Draft: Please Do Not Cite Without Permission
Schooling Decisions and Student Achievement Outcomes
under Interdistrict Open Enrollment
Deven Carlson
University of Oklahoma
Lesley Lavery
Macalaster College
Tyler Hughes
University of Oklahoma
September 2013
Abstract
Motivated by a simple model of cross-district choice, this paper presents empirical analyses of
three dimensions of Colorado’s statewide mandatory interdistrict open enrollment policy—the
characteristics of participants, the schooling decisions that participants make through the
program, and the relationship between interdistrict open enrollment participation and student
achievement outcomes. Our analyses indicate that open enrollment participants
disproportionately come from disadvantaged districts, although the students who participate are
among the more advantaged within those districts. The analyses further suggest that students
consider both quality and demographic composition of districts when making open enrollment
decisions, although there is heterogeneity along racial/ethnic lines in some of the measures of
these dimensions. Finally, we find open enrollment participation to have little effect on
achievement outcomes for the full sample of participants, although there is some evidence that it
has a negative effect on the achievement of Black students. We discuss the implications of these
results for research and policy.
1
1. Introduction
Virtually nonexistent only 25 years ago, today interdistrict open enrollment programs
operate in a large majority of states and millions of students use these programs annually to
attend schools located outside their district of residence. Despite the broad reach of these policies,
we know little about their operations and effects, especially relative to more visible school
choice policies such as private school vouchers, charter schools, or even magnet schools. There
has been a small amount of student-level research on the characteristics of open enrollment
participants (e.g, Phillips, Hausman, and Larson 2012; Lavery and Carlson 2013) and the effects
of open enrollment policies on student achievement outcomes (e.g., Bifulco, Cobb, and Bell
2009), but the only analyses of schooling decisions made by participants in these programs rely
on district-level data and can thus provide only limited insight into the topic (Reback 2008;
Welsh, Skidmore, and Statz 2010; Carlson, Lavery, and Witte 2011).
Motivated by a simple model of cross-district choice, this paper draws on individual-level
data from the universe of students attending Colorado public schools between 2005-06 and 200910 to present empirical analyses of three dimensions of Colorado’s statewide mandatory
interdistrict open enrollment policy—the characteristics of participants, the schooling decisions
that participants make through the program, and the relationship between interdistrict open
enrollment participation and student achievement outcomes. The results of our analysis reveal
that a broad range of factors—district achievement, socioeconomic composition, distance, and
others—play a role in the schooling decisions that families make under interdistrict open
enrollment policies. Some of these factors relate to schooling decisions in ways that are largely
predictable, but other factors enter into the decision calculus in less expected ways. Our results
also reveal substantial heterogeneity in the determinants of schooling decisions across
demographic and socioeconomic subgroups. Finally, we find open enrollment participation to
2
have little effect on achievement outcomes for the full sample of participants, although there is
some evidence that it has a negative effect on the achievement of Black students.
Taken as a whole, our analysis provides a broad perspective on the operation of
interdistrict open enrollment policies. We proceed by first providing an overview of interdistrict
open enrollment policies—devoting particular attention to the Colorado context—before
presenting the conceptual framework that underlies our analysis. We then describe the data we
use in our analyses, detail the specific analytical approach we take, and present the results of our
analysis. We close with a discussion of the implications of our results for both research and
policy.
2. Interdistrict Open Enrollment: Background and Context
Interdistrict open enrollment programs take two primary forms—voluntary and
mandatory. Voluntary policies permit school districts to decide whether or not to accept student
transfers from other districts. Mandatory policies, in contrast, require school districts to accept
transfers from other districts, although the policies typically specify a set of conditions under
which districts can legally refuse to accept transfers; we discuss the most common of these in
greater detail below. Both voluntary and mandatory policies generally prohibit districts from
restricting student transfers out of the district.
Although interdistrict open enrollment programs were among the first school choice
policies to appear on the educational landscape, they are still relatively recent additions. The
earliest voluntary programs only began to emerge in the early 1980s and the first mandatory
statewide program did not exist until the implementation of Minnesota’s policy in 1991 (Boyd,
Hare, and Nathan 2002). Enactment of that program, however, commenced a wave of state
adoptions and by 2011 only 15 states and the District of Columbia were without some form of
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interdistrict open enrollment (National Center for Education Statistics 2012). Table 1 presents
the number of states with voluntary and mandatory interdistrict open enrollment policies.1
[Insert Table 1 about here]
Our empirical analyses below rely on data from Colorado, which operates a mandatory
statewide program. Consequently, we discuss this class of policy—both generally and in the
specific context of Colorado—in further detail. Although the specifics of mandatory interdistrict
open enrollment policies vary across states, there are three foundational features of these
programs. First, the policies specify a process that allows students to attend public schools
located outside their district of residence. Historically, public school students have been
required—almost without exception—to attend the school specified by the district in which they
reside. Second, although by definition mandatory policies require districts to accept transfers
from other districts, they also typically specify a set of conditions under which school districts
can legally refuse to accept interdistrict transfers. The list of allowable conditions for transfer
refusal varies across states, but a lack of capacity and an applicant’s history of behavioral
problems—such as a record of suspension, expulsion, or substance abuse—are the two most
common conditions specified by state policies. Third, interdistrict open enrollment policies
generally specify that per-pupil state aid follows program participants; funds are disbursed to the
district of attendance rather than the district of residence. The precise amount of funding
accompanying a student transferring across district lines varies by state, but it is almost certainly
greater than the marginal cost of serving an additional student (Reback 2008).
1
Table 1 makes clear that two states have both voluntary and mandatory interdistrict open enrollment policies. In
most of these cases, the mandatory policies require districts to accept transfers with a specific characteristic (e.g. low
test scores, a learning disability, etc.) while acceptance of students without the specified characteristic(s) is
voluntary.
4
In addition to these three foundational aspects of mandatory interdistrict choice policies,
two other features of these transfer programs—transportation and desegregation policies—
warrant brief discussion. Transportation is a major challenge faced by states implementing an
interdistrict choice policy; there is no obvious solution for transporting program participants
from their district of residence to the district they choose to attend. Over time, states have
addressed issues of transportation in three primary ways. One set of states places all
transportation responsibilities upon the parents of transferring students while a second group of
states mandate that the district of residence provide all necessary transportation. Finally, a third
collection of states do not address the issue of transportation at all in their open enrollment
policies, thus leaving the issue to be sorted out by parents, the district of residence, and the
district of attendance. In addition to variance in the responsibility for providing transportation,
state policies also differ in the amount of funding provided to support the transportation of
interdistrict transfers. Policies range from providing no transportation funding at all to fully
reimbursing districts for the costs associated with busing interdistrict transfers.2
Finally, many states’ interdistrict transfer policies have historically permitted districts to
refuse transfers—both into and out of the district—if the transfer would either violate the
provisions of an established desegregation policy or upset the racial or socioeconomic balance of
the district. The legality of such provisions, however, is in doubt after the recent U.S. Supreme
Court decisions in Parents Involved in Community Schools Inc. v. Seattle School District and
Meredith v. Jefferson County (Ky.) Board of Education, which prohibited schools and districts
from considering race in school admissions processes.
The Education Commission of the States maintains a database that describes several features of each state’s
interdistrict open enrollment policy. The database can be found at:
http://ecs.force.com/mbdata/mbtab4ne?sid=a0i70000000Xk5v&rep=OET
2
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2.1.
Colorado’s Statewide Mandatory Interdistrict Open Enrollment
Program
Colorado’s mandatory interdistrict transfer program is authorized by The Public Schools
of Choice Act of 1990 (C.R.S. 22-36-101). Beginning with the 1994-95 school year, this
legislation allowed students to attend any public school in the state without paying any tuition to
the district in which the school was located. Like most mandatory interdistrict transfer policies,
however, there are five conditions under which Colorado districts can legally refuse to accept a
transfer application:





A lack of space or teaching staff required to serve the student;
The district or school is not equipped—either physically or with respect to curriculum—
to serve the student;
The student does not meet established eligibility criteria for participation in a requested
program;
Admission of the student would violate the terms of an established desegregation plan;
The student has been expelled from another district.
