estimating
equation, the estimated coefficient of the white dummy becomes 15 percent and statistically significant(t=1.98). Thus, our result is consistent with the previous studies regarding the pattern of the estimatedcoefficient in the 1980s and 1990s. The difference between our analysis and the previous studies
seems to derive from the exclusion of important covariates, such as the height, weight, and square ofexperience and age.

15

in which the race of the owner or GM is white if the primary reason of the rise of thewhite premium derives from the racial preference of owners or GM. The first blockof Table 5 shows the estimated coefficient of the white premium of players when thewhite dummy of the owner and its interaction with the white dummy of players areincluded. The second block of Table 5 shows the estimated coefficients of the White
dummy of players when the white dummy of GM and its interaction with the whitedummy of players are included. The first block and second block of Table 5 show thatthe pattern of the estimated coefficient of the White dummy does not change at all,even if we control the race of owner or GM.
In the third block of Table 5, we control the relative median income of white
residents over that of black residents in the state in which the team is located. If
the white premium is a reflection of a consumer’s willingness to pay for own race,then in an area in which the relative income of white is high, the white premium will
become higher. After the mid-2000s, the median income gap between white and blackincreased according to the CPS data. In the third block, we estimated the following
equation:ln Sijt = β0 + γ0 W hiteijt + γ1 W hiteijt × (Gapjt − Gap)(5)

+ γ2 × (Gapjt − Gap) + β1 X1,ij,t−1 + β2 Xjt + γj + γt + εijt
where Gapjt is the ratio of median income of white residents to the median income ofblack residents at time t in the state in which team j is located. Gap is the sample
average of Gapjt . The idea of equation (5) is that white premium becomes higher ina state in which the median income of white residents is higher than that of black
residents. The ratio of the median income of black and white residents is calculated
from the CPS data. The third block of Table 5 shows that the pattern of the estimatedcoefficient of white dummy of players does not change even when we include the median16

income ratio of white residents and black residents and its interaction with the whitedummy.

4

Conclusion

This study revisits the issue of racial salary discrimination in the NBA using panel datathat include information on annual salary from the 1985–1986 season to the 2015-2016
season and performance information from the 1984–1985 season to the 2014–2015 season. In contrast to the result of previous studies, in which racial salary discrimination
disappears in the 1990s and early 2000s, we find that racial salary discrimination starts
to emerge in the 2000s and reaches more than 20 percent in the 2010s. The results arequite robust with many specifications. In addition, by using a non-parametric method,
we show how a counter-factual salary density of non-white players—salary density of
non-white players if the attributes of non-white players are rewarded as the attributesof white players—have changed over time and confirm the rise of racial salary discrimination. One natural question is why salary discrimination in the NBA emerged in thelast 10 years. We examined whether the race of owner and GM or income gap of whiteand black fans affects white premium. We found that those factors did not affect thewhite premium at all. Thus, the cause of rising racial salary discrimination is unknown
and remains as a topic for future research.

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19

Yang, Chih-Hai and Hsuan-Yu Lin, “Is there salary discrimination by nationality
in the NBA? Foreign talent or foreign market,” Journal of Sports Economics, 2012,13(1), 53–75.

20

VARIABLES
Annual Salary ($1000)
Foreign Dummy
AgeExperience
Weight (lb)Height (inch)
Guard Dummy
Forward DummyCenter Dummy

Table 1: Summary Statistics of White Players and Non-white Players
white
non-white
mean
s.d.
mean
s.d
3,362
3,767
3,563
4,173
0.327
0.469
0.0639
0.245
27.07
3.775
26.95
4.079
5.150
3.509
5.620
3.823
227.1
27.86
215.1
27.36
80.64
3.731
78.64
3.594
0.285
0.452
0.413
0.492
0.352
0.478
0.433
0.496
0.363
0.481
0.154
0.361

