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SCHOOL EFFICIENCY, SOCIAL STRATIFICATION, AND
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SCHOOL EFFICIENCY, SOCIAL STRATIFICATION, AND SCHOOL CHOICE: AN
EXAMINATION OF MICHIGAN’S CHARTER SCHOOL PROGRAM

By

Yongmei Ni

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Education Policy

2007

ABSTRACT

SCHOOL EFFICIENCY, SOCIAL STRATIFICATION, AND SCHOOL CHOICE: AN
EXAMINATION OF MICHIGAN’S CHARTER SCHOOL PROGRAM

By
Yongmei Ni

As one of the most prominent developments in elementary and secondary education
reform in the US. since the 19905, school choice has been widely advocated to utilize
market incentives to promote educational equity and efﬁciency. This dissertation tests
these two hypotheses by examining the effects of school choice policies in Michigan on
racial segregation and social stratiﬁcation, as well as the competitive impact of charter
schools on the efﬁciency of traditional public schools.

Drawing on two years of student-level data, I examine patterns of student sorting
associated with school choice policies. How do choice policies inﬂuence the degree of
racial segregation and social stratiﬁcation in public schools? How are students’
propensities to select a choice school inﬂuenced by their own characteristics, and the
characteristics of their assigned public schools? Examining the dynamic student
movements between their assigned public schools and charter schools through a series of
multinomial Generalized Hierarchical Linear Models (GHLM), my analysis suggests that
while choice policies are providing new options for many students who were not served
well in their assigned public schools, it is also contributing to the creation of a stratum of
schools at the bottom in which truly disadvantaged students become ever more
concentrated.

In testing whether the competition from charter schools improves school efﬁciency of

traditional public schools, I assembled a statewide school-level panel dataset of Michigan

schools from 1994 to 2004. This analysis relied on ﬁxed effect estimations that implicitly
controlled for unobservable time invariant school characteristics, and explicitly controlled
for changing student composition and other factors induced by charter school policy. My
analysis shows that charter competition has a negative impact on student achievement in
Michigan’s traditional public schools. The effect is small or negligible at ﬁrst, but
becomes more substantial in the long run. While contradicting the positive competitive
effect typically predicted by school choice advocates, my results are consistent with the
conception of choice triggering a downward spiral in the most heavily impacted public

schools.

Copyright by
YONGMEI NI

2007

ACKNOWLEDGMENTS

I would never have been able to complete my dissertation without the guidance of my
committee members and help from friends and my family. I would like to express my
deepest gratitude to my dissertation committee chair and my advisor, Dr. David Arsen,
for his continual mentoring both academically and personally throughout my graduate
career. His insightful guidance and support signiﬁcantly contributed to my development
as a scholar. His patience and encouragement inspired conﬁdence in me and carried me
on through difﬁcult times. His accessibility for long discussions and thoughtful advice on
my work greatly smoothed the progress of my dissertation research. Dr. Arsen devoted
numerous hours to read and revise every page and provided extremely perceptive
comments in every phase of my dissertation. It has been a great honor to have had the
opportunity to be his student.

I am also very grateful for having an exceptional doctoral committee and wish to
thank them for their support and encouragement. I would like to thank Dr. Gary Sykes
and Dr. Dorothea Anagnostopoulos for the inspiration and high expectations they
provided to me during the doctoral study. I sincerely thank Dr. Ken Frank for his
insightful comments and constructive criticisms on my methodology and Dr. Jeffrey
Wooldridge for his invaluable comments and advice on the empirical analysis on this
dissertation.

I would like to acknowledge the help from the staffs at the Center for Educational
Performance Information and Michigan Department of Education for providing the data I
used in the dissertation. Special thanks go to Dr. Joseph Martino for his patience and the

great efforts in generating the data that I requested. Without their help, the dissertation

would not have been accomplished. I also want to thank the colleagues at the Education
Policy Center at MSU, in particular, Bettie Menchik and Jeannie Patrick, for their support
in administrative and technical assistance and also for many good laughs during the
stressful times.

I would like to extend many thanks to my writing group, Troy Hicks, Marisa Cannata,
and Tara Donahue, who not only read and commented on multiple versions of all the
chapters of this dissertation, but also provided many helpful suggestions to help me
improve my writing and clarify my arguments.

