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Racial Differences in Professional Players' Compensation Author(s): Lawrence M. Kahn and Peter D. Sherer Source: Journal of Labor Economics, Vol. 6, No. 1 (Jan., 1988), pp. 40-61 Published by: The University of Chicago Press on behalf of the Society of Labor Economists and the NORC at the University of Chicago Stable URL: http://www.jstor.org/stable/2534867 . Accessed: 30/07/2014 16:44

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This content downloaded from 128.148.231.34 on Wed, 30 Jul 2014 16:44:35 PM All use subject to JSTOR Terms and Conditions Racial Differencesin Professional BasketballPlayers' Compensation

LawrenceM. Kahn,University of Illinois at Urbana-Champaign

PeterD. Sherer,University of Illinois at Urbana-Champaign

This articleinvestigates racial differencesin 1985-86 salariesof in- dividualprofessional basketball players. White and blackplayers earn similarmean compensation; however, controlling for a varietyof pro- ductivityand market-relatedvariables and for the endogeneityof playerdraft position, we finda significantceteris paribus black com- pensationshortfall of about 20%. Further,we findthat all else equal, includingteam performance and marketfactors, replacing one black playerwith an identicalwhite player raises home attendanceby 8,000 to 13,000fans per season. The compensationand attendanceresults togetherare consistentwith the idea of customerdiscrimination.

I. Introduction The National BasketballAssociation (NBA) appears to be an example of racialprogress. Blacks compriseroughly 75% of the playersand about 80% of startingplayers. There are more black coaches in the NBA than in otherprofessional sports (Berry, Gould, and Staudohar1986). Many of themost highly paid playersare black: thetop threeNBA salariesfor the

Theauthors thank Roger Noll andthe seminar participants atthe Northwestern UniversityLabor Economics Workshop for helpful comments and suggestions.

[Journal of Labor Economics, 1988, vol. 6, no. 1] ? 1988 by The Universityof Chicago. All rightsreserved. 0734-306X/88/0601-0006$01.50

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1985-86 season went to EarvinJohnson ($2.5 million), ($2.145million), and KareemAbdul-Jabbar ($2.03 million), all blackplayers. Severalother black players earned over $1 million:($1.165 million),($1.1 million),($1.1 million), JuliusErving ($1.485 million),and PatrickEwing ($1.25 million).'Blacks have traditionallyheld leadershippositions in the National Basketball PlayersAssociation (NBPA), althoughits directoris white.2 Despite thisevidence of black economicreward, blacks remain a small minorityof coaches (two out of 23) and executives(one out of 23 general managers)in theNBA (see Berryet al. 1986).Bradley (1976) and Halberstam (1981) documentthe existence of racial prejudice in theNBA forthe 1960s and 1970s. In particular,basketball fans often suggest that there is a pre- miumfor being a whiteplayer. Indeed, this last outcome would be predicted in a model of customerdiscrimination (Becker 1975). Since basketball playersare more highlyvisible (both on the courtand on the bench) to fans than playersin othersports, customer discrimination may well be moreprevalent in basketballthan elsewhere, especially in view of therel- ativescarcity of whiteplayers. Economictheory predicts that customer discrimination can persistunder competition,while employeror co-workerdiscrimination is more likely to diminish(Becker 1975). In customerdiscrimination, the consumeris willingto pay a premiumfor white workers. In basketball,the white fan acts as if the whiteplayer is producingmore entertainmentvalue than a comparableblack player.If thereis customerprejudice in general,then black workersmay be able to escape discriminationby workingin sectors withoutproducer-consumer contact. However, if black serviceworkers have a largeenough comparative advantage in services,or if,compared to the size of the servicesector, the relativelabor intensityof servicepro- ductionor the relativesize of the black labor forceis largeenough, then customerprejudice will resultin discriminationeven undergeneral equi- libriumconditions (Kahn 1987). On the otherhand, underemployer or co-workerdiscrimination, buy outs by nondiscriminatoryor segregation by firmmay tendto reducewage discrimination(Becker 1975). This articleinvestigates NBA salarydetermination and particularlyracial salarydifferentials in theNBA. We are able to provideconsiderably more detailedcontrols for performance than is done in typicalstudies of wage determinationusing data such as the CurrentPopulation Survey or the NationalLongitudinal Surveys. While blacksand whitesearn comparable

' Thesesalary figures are from our data base, to be describedbelow. The highest- paidwhite players include ($1.8 million), ($1.6 million), MitchKupchak ($1.15 million), and Kevin McHale ($1 million). 2 Amongthe NBPA leadershave been ,Paul Silas,and ,all blackplayers (Berry et al. 1986).

This content downloaded from 128.148.231.34 on Wed, 30 Jul 2014 16:44:35 PM All use subject to JSTOR Terms and Conditions 42 Kahn/Sherer overallsalaries, we findthat, all else equal (i.e., performanceand market- relatedvariables), blacks are paid less thanwhites by about 20%, an effect thatis highlysignificant statistically. These resultsare robustto a variety of independentvariable specificationsand estimationtechniques. Our findingssuggest that although blacks have made major gains in professional basketball,unexplained racial salarydifferentials are of a similarorder of magnitudeas for the rest of the economy.3In addition,comparison of uncorrectedmean salarieswith regression results underscores the impor- tance of controllingfor otherinfluences on salariesin studiesof wage determination.Further, we findthat, all else equal, whiterepresentation on a teamcontributes to home attendance,providing evidence consistent withthe idea of customerdiscrimination. On the otherhand, we do not findevidence of discriminationin the draftselection process.

