Do Former College Athletes Earn Higher Wages?
by
Daniel J. Henderson, Alex Olbrecht, and Solomon Polachek1
Department of Economics
State University of New York at Binghamton
May 2, 2004
Abstract: In this paper, we apply the Li-Racine Generalized Kernel Estimation procedure
to measure how participation in college athletes affects earnings. We find no effect on
earnings but some effect on occupational choice.
JEL Classification: Semiparametric and Nonparametric Methods, Labor and
Demographic Economics, Wage Determination
1
Special thanks to James Long for providing the data set and original SAS code.
Introduction
Approximately 350,000 individuals participate in NCAA sports every academic
year, of which a select few will become professional athletes.2 Colleges and universities
have faced a budget crunch over recent years and have had to make funding choices
between supporting these athletes and academics. Understanding the effects of athletic
participation will allow administrators to make more informed funding decisions.
Long and Caudill (1991) argued that time spent playing sports can be a form of
human capital investment. Athletes are said to learn discipline, maintain better health,
acquire teamwork skills, gain a stronger drive to succeed and develop a better work ethic.
If athletic time is an investment in human capital, then this cohort should earn a wage
premium after graduation. However, following Becker’s (1965) allocation of time model,
athletes may receive this benefit if they substitute leisure time for athletic time when
deciding between the competing alternatives of studying, leisure and athletic training
times. This assumes that academic investments at least outweigh what is learned during
athletic time. Only this study has focused on the monetary effects of athletic
participation in college.
They obtained a wage benefit for males of about $650 six years after graduation
and participation in college athletics using Nelson’s maximum likelihood approach. We
used a newer and more accurate approach to analyze this data set to answer the same
question.
The advantage of generalized kernel estimation is that the data drives the
estimates so that no strong assumptions on the underlying functional form are required.
Since assumptions about the underlying distribution are not required, the model is more
able to conform to the data, creating a better fit. This nonparametric technique also leads
to more insightful results (a full discussion is forthcoming in the next section). As far as
we know, this is the only study to use this approach to analyze the impact of
intercollegiate athletics. Additionally, we also investigate whether athletic participation in
college has any occupational choice effects.
The paper is organized as follows. We first replicate Long and Caudill’s
approach. Next, we apply an ordered logistic model to the data so as to make
comprehension of the nonparametric results easier for individuals unfamiliar with this
approach. Next, we discuss the nonparametric results. Finally, we investigate
occupational choices made by athletes.
Methodology
The nonparametric technique used is the Li-Racine Generalized Kernel
Estimation procedure. For more information see Racine-Li (2003) and Li-Racine (2003).3
This procedure employs three different kernel estimators, depending upon whether a
regressor is continuous, ordered or unordered variable.
Local linear estimation can be thought of in the same light as ordinary least
squares. The major difference is that OLS estimates the best fit regression line through
2
NCAA.org reports that in 1998-1999 207,592 men and 145,832 women participated in intercollegiate
sports.
3
The software used was n©, available from http://faculty.maxwell.syr.edu/jracine.
the entire data set. The local linear approach estimates the best fit regression line at each
observation. More specifically, one orders points on a vector, from least to greatest. Next,
consider a point xi. The nonparametric approach estimates the best fit line through xi
using the points located between xi-h and xi+h. The variable, h, is known as the window
width. The optimal window widths are calculated by minimizing a cross validation
function, which the reader can loosely think of as similar to a likelihood function. The
optimal selection of the window widths gives the best fit local estimators. The procedure
assumes that the window width is constant for all observations.
Since these regression lines can be different across windows, the net effect is that
when one looks at the entire data set, a very nonlinear looking estimation has been
created. If however the linear parametric specification is the underlying model,
generalized kernel estimation will yield the same results. Ultimately, this procedure
yields a coefficient for every observation. OLS assumes one coefficient per variable for
all points. A more technical explanation now follows.
