the relationship between college football success and college
TRANSCRIPT
The Relationship Between College Football Success and College Admissions
Yiming Benjamin Wang
June 7, 2010
Mathematical Methods in the Social Sciences
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Acknowledgments
I would like to thank Professor Steffen Habermalz for his role as my
faculty advisor. His insight and guidance were instrumental to completing this
project. Another thank you goes out to my friends and family for supporting me
throughout my undergraduate education and making this work possible.
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Abstract
In this paper, I expound upon the results constructed by Tucker in his
paper Big-Time Pigskin Success: Is There an Advertising Effect? (Tucker 2005). In the
original paper, Tucker found a positive relationship between college football
success and SAT scores of incoming freshmen in the years after the establishment
of the current Bowl Championship Series system. Thus, he concluded this was
significant evidence for the existence of an advertising effect. After constructing
and analyzing an updated dataset, I find that, first of all, the positive correlation
is not observed for schools with high SAT scores. This was found using several
quantile regressions. Also, short-term on-the-field football success does not
translate into increased SAT scores when a fixed effects model of the panel data
is used. Because the observed effect from the ordinary least squares model is no
longer apparent in the fixed effects model, any positive academic externalities
derived from college football can only be attributed to school-specific factors.
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Table of Contents
Introduction __________________________________________________________ 5
Literature Review _____________________________________________________ 7
Descriptions of Data __________________________________________________ 10
Ordinary Least Squares (OLS) _________________________________________ 14
Quantile Regression __________________________________________________ 17
Fixed Effects Model ___________________________________________________ 19
Conclusions __________________________________________________________ 21
Limitations __________________________________________________________ 23
Appendix 1 ___________________________________________________________ 24
Appendix 2 ___________________________________________________________ 28
Bibliography _________________________________________________________ 34
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Introduction
The Division I Football Bowl Subdivision is unique in the sense that it is
the only NCAA sport to not have a champion determined by an NCAA
sanctioned championship event. Instead, schools compete in the Bowl
Championship Series (BCS). This system was established in the 1990’s.
Originally, it was called the Bowl Coalition from 1992-1994, then the Bowl
Alliance from 1995-1997, and the modern BCS system began in 1998.
Since the establishment of the Bowl Championship Series, college football
has been a prominent fixture in major sports programming in the United States.
The BCS system relies on computer rankings and sports polls to determine which
teams may participate in the championship game. Of course, this system is not
perfect, and the system is seemingly faced with criticism at the end of every
season. This often involves many sports analysts trying to predict which bowls
different schools will get, and in this process, many schools receive a large
amount of media coverage. Year after year, television networks devote large
chunks of time towards broadcasting college football games and events. In
recent years, cable channels, such as ESPNU and the Big Ten network, dedicated
solely to college sports have sprouted.
With its prominent place in the media, college football also comes with its
costs. The University of Alabama’s athletic program in the 2007-2008 school year
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had operating expenses of $123.4 million1. The University of California-
Berkeley’s athletic department ran a $5.8 million1 deficit in 2008-2009 that the
university had to cover. The most telling statistic, however, is that in 2009, only
14 schools1 out of the over 115 Division I FBS schools had athletic departments
that generated more revenue than expenses. In this calculation, revenue
included such items as ticket sales, donations, and media rights. A USA Today
analysis of college sports financial data from 2005-2009 found that only seven
schools had self-supporting athletic programs in those five years. Thus, very few
schools are able to cover their athletic expenses with athletic revenues alone yet
schools continue to invest heavily in athletic programs. These costs are of
interest especially considering the vast majority of Division I FBS schools are
public schools that are funded in part by tax payers in the state. The large
allocation of resources towards football programs by institutions of higher
education certainly begs the question of whether or not these investments have
positive academic externalities. That is, do investments in college athletics
further a school’s academic mission?
1 Statistic from USA Today article
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Literature Review
Previous literature has varied in methods and approaches used to
evaluate the relationship between college athletics and academic spillovers. One
of the first papers to address the issue of football success affecting academic
quality of incoming students was by McCormick and Tinsley in 1987. They
showed that being in a major sports conference was associated with a small
increase in average freshmen SAT scores. The data was limited to 44 top
performing football programs. The variable used in that study was winning
percentage of a program over a 15 year period. A Robert H. Frank report in 2004
concluded that athletic success only offers small indirect spillover effects.