II. Labor Relations and Salary Determination in the NBA The NBA playershave had unionrepresentation since the 1960s.4How- ever,as in otherprofessional sports, collective-bargaining agreements in basketballset the rulesfor salary determination rather than callingfor a specificsalary scale.5 The eraof free agency (i.e., a playerselling his services in an open market,once the initialcontract has been completed)in the NBA beganwith the 1976 collective-bargainingagreement. This contract providedfor two distinctperiods regarding free agency: 1976-81 and 1981- 87. Duringthe 1976-81interval, a playercould becomea freeagent when his existingcontract expired. If he were bid away by anotherteam, the two clubs involvedneeded to agreeon compensation;the NBA commis- sioneracted as arbitratorin theevent of no agreement.In 1981,this system was replacedby one in whichthe teams were given the right of first refusal: a teamcould keep a player'scontract by matchingthe bidding team's offer. By greatlyreducing employer monopsony power, the free-agency system appearsto have led to a rapidescalation of salaries.According to Berryet al. (1986), the averageplayer salary was $109,000in 1976,while our data for1985-86 show an averageof about$380,000.6 At thesame time, perhaps

'The 20% rangeis consistentwith findings for the male labor forceas a whole. For example,Blau and Beller(1984) foundthat, all else equal, black males faceda 14.5% weeklyearnings shortfall in 1981 comparedwith white males. 4 Much of thissection is drawnfrom Berry et al. (1986). 5 Basketball,as well as footballand baseball,has a minimumsalary ($70,000 for 1985-86). In addition,in 1983,a team salarycap was institutedin the NBA (see below). 6 Similarincreases have been observedin baseball followingthe institutionof freeagency (see Hill and Spellman1983). The NBA compoundedaverage annual rateof salaryincrease from 1976 to 1986 was about 13%, a substantiallyhigher figurethan the 7% annualhourly wage increasefrom 1976 to 1984 forthe private sector(see MonthlyLabor Review [January1986]).

This content downloaded from 128.148.231.34 on Wed, 30 Jul 2014 16:44:35 PM All use subject to JSTOR Terms and Conditions Compensationin ProfessionalBasketball 43 as a resultof this salary escalation,the owners began reportingsevere financialdifficulties. In 1982, it was claimed that the averageteam lost $700,000and thatonly six of 23 weremaking positive profits (Berry et al. 1986,p. 181). As a result,in 1983 a cap on totalteam salaries was agreed upon by theowners and theNBPA. While theoperation of thesalary cap is verycomplicated, involving multiple qualifications and clauses,its intent is clear-to slow down the spiralin playersalaries.7 It is probablytoo earlyto tell whetherthe cap has had any impacton overallsalaries.8 However, for the purposes of our study,the existenceof the cap poses no obvious difficultyin comparingplayers' salaries. As of 1985-86,salary determination in theNBA, at leastfor experienced players, is basicallymarket determined, as playersuse thefree-agent system to find thebest offer. If thereis customerdiscrimination and if ownersare profit maximizers,the free-agency system will establisha whitesalary premium. This premiumwill not be eroded by competitionas long as white fans preferto watchwhite basketball players. III. EstimatedMethods and Data Our basicmodel for the salary-determination process is of thefollowing form:

S = V, (1) InS a In V, (2) where

S = individualplayer's compensation for 1985-86, including an impu- tationfor deferred payments;9 V = a measureof theplayer's market value (marginalrevenue product).

If thereis customerdiscrimination, then V will dependon a player'srace as well as his actualperformance: In V= cP +dR, (3) where P = theplayer's performance level; R = 1 forwhite players, 0 forblack players.

7The basic salarycap for 1985-86 was the maximumof $3.8 million/team,or 53% of grossrevenues. On theother hand, there are enoughexceptions to thecap to put 20 out of 23 teamsover the $3.8 millionfigure. According to Berryet al. (1986), the cap has, at the margin,caused some teams to alter theirlineups to accommodatethe cap. 8 The increasefrom 1984-85 to 1985-86in averagesalaries was about 11%,similar to the 13% averagefrom 1976 to 1986 reportedearlier (see Berryet al. 1986). 9 Data are describedmore fully below.

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If we had data on V and P, thenwe could directlytest the model of customerdiscrimination as describedby (1)-(3). In particular,the model would predictthat once we controlledfor V, race would not affectcom- pensation(i.e., race would not entereq. [1]) if customersare the only source of discrimination.However, given performance(P), race would affectcompensation through its impacton theplayer's market value. The racialdiscrimination coefficient would equal ad. If teamsor whiteplayers as well as customersdiscriminated, then, even controlling for V, race would stillaffect salaries (i.e., R would enterinto eq. [1] as well as [3]). Finally, if customersdid not discriminatebut teams/playersdid, thend = 0 and race would affectcompensation given V. While data on V, P, and S would allow us to distinguishthe differing models,we do not observeV or P. Instead,we mustproxy P by a vector X of playerperformance indicators and teamand local metropolitanarea characteristics.'Rather than (2), we have:

InS = B'4X + R+ 4, (4) whereB4 is a coefficientvector, 5 is therace effect,and g4 is an errorterm. Equation (4), while estimable,does not give us the same information thatestimating (1)-(3) would. In particular,as noted,by adding a race termto (1), we could separatelyidentify team/player and customerdis- crimination.However, in (4), lack of data on P and V forcesus to combine theseforms of discriminationinto one coefficient. To estimatethe compensationmodel, we mergethree data bases: (1) playersalary information, (2) individualperformance data, and (3) team and metropolitanarea data. Playersalary data for1985-86 are takenfrom a surveyof the entire NBA bya teamof newspapers including The Sporting News,Houston Chronicle, Phoenix Gazette, Detroit Free Press,and New YorkDaily News." As noted,the salarydata include an imputationfor thevalue of deferredcompensation (as well as bonuses).More specifically, the player-compensationfigure includes "base salary,signing bonuses, 'reasonablyattainable' performance bonuses, and deferredpayments" (New YorkDaily News,December 26, 1985,p. 100). Thus,a seriousattempt was madein thenewspapers' survey to go beyonda base-salarymeasure. How- ever,our compensation variable does notinclude future deferred payments, and it is impossibleto breakdown currentcompensation into salaryand nonsalarycomponents. If black playerscame frompoorer families than whites,liquidity problems might lead the formerto receivemore of their

0 Thepossible omitted variable problem caused by use of X is discussedbelow. " Actualplayer compensation is published in the December 26, 1985, edition of theNew YorkDaily News (p. 100). This surveywas describedverbally to us by Mike Douchant,basketball editor of The SportingNews.

