Download ee10 Cullen 13631707 en

A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute for Economic Research
Area Conference on
Economics
of Education
03 - 04 September 2010 CESifo Conference Centre, Munich
Jockeying for position: strategic high school
choice under Texas’ top ten percent plan
Julie Berry Cullen, Mark C. Long
and Randall Reback
CESifo GmbH
Poschingerstr. 5
81679 Munich
Germany
Phone:
Fax:
E-mail:
Web:
+49 (0) 89 9224-1410
+49 (0) 89 9224-1409
[email protected]
www.cesifo.de
JOCKEYING FOR POSITION:
STRATEGIC HIGH SCHOOL CHOICE UNDER TEXAS’ TOP TEN PERCENT PLAN*
Julie Berry Cullen, University of California, San Diego
Mark C. Long, University of Washington
Randall Reback, Barnard College, Columbia University
Abstract: Beginning in 1998, all high school students in the state of Texas who graduated in the
top ten percent of their high school class were guaranteed admission to any in-state public higher
education institution, including the flagships. While the goal of this policy is to improve college
access for disadvantaged and minority students, the use of a school-specific standard to
determine eligibility could have unintended consequences. Students may increase their chances
of being in the top ten percent by choosing a high school with lower-achieving peers. Our
analysis of students’ school transitions between 8th and 10th grade three years before and after the
policy change reveals that this incentive influenced students’ enrollment choices in the
anticipated direction. In the initial years of the new regime, we estimate that at least one percent
of students with strategic opportunities inside their school district enrolled in a different high
school to improve their chances of being in the top ten percent—a moderate response relative to
the share that would have applied to a flagship prior to the policy reform (27 percent). Given
heterogeneity in these response rates and in the characteristics of students displaced from the top
ten percent pool, the net effect of this strategic behavior is to slightly increase black students’
representation in the top ten percent pool.
Keywords: Moral hazard; School choice; College admission; Affirmative action
JEL classification: D10; H31; H73; I28, J60; J78
*
We would like to thank the Communications and Student Assessment Divisions of the Texas Education Agency
for providing the data, as well as the University of Michigan’s Office of Tax Policy Research and Department of
Economics for providing funds for data acquisition. We would also like to thank Justine Hastings and seminar
participants at several institutions for useful suggestions and the National Center for Education Statistics for access
to the restricted-use version of the National Education Longitudinal Study (NELS). Excellent research assistance
was provided by Claudia Becker, Joelle Cook, and Danielle Fumia. The authors are accountable for all views
expressed and any errors.
1. Introduction
One of the fundamental difficulties confronting the design of effective redistributive policies
is targeting benefits to intended beneficiaries without attracting imitators. There is an extensive
literature documenting how individuals alter their behavior to qualify for welfare programs—by
reducing labor supply, changing living arrangements, and moving to new jurisdictions.1 In this
paper, we analyze this type of phenomenon in a novel setting where eligibility is determined by a
tournament and there is scope for endogenous group membership. In particular, we explore
whether students downgrade when choosing a high school, when access to a benefit—guaranteed
admission to flagship universities—depends on relative position within one’s class.
The policy that we consider, the Texas top ten percent plan, arose from the debate over
whether universities should be allowed to consider a student’s race in admissions decisions. In
1996, the Fifth Circuit Court of Appeals ruled in the case of Hopwood v. Texas that race could
not be used as a factor at the University of Texas School of Law, and this ruling led to a ban on
affirmative action at all public universities in Texas beginning in 1997.2 In response to mounting
public concern regarding the ensuing drop in minority matriculation to elite Texas public
universities,3 then Governor George W. Bush helped push through legislation guaranteeing that
all high school seniors with grades in the top ten percent of their own high school classes gain
admission to any public university within Texas. The Texas program began in the summer of
1998 and, since then, California and Florida have adopted similar plans.4
These x-percent plans potentially improve access to higher education for disadvantaged
students by using a school-specific standard. The admission guarantee ensures that students at
low-achieving high schools, who tend to be disproportionately poor and minority, are equally
represented among those automatically granted admission. However, these policies may also
lead to behavioral responses that alter the composition of student bodies at these high schools.
1
See Moffitt (1992, 2002) for comprehensive reviews.
Though the Supreme Court (Grutter v. Bollinger) upheld the constitutionality of non-formulaic affirmative action
policies in 2003, voter referenda and administrative decisions in five other states (California, Florida, Washington,
Michigan, and Nebraska) have also banned race-based admissions at public universities. Kane (1998), Arcidiacono
(2005), and Howell (2010) provide evidence on the magnitude of affirmative action available to various cohorts.
3
Between 1995 and 1997, black, Hispanic, and Native American students’ share of enrollment fell from 20 to 16
percent at UT-Austin and from 20 to 13 percent at Texas A&M (Long, 2007). There is mixed evidence regarding
how much of the enrollment response to the elimination of affirmative action is attributable to changes in application
behavior (e.g., Long (2004a), Card and Krueger (2005), and Long and Tienda (2010)).
4
Horn and Flores (2003) provide a detailed description of the x-percent programs. For simulations of the effect of
x-percent programs on minority representation, see Long (2004b) and Howell (2010).
2
1
Consider a student who would place below the top ten percent at the high school that this student
would have attended in the absence of the reform. With the reform in place, this student might
be able to obtain guaranteed access to a flagship,5 either by raising his or her grade point average
without changing high school enrollment plans, or by choosing to attend (or transfer to) another
high school with lower-achieving peers.
These policies change the relative attractiveness of high schools, and could therefore have
unintended positive and negative consequences. If relatively able students are more likely to
attend previously undesirable schools, then these transfers would reduce ability stratification
across high schools and might generate positive spillovers to students in the recipient schools
through peer effects. At the same time, this response may crowd out some of the automatic
admissions slots that would have gone to disadvantaged and minority students. In this paper, we
attempt to quantify strategic enrollment responses to the new admissions program in Texas,
providing direct evidence on gaming and indirect evidence on the potential welfare implications.
Our analyses follow the high school enrollment choices of 8th graders from the 1992-93
through 1997-98 cohorts. The first three of these cohorts chose their 10th grade schools prior to
the adoption of the top ten percent plan, while the latter three cohorts chose their 10th grade
schools after. We characterize high schools in terms of their top ten percent ―thresholds,‖
defined to be the achievement level associated with the 90th percentile among 10th graders from
the base-year cohort. We first examine the reduced-form effect by tracking how the thresholds
associated with the schools chosen vary across cohorts. Next, using a discrete choice model, we
more explicitly examine how policy-induced changes in students’ incentives influence their high
school enrollment choices.
Both types of analyses suggest that students responded strategically. Conditional on their 8th
grade schools, the types of students who had the most to gain from strategic behavior were more
likely to attend high schools with relatively low top ten percent thresholds after the top ten
percent policy was in force. Because we hold the thresholds fixed at initial year levels, the
observed changes isolate shifts in enrollment and are not confounded by other time-varying
policies that might affect the relative performance of high schools. ―Trading down‖ behavior is
most apparent when we restrict the sample to students in districts served by multiple high
5
The returns to attending a flagship may be substantial. Hoekstra (2009) finds that wages earned by white males ten
to fifteen years after high school were 20 percent higher for those applicants who were barely accepted by a flagship
institution relative to those applicants who were barely rejected by the flagship.
2
schools. Based on our discrete choice analysis for this sub-sample of students, approximately
one percent of students with the potential to gain from strategizing were induced to choose
different high schools. Black students trade down at higher rates than whites and Hispanics, and
the net effect of strategic responses is thus to slightly increase black students’ representation
among the top ten percent of high school classes. Thus, this form of gaming does not undermine
the top ten percent plan’s goal of promoting racial diversity in university admissions.
While the absolute magnitude of the strategizing we detect is low, it is not low relative to the
share of incentivized students who would have applied to a flagship in the pre-period (27
percent), and there are several reasons to believe our estimates are lower bounds.6 First, we use
students’ prior test scores as a proxy for their ability to place in the top ten percent of a school.
Students likely have more accurate perceptions of their chances than we can capture
empirically.7 Our incentive measures are also blunted by the need to attribute base year
incentives to all cohorts for clean identification. Second, conditioning on students’ middle
school choices facilitates a difference-in-differences estimation strategy, but also limits the range
of responses we can capture. Broader changes in residential and school choice at earlier grade
levels, in anticipation of high school, are missed. Finally, strategic responses to the program are
likely to have become more common as regular admissions spaces to the flagships have been
crowded out and high schools from a broader geographic area have been participating in the
program. Unlike behavioral responses in other settings, however, there is a natural moderating
tendency in the longer run as high schools’ top ten percent thresholds converge.
Our findings have more general implications as well. This study uncovers evidence of
behavioral responses in a context where the costs of strategizing are quite high. We would
expect that endogenous group membership would be important in other contexts where rewards
are allocated to individuals based on membership and membership can be affected by individual
choices.
Our paper unfolds as follows: Section 2 provides background information concerning college
admissions in Texas, Section 3 presents a conceptual framework for how an x-percent rule might
6
It is also important to recall that the take-up rates we estimate are among those who alter behavior in order to
qualify. Take-up rates are far from complete even among those who are mechanically eligible for transfer and social
insurance program benefits (Currie, 2006).
7
Among sophomores surveyed in 2002 by the Texas Higher Education Opportunity Project (THEOP), 25 percent
reported knowing their class rank, and 92 percent were able to supply a ―best estimate‖ of their class rank. Within
the select sub-sample that switched high schools by 2004, 10 percent answered ―yes‖ to the question ―Did you ever
change schools to improve your class rank?‖
3
influence high school enrollment decisions, and Section 4 describes our data. The empirical
strategies for testing the hypotheses and the results are presented in Sections 5 and 6, while
Section 7 offers a brief conclusion.
2. Background
The immediate goal of the top ten percent policy is to increase student diversity at selective
Texas universities without specifically using racial preferences in admissions. Automatic
admission to any of the 37 public universities in Texas is granted to students ranked in the top
ten percent of their high school graduating classes, as long as they apply to college within two
years of graduating. The policy pertains to both public and private high school students.