There is one more notable provision of Colorado’s interdistrict choice policy concerning student
admission. Specifically, the policy states that if the number of transfer applications received by a
district exceeds the number of available seats, the district is urged—but not required—to give
enrollment priority to applicants who attend a low-performing school and achieve a proficiency
level of unsatisfactory in one or more academic subjects according to the Colorado Student
Assessment Program. With respect to funding, Colorado’s policy mirrors most programs
nationally by disbursing state aid associated with a transferring student to the district of
attendance. Finally, issues of transportation are not addressed in the relevant statutes.
Colorado’s interdistrict open enrollment program quickly grew to serve a significant
number of students. By the 2000-01 school year—only six years after the inception of the
program—over 20,000 students were using the policy to attend a school located outside their
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district of residence.3 Over the following decade the program tripled in size and in recent years it
has served in excess of 68,000 students. Table 2 presents the number of students attending a
school located outside their district of residence. For purposes of comparison it also presents the
total K-12 enrollment in public schools in Colorado as well as the number of students enrolled in
the state’s charter schools. The table indicates that about 3.2 percent of students attended a
school located outside their district of residence during 2000-01 school year while approximately
8.1 percent of students did so in the 2011-12 school year. The corresponding numbers for
charter school enrollment are 2.9 and 9.1 percent, respectively.
[Insert Table 2 about here]
2.2.
Previous Research
Relative to the amount of scholarship on other school choice policies such as charter
schools and private school vouchers, the research literature on interdistrict open enrollment is
fairly limited. In the years after the initial wave of states adopted interdistrict choice policies—
Minnesota, Massachusetts, Wisconsin, Ohio, and others—a small number of studies provided
descriptive information about these programs. In the context of Massachusetts, both Fossey
(1994) and Armor and Peiser (1998) used simple mean comparisons to examine differences
between districts that were net senders versus net receivers of transferring students. Both studies
found net receiving districts to be more advantaged than net senders on several measures; median
family income, adult education, achievement scores, dropout rates, and per-pupil expenditures.
In Ohio, Fowler (1996) surveyed district superintendents and asked about the factors that
influenced their decision to participate (or not) in the state’s voluntary interdistrict transfer
program. Participating superintendents cited the desire to increase enrollments and funding as the
Data on the number of students utilizing Colorado’s interdistrict open enrollment program are not available prior to
the 2000-01 school year.
3
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primary driver of their decision. Superintendents who opted out of the program generally
reported a lack of space as motivation for denying transfers.
There was little scholarly analysis of interdistrict transfer policies in the decade or so
following these early studies, but there has been renewed interest in these programs in recent
years. This recent research can usefully be grouped into two main categories. The first set of
studies analyzes the effects of interdistrict transfer programs on outcomes of interest, including
student achievement, racial and socioeconomic segregation, and home values. Only two studies
examine the effect of interdistrict open enrollment programs on student achievement, but both
report positive results. Bifulco, Cobb, and Bell (2009) examine the effect of Connecticut’s
interdistrict magnet transfer programs and find it to have a positive effect on the achievement
scores of participants. In the context of Wisconsin, Welsch and Zimmer (2012) find positive
systemic effects of the state’s cross-district transfer program; districts that experience large
student losses exhibited improved test scores in the subsequent year. Studies of the stratifying
effects of interdistrict choice programs reach more varied conclusions. The Institute of
Metropolitan Opportunity (2013) found Minnesota’s cross-district transfer program to
significantly increase racial stratification across districts while Powers, Topper, and Silver (2012)
found Arizona’s program to have no such effects. Carlson’s (2013) analysis concludes that
Colorado’s program produces a decrease in racial segregation across districts, but a slight
increase in socioeconomic stratification. Considered together, these studies suggest that the
segregating effects of interdistrict transfer programs are likely context-specific.4
The second group of studies focuses on the operations of interdistrict transfer programs,
including characteristics of program participants and the correlates of cross-district transfer flows
4
Brunner, Cho, and Reback (2012) examine—both theoretically and empirically—the effect of interdistrict open
enrollment on residential location decisions and housing values. They find that school districts located near highquality schooling options exhibit significant increases in both housing values and population density.
8
or schooling decisions made by program participants. Two analyses have used student-level data
from Colorado to examine the characteristics of program participants. These studies provide
evidence that participants are disproportionately non-white and come from socioeconomically
advantaged contexts (Lavery and Carlson 2013; Holme and Richards 2009). Furthermore,
students with special designations—such as gifted and talented, English language learner, or
IEP—are much less likely to open enroll than their peers without those designations. Powers,
Topper, and Silver (2012) report similar findings from an analysis of 27 metropolitan Phoenix
school districts.
Several studies have used district-level data to examine the characteristics associated with
interdistrict transfer flows. These studies have been conducted in the contexts of Minnesota
(Reback 2008), Wisconsin (Welsch, Statz, and Skidmore 2010), and Colorado (Holme and
Richards 2009; Carlson, Lavery and Witte 2011). The analyses vary in their details, but they all
provide evidence that—at least to some degree—transfer flows are correlated not only with
district-level achievement scores, but also the demographic makeup, financial characteristics,
and structural considerations, such as distance. Although these studies provide valuable
evidence into the schooling decisions made by interdistrict open enrollment participants, the
inferences that can be drawn from the studies are limited by their reliance on district-level data.
Below we detail our approach to assessing whether similar conclusions emerge from analysis of
five years of student-level data on the universe of students attending Colorado public schools.
3. A Simple Model of Interdistrict Choice
Drawing upon previous theoretical work (e.g., Lankford and Wyckoff 1992; Lankford,
Lee, and Wyckoff 1995; Deming, Hastings, Kane, and Staiger 2011) we present a simple model
of interdistrict choice as motivation for our empirical analysis. The model begins with families
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distributed across school districts and all children assigned to attend a school located in—and
operated by—the district in which they reside. The presence of an interdistrict choice program,
however, allows families the option of enrolling their child in a district other than the one in
which they reside. Under this scenario, each household assesses the utility it would receive from
each district schooling option, where Uik, k = 1, 2,…K, is the utility that household i would
receive from enrolling its child in school district k. The set of K schooling options includes
households’ district of residence, r. After evaluating the utility expected by each schooling
option, the household elects to enroll its child in the district that maximizes utility. The
household will participate in the interdistrict open enrollment program if
Uir < Uik for any k ≠ r
(1)
We specify household utility in this model as a function of district quality, the
demographic composition of the district, travel and search costs, and—following Deming et al.
(2011)—an unobserved “fit” between households and each district alternative. More formally,
Uik = U(Qk, Dik, Cik, λik)
(2)
where Q represents observable measures of quality—such as average standardized test scores—
that are broadly valued by households, D represents the socioeconomic and demographic
makeup of a district that each household may value differently, C represents the travel and search
costs associated with attending a given school district, and λ is the unobserved fit noted earlier.
Following Deming et al. (2011) we assume λ is distributed normally with mean zero and
variance σ2. We further assume λ is independent of Q and also independent across district
options for a given household. We specify the household utility function as linear and assume
that each component enters it additively:
Uik = Qk + Dik - Cik + λik
(3)
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Because we assume λ ~ N(0, σ2), it is the case that E(Uik) = Qk + Dik - Cik and we can
rewrite (1) as
Qr + Dir - Cir + λir < Qk + Dik - Cik for any k ≠ r
(4)
Normalizing C such that the cost of attending the district of residence is zero produces
Qr + Dir + λir < Qk + Dik - Cik for any k ≠ r
(5)
which can be rearranged to produce
λir < (Qk - Qr) + (Dik - Dir) - Cik for any k ≠ r
(6)
Under this model a family will open enroll out of their district of residence if there is any
district where the combination of quality and demographic gains—less travel and search costs—
provide more utility than the unobserved “fit” with their district of residence. The inclusion of λ
in the model provides a justification, other than travel and search costs, for families that do not
open enroll out of an observably poor district. However, the model still predicts that families are
increasingly likely to open enroll as Qr and Dir decline, and as Qk and Dik increase. Finally, if
there are multiple nonresident districts that satisfy (6), the utility maximizing nature of
households leads them to select the district with the largest net gain.