This content downloaded from 128.148.231.34 on Wed, 30 Jul 2014 16:44:35 PM All use subject to JSTOR Terms and Conditions Compensationin ProfessionalBasketball 45 compensationas salaryrather than as deferredpayments. Lack of data on futuredeferred payments, then, may understatewhite compensation by morethan black compensation.Finally, the bonus component(which ob- viouslyis not separablein our sample fromdeferred payments) is not an actual "piece rate" but an estimateof what the surveyersthought was reasonablyattainable by any player.It should,therefore, be thoughtof as a deferredpayment. Playerperformance and teamdata are takenfrom the 1985-86 editions of TheSporting News NBA Guideand NBA Register.Finally, metropolitan area data foreach player'steam are takenfrom the StatisticalAbstract of theUnited States 1985 and 1986. The vectorX of explanatoryvariables includes the following (measured forthe startof the 1985-86 season):

SEASONS = totalseasons played,12 MINS = averageminutes played per game, GAMES = averagegames played per season, FTPCT = careerfree throw percentage (fraction made), FGPCT = careerfield goal percentage(fraction made), POINTS = careerpoints scored, = dummyvariable for centers,"3 FORWARD = dummyvariable for forwards, OFFREB = careerper game offensiverebounds,'4 DEFREB = careerper game defensiverebounds, ASSISTS = careerper game assists, PFOULS = careerper game personalfouls, STEALS = careerper game steals, BLOCKS = careerper game shotsblocked, HOMEATT = 1984-85 home attendanceof one's 1985-86 team, RACEMSA = 1980 percentof StandardMetropolitan Statistical Area (SMSA) populationthat was black in the SMSA where one's teamwas located, POPMSA = 1980 populationof one's team'sSMSA,

12 A smallnumber of players (e.g., Moses Malone, , , ArtisGilmore) had ABA experiencebefore the NBA-ABA merger in 1976.For theseplayers, we computedthe entire pro career, including ABA statistics. 13 In thecase of thosewho playmore than one position(e.g., Kevin McHale playsforward and center),we code his primaryposition as definedby theNBA Guide. 14 Reboundswere not broken down into offensive and defensive categories before 1973.For those whose careers started before 1973, we imputedoffensive and de- fensiverebounds by prorating the total rebounds for these years by the post-1973 reportedpercentages of totalrebounds in thesetwo categories.The numberof playersaffected was small.

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INCMSA = 1983 real per capitaincome in the SMSA,`5 DRAFTNO = numbera playerwas pickedin thedraft (e.g., the top player was picked number1), WINPCT = 1984-85 winningpercentage of one's 1985-86 team, WHITE = 1 if playeris white,0 if playeris black. The shooting,scoring, rebounding, assists, fouls, and defensestatistics are all obviousmeasures of on-courtplayer performance. Longevity (SEA- SONS) combinesa pure seniorityeffect and thevalue of a sustainedlevel ofper game and perseason performance. The positionvariables (CENTER, FORWARD) are includedto controlfor the possible differential value of thesepositions, especially for centers. It is oftenalleged that a good center is of specialimportance, and thatthe bestteams usually have a dominant center.In addition,good forwardsmay be morescarce than good guards. By includingCENTER and FORWARD, we testfor the notionthat the measuredperformance variable may not completely control for this position phenomenon.Minutes per game may measurea player'simportance but mayalso be a negativeproductivity indicator since we controlfor per game statistics(e.g., more minutesfor the same pointsper game). Games per season measuresfreedom from injury or willingnessto play injured. The team-relatedvariables HOMEATT, RACEMSA, INCMSA, and POPMSA all capturemarket factors. The customer-discriminationargu- mentwould suggest interacting RACEMSA withWHITE: we wouldexpect the premiumpaid to whiteplayers to be a negativefunction of the pro- portionof the local populationthat is black,and thistest was attempted (see below). WINPCT is includedto testfor the idea thatthe team "settles up" withits playerson the basis of the past year'sperformance. Finally,DRAFTNO is includedas a furtherindicator of playerquality, potential,or fan appeal. It is an inverseordinal measure of the league's desirefor a givenplayer as he enteredthe NBA. Whileone shouldcontrol as completelyas possible forplayer quality, DRAFTNO may confound playerquality and racial aspectsof fanappeal. The customer-(as well as team/player-)discrimination model would suggestthat, all else equal,white players would be draftedbefore black players. The endogeneityof DRAFTNO suggestsusing a two-stageleast-squares (2SLS) procedurefor the salaryequation. We thereforealso estimatewith 2SLS the following equationfor DRAFTNO: DRAFTNO = a'Z + B In S + es, (5)

15 Money income was takenfrom Statistical Abstract of the UnitedStates 1985 and 1986. This was thendeflated by the relativecost of livingin the area. Cost of livingwas calculatedby inflatingthe 1976budget for an intermediateliving standard (fora familyof four)by the area's increasein the CPI from1976 to 1983. Cost- of-livingfigures were taken fromU.S. Departmentof Labor, Bureau of Labor Statistics,Handbook of Labor Statistics,1978 and 1985.

This content downloaded from 128.148.231.34 on Wed, 30 Jul 2014 16:44:35 PM All use subject to JSTOR Terms and Conditions Compensationin ProfessionalBasketball 47 whereZ includes

WHITE = (definedearlier), EARLY = dummyvariable for those who leftcollege as underclass- men, SEASONS = seasons as a pro (definedearlier), COLLSEA = college seasons, CGAMES = totalcollege gamesplayed per season, CPTS = totalcollege pointsscored per season, CFGPCT = college fieldgoal percentage, CFTPCT = college freethrow percentage, CREB = total college reboundsper game (data on offensiveand defensiverebounds were not available), CAWARDS = numberof timesnamed to The SportingNews firstor sec- ond All-Americateam or won its College Playerof the Year award, In S = predictedlog compensationfrom a reduced-formmodel.

In the DRAFT equation,we have includedmeasures of college perfor- mance,plus SEASONS (as a pro) in orderto controlfor cohort effects in the playerdraft. Further, if there is discrimination,then at the same price (i.e.,compensation) whites should be draftedbefore blacks. Therefore, the DRAFT equationwas estimatedby includingpredicted log compensation as a measureof anticipatedcost of a playerat the timeof the draft. While the compensationdata are for only 1 year,it is possible that multiyearconsiderations affect compensation. Indeed, the notion of de- ferredpayments is clearlya multiyearphenomenon. Further insight into compensationdetermination can be gained by interactingseniority with performancevariables. Such a testwas also done. The salaryregression can shedlight on racialdifferences in compensation controllingfor qualifications. However, these techniques do not provide directtests of discrimination,although their results can be suggestive.To shed lighton fan preferences(and, implicitly,the idea of customerdis- crimination),we estimatea model of home attendance.We have obtained dataon homeattendance for the six-season period 1980-81 through 1985- 86 (collectedfrom The SportingNews NBA Guide foreach of theseyears). We thenpose the followingequation (unitsof observationare a team in a givenyear):

