Wage Discrimination in the NBA: Evidence using Free Agent Signings
Candon Johnson∗
West Virginia University
Eduardo Minuci†
West Virginia University
August 28, 2019
Abstract
This research paper investigates the prominence of wage discrimination in the National Basketball Association (NBA) using free agent signings from 2011-2017 allowing us to better capture the determinants of player wages, a limitation in previous NBA wage discrimination literature. Using the Oaxaca-Blinder decomposition and weighted linear regression models, we find that black athletes are paid significantly less than their counterparts. In addition, weighted quantile regressions show evidence of consumer discrimination presence in the league. This is observed through the result that black players with high audience visibility experience a larger racial wage gap; moreover, this gap is positively related to the share of white population of MSA where the player is employed.
Keywords: wage discrimination, National Basketball Association, free agency
JEL Codes: Z22, J71, L83
∗West Virginia University, College of Business & Economics, 1601 University Ave., PO Box 6025, Morgantown, WV 26506-6025, USA; Email: cjohns77@mix.wvu.edu
†West Virginia University, College of Business & Economics, 1601 University Ave., PO Box 6025, Morgantown, WV 26506-6025, USA; Email: egm0007@mix.wvu.edu.
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1 Introduction
The racial structure of host standard metropolitan statistical areas (SMSA) influences the racial structure of National Basketball Association (NBA) teams due to consumer preference to see play ers of their own race, potentially leading to a large racial wage gap (Burdekin and Idson, 1991). Racial wage gaps, their size, and their existence are essential topics of study in labor economics. Professional sports provides an appropriate setting to examine the potential impact of race on salary. Economists have studied racial wage discrimination in the National Basketball Association (NBA) throughout the 1980s, 1990s, and 2000s, specifically the discrimination against black ath letes. Some studies report that black athletes were not paid as highly as their white counterparts; however, the results found across the literature are largely inconsistent. Moreover, this literature has not been examined in recent NBA history. Thus, inconsistent and outdated results motivated this study. We utilize an improved data set and empirical approaches not previously used in the NBA labor market literature to examine the presence and size of the racial wage gap in this labor market.
A portion of our empirical approach most resembles that of Holmes (2011). First, we use the same sample selection process, restricting the sample to include only free agent contract signings. Moreover, we use weighted least squares and quantile regressions to further explore our findings of discrimination in the NBA, the main approaches used by Holmes (2011) to find discrimination within the MLB. Additionally, we use the Oaxaca-Blinder decomposition an approach previously seen in the general labor market and sports literature, but not previously used to analyze the NBA labor market.
Our analysis goes beyond investigating an average racial wage gap. This research, in addition, further investigates discrimination in the NBA by considering three sources of racial discrimina tion: consumer, employer, and employee discrimination(Becker, 1971). Consumer discrimination is explored using the weighted quantile regressions with an interaction term between black players and the share of the metropolitan statistical area (MSA) population that is white. Employer and employee discrimination are examined by interactions between the race of players with the race of
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coaches and general managers, which is an approach previously explored by Hamilton (1997). Our results show that black athletes are paid in the league on average 20.5% less than their counterparts, ceteris paribus. More importantly, 63.9% of this wage gap cannot be explained by observable characteristics and, therefore, is attributed to racial discrimination. Thus, our results indicate the presence of a racial wage gap of 13.1% in the NBA. The wage gap is shown to be ro bust through various econometric approaches using different specifications including or excluding population characteristics and using alternative statistics for player performance. We find that consumer discrimination is the primary source for this racial wage gap. This result is derived from our weighted quantile regressions which include an interaction term between the percentage of white population in the employing team’s MSA and an indicator variable for whether a player is black. The results indicate that the gap between black and non-black players increases as local share of white population increases. The quantile regressions also show the racial wage gap to only be significant for the upper portions of the salary distribution, which includes role and star players1. Role and star players are defined in this research as players with high court visibility relative to bench players, with bench players being located in the lower portion of the salary distribution.
This type of discrimination manifests itself through consumers due to their preference for watching those of the same race on the court (Burdekin and Idson, 1991). The experience of watching a game is the product consumed by customers in this market; hence, the most visible players should be the only ones significantly affected by consumer discrimination if it exists in this market. The conclusions drawn by this paper arise and differ from previous literature due to an important empirical contribution this papers brings to the NBA labor market literature, the use of a data sample which considers only free agents.
The data set we use includes NBA free agency signings from 2011-2017. Data has been a limitation in this literature, as previous papers do not use free agents or usually includes short sample periods. Using free agent signings, previous season performance, and the correct use of
1The characterization of players is given based on the distribution of salaries as done by Hamilton (1997). The specific criteria for characterization of players will be further defined in Section 4.
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other control variables provide an appropriate framework to explore a player’s compensation for his expected current level of output2. In other words, we are able to more accurately capture his marginal revenue product. Holmes (2011) recognizes this shortcoming of the sports literature regarding the racial wage gap, but investigates the MLB labor market. We are the first to apply this to the NBA setting to examine the racial wage gap3. The length of the data set used in this paper must also be highlighted since most NBA labor market papers, with the exception of Hill (2004), Groothuis and Hill (2013), and Hill and Groothuis (2017), investigated wage discrimination against black athletes in the NBA using two or fewer years of data. The data set used here covers free agents from six NBA seasons, which gives us a sample of nearly 800 free agents.
2 Literature Review
The amount of papers that study the wage gap between black and non-black men is extensive. Lang and Lehmann (2012) provide a theoretical and empirical review on wage discrimination in the U.S. labor market. The divergence of results in this literature are generally explained by the different control variables and data range used by different authors due to theoretical considerations and/or data limitations. After reviewing the literature, Lang and Lehmann conclude that a wage gap of approximately 10% exists between white and black male workers, which is similar to our results for the NBA labor market. Moreover, the authors point out an important result of Lang and Manove (2011), who state that the wages converge for workers with very high and very low levels of education, or human capital, which highlights the importance of analyzing different quantiles of the wage distribution.
A vital difference to be pointed out between typical goods and services market and the NBA is their final goods. Goods and services which can be consumed by individuals generally represent the U.S. labor market’s final goods. On the other hand, the NBA labor market offers a final good
2For instance, an analysis of a player’s pay compared to his current performance that, for example, is in his second year of a three year contract does not yield accurate results.
3Johnson and Hall (2017) utilizes free agent signings to examine the impact of variation in state income tax rates on NBA player salaries.
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which sells the experience of watching a basketball game. This is important because the NBA final goods are dependent on the exposure of its workers (players), which is not necessarily true for the U.S. labor market, since buyers frequently do not know which worker specifically produced their good or service they are consuming.
In regards to research on discrimination more specific to sports, the topics covered is broad. For instance, it covers the impact that race has on playing time and salaries in the NFL (Burnett and Van Scyoc (2013); Keefer (2013); and Keefer (2016)4), on the probability of an umpire calling a strike in the MLB (Parsons et al., 2011), and on the wages of English soccer players (Szymanski, 2000). Other studies, Hoang and Rascher (1999) and Groothuis and Hill (2004), have focused on exit discrimination finding contrasting results. The literature has also explored the connection between productivity and wage inequality (Berri and Jewell, 2004) and population racial struc ture and capital investments (stadium reforms) (Bodvarsson and Humphreys, 2013). Results put forward by Price and Wolfers (2010) suggest discrimination among NBA referees. Kahn (1991) provides a review of early studies on this topic related to all sports. Even though discrimination can be studied through several channels, the focus on this paper is to dig deeper on the empiri cal findings of wage discrimination against black players in the National Basketball Association (NBA).