4. Data
Our empirical analysis draws on a dataset constructed from student-level records
maintained by the Colorado Department of Education (CDE) supplemented with information
from the U.S. Census Bureau. Beginning with the 2005-06 school year and extending through
2009-10, the CDE records contain annual information—enrollment status, demographic and
socioeconomic characteristics, achievement outcomes, and school and district measures—on the
universe of students attending public schools in Colorado.
11
The enrollment information included in the CDE records include a unique student
identifier as well as annual records of the school each student attends and the district in which it
is located.5 In addition to recording the district of attendance, the data also indicate whether a
student attended a school operated by a district other than the one in which they reside—a
measure of open enrollment. For open enrollers, the data also record an identifier for the
students’ district of residence. Along with the individual-level information, the dataset also
contains relevant contextual data on the schools and districts that students attend, such as dropout
rates, mobility statistics, disciplinary information, staff data, available postsecondary options,
fiscal information, and socioeconomic composition. For students who open enroll, this
information is also available for students’ district of residence.6
Our data contain standard demographic characteristics—age, grade, gender,
race/ethnicity—as well as measures of several other characteristics such as gifted and talented
status, free or reduced lunch status, disability status, English language learner status, a measure
of language proficiency, and students’ primary language. The CDE records also contain student
achievement results. Specifically, the data record students’ scale scores on the reading and math
portions of the Colorado Student Assessment Program (CSAP), which was administered to all
students in grades 3-8 and 10 to meet the accountability provisions of the No Child Left Behind
Act. We standardized the CSAP scale scores using the statewide mean and standard deviation
for the proper year, grade, and subject. Taken as a whole, the dataset we created from the CDE
5
More specifically, the data contain a record for each school attended by a student during a given school year. The
fact that the data contain multiple observations for students who attended more than one school in a given year
represents a potential complication for student-level analyses. To address this issue, we implemented the following
decision rule. First, for students with test scores, we kept the record containing the school in which the student was
tested. This eliminated approximately half of the duplicate records. For the remaining students with multiple
records—those without test scores—we kept the record in which the disposition code listing the reason that a student
left a school was not applicable; in effect, we kept the student record for the school in which a student finished the
year.
6
The data do not contain a record of the “school of residence” for open enrolling students. Consequently, we do not
possess information about the schools out of which students are open enrolling.
12
records contains nearly 4.3 million observations from approximately 1.25 million unique
students. We have extensive information on each student’s demographic and achievement
profile, their open enrollment status, and data on the schools that students attend and the districts
in which they reside.
As the final step in creating our dataset, we supplemented the student-level CDE records
with geographic data on school districts maintained by the U.S. Census Bureau. Specifically, we
used ARCGIS software to calculate the geographic centroid of each school district and then, for
each student-year observation, merged the longitude and latitude coordinates of the district of
attendance into the dataset. For students who open enroll, we also merged the latitude and
longitude coordinates for the district of residence. These geographic coordinates play an
important role in our analyses, as we describe in greater detail below.
5. Empirical Analysis
Our model of interdistrict choice presents testable propositions for several dimensions of
open enrollment policies, including the characteristics of participants, the schooling decisions
participants will make through the program, and—more indirectly—the educational outcomes
that participants might exhibit. Here we explicitly identify the testable propositions within each
of these dimensions and describe our approach to testing each of them empirically.
5.1.
Characteristics of Participants
The model presented above provides two main insights into the characteristics of
interdistrict open enrollment participants. First, it holds that individuals with a good “match”
with their district of residence will be less likely to open enroll, all else equal. Empirically, we
might expect that families who have children with certain characteristics and educational
designations—such as gifted and talented or special educational needs—select their district of
13
residence with careful consideration of how it “matches” their child on such dimensions. If
accurate, students with these characteristics would be less likely to open enroll. Similarly, it is
reasonable to expect that—all else equal—students with low achievement levels might perceive a
poor “match” with their district of residence and thus be more likely to open enroll. Second, the
model makes clear that open enrollment becomes increasingly likely as Qr and Dir decline. That
is, a student will be more likely to open enroll as the quality of his district of residence declines
or as its demographic profile becomes less desirable, a perception that may vary by student.
We begin to assess whether these theoretical predictions are corroborated empirically by
first presenting descriptive characteristics on the characteristics of interdistrict open enrollment
participants. The top panel of Table 3 presents individual-level characteristics of participants for
each of the five years in our dataset while the bottom panel presents average characteristics of
participants’ district of residence for each year over this time period. In both cases the
characteristics of nonparticipants are presented to provide a point of comparison. Overall, the
statistics presented in Table 3 are largely consistent with the expectations laid out above.
Specifically, Table 3 demonstrates that students with the designations noted previously—special
education, gifted and talented, and ELL—all open enroll at disproportionately low rates.
Moreover, the district-level characteristics are also generally in line with expectations. Open
enrollers reside in districts that fare worse on several common measures of school quality—
dropout rates, truancy rates, Advanced Placement (AP) course offerings, and average district
achievement, at least in some years—relative to their non-open enrolling peers.
Demographically, open enrollers reside in districts with higher levels of students eligible for free
or reduced-price lunch, relative to non-open enrollers. The evidence regarding the relationship
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between student achievement and open enrolling is more mixed; students who open enroll have
slightly lower math scores, but somewhat higher reading scores.
[Insert Table 3 about here]
To further explore this issue, we estimate a simple logistic regression model that predicts
interdistrict open enrollment participation during the 2006-07 school year as a function of
student characteristics as well as the characteristics of a student’s district of residence and can be
written as:
Pr⁡(𝑂𝑖𝑑2006 = 1) = 𝑙𝑜𝑔𝑖𝑡 −1 (𝜹𝑺𝒊𝟐𝟎𝟎𝟓 + 𝜽𝑫𝒅𝟐𝟎𝟎𝟓 )
(7)
where the probability that student i residing in district d open enrolls in 2006-07 is a function of a
vector of student and family background characteristics, S, and a vector of characteristics of the
student’s district of residence, D; logit-1 (x) = ex/(1+ex). The variables contained in S and D
mirror those presented in Table 3. Results from this model, which we estimate separately for
kindergarteners, 6th graders, and 9th graders, are presented in Table 4 and are mostly consistent
with the bivariate results presented in Table 3. Specifically, Table 4 again demonstrates that
students with special designations are less likely to open enroll and students who reside in
districts with lower levels of quality on the measures noted above are more likely to open enroll,
even conditional on other factors. Finally, the mixed findings regarding the relationship between
achievement and open enrollment participation that were observed in Table 3 are also present in
the multivariate results.
[Insert Table 4 about here]
5.2.
Schooling Decisions
In addition to insights about the characteristics of participants, the theoretical model also
presents testable propositions regarding the schooling choices made by open enrollment
participants. Specifically, the model holds that the probability of open enrolling into a given
15
district is increasing in both the quality of that district and the desirability of the demographic
profile—represented by Qk and Dik, respectively—while decreasing in travel and search costs, Cik.