ATTEND = mo+ m1YEAR + m2WINPCT + m3 STARS + m4ARENA + m5RACEMSA + m6POPMSA (6) + m7TEAMS + m8PRICE + m9INCMSA

+ m10PCTWHITE + 86,

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where

ATT = team'shome attendance for a givenyear, YEAR = timetrend (i.e., 81 for1980-81, . . . , 86 for1985-86), WINPCT = team'swinning percentage for a givenyear, STARS= numberof teammembers on firstor secondall-NBA team(chosen by The SportingNews), ARENA = arenacapacity, TEAMS = numberof othermajor league sports franchises in the area, PRICE = minimumticket price in 1967dollars, PCTWHITE = fractionof team members who were white

(RACEMSA,INCMSA, and POPMSA havebeen defined earlier). Estimationof (6) is a directtest of the idea of customer discrimination. The PCTWHITE coefficienttells us theimpact on attendanceof adding whiteplayers of equal ability to theblack players replaced. WINPCT and STARSare further indicators of team fan appeal, ARENA controlsfor the upperlimit on attendance,and RACEMSA,INCMSA, POPMSA, and TEAMS aredemand-related variables. Minimum ticket price is usedsince averageticket price data were unavailable.16 Since teams choose ticket prices, PRICE is likelyto be endogenous.Therefore, (6) was also estimatedwith PRICE omitted-thatis, a reducedform. However, even in thiscontext, PCTWHITE mayyield interesting information about fan preferences. IV. Basic EmpiricalResults Table 1 providesmean values for the sample used in thewage and draft regressions(cases with missing values were deleted). Black players make up 74.3% ofthe sample, a figurevery close to Berryet al.'s (1986) estimate of75%. Blackson averagehave a $10,620compensation advantage (2.7%) overwhites, while the difference in mean log compensationwould imply a 10.5% blackadvantage (e1 1.105).However, blacks on averagehave moreexperience (both seasons and minutesper game),better shooting statistics,more points per game, more points per minute, and are drafted earlierthan whites. Blacks are more likely to leavecollege before using up theireligibility, score and reboundmore as collegiansthan whites, and winmore college awards. On theother hand, whites play for teams with betterrecords, a possibleCeltic effect.17 The otherteam-related variables suggestthat whites play for teams with higher home attendance, located

16 For somecases, even minimum ticket price was missing.In theseinstances, we interpolatedtoapproximate this variable. 17 WithCeltics excluded, average WINPCT is .490for whites and .487 for blacks, butthe race coefficient in the log wageregression is unchanged.

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Table 1 Mean Values of the Wage-RegressionSample Variable Whites Blacks SEASONS 4.414 4.8571 FTPCT .729 .737 FGPCT .486 .490 MINS 20.862 25.446 POINTS 8.69 12.11 GAMES 66.17 71.09 CENTER .345 .173 FORWARD .448 .399 OFFREB 1.372 1.634 DEFREB 3.052 3.142 ASSISTS 1.858 2.665 PFOULS 2.457 2.699 STEALS .626 .971 BLOCKS .648 .638 HOMEATT 473,540 454,080 RACEMSA 11.0% 13.6% POPMSA 271.5X 104 314.8X 104 DRAFTNO 29.1 24.8 WINPCT .524 .491 INCMSA $9,410.9 $9,640.7 EARLY .1207 .1905 COLLSEA 3.8103 3.5774 CGAMES 27.292 27.993 CPTS 13.271 16.155 CFGPCT .5393 .5243 CFTPCT .7201 .7051 CREB 6.6063 7.3616 CAWARDS .3793 .4167 S $396,570 $407,190 InS 12.57 12.67 Samplesize 58 168

iti smallermetropolitan areas, and witha greaterpercentage of whitesin the area. These team-variablemeans are consistentwith the customer- discriminationidea, as teamswith more white players draw more fans and are locatedin relativelywhite areas. The effectof whiteplayers on home attendanceis testedmore formally below.

A. CompensationRegression Results While table 1 shows a slightblack salaryadvantage over whites,tables 2 and 3 presentregression results suggesting that, all else equal, blacksare paid significantlyless thanwhites in the NBA.18First, the ordinaryleast

18 Theexistence of a $70,000minimum salary suggests the possibility ofa truncated dependentvariable. However, in our sample,those earning $70,000 and having completedata on their explanatory variables comprised less than 1% of the regression sample.Thus the truncation problem is notlikely to be severein thiscase. On the otherhand, the mean salary figures in table1 are2%-5% higher than the $380,000 figurereported earlier, indicating that low-paid players were slightly less likely to havecomplete data than highly paid players.

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Table 2 OLS and 2SLS Resultsfor In (Compensation) Explanatory Variables OLS OLS OLS 2SLS CONSTANT 10.378 10.660 10.574 10.643 (.4265) (.4203) (.4512) (.4887) SEASONS .0300 .0352 .0316 .0286 (.0105) (.0102) (.0101) (.0111) FTPCT -.2191 -.3434 -.2735 -.2761 (.4225) (.4080) (.3977) (.4189) FGPCT 1.2761 1.4045 1.1678 .9052 (.6799) (.6597) (.6451) (.6751) MINS .0095 .0128 .0142 .0124 (.0129) (.0125) (.0122) (.0128) POINTS .0558 .0470 .0444 .0471 (.0114) (.0111) (.0108) (.0125) GAMES .0081 .0057 .0066 .0097 (.0027) (.0027) (.0027) (.0032) CENTER .0808 .0599 .0844 .1105 (.1318) (.1283) (.1252) (.1308) FORWARD -.0297 -.0175 -.0132 -.0197 (.0915) (.0889) (.0865) (.0900) OFFREB .1022 .0660 .0854 .1166 (.0758) (.0736) (.0720) (.0780) DEFREB .0491 .0464 .0352 .0288 (.0370) (.0357) (.0352) (.0366) ASSISTS .0396 .0296 .0281 .0250 (.0325) (.0313) (.0304) (.0322) PFOULS -.0732 -.0418 -.0315 -.0498 (.0530) (.0515) (.0509) (.0569) STEALS -.0612 -.0630 -.0552 -.0488 (.1019) (.0982) (.0956) (.0993) BLOCKS .0184 .0342 .0389 .0426 (.0620) (.0604) (.0591) (.0625) HOMEATT (%103) ...... 00009 .00008 (.0003) (.0003) RACEMSA ...... 0003 -.0012 (.0040) (.0042) POPMSA ...... 0004 .0004 (.0001) (.0001) INCMSA (%103) ...... -.0092 -.0144 (.0177) (.0187) DRAFTNO ... -.0048 -.0050 -.0063 (.0011) (.0011) (.0033) WINPCT ... .0730 .0199 .0086 (.1955) (.2449) (.2559) RACE .2065 .1914 .2130 .2262 (.0679) (.0660) (.0647) (.0674) Samplesize 226 226 226 226 R2 .7224 .7462 .7660 S.E.E. .4002 .3845 .3728 .3870 NOTE.-(Asymptotic)standard errors in parentheses. squares(OLS) and 2SLS race effectsfor In (compensation)in table 2 are highlysignificant and amountto a whitepremium of about20%. The first columnof table 2 includesonly individual performance measures and race,

