do former college athletes earn more at work? · pdf file · 2018-03-03do former...

Do Former College Athletes EarnMore at Work?A Nonparametric Assessment

Daniel J. HendersonAlexandre OlbrechtSolomon W. Polachek

A B S T R A C T

This paper invesligutes how students' rt>llegi(ite athletic ptiriiciparion iiffeit.s

their subsequent labor market .success. By using newly developed techniques

in nonparametric regre.\sion. it show.s that on average former college ath-

letes earn a wai^e premium. However, the premium (.v not uniform, but

skewed so that more than half the athletes actually earn less than nonalh-

letes. Further, the premium is not uniform across nccupations. Athletes earn

more in the fields of business, military, and manual labor, but surprisingly,

athletes are mare likely lo become high school teachers, jobs thai pay rela-

tively lower wages to athletes.

Dim'u'l .1. Henderson is an a.ssi.stcmt professor iifi'iontmics ill llw State University of New York utBinfihdtniim {BinghcimUm University i. AU'ximdre Oihrccbl is tin ii.ssi.sltint priifes.^iiriif ecoiwmiis at theAnisfieUI School of tiusiiwss ill Rama/m Ciilleffe of New Jer.sey. Siilonum W. /'I'liichck is a dislini-uisheilprofessor of eionomics at the State University of New York ul Binfihiimton Itiinaluiinion University). Theauthors would like lo tinmk Cliff Kern. Jeff Racine and two anonymous referees for u.scful comments on thesubject matter of Ihis paper. The icsecirch on this projeet has aho henejited from participunt.s of theBinghamton University Departmental Seminar Series. Riimapii Ciillege of New Jersey DeparttitentalSeminar as well as participants at the 2004 Anmiat Meeting of the Canadian Economic Association.Toronto. Finally, the authors thank .lames Ixm^ for providing; the data necessary for ihi.s project along withhis SAS code. The data used in this article can he obtained beginning January 2IK)7 through December2010 from Daniel J. Henderson. Department of Economics. State University of New York. Binghamton. NY13902-6(XII). email: djhender&'binghamlon.edii. Contact information: Daniel J. Henderson. DepartmentofEconomits. State University of New York. Binghamton. NY IJW2-6OOO. e-nuiit: djhender^hingham-lon.edu 1607) 777-44H0. Fax: (607} 777-26lil. Alexandre Olbreeht. Anisfiekl School of Business. RamapoCollege of New Jersey. Mahwah. NJ 07430-1024. (201 j 6H4-7346. Fax: (201) f>S4-7957. e-mail:[email protected]. Solomon W. Polaehek. Department of Economics. Slate University of New York.Binghamton. NY !.i9O2-60OO. (607) 777-6HMi. Fax: (607) 777-26HI, e-mail: [email protected].[Submilted May 2005; acccpled November 2005]ISSN 022-166X E-ISSN 1548-8004 © 2006 by the Board of Regents of rhe University ot Wisconsin System

THE JOtlRNAL OF HUMAN RESOURCES • XLI • 3

Henderson, Olbrecht, and Polachek 559

I. Introduction

Evaluating how undergraduates benefit from coHegiate athletic partic-ipation is important both to universities and students. Whereas a number of studiesestimate the link between high school athletic participation and suhseqiient earnings(Barron, Ewing. and Waddcll 2000; Eide and Ronan 2001). the only comparableanalysis for collegiate sports finds that males who participated in intercollegiate ath-letics receive approximately a 4 percent wage premium (Long and Catidill 1991).However. Long and Caudill (1991) make a number of restrictive assumptions limitingthe inferences one can draw. For this reason our research reexamines the question howearnings relate to collegiate athletic participation. We use a new nonparametricapproach which enables us to generate unique estimates for each former college stu-dent. From this, we are able to assess how collegiate athletic returns are distributedacross the population as well as determine whether former college athletes actuallygravitate to occupations with the highest wage premium.

To motivate our analysis, note that the National Collegiate Athletic Association(NCAA) Division !-A athletic departments lose an average of $600,000 per year onrevenues of $25,100,000, after subtracting institutional support. Similarly, in 2001,NCAA Division I-AA, and I-AAA schools lost on average $3,390,000, and$2,82O,O(X). respectively. Although numbers were not directly reported. Division 11.and UI schools also sustained losses, though smaller in magnitude (see the 2(X)INCAA Revenues and Expenses Report). Indeed, of the 1,266 colleges, and universi-ties participating in the membership led organization of the NCAA, which servesalmost 350,000 student-athletes, only 41 athletic departments showed a profit in 2001.

For the mere 3.24 percent of profitable NCAA members, the revenue sports ol' foot-hall and basketball are primarily responsible. Revenues generated hy these two sportsare large enough to offset the expenses incurred in ail the other sports supported bythose particular athletics departments. At lower NCAA levels, football and basketballare also money-losing sports partly because post-season appearance prizes andnational television contracts are nonexistent. Other than some Division I-A football,Division 1 basketball, and ice hockey programs, collegiate athletic teams, regardlessof the division of competition, have expenses that exceed revenues.

If athletics are for the most part "money losing," universities must have reasons tofund these endeavors. Among the reasons given are institutional and instructionalarguments conceming what players leam. For example, successes of athletic pro-grams may improve a university's image and lead to a higher numher of applications.Because academic reputation is partially hased upon the number of applications andacceptance rates, this may. in tum help raise a university's standing. Athletic successmay even lead to an increase in donations. Generally, lower-division teams do notreceive national acclaim but such schools also may view financial losses as an invest-ment in the tuture (for example, if a school plans to move up to Division 1).