There exists a substantial literature regarding NBA wage discrimination; however, the incon sistency of their results piqued our interest in this topic. Kahn and Sherer (1988) examine salaries in the 1985-1986 season to find that black players are underpaid by 20%. Moreover, they also finds that replacing a black player with a white player increases attendance, which indicates the presence of consumer discrimination. Burdekin and Idson (1991) studies consumer based discrim ination testing the hypothesis that “whites prefer to see white players.” Interestingly, they find that the percentage of white population in the host SMSA is strongly correlated with the percentage of white athletes on the respective NBA team5. Gius and Johnson (1998) claim that the racial wage
4Keefer (2016) finds black players start and play more.
5The hypothesis posited in Burdekin and Idson (1991) implies that “blacks prefer to see black players”. Murray (2015) replicates the results found in Burdekin and Idson (1991) using data from the NBA for the 2009-10 through 2013-14 seasons finding a similar result.
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gap was gone by 1996-1997. Hamilton (1997) shows no premium on average received by whites; however, using a quantile regression he highlights a preference from the audience for white play ers. Groothuis and Hill (2013) study exit discrimination, pay discrimination, and career earnings of NBA athletes using data from 1990-2008, finding conflicting results. Both reverse discrimination and discrimination are found to be potentially present, however the results found are not robust.
Hill (2004) finds that black players are underpaid by 14% to 20% after analyzing a period from 1990 to 2000, but that such wage gap drops out when controlling for height. Hill points out that not controlling for height caused the white indicator variable coefficient to capture the premium that taller players received, due to the fact that white players are on average taller than black players in the NBA. In addition, Kahn and Shah (2005) shows, with a monopsony model, that nonwhite players that were not free agents nor on rookie contracts were underpaid, but the difference was small under rookie contracts and small and insignificant for free agents in the 2001-2002 NBA season. Lastly, Ajilore (2014) focuses on whether white players suffer statistical discrimination finding no statistical differences between black and white.
Recent literature has focused more on the influx of foreign players. Eschker et al. (2004) shows a wage premium for foreign players for the 1996-1997 and 1997-1998 season, and Hoffer and Freidel (2014) finds that foreign players receive an average wage premium of approximately $900,000. Moreover, Hill and Groothuis (2017) find that foreign born who did not attend to college in the U.S. earn a premium in the 1990s, but that such premia disappears in earlier years. Foreign athletes changed how NBA teams scouted, drafted, and acquired talent. Our paper addresses this concern by including indicators for both foreign-born players who played US college basketball and for those who developed their talents abroad.
The NBA discrimination literature experiences shortcomings. Most papers focus only one or two seasons 6and do not use free agents data to determine wage discrimination. Using players that are in the middle of their contract to test for discrimination by using their past season or current season performance as control variables will not accurately estimate the determinants of a player’s 6With the exception of Hill (2004), Groothuis and Hill (2013), and Hill and Groothuis (2017)
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contract. Player performance in the prior season should not have any power in determining the player’s contract value if it is not a newly signed deal during free agency.
A player can regress or improve drastically throughout the duration of his contract making him far outperform or underperform the expectations of his predetermined salary. Player injury is also a concern when considering players in the midst of a current contract7. The same intuition is valid for other control variables such as coach’s and GM’s race, signing team and original team win percentages, age, etc. For instance, this gives a possible explanation for the inconsistency of the presence and size of a racial wage gap presented by the NBA labor market literature. These inconsistencies in data sets that do not capture wage determinants provide us with an opportunity to add to this strand of literature.
3 NBA Labor Market
The data utilized in this paper contains free agency signings over a period of 2011 to 2017. The NBA labor market contains many intricacies. New incoming players generally enter the NBA through an entry draft. The structure of a player’s contract is determined by his draft position, or a player can be undrafted in which he becomes a free agent. Salaries for first round draft picks follow a rookie salary scale. The value of the contract of a first round pick decreases as the number of the slot they are selected later in the draft, and can be negotiated between 80-120% of the scale value. Contracts for first round selections contain two guaranteed years followed by team options for each the third and fourth season. Going into the fifth season of the contract a player can sign an extension, sign a qualifying offer, or become a restricted free agent. Second round picks and undrafted players do not receive guaranteed contracts and are able to negotiate their contracts. Rookie contracts are not considered in this paper as they are largely fixed and negotiated without regarding prior NBA performance.
Restricted free agency differs from unrestricted free agency in that players are not able to
7For example, Derrick Rose played only 10 games in the 2013-2014 NBA season, while being paid over $17 million as part of a contract extension he and the Chicago Bulls agreed to in 2011.
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sign and play for any team. Unrestricted free agents are free to sign with any team they choose, conditional on that team desiring their services. In contrast, a restricted free agent is subject to his team’s right of first refusal. Restricted free agents can sign an offer sheet from another team, of which his current team has the ability to match the offer and retain the rights to the player. Restricted free agents are generally paid a higher salary than unrestricted free agents, which is highlighted in our results.
Restricted free agency can impact the free agency period of the player, as well as teams that are interested in pursuing their services. Free agency during our sample period begins on July 1st followed by a short moratorium period. After the moratorium period, players can sign a contract or an offer sheet. For restricted free agents, after signing an offer sheet their current team has a three day period to match the offer. This three day period can affect a teams pursuit of other free agents and potential trade offers.
During free agency periods, teams are constrained by the amount they compensate players. Contracts have a minimum and maximum value that vary based on a player’s accolades, NBA ex perience, whether or not a player is re-signing with their current team, among other characteristics. A maximum contract can be generally 20-35% of the total salary cap space of the team. A player can be incentivized to re-sign with their current team when he is a player that can draw a max contract. For instance, during the 2018 NBA free agency period Lebron James was eligible for a 5 year $205 million contract if he had chosen to re-sign with the Cleveland Cavaliers. He ultimately chose to receive “only” a maximum contract of 4 years for $152 million when he decided to sign with the Los Angeles Lakers.
Players can also receive performance bonuses written into their contracts such as playing a certain amount of games, and keeping a certain level of performance, which is evaluated through their statistics. Ideally, the minimum and maximum values should be censored for in the empirical analysis used in this paper. This required us to individually investigate which player received a max contract every time they appear in our sample. This investigation was done by reading news articles about new contracts signed. Unfortunately, we cannot say with certainty that the
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media indeed reported all players which received a max contract; hence, this variable may be misrepresenting the sample of players which signed a max contract. Due to this data limitation, our baseline results including an indicator for max contracts are presented in the appendix. The results with the inclusion of max contracts are similar in significance and magnitude.
4 Empirical Analysis
4.1 Data Description
The data on NBA player race was retrieved similarly to Price and Wolfers (2010) and Van Scyoc and Burnett (2013). At least three different observers analyzed the pictures from NBA player bios on the NBA’s official website and basketball-reference.com to determine whether a player appears to be black or non-black. This approach is appropriate as players will be discriminated against based on their appearance, and not their genetic race or ethnic background. An indicator is used to identify black players that takes a value of 1 or 0. The same approach is used to determine the race of coaches and general managers. Coaches’ and GMs’ information were gathered from a combination of basketball-reference.com, basketball.realgm.com, and news articles.
Information on NBA free agency signings from 2011-2017 will be used to find if discrimination exists in the NBA currently. Data on 797 NBA free agent signings was taken from spotrac.com, a website that aggregates data from various reliable sources of NBA information including trans actions, signings, and contracts. Player salaries are taken as an average salary value by dividing the total value of their contract by the length of the contract in years. The natural log of a player’s annual salary is the dependent variable of all the empirical specifications explored in this paper. The empirical specifications used in this paper also include proper control variables to allow us to better identify the impact of race on player’s annual salary. Various statistics and characteristics are used for both team and player. These include: team winning percentage, player characteristics, performance statistics, and information on the MSA that contains the team.