For determining eligibility, a student’s class rank is based on his or her position at the end of
11th grade, middle of 12th grade, or at high school graduation, whichever is most recent at the
college’s application deadline. Application deadlines for fall matriculation to the more selective
universities are generally in early February. Therefore, for students applying during their senior
year, top ten percent eligibility would be based on their class rank either at the end of 11th grade
or in the middle of 12th grade. Class rank is computed by the individual high school, and
administrators have discretion regarding the formula and how to handle transfers. To avoid
displacing incumbent students, school administrators typically require transferring students to
attend for some period of time before qualifying as being eligible for top ten percent placement.
This mitigates the scope for gain from late-term transfers during junior or senior year.
Among 10th graders, only those students who would consider attending a Texas public fouryear college will be sensitive to the change in admissions policy when deciding which high
school to attend. Of those freshmen attending a four-year college in the Fall of 1998 who had
graduated from a Texas high school in the prior year, 66 percent went to a Texas public college,
13 percent went to a Texas private college, and 21 percent went to an out-of-state college.8
Given that only one-fourth of Texas high school students attend a four-year college, the fraction
of all 10th graders who enroll in a Texas public college is about 16 percent.9 Among students in
the top ten percent of their high school classes who enrolled in a Texas public college, the
8
These are estimates based on data from the Department of Education (2001) and the Texas Higher Education
Coordinating Board (2002).
9
This percentage is calculated as the number of enrolled students divided by an estimate of the 10th grade population
in 1996-97. The estimate comes from dividing the number of public school 10 th graders observed in our data by
0.953, the public school enrollment share (Department of Education, 2001).
4
majority attended one of the flagships, Texas A&M (28 percent) and UT-Austin (29 percent).
Nearly all applicants placing in the top decile of their high school class had been admitted to
these campuses prior to the top ten percent rule. In the absence of behavioral responses, only
about 0.1 percent of all 10th graders would have benefited from automatic admission to one of
the two flagships.10 However, the fraction of students potentially benefiting is much larger once
endogenous applications and high school enrollment choices are considered. Between 1997 and
2003, the share of Texas high schools sending at least one student to UT-Austin increased from
53 to 63 percent (Long, Saenz, and Tienda, 2010).
The top ten percent policy currently poses a challenge for UT-Austin since the number of
students automatically admitted has risen rapidly, leaving less flexibility for the university to use
its discretion in admitting students. The share of automatically admitted students rose from less
than 50 percent in the early years of the policy to 81 percent of applicants for the 2008-09
entering class (Long, Saenz, and Tienda, 2010).11 The concern that top ten percent students are
crowding-out admissions slots for other meritorious students has led to a backlash from families
of students attending more elite, typically suburban, high schools.12 The incentive for strategic
high school choice has clearly strengthened due to this recent admissions squeeze relative to the
early years of the regime that we study.
3. Conceptual Framework for Strategic High School Choice
The joint choice of residential location and elementary and secondary schooling derives from
a complicated family maximization problem. We presume that the decisions for families with
school-aged children are partly driven by the expected effect that attending a particular school
system will have on their children’s future earnings (and any other correlated outcomes). All
else equal, families will prefer to send their children to schools that increase earnings capacity
both directly through skills and knowledge acquisition and indirectly by improving access to
10
From 1992 to 1997, only 817 (3 percent) of in-state top ten percent applicants to UT-Austin were rejected, while
only 535 (2 percent) of such applicants to Texas A&M were rejected (authors’ calculations based on THEOP
administrative admissions data). Thus, on an annual basis, roughly 225 in-state top ten percent applicants were
rejected at one of these institutions, or 0.1 percent of Texas tenth grade students in 1996.
11
In 2007, the state legislature’s effort to cap the automatic admission share at UT-Austin to half of the admitted
class failed, as lawmakers supportive of the status quo fought to protect the increased access for their constituents,
particularly in rural areas (Hughes and Tresaugue, 2007). In the 2009 session, the legislature passed a less
restrictive bill capping the share at 75 percent starting in 2010-11.
12
For anecdotal evidence, see Hart (2001), Yardley (2002), and Glater (2004).
5
institutions of higher education. The introduction of a top ten percent policy thus increases the
relative attractiveness of communities and schools in which the child is likely to be in the top ten
percent of the high school graduating class.
In order to provide intuition concerning the relevant strategic responses and the types of
families that might take these actions, we present an indirect utility function that each household
seeks to maximize. This function is defined from the perspective of families of 8th graders
making housing and schooling choices for 10th grade. Though this perspective is dictated by the
structure of our data and identification strategy, schooling transitions between these grades are
appropriate to study for two reasons. First, most students move from middle to high school
between these grades, so are already changing schools and considering alternatives. Second,
strategic transfers later than the spring of the 10th grade year may not be rewarded due to locally
imposed barriers to top ten percent eligibility. Focusing on this transition, though, overlooks
responses for families of younger children that would be likely to arise over the longer run.
For simplicity, assume that families have only one child. Define i as an index for both the
family and the child, j as an index for the house/neighborhood where the family resides, and k as
an index for the high school the student attends. Define ei(i, Qk, pik) as the child’s expected
future earnings, which depend on the student’s own ability level (i), the quality of the student’s
high school (Qk), and the likelihood of being accepted to a flagship (pik).13 In addition to the
child’s future earnings, the family’s indirect utility is a function of neighborhood characteristics
(Nj), housing prices inclusive of property taxes (Pj), tuition prices if school k is a private school
(k), and transportation costs from neighborhood j to school k (djk). If the family chooses to
move to a new neighborhood for high school, this will involve fixed mobility costs (Mij).
Indirect utility is given by the following:
(3.1)
Vijk = vi (ei(i, Qk, pik) , Nj, Pj, k, djk, Mij)
We presume the family will choose the neighborhood and high school combination that
maximizes indirect utility, subject to the constraint that, depending on the schools’ transferring
policies, some neighborhood and school combinations will not be allowed.14
13
The ability measure γi can be thought of as a combination of the student’s innate ability and the amount of
learning that takes place in the years preceding high school. Any effects of access to other higher education
institutions are implicit in the functions of student ability and high school quality.
14
In Texas, several programs permit transfers without changes of residence. The state adopted a formal inter-district
choice program in 1995, but participation in this program is low since district participation is voluntary. On
average, 2.8 percent of students in a district are nonresident transfers (Schools and Staffing Survey, 1999-00). Large
6
Given this framework, we consider some simple analytics for children who are interested in
an admissions offer from a flagship (i.e., for whom ∂ei /∂pik > 0). The top ten percent plan will
alter some of these children’s schooling choices due to changes in pik. We assume that general
equilibrium effects on housing prices, neighborhood characteristics, school quality, and tuition
are likely to be small within the first years of policy implementation, attributing changes in
behavior to the salient and immediate changes in flagship access.15
𝑝𝑟𝑒
𝑝𝑜𝑠𝑡
In order to formalize how access changes, we define 𝑎𝑖𝑘
and 𝑎𝑖𝑘
to be the likelihood that
student i gains admission, conditional on applying from school k, through the regular admissions
processes existing before and after the top ten percent plan. Define Post as a dummy variable,
equal to one if the new policy is in place. Assume parents are uncertain whether their child
would place in the top ten percent of a particular high school class, but can predict the likelihood,
ik, of this occurring given their knowledge of the child’s ability and their expectations of the
composition of that class.
A child’s likelihood of being accepted at a flagship, conditional on applying, is then the
following:
(3.2)
𝑝𝑜𝑠𝑡
𝑝𝑟𝑒
pik = Post × [ik × 1 + (1−ik) × 𝑎𝑖𝑘
] + (1−Post) × 𝑎𝑖𝑘
Before the policy change, it is simply the regular admissions policy that is relevant. Afterward,
the regular admissions policy is only relevant if the child does not place in the top ten percent.
The change in access can thus be expressed:
𝑝𝑜𝑠𝑡
𝑝𝑜𝑠𝑡
𝑝𝑟𝑒
(3.3.1) ∆𝑝𝑖𝑘 = ik × (1− 𝑎𝑖𝑘
) + (𝑎𝑖𝑘
− 𝑎𝑖𝑘
)
Newly accepted students from the top ten percent plan could potentially displace students who
would otherwise have been accepted, as reflected in the last term on the right side of equation
3.3.1. For simplicity, we assume that traditional college admissions decisions are independent of
a student’s choice of high school and are not influenced by the top ten percent plan—i.e.,
𝑝𝑟𝑒
𝑝𝑜𝑠𝑡
𝑎𝑖 = 𝑎𝑖𝑘
= 𝑎𝑖𝑘
. Abstracting from these realities of the regular admissions policy, including
the elimination of affirmative action, is not particularly problematic in our setting. These
districts also offer a variety of formal and informal intra-district school choice programs, such as magnet
schools/programs and transfers to schools with underutilized space. About one-quarter of Texas school districts
contain more than one regular or magnet high school, and these districts serve the majority of students.
15
The policy change should increase house prices in communities with low quality schools, since it is these schools
where access to selective higher education institutions is improved the most. Broadly consistent with expectations,
Cortes and Friedson (2009) find property tax values rose in previously low performing districts. These types of
capitalization effects would reduce incentives for gaming via residential relocation over time.
7
correlated shifts lead to variation in access either by cohort or by school, but are not likely to
have dramatic effects on differential access across schools by cohort the way the top ten percent
plan does. With our assumption, equation 3.3.1 reduces to:
(3.3.2) ∆𝑝𝑖𝑘 = 𝜏𝑖𝑘 × 1 − 𝑎𝑖
The change in access varies directly with the likelihood of placing in the top ten percent, and is
moderated by the likelihood of being rejected under the regular admissions process.
The robust prediction that comes out of our framework is that any child who strategically
chooses a high school other than the one that would have been chosen before the policy reform
should attend a school where he/she expects to have a greater chance of being in the top ten
percent of the graduating class. Starting from a family’s pre-reform ranking of high schools,
equation 3.3.2 suggests that lower-achieving high schools offering greater top ten percent
opportunities will move up in the rankings. As a result of any induced downgrading, top ten
percent thresholds at relatively low-achieving schools will tend to rise and converge toward
those at higher-achieving schools, dampening the scope for further gaming. If such behavior
were costless, perfect arbitrage would imply that the top ten percent of each high school would
include only students in the top decile statewide.