Athletes are also said to leam valuahle life lessons from athletic participation.Student athletes may learn skills that will be useful later in the labor market. For thesmall percentage of individuals who have realistic expectations of playing profes-sional sports, athletic participation may he viewed as an investment in their futurecareers. The majority of the investment-type arguments are anecdotal in naturebecause earnings data that also records athletic participation in coliege are rare.

560 The Journal of Human Resources

As mentioned, the only known exception is Long and Caudill (1991). hereafter LC.They argue that athletic participation is a form of human capital investment becauseathletic participation teaches athletes added discipline, teamwork skills, a strong driveto succeed, and a hetter work ethic' If these student athletes gain more skills (or ifstudent athletes use coiiegiate sports to improve their existing skills), then, ail elseconstant, one would expect participation in college athletics to yield a wage premiumwhen compared with nonathletes with similar demographic and academic abilitycharacteristics.

Using a maximum likelihood procedure that deals with the limited dependent vari-able problem, LC estimate a wage function, and find that former male athletes sixyears after expected college graduation earned approximately a $650 (or approxi-mately 4 percent) wage premium in 1980. Although popular, maximum likelihoodtechniques require several restrictive assumptions. First, the etrors are assumed tocome from a particular distribution. Futiher. the functional form for the technology isgiven a priori. These are hoth very strong assumptions, which may. or may not he cor-rect. For example, if one chooses a specific technology, and that assumption is false,estimation will most likely lead to biased estimates. Partly for these reasons, we adopta nonparametric approach that addresses these concerns.'

Nonparamettic estimation procedures relax the functional form assumptions asso-ciated with the traditional parametric regression model, and create a tighter fittingregression curve through the data. These procedures do not require assumptions onthe distrihution of" the error nor do they require specific assumptions on the form ofthe underlying technology. Further, the procedures generate unique coefficient esti-mates for each observation for each variable. This attrihute enables us to estimate theearnings benefit of athletic participation for each individual.

Although nonparametric techniques are attractive, issues employing the proceduresarise with this and similar data sets. Here the complication occurs because most non-parametric techniques require the variables to be continuous. This is problematic forus hecause of the abundance of ordered and unordered categorical variables in theonly available data set on college athletes that contain post college earnings. As willbe explained, to get around the nonparametric estimation problems encountered whenhaving categorical data, we apply the Li-Racine Generalized Kernel Estimation pro-cedure, which, unlike most other nonparametric procedures, can smooth categoricalvariables.

In implementing the empirical procedure, we first establish that the wage distribu-tions between former athletes and nonathletes are significantly different. Second, wemake a statistical argument that athletic participation is a determining factor of thewage distribution. We then apply the Generalized Kernel Estimation procedure to getat the main contribution of this paper, which is to investigate the occupations In whichathletes receive a wage premium. We find that former college athletes receive a wage

t. Several studies have focused on the effects of high school athlelics participation on eamings (for exam-ple. Ewing 19951 using the National Longitudinal Survey of Youth, and ihe National Longitudinal Survey ofthe High School Class ot 1972. These surveys did not ask ahout collegiaie participation.2. Nonparametric and semi parametric estimaiion have been used in other labor economics domains to avoidrestrictive functional form assumptions. As an example regarding how policies to reform personal incometax affect the speud of labor supply adjustment, .see Kniesner and Li (2002).

Henderson, Olbrecht. and Polachek 561

premium in husiness, manual lahor. and military occupations, but former athletes whoselect high school teaching as an occupation are linked with lower wages, cetedsparibus.

If individuals know these wage premiums for specific occupations, one wouldexpect fomier college athletes to be more likely to enter a particular field where theymay have a wage advantage over nonathletes. To test this premise, we further extendLC's work by using logit models to determine whether athletic participation helpspredict occupational choice. Our findings suggest that college athletic participation isa positive factor in selecting a high school teaching occupation, but seemed not toinfiuence any other occupational choices. Although it may seem to be irrationalbehavior for fomier athletes to be more likely to select a particular job associated withlower wages, nonpecuniary factors could be responsible.

II. Methodology

A. Model

Generally economists estimate an eamings function to investigate how an indepen-dent variable affects eamings. In our particular case, we are Interested in understand-ing the role of collegiate athletics on earnings, and would like to estimate the widelyused parametric specification of the eamings function

(1) .v,-/(.v,,P)-Fe,, / - 1.2 N

where u', (measured in logs) is a directly observable and continuous wage variablefor each individual t,xisaN xd matrix of exogenous control variables (for example,athlete), P is a rfxl vector of parameters to be estimated, and e^ is the random dis-turbance. Ifthe dependent variable and the residuals are well behaved, estimation byordinary least squares is appropriate.

Unfortunately, in our data we face a limited dependent variable problem. As will beexplained later, wages in this data set are reported as Income categories, with the high-est bracket having no upper bound. Because OLS results would be biased since theerror femis no longer have zero expectations, LC select a method developed by Nelson(1976). Nelson's Maximum Likelihood procedure, to which both probit and logit mod-els are special cases, handles the problems associated with limited dependent variablesof the above nature. However, as stated previously. Nelson's methodology requires oneto make assumptions regarding both the functional form for the technology and the dis-tribution of the error term. In addition, the procedure gives a single coefficient estimatefor each variable. This implicitly assumes that the coefficient for each variable is con-stant across individuals, which also may or may not be true.