However, in a 2005 report by Irvin B. Tucker, Tucker concluded that a positive
externality exists for schools since the formation of the Bowl Alliance in 1995.
The Tucker paper in 2005 found the relationship between success in the
BCS system and SAT scores to be statistically significant at the 5% level. The
estimates for coefficients in the Tucker model suggest that an increase of 10% in
winning percentage over a 5-year period will increase average SAT scores by 14
points. Additionally, Tucker’s paper suggested that an extra bowl appearance in
a 5-year period is related to an increase of more than 12 points in the average
SAT score.
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The methodology in the Tucker paper used an ordinary least squares
regression to estimate the impact various factors had on SAT scores. In this
paper, a fixed effects model with panel data and a quantile regression will be
used to explore the topic further. Also, Tucker’s paper used only 78 schools
while this paper includes 105 schools.
Although a spillover effect may be observed, Robert H. Frank in a 2004
article argues that the net effect is still very costly for colleges. The investment in
sports is akin to a game theoretic model of an expenditures arms race where
costs escalate with seemingly no limit. That is, relative investment is what is
most important since schools compete for the same players and coaches. If one
school raises its investment level, another school has an incentive to increase
sports expenditures to keep relative expenditures at comparable levels. The net
effect is both schools spend more money, but the level of the sports programs
remains static.
The length of time a spillover effect lasts may be able to offset some of the
high costs of sports programs. Schools need to keep investing in sports
programs if peers are doing the same, but ultimately, once costs become
prohibitively high, resources may be better spent funding other programs such
as financial aid. This analysis will hopefully deepen the current understanding
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of any lasting positive advertising effects schools experience from investments in
college football.
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Descriptions of Data
The dataset contains 105 Division I Football Bowl Subdivision schools.
The following variables were used in this paper:
SAT25 is the 25th percentile combined math and verbal score on the SAT
for the entering freshmen class. The score on the SAT ranges from 400 to
1600 and is used widely across the United States for college admissions
purposes. A new SAT test was introduced in 2006 that includes a writing
section, but in order to remain consistent with the data before 2006, only
the math and verbal scores will be considered for the new SAT. Also,
schools that report only ACT scores had those scores converted to an SAT
equivalent score using a conversion table. This is the dependent variable
used to roughly measure if academic quality of freshmen is related to
college football success metrics.
SAT75 is the 75th percentile combined math and verbal score on the SAT
for the entering freshmen class.
SATDIST is the absolute value of the difference between SAT75 and
SAT25. This number gives us some indication of the distribution of SAT
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scores for the incoming freshmen class. If students who are more likely
influenced by football success have different SAT scores, this variable
would be likely to change with football success.
SFR is the student-faculty ratio. It is student enrollment divided by the
number of faculty at each institution. Lower ratios indicate greater
opportunities for students to receive personalized attention, and thus,
students with high test scores may choose to attend schools with lower
student-faculty ratios for the individual attention. In general, student-
faculty ratios were collected from college self-reporting using the
Common Data Set standard.
AP is a binary variable that is equal to one if the school is ranked in the
top 25 at the end of the season in the ranking published by the Associated
Press. The AP poll is based on votes from sports writers who consider the
school’s record while keeping in mind the strength of opposition.
Although there is no perfect measurement or definition for a “good”
college football season, a ranking in the AP poll generally signifies a high
caliber football program. As such, this measure is sufficient in
approximating football success.
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Rank1 counts the number of weeks a school is ranked in 1st place in the AP
poll in a given season. This number is meaningful in the context of trying
to determine evidence for an advertising effect. The advertising effect
hypothesis is dependent upon schools receiving positive press coverage
from having success on the field. Certainly, being ranked in first place is a
great way to receive positive press coverage especially since the media
tends to place a focus on covering the schools ranked first.
A private school dummy variable will take on a value of 0 for public
schools and 1 for private schools. This may have a positive coefficient
with SAT score if private schools are perceived to be better at educating
students and can somehow attract the students with higher scores.
A dummy variable will be used for each year to account for any sort of
effects that are related to events in a given year. For example, the strength
of the economy in one year could result in more people applying to public
schools since they would rather pay lower tuition. These kinds of effects
can be controlled for by including a year dummy variable.