Player characteristics include age, height, race, foreign-born indicators, draft position, and 9
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position played. Performance statistics used will be points, rebounds, assists, blocks, steals per game, and field goal percentage. Also included is the amount of games played by the player, their minutes played per game, and in what percentage of games played did the player start. The percentage of games started is used to help control for a starter versus a bench player. Games played is included to help control for players that are signed but do not play whether for skill deficiency or injury. All of the performance and games played statistics are from the season before the players signed their new contracts as their output in the previous season is assumed to be the main driver in their salary following their free agency. Most player statistics, player characteristics, and team winning percentage were all obtained from basketball-reference.com. Height and draft position were obtained from basketball.realgm.com.
An additional statistic is used in various specifications throughout this paper referred to as Value Over Replacement Player (VORP). VORP gives an aggregate measure of a players on court performance and their overall value to their team. This measurement comes from basketball reference.com and was constructed by Daniel Myers. VORP compares the impact of players to a theoretical replacement player based on their Box Score Plus/Minus (BPM) and the actual percent age of their team’s minutes played. Box Score Plus/Minus estimates how well a player performs compared to an average player per 100 possessions, which is defined as 0.0. For example, the highest BPM in the sample is LeBron James in 2015-2016 when he posted a 9.1 BPM, which means James was 9.1 points better per 100 possessions than the average player in the league. For the purposes of VORP, -2 is considered the value of a replacement player. The formula for VORP is [BPM −(−2.0)] ∗ (percentage o f minutes played)*(team games/82).
While any box score based metric is not perfect as they can not account for the importance of basketball IQ, fundamental skills, or how effective of a team defender a player may be, VORP is an appropriate measure to be used. In the specifications using VORP, the number of minutes, points, rebounds, assists, steals, and blocks per game and the number of games played in the previous season are all dropped. This is because VORP includes proxies for these performance measures among others in its calculations.
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We also ran the regressions using Win Shares (WS), Player Efficiency Ratings (PER), and Wins Produced (WP) as alternative advancement measurements for performance8. These advanced per formance statistics are able to capture the efficiency and productivity of a player better than the alternative specifications using per game statistics. Nonetheless, our results are robust across the use of any of these performance variables. The results are nearly identical in size and signifi cance when using either VORP or WP. PER and WS yield similar significance, but slightly lower coefficients compared to VORP and WP. VORP, WS, and PER are each retrieved from basketball reference.com, while WP comes from boxscoregeeks.com9.
To investigate the effect of coach and general manager characteristics in the contracting pro cess, this study considers the coach and general manager race as well. Race information for coaches and general managers were retrieved from a combination of basketball-reference.com, basketball.realgm.com, and news articles.
Metropolitan Statistical Area (MSA) data to control for demographic characteristics of the city hosting the team includes total population and percentage of the total population that is white. This approach to control for population characteristics is motivated by Bodvarsson and Humphreys (2013). The population data came from the American Community Survey website. Statistics Canada from the government of Canada was used to gather population characteristics for the Toronto Raptors.
Table 1 shows summary statistics for the entire sample of free agents, black players, and non black players. The average annual salary received by NBA free agents was over $5 million for each sample, with non-black players having a higher average salary than black players. This initial comparison served as a motivation to further investigate this finding. Figure 1 shows the kernel density of black and non-black athletes. Overall, the differences in density across the salary distribution of non-black players appear to lie slightly above black players in the both the middle and upper sections of the salary distribution.
8The results including these alternatives can be provided upon request.
9https://www.basketball-reference.com/about/glossary.html provides more information on the calculation of these VORP, WS, and PER. Wins Produced is discussed in Berri (2010).
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To produce meaningful results, we must first deter whether our data consists of representative sample of the NBA athletes. To do so we compare the distribution of black players in our sample, 78%, to the distribution of black players in the NBA as a whole, around 75-80%, which is fairly representative (Spears, 2016). As highlighted in the literature, the role of foreign players is impor tant in the NBA. In our sample, almost half of non-black players, 46%, are foreign. Nonetheless, foreigners only constitute 16% of all the players in our sample. Overall, information on 797 free agent signings was obtained. Other noticeable differences between black and non-black players are the frequency which players re-signed, average draft position, and average performance (ac cording to VORP). In general, non-black players perform better, re-sign more, and are drafted later in the draft.
4.2 Methodology
Three main econometric specifications are explored to investigate whether a racial wage gap is present in the NBA: a weighted Oaxaca-Blinder decomposition, a weighted least squares (WLS) wage model, and weighted quantile regressions. The weighted twofold Oaxaca-Blinder decom position follows an approach previously used in the general labor market (e.g.: Neal and Johnson (1996), Neumark (1988), and Boudarbat and Connolly (2013)) and sports literature (e.g.: Bur nett and Van Scyoc (2013), Keefer (2013), Van Scyoc and Burnett (2013), and Leeds and Leeds (2017)), but that from the best of our knowledge is for the first time being explored to analyze the NBA labor market. This decomposition was first introduced by Oaxaca (1973) and Blinder (1973). This approach explores how much of the gap between the regressions results of two different sam ples is explained by observable characteristics (Elder et al., 2010). It allows us to evaluate how much of the wage gap between two groups is not explained by the vector of predictors; in other words, we are able to determine how much of the wage gap is due to discrimination given that we have an appropriate set of control variables. In this section, we will present the standard twofold specification10.
10For a more detailed explanation of the model please refer to Jann (2008).
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First, consider two groups: non-black (1) vs. black (2) players. Let g be an indicator variable for 1 or 2. Let Yg be the log of the average salary for a member of group g and for it to be defined by Yg = X0gδg +εg. We take the log of the average salary to transform the data to handle skewness. Xg represents a vector with predictors for group g. δg is the vector of coefficients for each predictor and the intercept and εg the residual for group g. Assuming that E(δg) = δg and E(εg) = 0, after estimating the regression coefficients for both groups, it is straightforward to define the racial wage gap as
G = Y1 −Y2 = (X1 −X2)δ 1 +X2(δ 1 −δ 2), (1)
Redefining the two terms on the right-hand side of the equation above as E and U, respectively, allows us to rewrite the equation as
G = E +U. (2)
E represents the racial wage gap that is “explained” by systematic differences in the predictors of both groups. In other words, the “endowment effect” (Jann, 2008). U, on the other hand, indicates the log salary differential that is “unexplained” by our predictors, which is defined in the literature which used this decomposition as the “discrimination effect”.
In our model, we control for population, team, coach, general manager and player charac teristics; race; performance; and season, team, and position fixed effects. Moreover, the model is weighted by the inverse of the amount of contracts signed by a player. It is weighted in this manner to control for players that sign multiple contracts throughout the period so the results are not driven by few players signing multiple short contracts. In the sample 250 players signed one contract, 143 signed two, and one player (Ronnie Price) signed six. The rest of the sample signed between three and five contracts. In the regressions, a player that signs one contract will have a weight of 1, a player signing two contracts will have a weight of 0.5, and so on.
The standard twofold decomposition creates a counterfactual base concern as noted by Boudar
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bat and Connolly (2013). Since the result generated from the model specified above is based on the perspective of group 2 (black players), altering the definition of group 1 and 2 can theoretically generate different results to some extent. As an answer to this concern, we instead run a pooled twofold Oaxaca-Blinder decomposition as suggested by Neumark (1988). This specification uses coefficients from a pooled regression (black and non-black together), where an indicator variable for whether a player is black is included (Jann, 2008). In addition, robust standard errors are also applied in the derivation of our results.
Another potential concern is the pooled twofold Oaxaca-Blinder decompositon may potentially understate the discrimination effect compared to OLS. To answer this concern, we use another approach to validate our racial wage gap empirical results, a weighted least squares (WLS) wage model. This empirical framework is very comparible with previously used econometric models seen in the NBA racial discrimination literature. The closest specification to ours, however, was used in the analysis of the MLB labor market by Holmes (2011). To determine the NBA racial wage gap, once again we take the log of the average salary. The log-linear model to test for discrimination based on race is then defined by
ln(Salaryi j ps) = γ j +αi +τs +β1Per f ormancei j(s−1) +β2Populationj +β3Racei (3)
+β4WinningPctj(s−1) +β5His +β6Coach/GMRace js +ei js.