B. Generalized Kernel Estimation

Given the limitations of Nelson's procedure, we adopt a nonparametric approach. Inthis section, we describe Li-Racine Generalized Kernel Estimation (see Ll and Racine2004; Racine and Li 2(X)4). which will be used in order to estimate the retums to col-legiate athletic participation. First, consider the nonparametric regression model


(2) / = i,2 N

where m is Ihe unknown smooth earnings function with argument .x,- l.i,' ,.r",.r,"l,A ;̂ isa vector of continuous regressors {for example, standardized test scores), x" is a vec-tor of regressors that assume unordered discrete values {for example, athlete), x" is avector of regressors that assume ordered discrete values {for example, number of chil-dren), e, is an additive error. and/V is the number of individuals in the sample. Takinga tirsl-order Taylor expansion of Equation 2 with respect to x yields

{3) w-^m(Xj) + (x;-x-j)^lXj) + E,,

where P(J^) is detined as the partial derivative of mU^) with respect to x'\ Here, ifH', is the log wage, the estimated coefficient of ^IXj) is interpreted as the retum towages for a given x'\ specific to each individual /.

lmix)\The estimator of b{Xj) = o , J is given by

(4)

where Kj^= f l (V,) /'I':.

n l"{r" 1-" 1 " i 1 1 J

= 1 5 = 1^, X';). A:^ is the com-

monly used product kernel {see Pagan and Ullah 1999). where /' is the standard nor-mal kernel function with window width X[ - X\ (N) associated with the s'^ componentof J:'. /" is a variation of Aitchison and Aitken's {1976) kernel function which equalsone if x",- x"j, and X." otherwise, and /" is the Wang and van Ryzin (1981) kernel func-tion which equals one if .v̂ ) = .v;,|.,and(X.")l "'•" "- otherwise.

Estimation of the bandwidths { V . V . V ) Is typically the most salient factor whenperforming nonparametric estimation. For example, choosing a very small bandwidthmeans that there may not be enough points tor smoothing and thus we may get anundersmoothed estimate {low bias, high variance). On the other hand, choosing a verylarge bandwidth, we may include too many points and thus get an oversmoothed esti-mate (high bias, low variance). Tbis tradeoff is a well known dilemma in applied non-parametric econometrics and thus we resort to automatic determination procedures toestimate the bandwidths. Although there exist many selection methods, one popularprocedure {and the one used in this paper) is that of Least-Squares Cross-Validation{LSCV). In short, the procedure chooses {X'\X",X") which minimize the least-squares cross-validation function given by

(5)

where /M_^{X,) is tbe commonly used leave-one-out estimator oiFinally, casual observation of Equation 4 shows that estimates of p {x ) are obtained

only for the continuous regressors. The returns to the categorical variables must be

3. All handwidths in this paper were calculated using N ©.


obtained in a separate step. For the unordered categorical variables, for example, thecoefficient on ATHLETE = / is calculated as the counterfactual increase in theexpected wage of a particular individual when they go from not being a collegiate ath-lete to being a collegiate athlete, ceteris paribus. Similarly for the ordered categoricalvariables, for example, the coefficient on NCHILDREN = / is calculated as the coun-terfactual increase in the expected wage of a particular individual when you increasethe number of children they have from zero to one. ceteris paribus. At the same time,NCHILDREN = 2 would show the cou nterf actual increase in the expected wage of aparticular individual when you increase the number of children from zero to two.ceteris paribus. If the linear structure is appropriate (parametric dummy variableapproach), one would expect the coefficient on NCHILDREN = 2 to be twice that ofNCHILDREN = /. This is often not the case. See Hall. Racine, and Li (2004); Li andRacine (2004); Racine and Li (2004); Li and Ouyang (2005); and Li and Racine(2006) for further details.

III. Data

The Cooperative Institutional Research Survey (CIRP) collectedinfomiation from college freshmen (both men, and women) in the 1970-71 academicyear, and included one followup in 1980, six years after expected collegiate gradua-tion (see Astin 1982). Respondents were asked a variety of questions pertaining todemographic factors, including family income and background, college majors, ath-letic participation in high school, race, and goals considered important during theirfirst year of college. The followup questionnaire asked respondents about their livesafter college, including earnings (in categories), occupational choices, graduatedegrees attained and athletic participation in college (definitions for all variables canbe found in Appendix 1).

Because the purpose of the paper is to examine the role of athletic participation oneamings. it is important for included individuals to have had an opportunity to partic-ipate in sports. At the time the information was collected, females still lacked fullenforcement of Title IX, which requires gender equality in sports, and as a result,females were not included because of the limited number of female athletes.Dropping women from the sample left 4.209 males, of which 646 (approximately 16percent) were considered athletes in our data. Individuals responding in the affirma-tive to the question of whether they eamed a varsity letter in college were assigned avalue of one for the collegiate athletic participation variahle. ATHLETE, and zero oth-erwise. Information on which sport or division the individual participated in was notcollected.

College athletes participating in "big-time" athletics programs could be seen astraining for a prpfessional career in athletics and would eam wages significantlyhigher than nonathletes if they attained their career goal. If enough individualsworked in that profession, there could be an upward bias on the athletic participationcoefficient. However, LC believe that it is unlikely that these individuals attendedschools to train for a professional career. Their main argument was that the profile ofthe schools attended by the athletes in this sample did not match with the expectedprofile of a school with "big time" athletics. Specifically, as shown by Table 1, former


Table 1Descriptive Skitistics for CIRP Dala

Variable

Income (bracket)Income (in dollars)ACT ScoreAfrican AniericanBachelors degreeDrive dummyFaniily dummyFirm sizeGradesMarriedMasters degreeNumber of childrenPart-time employedPh.D. or professional

degreePrivateRunbusSchool enrollmentSelf employedVeteranWell dummy

Nonathletes

Mean

4.68518424.320

23.0300.1270.5210.2800.2674.0404.4590.5020.1430.3850.0680.086

0.5780.1655.3740.0540.0290.144

(N = 3.563)