As the starting point for assessing these predictions we used our data to construct,
uniquely for each kindergartener observed open enrolling in our data, a choice set containing all
districts located within 100 miles of the student’s district of residence.7 Then, using this dataset
containing the district choice sets of all 16,747 open enrolling kindergarteners, we estimated the
following conditional logistic regression model of the district each student chooses to attend:
Pr⁡(𝑆𝑖𝑘 = 1) = 𝑙𝑜𝑔𝑖𝑡 −1 (𝜹𝑸𝒌 + 𝜽𝑫𝒌 + 𝜷𝑪𝒊𝒌 + 𝜸𝒊 )
(8)
where, S represents school districts in an individual’s choice set, i and k index individuals and
school districts, respectively; Q represents a vector of observable school quality measures, such
as average district achievement, the truancy and dropout rates, and the number of AP courses
offered; D represents a vector of observable district demographic characteristics, including the
racial/ethnic composition of the district and the percentage of students eligible for free or
reduced-price lunch; C represents the costs of open enrolling, operationalized as the distance
from an individual’s district of residence, and 𝜸 is a student fixed effect.
To construct each student’s choice set we first created a dataset containing every pairwise combination of open
enrolling kindergarteners and Colorado school districts. Then, using the school district centroids in our data, we
used the Great Circle Distance Formula to calculate the distance between each student’s district of residence and
every other school district in Colorado. The Great Circle Distance Formula is calculated as follows: distance =
3963.0 * arccos[sin(lat1/57.2958) * sin(lat2/57.2958) + cos(lat1/57.2958) * cos(lat2/57.2958) * cos(lon2/57.2958 lon1/57.2958)]. Upon calculation of the distances between a student’s district of residence and all other Colorado
school districts we deleted those observations containing districts that were more than 100 miles from the student’s
district of residence. We also deleted observations containing students’ districts of residence. The 100 mile cutoff
may seem excessive upon first glance, but two main reasons underlie our belief that it is not. First, the distances are
measured from the geographic center of one district to the geographic center of another. It is clearly not the case
that all students live at the geographic centers of school districts, and we wanted our cutoff to account for this
reality. Second, the cutoff of 100 miles was located at approximately the 98th percentile of observed distances.
Specifications using cutoffs of 120 miles and 75 miles were also tested and the results were substantively similar
and are available from the authors. Finally, we exclude any observed flows that exceeded 100 miles from the
dataset. These represented a very small proportion of cases and are most likely attributable to enrollment in virtual
schools. Virtual schools are undoubtedly an important topic of study, but they are beyond the scope of this analysis;
we are only interested in interdistrict transfers where students physically attend a district other than the one in which
they reside.
7
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Table 5 presents the results from this model and although there are some unanticipated
outcomes, the results are largely consistent with the theoretical expectations developed above.
Most notably, the coefficient on average district achievement—the most common, if imperfect,
measure of educational quality—is positive and significant, as is the coefficient on the number of
AP courses offered by the district. Additionally, the coefficient on the district truancy rate is
negative, but not statistically significant. Taken together, these results support the proposition
that the probability of enrolling into a given district increases as its quality rises. The results in
Table 5 also lend empirical support to the proposition that individuals become less likely to open
enroll into a district as the cost of doing so increases, as evidenced by the negative and highly
significant coefficient on the distance measure. Finally, the results indicate that individuals
became less likely to open enroll into a given district as the percentage of students eligible for
free or reduced-price lunch increased, but more likely to do so as the percentage of students who
were Black or Hispanic increased.
[Insert Table 5 about here]
Although the results in Table 5 clarify the direction and statistical significance of the
relationships between district characteristics and schooling decisions, the substantive magnitudes
of the relationships are somewhat more difficult to discern. Consequently, we present Figure 1,
which plots the predicted probability of selecting a given district across the observed range of
each of the nine variables in the model when all other variables are held at their mean. Figure 1
makes clear that travel cost—as measured by distance—exerts the strongest substantive effect on
district choices, with a predicted probability of nearly 0.4 for districts that are very close to a
student’s district of residence all the way down to approximately 0.01 for districts that are 100
17
miles away.8 The plots also indicate that enrollment is a substantively meaningful determinant
of schooling choices. All else equal, students are much more likely to open enroll into a large
district than a small one. Although the data do not permit any firm inferences regarding the
mechanisms responsible for this result, we speculate that enrollment into large districts may be at
least partially driven by the availability—or expected availability—of particular educational
programs or opportunities that the family perceives will be a good match for their child. This
speculation could be examined empirically in future research.
[Insert Figure 1 about here]
Moving on to the measures of educational quality and district demographics, the plots in
Figure 1 reveal that, while statistically significant, the relationships between schooling decisions
and these measures are weaker, substantively speaking, than the distance and enrollment
variables. For most of these measures, including the percentage of students eligible for free or
reduced-price lunch and the variables measuring the racial or ethnic composition of the district,
the change in the predicted probability of a student enrolling into a district at the observed
minimum versus enrolling into a district at the observed maximum is in the range of
approximately 0.05 to 0.10, depending upon the specific quality or demographic measure. The
single unexpected result in Figure 1 is the positive relationship between the district dropout rate
and open enrollment decisions, a result potentially attributable to the large inflows into Denver.
5.2.1. Heterogeneity by Socioeconomic Status and Race/Ethnicity
Recent research on families’ schooling preferences suggests that, all else equal, families
prefer schools where the student body matches their demographic and socioeconomic profile
(e.g., Hastings, Kane, Staiger 2008). Our model of interdistrict choice recognizes this potential
for preference heterogeneity by allowing the definition of a desirable district demographic profile
8
This result lends further support to our choice of the 100 mile cutoff.
18
to vary by student. Empirically, we assess the extent to which such heterogeneity is present by
estimating equation (8) separately for White students, Black students, and Hispanic students as
well as for students who are and are not eligible for free or reduced-price lunch.
[Insert Table 6 about here]
The results disaggregated by race/ethnicity are presented in the first three columns of
Table 6 and the plots of the accompanying predicted probabilities—analogous to those in Figure
1—are presented in Figure 2. The results indicate that students in all three racial/ethnic groups
we analyze become less likely to open enroll in a given district as the proportion of students
eligible for free or reduced-price lunch in that district increases; the preference for attending
socioeconomically advantaged districts appears to be common across racial/ethnic groups.
However, the relationships between schooling decisions and the racial/ethnic composition of
school districts differ across the three racial/ethnic groups we analyze, a finding consistent with
previous research. For example, Figure 2 demonstrates that both White and Hispanic students
become increasingly likely to open enroll into a district as the proportion of Hispanic students in
the district increases. For Black students, however, the relationship is negative and significant.
There is a positive relationship between the district into which a student open enrolls and the
percentage of Black students for all three groups, but the relationship is substantively stronger
for Black and White students relative to Hispanic students.
There is also heterogeneity across these three groups along the quality and cost
dimensions. Perhaps most notably, the relationships between schooling decisions and the
average standardized test scores in a district vary across the three racial/ethnic groups; the
relationship is strong and positive for White students but negative and significant for Black
students; there is no statistically discernible relationship for Hispanic students. With respect to
19
distance, Figure 2 indicates that the relationship between distance and open enrollment decisions
is stronger for White and Hispanic students than for Black students. Similarly, the relationship
between district enrollment and the likelihood of open enrolling into a given district is weaker
for Black students than it is for their White or Hispanic peers.
[Insert Figure 2 about here]
The fourth and fifth columns of Table 6 present the respective results from separate
estimation of equation (8) over students who are not eligible for free or reduced-price lunch and
those who are eligible to received subsidized meals. The accompanying predicted probabilities
for these groups are presented in Figure 3. These results identify some measures of district
demographics for which the two groups exhibit substantively similar results. For example, both
groups become less likely to open enroll into a given district as the proportion of students
eligible for free or reduced-price lunch increases. On other demographic measures, however, the
two groups diverge in their results. Specifically, relatively to their eligible peers, students who
are not eligible for subsidized lunches become increasingly likely to enroll into a given district as
the proportion of minority students—both Black and Hispanic—increases. Figure 3 also
demonstrates differential results for the two groups on some of the district quality measures, such
as average district standardized test score or the truancy rate. For both measures,
socioeconomically advantaged students become more likely to enroll into a given district as its
quality increases; the corresponding relationships for students who are less socioeconomically
advantaged are either negative or null.
[Insert Figure 3 about here]
20
5.3.