Trading down is associated with costs, however, and schooling choices will only change if
initial gaps in net benefits are overcome. Due to mobility costs, the most likely form of
behavioral response would be to remain in the same home but choose an alternate school, though
families moving for other reasons might choose different neighborhoods than they otherwise
would have. We expect the highest rates of strategic choices to occur for students with nearby
top ten percent opportunities, especially if those opportunities are within the same school district
and do not require a significant sacrifice in terms of school or peer quality. In our empirical
analyses, we attempt to identify students with such opportunities.
4. Data and empirical counterparts
The primary data source for our analysis is individual-level Texas Assessment of Academic
Skills (TAAS) test score data collected by the Texas Education Agency (TEA). In the spring of
each year, students are tested in reading and math in grades 3-8 and 10, and writing in grades 4,
8, and 10. Each school submits test documents for all students enrolled in every tested grade.
These documents include information on students that are exempted from taking the exams due
8
to special education and limited English proficiency status and students in the 10th grade who
have passed alternative end-of-course exams and are not required to take the TAAS exams. The
test score files, therefore, capture the universe of public school students in the tested grades in
each year. In addition to test scores, the reports include the student’s school, grade,
race/ethnicity, and indicators of economic disadvantage. TEA provided us with a unique
identification number for each student. This number is used to track the same student across
years, as long as the student remains within the Texas public school system.16
We follow six cohorts as they make the transition from middle schools in 8th grade to high
schools in 10th grade as revealed by the school identifiers in the test score documents, beginning
with Cohort 0 (1992-93 8th graders) and ending with Cohort 5 (1997-98 8th graders). The first
three cohorts attended 10th grade under the old admissions regime, while the latter three cohorts
attended 10th grade after the new policy had been introduced. The first five cohorts would have
chosen their 8th grade schools under the old regime, so that these locations are not endogenous to
the policy change. The last cohort began 8th grade in the Fall of 1997, while the new policy was
signed by Governor Bush on May 20, 1997 and became effective on September 1, 1997. Thus,
this cohort also had little scope or reason to adjust 8th grade school choices and we also treat
these as predetermined. We rely on the early cohorts to establish the pre-policy 10th grade
enrollment patterns for 8th graders from each middle school. We then explore how these patterns
change for the later cohorts whose transitions are affected by the new policy regime.
To identify students with strategic incentives, we need to first estimate where students would
place in the distribution at any given high school among his/her cohort. The only information
available to us to make this assignment is test scores, and we use these to construct a cohortspecific statewide ranking that can be used to estimate a student’s place in any student grouping.
Since we have multiple scores, we attempt to combine them in a way that is as informative as
possible about a student’s potential class rank. We therefore define a student’s predicted
statewide percentile rank, 𝛾𝑖𝑡 , based on a weighted average of the student’s 8th grade math and
reading percentile test scores, where all percentiles are defined with respect to the statewide
distribution for the student’s 8th grade cohort and t represents the year the student is in 8th
16
There appears to be relatively little noise in the matching process. Across our six cohorts, 71 percent of 8 th
graders are observed in the 10th grade data two years hence. The loss can be almost entirely explained by students
who are retained or who leave legitimately by dropping out, transferring to the private sector, or moving out of the
state (as we can infer from information from TEA’s Academic Excellence Indicator System and Snapshot School
District Profiles).
9
grade.17 More details on this procedure and all constructed variables described in this section are
in the appendix. For shorthand, we refer to the predicted percentile rank as the student’s ability.
With 𝛾𝑖𝑡 in hand, we can then calculate the minimum level of ability associated with top ten
percent placement at any school. For each 8th grade cohort and high school, we calculate this
threshold as the 90th percentile of the distribution of 𝛾𝑖𝑡 (also based on 8th grade scores in year t)
among tenth graders attending the school in t+2, when the majority of the cohort has progressed
90
to this grade. We refer to this measure, 𝛾𝑘𝑡
, as the ―threshold.‖ A student is expected to place in
the top ten percent at a school if own ability exceeds the threshold.18
We then incorporate uncertainty, presuming that parents’ uncertainty mirrors ours. To
account for uncertainty arising from the mapping from test scores to class ranks, we assume that
a student’s expected statewide rank is distributed normally, with a common variance determined
by the variance of our prediction error. To account for variation in the specific composition of
the high school class, which is particularly important for smaller schools, we simulate the
variances of the thresholds.19 Under joint normality, we can then calculate the probability that
the student will place in the top ten percent, 𝜏𝑖𝑘𝑡 .
Finally, we estimate the hypothetical effect of the top ten percent plan on the likelihood that
student i would gain admission to a flagship after attending high school k, ∆𝑝𝑖𝑘 . In the
conceptual framework, this term was defined from the perspective of students interested in
attending a flagship. Since we cannot identify which 8th graders will eventually apply to a
flagship, even though their parents likely can, our empirical counterpart scales this term by an
estimate of the probability student i applies. This is equivalent to substituting the unconditional
probability of rejection in place of the probability conditional on applying in equation 3.3.2.
To calculate this incentive measure, we rely on additional survey and administrative data.
We turn to the National Education Longitudinal Study (NELS) to estimate how flagship
17
The math and reading scores are assigned weights of 0.69 and 0.31, respectively. These weights reflect relative
power in predicting high school class rank observed in the NELS, which has both 8th grade test scores and high
school class rank. The higher relative importance of math scores is consistent with prior studies’ findings. For
example, Hanushek et al. (1996) find math scores are three times as important in predicting the probability that
sophomores continue in high school to 12th grade.
18
Defining expectations in this way presumes perfect foresight, including regarding any changes in a school’s
ability distribution due to strategic mobility. For our central results, we characterize incentives based on those faced
by the initial middle school cohort to avoid introducing endogeneity and to be more agnostic regarding families’
expectations.
19
In each of 1000 rounds, we calculate the threshold by drawing with replacement a class of the same size as the
observed size and assigning each 10th grader a random draw from his/her predicted statewide rank distribution.
10
application rates depend on a measure comparable to 𝛾𝑖𝑡 and then apply this estimated
relationship to our sample. To assign rejection rates, we rely on administrative data from the
Texas Higher Education Opportunity Project (THEOP) to map conditional rejection rates to 𝛾𝑖𝑡
using applicants’ SAT test score percentiles.
Table 1 presents summary statistics for the overall and analysis samples. The first column is
based on students enrolled in 8th grade with one of our six cohorts, omitting the small number of
isolated students attending middle schools with fewer than two high schools within 30 miles.20
The next column includes only those students (71 percent) who remain in the Texas public
school system and progress with their cohort. These are the students for whom we can observe
high school choices via the test score files. The attrition is attributable to retained students,
dropouts, and students who move to the private sector or out of state. We have tested whether
8th graders are more likely to remain in our sample after the policy change and find evidence for
a small increase, but the increase does not appear to be correlated with strategic opportunities.21
Comparing column 2 to column 1, it is evident that students who progress and remain with
their cohort are of above-average ability. In this subsample, the mean predicted statewide rank
𝛾𝑖𝑡 rises from the 50th to the 56th percentile of all 8th graders. The average threshold for top ten
90
percent placement 𝛾𝑘𝑡
at the chosen high school is 87.8. This implies that a student would
have to achieve at nearly the 88th percentile statewide in 8th grade to place in the top ten percent
at the high school attended by the typical student. Though the average threshold is high, the
standard deviation of 8.3 shows there is room for arbitrage. Not surprisingly, the chance of
placing in the top ten percent at the high school attended 𝜏𝑖𝑘𝑡 is about ten percent.
The average effective change in flagship access ∆𝑝𝑖𝑘 is negligible due to the low
unconditional probability of rejection. Figure 1 displays the variation in application and
rejection rates by student ability that is masked by the average. The share applying to flagships
rises (nearly) monotonically with student ability. Though an increase in ability lowers the
probability of rejection conditional on application, the substantial positive effect of ability on the
20
We also exclude students with missing demographic information and students whose 8th grade or plurality high
schools: (i) ever serve less than 20 students in a grade, (ii) are majority special education, or (iii) are alternative
education (i.e., juvenile detention center). Together these restrictions reduce the sample by approximately five
percent. Note that, for the first column of Table 1, we assign students to the most recent cohort if they show up in
more than one cohort due to grade retention.
21
In particular, we estimate specifications parallel to equation 5.2 with the dependent variable equal to an indicator
for remaining in the sample. The coefficient estimates for the three-way interactions between ability deciles, post
and opportunity are universally small and almost never statistically significant.
11
probability of applying dominates the conditional rejection effect in some ranges. The
unconditional probability of rejection, which is what moderates the importance of the probability
of a top ten percent placement, peaks in the third decile of the ability distribution, then modestly
falls. Thus, we might expect to see strategic behavior exhibited most by students in the third
decile of the ability distribution, particularly when these students have nearby top ten percent
schooling options.
The final two columns of Table 1 show statistics for samples that condition further on the
availability of multiple accessible high school alternatives. Column 2 excludes students from
middle schools with fewer than two high school options within 10 miles, while column 3
excludes students with fewer than two within-district options within 10 miles. Other than the
drops in sample size (by 14 percent, and then again by 39 percent), there are few notable
differences from the sample in column 2. As the samples become more urban, student minority
rates rise somewhat, and the plurality high school (i.e., the high school that is the most common
destination for a middle school’s students) is more likely to have a feeder relationship with UTAustin.22
5. Analysis of thresholds at chosen high schools
For the first set of tests of strategic transitions, we relate the threshold at the high school the
student attends to the student’s incentives. Students who have convenient top ten percent
opportunities and would otherwise have applied to and been rejected at a flagship university
should enroll in high schools with lower thresholds after the policy is introduced. Thus, we
predict that the threshold at the actual high school attended should fall for these students, while
the threshold will actually rise on average for other students since the thresholds will be pushed
up by those who enroll strategically.
5.1 Introductory differences analysis
We build from a simple specification that incorporates only the role of the student’s ability.
Though ability is only one factor that determines incentives, starting with this helps us to refine
our approach. We assign students to statewide ability deciles, 𝐴𝑖 , based on 𝛾𝑖𝑡 . Define Postt to
22
We identify high schools that feed UT-Austin as those that sent more than 2.5 percent of its 10th graders to UTAustin on average across the 1994-95 through the 1998-99 10th grade cohorts. We chose this cut off since this
would represent 1/10 of college-goers for the typical school. These feeder high schools are distributed widely across
the state, but there are notably high rates from the suburbs of Dallas, Houston, and Austin.