StandardDeviation

] .605

3.8890.3330.5000.4490.4431.7561.1070.5(X)0.3500.7280.2510.281

0.4940.3711.8710.2250.1690.351

Athletes

Mean

4.85419269.150

23.8890.1780.5760.3480.3054.I4I4.4300.5060.1560.3640.0500.105

0.7380.1494.7170.0370.0060.161

(N = 646)

StandardDeviation

1.516

3.7850.3830.4950.4770.4611.7221.0300.5000.3630.7080.2170.307

0.4400.3561.6500,1890,0790.368

Notes: Descriptiiins of eitch variable are pruvjdetl in Appendi.t I uncl inaime brackeii are de.scribcd inTable 2.

college athletes attended smaller enrollment schools than nonathletes. Although asomewhat weak assumption, we feel that even if some athletes attended largerschools, this will not be the source of any bias."" The other source of concern with thisdata deals with the reporting of the dependent variable.

As previously stated, income was reported as a limited dependent variable. Thevariable was reported in intervals defined in the following manner: I = $1 to S6.999,2 = $7,000 to $9,999, 3 = $10,000 to $14,999. 4 = $15,000 to $19,999. 5 = $20,000to $24,999. 6 = $25,000 to $29,999. 7 = $30,000 to $34,999, 8 = $35,000 to $39,999,

4. Only one athlete in the sampk' w;ts in the highest income bracket, and had an nuciipatidn listed as ""other."Pri)lessioiial athletes would be expected lo be in the highest income bracket, and select an OLCtipation of""olher."" Using lhe preceding criteria, il i>. unlikely any of the remaining iormer college athlelcs were pro-fessional alhleies. tixcluding him Inim the data did not affet;i the results.


Table 2Income Brackets

Income Brackets

$1 to $6,999$7,000 to $9,999$10,000 to $14,999$15,000 to $19,999$20,000 to $24,999$25,000 to $29,999$30,000 to $34,999$35,000 to $39,999$40,000 or more

Income

123456789

Nonathletes

378308999921569231

842053

%ofNonathletes

10.618.64

28.0425.8515.976.482.360.561.49

Athletes

4853

163177138381766

%ofAthletes

7.438.20

25.2327.4021.36

5.882.630.930.93

Noles: Individuals reported which income bracket they belong to amongst the lisled categories. Intlividualswho reported no income were dropped from the sample.

and 9 = $40,000, or more. The distribution of athletes, and nonathletes across incomeintervals is not identical. Table 2 and Figure I show that a slightly higher percentageof athletes are in the higher income brackets, which most likely accounts for the slightlyhigher average wage enjoyed by athletes.

In addition to income. Table I shows that athletes seem to enjoy a slight advantagein certain other categories. A higher percentage of athletes completed their bachelors.masters, and doctoral or professional degrees. Athletes were more likely to attend aprivate institution and reported themselves to be on average more driven and morelikely to have a goal to be financially well-off compared with nonathletes. Neithergroup had a significant average advantage regarding ACT scores and course grades,but choice of school and motivation seemed to differ between the two groups. Theywere less likely than nonathletes to want to own their own business. Each of thesevariables were included as control variables because individuals with a strong com-petitive drive, a goal to be tinancially well-off, and a motivation to own their ownbusiness would be expected to eam higher wages, ceteris paribus. In the statisticalanalysis to follow, possessing these traits also might make it more likely for an indi-vidual to play competitive athletics, and failure to address these traits could cause abias in the coefficient of the ATHLETE variable.

IV. Results

A. Distribution Tests

Before jumping into the regression, we feel it necessary to perform two distributionaltests. First, we want to establish that the distribution of wages between athletes, andnonathletes are significantly different from one another. Second, we will test whetherthe distribution of wages is dependent on athletic participation. Performing these tests


Athletes

Nonathletes

Figure 1Kernel Distributions of Income Brackets

not only strengthens the argument for inclusion of the ATHLETE variable on the right-hand side of our wage regression, hut it makes Ihe argument that athletic participationhas a significant impact on the wages of former college students.

A number of kernel-based tests measure the equality of distributions (for example,see Li 1996); however, generally they require that the underlying variable of interestis continuous in nature. As previously slated, the variable of interest is ordered andcategorical, and thus any kernel-based test used requires a kernel function equippedfor discrete data. For this reason, we seleet the Li, Maasoumi, and Racine (2004) non-parametric test for equality of distributions with mixed categorical and continuousdata. In our particular case, we are interested in testing whether the probability den-sity function of wages for former college athletes is significantly different from thatof nonathletes. Intuitively, if the null hypothesis is rejected, then an investigation ofwhy these two distrihutions are significantly different may be warranted. With thesedata, we firmly reject the null hypothesis (/j-valuc = 0.0071).

After establishing a statistical difference between two wage distributions, it is pru-dent to test whether explanatory variables have a detenninistie effect on the distribu-tion of wages. The question now becomes, does athletic participation influence thedistribution of wages? If the/\r//Z./:7'ft'variable is found to significantly affect the sta-bility of the conditional probability density function, then a strong argument can bemade as to why this variable should be included in the wage regression. Here weemploy Racine's (2002) invariancc test. This test examines the validity of the nullhypothesis, which states that an underlying distribution doe.s not change with partic-ular values of a conditioning variable. To test the null, a gradient is constructed using


kernel estimates of the conditional probability density funetion with respeci to theconditioning variable of interest, namely the ATHLETE variable. Intuitively, if wereject the null hypothesis, it is argued ihat athletic participation has a statistically sig-nificant cffeet on tbe distribution of wages. We find that it does by rejecting the nullat the I percent level of significance (/?-valuc - 0.0005).