The model includes all the predictors used in the Oaxaca-Blinder model. More specifically, Per f ormancei j(s−1) contains a vector of performance measures for player i and team j in season s−1. Populationj controls for the population level and proportion of the population that is white in the area surrounding team j. Raceiis an indicator variable for player i taking a value of 1 if a player is identified as black. WinningPctj(s−1) controls for the performance of the team a player was under contract with in the previous year, and the team they signs with during free agency. The vector His contains player characteristics variables. Coach/GMRace js controls for race of coach and general manager in charge of team j at the beginning of season s. γ j represents a fixed
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effect for the team a free agent signs with, αiis a fixed effect for the position player i plays, and season fixed effects is defined by τs. This model is weighted by the same approach described in the weighted Oaxaca-Blinder model. Running an unweighted ordinary least squares regression yields similar results, which can be provided upon request.
To explore whether the discrimination is concentrated in certain types of players, we also run weighted quantile regressions. These regressions are extremely useful in this scenario since their results are not based on the sample mean as the WLS regression; rather, they estimate the function for the natural log of salary quantiles conditional on the control variables specified by the model. According to Holmes (2011), such model diminishes the effect of outliers since they are based on the median of determined quantiles of the distribution of the dependent variable, which in this case is the log of a player’s salary. The quantile regressions in this research solve the following minimization problem:
minβ∈R
n∑
ρθ (ln(Salaryi j ps)−Ai j psβ) (4) i=1
where using an indicator function, I(.), allows us to define ρθ as:
ρθ (A) = (θ −I(A ≤ 0))A (5)
For Equation (4) and Equation (5), A represents a vector including all the control variables specified on the right-hand side of Equation (3), and β represents the vector of coefficients of Ai j ps. Moreover, changing θ defines which quantile we are getting our results based upon. Players once again are weighted by the inverse of the number of contracts which they signed during the sample period we analyze. The following section will analyze empirically such models and further investigate the results they generate.
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4.3 Results: Is the Racial Wage Gap Present in the NBA?
To examine the size of the racial wage gap we begin our discussion by interpreting the results from the Oaxaca-Blinder decomposition. We then re-evaluate our results using a weighted least squares (WLS) model. We follow the examination of the size of the racial wage gap by testing for the three different sources of discrimination previously highlighted by Becker (1971): employer, employee, and consumer.
Employer discrimination refers to an employer paying his/her employee less due to racial char acteristics. In the NBA, we can think of this channel being translated to the relationship between players and general managers (GM) as well as their coaches, since a GM generally has control of the team, but with input from coaches. This relationship can also serve as the channel for em ployee discrimination. Consumer discrimination, on the other hand, refers to a decrease in salary explained by consumer preferences. In this league, since around 75-80% of players are black, a premium for non-black players could be seen as a preference of the audience for watching non black players on the court. This paper follows Becker (1971), in which each of the channels of discrimination defines discrimination as being correlated to individuals’ tastes for characteristics similar to theirs.
To investigate the relationship between the race of players with the races of coaches and GMs to test for employer and employee based discrimination, the WLS specification is used. In addition, we use quantile regressions to test for consumer discrimination.
4.3.1 Oaxaca-Blinder Decomposition Model
The results of our pooled twofold Oaxaca-Blinder decomposition are reported in Table 2. Columns 1-4 show different specifications, adjusting for alternative performance measures and adding pop ulation controls. Each specification includes player, team, GM, and coach characteristics. Control variables for columns (1) and (3) for performance include points, assists, rebounds, blocks, and steals per game as well as field goal percentage. Columns (2) and (4) use VORP instead of per game statistics to control for performance. In specifications using VORP, games played and field
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goal percentage are also dropped, as they are included in VORP. We also run regressions with different specifications using alternative advanced metrics such as WP, WS, and PER, which yield similar results and can be provided upon request. In columns (3) and (4), population controls are added, including population size and the percentage of the population that is white from the MSA hosting the player’s signing team.
We select Column 4 as our preferred specification, proposing that it includes the most appro priate control variables based on the current data availability. In this paper, we select VORP as our preferred performance measurement for two reasons: (1) its ability to be interpreted as a measure of a player’s value and (2) its aggregation characteristic, which allows us to have a more concise measure of performance of a player.
Table 2 indicates the existence of a 20.5% gap in the mean average salary between black and non-black players, with the latter receiving this premium. 36.2% of this gap is attributed to system atic differences in characteristics of black and non-black athletes; however, this is not significant. The remaining portion of this gap is unexplained by the predictors used in our decomposition model. Following the papers in the literature which explore the Oaxaca-Blinder decomposition, we interpret this unexplained portion of the wage gap as the discrimination that black players suffer in the NBA labor market. Thus, this model indicates that black NBA players on average receive 13.1% less than non-black NBA players, all else equal.
4.3.2 Weighted Least Squares Regression
We estimate a weighted least squares model to further explore the existence of the racial wage gap in the NBA using Equation (3). This allows us to compare our results with the previous literature, which used similar econometric specifications, but data sets containing certain limitations as dis cussed in Section 1. Moreover, Elder et al. (2010) shows that the twofold Oaxaca-Blinder may overstate the contribution of observed characteristics, thus understating the discrimination effect; hence, this specification also function as a robustness check for the Oaxaca-Blinder decomposition results. The results are shown in Table 3.
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The results for player and team characteristics are as expected. Age is found to have a quadratic relationship with salary, also seen in Johnson and Hall (2017). A player is compensated more when re-signing with their current team, when they are restricted free agents, or when signing multi-year contracts. An explanation for players that re-sign receiving a higher salary comes from these players being eligible for a higher maximum salary from their respective team. Also, if a team values a player they can pay more to retain his services. This result shows that players do not on average give teams a “hometown discount”. Restricted free agents are generally young players completing their rookie contracts that have higher potential than other free agents. Their current team has the ability to match an offer sheet and the player will be forced to stay with this team. This, as well as the NBA salary cap structure, leads to these players receiving large contract offers from other teams to make it more difficult for their current team to match.
We posit that multi-year contracts have a positive effect on wages because a player on a one year contract may be signed roster filler or otherwise not included in the long term plan for his team, while players with multi-year contracts will be on the team long-term. Contract length and salary are shown to be positively related as in Krautmann and Oppenheimer (2002). Points, rebounds, assists, and minutes per game are found to be positive as expected. Due to the amount of variables, per game statistics are not reported. In specifications using VORP, a higher VORP increases salaries. We also find that players signing after playing for a team with a high winning percentage receives a higher salary, and players that sign with a team that has a high winning percentage will receive a lesser salary. The lesser salary from signing with a better team could be a partial result of “ring chasing” behavior in the NBA. 11
In each specification, discrimination is shown to be present in the NBA, ranging from black players being underpaid between 11.6 - 13.1% with our preferred specification being column 4. Column 4 shows a wage gap of 13.1%. The wage gap is identical when using both the Oaxaca Blinder decomposition and WLS regression. Our general findings of wage discrimination goes against the qualitative results found by Ajilore (2014) and Hill and Groothuis (2017), but it agrees
11For instance, veteran player David West opted out of a $12.6 million dollar contract, then signed with a San Antonio Spurs for the veterans minimum of approximately $1.5 million.