12
be an indicator for whether a student’s 8th grade cohort attends 10th grade after the policy is
implemented, so that t indexes cohorts. To test whether there are any systematic changes in high
school enrollment patterns across the ability distribution, we interact Postt with a set of dummy
variables indicating the students’ ability deciles. Our baseline ordinary least squares
specification is:
(5.1)
90
𝛾𝑖𝑐𝑘𝑡
= 𝛽0 +
10
𝑛=1
𝛽𝑛 × 1𝐴𝑖 =𝑛 × 𝑃𝑜𝑠𝑡𝑡 + 𝐗 𝑖 Γ + Θ𝑐𝑛 + 𝜀𝑖𝑐𝑘𝑡
The vector X includes controls for student race/ethnicity and poverty status, and Θ𝑐𝑛 is a vector
of high school catchment area (c)  statewide ability decile fixed effects.23 The high school
catchment area is defined to be the set of middle schools that share the same plurality high
school. The identifying assumption for the estimated coefficients on the interaction terms to be
interpretable as responses to the policy change is that students in the later cohorts would
otherwise have made the same transitions as students of similar ability from the same catchment
area in prior years.
Table 2 presents the regression results for the interactions between the post policy change
indicator and the top five deciles statewide. The first column in Table 1 shows that there was a
slight increase in thresholds, with the magnitude of the increase varying inversely with ability.
While these results could reflect an influx of strategic movers into the high schools attended by
lower ability students, it could also be attributable to increased school accountability efforts
(starting in 1993-94). By improving the scores of students in poor performing middle schools,
accountability reform could have produced the observed patterns without any changes in
students’ high school enrollment choices.
In the second column, we conduct a placebo test to distinguish these interpretations. We
replace the threshold at the chosen high school with the ability associated with the 90th percentile
by middle school catchment area and year. Since strategic school choice is not reflected in this
measure, we should not observe any systematic patterns. We in fact observe a pattern very
similar to that in column 1. It appears that the Texas student test score distribution was
becoming more compressed across districts during our sample period for reasons unrelated to the
top ten percent plan.
In order to eliminate these contaminating time series patterns and isolate the impact of
23
Results in this section are insensitive to whether we control for interactions between ability decile and catchment
area indicators or interactions between ability decile and 8th grade campus indicators.
13
changes in enrollment, we hold the ability distribution fixed based on the initial year of our
sample. First, we set high school thresholds to the base year level, and refer to these thresholds
90
(𝛾𝑖𝑐𝑘
0 ) as static thresholds. Next, we treat students analogously by assigning them the ability
levels associated with base year students who are similarly situated within the catchment area.
That is, the student with median ability within the catchment area distribution in cohort t would
be assigned the ability 𝛾𝑖0 of the student at the median in the base year cohort. We refer to this
as static ability.
Columns 3 and 4 implement these adjustments sequentially, first replacing time-varying
thresholds with static thresholds, and then replacing actual ability deciles with deciles derived
from static ability. This reveals that students in the top four deciles moved towards schools with
lower thresholds in the baseline year, though the drop is only statistically significant for the top
decile. The apparent downgrading in school quality by top decile students is very small,
lowering the static threshold of the high school attended by less than one-tenth of a percentage
point. The lack of systematic impacts is not particularly surprising, since only a subset of
students within each ability decile has choice among alternative local schools that present
divergent top ten percent chances. When we estimate behavioral responses allowing for greater
heterogeneity in the following sections, we apply the lesson from this section and use the static
threshold and static student ability approach.
5.2 Difference-in-differences analysis
In this subsection, we expand the specification from the prior section to differentiate students
with and without scope for gaming. We continue to include indicators for the statewide ability
deciles, allowing these to capture differences in the impact of a top ten percent opportunity on
flagship access (through application and rejection probabilities) in a nonparametric way. We
then implement a difference-in-differences identification strategy within each ability group,
adding interactions between these deciles and indicators for the presence of strategic
opportunities.
We create two discrete measures of students’ strategic opportunities, both based on static
thresholds and abilities. Our first measure is an indicator for whether there is at least one local
90
high school h where the student is predicted to place in the top ten percent 𝛾𝑖0 ≥ 𝛾ℎ0
and one
local high school j where he/she is not 𝛾𝑖0 < 𝛾𝑗90
0 . We refer to this as a ―certainty‖ measure of
opportunity, because students behaving strategically in this context expect to place in the top ten
14
percent of their high school class. Our ―uncertainty‖ measure of opportunity is an indicator
variable equal to one if there is wide variation in the likelihood that a student would place in the
top ten percent across local high schools.24 We calculate both measures for our three definitions
of local area: i) high schools within 30 miles of the 8th grade school, ii) within 10 miles, and iii)
within 10 miles and within the same district.
Figure 2 shows the share of students defined to have opportunities for definitions ii) and iii).
In each case, we restrict the sample to students with multiple high schools within the relevant
definition of the local area. High-ability students are generally more likely to have nearby
schools with (static) thresholds above and below their own (static) ability, though rates are lower
in the top decile than in the second decile since students in the top decile statewide are likely to
place in the top ten percent at all local schools. Not surprisingly, the indicator derived from the
more continuous measure of the potential gains from trading down leads to a more even
distribution of opportunity across ability deciles.
Our difference-in-differences specification adds interaction terms between opportunity
indicators 𝑂𝑝𝑝𝑖0 and students’ statewide ability deciles 𝐴𝑖0 , as well as further interactions of
these terms with the post-policy indicator:
(5.2)
90
𝛾𝑖𝑐𝑘
0 = 𝜆0 +
10
𝑛=1
𝜆1𝑛 × 1𝐴𝑖0 =𝑛 × 𝑃𝑜𝑠𝑡𝑡 +
10
𝑛=1
𝜆2𝑛 × 1𝐴𝑖0 =𝑛 × 𝑂𝑝𝑝𝑖0 +
𝑛=110𝜆3𝑛×1𝐴𝑖0=𝑛×𝑃𝑜𝑠𝑡𝑡×𝑂𝑝𝑝𝑖0+𝐗𝑖Γ+Θ𝑐𝑛0+𝜀𝑖𝑐𝑘𝑡
We report the corresponding estimates in Table 3. The left and right-hand panels show results
for the certainty and uncertainty opportunity measures, respectively. Within each panel, the
definition of the local market becomes narrower moving across the three columns.
These results reveal that, compared to behavior prior to the top ten percent policy, students
with strategic opportunities moderately ―downgrade‖ the quality of their high schools compared
to students with similar academic ability lacking strategic opportunities. The point estimates are
consistently negative across specifications for the top four student ability deciles, though the
differences are only sporadically significant. The behavioral response appears stronger among
students with intra-district opportunities to strategically select their high schools. Our
interpretation is strengthened by the fact that there was almost no change in the thresholds of
high schools attended by students who lacked incentives to alter plans.
24
In particular, we calculate whether the gap between the 10 th and 90th percentile of the (enrollment-weighted)
distribution of 𝜏𝑖𝑘0 exceeds 20 percentage points.
15
While these results show opportunistic downgrading is occurring, the magnitudes are
difficult to interpret since a large drop in thresholds can indicate either many students altering
high schools plans or a few students heavily downgrading. We postpone consideration of
heterogeneity in responsiveness to the next section where we are able to separate the intensive
and extensive margins.
6. Discrete choice analysis of high school enrollment decisions
6.1 Conditional logit model and baseline estimates
The second set of tests of strategic enrollment decisions imposes more of the structure
suggested by the model of high school choice derived in the theoretical section. The results of
our analysis of high school thresholds suggest that the greatest trading down behavior occurs
among students with multiple local high school options in the same district, and we thus restrict
our attention to students in districts served by more than one high school. Treating each district
as a distinct market and pooling across markets, we examine students’ high school enrollment
choices using a conditional logit model. This approach allows us to more easily characterize
students’ opportunity sets and to simulate policy-induced changes in high school enrollment
shares and in the composition of the top ten percent pool.
Let 𝐶𝑖 denote the choice set of high schools in the district where student i attends middle
school during year t.25 We presume that the attractiveness of a school to a student is determined
by characteristics that vary by student and school:
(6.1)
𝑉𝑖𝑘𝑡 = 𝑣𝑖𝑘𝑡 + 𝜀𝑖𝑘𝑡
= 𝛼𝑘 + 𝜂1 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0 × 𝑃𝑜𝑠𝑡𝑡 + 𝜂2 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0 + 𝑿𝑖𝑘0 Γ + 𝜀𝑖𝑘𝑡
With the assumption that the error terms follow an extreme value distribution,26 the probability
the student chooses high school k can be expressed:
(6.2) 𝑃𝑖𝑘𝑡 =
𝑒 𝑉 𝑖𝑘𝑡
𝑚 ∈𝐶 𝑖
𝑒 𝑉 𝑖𝑚𝑡
Under the random utility interpretation of this model, student i will choose to enroll in high
25
We exclude students who remain in the TX public school system, but attend a high school outside the middle
school district (7.1 percent). The great majority of these students appear to have moved residences, with the median
travel distance being 13.9 miles (compared to 1.3 for students staying within the district). We also exclude high
schools that do not exist during all years of our sample period.
26
By pooling across districts, we are assuming the variance of the errors is the same across districts. Pooling relaxes
the constraint on the number of high school characteristics that can be included in the control set.
16
school k if this provides the greatest indirect utility out of all high schools in the set 𝐶𝑖 . Rather
than taking this interpretation literally, we use this model primarily as a predictive tool to
estimate the number of students whose school enrollment choices are altered by the introduction
of the top ten percent plan. By limiting student i's choice set to high schools within the 8th grade
school district, our model includes student i's most relevant alternatives. The inclusion of high
school fixed effects, 𝛼𝑘 , also controls for time-invariant differences in the relative attractiveness
of alternatives.