B. Regression Results

When encountering a situation in which a regression must be estimated using a lim-iled dependent variable, econometricians often use an ordered logit model.'̂ However,using this method not only requires several restrietive assumptions, but it also limitsdiscussion to calculating self-determined marginal effects, and makes it difficult toinvestigate the returns to athletic participation for specific occupations. The nonpara-metric method we use allows for a more straightforward and flexible interpretation oftbe regression coefficients estimated.

Given the number of parameters obtained from the Generalized Kernel Estimationprocedure, it is tricky to present results. Unfortunately no widely accepted presenta-tion format exists. Therefore, in Figure 2, we give the mean, and the 25th. 5()th, and75th perccntile along with tbeir respective bootstrapped standard errors (labeledQuartile 1, 2, and 3). as well as a kernel density plot of the coefficients for the athleticparticipation variable for each athlete included in the data set (by definition, the ath-letic participation coefficient for all nonalhletes is zero). Haeh coefficient representsthe impact on earnings (category) for a one unit increase of the associated indepen-dent variable (in other words. ATHLETE going from 0 to 1).''

One eonsideration is important in interpreting the ATHLETE coefficient. For thecoefficient to be unbiased, ATHLETE must be truly exogenous^implying athletic sta-tus must be randomly assigned. However, il is possible students become athletesbecause they are innately motivated and disciplined—qualities that are unobservablebut positively correlated with earnings (Duncan and Dunifon 1998). If this is the case,athletes may earn more not because universities provide value-added, but because bet-ter students become athletes. There are two ways to get at this potential bias, thougheach is imperfect. One possibility is to model athlelic participation using a selectionrule, and then account for this selectivity in the earnings equation (Willis and Rosen1979). For this approaeh to work, one ideally should identify factors that affect ath-letic prowess such as height, and weight (unavailahle in the data) bul that are unre-lated to earnings. The problem finding sucb variables is at best tricky. Participating inhigh school athletics is a possibility, but this variable imperi'ectly predicts collegiateathletic participation, and besides may be correlated with earnings. A second, bul alsoimperfect, approach is to include motivational variables in the original earnings func-tion in order to hold eonstant the type "drive" that inspires athletes, but also raisesearnings. We adopt this latter approach because the data contain iwo such variables:first, a dummy categorical variable indicating whether the respondent rates himself in

5. When eslimating an ordered logit model while using ihe same setup a.s LC, a coefficient of 0.269 {stan-dard error of 0.078) tor the ATHLETE variable is obtained.6. The mean coefficieni values (or the remaining regressors are ijualiiatively similar lo the results in VXl.They are availxible from the ;tuthors upon request.


Mean: 0.028(0.0019)

QI: -0.115(0.0001)

Q2: -0.007(0.0002)

03:0.148(0.0020)

-2.0 -1.5 -1.0 -0.5 0.0 0,5 1.0 1.5

Figure 2Kernel Distribuiioti of Athletic Wage Premium Coefficients

2.0

the highest 10 percent in "drive, and amhition" (Drive Dummy); and second, adummy categorical variable indicating that heing "well-off financially is an importantgoal" (Well Dummy). Perhaps more importantly, because our true goal is to compareour nonparametric approach to LC, we follow their lead to treat ATHLETE as exoge-nous by assuming innate athletic ability to be a god-given talent.

The mean of the coefficients for the ATHLETE variable, 0.028, indicates that for-mer college athletes are in a 0.028 higher earnings category than nonathletes, ceterisparibus. Because most income categories represent a $5,000 wage gap, this coefficientean be interpreted as approximately a $140 wage benefit. Although qualitatively sim-ilar, this is smaller than the 4 percent premium reported by LC. But the variation inindividual wage premiums is more interesting. Less than half the college athletesaciually receive a positive gain. The median of the coefficients {Q2) is negative,implying a skewed distribution with more than half of former college athletes actuallyearning lower wages than nonathletes, ceteris paribus.

Discussing individual variation in parameter values is one of the major benefits wegain by using the nonparametric technique. Although we found that on average ath-letes obtain a wage premium, we were able to show that over half of them did not.Simply stereotyping all athletes under one estimate is misleading. For example, thetypical parametric approach, such as used by LC, suggests that athletes earn higherwages than nonathletes. ceteris paribus. If individuals choosing whether to participatein college athletics take this information as a given, it could affect their decision-making. Given the positive coefficient on ATHLETE found by LC. individuals maydecide to participate in sports because they believe that their wages will rise in the


future. Similarly, universities may opt lor sports programs believing that individualstudents necessarily benefit. However, our result shows that the wage premium is notuniform across athletes. Although some athletes enjoy large wage benelits, otherseam less than nonathletes. Thus, for students, the more appropriate question is notwhether to participate in sports, but the more specific question should be, if an indi-vidual participates in a sport, in which occupations will that individual most likelyearn a wage premium over nonathletes?