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Table 3 Selected OLS Log Compensation Results from a Seniority-InteractionModel

[aln(Compensation) bySeniority L aRace jye~rt

Explanatory a ln(Compensation) Variables Coefficients Seasons aRace RACE .0968 1 .1251 (.1164) (.0975) DRAFTNO -.0047 2 .1534 (.0017) (.0811) RACE * SEASONS .0283 3 .1817 (.0232) (.0688) DRAFT * SEASONS .0001 4 .2100 (.0003) (.0631) FTPCT * SEASONS -.4413 5 .2383 (.1267) (.0656) FGPCT * SEASONS .4901 6 .2666 (.2283) (.0755) POINTS * SEASONS .0041 7 .2949 (.0023) (.0904) OFFREB * SEASONS .0399 8 .3232 (.0217) (.1084) DEFREB * SEASONS -.0373 ...... (.0102) ASSISTS* SEASONS .0021 ...... (.0094) FOULS * SEASONS .0055 ...... (.0176) STEALS* SEASONS .0149 (.0294) BLOCKS * SEASONS .0004 ...... (.0178) S.E.E. .3479 ......

NOTE.-See table2, col. 3, fora list of theother explanatory variables. while the second columnadds DRAFTNO and WINPCT, and the third columnadds thesetwo and themarket variables. Although the raw means of log compensationshow a 10% advantagefor blacks (table 1), as soon as we controlfor individual performance, we get a significant20% black compensationshortfall. This effectholds with the inclusion of DRAFTNO, WINPCT, and the market-relatedvariables. Among other results from table 2, scoring appears to strongly affect salary;for example, a 10 per game scoringdifferential contributes to an all else equal 40%-50% compensationpremium. Longevity (SEA- SONS) and durabilitywithin a season(GAMES) bothcontribute to salaries, althoughthese variables may be indicationsof playingability: the coach (or generalmanager) chooses to keep thebetter players on thecourt. Players in largemarkets (POPMSA) make a clear salarypremium. For example, moving fromWashington, D.C., to Los Angeles raises salaries about 18%.

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Such a findingmay indicatethat in morelucrative markets, the marginal revenueproduct of, say, the fifthstar of a team is greaterthan in less lucrativemarkets. Finally, the negative effect of DRAFTNO suggeststhat thisvariable is a furtherindicator of playerquality or fanappeal, beyond what is measuredby the performancestatistics.19

1. Life-CycleConsiderations While our data are foronly 1 year,it is possiblethat multiyear consid- erationsaffect salary determination. The table 2 findingscontrol for se- niority,so whitesand blacks are in the regressionsroughly at the same point in theirlife-cycle. However, additionalinsight into compensation can be gained by investigatingthe interactionof performancevariables and seniority.Table 3 shows the resultsof such a test.As a group,the interactions are significantat better than 1/%,F(1 1,204) = 3.3, with a 1/% criticalvalue of about 2.3. Importantwage-influencing variables such as scoringor fieldgoal percentagehave significant positive interaction effects with seniority.Evidently, sustained performance in theseareas is partic- ularlyrewarded. On theother hand, percentage and defensive rebounding,both less importantdeterminants of salary,have significant negative seniorityinteractions. The race-seniorityinteraction is positivebut insignificant. However, the derivativeof log wages withrespect to race is insignificantat 0 or 1 year senioritybut becomes significant with 2 or moreyears in theleague. While this derivativerises with seniority,the insignificanceof the interaction suggestscaution in interpretingsuch a rise. Finally,the effectof draftdoes not decay with seniority-thepoint estimatefor DRAFT* SEASONS is insignificantand verysmall compared to themain DRAFTNO effect.Evidently, DRAFTNO is close to a "fixed" effect,controlling for the othervariables. Comparing two hypothetical playerswith the same performance but different draft numbers, we conclude thatthe league drafted the earlier player because of somefixed, unmeasured playingability or fanappeal. For example,the Celtics recognized something in ,Larry Bird, and KevinMcHale thatcould not be measured withthe usual playerperformance statistics.

19 Heteroscedasticitytests suggested by Dutta(1975) did notindicate that this problemwas present in our data. In addition,regressing the squared residuals from thefull OLS In (compensation)model on thepredicted value of thedependent variable(and a constant)yielded a coefficientof .0154(.0181). Further, reverse regressiontests indicated black overqualification to obtain a givencompensation level.That is, when the predicted value of In (compensation)for RACE = 0 was regressedon RACE and actualIn (compensation),we obtaineda raceeffect of -.2359 (.0476)and a coefficienton In (compensation)of .7652(.0283). Therefore, thistest did not indicate an omitted-variableproblem.

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2. AlternativeSpecifications The raceeffect on compensationwas robustto alternativespecifications. For example,inclusion of height,weight, all-star games, number of team changes,or team abilityto pay (as measuredby team salaryminus the player'ssalary) did notaffect the race results. In particular,the insignificant effectsfor "ability to pay" are consistentwith team profit maximization: teamsare only willingto pay playerswhat theyare worth.Further, tests forstructural differences between black and whitelog salaryregressions acceptedthe hypothesis of a commonstructure-except for the race dummy variable.In particular,interactions between RACE and RACEMSA were insignificant.