Student Achievement Outcomes
Our model of interdistrict choice produces clear predictions about the characteristics of
participants and the schooling decisions they will make, but it only indirectly addresses the issue
of how interdistrict open enrollment participation might affect student educational outcomes.
Specifically, the model addresses this issue to the extent that it incorporates district quality into
the schooling decision process. The empirical analyses presented provide evidence that families
do incorporate district quality as a consideration in their schooling decisions under interdistrict
open enrollment. Furthermore, the analyses disaggregated by demographic and socioeconomic
subgroups suggest that quality considerations play a larger role in schooling decisions for some
subgroups than for others. Considered together, these findings provide a basis for expecting that
interdistrict open enrollment could improve the achievement outcomes of participants.
At the same time, however, both our model and empirical analyses make clear that school
quality is not the sole determinant of families’ schooling choices—demographics and
convenience play a large role. Furthermore, there are features of open enrollment participation
that could have a negative effect on student achievement and other educational outcomes.
Notable among these is the fact that open enrollment participation typically requires students to
switch schools, and there is a large body of scholarship demonstrating that switching schools
often has a disruptive effect on academic achievement, at least initially (Alexander, Entwisle,
and Dauber 1996; Hanushek, Kain, and Rivkin 2004; Ingersoll, Scamman, and Eckerling 1989;
Kerbow, Azcoitia, and Buell 2003; Lash and Kirkpatrick 1990, 1994; Rumberger et al. 1999;
South, Haynie, and Bose 2007; Temple and Reynolds 1999; Xu, Hannaway, and D’Souza 2009;
Zimmer et al. 2009; Engberg et al. 2012). Thus, the overall effect of open enrollment
participation on student educational outcomes is a question of whether the potential positive
aspects of participation—such as increased school quality or an improved educational “match”
21
with a student’s interests or needs—are greater than the relevant negative features, such as the
penalty for switching schools. Given the theoretical ambiguity, we estimate a series of models to
gain empirical insight into the matter.
We analyze the relationship between student achievement and interdistrict open
enrollment participation using two techniques that are well-suited to the panel structure of our
data. We first specify a series of models containing a lagged outcome measure on the right-hand
side—we take a value-added approach. Such an approach has been used in the analysis of other
school choice programs, including charter schools (e.g., Hanushek et al. 2007; Sass 2006),
private school vouchers (e.g., Witte et al. 2011; Carlson, Cowen, and Fleming 2013), and even
open enrollment programs (Bifulco, Cobb, and Bell 2009). The primary appeal of the valueadded approach is that it represents a straightforward way to control for the accumulation of
factors and experiences—both observed and unobserved—that may affect current achievement;
it possesses the implicit ability to control for factors that evolve over time. The model we
estimate can be written as:
𝑌𝑖𝑟𝑡 = 𝑌𝑖𝑟𝑡−1 + 𝜃𝑋𝑖𝑟𝑡 + 𝛿𝑂𝑖𝑟𝑡 + 𝜓 + 𝜀𝑖𝑟𝑡
(9)
where student achievement, Y, for student i in district of residence r at time t is a function of
lagged achievement, a vector of observed demographic characteristics X, an indicator of
interdistrict open enrollment participation O, a grade-by-year-by-district fixed effect 𝜓, and an
error term capturing additional unmeasured influences 𝜀.9 We estimate the model via OLS
separately for reading and math achievement.
The results from estimation of this model are presented in the bottom panel of Table 7.
For purposes of comparison, the top two panels of Table 7 present results from estimation of
9
The district component of the grade-by-year-district fixed effect is the district of residence, not the district of
attendance.
22
slight variants of the model presented in equation 9; the top panel presents results from a model
containing just a measure of lagged achievement while the middle panel presents results from a
model containing lagged achievement and the vector of demographic characteristics. Overall,
the results are substantively similar across the three specifications and they suggest that open
enrollment participation has little substantive effect on student achievement in either subject.
Although all estimates of the relationship between open enrollment participation and math
achievement are negative and statistically significant, the magnitudes of these estimates are only
approximately 0.01 standard deviations. In reading, the estimates are positive and significant,
but similarly small from a substantive standpoint.
[Insert Table 7 about here]
To assess whether these results are robust to an alternative analytical approach we
estimate a second model containing a student fixed effect. This approach removes threats of bias
from all time-invariant characteristics—observed or unobserved—and the resulting estimates
from this model should be interpreted as the effect of interdistrict open enrollment participation
on a student’s level of achievement. This contrasts with the estimates produced from the valueadded model depicted in equation (9), which represent the effect of interdistrict open enrollment
participation on student achievement growth. The student fixed effects model we estimate can
be written as:
𝑌𝑖𝑟𝑡 = 𝛼𝑖 + 𝜃𝑋𝑖𝑟𝑡 + 𝛿𝑂𝑖𝑟𝑡 + 𝜀𝑖𝑟𝑡
(10)
where 𝛼 represents the student fixed effect and the remaining contents of the model were
described previously. Results from estimation of equation (10) are presented in the middle panel
of Table 8. For comparison purposes, the top panel of the table presents the results of the model
containing just the student fixed effects and the open enrollment indicator—there are no time-
23
varying demographics. The results from these two model variants are virtually identical and
indicate that open enrollment participation decreases students’ math and reading achievement by
approximately 0.06 and 0.03 standard deviations, respectively.
[Insert Table 8 about here]
In each subject, the student fixed effects estimates of the relationship between student
achievement and open enrollment participation are 0.03 to 0.04 standard deviations lower than
the corresponding value-added estimates. To gain insight into whether these discrepancies are
attributable to different analytic samples—the value-added model includes a lagged outcome
measure and thus excludes a year of observations—or the different techniques utilized, we
estimated equation (10) over the value-added analytic sample. These results are presented in the
bottom panel of Table 8. In math, the results are substantively similar to the full-sample results,
but in reading they are noticeably more negative. Together, these results suggest that the
divergent results between the value-added and student fixed effects models are attributable to the
different estimation techniques, rather than different analytic samples. The difference in the
results across the two analytic approaches is consistent with open enrolling being an endogenous
decision. Although the evidence is not definitive, the results are consistent with families
choosing to open enroll after a particularly poor year of academic performance. Such a scenario
could result in open enrollment participation being associated with lower achievement levels, but
not lower growth in achievement, which is exactly the pattern we observe in Tables 7 and 8.
5.3.1. Heterogeneity in Achievement Outcomes by Race/Ethnicity and
Socioeconomic Status
Our earlier analysis revealed significant heterogeneity in the determinants of schooling
choices across demographic and socioeconomic subgroups. These differences in the
determinants of schooling choices suggests the potential for heterogeneity in the outcomes that
24
can be influenced by those choices. Consequently, we estimate equations (9) and (10) separately
for the racial/ethnic and socioeconomic subgroups we examine previously. The results separated
by race/ethnicity are presented in Table 9 and they demonstrate heterogeneity in outcomes.
Whether we examine the value-added results of (9) or the student fixed effects results of (10), we
see that the White and Hispanic results are similar to both the full-sample results and to each
other. Specifically, the value-added results demonstrate interdistrict open enrollment
participation has little substantive effect on student achievement growth while the student fixed
effects results suggest that participation has a negative effect on the level of student achievement,
particularly in math. Results for Black students, however, do not follow the same pattern. Both
the value-added and fixed effects results indicate a negative relationship between open
enrollment participation and student achievement. The magnitude of these results are in the
range of 0.04 to 0.08 standard deviations. As we discuss in greater detail in the following
section, these results generally mirror the patterns observed in our analysis of the determinants of
schooling decisions. In that analysis, White and Hispanic students exhibited substantively
similar results, but the results for Black students differed on measures of both demographics and
quality. The results in Table 9 demonstrate that these differences carry over into the analysis of
the relationship between open enrollment participation and student achievement outcomes.