C. Results by Occupation

Table 3 shows the estimates on the ATHLETE variable for four job categories; as wellas for a fifth category depicting all other occupations combined. The four occupations,high school teaching, business, military, and manual labor are ones with a significantnumber of former athletes (arbitrarily chosen as those occupations with at least 35athletes). For the latter three occupations (business, military, and manual labor), themean, and median are positive, indicating that a wage premium is present for a major-ity of athletes in those occupations. Intuitive arguments could be made that skillsobtained, or improved during athletic participation would justify wage premiums inthese occupations. Teamwork skills, and an enhanced competitive drive to succeedcould be useful in the business world. Physical strength, and other athletic attributesmay make manual laborers and military professionals more productive at their jobs,justifying higher wages. The ability to apply strategic thinking, and adjust a particu-lar strategy during a game may be particularly important, while using military tacticsmay be impt)rtant during a busines.s negotiation, or when operating as a team to per-form some physical task. Many of these reasons apply to the conglomerate occupa-tion, as well.

Although most job categories were associated with wage premiums, the highschool teaching occupation was not. In teaching, a majority of former college athleteseam lower wages, ceteris paribus. as compared with nonathletes in this category.Although we will shortly di.scuss potential explanations of this observation, a wagepremium can affect occupational choice. Specifically one would expect former ath-letes to enter jobs where they eam high wages, and shy away from jobs where they donot. But this is not the case for athletes.

Table 4 reports the results of a logit model where the binary dependent variable.HSTEACHER. takes a value one if an individual reported high school teaching as anoccupation, zero otherwise. In this data, former college athletes were found to bemore likely to select high school teaching as an occupation despite earning lowerwages. Similarly, we found this result to hold on population subsamples such as forAfrican Americans. Several arguments can be levied to explain this behavior, but noevidence in the data clearly supports any claim in particular.

First, becoming a teacher may be driven by a nonpecuniary desire for upward socialmobility. Falk, Falkowski, and Lyson (1981). and Schwar/weller and Lyson (1978)report that the highly respected teaching profession is a source of upward social andprofessional intergenerational mobility for rural whites and African Americans, espe-cially during fhe 1970s. If athletes are more likely fo be motivated to improve theirlives, they may have viewed a teaching profession as a means to improve their statusin life. The teaching occupation generally provides fewer barriers to entry, and as a

570 The Joumai of Human Resources

ri

a

oo o

oc

— o

f", m Tf Tf TT Tf

— C i OCC' O Cl•--. oo riCi "^ Ci

O C i O C l O C i O C S C O O C S

r', rs] 00 C;

o (S q Ci q "5 q

I

O C i o o C i O C i Q l U i O- C O o o O O v O — O — Cl— ' C i q c i q o — o — od c i o ^ o c i o c i d o

qd

O — O oo O —O O Ci O Ci O Ci q ei

ci d o

oo

J=01}

X

in

C

CQ

OX)

o

a.3o

6

ties

oc

*.

'age

larl

'

^11 d

1, c•5 K •"

1 ^ >


Table 4Logit Model—Determinants of Becoming a High School Teacher

Variable

InterceptACT .scoreAfrican AmericanAthleteBachelor's degreeDrive dummyFirm sizeGradesMajor 1Majar2Major3Major4Major5Major6Major7MajorsMajor9Major! 0Major 11MarriedMaster's degreeNumber of childrenPh.D. or professional degreePrivateRunbusSchool enrollmentVeteran

Estimate

-3.004-0.056-0.102

0.9702.3970.179

-0.1320.142

-0.899-1.040-0.791-3.254-3.295-1.244-1.830

5-1.637-1.041-1.267

0.1762.418

-0.1610.2110.020

-0.9010.032

-0.047

Standard Error

0.7400.026*0.2640.180*0.435*0.1750.052*0.0920.466*0.240*0.295*0.478*0.733*0.300*0.741*

50.245*0.7610.545*0.1730.466*0.1370.7430.2270.306*0.0580.541

Noles: The dcpcndcm variable in this logil regression i.s ihe High Schiiol Teaching Occupmion. SeeAppendix 1 for descriptions of each of ihe variables. See Appendix 3 for [he delinitlons of the aeademiclieids constituting each major. The asterisk (*) signifies thai tlie estintate is significant at the 5 percenl level.The Greek letter delta (8) signifies thai the standard error is t(H> large lo allribute any meaning lo ihe coefti-cient. Further, the results are robust lo the exclusion of Major8.

governmental organization is not allowed by law to discriminate against any particu-lar group. The accessibility and attractiveness of teaching may explain why AfricanAmerican former college athlefes are more likely to choose this profession.

Several other theories are worth mentioning. If athletics fosters an increased affec-tion for a school, then an athlete may wish to retum to his high school to work. Athletesalso may wish to pursue coaching. Because high school teachers often serve ascoaches, this desire may be reflected in their occupational choice decision. Even if for-mer athletes choosing this profession realize they will be expected to eam lower aver-age wages, the increased utility generated by coaching may offset any monetary losses.


Regardless of the reason(s) for becoming teachers, a relatively large supply of for-mer athletes could exert downward wage pressure in the teaching occupation. If afabor market is inordinately supplied with individuals possessing similar traits, thenthat group's wages could be lower than comparably skilled workers in other markets.For example, if many former athletes are trying to become physical education teach-ers, then the wages of physical education teachers couid be lower than other teachers.

V. Conclusion

Estimating the impact of individual behavior is an important aspect ofsocial research. Often outcomes can be measured in monetary units. When this Is thecase, one can estimate an earnings function to determine how an individual's actionsaffect his or her earnings. In most cases, parametric models are used. However, para-metric models have certain restrictions regarding functional form. In addition, theyare usually specified in ways to yield a single coefficient estimate.