Vector 𝑿𝑖𝑘0 contains the geographic distance between student i’s 8th grade school and high
school k, an indicator for whether school k is the plurality high school, the ratio of the fraction of
students in school k who are nonwhite to the fraction of students who are nonwhite in the
plurality high school, and a similar ratio comparing the median student ability level at these two
schools. As with the other controls, these are all set to static values from the base year.
In various specifications, we set students’ top ten percent plan incentives 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0
90
equal to one of three incentive measures—𝛾𝑘0
(―threshold‖), 𝜏𝑖𝑘0 (―top ten percent probability‖),
or ∆𝑝𝑖𝑘0 (―college admissions motive‖). The threshold measure of incentives allows us to
compare the conditional logit analyses to the earlier OLS analyses, and the next two incentive
measures impose more of the structure suggested by our theoretical framework. We always use
static incentive measures—i.e., for all years, 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0 is calculated by first assigning student
i to the same statewide percentile as the student that was in the same place in the ability
distribution of student i's catchment area during the initial year of our sample. The specifications
include a main effect for the incentive term to pick up any underlying relationship between
school enrollment patterns and students’ absolute and relative ability, though this coefficient, 𝜂2 ,
will not have a meaningful interpretation. Our key coefficient of interest, 𝜂1 , captures the change
in the ―weight‖ placed on the opportunity offered at a school once the top ten percent plan is in
effect.
Table 4 displays the estimates of equation 6.1 for each of the three measures of incentives.
The first row of Table 4 displays our estimates of 𝜂1 , the key coefficient of interest. In all three
cases, the estimate confirms our theoretical prediction and is statistically significant at the .05
level. Compared to years preceding the top ten percent plan, students prefer schools with lower
top ten percent thresholds (column 1), where they have better chances of placing in the top ten
percent (column 2), and where flagship university admissions probabilities were most improved
17
(column 3). As expected, the estimate in column 1 of the first row is qualitatively similar to our
OLS results for changes in thresholds and the estimates of strategic responses in columns 2 and 3
imply quantitatively similar effects as those OLS results. In particular, when we simulate the
reallocation of students across high schools using the estimates in columns 2 and 3, students in
the top five statewide ability deciles who behave strategically choose high schools with top ten
percent thresholds 0.219 and 0.225 percentile points lower, respectively—similar to the mean
decrease across the analogous estimates displayed in the first five rows of column 3 of Table 2.
Students’ behavior also entails choosing high schools that, on average, have lower median
student ability (0.49 percentage point decrease), greater poverty rates (0.84 percentage point
increase), and higher percentages of nonwhite students (0.51 percentage point increase).
The second row of Table 4 displays the estimated coefficients for the main effects of the
incentive measures, 𝜂2 . Note that in the first column, where the incentive is the threshold, the
main effect is not included because the threshold is held fixed at values in the baseline year so is
collinear with the school fixed effects. The estimated coefficients for the other control variables
in the remaining rows are very similar across the three specifications. Students are more likely
to choose to attend the plurality high school (tautologically), less likely to attend high schools
located far from their middle school, and less likely to attend a high school with a relatively high
fraction of nonwhite students. Unlike the estimated coefficients for the other controls, the
coefficient on relative median student ability measure is statistically insignificant, but it is
important to keep in mind that this estimated effect is conditional on the values of the baseline
incentive measure—which is highly correlated with median student ability.
6.2 High school enrollment choices by student ability
The models in Table 4, particularly in columns 1 and 2, do not fully incorporate the
heterogeneous incentives suggested by our conceptual model. In this section, we allow for more
flexibility by separately estimating conditional logit models by (static) ability decile. Table 5
displays our estimates of 𝜂1 for the top five deciles, with columns 1 through 3 analogous to the
first row of Table 4. Students in the 1st through 4th statewide ability deciles respond to top ten
percent plan incentives—i.e., the estimates are all statistically significant across the various
incentive measures for these samples—but responses among students in the 5th statewide ability
decile are not statistically significant. These results are consistent with the idea that higher
ability students are more likely to be interested in attending the flagship universities.
18
Since the coefficient estimates are not readily comparable across samples, columns 4 and 5
of Table 5 provide information to help gauge the relative importance of top ten percent
incentives in determining high school enrollment decisions. We report students’ apparent
willingness to travel to a farther high school for a one standard deviation gain in the likelihood of
placing in the top ten percent (column 4) or a one standard deviation gain in the likelihood of
acceptance to a flagship university (column 5). We continue to proxy for students’ home
locations using middle school locations and to proxy for incentives using a limited set of
observables. Therefore, the estimates in columns 4 and 5 should not be interpreted as identifying
indirect utility parameters, but as a heuristic for gauging the relative importance of the incentives
under the top ten percent plan.
For students in the top statewide ability decile, a one standard deviation gain in the
probability of placing in the top 10 percent has a similar effect as traveling 0.26 fewer miles to
school, and a one standard deviation gain in the likelihood of admission into a flagship university
has a similar effect as traveling 0.35 fewer miles to school. Students in the second through
fourth deciles appear to place slightly less value on these strategic opportunities, ranging from
0.18 to 0.23 miles. To put these distances in perspective, note that the median difference
between a student’s closest high school option and his/her second-closest high school option is
only 1.5 miles in this sample.
6.3 Take-up rates for strategic within-district high school choices
We next examine student take-up rates for strategic behavior—i.e., the fraction of students
changing high school enrollment choices due to top ten percent plan incentives. To generate
these predictions, we use a conditional logit model equivalent to the model used for column 2 of
Table 5. Because Table 5 revealed statistically insignificant responses for students of lower
abilities, we restrict the sample to students in the top four statewide (static) ability deciles. For
this pooled sample, the resulting estimated coefficient of the 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0 × 𝑃𝑜𝑠𝑡𝑡 term equals
0.590 and has a standard error of 0.235. This estimate implies that the incentives created by the
top ten percent plan have induced more than two hundred students per year (within our restricted
sample) to attend different high schools.
Table 6 displays take-up rates conditional on students having either our "certainty" or
"uncertainty" definitions of top ten percent opportunities. For either definition, our estimates in
the first row of Table 6 suggest that, among the roughly 33 percent of students in this sample
19
who had the opportunity to behave strategically, more than one percent of these students changed
high schools within their districts. Though small in absolute magnitude, the response is
moderate relative to the share of these students (27 percent27) who would have applied to a
flagship in the pre-reform period.
The remaining rows of Table 6 examine heterogeneity in these take-up rates. In each case,
we restrict the sample to the relevant subgroup of students, estimate the conditional logit model
for this subgroup, and then calculate the implied take-up rates.28 Conditional take-up rates are
slightly lower for the highest ability students, but unconditional rates are still relatively high for
these students. Relatively strong responses from students in the third or fourth statewide ability
deciles may reflect the lower acceptance rates they face at selective universities through the
traditional application mechanism.
The largest conditional take-up rates are actually among black students—2.9% for the
certainty definition of opportunity. Black students’ conditional take-up rate is roughly six times
the rate for white students (0.5% for the certainty definition of opportunity). Black students are
also more likely to have strategic opportunities than white students. Take-up rates are fairly
similar across white and Hispanic students. The underlying coefficients used to determine these
white and Hispanic student take-up rates are not very statistically significant for these groups,
partly due to the imprecision of our estimates once we divide the sample so that only moderate
numbers of students have strategic opportunities. In the case of white students, the relatively low
reported take-up rate belies a fairly large take-up rate among high-ability white students; white
students in each of the top two statewide ability deciles have conditional take-up rates of at least
1.1%. One should not exaggerate the importance of these differences given that the underlying
conditional logit estimates are not statistically significant with the sample cut so thinly. The
safest conclusion is that strategic responses seem to occur both among high-ability students of all
races and among slightly-lower-ability students who are black.
Much of the difference in take-up rates across black and white students is due to differences
in the types of within-district strategic opportunities that these students face. If we repeat these
𝑝𝑟𝑒
We calculate this 27% application rate by finding the mean of our estimate of 𝑎𝑖𝑘 among the pool of students in
the conditional logit sample who have strategic opportunities.
28
Take-up rates for the certainty version are based on changes in the likelihood that students attend schools where
we expect them to place in the top ten percent; for the ―uncertainty‖ version, take-up rates are based on the product
of the change in likelihood of attending various schools and our estimated probability that a particular student would
place in the top ten percent at a particular school.
27
20
estimates using homogenous conditional logit coefficients for all racial groups, then we continue
to observe take-up rates for blacks that are more than twice as large as those for whites.
Hispanic students’ opportunities, however, are just as conducive to strategizing as black
students’ opportunities—the differences for these two races are thus solely due to greater
behavioral responses from black students than from Hispanic students.
Given black students' relatively high take-up rates, we find that the black share of the top ten
percent pool modestly increases due to students' strategic high school enrollment choices. The
total number of black students behaving strategically only slightly outnumbers the total number
of white students behaving strategically, because white students outnumber black students by
more than 3 to 1 in this sample. On the other hand, because the top ten percent of high schools is
predominately composed of white students, the strategic enrollment decisions of both white and
black students primarily displace white students out of the top ten percent of the receiving
schools. A black student strategically selecting a high school is therefore relatively likely to
displace a white student at the receiving school, while a white student strategically selecting a
high school is relatively unlikely to displace a black student. Simulations based on our
conditional logit models’ estimates suggest that the statewide pool of top ten percent plan
qualifiers increases by one black student for every 1.3 black students successfully moving into
the top ten percent via their high school choices, but only by one white student for every 3 white
students successfully moving into the top ten percent.29
Racial displacement due to strategic behavior is also relevant for Hispanic students'
representation in the top ten percent pool. Our analyses suggest that strategic behavior modestly
decreases the number of Hispanic students in the top ten percent pool due to their low take-up
rates. The decline in Hispanic student representation is less than the increase in the black
29
We impute these ratios focusing on the students of a particular race in our conditional logit sample, (students in
the top 4 statewide ability deciles attending multi-high school districts), that have an opportunity to behave
strategically based on our "certainty" measure. We estimate the number of students of the opposite race who they
displace out of the top ten percent by summing across the products of: (i) the predicted change in probability that the
student chooses a particular high school due to strategic incentives, (ii) an indicator variable for whether we expect
the student to place in the top ten percent of that high school, and (iii) the baseline-year percent of students in the top
two deciles of that school who were of the opposite race. We then divide this estimate by our estimate of the total
number of students of this race who successfully moved into the top ten percent due to strategizing—i.e., the sum of
the products of (i) and (ii) for these students. Note that while these reported ratios are based on the ―certainty‖
concept of opportunity, black students would have a more difficult time crowding out other students in the statewide
top ten percent pool based our "uncertainty" measure, because they would tend to be vacating schools where they
would have moderate probabilities of displacing white students out of the top ten percent for schools in which they
have very high probabilities of displacing other black students out of the top ten percent pool.