First consider a nonparametric regression model:
y = m( xi ) + ui ,
i= 1,2,…,NT
(1)
where m is assumed to be a smooth function whose form is unknown. Note that if m is a
linear function in its parameters, this yields the linear parametric model. Define xi as
xi=(xic, xio, xiu) where xic is a continuous random vector of dimension q, xio is a p x 1
vector of regressors that take ordered discrete values (e.g. number of kids), and xiu is an
r x 1 vector of regressors that take discrete but ordered values (e.g. two digit occupation
codes). Taking a first order Taylor expansion around xjc from equation one yields:
y ≈ m( xj ) + ( xi c − xj c ) B( xj ) + ui
(2)
c
where β ( xj ) is defined to be the partial derivative of m(x) with respect to xj . Next we
obtain the window widths, or bandwidths, we obtained the leave one out local kernel
estimator which is defined as:
−1
1
1
(xi c - xj c )
δ − j ( xj ) = [∑ Kh( c c
)] ∑ Kh( c
) yi
(3)
c
c
c
c
(xi - xj ) (xi - xj )(xi - xj )′
(xi - xj c )
i≠ j
−1
p
(xsi c - xsj c ) r u
)∏ l ( xsi u , xsj u λu )∏ l o ( xsi o , xsj o λo )
(4)
hs
s =1
s =1
s =1
where Kh is the product kernel function (see Pagan and Ullah 1999) with bandwidth
hs=hs(NT) associated with the sth component of xc. The function w is the standard normal
kernel function, lu is a version of Aitchison and Aitken’s (1976) kernel function4 and lo is
the Wang and Van Ryzin (1961) kernel function.5 Next using the leave one out estimator,
we minimize the least squares cross validation function by selecting (h, λu λo) such that
q
where Kh = ∏ hs w(
1
CV (h, λ λ ) =
NT
u
o
∑ [ y − mˆ
j
2
− j
( xj )]
is minimized.
Finally the optimal window widths are used to estimate δˆ ( x) by:
4
5
Takes the value one if xsio=xsjo, otherwise (λso)^| xsio-xsjjo|..
Takes the value one if xsiu=xsju, otherwise λsu
(5)
1
(xi c - xj c )
mˆ ( x)
)]
δˆ( x) = ( ˆ ) = [∑ Khˆ( c c
(xi - xj ) (xi c - xj c )(xi c - xj c )′
β ( x)
i≠ j
−1
∑ K ((x
hˆ
i
c
1
) yi
- xj c )
(6)
−1
p
(xsi c - xsj c ) r u
ˆ
where K = ∏ hs w(
)∏ l ( xsi u , xsj u λˆu )∏ l o ( xsi o , xsj o λˆo ) .
ĥs
s =1
s =1
s =1
q
hˆ
(7)
Data
The data for the Cooperative Institutional Research Programs (CIRP) were
collected at two points in time. It surveyed college freshmen in 1971 and had one followup in 1980, six years after expected graduation. Details can be found in Astin (1982).
Information was collected on income in 1980, family background, activities such as drug
use, and athletic participation. Definitions of all variables can be found in Appendix A.
This investigation used virtually the same data set as the Long and Caudill (1991)
study did. Observations were dropped for a variety of reasons. Following the previous
study, individuals reporting no income were dropped. Additionally, since outliers can
have a devastating impact on bandwidth selection, observations reporting an ACT score
of zero were dropped. Zero scores were interpreted to mean that the individual did not
take the ACT exam.
This left 4,209 males in this sample, of which 646 (or about 16 percent) earned a
varsity letter in college. Specifically, the question asked on the follow-up survey was
whether an individual earned a varsity letter in a sport, leaving which sport the
respondent participated in a mystery. The athletic division is also unknown since a
respondent’s college is unreported.
Therefore the definition of the athletic participation variable, athlete, is equal to
one if an individual participated in a varsity sport in college for four years, or zero
otherwise. No distinction is made between Divisions I-A, I-AA, I-AAA, II and III, but
Long and Caudill (1991) made a rather convincing argument that most athletes probably
did not come from schools specializing in “big-time college athletics.”
To account for other factors that may influence earnings, many other independent
variables were used (following the lead of Long and Caudill (1991)). College majors and
occupations were used as controls. Differences in grades, intelligence, and the will to
succeed were included.