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SAL is a variable that represents the average full time instructional faculty
salary for that school year. The salary numbers are reported from the
Integrated Postsecondary Education Data System (IPEDS). The nominal
wages are then adjusted for inflation using the Consumer Price Index
published by the Bureau of Labor Statistics.
DPI is the disposable personal income of the state the school is in. This
variable serves as a proxy for the local economy for the particular school.
Students may want to go to a school with higher DPI since that represents
more lucrative career and job opportunities near the school. The DPI
numbers in the data set were adjusted for inflation using the Consumer
Price Index published by the Bureau of Labor Statistics.
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Ordinary Least Squares (OLS)
An OLS regression was used on this dataset with the AP rank lagged one
year, and the results are consistent with those found in Tucker’s paper.
An OLS regression on the 25th percentile SAT scores:
SAT 25th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 32.6700 5.3066 22.2489 43.0912
SFRt -2.3043 0.9811 -4.2308 -0.3777
Enrollmentt -0.0001 0.0004 -0.0008 0.0006
DPIt -0.0009 0.0007 -0.0023 0.0005
Private Schoolt 80.2116 8.7812 62.9671 97.4561
SALt 0.0053 0.0003 0.0048 0.0058
2002 0.6121 10.1068 -19.2355 20.4597
2003 14.9797 9.9555 -4.5709 34.5302
2004 16.1229 9.9249 -3.3675 35.6134
2005 26.5727 9.8025 7.3226 45.8227
2006 22.3093 9.8498 2.9663 41.6523
2007 19.7430 9.8297 0.4395 39.0464
2008 27.3324 9.8221 8.0439 46.6209
Constant 640.7776 32.4018 577.1472 704.4079
OLS Regression on the 75th Percentile SAT scores:
SAT 75th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 24.5018 4.8083 15.0593 33.9443
SFRt -1.0644 0.8889 -2.8101 0.6813
Enrollmentt -0.0003 0.0003 -0.0009 0.0003
DPIt -0.0017 0.0006 -0.0030 -0.0005
Private Schoolt 64.3874 7.9566 48.7623 80.0126
SALt 0.0054 0.0002 0.0050 0.0059
2002 -2.7489 9.1577 -20.7327 15.2348
2003 8.0171 9.0206 -9.6975 25.7317
2004 10.7543 8.9929 -6.9058 28.4145
2005 22.9006 8.8820 5.4583 40.3430
2006 17.6512 8.9249 0.1246 35.1778
2007 17.4793 8.9066 -0.0115 34.9700
2008 22.3718 8.8997 4.8946 39.8490
Constant 854.4918 29.3591 796.8367 912.1469
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This OLS model was considered to offer comparability to the results
found in the existing literature. This dataset is comprised of data from 105
schools, and regressions were run on data primarily collected after 2001. The
results here are largely consistent with Tucker’s findings in 2005 that post-1995
SAT scores are positively correlated with college football performance. The AP
rank variable has a statistically significant positive relationship with SAT scores
at the 95% confidence level.
An interesting observation that can be made about the data is that the 25th
percentile SAT score seems to be affected more by football success than the 75th
percentile score is affected. The coefficient on AP rank is 32.67 compared to 24.50
for the 25th and 75th percentile scores, respectively. This discrepancy warranted a
deeper investigation of the data to see if football success had any effect on the
distribution of SAT scores for incoming classes. To assess this, a variable called
SAT distance was created to measure the difference between the 75th and 25th
percentile SAT scores for a school.
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OLS Regression on SAT distance:
SAT Distance Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 -8.1683 2.4979 -13.0737 -3.2629
SFRt 1.2398 0.4618 0.3330 2.1467
Enrollmentt -0.0002 0.0002 -0.0006 0.0001
DPIt -0.0008 0.0003 -0.0015 -0.0002
Private Schoolt -15.8242 4.1335 -23.9415 -7.7069
SALt 0.0001 0.0001 -0.0001 0.0004
2002 -3.3610 4.7574 -12.7037 5.9816
2003 -6.9626 4.6862 -16.1654 2.2402
2004 -5.3686 4.6718 -14.5431 3.8060
2005 -3.6721 4.6142 -12.7334 5.3893
2006 -4.6581 4.6365 -13.7632 4.4471
2007 -2.2637 4.6270 -11.3502 6.8228
2008 -4.9606 4.6234 -14.0400 4.1189
Constant 213.7142 15.2522 183.7622 243.6663
From this analysis, the coefficient on AP rank is statistically significantly
different from 0 and has a value of approximately -8. Therefore, being ranked in
the AP top 25 has some effect on the distribution of SAT scores within a school.