[Insert Table 9 about here]
Table 10 presents the results of estimating equations (9) and (10) separately for students
who are and are not eligible for free or reduced-price lunch. In contrast to the results
disaggregated by race/ethnicity, the results broken down by subsidized lunch eligibility reveal
little heterogeneity. For both groups the value-added results indicate little substantive effect of
interdistrict open enrollment participation on student achievement outcomes while the fixed
25
effect results demonstrate a slightly more negative relationship. Detailed results can be found in
Table 10 below.
[Insert Table 10 about here]
6.
Discussion and Conclusion
Motivated by a simple model of cross-district choice, this paper presents empirical
analyses of three dimensions of Colorado’s statewide mandatory interdistrict open enrollment
policy—the characteristics of participants, the schooling decisions that participants make through
the program, and the relationship between interdistrict open enrollment participation and
individual student achievement outcomes. Considered as a whole, the analyses comprise a
multi-part narrative that provides significant insight into the operations and effects of this largescale—if oft-overlooked—school choice policy, and the results have several implications for
both research and policy.
Our first line of inquiry concerned the characteristics of individuals who elected to
participate in interdistrict open enrollment. Our model generated two insights on this topic. First,
it predicted that individuals who were a good “match” with their district of residence would be
less likely to open enroll. We conjectured that parents with children who have specific
educational designations—such as gifted and talented or special educational needs—would place
a disproportionate amount of attention on ensuring that their district of residence provides a good
match on these dimensions and such students would thus be less likely to open enroll. Second,
our model holds that the likelihood of open enrollment increases as the quality of the district of
residence decreases. Both of these insights are generally corroborated empirically. Students
with special designations are significantly less likely to open enroll than their non-designated
peers. Additionally, Tables 3 and 4 demonstrate that, on average, open enrollers reside in
26
districts that perform worse on several measures of quality, including dropout rates, truancy rates,
and number of AP course offerings, relative to non-open enrolling students. Interestingly, the
average standardized test score of open enrollers’ district of residence are not appreciably
different—and perhaps even somewhat better—than the average district scores for students who
remain in their district of residence. Examination of the individual-level characteristics indicates
that—conditional on the characteristics of their district of residence—students who open enroll
are disproportionately advantaged from a socioeconomic standpoint.
Upon gaining an understanding of the characteristics of individuals who participate in
Colorado’s interdistrict open enrollment program, we turned to analyzing the schooling decisions
participants make under the program. Our model holds that district quality and demographic
composition will both enter into the decision process and the empirical analyses largely bear
these predictions out, although the results indicate heterogeneity along racial/ethnic and
socioeconomic lines for some of the quality and demographic measures. Specifically, our results
provide suggestive evidence that, relative to White and Hispanic students, Black students may
place a larger emphasis on demographic composition than traditional measures of quality—
particularly average student achievement—when making schooling decisions through Colorado’s
interdistrict open enrollment program.
The insights drawn from our analysis of the determinants of schooling decisions inform
our analyses of the relationship between interdistrict open enrollment participation and student
achievement. Specifically, we recognize that the heterogeneity in the determinants of schooling
decisions made under interdistrict open enrollment may also manifest itself in achievement
outcomes. And indeed, the results indicate that interdistrict open enrollment participation has
little substantive effect on the achievement of the full sample, but there is evidence of a modest
27
negative relationship between program participation and achievement outcomes for Black
students. Such a finding is consistent with the results of our analysis of the determinants of
schooling decisions described above.
We employ both value-added and student fixed effects approaches in our analysis of the
relationship between open enrollment participation and the two techniques return somewhat
inconsistent results. Almost without exception, the student fixed effects results are more
negative than the value-added results. Although such a discrepancy initially seems problematic,
it can actually provide substantive insight into the operations of the program. Specifically, this
pattern of results is consistent with a scenario where families decide to open enroll after a
particularly poor year, academically speaking, but do not exhibit significant improvements in
achievement following enrollment in a nonresident district.
Of course, the results are only suggestive of the scenario described above and do not
provide definitive evidence on the score. Consequently, a more in-depth, and perhaps qualitative,
analysis of the conditions that influence interdistrict open enrollment decisions is a natural topic
for future research. In addition, there are several other areas where the results presented above
are suggestive of a specific scenario, but do not provide sufficient evidence to be fully confident
in drawing specific conclusions and would thus benefit from additional inquiry. Specific
examples include the sources of heterogeneity in schooling decisions and a more detailed
analysis of how heterogeneity in schooling decisions relates to heterogeneity in schooling
outcomes. Finally, future research would do well to assess whether different policy contexts
produce substantively similar results.
Along with the research implications that emerged from our analysis, the results also
have several implications for policy. At a basic level, our analysis provides evidence that open
28
enrollment participation is unlikely to meaningfully increase student achievement, at least in the
short term. At the same time, it also seems likely that the policy increases at least some
participants’ satisfaction with their schooling option, an outcome with inherent value. Finally,
the results of the analysis of the determinants of schooling decisions suggests that policymakers
may wish to assess whether all families have easy access to information relevant to their
schooling decisions. Similarly, administrators of Colorado’s interdistrict open enrollment
program may consider examining the extent to which there are supply-side constraints on the
decisions that families can make under the policy, and assess whether specific groups (e.g.,
students with disabilities, English language learners, etc) experience more constraints than other
groups. Overall, this analysis provides us with a better understanding of the operations and
effects of the nation’s largest school choice program—interdistrict open enrollment—but it is
clear that there is still much to be learned.
29
7.
References
Alexander, K. L., Entwisle, D. R., & Dauber, S. L. (1996). Children in Motion: School Transfers
and Elementary School Performance. Journal of Educational Research, 90 (1), 3-12.
Armor, D. J., & Peiser, B. M. (1998). Interdistrict Choice in Massachusetts. In P. E. Peterson, &
B. C. Hassel (Eds.), Learning from School Choice. (pp. 157-186). Washington D.C: Brookings
Institution Press.
Bifulco, R., Cobb, C. D., & Bell, C. (2009). Can interdistrict choice boost student achievement?
The case of Connecticut’s interdistrict magnet school program. Educational Evaluation and
Policy Analysis, 31(4), 323-345.
Boyd, W.L., Hare, D., and Nathan, J. 2002. “What Really Happened?” In Hubert H (Ed.)
Minnesota’s experience with statewide public school choice programs: Center for School
Change. Humphrey Institute of Public Affairs, University of Minnesota; Minneapolis, MN: 2002.
Carlson, D. (2013). School Choice and Educational Stratification. Working Paper.
Carlson, D., Lavery, L., and Witte, J. (2011). The Determinants of Interdistrict Open Enrollment
Flows. Educational Evaluation and Policy Analysis, 33(1), 76-94.
Colorado Revised Statute. 22-36-101
Deming, D., Hastings, J., Kane, T., & Staiger, D. (2011). School choice, school quality and
academic achievement. NBER Working Paper, 17438.
Engberg, J., Gill, B., Zamarro, G., and Zimmer, R. (2012). Closing Schools in a Shrinking
District: Do Student Outcomes Depend on Which Schools are Closed? Journal of Urban
Economics, 71 (2): 189-203.
Fossey, R. (1994). Open Enrollment In Massachusetts: Why Families Choose. Educational
Evaluation And Policy Analysis, 16(3), 320.
Fowler, F. C. (1996). Participation In Ohio's Interditrict Open Enrollment Option: Exploring The
Supply-Side Of Choice. Educational Policy, 10(4), 518-536.
Hanushek, E. A., Kain, J. F., & Rivkin, S. G. (2004). Disruption versus Tiebout Improvement:
The Costs and Benefits of Switching Schools. Journal of Public Economics, 88 (9-10), 17211746.
Hastings, J. S., Kane, T., & Staiger, D. (2008). Heterogeneous preferences and the efficacy of
public school choice. NBER Working Paper, 2145.
Holme, J. J., & Richards, M. P., (2009). School Choice and Stratification In Regional Context:
Examining The Role Of Inter-District Choice. Peabody Journal Of Education, 84, 150-171.