Our empirical model modifies Mincer’s earnings function in several ways.
Mincer’s model was estimated using ordinary least squares and is defined as follows:
Ln W = β0 + β1 S + β2 E + β3 E2 + ε
(8)
where W is the wage, S refers to years of schooling and E refers to years of experience.
The timing of data collection proved to be problematic. The experience variable
for all individuals would be equal for all those who did not attend some professional or
graduate program. For those that did not immediately enter the workforce, it is unknown
how many years they had worked before the follow-up questionnaire.
The three educational categorical variables are included to capture the specific
returns to schooling for each degree. In addition, vintage effects are not a concern since
the time after graduation is relatively short.
The other reason why Mincer’s function needed to be adjusted in our model was
the manner in which the dependent variable was reported. Income was reported as
follows: 1 = no income, 2 = $1 to $6,999, 3 = $7,000 to $9,999, 4 = $10,000 to $14,999,
5 = $15,000 to $19,999, 6 = $20,000 to $24,999, 7 = $25,000 to $29,999, 8 = $30,000 to
$34,999, 9 = $35,000 to $39,000, and 10 = $40,000 or more. The reporting of income in
this manner creates two separate problems. First, the true dependent variable is
unobserved. Second, there is an open ended upper bound and the divisions between
ranges are unequal.
Thus ordinary least squares will produce biased results, but the estimated
coefficients do provide a good starting point. We use both solutions to this problem.
Following the work of Long and Caudill (1991), we use Nelson’s maximum likelihood
procedure.6 Next we use an ordered logistic model. Both models produce results that
support each other’s conclusions.
Parametric Results
Two parametric models were estimated. First, Nelson’s maximum likelihood
function is fitted to the data7. The advantage to this approach is that there is a direct
interpretation of the coefficients. Specifically, if there is an increase in one unit of the
independent variable, one can expect an average increase (or decrease) in the wage by the
value of the coefficient. However, the interpretation for each coefficient of the
nonparametric model is different. It is most similar to the coefficients generated by an
ordered logit or probit model. That is, each coefficient in the simplest interpretation
argues whether a variable has a positive or negative effect on the dependent variable. The
main difference between the two models is how the dependent variable enters. In the
likelihood function approach, the income boundaries are used, causing the dependent
variable’s units of measurement to be dollars. In the ordered logit model, the income
categories are used.
Both models provide evidence that athletic participation increases wages. Table 1
displays the results from the maximum likelihood function. The coefficient of 730.937
can be interpreted as follows: if an individual was an athlete in college, six years after
graduation he can expect a wage about $731 greater than an individual who was not a
collegiate athlete. Table 2 displays the results of the other parametric model. The
coefficient of .1784 in front of the athlete variable indicates that participation in sports
will on average lead to a higher wage.
These two models lend evidence to the human capital model. Apparently,
athletics can be seen as creating human capital and can serve as a source of investment
6
See “On a General Computer Algorithm for the Analysis of Models with Limited
Dependent Variables,” by Forrest Nelson, Annals of Economic and Social Measurement,
1975, pages 493-509.
7
In this model, the unobserved income, W*, is assumed N~(Xβ, σ2) and the model can
be written as W* = Xi β + εi . However, the boundaries of W* are known such that WL ≤
W* ≤ WH. This implies that the statement can be rewritten as ( WL - Xi β )/ σ ≤ ( W* - Xi
β )/ σ ≤ ( WH - Xi β )/ σ . The probability of this event can be written as Pi (WL ≤ W* ≤
WH) = F{( WH - Xi β )/ σ} - F{( WL - Xi β )/ σ}. The likelihood function maximized is L
= Π Pi .
for individuals in addition to school. Additionally, this seems to suggest that individuals
are substituting time on the field of play for leisure, rather than academic time.
While the primary point of the paper is to discuss the relationship between wages
and athletics, other coefficients should be mentioned. If other coefficients provide
intuitive results, then one may feel more comfortable with the variable of interest.
Specifically, in both models the coefficient on the race variable is negative. The
likelihood model has the expected sign on the variable, but is not significant. The ordered
logit model though has a strongly negative coefficient.