That is, the effect is not uniform across students of varying SAT scores and may
have a bigger impact on students with low SAT scores than students with high
SAT scores. To address this issue, a quantile regression is used.
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Quantile Regression
A quantile regression approximates the effects on the median of the
response variable, SAT scores in this case. The more common OLS method
measures the effects on the mean. While the mean and median both measure
central tendencies, the quantile regression does have some other nice features.
The most notable is the fact that any quantile can be estimated (Appendix 1).
In this model, it was found that quantile regressions on the 50th percentile
and 15th percentile schools ranked by SAT scores are all statistically significant at
the 99% level when looking at
lagged AP. In both cases (left), SAT
scores were statistically different
from zero and had coefficients
ranging from 27 to 36. Thus, a
successful football program at a school with median SAT scores or lower could
expect to approximately have a 30 point increase in SAT scores of incoming
freshmen compared to schools without successful football programs. However,
this changes when the same regression is run on the 85th percentile schools. For
these schools with high SAT scores, football success on the field did not translate
to increased SAT scores of incoming freshmen for the 75th percentile SAT scores.
SAT75 Quantiles
0.1500 0.5000 0.8500
AP 34.62994** 27.05828** 7.8291
Rank1 2.4550 -0.1270 0.3881
SAT25 Quantiles
0.1500 0.5000 0.8500
AP 33.24985** 35.36776** 25.0187**
Rank1 0.7735 2.2141 0.6343
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The quantile regressions show that while an effect can be observed, this
effect is not as strong for schools that already have high SAT scores. This
analysis implies that the result is not uniform across students, and the effect
varies depending on SAT scores. Students with high SAT scores do not respond
as well as other students to positive performance on the football field.
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Fixed Effects Model
The OLS and quantile regression models are useful tools for assessing the
relationship between college football performance and SAT scores of incoming
freshmen, but both of those models do not take into consideration any school
specific effects. In other words, those models do not control for factors
inherently part of certain schools. To remove school specific effects from the
model, a fixed effects model is used on the panel data.
Similar to the quantile regression model, the fixed effects regression was
run with lagged AP and Rank1 variables. This was done with the same
reasoning as above. Interestingly, the results change considerably from the OLS
regression. With the exception of Rank1 lagged two years, no other coefficient
for football success is found to be statistically significant (Appendix 2). Also, the
coefficients all tend to be very small with many negative numbers as well. The
coefficient on the only variable that is statistically significant is 1.1779. This
shows that being ranked in first place for an additional week in one season is the
equivalent of a less than 2 point boost to a school’s SAT 75th Percentile score for
incoming freshmen. A 2 point increase to a test that is scaled from 400 to 1600 is
virtually irrelevant. Thus, this model shows very little evidence for the
advertising effect. This is especially surprising considering that Rank1 was
expected to be statistically significant. That is, being ranked in first place was not
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enough for a school to see meaningful and statistically significant improvements
in its incoming freshmen class SAT scores.
This result may imply that any realized advertising effects do not come
from having a few great seasons. The spillover effect does not come from short
term performance on the field, but instead, it may only be attributed to factors
intrinsic to schools with successful football programs. That is, the effect is not
immediately realized after having a successful season, but because of significance
in the OLS model, school-specific long term factors such as a school’s sports
culture or tradition of sports may play the more significant role in driving the
effect.
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Conclusions
The models used in this paper show no evidence for the advertising effect
in a fixed effects regression. Also, there are virtually no statistically significant
results when looking at the coefficient on the Rank1 variable. Thus, the
advertising effect may not be as driven by on field performance as originally
presumed.
Instead, the effect may have more to do with a school’s football culture
and traditions. These effects are certainly affected by performance on the
football field, but these are also long term effects developed over time.
Therefore, while a surprise season in which a school is successful in football may
have a negligible effect on the SAT scores of incoming freshmen, the
development of a school culture where football plays a big role is likely to
influence test scores of a school’s incoming class.