One such example is the effect of a student's participation in college athletics on eam-ings years after leaving college, a topic not well studied because of the paucity of data.However, in one such study Long and Caudill (1991) Iind that college athletes eam abouta 4 percent positive retum from collegiate sports. Because of certain data restrictions (acategorical dependent variable) they use Nelson's (1976) maximum likelihood proce-dure, but as with most parametric procedures, that paper limits itself to obtaining a sin-gle coefficient without exploring how robust their findings are across the population.

This paper reexaniines the issue using a new technique. The Li-Racine GeneralizedKernel Estimation procedure is able to assess the impact of an exogenous variablewithin a mode! containing an ordered categorical dependent variable along with con-tinuous, unordered, and ordered categorical regressors. Of course, the beauty of thetechnique is its ability to estimate coefticients for each individual so that one canassess the impact of athletic participation across the sample.

This paper examines the CIRP data. Unlike past studies, we find that the wagepremiums a.ssociated to former college athletes are not uniform. Rather, athletesearn between a 1.5. and 9 percent average wage premium in business, manual labor,and military careers, but nonetheless enter teaching occupations with a higher prob-ability than nonathletes despite facing an average wage deficiency of 8 percent.Whereas wage premiums in the former three occupations conform to the humancapital type matching models of occupational choice (Polachek 1981). the latterresult regarding teaching are consistent with nonpecuniary incentives explainingoccupational choice. This latter result regarding nonpecuniary motivators impliesbroader implications than usually inferred from typical economics models basedsolely on pecuniary factors.

Institutions of higher education need good reasons for how they spend limitedfunds. If a financial value can be linked to athletics, a stronger argument may beemployed to justify investment in athletics programs. This paper argues that Hnancialbenefits are not uniform to all Individuals who play sports. On average athletes receivea modest return, and go into occupations where they do best. But this is not the casefor all collegiate athletes. Almost 10 percent enter teaching, an occupation with anespecially low wage for athletes. Further, a good 50 percent do no better than the col-lege population at large.

Henderson, Olbrecht. and Polachek 573

Appendix 1Variable Defitiitions

Variable Meaning

ACT ScoreAfrican AmericanAlhleteBachelor's degreeBusiness

Drive dummy

Family dummy

Firm size

GradesManual labor

MAJXXMarriedMasters degreeMilitary

Number ot childrenOCCXXPart-time employedPh.D. or professional

degreePrivate

Runbus

School enrollmentSelf employedTeacher

VeteranWell Dummy

Score on American College Test (range from 9 to 30}1 if African American, 0 otherwise1 if earned a varsity letter in college. 0 otherwiseI if holds bachelors degree. 0 otherwise1 if individual reported occupation as business clerical,

business management or business sales, 0 otherwise1 if individual rates themselves in the highest 10 percent

to "drive to achieve." 0 otherwise1 if an individual reported that having a family was an

important goal. 0 otherwiseNumber of employees in tirm individual works for,

reported in categoriesSelf reported average college grades (A to F scale)1 if individual reported occupation as skilled, semi-skilled

or unskilled labor, 0 otherwiseRepresents various college majors (See Appendix 3)I if married, 0 otherwise1 if holds masters degree. 0 otherwise1 if individual reported occupation as military career,

0 otherwiseNumber of offspringRepresents various occupations (see Appendix 2}I if an individual was employed part-time, 0 otherwiseI if holds Ph.D. or advanced professional degree,

0 otherwise1 if eollege attended was a privately owned institution,

0 otherwise1 if an individual reported that owning their own business

was a goal. 0 otherwiseTotal enrollment of college, reported in categoriesI if individual was self-employed, 0 otherwise1 if individual reported occupation as secondary or

elementary teacher, 0 otherwise1 if military veteran, 0 otherwise1 if "be well off fmancially" is an important goal.

0 otherwise

574 The Joumal of Human Resources

Appendix 2Definitions of Occupations

OCCOCCOCC

1: 12: 15.25,29,30,31,403: 43 thru 47

OCC 4: 17OCCOCCOCCOCCOCCOCCOCCOCCOCCOCCOCCOCC

12345678910111213141516171819202122232425

5: 23, 28, 35, 376: 6, 7, 87:2,4,27,418:39: 11, 13,34,3610: 14, 1811: 19,22,24,2612: 1213:9, 1014: 16,2115:4216:5

AccountingActor/enierlainerArchitectArtistBusiness clericalBusiness managementProprietorBusiness salesClergyOther religiousPsychologistCollege teacherComputer programmerConservationist or foresterDentistDietician/home economicsEngineerFarmer/rancherForeign Service workerHomemakerInterior decoratorInterpreterLab technicianLaw enforcementLawyer

2627282930313233343536373839404142

4344

45

4647

Military serviceMusicianNurseOptometristPharmacistPhysicianSchool counselorSchool principalScientific researcherSocial workerStatisticianTherapistTeacher (elementary)Teacher (high school)VeterinarianWriter/journalistSkilled trades/skilled

manual laborOtherUnskilled worker/unskilled

manual laborSemi skilled worker/

semi-skilled manual laborOther occupationUnemployed

Henderson. Olbrecht, and Polaehek 575

Appendix 3Definitions of Majors

MAJlMAJ2:MAJ3MAJ4MAJ5MAJ6

12345678910111213141516171819202122232425262728293031323334

: 1,62: 2 thru 12. .56: 13 thru 18,58: 19.20,21,23.57: 24 thru 30, 59: 31 thru 36

ArchitectureEnglish literatureFine artsHistoryJournalismModern languageOther languageMusicPhilosophySpeech or dramaTheologyOther arts & humanitiesBiology (general)BiochemistryBiophysicsBotanyZoologyOther biological sciencesAccountingBusiness administrationElectronic dala processingSecretarial studiesOther businessAeronautical engineeringCivil engineeringChemical engineeringElectrical engineeringIndustrial engineeringMechanical engineeringOther engineeringChemistryEarth sciencesMathematicsPhysics