Additionally each education variable predicts a higher wage. A higher ACT score,
which acts as a proxy for intelligence, predicts higher wages, as do grades. Married
individuals and individuals with kids also earn a higher wage for men.
Nonparametric Results
The advantage to using a nonparametric approach is that one is not limited to
analyzing what happens on average. Additionally, this approach leads to a better fit of the
data, and thus as some would argue, more precise results. No standard approach exists as
to how to report nonparametric results, but the graphical approach is one of the easiest
and clearest method. The interpretation of the results is rather straight forward. A positive
coefficient in front of the athlete variable would indicate that an athlete would be more
likely to earn a higher wage ceteris paribus.
Figure 1 shows the distribution of the coefficients generated for individuals listed
as athletes.8 The mean is just slightly positive. The median is negative. The histogram
indicates that the distribution is fairly symmetric around zero. This leads to a rather
simple conclusion. In some instances, there seems to be a benefit associated with having
been a college athlete. In some instances, it seems not to have mattered. And for others,
athletic participation may have had a negative effect.
If a student athlete were to substitute leisure for athletic time, then that individual
will graduate from college with a higher human capital stock, assuming academic time
remains fixed. A higher level of human capital will lead to higher earnings, and a positive
coefficient for that variable. However, if a student-athlete substitutes studying for sports
time and academic time produces more human capital than playing time, then that
individual will graduate with less human capital. An athlete may also substitute playing
time for both leisure and academic time. If done in the proper ratio, this would lead to a
coefficient close to zero for the athlete. If athletes substitute away from leisure time,
participation in sports can lead to higher wages.
While it would be nice to have information on how students in this sample spent
their time at college, that data was not available. Had this information been available, one
could test the relationship between leisure time spent and the returns on earnings. These
results do support this theory however. At the very least, the claim that athletes earn
systematically higher wages can be refuted.
Figure 2, shows the distribution of the coefficients of athlete against occupations.
Occupations were coded between one and 45, with no apparent pattern as to how
occupations were assigned to a value. If a relationship exists between an occupation and a
return on the wage, then one could expect athletes to be more likely to enter that
8
The coefficients for athlete for individuals who weren’t athletes are equal to zero by definition.
profession in order to gain a wage advantage. However, each occupation shows a fairly
symmetric distribution of coefficients around a mean of zero. Athletes do not have a
systematic wage advantage in any particular field. Therefore, if we find athletes are more
likely to enter a profession in the next section, we can safely argue that the reasons will
be non-monetary.
Occupational Choices
Five occupational choice models were estimated. The choice of occupation was
based upon the number of athletes selecting an occupation. In this case, any group with
20 or more athletes was included.9 Some occupations, such as business sales and business
management were combined into one group.
Table 3 reports the results from the five occupational choice models. In models
two through five, athletes are not more or less likely to select a particular occupation.
They are, however, more likely to become teachers.
Why are athletes systematically more likely to become teachers? Figure 3 plots
the histogram of the coefficients for the athlete variable for teachers only and is a specific
portion of Figure 2. As one can more clearly surmise, there seems to be no wage
premium for teachers who participated in collegiate athletics. The graph does show a
premium for some athletes, but the advantage is not systematic to the group. The question
then becomes why athletes pick the teaching profession.
Participation in sports creates a greater sense of belonging to a school. Athletes
may feel a unique connection with an academic institution and want to return to their
“home.” Additionally, these individuals may want to continue being involved with sports.
They may simply want to remain active in the sport they love or they may have
aspirations of coaching.
Since most school coaches are also teachers, this desire to continue involvement
with sports may be reflected in an increased likeliness of teaching. However, since
coaches at this level are not well paid, one would not expect to see any significant wage
premium for athletes who chose a teaching profession. In fact, if the individual does want
to pursue a college coaching career, they may view their time spent coaching as on-thejob training or an investment in human capital, and thus may be willing to accept no
wage premium for supervising athletics. But is there any evidence to support this claim?