3. ExtremeValues Having establisheda findingof a significantblack shortfallin compen- sation,all else equal, we now investigatethe extent to whichsuch a finding reflectsextreme values. For example,in our sampleof 58 whiteplayers, a raisefor one playerfrom $100,000 to $2,000,000salary raises the average whitesalary by about $33,000,or over 8%. Figures1 and 2 shed lighton the extremevalue issue: the figuresplot, respectively,white and black residualsfrom a pooled OLS log compensationregression from table 2, column 3. There are severalhighly paid white playerswith very large residuals,although, as noted,heteroscedasticity tests did not indicatethat thiswas a problem.20A largepositive residual for such players could indicate fanappeal due to theirrace or unmeasuredplaying ability. To assessthe impact of such extreme values on racialsalary differentials, we estimatedthe basic log salaryregression but excludedplayers making over$800,000/year, that is, we excludeda totalof 20 players(five whites and 15 blacks). The race coefficientbecame: .1560 (.0646). When we re- strictedthe sample to thoseearning less than$600,000 (an exclusionof 12 whitesand 25 blacks), the RACE effectbecame: .1293 (.0693). Finally, when we restrictedthe model to those earningat least $100,000 (due to largenegative black residualsat low salarylevels), the RACE effectwas .2327 (.0665). The findingsfor the samples excluding highly paid playersindicate that extremevalues contributeto some but not all of the ceterisparibus racial compensationdifferential. Even among low to moderatelypaid players (earningsless than $600,000),there is a race effectof about 13% thatis significantat 6.1% (two-tailedtest).

B. DraftPosition Results Table 4 containsOLS and 2SLS resultsfor the determination of a player's draftposition. In all specifications,white playersare draftedlater than

20 Ibid.

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11.44 11.71 11.98 12.25 12.52 12.80 13.07 13.34 13.61 13.88 .89 . . . . .I I...... I - .89

.73 .73

.56 * .56

.39 ** .39

.23 * * * .23

.06 ** **.06

,11] * *a* * * * }1

-.28-.44 t -28* * -.44

-.78 l * -.287

11.30 11.57 11.85 12.12 12.39 12.66 12.93 13.20 13.47 13.74 14.02 FIG. 1.-White residualsfrom basic OLS logsalary model by predicted level of log salary black players,other things equal, althoughthe RACE coefficientis never significant.Such a findingdoes not supportthe idea of discrimination. Further,the compensation effect is negativeand significantin all cases: in the 2SLS models, this means that predictedcompensation is relatedto being selectedearlier in the draft.Clearly, the compensationvariable is not actingas a price term,which should have a positivecoefficient, con- trollingfor ability. It is likelythat compensation (or its predictedvalue) in table4 is reallya measureof playerquality. The overallresults for the draft equations are disappointing.Other than compensation,the only significantcoefficients are EARLY, COLLSEA,

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11.44 11.79 12.15 12.51 12.87 13.22 13.58 13.94 14.30 14.65

.97 * .97

.77 * .77

.57 '.*** * *.*.57

** ****

37 * * * *

* ** 3* **

*** * * * *16 **1* *7 .37* * * * .37 ~~~~~***2* * * * * * * * * * ** * -.04 * * * *** * *.*-.04 .16 * * ** * *.1

-.24 * * * * * * * * . 24 * ** * *

-.44 .4 2 * * *4

-.24 *-.24

-.64 4* * * *

-1.04 -1.04

11.26 11.61 11.97 12-33 12-69 13.04 13.40 13.76 14.12 14.47 14.83

FIG. 2.-Black residualsfrom basic OLS logsalary model by predicted level of log salary

CGAMES, and CAWARDS. To makea fullstudy of thedraft process, we would need collegestatistics and draftnumbers for all playersdrafted and forthose not drafted.Our sample includesonly thosewho were drafted and who made it into the NBA. Unfortunately,complete data on the draftablepopulation are unavailable.

C. Home AttendanceResults Table 5 containsregression results for the determinantsof home atten- dance. We reportboth OLS and generalizedleast squares (GLS) coefi;-

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Table 4 OLS and 2SLS Results for Position in Draft DependentVariable DRAFTINO ln(DRAFTNO) Explanatory Variables OLS 2SLS OLS 2SLS CONSTANT 320.07 325.71 17.225 17.638 (39.335) (45.91) (2.1234) (2.3019) SEASONS .5322 .6143 .0528 .0604 (.7589) (.8433) (.0268) (.0302) EARLY -8.4788 -8.2754 -.4023 -.3832 (4.6858) (4.902) (.1714) (.1812) COLLSEA* -6.0410 -6.0382 -.1727 -.1733 (2.7404) (2.8307) (.0994) (.1038) CGAMES -1.4035 -1.3759 -.9635 -.9054 (.6033) (.6319) (.5684) (.5998) CPTS* -.1737 -.1648 -.0574 -.0542 (.4881) (.5055) (.2350) (.2455) CFGPCT 6.3856 8.8789 -.9577 -.7437 (41.845) (44.255) (1.5240) (1.6234) CFT1PCT -34.488 -34.710 -.8758 -.8752 (24.464) (25.291) (.9126) (.9530) CREB* .8441 .8445 .0611 .0684 (.5827) (.6019) (.1383) (.1448) CAWARDS -3.5230 -3.4365 -.4573 -.4480 (1.9739) (2.0656) (.0708) (.0752) RACE 3.1735 3.1728 .1997 .1987 (3.8542) (3.9823) (.1439) (.1502) ln(Compensation) -17.085 -17.731 -.7573 -.8192 (2.7646) (3.7618) (.1007) (.1401) S.E.E. 22.754 23.511 .8301 .8668 R2 .3244- ..: .5109 ... *These variables are logged when the dependent variable isln(DRAFT).

cients-the latterestimates correct for serial correlation in our timeseries usinga methodproposed by Pindyckand Rubinfeld(1976). We interpret the GLS resultswith cautiondue to the shorttime seriesused. In both OLS specifications,PCTWHITE has positivesignificant (at 2% in col. 1 and 11% in col. 2 on two-tailedtests) effects on home attendance.These OLS resultsimply that going froman all-blackto an all-whiteteam in- creasesattendance by 137,885fans (col. 3's coefficientapplied to themean attendancelevel) to 157,040fans (col. 1). At $10 per head (a conservative estimateof averageticket price plus concessionrevenue) and 12 players per team,these estimatesimply an arena revenueeffect of $114,904 to $130,887per white player. This estimateis somewhathigher than the 20% ceterisparibus racial salary differential (about $80,000) in table2, suggesting thatteams and whiteplayers share in the gainsfrom serving fans' desires to see whiteplayers. The GLS resultsshow positivebut smallerand less significanteffects of PCTWHITE on attendance(or itslog). The effecton