21
students’ representation, so there is a net increase in the total number of nonwhite top ten percent
plan qualifiers as a result of students' strategic choice of high schools.
Our results also suggest that concerns about other types of compositional changes in the top
ten percent pool due to strategic behavior may be unwarranted. The media has highlighted
affluent parents’ recognition of their incentives to change their children’s high schools and these
parents’ increased concerns with both gaming and the general crowd-out of admissions offers for
students below the top ten percent of their classes. While these affluent parents might be
especially vocal commentators on strategic high school enrollment, they are not the only ones
witnessing or engaging in this behavior. Take-up rates do not vary much by the whether the high
schools in the district have feeder relationships with UT-Austin (as shown in Table 6), and in
results not shown here we find that take-up rates also do not vary by students’ families’ poverty
status.
7. Conclusions
Texas’ top ten percent plan was instituted in 1998 after the elimination of affirmative action
following the 1996 Hopwood v. Texas decision. An explicit goal of this program was to
maintain minority college enrollment, particularly at Texas’ selective public universities. By
basing this admission possibility on school-specific standards, the policy also encourages
strategic high school enrollment that might change the composition of the eligible population and
more generally reduce the degree of sorting by ability across high schools.
In both reduced-form analyses of changes in schools’ top ten percent thresholds and discrete
models of students’ intra-district sorting across high schools, we find evidence that some
students and families did change their behavior in a strategic manner after the policy was
instituted. Students with strong chances of placing in the top ten percent at nearby high schools
tended to ―downgrade‖ in peer quality by attending high schools with lower initial top ten
percent thresholds. This strategic mobility changed the composition of beneficiaries of the new
program, raising both the average ability level of these qualifiers and the average high school
thresholds for qualification. Black students engage in trading down at greater rates and often
displace students of other races from the top ten percent pool, so the net effect of students'
strategic behavior is to slightly increase the black student share in the top ten percent pool.
Strategic high school choice does not undermine the racial diversity goal of the top ten percent
22
plan at the university access level, and introduces a tendency toward de-stratification by ability at
the high school level.
Top x-percent programs are likely to become increasingly important in the future. Justice
O’Connor’s majority opinion in the 2003 Grutter v. Bollinger case stated: ―We expect that 25
years from now, the use of racial preferences will no longer be necessary to further the interest
approved today.‖ In contrast, Krueger, Rothstein, and Turner (2006) find that (in the absence of
a rapid convergence in test scores controlling for income) future declines in black–white family
income gaps alone are unlikely to eliminate the need for racial preferences to maintain minority
enrollment in highly selective institutions. We can expect increasing court challenges to the use
of affirmative action in admissions decisions juxtaposed with continued demand for substitute
policies.
23
References
Arcidiacono, Peter. 2005. ―Affirmative Action in Higher Education: How do Admission and
Financial Aid Rules Affect Future Earnings?‖ Econometrica, 73(5), 1477-1524.
Barron’s Profiles of American Colleges. 1992. 17th Edition, Barron’s Educational Series, Inc.,
Hauppauge, NY.
Cortes, Kalena E., and Andrew I. Friedson. 2009. ―Ranking Up by Moving Out: The Effect of
the Texas Top 10% Plan on Property Values.‖ September 25, mimeo.
Currie, Janet. 2006. ―The Take Up of Social Benefits.‖ in Alan Auerbach, David Card, and
John Quigley (eds). in Poverty, The Distribution of Income, and Public Policy, (New York:
Russell Sage), 2006, 80-148.
Department of Education, National Center for Educational Statistics. 2001. Digest of
Educational Statistics. U.S. Government Printing Office, Washington, D.C.
Glater, Jonathan D. 2004. ―Diversity Plan Shaped in Texas is Under Attack.‖ The New York
Times, June 13.
Hanushek, Eric A., Steven G. Rivkin, and Lori L. Taylor, Aggregation and the Estimated Effects
of School Resources. The Review of Economics and Statistics, 78(4), pp. 611-27, November
1996.
Hart, Patricia Kilday. 2001. ―Imperfect 10.‖ Texas Monthly, pp. 52-, April.
Hoekstra, Mark. 2009. ―The Effect of Attending the Flagship State University on Earnings: A
Discontinuity-Based Approach.‖ Review of Economics and Statistics, 91(4), 717-724.
Horn, Catherine L., and Stella M. Flores. 2003. ―Percent Plans in College Admissions: A
Comparative Analysis of Three States’ Experiences.‖ The Civil Rights Project, Harvard
University.
Hughes, Polly Ross, and Matthew Tresaugue. 2007. ―Small-town GOP behind survival of top
10% rule.‖ Houston Chronicle, May 30.
Howell, Jessica S. 2010. ―Assessing the Impact of Eliminating Affirmative Action in Higher
Education.‖ Journal of Labor Economics, 28(1), 113-166.
Kane, Thomas J. 1998. ―Racial and Ethnic Preferences in College Admissions.‖ In The BlackWhite Test Score Gap, edited by Christopher Jencks, and Meredith Phillips, Brookings
Institution Press, Washington, DC, 431 – 56.
Krueger, Alan B., Jesse Rothstein, and Sarah E. Turner. 2006. ―Race, Income, and College in
24
25 Years: Evaluating Justice O'Connor's Conjecture.‖ American Law and Economics
Review, 8(2), 282-311.
Long, Mark C. 2004a. ―College Applications and the Effect of Affirmative Action.‖ Journal of
Econometrics, 121(1–2), 319 – 42.
Long, Mark C. 2004b. ―Race and College Admissions: An Alternative to Affirmative Action?‖
The Review of Economics and Statistics, 86(4), 1020-1033.
Long, Mark C. 2007. ―Affirmative Action and its Alternatives in Public Universities: What Do
We Know?‖ Public Administration Review, 67(1), 311-325.
Long, Mark C., Victor B. Saenz, and Marta Tienda. 2010. ―Policy Transparency and College
Enrollment: Did the Texas Top 10% Law Broaden Access to the Public Flagships?‖ The
ANNALS of the American Academy of Political and Social Science, 627, 82-105.
Long, Mark C. and Marta Tienda. 2010. ―Changes in Texas Universities’ Applicant Pools after
the Hopwood Decision.‖ Social Science Research, 39(1), 48-66.
Moffitt, Robert. 1992. ―Incentive Effects of the U.S. Welfare System: A Review,‖ Journal of
Economic Literature, 30(1), 1-61.
Moffitt, Robert. 2002. ―Economic Effects of Means-Tested Transfers in the U.S.,‖ Tax Policy
and the Economy (16).
Texas Higher Education Coordinating Board. 2002. ―First-time Undergraduate Applicant,
Acceptance, and Enrollment Information for Summer/Fall 1998-2001.‖
http://www.txhighereddata.org/, Mimeo.
Yardley, Jim. 2002. ―The 10 Percent Solution.‖ New York Times, pg. 4A.28, April 14.
25
Figure 1. Application and unconditional
rejection
rates, by
ability decile
Applications
to four-year
institutions
0.70
0.65
0.60
0.55
0.50
Fraction of students
Applied to any college
0.45
0.40
Applied to any public, instate, college
0.35
Applied to a highly selective college
0.30
0.25
Applied to a public, instate, highly
selective college
0.20
Rejected by a public, instate, highly
selective college
0.15
0.10
0.05
0.00
Bottom
2
3
4
5
6
7
8
9
Top
Statewide ability decile
Notes: The application rates are based on data from Texas students in the NELS second follow-up, while the
unconditional rejection rates are inferred from administrative data from the Texas flagships. Statewide ability is
determined by a weighted average of 8th grade reading and math percentile scores. See the appendix for more
details.
26
Figure 2. Share with opportunities, by ability decile
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Top decile
2nd decile
3rd decile
4th decile
5th decile
Certainty
Uncertainty
>1 high school
within 10 miles
Certainty
Uncertainty
>1 high school within 10
miles and the same district
Notes: The assignment to ability deciles is based on a weighted average of 8th grade reading and math percentile
scores. The height of the bars indicates the share of students classified as having an opportunity to exercise strategic
choice within the set of high schools indicated, from the certainty and the uncertainty perspectives described in the
text.
27
Table 1. Summary statistics
Full sample
Multiple
HSs w/in 30
miles
(1)
Student characteristics
Black
Hispanic
Poor
Plurality high school feeds UT-Austin
Statewide percentile rank 𝛾𝑖𝑡
Analysis sample: Students who remain in
the TX public school system
Multiple
Multiple
Multiple
withinHSs w/in 30 HSs w/in
district HSs
miles
10 miles
w/in 10 miles
(2)
(3)
(4)
0.14
0.35
0.42
0.24
50.4
0.13
0.31
0.36
0.25
56.4
0.14
0.31
0.35
0.28
56.5
0.16
0.36
0.38
0.37
55.8
90
Threshold for top 10% placement 𝛾𝑘𝑡
--
Probability of top 10% placement 𝜏𝑖𝑘𝑡
--
Change in flagship access ∆𝑝𝑖𝑘
--
87.8
(8.3)
0.11
(0.13)
0.01
(0.01)
87.6
(8.6)
0.11
(0.13)
0.01
(0.01)
86.6
(9.7)
0.11
(0.13)
0.01
(0.01)
0.14
(0.13)
0.53
(0.32)
0.03
(0.02)
979,384
0.14
(0.13)
0.53
(0.32)
0.03
(0.02)
846,271
0.14
(0.13)
0.54
(0.32)
0.03
(0.02)
517,252
Opportunities at chosen high school
Student flagship access
Probability of applying
Probability of rejection conditional on
applying
Unconditional probability of rejection
Sample Size
0.12
(0.12)
0.60
(0.33)
0.03
(0.02)
1,388,632
Notes: Each column presents means (standard deviations in parentheses) for 8 th grade students from the 1992-93
through 1997-98 TX cohorts. The sample is progressively restricted moving across the columns. The first column
includes all students in these cohorts attending a middle school within 30 miles of more than one high school.