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qualitatively with Kahn and Sherer (1988). Groothuis and Hill (2013) finds similar quantitative results, but their results are not robust. We believe our results diverge from previous literature due to the use of a data set including free agents only, which is something not explored by previous authors. As previously highlighted, our sample of free agents can more properly control for the marginal revenue productivity of each player when determining wages. Moreover, interestingly our results are comparable with the average wage gap found in the U.S. labor market (Lang and Lehmann, 2012). We however do not find any significant results on the effect of GM and coach race on player salary.
4.3.3 Employer and Employee Discrimination
We further explore the impact of coach’s and GM’s race to examine different sources of discrimi nation, such as through employer and employee preferences for working with an individual of the same race. In the WLS results shown in Table 3, there are no results found to show a significant effect of coach’s or GM’s race on player salaries. However, we are motivated to explore this re lationship by Hamilton (1997). Hamilton finds no evidence of these variables being significant in determining a player’s wage. We explore this relationship further because using data with free agents only could yield different results. Thus, we run WLS regression models as specified in col umn (4) of Table 3, but including an interaction term between player’s and GM’s race or between player’s and coach’s race. These results are shown Table 4 columns (1) and (3). Additionally, we use a logit regression to determine if black players are more likely to re-sign with a black coach or GM relative to a white coach or GM. As in the WLS regressions, players here are weighted based on the inverse of the number of contracts each player signed during the sample period which the data was collected. These results are shown Table 4 columns (2) and (4). The interaction terms between player with coach’s and GM’s race yields no significant results on player salaries or their likelihood to re-sign. When adding an interaction term between player and coach the wage gap is found to increase, but it lowers when interacting player’s and GM’s race.
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4.3.4 Consumer Discrimination
In this subsection we investigate whether the results found above are due to consumer discrimina tion. Since around 75% of players in the NBA are black, we hypothesize that the discrimination results from a preference of the audience to observe a group of players on the court similar to themselves, as in Burdekin and Idson (1991). We do not assume that audiences have disdain for the opposite race (Becker, 1971). We posit the idea that consumer discrimination connects with players’ visibility, in other words, it connects with the amount of time a player is on the court. Hence, we run quantile regressions, an approach previously used in the sports wage discrimina tion literature, as specified by Equation (4) and (5) to investigate if the discrimination result is concentrated on more visible players, players who spend more time on the court.
We assume here that the lower quantiles (10th and 25th) capture bench players, players who do not consistently play a large amount of minutes, as previously assumed by Hamilton (1997). We allow the 90th quantile to capture star players. This label is due to results from Humphreys and Johnson (2017) and Hausman and Leonard (1997), who show that star players are drivers of attendance in the NBA. Star players are the most visible players on the team, thus we can expect them to be subject to the highest amount of discrimination. Figure 2 plots minutes per game and salary, showing that players who receive a higher salary generally play more minutes per game. Additionally, the correlation between minutes per game and salary is 0.6268. Initially, utilizing quantiles to capture star players raises concern regarding the proportional of players that are black and non-black across the salary distribution, particularly star players. The racial breakdown in the top 10% of salaries and the entire sample are 77% and 78%, respectively. We refer to the 50th and 75th quantiles as role players, who can be seen as players who stay on the court the longest after the teams’ star players (90th quantile). If consumer discrimination is present, we expect such result to be found on the 50th, 75th, and 90th quantiles due to the higher visibility of those players. Our quantile regressions results can be seen in Table 5.
Given our classification of different players based on distribution of salaries this table provides support for our hypothesis of presence of consumer discrimination in the NBA. This result can
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be observed in columns 3 through 5, which reports that black players who are role or star players (50th, 75th, and 90th quantiles, respectively) receive a significantly lower pay due to their race relative to their counterparts, all else equal. More importantly, the empirical results show that as a black player becomes more visible to the audience, higher is the racial wage gap he faces. In addition, the result of no discrimination found for bench players seems plausible due to their low average of minutes played per game.
To state with confidence that the NBA faces consumer discrimination warrants further analysis. In response, we ran additional quantile regressions including an interaction term between black players and the share of white population in the MSA which the player’s team is located. The result of a negative and significant coefficient for the interaction term would indicate that the gap between black and non-black athletes’ salaries increases in MSAs with a higher share of white population. The results of the quantile regressions including this interaction term are reported in Table 6.
In general, a higher share of white population in the MSA where the team is located is as sociated with higher salaries for both black and non-black players; nonetheless, this effect is not symmetric. Salaries for black athletes increase at a slower rate than non-black athletes as white population increases when interacting the two variables, increasing the racial wage gap. While the discrimination on the 50th percentile from Table 5 loses significance, the interaction term is found to be negative and significant for both the 75th and 90th quantiles, with the 90th percentile experi encing a larger effect. Burdekin and Idson (1991) supports this result as the authors find consumer preferences to watch their own race play shapes NBA team structure. This consumer preference leads to a higher value placed on non-black athletes as white population increases, due to the NBA being approximately 75% black. Since the final good consumed during an NBA basketball game is watching players play in the game, consumers are concerned with the race of players who are on the court. The preference of consumers to interact with those of their own race is apparent in the results shown in Table 6 and provides empirical evidence of the existence of consumer discrimina tion in the NBA.
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Tables 5 and 6 indicate a possible premium being given to foreign-born players. At the bottom of the salary distribution foreign-born players with no U.S. college experience receive a premium, while foreign-born players with U.S. college experience who we label as role players receive a premium. A premium for foreign players is not found in other specifications. We do not make any claims to a foreign premium existing, as the results are not robust.
5 Conclusion
This study investigates empirically wage discrimination against black players in the NBA using an empirical method not previously used to study the NBA, as well as methods commonly used to strengthen the results found. We also use a more suitable data set considering only free agency signings. This allows us to more properly capture how a player is compensated for his marginal revenue product. Using both the Oaxaca-Blinder decomposition and a weighted linear wage model controlling for player performance, player, team, and employer characteristics, it is found that black NBA athletes are on average underpaid by 13.1% compared to their non-black counterparts. Moreover, our results suggest the presence of consumer discrimination in the NBA, finding an increase in the racial wage gap as the share of white population in the player’s team MSA increases.
6 Acknowledgments
We thank Amir Borges Ferreira Neto and Dr. Brad Humphreys of West Virginia University, Hyun woong Pyun of Ruhh-University Bochum, Joseph Kuehn of California State University-East Bay, Peter Groothius of Appalachian State University, and anonymous referees for their helpful feed back and suggestions on earlier drafts of this paper.
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References
Ajilore, O. (2014). Do white nba players suffer from reverse discrimination? Economics Bulletin, 34(1):558–566.
Becker, G. (1971). The economics of discrimination. chicago: Univ.
Berri, D. J. (2010). Measuring performance in the national basketball association. The Oxford Handbook of Sports Economics.
Berri, D. J. and Jewell, R. T. (2004). Wage inequality and firm performance: Professional basket ball’s natural experiment. Atlantic Economic Journal, 32(2):130–139.
Blinder, A. S. (1973). Wage discrimination: reduced form and structural estimates. Journal of Human resources, pages 436–455.
Bodvarsson, O. B. and Humphreys, B. R. (2013). Labor market discrimination and capital: The ¨ effects of fan discrimination on stadium and arena construction. Contemporary Economic Policy, 31(3):604–617.
Boudarbat, B. and Connolly, M. (2013). The gender wage gap among recent post-secondary grad uates in canada: a distributional approach. Canadian Journal of Economics/Revue canadienne d’economique ´ , 46(3):1037–1065.
Burdekin, R. C. and Idson, T. L. (1991). Customer preferences, attendance and the racial structure of professional basketball teams. Applied Economics, 23(1):179–186.
Burnett, N. J. and Van Scyoc, L. J. (2013). Compensation discrimination for defensive players: Applying quantile regression to the national football league market for linebackers and offensive linemen. Journal of Sports Economics, 16(4):375–389.