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Table 5 OLS and GLS, AnnualHome Attendance(1980-81 to 1985-86) DependentVariable

ATTEND (%103) In (ATTEND)

Explanatory (Mean = 440 X 103) (Mean = 12.952) Variables OLS GLS OLS GLS

CONSTANT -1254.1 -1247.4 3.6227 -2.8322 (340.48) (349.76) (1.5406) (1.8165) YEAR 14.010 14.814 .0344 .0359 (3.9825) (4.0703) (.0100) (.0104) WINPCT 473.670 448.25 1.2532 1.1682 (66.154) (60.913) (.1665) (.1572) STARS 18.377 13.479 .0230 .0134 (16.569) (14.450) (.0418) (.0371) ARENA* 5.2067 .0416 .2220 .1385 (1.5808) (.0176) (.0893) (.1021) RACEMSA* -2.1441 -2.8483 -.0067 -.0084 (1.1652) (1.3887) (.0033) (.0040) POPMSA* .0140 .0170 .1011 .1330 (.0053) (.0062) (.0497) (.0592) INCMSA* .0116 .0126 .3116 .3313 (.0049) (.0059) (.1137) (.1403) TEAMS .8327 .0971 -.0005 -.0004 (4.7144) (5.6476) (.0121) (.0146) PRICE 13.533 -3.8426 .0260 -.0259 (18.132) (17.926) (.0448) (.0458) PCTWHITE 157.040 96.089 .2726 .1619 (68.117) (60.888) (.1708) (.1558) S.E.E. 79.55 65.30 .1992 .1671 R2 .6304 ... .6079 n 138 138 138 138 NOTE.-Unitsof observation are team years for 23 teamsand 6 years. * Thesevariables are logged when the dependent variable is ln(AITEND).When the dependent variable is ATTEND,these variables are in thousands.

ATTEND is stillsignificant at 11% (two-tailedtest), however, and suggests a per playerrevenue effect of $80,000. Table 5 also indicatesthat teams playing in largearenas, with high win- ning percentages,and in areas with small numbersof blacks and high incomes,have higherhome attendance,other things equal. The effectof priceis small,and muchsmaller than its standard error. Price is obviously an endogenousvariable, and itmay be pickingup demandeffects, although excludingprice did not affectthe results. Finally, when PCTWHITE was interactedwith other variables, there was no evidencethat the impactof whiteplayers on attendancevaried with the racial compositionof the market.Table 6 containsthe results of such interactions.The only signif- icantinteraction is a negativeone withARENA: whitesadd morefans in smallarenas.21 Whites may be especiallygood draws in citieswith small

21 Theother interactions were insignificant as a groupas wellas individually.

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Table 6 SelectedOLS Coefficientsfrom Attendance (Model withPCTWHITE Interactions)

ATTEND (%103) ln(ATTEND)

PCTWHITE 347.88 5.0104 (746.60) (13.920) PCTWHITE * RACEMSA 15.606 .0289 (12.934) (.0364) PCTWHITE * POPMSA* .0701 .5369 (.0642) (.6295) PCTWHITE * INCMSA* .0449 .8656 (.0514) (1.2736) PCTWHITE * WINPCT 45.410 -.2098 (586.86) (1.5796) PCTWHITE * STARS 66.944 -.0639 (139.89) (.3641) PCTWHITE * PRICE -180.79 .5262 (156.16) (.4101) PCTWHITE * ARENA* -41.052 -1.6329 (13.809) (.8130) PCTWHITE * TEAMS -8.303 -.0986 (56.023) (.1582) S.E.E. 76.535 .1979 R2 .6794 .6375 NOTE.-Forother variables, see table 5. * Thesevariables are logged when the dependent variable is ln(ATTEND).When thedependent variable is ATTEND,these variables are in thousands. arenas such as Portland or Sacramento, as compared with those with large arenas like Detroit.22

V. Today's NBA Salaries in Historical Perspective Since the 1950s, many factors have combined to raise NBA players' salaries: unionization, freeagency, the increasingpopularity of professional sports, television, and so on (Berry et al. 1986). To provide an indication of how farplayers' salaries have come, we have, based on our salary model, computed predicted 1985-86 salary levels for selected all-timegreat players. The resultsare shown in table 7. Of this group of players,only Wilt Cham- berlain at $2.317 million would have been paid at the top levels of the salary structure,as he was when he played. All of these players actually

22 Withthe exceptionof PRICE, our resultsfor attendance are similarto those ofNoll (1974,chap. 4, pp. 115-57),who did not includeracial makeup of theteam or arena size. He suggestsincluding each variable other than RACEMSA or POPMSA as an interactionwith POPMSA but with no main term.When this specificationwas attempted,the results were similar to thosein table5. In particular, thePCTWHITE effectin theNoll-type specification was positiveand significant. Finally,when we omitCeltics (due to theuniqueness of Larry Bird, Kevin McHale, et al.), the attendanceresults get stronger:in OLS regressionsthe PCTWHITE effectbecomes 188.57(81.38) (ATTEND) and .4239 (.2048) (In ATTEND).

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Table 7 Actualand PredictedSalaries of SelectedAll-Time Greats ActualSalary Salaryin Calendar Year of at theTime 1985 Predicted Player Year Career ($) Dollars Salary($)*

El&inBaylor 1962-63 5th 30,000 106,656 1,712,357 1972-73 14th 450,000 1,157,143 2,317,489 1962-63 13th 50,000 177,760 956,233 Dave DeBusschere 1971-72 10th 100,000 265,622 1,021,142 1973-74 7th 300,000 726,221 946,418 JohnHavlicek 1969-70 8th 140,000 410,820 797,346 1971-72 4th 87,500 232,420 1,349,803 1972-73 6th 200,000 514,286 743,270 1962-63 9th 30,000 106,656 1,506,648 Oscar Robertson 1971-72 12th 233,333 619,785 1,312,598 Bill Russellt 1966-67 11th 125,001 414,149 1,558,021 JerryWest 1973-74 14th 300,000 726,221 1,331,624 SOURCES.-Koppett(1968)-Hayes and Russell; Koppett (1973)-Monroe; Hirschberg (1963)-Baylor, Pettit,and Cousy; Bradley (1976)-Frazier; Libby (1977)-Chamberlain and West; U.S. Senate Subcommittee on Antitrustand Monopoly (1972)-DeBusschere and Robertson; Halberstam (1981)-Havlicek. NOTE.-The resultsare based on wage-levelregressions, not log wageregressions. For superstars,it maybe unrealisticto saythat, for example, each increase in pointsper game raises salary by the same percentage(as a log wageregression requires). The salarylevel regression produced a largerrace effect ($111,590)(34,743) than did the log wage regression. * Basedon SALARYlevel OLS regressionand statistics as ofthe indicated year of career. t Player-coach. earned in 1985 dollars considerably less money than they would have if they were playing today. In particular,players such as , Wilt Chamberlain, Bob Pettit, Bob Cousy, and Bill Russell paid a high price by being born too soon.