Column 2 includes only the subset of these students who remain in the public school system and progress with their
cohort to 10th grade (to a high school that operates in all years). Column 3 then excludes students with fewer than
two high schools within 10 miles, and column 4 excludes students with fewer than two within-district high schools
within 10 miles.
28
Table 2. Impact of the policy on the threshold of the high school attended, by student ability
Dependent variable
Actual high
Catchment area
Static high school threshold
school threshold
threshold
(1)
(2)
(3)
(4)
***
Post × top decile
-0.010
-0.075
-0.088
-0.058**
(0.081)
(0.097)
(0.026)
(0.027)
nd
*
Post × 2 decile
0.150
0.082
-0.045
-0.045
(0.089)
(0.108)
(0.031)
(0.029)
Post × 3rd decile
0.259***
0.193*
-0.041
-0.028
(0.099)
(0.117)
(0.025)
(0.024)
Post × 4th decile
0.409***
0.358***
0.004
-0.020
(0.110)
(0.128)
(0.028)
(0.028)
Post × 5th decile
0.504***
0.471***
-0.024
0.010
(0.120)
(0.139)
(0.029)
(0.026)
Observations
979,384
979,384
979,384
979,384
Assignment to deciles
Own cohort-specific statewide percentile rank
Static rank
Notes: Each column corresponds to a separate OLS regression on the sample of students with multiple high schools
within 30 miles who progress with their cohort between 8 th and 10th grade. The dependent variable and the method
used to assign students to ability deciles vary across columns. The dependent variable is the actual time-varying
threshold at the high school attended in column 1; the equivalent concept for the catchment area in column 2; the
threshold in the base year at the high school attended (defined only for schools that operated in all years) in the last
two columns. The ability deciles are based on students’ within-cohort statewide percentile ranks in the first three
columns; in column 4, they are based on the statewide percentile rank associated with students located at the same
place in the within-catchment area ability distribution in the initial year of the sample. All specifications include
catchment area × ability decile fixed effects and indicators for student race/ethnicity and poverty status. Robust
standard errors allowing for clustering at the level of the fixed effects are reported in parentheses. ***Significant at
the 1% level; **5% level; *10% level.
29
Table 3. Impact of the policy on the threshold of the high school attended, by student ability
Dep. Var. = Static high school
Certainty opportunity measure
Uncertainty opportunity measure
threshold
(1)
(2)
(3)
(4)
(5)
(6)
**
*
**
*
Post × top decile × has opp.
-0.076
-0.064
-0.126
-0.074
-0.086
-0.090
(0.032)
(0.040)
(0.074)
(0.038)
(0.047)
(0.107)
Post × 2nd decile × has opp.
-0.024
-0.069
-0.113
-0.058
-0.070
-0.251**
(0.081)
(0.053)
(0.111)
(0.049)
(0.058)
(0.124)
Post × 3rd decile × has opp.
-0.032
-0.106*
-0.325***
-0.045
-0.121**
-0.321***
(0.041)
(0.056)
(0.123)
(0.040)
(0.053)
(0.115)
Post × 4th decile × has opp.
-0.001
-0.029
-0.237
-0.018
-0.090
-0.285
(0.051)
(0.079)
(0.196)
(0.050)
(0.076)
(0.175)
th
Post × 5 decile × has opp.
-0.113
-0.258
-0.364
0.020
0.055
0.248
(0.085)
(0.202)
(0.374)
(0.070)
(0.124)
(0.221)
Post × top decile
-0.002
-0.022
-0.013
0.004
0.001
-0.029
(0.029)
(0.027)
(0.036)
(0.019)
(0.016)
(0.036)
Post × 2nd decile
-0.023
0.003
0.001
-0.001
-0.003
0.048
(0.075)
(0.030)
(0.045)
(0.032)
(0.025)
(0.040)
Post × 3rd decile
-0.005
0.024
0.048
0.004
0.032
0.056
(0.025)
(0.024)
(0.037)
(0.021)
(0.023)
(0.038)
Post × 4th decile
-0.02
-0.003
0.047
-0.010
0.029
0.066*
(0.026)
(0.025)
(0.039)
(0.026)
(0.025)
(0.039)
th
Post × 5 decile
0.027
0.023
0.058
0.006
0.000
0.011
(0.029)
(0.030)
(0.048)
(0.028)
(0.030)
(0.046)
Observations
979,384
846,271
517,252
979,384
846,271
517,252
Multiple
Multiple
Multiple HSs Multiple HSs within-district Multiple HSs Multiple HSs within-district
Sample restriction
w/in 30 miles w/in 10 miles
HSs w/in 10
w/in 30 miles w/in 10 miles
HSs w/in 10
miles
miles
Notes: Each column corresponds to a separate OLS regression, with the estimation sample varying across the columns as indicated in the bottom row. The
dependent variable is the threshold in the base year at the high school attended (defined only for schools that operated in all years). The ability deciles are based
on the statewide percentile rank associated with students located at the same place in the within-catchment area ability distribution in the initial year of the
sample. All specifications include catchment area × ability decile fixed effects and indicators for student race/ethnicity and poverty status. Robust standard
errors allowing for clustering at the level of the fixed effects are reported in parentheses. ***Significant at the 1% level; **5% level; *10% level.
30
Table 4. Conditional logit estimates of within-district high school enrollment choices
Incentive Measure
Threshold
Top ten percent
Flagship
90
probability
admission motive
𝛾𝑘0
𝜏𝑖𝑘0
∆𝑝𝑖𝑘0
(1)
(2)
(3)
-0.64***
(0.22)
0.58**
(0.23)
11.84***
(4.38)
--
-6.97***
(0.44)
-35.30***
(4.99)
Indicator for Plurality High School
1.86***
(0.15)
1.87***
(0.15)
1.86***
(0.15)
Distance from 8th Grade School to
High School
-0.41***
(0.05)
-0.41***
(0.05)
-0.41***
(0.05)
% Nonwhite at high school /
%Nonwhite at plurality HS
-0.55**
(0.25)
-0.55**
(0.25)
-0.55**
(0.25)
-0.26
0.22
-0.23
(0.43)
(0.52)
(0.43)
Incentive × Post
Incentive
Median ability level at HS /
Median ability level at plurality HS
Notes: Each column corresponds to a separate conditional logit model examining 8th grade students’ high school
choices, with 274,252 students choosing within 65 multi-high school districts. We report robust standard errors (in
parentheses below each estimated coefficient) that allow for clustering at the district level. There are a total of
1,640,737 student–high school combinations in these data. Each student’s plurality high school is the high school
where the plurality of his/her schoolmates from 8th grade school attends across all years in the sample.
***
Significant at the 1% level; **5% level; *10% level.
31
Table 5. Conditional logit estimates of responses to incentives, by student ability subgroups
Average extra distance (in
miles) willing to travel to
Incentive measure
high school for a 1 standard
deviation gain in…
Flagship
Top ten
admission
Threshold
percent
Statewide
𝜏𝑖𝑘0
∆𝑝𝑖𝑘0
90
motive
probability
𝛾𝑘0
ability decile
∆𝑝𝑖𝑘0
𝜏𝑖𝑘0
(1)
(2)
(3)
(4)
(5)
Top decile
-1.17**
(0.49)
0.59*
(0.32)
26.08**
(11.07)
.26
.35
2nd decile
-0.78**
(0.37)
0.59**
(0.28)
11.46**
(5.44)
.22
.21
3rd decile
-0.84***
(0.31)
0.70**
0.28)
11.49**
(4.66)
.23
.22
4th decile
-0.74***
(0.25)
0.76**
(0.30)
12.65**
(5.12)
.18
.18
5th decile
-0.30
(0.26)
0.45
(0.51)
9.79
(11.34)
.08
.08
Notes: Each cell in columns 1 through 3 displays an estimate from a separate conditional logit model examining 8th grade
students’ high school choices within 65 multi-high school districts. These models also include the same control variables listed
in Table 4. We report robust standard errors (in parentheses below each estimated coefficient) that allow for clustering at the
district level. The sample in each row is limited to students in a particular ability decile of the statewide ability distribution
(based on the baseline performance distribution rather than the actual, year-specific distribution); the estimates reported in the
first through fifth rows, respectively, are based on samples with 304,436; 313,039; 321,560; 317,131; and 312,660 student–high
school combinations. The estimates in columns 4 and 5 are calculated using the same models used for the corresponding model
in columns 2 and 3, respectively, and are equal to -1 times the ratio of the incentive measure’s coefficient to the distance
variable’s coefficient. ***Significant at the 1% level; **5% level; *10% level.
32
Table 6. Rates of strategic behavior for gaining top ten percent status
Certainty opportunity
Uncertainty opportunity
measure
measure
Percent with
Percent with
opportunity Conditional opportunity Conditional
to behave
take-up rate
to behave
take-up rate
strategically
strategically
(1)
(2)
(3)
(4)
Statewide Ability Decile
Top 4 deciles
Top decile
2nd decile
3rd decile
4th decile
Top 4 Deciles Divided by…
Race
White
Black
Hispanic
High School District Feeder Status
Feeds UT-Austin
Does not feed UT-Austin
33.4%
1.1%**
33.2%
1.2%**
41.5%
42.6%
27.7%
19.1%
0.8%*
1.0%**
1.6%**
1.7%**
40.0%
37.5%
31.0%
22.5%
1.1%*
1.2%**
1.5%**
1.5%**
28.5%
43.8%
41.4%
0.5%
2.9%***
0.4%
28.0%
43.9%
42.3%
0.6%
3.1%***
0.4%
32.4%
35.1%
1.1%**
1.0%
32.0%
35.3%
1.3%**
1.1%
Notes: The conditional take-up rates are calculated using conditional logit models similar to the ones used to create
Tables 4 and 5, except that students in the fifth statewide ability are always excluded from the sample in these
analyses. Mean conditional take-up rates across subgroups of students may differ from the reported take-up rates in
row 1 because these are based on conditional logit models estimated over different samples. The first row shows the
results for the entire resulting sample, and then every other row estimates this conditional logit model while
restricting the sample to a subset of these students. See the Notes to Table 5 for decile-specific sample sizes.