Finally, I would like to thank my family for all their encouragement. My husband and
best friend, Xiangyang, has unconditionally been there supporting, encouraging, and
believing in me, even in the darkest moments along this journey. I am grateful to my
parents and parents-in-laws who have been a constant source of love, support, and
understanding all these years. I thank them especially for their help in taking care of my
children, Xinyuan and Siyuan, so I could spend long hours and weekends working during

the most hectic periods of writing this dissertation.

vi

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. ix
LIST OF FIGURES .......................................................................................................... xii
CHAPTER 1 INTRODUCTION ........................................................................................ 1
Framing the Questions ................................................................................................ 3
Structure of Dissertation ............................................................................................. 4
Theoretical Framework ............................................................................................... 5
Sorting Mechanism ............................................................................................. 6
Competition Mechanism ................................................................................... 10
School Choice Context in Michigan ......................................................................... 12
Charter School Program ................................................................................... 12
Inter-district Choice Program .......................................................................... 13
Proposal A ........................................................................................................ 14
CHAPTER 2 CHARTER SCHOOLS AND STUDENT SORTING ............................... 18
Previous Research: Consequences of Sorting under Public School Choice ............. 18
Who Chooses Charter Schools? ........................................................................ 19
Student Composition in Charter Schools and TPSs .......................................... 21
The Impact of Charter Schools on Student Composition in TPSs .................... 23
Inter-district Choice .......................................................................................... 26
Research Questions ................................................................................................... 28
Data and Empirical Strategies ................................................................................... 29
Descriptive Analyses ................................................................................................ 31
Who Participates in Charter School Program in Michigan? ........................... 32
Are Charter Schools More Racially Segregated Than TPSs? .......................... 38

Are Charter Schools Serving More Socioeconomically Advantaged Students
Than TPSs? ....................................................................................................... 51
Comparison of Performance Level in Charter Schools and T PSs .................... 55
Discussion ................................................................................................................. 56

CHAPTER 3 THE IMPACT OF SCHOOL CHOICE ON STUDENT COMPOSITION

IN TRADITIONAL PUBLIC SCHOOLS ........................................................................ 60
Student Flow under School Choice Programs .......................................................... 61
Research Questions ................................................................................................... 63
Methodology ............................................................................................................. 64

Explanatory Variables ...................................................................................... 64
Multinomial HGLM Descriptions ..................................................................... 66
Sampling Strategies .......................................................................................... 70
Findings ..................................................................................................................... 72
Question (1): Transferring from Assigned Schools to Choice Schools ............ 72

vii

Question (2): Transferring ﬁom Charter Schools to Assigned Schools ........... 90
Question (3): Transferring ﬁom Inter—district Schools of Choice Back to
Assigned Public Schools ................................................................................... 98

Discussion ............................................................................................................... 104

CHAPTER 4 THE IMPACT OF CHARTER SCHOOLS ON EFFICIENCY OF

TRADITIONAL PUBLIC SCHOOLS ........................................................................... 110
Conceptualization of Competition and School Efﬁciency ...................................... 112
Existing Research .................................................................................................... 114
Research Questions ................................................................................................. 120
Data and Methodology ............................................................................................ 121

Data Sources ................................................................................................... 121
Measure of Competition .................................................................................. 122
Estimation Strategies ...................................................................................... 124
Findings ................................................................................................................... 128
Descriptive Statistics ....................................................................................... 128
Pooled OLS ..................................................................................................... 133
Fixed Effect Estimations and Potential Source of Bias .................................. 136
Discussion ............................................................................................................... 147

CHAPTER 5 CONCLUSIONS AND POLICY IMPLICATIONS ................................ 152

Summary and Analysis of Findings ........................................................................ 152
Equity .............................................................................................................. 153

Social Cohesion .............................................................................................. 155
Productive Efﬁciency ...................................................................................... 156
Inter-district Choice ........................................................................................ 158

Policy Implications ................................................................................................. 159
APPENDICES ................................................................................................................ 161
REFERENCES ............................................................................................................... 165

viii

LIST OF TABLES

Table 2.1 Aggregate Participation in Michigan’s School Choice Policies in Selected
Years .................................................................................................................. 31

Table 2.2 Percentages of Students in PSAs and TPSs by Race/ethnicity, 2003-04 .. 33