VI. Conclusion In this article,we have investigatedracial salary differentialsin the NBA. A variety of specifications and statistical techniques indicate that, ceteris paribus, black NBA players earn significantlyless than white players by about 20%. In addition, ceterisparibus, home attendance is a positive func- tion of white representationon the team. Such findingsare consistent with the notion of customer discrimination. On the other hand, our results for draftposition do not indicate discrimination in hiring.23

23 As thisarticle goes to press, we havebecome aware of two recently completed papersby sociologists on theNBA. First,Wallace (in press) analyzed NBA salary determination.While race was not his majorconcern, he did finda significant salaryadvantage for whites, other things equal. However, he did notcontrol for market-relatedvariables other than population or teamwinning percentage, did notconsider the endogeneity ofdraft position, and did not perform reverse regres- siontests or seniorityinteractions. Further, he did notdeal with the issue of the sourceof discrimination against blacks and did not provide an economic framework (profit-maximizingorotherwise) to analyze the consequences of prejudice. Second, Schollaertand Smith(1987) analyzed the impact of teamracial composition on

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Whilesome of our findingsare consistentwith the existence of discrim- inationagainst blacks in the NBA, two recentanalyses of professional baseballduring the free-agencyera failto findracial discrimination there (Raimondo 1983; Hill and Spellman1984). What accountsfor the differ- encesbetween our findingsand theirs?We believethat the relative scarcity of whiteNBA playersand the greatervisibility of basketballplayers to fans(compared with baseball) account for our findings.For example,Hill and Spellman (1984) reportthat about 30.8% of major league baseball playersin 1976 were black,a farsmaller figure than we findin the NBA. In addition,while the ceterisparibus racial compensationdifferential we foundis large(20%), it existsin thecontext of roughlyequal overallblack and whitesalaries. Social pressuresto eliminatediscrimination in thissit- uationmay well be less thanif therewere a highlyvisible black shortfall in mean salaries.The factthat several black playersare among the most highlypaid in the league may deflectany suspicionthat blacks face dis- crimination. It is noteworthythat such estimatesof blacks' ceterisparibus salary shortfallsare found10 yearsafter the adventof freeagency in the NBA. In addition,the high losses claimedby owners(Berry et al. 1986) suggest thatthey are undersome pressureto maximizeprofits. If discrimination existsin such a competitivemarket, then it is eitherprofitable, or owners are willingto take negativeprofits in orderto indulgetheir preferences forwhite players. Our resultssuggest that customer (fan) discrimination maybe theultimate cause of the black shortfall.As long as fansprefer to see whiteplayers, profit-oriented teams will make discriminatorysalary offers.

References Becker,Gary. The Economics of Discrimination. 2d ed. Chicago: University of Chicago Press,1975. Berry,Robert C.; Gould, William B. IV; and Staudohar,Paul D. Labor Relationsin ProfessionalSports. Dover, Mass.: AuburnHouse, 1986. Blau, FrancineD., and Beller,Andrea. "Trends in EarningsDifferentials bySex and Race: 1971-1981."Paper presented at theAmerican Economic AssociationMeetings, Dallas, December 1984. Bradley,Bill. Lifeon theRun. New York: Quadrangle/NewYork Times, 1976. attendance.Using a similarspecification toours, but for a smallersample of teams andearlier time period (1969-82 or 1977-82),they did notfind a raceeffect. Our attendanceresults for 1980-86 are probably due to thefact that the league has becomethree-quarters black in these years. In theearlier periods, blacks comprised 60%-70%of the league. As whiteplayers have become more scarce, an increasein theirpresence now has a greatermarginal effect on attendance.The resultsof our article,compared to earlierwork, are thus consistent with the idea of customer discrimination.

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Dutta,M. EconometricMethods. Cincinnati: South-Western, 1975. Halberstam,David. The Breaksof the Game. New York: Knopf,1981. Hill, James,and Spellman,William. "Professional Baseball: The Reserve Clause and SalaryStructure." Industrial Relations 22 (Winter1983): 1- 19. . "Pay Discriminationin Baseball: Data fromthe Seventies."In- dustrialRelations 23 (Winter1984): 103-12. Hirschberg,Al. Basketball'sGreatest Stars. New York: Putnam,1963. Kahn,Lawrence M. "CustomerDiscrimination in a GeneralEquilibrium Framework."Mimeographed. University of Illinois,May 1987. Koppett,Leonard. 24 Secondsto Shoot.New York: Macmillan,1968. . The Essenceof the Game is Deception.Boston: Little, Brown, 1973. Libby,Bill. Goliath:The WiltChamberlain Story. New York: Dodd, Mead, 1977. Noll, Roger D. "Attendanceand Price Setting."In Governmentand the SportsBusiness, edited by R. Noll. Washington,D.C.: BrookingsInsti- tution,1974. Pindyck,Robert S., and Rubinfeld,Daniel L. EconometricModels and Eco- nomicForecasts. New York: McGraw-Hill,1976. Raimondo,Henry J. "Free Agents' Impact on theLabor Market for Baseball Players."Journal of Labor Research4 (Spring1983): 183-93. Schollaert,Paul T., and Smith,Donald Hugh. "Team Racial Composition and SportsAttendance." Sociological Quarterly 28 (1987): 71-87. U.S. SenateSubcommittee on Antitrustand Monopoly.Hearing on S.2373, a Bill toAllow theMerger of Two orMore Professional Basketball Leagues, Sept.21-23, 1971. Washington,D.C.: U.S. GovernmentPrinting Office, 1972. Wallace, Michael. "Labor Market Structureand Salary Determination amongProfessional Basketball Players." Work and Occupations,in press.

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