MAJ7MAJ8MAJ9

: 37, 38, 44, 45. 52: 39 thru 43:46. 47. 49. 50. 51.53. 54. 64

MAJ 10: 66 thru 68MAJl 1: 55, 60MAJ 12: All other majors

35363738394041424344454647484950515253545556575859606162636465666768

StatisticsOther physical scienceHealth technologynursingPharmacyPre-dentistryPre-lawPre-medPre-vetTherapyOther professionalAnthropologyEconomicsEducationHistoryPolitical sciencePsychologySocial workSociologyOlher soeial scienceAgricultureCommunicationsComputer scienceEnvironmental scienceElectronicsForestryHome economicsIndustrial artsLibrary scienceMilitary sciencePhysical education and recreationOther technicalOther nontechnicalUndecided

576 The Joumal of Human Resources

References

Aitchison. John, and Colin G. G. Aitken. 1976. •"Multivariale Binary Discrimination by theKernel Mclhud." Biomeiriku 63(3 ):413-20.

Aslin. Alexander. 1982. Minorities in Ameiiciui Higher Educaiion. San Francisco:Jossey-Bass.

Biirron, John M.. Brtidley T. Ewing. iind Glen R. Waddell. 200(). "The Effects of High SehooiAlhlelic Participation on Education and Labor Market Outcomes." Review of Economicsand Siati.stics S2Oy.4iyi-2\.

Dunean, Greg J.. and Rachel Dunitbn. 1998. - "Soft-Skills' and Long-Run Labor MarketSuccess." Research in Labor Economics 17:123-49.

Eide. Eric R.. and Nick Ronan. 2001. "Is Participation in High School Athletics an Inveslmentor a Consumption Good? Evidence from High School and Beyond." Economics ofEducation Review 2()(S):43l-42.

Ewing. Bradely T. \995. "High School Athletics and the Wages of Blaek Males." Review ofBlack PoliUciil Economy 24( I ):65-78.

Falk, William W.. Carolyn K. Falkowski. and Thoma.s A. Lyson. 1981. "Some Plan toBecome Teachers: Further Elaboration and Speciticalion." Sociology of Education 54( 1):64-9.

Hall, Peter, Jeff Racitie, and Q\ Li, 2004. "Cross-Validation and the Estimation ofConditional Probability Densities." Joiirnul of The American Statistical Association9y(468):10l5-26.

Kniesner. Thomas, and Qi Li. 2002. "Nonlinearity in Dynamic Adjustment: SemiparametricEstimation of Panel Labor Supply." Empirical Economics 27{1): 131^8.

Li. Qi. 1996. "Nonparametric Testing of Closeness between Two Unknown DistributionFunctions." Econometric Reviews l5(3):26l-74.

Li. Qi. and Desheng Ouyang. 2005. "Uniform Convergence Rate of Kemel Estimation withMixed Categorical and Continuous Data." Economics Leiter.s 86(2):291-6.

Li. Qi, Esfandiar Maasoumi. and Jeff Racine. 2(K)4. "A Nonparametric Test for the Equalityof Distributions With Mixed Categorical and Continuous Data." Hamilton: McMasterUniversity. Unpublished.

Li, Qi, and Jeft Racine. 2004. "Cross-Validated Local Linear Nonparametric Regression."Statistica Sinica 14(2):485-512.

>. Nonparametric Econometrics: Theory and Practice. Princeton: PrincetonUniversity Press. Forthcoming.

Long. James, and Steven Caudill. 1991. "The Impact of Participation in IntercollegiateAthletics on Income and Graduation." Review of Economics and Statistics 73(3):525-31.

N ©. Nonparametric software by Jeff Racine (http://www.economics.mcnia.ster.ca/racine/).NCAA. 2(K14. "Revenues and Expenses of Intercollegiate Athletics Programs."

(http://www.ncaa.org).. 2{X)4. "NCAA Facts." (http://www.ncaa.org).

Nelson, Forrest. 1976. "On a General Computer Algorithm for the Analysis of Modelswith Limited Dependent Variables." Annals of Economic and Social Measurement5:493-.'S09.

Pagan, Adrian, and Aman Ullah. 1999. Nonparametric Econometrics. Cambridge: CambridgeUniversity Press.

Polachek, Solomon. 1981. "Occupational Self-Selection: A Human Capital Approach toSex Differences in Occupational Structure." Review of Economics and Statistics63(0:60-69.


Racine. Jeff. 2(X)2. "A Consistent Nonparametric Distributional liwarlance Test." Hamilton:McMaster University. Unpublished.

Racine. Jef̂ \ and Qi Li. 2(X)4. "Nonparametric Estimation of Regression Functionswith both Calegorical and Continuous Data." Joitnud of Evtmomeirics 119( I):99-130.

Schwarzweller. Harry K., and Thomas A. Lyson. 1978. "Some Plan to Become Teachers:Determinants of Career Specification among Rural Youths in Norway. Germany, and theUnited Slates." Sociolof^y of Eihicalioii 51( 11:29^3.

Wang. Min-Chlang, and John van Ryzin, 1981. ""A Class of Smootfi Estimators for DiscreteEstimalion." Bionielrika 68( 1 t:3()l-9.

Willis. Rohert J., and Sherwin Rosen. 1979. "Educaiion and Self-Selection." Journal ofPolitical Economy 87(5):S7-36.

do former college athletes earn more at work? · pdf file · 2018-03-03do former...

Documents