Performance indicesthe number of the games the athlete played in the season.
the average minutes the athlete played in one gamethe average number of the successful field goal in one gam
the probability of the successful shoots.
the average number of three point shoots in one gamethe probability of the successful three point shootthe average number of the free throw shoots in one gamethe probability of the successful free throw
the average number of taking rebound in one gamethe average number of assists in one gamethe average number of turn-over in one gamethe average number of steals in one gamethe average number of blocks in one gamethe averaged scores in one gamethe average number of fouls
the contribution to the team
N

57.36
22.32
20.04
9.717
2.924
1.997
0.448
0.0796
1.165
1.517
0.218
0.192
1.454
1.240
0.719
0.162
3.778
2.504
1.788
1.966
1.174
0.744
0.587
0.422
0.462
0.525
7.727
5.345
2.009
0.821
9.273
6.060
n=2394

60.51
21.83
23.50
9.890
3.712
2.311
0.447
0.0744
1.362
1.643
0.223
0.174
1.919
1.537
0.720
0.146
4.065
2.645
2.170
1.957
1.448
0.825
0.792
0.494
0.487
0.559
9.811
6.216
2.125
0.795
10.78
6.368
n=7428Differenceof the mean
201.16
0.26
0.12
-0.47
11.97
2.00
-0.13
-0.08
0.21

S.E.
95.83
0.01
0.09
0.09
0.65
0.09
0.01
0.01
0.01

-3.15
-3.47
-0.79
0.00
0.20
0.00
-0.46
0.00
-0.29
-0.38
-0.27
-0.20
-0.02
-2.08
-0.12
-1.51

0.52
0.23
0.05
0.00
0.04
0.00
0.03
0.00
0.06
0.05
0.02
0.01
0.01
0.14
0.02
0.15

Table 2: Estimated Coefficients of White Dummy in OLS and Quantile Regressions
(1)
(2)
(3)
(4)
(5)
Estimation Method
all
1980s
1990s
2000s
2010s
OLS
White
0.0757** 0.0295 -0.0455 0.0993** 0.259***(0.0322) (0.0559) (0.0491) (0.0475) (0.0618)
N
9,822
745
3,203
3,650
2,224
R-squared 0.655
0.712
0.589
0.566
0.492
Quantile Regression(50%)
White
0.0443 0.0257 -0.111** 0.104** 0.222***(0.0307) (0.0672) (0.0503) (0.0522) (0.0562)
N
9,822
745
3,203
3,650
2,224
R-squared 0.652
0.699
0.579
0.560
0.470
Quantile Regression (25%)
White
0.108*** 0.0804 -0.0460 0.148*** 0.200***(0.0339) (0.0827) (0.0740) (0.0571) (0.0589)
N
9,822
745
3,203
3,650
2,224
R-squared 0.649
0.696
0.579
0.554
0.476
Quantile Regression (75%)
White
0.0181 0.0100 -0.0531 0.0362 0.197***(0.0325) (0.0791) (0.0486) (0.0480) (0.0721)
N
9,822
745
3,203
3,650
2,224
R-squared 0.641
0.692
0.561
0.551
0.456
Notes: The dependent variable of the regression equation is the logarithm of the annual salaryat season t. The explanary variables are the white dummy, foreign player dummy, allperfomance variables at season t-1 listed in Table 2, position dummy to control positions(guard, center, forward), age, age squared, experince, experience squared, year dummy, height,
weight, and team dummy at season t. The regression equation is estimated by using theunbalanced panel data covering salary information from the 1985 –86 season to the 2015–16
season. The row white shows the estimated coefficient of the white dummy in different
specificatons. Clustering robust standard errors in parentheses and the error term is clustered at
the player's level in all specifications. Columns (1), (2), (3), (4), and (5) show the esimatedcoefficients of white dummy, its standard error, the number of observations, and R² when weuse all observations, observations in the 1980s, observations in the 1990s, observations in the
2000s, and observations in the 2010s, respectively. The first, second, third, and fourth blocks
display the results of OLS, the 50 percentile quantile regression, 25 percentile quantile
regresion, and 75 percentile qunatile regression, respectively.