Elder, T. E., Goddeeris, J. H., and Haider, S. J. (2010). Unexplained gaps and oaxaca–blinder decompositions. Labour Economics, 17(1):284–290.
23
Electronic copy available at: https://ssrn.com/abstract=3276247
Eschker, E., Perez, S. J., and Siegler, M. V. (2004). The NBA and the influx of international basketball players. Applied Economics, 36(10):1009–1020.
Gius, M. and Johnson, D. (1998). An empirical investigation of wage discrimination in profes sional basketball. Applied Economics Letters, 5(11):703–705.
Groothuis, P. A. and Hill, J. R. (2004). Exit discrimination in the nba: A duration analysis of career length. Economic Inquiry, 42(2):341–349.
Groothuis, P. A. and Hill, J. R. (2013). Pay discrimination, exit discrimination or both? another look at an old issue using nba data. Journal of Sports Economics, 14(2):171–185.
Hamilton, B. H. (1997). Racial Discrimination and Professional Basketball Salaries in the 1990s. Applied Economics, 29(3):287 – 296.
Hausman, J. A. and Leonard, G. K. (1997). Superstars in the national basketball association: Economic value and policy. Journal of Labor Economics, 15(4):586–624.
Hill, J. R. (2004). Pay discrimination in the nba revisited. Quarterly Journal of Business and Economics, pages 81–92.
Hill, J. R. and Groothuis, P. A. (2017). Is there a wage premium or wage discrimination for foreign-born players in the nba? International Journal of Sport Finance, 12:204–221.
Hoang, H. and Rascher, D. (1999). The nba, exit discrimination, and career earnings. Industrial Relations: A Journal of Economy and Society, 38(1):69–91.
Hoffer, A. J. and Freidel, R. (2014). Does salary discrimination persist for foreign athletes in the nba? Applied Economics Letters, 21(1):1–5.
Holmes, P. (2011). New evidence of salary discrimination in major league baseball. Labour Economics, 18(3):320–331.
24
Electronic copy available at: https://ssrn.com/abstract=3276247
Humphreys, B. R. and Johnson, C. (2017). The effect of superstar players on game attendance: Evidence from the nba. Working Paper, pages 1–22.
Jann, B. (2008). The blinder-oaxaca decomposition for linear regression models. The Stata Jour nal, 8(4):453–479.
Johnson, C. and Hall, J. (2017). Do National Basketball Association players need higher salaries to play in high tax states? Evidence from free agents. Applied Economics Letters, pages 1–3.
Kahn, L. M. (1991). Discrimination in professional sports: A survey of the literature. Industrial and Labor Relations Review, 44(3):395–418.
Kahn, L. M. and Shah, M. (2005). Race, compensation and contract length in the nba: 2001–2002. Industrial Relations: A Journal of Economy and Society, 44(3):444–462.
Kahn, L. M. and Sherer, P. D. (1988). Racial differences in professional basketball players’ com pensation. Journal of Labor Economics, 6(1):40–61.
Keefer, Q. A. (2016). Race and NFL playing time. International Journal of Sport Finance, 11(2):144.
Keefer, Q. A. W. (2013). Compensation discrimination for defensive players: Applying quantile regression to the national football league market for linebackers. Journal of Sports Economics, 14(1):23–44.
Krautmann, A. C. and Oppenheimer, M. (2002). Contract length and the return to performance in major league baseball. Journal of Sports Economics, 3(1):6–17.
Lang, K. and Lehmann, J.-Y. K. (2012). Racial discrimination in the labor market: Theory and empirics. Journal of Economic Literature, 50(4):959–1006.
Lang, K. and Manove, M. (2011). Education and labor market discrimination. American Economic Review, 101(4):1467–1340.
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Electronic copy available at: https://ssrn.com/abstract=3276247
Leeds, E. M. and Leeds, M. A. (2017). Monopsony power in the labor market of nippon profes sional baseball. Managerial and Decision Economics, 38(5):689–696.
Murray, M. (2015). Customer preference and race in the nba. FanSided.
Neal, D. A. and Johnson, W. R. (1996). The role of premarket factors in black-white wage differ ences. Journal of Political Economy, 104(5):869–895.
Neumark, D. (1988). Employers’ discriminatory behavior and the estimation of wage discrimina tion. Journal of Human Resources, 23(3):279 – 295.
Oaxaca, R. (1973). Male-female wage differentials in urban labor markets. International economic review, pages 693–709.
Parsons, C. A., Sulaeman, J., Yates, M. C., and Hamermesh, D. S. (2011). Strike three: Discrimi nation, incentives, and evaluation. American Economic Review, 101(4):1410–35.
Price, J. and Wolfers, J. (2010). Racial Discrimination among NBA Referees. Quarterly Journal of Economics, 125(4):1859 – 1887.
Spears, M. J. (2016). Where are all the white american nba players? The Undefeated.
Szymanski, S. (2000). A market test for discrimination in the english professional soccer leagues. Journal of Political Economy, 108(3):590–603.
Van Scyoc, L. J. and Burnett, N. J. (2013). How times have changed: racial discrimination in the market for sports memorabilia (baseball cards). Applied Economics Letters, 20(9):875–878.
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Tables and Figures
Salary: Black vs Non-black
Density
0 10000200003000040000Salary(in 000s)
BlackNon-black
Figure 1: Kernel Density for Black and Non-black Players
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Table 1: Mean of variables used in the regressions, by race Non-black Black Total