Table 3 states that 91 college athletes chose a teaching occupation. Of those
individuals, 81 were also high school athletes. We also found that high school athletes
were more likely to choose teaching as a career.10
If these individuals want to be coaches, one would expect them to be high school
teachers as opposed to elementary school teachers who do not have coaching jobs
associated with their positions. If this is the case, college athletes should be more likely to
become high school teachers and participation in sports should have a non-positive effect
on choosing an elementary school teaching job.
9
The one exception was the category of semi-skilled labor. Only 17 athletes reported this as an occupation.
A logistic model with teacher as the dependent variable reveals a coefficient of .3696 (Wald Chi Sq of
7.0856) in front of a high school athletic participation variable that replaced ATHLETE in model one of the
occupational choice models.
10
Table four displays the results from the two models estimated. The variable
HSTeacher is defined as 1 if an individual listed “Teacher: secondary” as an occupation
and zero otherwise. The variable EleTeacher is defined as one if an individual reported
“Teacher” elementary” as an occupation and zero otherwise.
Two results are visibly evident. High school athletes are more likely to become
high school teachers and high school athletes are less likely to become elementary school
teachers.11 This supports the hypothesis that the desire to coach maybe the non-monetary
driving force behind this occupational selection.
Conclusion
This paper reached two conclusions. First, some college athletes earned a wage
premium unrelated to occupational choice after entering the workforce. Whether an
individual earns that wage benefit results from a time allocation decision between
academic investment, leisure time and athletic training time. Previous approaches treated
all athletes as a collective group, while this approach focused on each individual. In this
case, the nonparametric approach yielded a conclusion in direct contrast with the
parametric approach.
Second, athletic participation made it more likely for an individual to become a
high school teacher, but didn’t affect other occupational choices.
11
The same teaching models were estimated using college athletic participation on the independent side.
College athletes were more likely to become high school teachers (coefficient of .9695 and wald chi sq of
29.0727). College athletes were not more or less likely to become elementary school teachers.
Bibliography
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Method,” Biometrika, Vol. 63, Number 3, December 1976.
Astin, Alan, “Minorities in American Higher Education,” Jossey-Bass, San Francisco,
1982.
Becker, Gary, “A Theory of the Allocation of Time,” Economic Journal, September
1965, pages 493-517.
Becker, Gary, “Human Capital: A Theoretical and Empirical Analysis with Special
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Continuous Data,” Journal of Multivariate Analysis, August, Volume 86, Issue 2, pp 266292, 2003.