*** p<0.01, ** p<0.05, * p<0.1

22

Table 3: Estimated Coefficient of White Dummy in Restricted Samples andHeckman's Two-step Model
(1)
(2)
(3)
(4)
(5)
all
1980s
1990s
2000s
2010s
Specifications
OLS: Restricted sample(Expereince≥5_)WhiteN
R-squared
Restricted sample(US born only)White
N
R-squared

0.105**(0.0419)
5,171
0.647

0.0382(0.0711)360
0.716-0.0231(0.0598)
1,670
0.562

0.161** 0.329***(0.0694) (0.0890)
1,940
1,201
0.480
0.409

0.0480(0.0379)
8,565
0.658

0.0229(0.0584)715
0.707-0.0607(0.0531)
2,988
0.580

0.111* 0.233***(0.0566) (0.0757)
3,089
1,773
0.565
0.500

Heckman twostep estimation
White

0.0633** 0.0161-0.0515 0.0992** 0.229***(0.0305) (0.0620) (0.0533) (0.0487) (0.0575)
Mill's ratio -0.537*** -0.444*** -0.242 -0.592*** -0.606**(0.115)(0.131)(0.165)(0.230)(0.290)N
12,308
1,423
3,872
4,307
2,706
Notes: Clustering robust standard errors in parentheses and the error term isclustered at the player's level in all specifications. The dependent variable and the
explanatory variables are the same as those in Table 3. The row white displays theestimated coefficient of the white dummy in different specificatons. In the first block,the sample is restricted to players who have 5 or more years of experience at theNBA. In the second block, the sample is restricted to US-born players. In the third
block, the Heckman two-step estimation is applied to control the endogeniety of
having a contract in season t. Players who played in season t-1 but who did not havea contract in season t are included in the first stage. The row Mill's ratio displays theestimated coefficients of the inverse Mill's ratio. In the third block, the standard error
is calculated by using the bootstrap. The regression equation is estimated by using
the unbalanced panel data covering salary information from the 1985–1986 season to
the 2015–2016 season. Columns (1), (2), (3), (4), and (5) show the esimatedcoefficients of white dummy, its standard error, the number of observations, and R²
when all observations, observations in the 1980s, observations in the 1990s,
observations in the 2000s, and observations in the 2010s are used.

23

Table 4: Estimated Coefficient of White Dummy with Other Controls
(1)
(2)
(3)
(4)
(5)
all
1980s
1990s
2000s
2010s
Specifications
OLS: controlling theperfomance at t-2
White
0.0724** -0.00750 -0.0463 0.120** 0.275***(0.0360) (0.0771) (0.0515) (0.0468) (0.0749)
N
8,248
429
2,754
3,172
1,893
R-squared
0.612
0.681
0.560
0.528
0.416
OLS: controlling theperfomance at t-3
White
0.0759* 0.00390 -0.0581 0.102* 0.335***(0.0391) (0.0820) (0.0561) (0.0549) (0.0906)
N
7,135
360
2,397
2,750
1,628
R-squared
0.591
0.699
0.526
0.487
0.352
OLS: including players
who experienced
mutliple teams inseason t
White
0.0696** 0.0295 -0.0366 0.0804* 0.246***(0.0321) (0.0559) (0.0486) (0.0471) (0.0615)
N
10,091
745
3,265
3,773
2,308
R-squared
0.650
0.712
0.585
0.560
0.493
Adding year dummy×team dummyWhite
0.0761** 0.0286 -0.0471 0.0936** 0.255***(0.0323) (0.0556) (0.0499) (0.0474) (0.0629)
N
9,822
745
3,203
3,650
2,224
R-squared
0.682
0.728
0.620
0.593
0.526
Notes: Clustering robust standard errors in parentheses and the error term is clustered at the player's
level in all specifications. The dependent variable and control variables are the same as those in Table
3, except the performance variables at t-1. In the first and second blocks, the performance variables at
t-1 are replaced by the performance variables at t-2 and t-3. The row white dipalys the estimatedcoefficients of the white dummy. In the fourth block, players who experienced multiple teams areadded to the sample. For such players, the total salary in season t is used as the dependent variable.
The team that gave the highest salary during season t is classified as the team for such players. In the
fourth block, the interaction term of year dummy and team dummy is added as an additional control
variable.