30
Ingersoll, G. M., Scamman, J. P., & Eckerling, W. D. (1989). Geographic Mobility and Student
Achievement in an Urban Setting. Educational Evaluation and Policy Analysis, 11 (2), 143-149.
Institute of Metropolitan Opportunity. (2013). Open Enrollment and Racial Segregation in the
Twin Cities: 2000-2010. University of Minnesota Law School: Minneapolis, MN. Retrieved
September 3, 2013 from
http://www.law.umn.edu/uploads/30/c7/30c7d1fd89a6b132c81b36b37a79e9e1/OpenEnrollment-and-Racial-Segregation-Final.pdf
Kerbow, D., Azcoitia, C., & Buell, B. (2003). Student Mobility and Local School Improvement
in Chicago. Journal of Negro Education, 72 (1), 158-164.
Lankford, H., & Wyckoff, J. (1992). Primary and secondary school choice among public and
religious alternatives. Economics of Education review, 11(4), 317-337.
Lankford, R. H., Lee, E. S., & Wyckoff, J. H. (1995). An analysis of elementary and secondary
school choice. Journal of Urban Economics, 38(2), 236-251.
Lash, A. A., & Kirkpatrick, S. L. (1990). A Classroom Perspective on Student Mobility. The
Elementary School Journal, 91 (2), 176-191.
Lash, A. A., & Kirkpatrick, S. L. (1994). Interrupted Lessons: Teacher Views of Transfer
Student Education. American Educational Research Journal, 31 (4), 813-843.
Lavery, L., & Carlson, D. (2013). Dynamic Participation in Interdistrict Open Enrollment.
Working Paper.
National Center for Education Statistics (2012). State Education Reforms-Table 4.2. Numbers
and types of state open enrollment policies, by state: 2011. Retrieved August 30, 2013 from
http://nces.ed.gov/programs/statereform/tab4_2.asp
Phillips, K. J., Hausman, C., & Larsen, E. S. (2012). Students Who Choose And The Schools
They Leave: Examining Participation in Intradistrict Transfers.The Sociological Quarterly, 53(2),
264-294.
Powers, J. M., Topper, A. M., & Silver, M. (2012). Public School Choice and Student Mobility
in Metropolitan Phoenix. Journal of School Choice, 6(2), 209-234.
Reback, R. (2008). Teaching To The Rating: School Accountability And The Distribution Of
Student Achievement. Journal Of Public Economics 92(5-6): 1394–1415.
Rumberger, R. W., Larson, K. A., Ream, R. K., & Palardy, G. J. (1999). The Educational
Consequences of Mobility for California Students and Schools. Berkeley, CA: Policy Analysis
for California Education.
South, S. J., Haynie, D. L., & Bose, S. (2007). Student Mobility and School Dropout. Social
Science Research, 36 (1), 68-94.
31
Temple, J. A., & Reynolds, A. J. (1999). School Mobility and Achievement: Longitudinal
Findings from an Urban Cohort. Journal of School Psychology, 37 (4), 355-377.
Xu, Z., Hannaway, J., & D'Souza, S. (2009). Student Transience in North Carolina: The Effect of
School Mobility on Student Outcomes Using Longitudinal Data. Washington, DC: Urban
Institute.
Welsch, D.M., Statz, B., & Skidmore, M. (2010). An Examination Of Inter-District Public
School Transfers In Wisconsin. Economics of Education Review, 29(1): 126-137.
Welsch, D. M., & Zimmer, D. M. (2012). Do student migrations affect school performance?
Evidence from Wisconsin's inter-district public school program. Economics of Education
Review, 31(1), 195-207.
Zimmer, R., Gill, B., Booker, K., Lavertu, S., Sass, T. R., & Witte, J. (2009). Charter Schools in
Eight States: Effects on Achievement, Attainment, Integration, and Competition. Santa Monica,
CA: RAND.
32
Tables and Figures
Table 1. Number of states with interdistrict open enrollment programs, by program type
Program type
Number of states
Any interdistrict open enrollment program
35
Voluntary only
21
Mandatory only
12
Both voluntary and mandatory
2
33
Table 2. Total enrollment in Colorado, interdistrict open enrollment, and charter schools, by year
Year
Total (K-12)
OE
Charter
2000-01
724,508
22,993
21,064
2001-02
742,145
23,979
24,658
2002-03
751,862
30,846
28,782
2003-04
757,668
35,752
31,529
2004-05
766,657
38,780
36,658
2005-06
780,708
42,278
44,254
2006-07
794,026
48,543
52,242
2007-08
802,639
51,430
56,772
2008-09
818,443
57,274
57,843
2009-10
832,368
60,916
66,556
2010-11
843,316
66,296
72,989
2011-12
854,265
68,829
77,853
Source: Colorado Department of Education
34
Table 3. Average characteristics, by open enrollment status and year
2005-06
Characteristic
OE
Not OE
2006-07
OE
2007-08
Not OE
OE
2008-09
Not OE
2009-10
OE
Not OE
OE
Not OE
Individual Characteristics
Male
49.5
51.5
49.5
51.5
49.2
51.6
48.8
51.5
49.0
51.6
White
64.5
62.1
63.2
61.2
63.4
60.7
63.4
60.2
63.0
60.0
Hispanic
23.9
27.4
24.4
28.1
24.1
28.5
24.6
28.9
24.8
29.0
Black
7.1
6.0
8.0
6.1
8.0
6.1
7.3
6.1
7.4
6.0
Asian
3.2
3.3
3.3
3.4
3.3
3.5
3.5
3.6
3.5
3.8
Native American
1.2
1.2
1.1
1.2
1.1
1.2
1.1
1.2
1.3
1.3
Free Lunch
19.0
25.9
19.0
26.4
19.7
27.6
21.9
28.4
23.3
30.6
Reduced Lunch
6.0
5.8
6.4
5.9
7.2
6.3
7.6
6.8
7.4
6.8
No Lunch
74.7
68.2
73.8
67.3
72.8
65.9
66.8
63.1
69.3
62.6
Gifted and Talented
7.3
9.9
4.8
7.0
4.7
7.2
4.8
7.3
4.8
7.5
Special education
6.7
12.3
6.4
12.2
6.4
12.5
7.1
12.7
6.8
13.0
English language learner
8.1
11.1
6.2
9.7
6.5
9.5
6.2
9.4
6.2
9.4
Standardized math score
0.01
0.00
-0.03
0.00
-0.01
0.00
-0.04
0.00
-0.02
0.00
Standardized reading score
0.08
0.00
0.04
0.00
0.06
0.00
0.05
0.00
0.06
0.00
ACT Composite
18.6
18.9
18.7
19.0
19.0
19.4
19.5
19.6
18.8
19.4
Characteristics of District of Residence
Percent Free or Reduced Lunch
41.0
33.9
42.4
34.8
43.6
35.8
47
38.7
48.2
40.3
Percent White
54.8
61.8
53.3
61.2
53.3
60.7
53.1
60.5
50.1
56.7
Average District Achievement Reading
-0.04
-0.01
-0.08
-0.01
-0.08
-0.01
0.01
-0.01
0.01
-0.01
Number of AP Courses Offered
10.6
11.7
14.6
17
15.6
18.1
15.0
18.1
15.6
18.4
District Enrollment
27,941
33,462
28,918
33,676
28,386
34,099
28,796
34,893
29,915
35,712
District Dropout Rate
5.2
4.3
5.2
4.3
4.2
3.6
4.1
3.5
3.6
3.0
Pupil/Teacher Ratio
17.1
17.4
17
17.3
16.9
17.3
17.0
17.3
17.6
17.9
District Truancy Rate
2.4
2.1
2.4
2.0
2.5
2.2
2.3
2.0
2.3
2.1
35
Table 4. Log Odds from logit model predicting open enrollment in 200607, by grade
Characteristic
KG
6th Grade
9th
Grade
Student Characteristics
Female
1.0312
1.0485
1.0879**