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Limited Dependent Variables,” Annals of Economic and Social Measurement, 1975,
pages 493-509.
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Categorical and Continuous Data,” Journal of Econometrics, forthcoming.
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Biometrika, 1961.
Appendix
List of Variables
Variable
Meaning
ACT
Score on American College Test
Athlete
1 if earned a varsity letter in college, 0 otherwise
BA
1 if holds bachelors degree, 0 otherwise
Business
1 if individual reported occupation as accountant, business clerical, business management
or business sales, 0 otherwise
Cgrades
Self reported average grades
CR
College Region
Collacad
Self reported academic achievment
Drivedum
1 if individual rates themselves in the highest 10 percent to “drive to achieve”
Enroll
Total enrollment of college, reported in categories
Famdum
1 if respondent indicates that raising a family is an essential goal, 0 otherwise
Firmsz
Number of employees in firm individual works for, reported in categories
Graddeg
1 if Ms=1 or phdprof=1, else 0
Hsathlete
1 if earned a varsity letter in high school, 0 otherwise
Hsgrades
Categorical variable denoting high school grades
Kids
Number of offspring
Labor
1 if individual reported occupation as skilled, semi-skilled or unskilled labor, 0 otherwise
Lastmaj
Last declared major respondent reported while in college
Lawyer
1 if occupation reported as a lawayer, 0 otherwise
Lowasp
1 if person did not aspire to earning a bachelor’s degree or higher, 0 otherwise
MajXX
Represents various college majors
Military
1 if individual reported occupation as military career, 0 otherwise
Msp
1 if married, 0 otherwise
MS
1 if holds masters degree, 0 otherwise
MW
1 if college located in midwest region, 0 otherwise
Occ or OccXX
Represents various occupations
Peduc
1 if parents graduated from college, 0 otherwise
Parinc
Parent’s income before taxes in 1970, reported the same way as income
Part
1 if the job worked was part-time, 0 otherwise
Phdprof
1 if holds Phd or advanced professional degree, 0 otherwise
Private
1 if college attended was a privately owned institution, 0 otherwise
Race
1 if African American, 0 otherwise
Runbus
1 if respondent indicated running their own business was an essential goal, 0 otherwise
S
1 if college located in south region, 0 otherwise
Selfemp
1 if individual was self-employed, 0 otherwise
Teacher
1 if individual reported occupation as secondary or elementary teacher
Vet
1 if military veteran, 0 otherwise
W
1 if college located in west region, 0 otherwise
Welldum
1 if “be well off financially” is an essential goal, 0 otherwise
Yrscomp
number of academic years completed
Appendix
Table One: Maximum Likelihood Estimates
Variable
Coefficient
T-Statistic
Constant
Athlete
Race
Msp
Kids
Veteran
Selfemp
Part
Firmsz
Act
Cgrades
Ba
Ms
Phdprof
Private
Enroll
Mw
S
W
Occ1
Occ2
Occ3
Occ4
Occ5
Occ6
Occ7
Occ8
Occ9
Occ10
Occ11
Occ12
Occ13
Occ14
Occ15
Occ16
Maj1
2864.8691
730.937
-605.708
1216.9208
1013.112
1387.7445
-508.1706
-7108.123
672.67571
108.17337
314.2632
100.5809
1409.5356
1989.0313
547.68059
231.5471
355.9974
-526.4403
818.61659
4863.9709
4783.3142