24

Table 5: Estimated Coefficients of White Dummy in Other Specifications
(1)
(2)
(3)
(4)
(5)
all
1980s
1990s
2000s
2010s
Specifications
OLS: Adding owner's
race dummy and its
interaction with thewhite dummy
White
0.128
-0.0933
0.04470.297* 0.259***(0.0919)(0.131)(0.153)(0.160) (0.0618)
N
9,822
745
3,203
3,650
2,224
R-squared
0.655
0.713
0.590
0.566
0.492
OLS: Adding GM's race
dummy and its
interaction with thewhite0.142**
0.05780.01440.193** 0.325***(0.0605)(0.112)(0.112)(0.0774) (0.108)
N
9,822
745
3,203
3,650
2,224
R-squared
0.656
0.713
0.589
0.566
0.493
OLS: Adding relative
income and its
interaction with theWhite
0.0848**0.0336-0.0302 0.0991** 0.261***(0.0337) (0.0587) (0.0537) (0.0481) (0.0634)
N
9,470
736
3,080
3,505
2,149
R-squared
0.659
0.714
0.595
0.570
0.494
Notes: Clustering robust standard errors in parentheses and the error term is clustered at the player's
level in all specifications. The dependent variable is the log of the annual salary in all three blocks. The
explanatory variables in the first block are the explanatory variables used in Table 3 and the owner's
race dummy and its interaction with the white dummy of the player. The owner's race dummy is equal
to 1 if the race of the owner is white, and 0 otherwise. In the second block, the explnatory variables are
the variable used in Table 3 and the GM's race dummy and its interaction with the white dummy of theplayer. The GM's race dummy is equal to 1 if the race of the GM is white, and 0 otherwise. In the third
block, the explanatory variables are the explanatory variables used in Table 3, the relative medianincome of white residents over black residents in the state where the team is located and its interaction
with the white dummy of the player.

25

.4
.3
density
.2
.1
0

10

12

14

16

ln(salary)non−whitecounter−factual of salary distribution of non−white players

white

Figure 1: Estimated densities of log of annual salary of different players in 1985–1995. The
solid green line is the estimated annual salary density of white players. The blue dash lineis that of non-white players. The red dotted line is the counter-factual of salary density of
non-white players. The counter-factual salary density is the log of the annual salary densitythat non-white players would have if the attributes of non-white players (other than race)
were rewarded in the same way as the attributes of white players. For estimating the density,
we conduct the kernel density estimation with Gaussian kernel with the optimal bandwidth.
The calculated optimal bandwidth is 0.178. To calculate the counter-factual density, we use
the same explanatory variables as those used in Table 3.

26

.5
.4
density
.2
.3
.1
0

8

10

12
ln(salary)14

non−whitecounter−factual of salary distribution of non−white players

16
white

0

.1

.2

density.3.4.5

Figure 2: Estimated densities of log of annual salary of different players in 1996–2005.

10

12

14

16

ln(salary)non−whitecounter−factual of salary distribution of non−white players

white

Figure 3: Estimated densities of log of annual salary of different players in 2006–2015.
27

Appendix(This appendix is for the purpose of refereeing. It will become

−.4

−.2

0

.2

.4

.6

available from author’s website and journal’s website)

coefficient of white dummy
90%CI(lower bound)
1980

1990

2000
year

90%CI(upper bound)

2010

2020

Figure A1: Coefficients of white dummy and its 90% confidence intervals. The estimatedcoefficient of the white dummy is plotted when the equation used in Table 3 is applied foreach year separately.

28