Regardless of what the driving force is behind the advertising effect, many
of these athletic departments in public schools are running a deficit and are using
taxpayer money to cover losses. The positive spillovers seem to be negligible
unless large investments are made to develop a strong and long-standing
tradition of football. Schools may need to reevaluate their athletic budgets since
the money spent on athletic programs might help a school’s academic mission
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more if it were spent on research facilities and financial aid programs rather than
football stadiums and a large coaching staff.
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Limitations
This analysis considers only one specific positive externality from college
football success. While academic quality of incoming students is an important
aspect of a university’s academic mission, it is only one measure and using SAT
scores as a proxy is a crude approximation for actual student quality. There are
other externalities to consider when looking at spillover effects from collegiate
football success. For example, this model did not include alumni giving rate
which may be affected by successes on the field. Also, there are factors which are
hard to measure such as a school’s perceived reputation and the value in having
increased school pride and student cohesion. These ulterior factors could also be
influenced by football performances.
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Appendix 1
Quantile Regression (0.5 Quantile):
SAT 25th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 35.3678 5.1523 25.2497 45.4859
SFRt -2.0827 0.9329 -3.9148 -0.2506
Enrollmentt 0.0002 0.0003 -0.0004 0.0009
DPIt -0.0001 0.0007 -0.0015 0.0012
Private Schoolt 94.9125 8.3805 78.4550 111.3701
SALt 0.0048 0.0002 0.0043 0.0053
2002 -5.0103 9.7878 -24.2316 14.2110
2003 8.6907 9.6356 -10.2316 27.6130
2004 15.1327 9.5891 -3.6982 33.9637
2005 25.5156 9.4386 6.9801 44.0510
2006 14.5233 9.5107 -4.1539 33.2004
2007 13.1854 9.5168 -5.5035 31.8744
2008 16.5983 9.5006 -2.0588 35.2555
Constant 646.7721 30.6989 586.4859 707.0583
SAT 75th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 27.0583 6.9958 13.3200 40.7966
SFRt -0.3366 1.2967 -2.8830 2.2098
Enrollmentt -0.0014 0.0005 -0.0023 -0.0004
DPIt -0.0022 0.0009 -0.0040 -0.0004
Private Schoolt 46.8039 11.5768 24.0694 69.5384
SALt 0.0060 0.0003 0.0054 0.0067
2002 -12.3510 13.2142 -38.3009 13.5990
2003 -3.5005 13.0169 -29.0630 22.0620
2004 -1.3629 12.9540 -26.8019 24.0762
2005 20.0330 12.8316 -5.1655 45.2315
2006 14.7593 12.8455 -10.4667 39.9852
2007 18.3162 12.8172 -6.8540 43.4865
2008 19.5508 12.8381 -5.6606 44.7622
Constant 836.0794 42.8614 751.9086 920.2501
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SAT Distance Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 -11.3373 3.6146 -18.4357 -4.2389
SFRt 1.3440 0.6629 0.0421 2.6458
Enrollmentt -0.0002 0.0002 -0.0007 0.0003
DPIt -0.0007 0.0005 -0.0016 0.0002