Students have a ―certainty‖ opportunity if there is at least one high school in the district where they would expect to
place in the top ten percent and at least one high school in the district where they would not; students have an
―uncertainty‖ opportunity if the gap between the 10 th and 90th percentile of the (enrollment-weighted) distribution of
their within-district top ten percent probabilities exceeds 20 percentage points. The conditional take-up rate is
computed using the subset of students in the sample defined as having an opportunity. The take-up rate is the
student-level mean of the sum of all positive changes in the predicted probability that a student attends various high
schools when the estimated coefficient of the 𝐼𝑛𝑐𝑒𝑛𝑡𝑖𝑣𝑒𝑖𝑘0 × 𝑃𝑜𝑠𝑡𝑡 variable enters the prediction. Because
students’ predicted probabilities of attending the within-district high schools are constrained to sum to one, the sum
of these positive values will have the same magnitude as the sum of the negative values and will reflect the total
estimated probability that the student changes schools due to strategic incentives. Asterisks denote the statistical
significance of the estimated coefficient used to calculate the take-up rate: ***Significant at the 1% level; **5% level;
*
10% level.
33
Appendix
Data sources
Table A1. Variables by data source
Data
Source
Administrative
Data for fiscal years 1993 to 2000
student-level test
were provided on request by the
score documents
Communications and Student
Assessment Divisions of the Texas
Education Agency
Administrative
annual school-level
data
Texas Academic Excellence
Indicator System (AEIS)
School geographic
coordinates
NCES Common Core of Data for
the years 1992 to 2002
UT Austin Texas
feeder high schools
UT Austin Office of Admissions
annual ―Texas Feeder Schools‖
report for the years 1996 to 2000
Variables
Unique student ID; reading, math,
and writing test scores; exemption
status; LEP status; special education
status; free and reduced-price lunch
status; ethnicity; grade; school and
district identifiers
Campus number; enrollment by
grade and program (e.g., special
education); charter school status;
alternative school status
Location and mailing addresses for
each school are available all years;
for schools with missing latitude and
longitude data (available starting
2000), we used EZ-Locate
(www.geocode.com)
Number of graduates entering the
freshman class from each public high
school in the state
Imputing missing test scores
In all of our analysis years, students were tested through the Texas Assessment of Academic
Skills (TAAS). We use the reading and math Texas Learning Index (TLI) scores which are designed
to assess learning progress. These scores describe how far a student’s performance is above or
below the passing standard (70), and range from approximately 0 to 100. Receiving the same score
in the following grade indicates the student has demonstrated one year’s typical progress, regardless
of where the student is on the scale. The TLI is not available for writing, since this exam is not
administered in consecutive grades, so we use the writing scale score. This score ranges from
approximately 400 to 2400, with 1500 representing minimum expectations. It is designed to allow
comparisons across years within a grade, adjusting for differences in test difficulty. The Texas
Education Agency Technical Digest (1998-99) describes in detail how the math and reading TLI
scores and the writing scale scores are created.
Appendix p.1
In order to rank students, we require 8th grade test scores for all students in our 8th grade cohorts,
as well as for students who attend 10th grade with these cohorts. We start by combining the sample
of all 8th graders in 1993 to 1998 and the sample of all 10th graders in 1995 to 2000, linking
observations from students that are in both 8th and 10th grades with their cohort.
Approximately 16 percent of 8th graders are missing reading and/or math scores. We impute
these using linear regressions on the best available subset of alternative 8th grade exams, including
writing. Scores on the alternative exams are entered as cubics. For those students with no available
scores, we assign the average across students with similar test code patterns on the other two 8th
grade exams (i.e., absent or exempt for the same set of exams). Those exempt due to special
education or limited English proficient (LEP) classification are assigned the minimum test score for
that exam. We are able to use alternative test scores in the imputation for 34 percent of students with
missing test scores. We do not use any information on future test scores, since these could be
endogenous to choices about which high school to attend.
Nearly one-third of 10th graders is missing either math or reading scores from two years prior
(meaning they were either not in 8th grade with their cohort or did not have their exams scored).
However, only one-quarter of these cases (primarily special education exempt students) have no
current or prior test score information to aid in the imputation. For those students with missing
scores who have alternative 8th or 10th grade scores available, we use linear regressions on the best
available subset to impute values. Included in the control set are cubics in 8th and 10th grade reading,
math, and writing scores, as well as indicators for students credited with automatic passes on the 10th
grade TAAS due to their scores on the end-of-year course examinations. For non-special education
students with no available 8th or 10th grade scores, we assign the average score for students with the
same missing test score patterns for all but the exam in question. For special education exempt
students with no prior scores, we assign the minimum test score for that exam. No students are LEP
exempt in 10th grade.
Predicting students’ class ranks
The main text describes how we assign students to a cohort-specific statewide ranking based on a
weighted average of 8th grade math and reading test score percentiles. Here we explain how we
chose the weights for this measure and how we incorporate the estimation error to proxy for
uncertainty.
Appendix p.2
We turn to the second follow-up of the National Education Longitudinal Study NELS data for
choosing weights since we cannot link 8th grade test scores to students’ actual high school class rank
(either in the high school they attend or in other possible high schools) in our main data set. The
NELS surveyed a nationally representative sample of 8th grade students in 1988. These students
were then followed as they progressed to 10th and 12th grade in 1990 and 1992. Students were
tested in reading and math in the base survey, and class rank and class size are reported in the
student’s senior year (or terminal year for dropout and alternative completers) allowing us to
compute a student’s percentile class rank.
Prior to analyzing the relationships between class rank and test scores, we first also convert the
NELS math and reading aptitude scores to percentile ranks and then downgrade their quality to
match that of the TAAS scores. In calculating the percentile test score ranks, we use the longitudinal
weights provided by NCES which are meant to adjust for unequal probabilities of selection into the
sample and non-response. The TAAS tests have many fewer distinct scores (approximately 65 vs. a
nearly continuous distribution on the NELS exams), and distinguish better among lower than higher
performers. We merge neighboring percentiles in the NELS data where the TAAS cumulative
distribution is flat, yielding an equally clumpy distribution.
Our prediction equations relate a student’s percentile class rank to the student’s adjusted math
and reading percentile ranks, with all percentiles computed to range from a low of zero to a high of
one. In order to address the fact that class rank is relative to the ability level of one’s peers, the
specifications also include high school fixed effects. We estimate the models using ordinary least
squares with observations weighted by the appropriate longitudinal sample weight, and report robust
standard errors.
Table A2 shows the results for both a TX-only and a nationally-representative sample. For both
the nation as a whole and for Texas, math and reading test scores explain slightly more than one
third of the variation in class rank within schools. The implied relative weight on math is quite
similar in Texas and the whole nation (0.69 vs. 0.65). Though we found some evidence for
nonlinearities in the underlying relationships, specifications that included squared and interacted test
score terms had only marginally greater explanatory power than our chosen specification. In
particular, allowing for nonlinearities does not improve our ability to accurately predict whether a
given student places in the top-10 percent of his or her class.
In order to calculate predicted ranks for students from the TX administrative data, we convert 8th
Appendix p.3
grade reading and math TAAS scores (or predicted scores if these are missing) into percentile scores
by cohort. We then calculate predicted percentile class ranks by applying the coefficients for the
TX-only sample in Table A2. As a final adjustment, we rescale the predictions to range from 0 to 1
within each cohort by replacing each predicted value with its percentile within the cohort-specific
distribution, to yield
.
When incorporating uncertainty, we assume the error distribution is normal and that the overall
standard deviation of the estimation error describes the distribution of the predicted rank for each
student (prior to the final adjustment). Although applying ordinary least squares ignores the special
nature of the dependent variable (which is uniformly distributed with unequal intervals, i.e., the
distance between 0.50 and 0.51 is not the same as between .90 and .91), we find that the errors are
approximately normally distributed and homoskedastic when the test score variables are also
specified as percentile ranks. So, our assumption of a common degree of uncertainty across the
distribution is not at odds with our estimation strategy.
Table A2. Predicting high school percentile class rank
NELS longitudinal 2nd follow-up sample
Independent variable
Texas-only
Nationally-representative
th
8 grade math percentile rank
0.493
0.466
(0.043)
(0.014)
8th grade reading percentile rank
0.226
0.251
(0.047)
(0.013)
Number of observations
787
10,918
R-squared
0.384
0.361
Correlation between math and
0.701
0.680
reading percentile ranks
Implied math relative weight
0.686
0.650
Notes: Each column reports the results from a separate ordinary least squares regression based on the sample indicated.
The dependent variable is the student’s percentile high school class rank, and ranges from 0 to 1. In addition to the
variables shown, the specifications also include high school fixed effects. Robust standard errors are shown in
parentheses. The R-squared is based on within-high school variation. The implied math relative weight is the ratio of
the estimated coefficient for the math test score measure to the sum of the coefficients for math and reading.
Predicting students’ likelihoods of applying to and being rejected by a flagship university
To compute the probability that a student would eventually apply to a selective public college,
we again utilize the NELS data. We use the sample of students in the Third-Follow Up of the NELS
with non-missing 8th grade test scores. The survey provides information on two application schools,
the two the student believed he/she was most likely to attend. We then identify which of the
Appendix p.4
applications were to selective in-state public four-year institutions, using the 1992 Barron’s Guide to
assign selectivity. We use probit specifications to estimate the probability of application conditional
on predicted class rank, calculated using the strategy described above.
Though the NELS also reports the outcomes of applications, these data appear to be
contaminated by the wording of the question. Rejection rates conditional on applying are nonmonotonic across the achievement distribution, and in particular, implausibly low toward the
bottom. For the TX flagship institutions, we have information on the outcome of applications for
several pre-Hopwood years (Texas Higher Education Opportunity Project, 1992-1996). We apply
the coefficients from Table A1 to verbal and quantitative SAT percentile scores to rank applicants, in
order to determine how the likelihood of rejection at one of the flagships evolves across the
applicant-only achievement distribution. Assuming this same pattern applies, we impute conditional
and then unconditional rejection rates for our NELS and then our Texas students.
Appendix p.5