(0.0363)
(0.0433)
(0.0385)
Hispanic
0.6291***
0.8391***
0.8793**
(0.0368)
(0.0514)
(0.0445)
Black
1.2173***
1.1640*
0.9639
(0.0831)
(0.1006)
(0.0714)
1.4146***
0.9098
0.7925**
(0.1251)
(0.1081)
(0.0936)
0.7084**
0.7298
0.9495
Asian
Native American
Reduced-price lunch
Not eligible for free/reduce lunch
Lunch eligibility missing
Gifted and talented
Limited English proficiency
Disability
Math achievement
(0.1235)
(0.1651)
(0.1453)
1.9178***
1.4304***
1.1064
(0.1670)
(0.1255)
(0.0911)
2.3288***
1.8528***
1.7081***
(0.1338)
(0.1156)
(0.0866)
6.7580***
2.9959***
1.0000
(0.9964)
(1.0165)
Omitted
0.6692
0.8571**
0.7761***
(0.1879)
(0.0665)
(0.0487)
0.3101***
0.6277***
0.6934***
(0.0267)
(0.0686)
(0.0629)
0.4479***
0.8749*
0.8165***
(0.0428)
NA
(0.0657)
0.8700***
(0.0508)
NA
NA
1.0985**
(0.0310)
Reading achievement
NA
(0.0418)
District Characteristics (Lagged)
Percent eligible free/reduced lunch
Percent White
Average district achievementReading
District made AYP
1.0012
1.0201***
1.0209***
(0.0023)
(0.0028)
(0.0025)
0.9805***
0.9788***
0.9828***
(0.0028)
(0.0027)
(0.0024)
1.4655
26.3220***
6.3312***
(0.3895)
(5.3888)
(1.1728)
1.4182***
1.5148***
2.1245***
(0.1280)
(0.1418)
(0.1786)
36
Table 4. Log Odds from logit model predicting open enrollment in 200607, by grade
Characteristic
Number of AP courses offered
Enrollment (thousands)
Dropout rate
Student-teacher ratio
Truancy rate
Constant
Observations
KG
1.0014
6th Grade
9th
Grade
0.9660***
0.9749***
(0.0049)
(0.0027)
(0.0025)
0.8946***
0.9115***
0.9820**
(0.0143)
(0.0089)
(0.0078)
1.0655***
1.0998***
1.0634***
(0.0109)
(0.0125)
(0.0101)
0.9448***
0.9985
1.0525***
(0.0162)
(0.0198)
(0.0192)
1.0018
1.1845***
1.1042***
(0.0233)
(0.0331)
(0.0284)
0.2996***
0.0515***
0.0182***
(0.1059)
(0.0227)
(0.0073)
64792
54875
57389
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
37
Table 5. Results of conditional logistic regression model predicting district into
which student open enrolls
Variable
Coefficient
Dropout Rate
0.050*
(0.003)
Truancy Rate
-0.012
(0.007)
Percent Free or Reduced Lunch
-0.020*
(0.001)
Percent Black
0.040*
(0.002)
Percent Hispanic
0.018*
(0.001)
Number AP Courses Offered
0.026*
(0.002)
Enrollment (10,000s)
0.0224*
(0.001)
Average Reading Achievement
0.450*
(0.086)
Distance (10s)
N
Number of groups
Log-Likelihood
-0.470*
(0.004)
1,210,022
16,747
-49,431
38
39
Table 6. Results of conditional logistic regression model predicting district into which student
open enrolls, by subgroup
Free or
Variable
White
Black
Hispanic No Lunch
Reduced
Lunch
Dropout Rate
0.068*
0.003
0.041*
0.046*
0.051*
(0.004)
(0.013)
(0.007)
(0.004)
(0.006)
Truancy Rate
-0.051*
(0.010)
0.100*
(0.016)
0.063*
(0.013)
-0.065*
(0.010)
0.077*
(0.009)
Percent Free or Reduced Lunch
-0.015*
(0.001)
-0.043*
(0.004)
-0.015*
(0.002)
-0.023*
(0.001)
-0.007*
(0.002)
Percent Black
0.051*
(0.002)
0.064*
(0.006)
0.017*
(0.004)
0.056*
(0.002)
0.009*
(0.003)
Percent Hispanic
0.025*
(0.001)
-0.022*
(0.003)
0.018*
(0.002)
0.023*
(0.001)
0.004*
(0.002)
Number AP Courses Offered
0.014*
(0.002)
0.049*
(0.007)
0.034*
(0.004)
0.025*
(0.002)
0.038*
(0.003)
District Enrollment (10,000s)
0.250*
(0.006)
0.199*
(0.023)
0.207*
(0.012)
0.223*
(0.006)
0.208*
(0.010)
Reading Achievement
1.726*
(0.096)
-3.404*
(0.143)
0.109
(0.207)
0.823*
(0.106)
-0.206
(0.157)
-0.492*
(0.005)
764,310
10,496
-31709.08
-0.401*
(0.014)
119,865
1,478
-3868.85
-0.438*
(0.009)
261,333
3,437
-10397.8
-0.474*
(0.005)
863,733
11,654
-35141.28
-0.478*
(0.008)
323,848
4,352
-12932.54
Distance (10s)
N
Number of groups
Log-Likelihood
40
41
42
Table 7. Results of OLS regression of standardized reading and math
achievement on open enrollment participation: Models contain lagged
outcome measure in addition to variables noted in headers
Variable
Math Scores
Reading Scores
No demographics
Open Enrollment
-0.007*
0.021*
(0.003)
(0.003)
Demographic characteristics
Open Enrollment
-0.011*
0.007*
(0.003)
(0.003)
Demographic characteristics & grade-by-districtby year fixed effect
Open Enrollment
-0.011*
0.009*
(0.003)
(0.003)
43
Table 8. Results of OLS regression of standardized reading and math
achievement on open enrollment participation: Model contains student fixed
effects
Variable
Math Scores
Reading Scores
No demographics—Full sample
Open Enrollment
-0.063*
-0.033*
(0.003)
(0.003)
Open Enrollment
Time-varying demographics—Full sample
-0.057*
-0.030*
(0.003)
(0.003)
Open Enrollment
Time-varying demographics—Value-added sample
-0.061*
-0.082*
(0.004)
(0.004)
44
Table 9. Results of OLS regressions of standardized reading and math
achievement on open enrollment participation, by racial/ethnic subgroup and
model type
Variable
Math Scores
Reading Scores
White
Value-added
Student fixed effects
-0.008*
0.006
(0.002)
(0.004)
-0.061*
-0.043*
(0.005)
(0.005)
Black
Value-added
Student fixed effects
-0.084*
-0.041*
(0.011)
(0.014)
-0.084*
-0.056*
(0.013)
(0.017)
Hispanic
Value-added
Student fixed effects
-0.011
0.013*
(0.006)
(0.007)
-0.057*
-0.034*
(0.007)
(0.008)
Note: Robust standard errors in parentheses below coefficients. Value-added
models contain lagged outcome measure, demographic characteristics, and gradeby-district-by-year fixed effects. Student fixed effects models contain timevarying demographics and are estimated over value-added analytic sample.
45
Table 10. Results of OLS regressions of standardized reading and math
achievement on open enrollment participation, by socioeconomic subgroup and
model type
Variable
Math Scores
Reading Scores
Eligible for Free or Reduced-price Lunch
Value-added
Student fixed effects
-0.022*
0.007
(0.005)
(0.006)
-0.058*
-0.030*
(0.007)
(0.007)
Ineligible for Free or Reduced-price Lunch
Value-added
Student fixed effects
-0.004
0.007
(0.004)
(0.004)
-0.046*
-0.027*
(0.005)
(0.005)
Note: Robust standard errors in parentheses below coefficients. Value-added
models contain lagged outcome measure, demographic characteristics, and grade-bydistrict-by-year fixed effects. Student fixed effects models contain time-varying
demographics and are estimated over value-added analytic sample.
46