Private Schoolt -10.6856 5.7234 -21.9251 0.5539
SALt -0.0001 0.0002 -0.0004 0.0003
2002 -1.5346 6.7822 -14.8535 11.7842
2003 -9.1769 6.6836 -22.3022 3.9483
2004 -7.7840 6.6267 -20.7975 5.2295
2005 -6.9972 6.5781 -19.9151 5.9208
2006 -7.0126 6.6117 -19.9966 5.9714
2007 -3.7840 6.5803 -16.7063 9.1382
2008 -6.7512 6.5910 -19.6946 6.1921
Constant 227.7186 22.0244 184.4673 270.9700
Quantile Regression (0.15 Quantile):
SAT 25th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 33.2499 6.7455 20.0031 46.4966
SFRt -4.6749 1.1562 -6.9454 -2.4044
Enrollmentt -0.0001 0.0004 -0.0010 0.0007
DPIt 0.0002 0.0008 -0.0014 0.0017
Private Schoolt 86.1853 10.5093 65.5473 106.8234
SALt 0.0047 0.0003 0.0041 0.0053
2002 0.7315 12.7444 -24.2959 25.7588
2003 8.8981 12.3616 -15.3775 33.1736
2004 8.1042 12.2402 -15.9330 32.1415
2005 21.6958 12.3959 -2.6471 46.0388
2006 17.3687 12.4652 -7.1105 41.8478
2007 21.1988 11.9973 -2.3614 44.7591
2008 24.0035 12.1376 0.1678 47.8391
Constant 634.2103 38.8667 557.8841 710.5364
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SAT 75th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 34.6299 5.8663 23.1098 46.1501
SFRt -2.6764 1.0520 -4.7423 -0.6104
Enrollmentt 0.0005 0.0004 -0.0003 0.0012
DPIt -0.0001 0.0007 -0.0015 0.0013
Private Schoolt 86.1379 9.2219 68.0280 104.2479
SAL 0.0045 0.0003 0.0040 0.0050
2002 -5.7951 11.7369 -28.8439 17.2536
2003 4.3291 11.5278 -18.3092 26.9674
2004 -1.7148 11.7335 -24.7570 21.3274
2005 5.2185 11.4282 -17.2241 27.6610
2006 3.5129 11.3102 -18.6979 25.7237
2007 2.1524 11.3164 -20.0707 24.3755
2008 3.1347 11.4220 -19.2957 25.5651
Constant 840.6840 34.9755 771.9994 909.3685
Quantile Regression (0.85 Quantile):
SAT 25th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 25.0181 8.2846 8.7489 41.2873
SFRt -1.2350 1.6418 -4.4592 1.9891
Enrollmentt 0.0006 0.0005 -0.0004 0.0017
DPIt -0.0032 0.0010 -0.0051 -0.0013
Private Schoolt 63.2610 15.4175 32.9843 93.5378
SALt 0.0064 0.0004 0.0056 0.0072
2002 4.2554 15.1107 -25.4189 33.9297
2003 20.0591 14.9915 -9.3811 49.4992
2004 25.0831 15.0614 -4.4943 54.6604
2005 29.1784 15.0213 -0.3202 58.6770
2006 30.0748 15.1525 0.3185 59.8311
2007 30.7329 14.8396 1.5910 59.8747
2008 37.6145 15.2277 7.7105 67.5184
Constant 642.9581 49.6202 545.5145 740.4018
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SAT 75th
Percentile Coefficient Std. Err.
95% Confidence
Interval
AP Rankt-1 7.8291 5.7269 -3.4175 19.0756
SFRt 0.7436 1.1382 -1.4915 2.9787
Enrollmentt -0.0005 0.0004 -0.0012 0.0003
DPIt -0.0022 0.0007 -0.0036 -0.0009
Private Schoolt 61.3577 8.6854 44.3014 78.4141
SALt 0.0058 0.0003 0.0053 0.0063
2002 0.5111 10.7930 -20.6841 21.7062
2003 14.9989 10.7154 -6.0438 36.0416
2004 21.1002 10.7418 0.0056 42.1948
2005 25.8482 10.6464 4.9409 46.7554
2006 24.5730 10.3854 4.1783 44.9677
2007 23.9186 10.6213 3.0605 44.7767
2008 24.4218 10.3902 4.0175 44.8261
Constant 859.5604 36.3556 788.1656 930.9552
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Appendix 2
Fixed effects:
SAT 25th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 -0.2555 2.2997 -4.7730 4.2621
SFRt -0.1806 0.7596 -1.6728 1.3116
Enrollmentt -0.0010 0.0008 -0.0024 0.0005
DPIt -0.0020 0.0012 -0.0044 0.0004
SALt 0.0000 0.0003 -0.0006 0.0005
2001 -35.4208 4.9457 -45.1364 -25.7051
2002 -28.6230 4.2787 -37.0282 -20.2178
2003 -16.9056 3.8311 -24.4315 -9.3797
2004 -10.3954 3.2059 -16.6933 -4.0975
2005 -3.9289 3.0703 -9.9603 2.1024
2006 -2.2597 2.7585 -7.6786 3.1592
2008 7.0811 2.7636 1.6520 12.5101
Constant 1156.8710 47.0550 1064.4340 1249.3070
SAT 75th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 -2.6086 2.2036 -6.9376 1.7203
SFRt -0.5826 0.7279 -2.0125 0.8473
Enrollmentt -0.0006 0.0007 -0.0020 0.0008
DPIt -0.0002 0.0012 -0.0025 0.0021
SALt 0.0003 0.0003 -0.0002 0.0008
2001 -25.8290 4.7393 -35.1390 -16.5190
2002 -21.9542 4.1000 -30.0085 -13.8999
2003 -14.9305 3.6711 -22.1422 -7.7188
2004 -10.0052 3.0721 -16.0401 -3.9703
2005 -2.0844 2.9421 -7.8640 3.6952
2006 -3.9051 2.6433 -9.0978 1.2876
2008 4.5748 2.6483 -0.6276 9.7772
Constant 1274.3370 45.0906 1185.7590 1362.9150
29
SAT Distance* Coefficient Std. Err. 95% Confidence Interval
AP Rankt-1 -2.3532 2.0590 -6.3980 1.6916
SFRt -0.4020 0.6801 -1.7380 0.9341
Enrollmentt 0.0003 0.0007 -0.0010 0.0017
DPIt 0.0018 0.0011 -0.0004 0.0039
SALt 0.0003 0.0002 -0.0001 0.0008
2001 9.5917 4.4282 0.8928 18.2906
2002 6.6688 3.8309 -0.8568 14.1945
2003 1.9750 3.4302 -4.7633 8.7134
2004 0.3902 2.8705 -5.2486 6.0290
2005 1.8445 2.7490 -3.5557 7.2448
2006 -1.6455 2.4699 -6.4973 3.2064
2008 -2.5063 2.4745 -7.3672 2.3546
Constant 117.4666 42.1310 34.7027 200.2306 *SAT Distance = SAT 75th Percentile Score – SAT 25th Percentile Score
SAT 25th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-2 0.1718 2.2518 -4.2517 4.5954
SFRt -0.1763 0.7589 -1.6671 1.3144
Enrollmentt -0.0010 0.0008 -0.0024 0.0005
DPIt -0.0020 0.0012 -0.0044 0.0004
SALt 0.0000 0.0003 -0.0006 0.0005
2001 -35.4658 4.9452 -45.1803 -25.7513
2002 -28.6473 4.2832 -37.0615 -20.2332
2003 -16.9327 3.8306 -24.4577 -9.4076
2004 -10.4196 3.2020 -16.7097 -4.1294
2005 -3.9446 3.0706 -9.9766 2.0875
2006 -2.2684 2.7577 -7.6858 3.1490
2008 7.0818 2.7638 1.6525 12.5110
Constant 1157.2220 47.0829 1064.7300 1249.7140
30
SAT 75th Percentile Coefficient Std. Err. 95% Confidence Interval
AP Rankt-2 -1.7861 2.1592 -6.0278 2.4556
SFRt -0.5490 0.7277 -1.9785 0.8804
Enrollmentt -0.0007 0.0007 -0.0021 0.0007
DPIt -0.0002 0.0012 -0.0025 0.0021
SALt 0.0003 0.0003 -0.0002 0.0008
2001 -25.9227 4.7419 -35.2379 -16.6076
2002 -21.8714 4.1071 -29.9396 -13.8031
2003 -14.9913 3.6731 -22.2070 -7.7757
2004 -10.1477 3.0704 -16.1794 -4.1161
2005 -2.1019 2.9444 -7.8860 3.6822
2006 -3.9708 2.6444 -9.1655 1.2239
2008 4.5402 2.6502 -0.6659 9.7463
Constant 1274.3530 45.1474 1185.6630 1363.0420
SAT Distance Coefficient Std. Err. 95% Confidence Interval
AP Rankt-2 -1.9579 2.0168 -5.9199 2.0041
SFRt -0.3727 0.6797 -1.7079 0.9625
Enrollmentt 0.0003 0.0007 -0.0010 0.0016
DPIt 0.0018 0.0011 -0.0004 0.0039
SALt 0.0003 0.0002 -0.0001 0.0008
2001 9.5431 4.4292 0.8423 18.2440