2782.7371
6100.9545
1293.6319
5661.228
2299.3772
2672.508
4495.1524
3369.1996
1824.3997
-1746.835
-724.2067
4876.3915
3118.4827
1797.0261
561.72997
2.2912125
2.2184249
-1.695354
4.880334
5.4995927
1.9515873
-1.278199
-15.77781
9.1702043
2.6735568
2.7280173
0.3173899
3.2609143
2.9962647
1.7489869
3.0368675
1.2357973
-1.379601
2.5492991
5.6950228
5.5014503
4.1044833
6.6337379
1.4065517
8.5292046
2.6710531
0.8915418
6.1026487
3.6995479
2.1728581
-1.242023
-0.653447
1.6813597
4.0994386
2.049067
0.448171
Maj2
Maj3
Maj4
Maj5
Maj6
Maj7
Maj8
Maj9
Maj10
Maj11
Drivedum
Welldum
Runbus
Famdum
Sigma
-1372.355
-1385.387
874.31622
2136.8772
-39.36995
-280.263
1609.6144
-902.2263
97.70968
-205.1038
2065.6263
668.48076
1536.8381
-197.7013
42208480
-2.522944
-2.288997
1.6700445
3.3657653
-0.066616
-0.282811
1.6787699
-1.753461
0.1053729
-0.205684
8.536258
2.1645151
5.437688
-0.696708
667919.25
Table Two: Ordered Logit Model
Standard
Parameter
Intercept
Intercept
Intercept
Intercept
Intercept
Intercept
Intercept
Intercept
ATHLETE
ACT
RACE
CGRADES
CR
DRIVEDUM
ENROLL
FAMDUM
FIRMSZ
HIGHDEG
KIDS
LASTMAJ
MSP
OCC
PART
10
9
8
7
6
5
4
3
DF
Estimate
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
-7.8063
-7.4322
-6.6105
-5.5964
-4.3025
-2.9437
-1.2409
-0.2908
0.1784
0.0289
-0.3958
0.0713
0.0134
0.51
0.1108
-0.0697
0.2869
0.066
0.2952
0.00119
0.3997
-0.0218
-3.1121
Error
0.3176
0.3093
0.2982
0.2915
0.2863
0.2822
0.2802
0.282
0.0792
0.00927
0.0869
0.0291
0.0271
0.0646
0.0195
0.0681
0.0181
0.0202
0.0456
0.00149
0.0635
0.00189
0.1367
Wald
ChiSquare
604.0532
577.5724
491.3582
368.6209
225.7863
108.772
19.6194
1.0635
5.0677
9.7592
20.7313
6.0021
0.2447
62.2478
32.2966
1.0457
251.3977
10.6497
41.9651
0.6368
39.6032
133.0272
517.9777
Pr >
ChiSq
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.3024
0.0244
0.0018
<.0001
0.0143
0.6208
<.0001
<.0001
0.3065
<.0001
0.0011
<.0001
0.4249
<.0001
<.0001
<.0001
Table Three: Occupational Choices
Variable
Intercept
ATHLETE
RACE
KIDS
MSP
VETERAN
CGRADES
ACT
PRIVATE
FIRMSZ
ENROLL
BA
MS
PHDPROF
DRIVEDUM
RUNBUS
MAJ1
MAJ2
MAJ3
MAJ4
MAJ5
MAJ6
MAJ7
MAJ8
MAJ9
MAJ10
MAJ11
N in Occ
N Ath in Occ
N Total Ath
N Total
Sample
Variable
Intercept
ATHLETE
RACE
KIDS
MSP
VETERAN
Dependent Variable
TEACHER
Wald Chi
Coefficient sq
-1.6761
7.7721
0.6838
18.0175
0.1238
0.3356
-0.2293
3.7774
0.1783
1.4617
-0.225
0.2328
0.1518
3.8974
-0.0671
9.6032
-0.0619
0.1048
-0.0891
4.2336
-0.00971
0.0401
2.6505
58.2938
2.8666
58.4242
0.7218
1.5129
-0.0639
0.1699
-0.911
12.7523
-1.6176
16.9205
-1.8671
83.1966
-1.7992
45.1273
-4.2301
95.4725
-4.0655
45.9274
-2.0123
63.137
-2.6608
18.8064
-15.5082
0.0012
-2.331
133.8938
-2.1569
8.2476
-2.2505
21.1587
LABOR
Coefficient
1.4452
-0.2056
-0.2771
0.0279
-0.0744
0.376
-0.1658
-0.0506
0.0608
-0.066
0.00486
-1.2797
-2.6237
-3.0224
-0.2887
-0.3452
0.7911
0.161
0.1712
-0.2903
-0.0182
0.0632
-0.6007
-0.8919
0.0692
0.478
-0.1227
BUSINESS
Wald Chi
sq
14.7145
1.8871
3.3134
0.1631
0.4629
2.2087
14.0343
9.7814
0.2173
5.2333
0.0212
139.2531
97.3693
49.1646
5.5715
6.1132
6.7349
0.719
0.5017
2.4839
0.0068
0.0725
2.4524
3.1249
0.1445
2.5652
0.1451
Coefficient
-2.7879
0.0741
-0.2522
0.0319
0.1352
-0.1453