Avg Salary (in 000s) 5590 5144 5242 Player is Black 0.000 1.000 0.780 Foreign-Born – No College 0.38 0.04 0.11 Foreign-born – College 0.08 0.05 0.05 Age 28.66 27.69 27.90 Games Played 58.25 56.64 57.00 % of Games Started 0.377 0.374 0.375 Minutes Played Per Game 19.96 20.75 20.58 Points Per Game 7.741 8.244 8.134 Rebounds Per Game 3.842 3.437 3.526 Assists Per Game 1.766 1.826 1.813 Blocks Per Game 0.421 0.387 0.394 Steals Per Game 0.547 0.671 0.644 VORP 0.605 0.571 0.579 Previous Team Win % 0.518 0.508 0.511 Signing Team Win % 0.529 0.517 0.520 Re-sign 0.469 0.350 0.376 Height in Inches 80.62 78.45 78.93 Draft Position 33.69 28.59 29.71 Head Coach is Black 0.251 0.278 0.272 GM is Black 0.143 0.204 0.191 Population (in 000s) 6414 6157 6213 White Population 66.66 65.86 66.04 Restricted Free Agent 0.194 0.130 0.144 Multi-year Contract 0.606 0.592 0.595 Observations 175 622 797
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Table 2: Pooled Twofold Oaxaca-Blinder Decomposition
(1) (2) (3) (4)
Non-black 15.07∗∗∗ 15.07∗∗∗ 15.07∗∗∗ 15.07∗∗∗
(205.34) (202.87) (205.45) (203.44)
Black 14.86∗∗∗ 14.86∗∗∗ 14.86∗∗∗ 14.86∗∗∗
(361.58) (359.25) (361.49) (359.23)
Difference 0.205∗∗ 0.205∗∗ 0.205∗∗ 0.205∗∗
(2.44) (2.41) (2.44) (2.42)
Explained 0.0889 0.0780 0.0878 0.0743
(1.12) (1.02) (1.11) (0.97)
Unexplained 0.116∗∗ 0.127∗∗ 0.117∗∗ 0.131∗∗
(2.39) (2.08) (2.41) (2.14)
Observations 797 797 797 797
t statistics in parentheses
Position and year fixed effects included
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Salary and Minutes per Game
40000
30000 Salary(in 000s)
20000 10000
0
010203040
Minutes Per Game
Figure 2: Scatter plot for Minutes Per Game and Salary
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Table 3: Weighted Least Squares Regression Results (1) (2) (3) (4)
Salary Salary Salary Salary
Age 1.573∗∗ 3.210∗∗∗ 1.573∗∗ 3.208∗∗∗ (2.23) (4.13) (2.24) (4.15)
Age2-0.261∗∗ -0.542∗∗∗ -0.262∗∗ -0.543∗∗∗ (-2.16) (-4.05) (-2.18) (-4.09)
Multi-year Contract 0.397∗∗∗ 0.541∗∗∗ 0.399∗∗∗ 0.546∗∗∗ (7.93) (9.97) (7.92) (10.05)
Foreign-Born – No College -0.00949 0.0468 -0.00386 0.0560 (-0.14) (0.59) (-0.06) (0.70)
Foreign-born – College 0.123 0.0380 0.121 0.0305 (1.50) (0.35) (1.49) (0.28)
Restricted Free Agent 0.296∗∗∗ 0.392∗∗∗ 0.297∗∗∗ 0.392∗∗∗ (4.97) (5.75) (4.99) (5.77)
Games Played 0.00128 0.00125 (0.94) (0.92)
% of Games Started -0.0252 0.594∗∗∗ -0.0194 0.598∗∗∗ (-0.28) (7.75) (-0.22) (7.80)
Field Goal Percentage 0.103 0.0968 (0.34) (0.32)
Previous Team Win % 0.846∗∗∗ 0.319∗ 0.855∗∗∗ 0.341∗∗ (5.67) (1.93) (5.74) (2.09)
Signing Team Win % -0.773∗∗∗ -0.720∗∗∗ -0.777∗∗∗ -0.710∗∗∗ (-4.40) (-3.64) (-4.39) (-3.55)
Re-sign 0.156∗∗∗ 0.153∗∗∗ 0.156∗∗∗ 0.152∗∗∗ (3.35) (2.79) (3.34) (2.76)
Draft Position -0.000579 -0.00690∗∗∗ -0.000593 -0.00689∗∗∗ (-0.54) (-6.22) (-0.55) (-6.23)
Height in Inches 0.0198 0.00182 0.0191 -0.000596 (1.49) (0.13) (1.44) (-0.04)
Head Coach is Black -0.0413 -0.0233 -0.0527 -0.0549 (-0.65) (-0.32) (-0.78) (-0.72)
GM is Black -0.0690 -0.109 -0.0555 -0.0903 (-0.87) (-1.15) (-0.67) (-0.91)
Black -0.116∗∗ -0.127∗∗ -0.117∗∗ -0.131∗∗ (-2.29) (-2.00) (-2.31) (-2.05)
VORP 0.287∗∗∗ 0.284∗∗∗ (11.19) (11.13)
Population (000,000s) -0.134 -0.0463 (-0.56) (-0.15)
White Population 0.0231 0.0539 (0.82) (1.57)
Per Game Performance Y N Y N Position & Year Fixed effects Y Y Y Y Observations 797 797 797 797 R2 0.769 0.699 0.769 0.701
t statistics in parentheses
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
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Table 4: General Manager and Coach Relationship
(1) (2) (3) (4)
Salary Re-sign Salary Re-sign
Player is Black -0.138∗∗ -0.336 -0.124∗-0.301 (-2.01) (-1.16) (-1.92) (-1.08)
Head Coach is Black -0.0600 -0.318 -0.0535 0.107 (-0.48) (-0.59) (-0.70) (0.32)
GM is Black -0.0791 0.463 -0.0152 0.0822 (-0.80) (0.93) (-0.09) (0.12)
Black Player and Coach Interaction 0.00866 0.509
(0.07) (0.98)
Black Player and GM Interaction -0.0737 0.461 (-0.47) (0.76)
Player & Team Characteristics Y Y Y Y Position & Year Fixed effects Y Y Y Y Observations 797 797 797 797
t statistics in parentheses
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
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Table 5: Quantile Regression Results
(10%) (25%) (50%) (75%) (90%)
Salary Salary Salary Salary Salary
Age 3.667∗∗∗ 2.926∗∗∗ 4.288∗∗∗ 2.811∗∗∗ 1.916∗ (4.69) (4.53) (9.12) (3.41) (1.77)
Age2-0.601∗∗∗ -0.479∗∗∗ -0.727∗∗∗ -0.466∗∗∗ -0.322∗ (-4.62) (-4.32) (-9.31) (-3.25) (-1.75)
Population (000,000s) -0.162 -0.180 0.0922 -0.00956 0.219 (-0.42) (-0.55) (0.34) (-0.03) (0.55)
White Population 0.0188 0.0561∗∗ 0.0468 0.0478∗∗ 0.0623 (0.40) (2.16) (1.24) (2.01) (1.40)
Multi-year Contract 0.374∗∗∗ 0.477∗∗∗ 0.643∗∗∗ 0.664∗∗∗ 0.584∗∗∗ (6.05) (11.15) (13.94) (14.43) (7.97)
Foreign-Born – No College 0.188∗ 0.0967 0.0590 0.0497 -0.00705 (1.65) (1.45) (0.65) (0.68) (-0.08)
Foreign-born – College -0.0193 -0.0584 0.0458 0.191∗∗ -0.0679 (-0.15) (-0.45) (0.54) (2.48) (-0.51)
Restricted Free Agent 0.465∗∗∗ 0.460∗∗∗ 0.416∗∗∗ 0.340∗∗∗ 0.298∗∗∗ (4.46) (7.99) (6.64) (5.28) (2.76)
% of Games Started 0.510∗∗∗ 0.606∗∗∗ 0.612∗∗∗ 0.621∗∗∗ 0.604∗∗∗ (3.88) (9.26) (9.97) (8.13) (6.71)
VORP 0.273∗∗∗ 0.285∗∗∗ 0.235∗∗∗ 0.271∗∗∗ 0.270∗∗∗ (7.23) (11.31) (9.59) (8.79) (7.19)
Previous Team Win % 0.296 0.114 0.242 0.474∗∗ 0.404∗ (1.22) (0.64) (1.50) (2.52) (1.83)
Signing Team Win % -0.623∗∗ -0.645∗∗∗ -0.560∗∗ -0.760∗∗∗ -0.703∗∗ (-2.13) (-3.30) (-2.48) (-3.62) (-2.01)
Re-sign 0.146∗∗ 0.130∗∗∗ 0.154∗∗∗ 0.147∗∗∗ 0.133∗ (2.29) (3.13) (2.85) (3.00) (1.89)