2002 6.7759 3.8363 -0.7603 14.3121
2003 1.9413 3.4309 -4.7985 8.6812
2004 0.2718 2.8679 -5.3620 5.9057
2005 1.8426 2.7502 -3.5600 7.2453
2006 -1.7024 2.4700 -6.5545 3.1497
2008 -2.5416 2.4754 -7.4043 2.3212
Constant 117.1306 42.1701 34.2898 199.9713
31
SAT 25th Percentile Coefficient Std. Err. 95% Confidence Interval
Rank1t-1 0.1067 0.6284 -1.1277 1.3411
SFRt -0.1714 0.7595 -1.6634 1.3205
Enrollmentt -0.0010 0.0008 -0.0025 0.0005
DPIt -0.0020 0.0012 -0.0044 0.0004
SALt 0.0000 0.0003 -0.0006 0.0005
2001 -35.4152 4.9433 -45.1261 -25.7043
2002 -28.6057 4.2806 -37.0147 -20.1967
2003 -16.9046 3.8295 -24.4274 -9.3819
2004 -10.4018 3.2021 -16.6922 -4.1114
2005 -3.9045 3.0754 -9.9460 2.1370
2006 -2.2462 2.7604 -7.6689 3.1765
2008 7.0915 2.7644 1.6609 12.5221
Constant 1156.5150 47.1318 1063.9280 1249.1030
SAT 75th
Percentile Coefficient Std. Err. 95% Confidence Interval
Rank1t-1 0.4117 0.6027 -0.7722 1.5957
SFRt -0.5232 0.7284 -1.9542 0.9077
Enrollmentt -0.0007 0.0007 -0.0021 0.0007
DPIt -0.0002 0.0012 -0.0025 0.0021
SALt 0.0003 0.0003 -0.0002 0.0008
2001 -25.9810 4.7412 -35.2948 -16.6672
2002 -21.9396 4.1056 -30.0048 -13.8745
2003 -15.0326 3.6729 -22.2477 -7.8174
2004 -10.1512 3.0712 -16.1844 -4.1180
2005 -2.0456 2.9497 -7.8401 3.7489
2006 -3.9012 2.6475 -9.1022 1.2997
2008 4.6065 2.6514 -0.6020 9.8151
Constant 1274.0970 45.2045 1185.2960 1362.8990
32
SAT Distance Coefficient Std. Err. 95% Confidence Interval
Rank1t-1 0.3050 0.5632 -0.8013 1.4114
SFRt -0.3518 0.6807 -1.6889 0.9854
Enrollmentt 0.0003 0.0007 -0.0011 0.0016
DPIt 0.0018 0.0011 -0.0004 0.0039
SALt 0.0003 0.0002 -0.0001 0.0008
2001 9.4342 4.4303 0.7311 18.1374
2002 6.6661 3.8364 -0.8703 14.2024
2003 1.8721 3.4321 -4.8700 8.6142
2004 0.2506 2.8698 -5.3870 5.8883
2005 1.8589 2.7563 -3.5556 7.2735
2006 -1.6550 2.4739 -6.5149 3.2049
2008 -2.4849 2.4776 -7.3519 2.3821
Constant 117.5820 42.2406 34.6029 200.5612
SAT 25th
Percentile Coefficient Std. Err. 95% Confidence Interval
Rank1t-2 1.1779 0.5341 0.1288 2.2270
SFRt -0.6229 0.7257 -2.0485 0.8027
Enrollmentt -0.0007 0.0007 -0.0021 0.0007
DPIt 0.0000 0.0012 -0.0023 0.0023
SALt 0.0003 0.0002 -0.0002 0.0008
2001 -25.7206 4.7214 -34.9954 -16.4458
2002 -21.6942 4.0891 -29.7270 -13.6613
2003 -14.8575 3.6581 -22.0436 -7.6714
2004 -10.1985 3.0577 -16.2052 -4.1917
2005 -2.1327 2.9317 -7.8918 3.6264
2006 -3.9188 2.6341 -9.0934 1.2559
2008 4.4371 2.6403 -0.7496 9.6238
Constant 1271.5060 44.9680 1183.1690 1359.8430
33
SAT Distance Coefficient Std. Err. 95% Confidence Interval
Rank1t-2 0.8960 0.4997 -0.0857 1.8776
SFRt -0.4272 0.6790 -1.7611 0.9068
Enrollmentt 0.0003 0.0007 -0.0011 0.0016
DPIt 0.0019 0.0011 -0.0002 0.0041
SALt 0.0003 0.0002 -0.0001 0.0008
2001 9.6348 4.4179 0.9561 18.3135
2002 6.8547 3.8263 -0.6618 14.3713
2003 2.0066 3.4230 -4.7176 8.7308
2004 0.2156 2.8612 -5.4050 5.8363
2005 1.7952 2.7432 -3.5938 7.1841
2006 -1.6668 2.4648 -6.5088 3.1753
2008 -2.6129 2.4706 -7.4662 2.2404
Constant 115.5705 42.0776 32.9116 198.2294
34
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