-0.0514
-0.00381
0.5056
0.0718
0.0783
0.5517
0.1389
-1.6709
0.2677
0.3377
-0.1952
0.3187
0.2357
1.8685
-0.5488
-0.1176
-0.1046
-0.8849
0.8746
0.3522
0.0388
303
91
646
605
67
646
1144
187
646
4209
4209
4209
MILITARY
Coefficient
-10.0624
0.1125
0.9757
0.387
-0.2672
-0.9673
LAWYER
Wald Chi
sq
125.6549
0.2079
19.2652
8.9391
1.6193
2.1202
Coefficient
-10.258
0.3829
0.0962
-0.3525
0.315
-0.6963
Wald Chi
sq
30.3076
0.9953
0.0559
0.937
1.0743
0.2224
Wald Chi
sq
71.7676
0.4742
4.4912
0.282
2.5152
0.3567
1.6577
0.0898
22.5445
9.7118
8.4014
27.823
0.9205
40.3562
9.6834
10.4575
0.3157
3.2063
1.1755
129.1567
5.8469
0.3041
0.0902
3.2116
28.2819
1.0845
0.0146
CGRADES
ACT
PRIVATE
FIRMSZ
ENROLL
BA
MS
PHDPROF
DRIVEDUM
RUNBUS
MAJ1
MAJ2
MAJ3
MAJ4
MAJ5
MAJ6
MAJ7
MAJ8
MAJ9
MAJ10
MAJ11
0.00834
0.163
-2.0251
0.9931
-0.3676
0.3709
-0.9941
-0.9163
0.6697
0.0336
0.0879
0.02
0.035
-0.2676
0.39
0.275
-0.2782
0.3516
0.00626
0.1294
0.1745
0.0077
34.3737
72.0675
155.3231
35.9257
2.1579
4.6976
2.2866
11.9931
0.0147
0.0132
0.0018
0.0037
0.4034
0.8183
0.3519
0.1324
0.1589
0.0002
0.0376
0.0562
0.387
0.1103
-0.3212
-0.4354
0.0465
-1.1456
-1.3858
5.4756
-0.1389
-0.4424
2.3171
1.9485
-3.1801
2.7771
0.1434
-1.1659
-11.9309
-13.5871
2.4915
-9.3769
3.4515
4.7815
4.7243
0.5544
21.0948
0.2456
2.4808
1.4656
79.6478
0.2168
1.2271
1.9408
2.6759
4.3184
4.8993
0.0079
0.7947
0.0004
0.001
4.604
0.0001
5.2018
N in Occ
169
178
N Ath in Occ
35
38
N Total Ath
646
646
N Total
Sample
4209
4209
* The model predicts the probabilities that the dependent variable will be equal to one.
Table Four: Teaching Occupation Models
Parameter
Intercept
HSATHLETE
RACE
KIDS
MSP
VETERAN
CGRADES
ACT
PRIVATE
FIRMSZ
ENROLL
BA
MS
PHDPROF
DRIVEDUM
RUNBUS
MAJ1
MAJ2
HSTeacher
Wald ChiEstimate Square
-3.0969 17.5106
0.8456 24.2204
-0.0398
0.0234
-0.1812
1.7444
0.122
0.4922
-0.178
0.106
0.1277
1.933
-0.0587
5.2095
0.11
0.2367
-0.1298
6.383
0.0199
0.1219
2.4239 31.1689
2.4666 28.0748
0.2567
0.1194
0.1537
0.7684
-0.9375
9.4929
-0.8778
3.5575
-1.0936 21.1189
EleTeacher
Estimate
-2.0825
-0.5298
0.3847
-0.26
0.1853
-0.3843
0.0985
-0.0573
-0.192
0.0134
-0.077
2.5628
3.0313
1.277
-0.4941
-0.7203
-1.9934
-2.4453
Wald ChiSquare
5.1614
5.9123
1.5747
2.0305
0.6623
0.2502
0.7337
3.092
0.4586
0.0368
1.0693
22.3754
27.3461
1.9165
3.6009
3.0004
10.1747
57.7751
MAJ3
MAJ4
MAJ5
MAJ6
MAJ7
-0.8508
-3.336
-3.3081
-1.2628
-1.9366
14.8905
-1.6943
-1.0943
-1.4553
MAJ8
MAJ9
MAJ10
MAJ11
8.3861
48.8746
20.4398
17.9867
6.8325
-3.0465
-5.1597
-4.4235
-2.4074
-3.0543
25.0096
25.8174
18.7298
35.2693
8.8295
0.0007
48.6523
2.0647
7.155
-15.5217
-2.5444
-14.987
-3.132
0.0005
75.6857
0.0006
9.3485
N HS ATH
132
51
N Teachers
190
113
N Total Sample
4209
4209
* The model predicts the probabilities that the dependent variable will be equal to one.
Figure One: Nonparametric Model
Histogram of β ( Athlete)
Frequency
150
100
50
0
-1
0
1
2
B(Athlete)
Q1: -0.11479
Q2: -0.00687
Q3: 0.148423
Mean: 0.028134
Figure Two: Occupations and Returns to Athletic Participation
b(athlete)
2
1
0
-1
0
10
20
30
40
50
occ
Figure Three: Wage Returns for Athletic Participation for Teachers
Frequency
30
20
10
0
-0.6
-0.4
-0.2
0.0
B(Athlete)
0.2
0.4