Draft Position -0.00372∗∗ -0.00454∗∗∗ -0.00694∗∗∗ -0.00732∗∗∗ -0.0108∗∗∗ (-2.30) (-4.53) (-6.88) (-6.17) (-7.53)
Height in Inches -0.0231 -0.0259∗-0.0141 0.0182 0.0247 (-1.23) (-1.93) (-1.05) (1.32) (1.20)
Head Coach is Black -0.0911 -0.0421 -0.0570 0.0148 0.0511 (-0.75) (-0.75) (-0.82) (0.18) (0.51)
GM is Black 0.0765 -0.0434 -0.141 -0.126 -0.202 (0.55) (-0.42) (-1.38) (-1.46) (-1.52)
Black 0.0416 -0.0136 -0.105∗-0.163∗∗ -0.218∗∗∗ (0.49) (-0.20) (-1.76) (-2.31) (-2.63)
Position & Year Fixed effects Y Y Y Y Y Observations 797 797 797 797 797 t statistics in parentheses
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
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Table 6: Quantile Regression Results: Black Player and White Population Interaction (10%) (25%) (50%) (75%) (90%)
Salary Salary Salary Salary Salary
Age 3.673∗∗∗ 3.084∗∗∗ 4.313∗∗∗ 2.315∗∗∗ 1.885∗∗ (3.24) (6.28) (7.65) (2.70) (2.45)
Age2-0.601∗∗∗ -0.507∗∗∗ -0.732∗∗∗ -0.391∗∗∗ -0.311∗∗ (-3.16) (-6.09) (-7.71) (-2.64) (-2.24)
Population (000,000s) -0.149 -0.171 0.0969 0.0893 0.0784 (-0.39) (-0.59) (0.31) (0.26) (0.25)
White Population 0.0230 0.0519∗∗ 0.0500 0.0604∗∗ 0.102∗∗∗ (0.66) (2.27) (1.29) (1.99) (3.00)
Multi-year Contract 0.373∗∗∗ 0.475∗∗∗ 0.636∗∗∗ 0.674∗∗∗ 0.621∗∗∗ (5.97) (11.92) (13.73) (12.47) (10.78)
Foreign-Born – No College 0.188 0.114∗ 0.0552 0.0321 0.0374 (1.36) (1.78) (0.56) (0.38) (0.41)
Foreign-born – College -0.0266 -0.0803 0.0454 0.161∗-0.0259 (-0.27) (-0.62) (0.47) (1.72) (-0.22)
Restricted Free Agent 0.445∗∗∗ 0.460∗∗∗ 0.422∗∗∗ 0.282∗∗∗ 0.292∗∗∗ (3.71) (9.01) (6.25) (3.30) (3.48)
% of Games Started 0.510∗∗∗ 0.603∗∗∗ 0.612∗∗∗ 0.650∗∗∗ 0.574∗∗∗ (4.67) (11.20) (8.34) (9.21) (7.43)
VORP 0.270∗∗∗ 0.283∗∗∗ 0.240∗∗∗ 0.256∗∗∗ 0.264∗∗∗ (6.91) (16.17) (8.98) (8.72) (8.87)
Previous Team Win % 0.298 0.0824 0.249 0.493∗∗∗ 0.492∗∗∗ (1.20) (0.51) (1.49) (2.98) (2.62)
Signing Team Win % -0.614 -0.627∗∗∗ -0.562∗∗ -0.733∗∗∗ -0.755∗∗ (-1.63) (-3.86) (-2.38) (-3.22) (-2.53)
Re-sign 0.148∗∗ 0.141∗∗∗ 0.145∗∗ 0.156∗∗∗ 0.125∗∗ (2.55) (3.64) (2.57) (3.26) (2.19)
Draft Position -0.00357∗∗ -0.00464∗∗∗ -0.00703∗∗∗ -0.00803∗∗∗ -0.0111∗∗∗ (-2.13) (-4.82) (-6.16) (-6.56) (-8.16)
Height in Inches -0.0213 -0.0265∗∗ -0.0148 0.0162 0.0132 (-0.96) (-2.07) (-1.10) (1.10) (0.72)
Head Coach is Black -0.0891 -0.0413 -0.0531 -0.00397 0.0647 (-0.85) (-0.93) (-0.71) (-0.04) (0.74)
GM is Black 0.109 -0.0587 -0.145 -0.156 -0.232∗∗ (0.70) (-0.86) (-1.41) (-1.57) (-1.98)
Black -0.00562 0.109 -0.0161 0.484 0.546 (-0.01) (0.36) (-0.04) (1.53) (1.48)
Black Player and White Pop Int 0.000724 -0.00176 -0.00152 -0.00965∗∗ -0.0114∗∗ (0.10) (-0.42) (-0.28) (-2.05) (-2.18)
Position & Year Fixed effects Y Y Y Y Y Observations 797 797 797 797 797 t statistics in parentheses
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
33
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Appendix A : Tables with Max Contracts
Table 7: Pooled Twofold Oaxaca-Blinder Decomposition: With Max Contracts (1) (2) (3) (4)
Non-black 15.07∗∗∗ 15.07∗∗∗ 15.07∗∗∗ 15.07∗∗∗
(205.79) (204.00) (205.85) (204.59)
Black 14.86∗∗∗ 14.86∗∗∗ 14.86∗∗∗ 14.86∗∗∗
(363.16) (361.76) (363.08) (361.77)
Difference 0.205∗∗ 0.205∗∗ 0.205∗∗ 0.205∗∗
(2.44) (2.42) (2.44) (2.43)
[1em] Explained 0.0925 0.0806 0.0910 0.0766
(1.17) (1.06) (1.15) (1.00)
Unexplained 0.112∗∗ 0.124∗∗ 0.114∗∗ 0.128∗∗
(2.34) (2.07) (2.37) (2.14)
Observations 797 797 797 797
t statistics in parentheses
Position and year fixed effects included
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
34
Electronic copy available at: https://ssrn.com/abstract=3276247
Table 8: Weighted Least Squares Regression Results: With Max Contracts (1) (2) (3) (4)
Salary Salary Salary Salary
Age 1.574∗∗ 3.246∗∗∗ 1.579∗∗ 3.246∗∗∗
(2.24) (4.18) (2.26) (4.21)
Age2-0.259∗∗ -0.543∗∗∗ -0.261∗∗ -0.544∗∗∗ (-2.15) (-4.07) (-2.17) (-4.11)
Multi-year Contract 0.400∗∗∗ 0.547∗∗∗ 0.403∗∗∗ 0.552∗∗∗
(7.99) (10.06) (7.99) (10.15)
Foreign-Born – No College 0.00988 0.0701 0.0151 0.0791
(0.15) (0.88) (0.22) (0.98)
Foreign-born – College 0.120 0.0470 0.117 0.0383
(1.46) (0.43) (1.43) (0.36)
Restricted Free Agent 0.292∗∗∗ 0.390∗∗∗ 0.293∗∗∗ 0.390∗∗∗
(4.91) (5.75) (4.92) (5.75)
Max Contract 0.487∗∗∗ 0.640∗∗∗ 0.487∗∗∗ 0.643∗∗∗
(5.90) (6.46) (5.95) (6.59)
Games Played 0.00167 0.00163
(1.24) (1.22)
% of Games Started -0.0390 0.564∗∗∗ -0.0336 0.568∗∗∗
(-0.43) (7.35) (-0.37) (7.40)
Field Goal Percentage 0.163 0.160
(0.54) (0.53)
Previous Team Win % 0.812∗∗∗ 0.323∗∗ 0.821∗∗∗ 0.344∗∗
(5.48) (1.97) (5.55) (2.12)
Signing Team Win % -0.750∗∗∗ -0.687∗∗∗ -0.751∗∗∗ -0.673∗∗∗ (-4.28) (-3.50) (-4.25) (-3.39)
Re-sign 0.148∗∗∗ 0.142∗∗∗ 0.147∗∗∗ 0.141∗∗∗
(3.18) (2.62) (3.17) (2.59)
Draft Position -0.000703 -0.00680∗∗∗ -0.000728 -0.00681∗∗∗ (-0.66) (-6.23) (-0.69) (-6.24)
Height in Inches 0.0178 -0.00186 0.0169 -0.00444 (1.34) (-0.13) (1.28) (-0.31)
Head Coach is Black -0.0329 -0.0143 -0.0462 -0.0477
(-0.51) (-0.20) (-0.68) (-0.63)
GM is Black -0.0633 -0.0992 -0.0509 -0.0813
(-0.80) (-1.05) (-0.62) (-0.83)
Black -0.112∗∗ -0.124∗∗ -0.114∗∗ -0.128∗∗
(-2.24) (-1.98) (-2.26) (-2.03)
VORP 0.262∗∗∗ 0.258∗∗∗
(10.64) (10.54)
Population (000,000s) -0.0935 -0.00587 (-0.39) (-0.02)
White Population 0.0251 0.0559∗
(0.89) (1.65)
Position & Year Fixed effects Y Y Y Y
Observations 797 797 797 797
R2 0.774 0.708 0.774 0.710
t statistics in parentheses
∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01
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