Table 2.3 Percentages of Students Eligible for Free/reduced Lunch by Race/ethnicity
and Community Type, 2003-04 ........................................................................ 35

Table 2.4 Average MEAP Scores of TP85 and PSAs at Certain Grades, 2003-04 36

Table 2.5 Grade 4 Math MEAP Scores by Race/ethnicity and Community Type,

2003-04 ............................................................................................................. 37
Table 2.6 Number of PSAs in Michigan, by Location, 2003-04 .............................. 40
Table 2.7 PSAs and Comparing TPSs in Michigan, 2003-04 ................................... 42
Table 2.8 Student Compositions of PSAs, 2003-04 .................................................. 43
Table 2.9 Racial Diversity Measures of PSAs and TPSs, 2003-04 ........................... 44

Table 2.10 Racial Diversity of PSAs located in Detroit or Drawing Students
Primarily from Detroit and Their Sending Districts ......................................... 46

Table 2.11 Racial Diversity of Type I PSAs and Host Districts, by Host District DR

........................................................................................................................... 47
Table 2.12 Racial Diversity of Type II PSAs and Sending Districts, by DR of
Sending Districts ............................................................................................... 49
Table 2.13 DR of Type III PSAs and Host Districts, by DR of Host District ........... 49
Table 2.14 Percentages of FRL of PSAs Located in Detroit or Drawing Students
Primarily from Detroit and Their Sending Districts ......................................... 52
Table 2.15 Percentages of FRL of Type I PSAs and TPSs in Host Districts, by
Percentage of FRL of Host Districts ................................................................. 53

Table 2.16 Percentages of FRL of Type II PSAs and TPSs in Sending Districts, by

Percentage of FRL of Sending Districts ........................................................... 53

Table 2.17 Percentages of FRL of Type III PSAs and TPSs in Host Districts, by
Percentage of FRL of Host Districts ................................................................. 54

Table 3.1 Attendance Status of Michigan Public School Students, 2002-03 and 2003-
04 ....................................................................................................................... 71

Table 3.2 Variables and Description, All Students in the Assigned Schools in 2002-
03 ....................................................................................................................... 74

Table 3.3 Unconditional Models on the Likelihood of Transfer, from Assigned
Schools to Choice Schools ................................................................................ 75

Table 3.4 Estimated Effects of Student and School Characteristics on the Likelihood
of Transfer from Assigned Schools to Choice Schools ..................................... 77

Table 3.5 Slope-as-outcome Models: School Fixed Effects on the Likelihood of
Transfer from Assigned Schools to Choice Schools, Students with Different
Race and SES Backgrounds .............................................................................. 82

Table 3.6 Unconditional Models on the Likelihood of Transfer from Assigned
Schools to Choice Schools, Selected Grades .................................................... 87

Table 3.7 Estimated Fixed Effects on the Likelihood of Transfer from Assigned
Schools to Choice Schools, Selected Grades .................................................... 88

Table 3.8 Variables and Description, All Charter School Students in 2002-03 ........ 91

Table 3.9 Unconditional Models on the Likelihood of Transfer, from Charter
Schools to Assigned Public Schools ................................................................. 94

Table 3.10 Fixed Effects of Student and School Characteristics on the Likelihood of
Transfer from Charter Schools to Assigned Public Schools ............................. 96

Table 3.11 Variables and Description, All students in Inter-district Schools of Choice
in 2002-03 ......................................................................................................... 99

Table 3.12 Unconditional Models on the Likelihood of Transfer, from Inter-district
Schools of Choice to Assigned Schools .......................................................... 101

Table 3.13 Fixed Effects of Student and School Characteristics on the Likelihood of

Transfer from Inter-district Schools of Choice to Assigned Schools .............. 102

Table 4.1 Numbers of TPSs Facing Strong Charter Competition, by Year and
Duration .......................................................................................................... 129

Table 4.2 TPSs Facing Strong Charter Competition in 2004, by Community Type129

Table 4.3 Summary Statistics of Satisfactory Rates, by Year, Charter Competition,
and Subjects .................................................................................................... 131

Table 4.4 Description of Explanatory Variables ..................................................... 133

Table 4.5 Pooled OLS Results: the Impact of Charter Competition on School
Efficiency ........................................................................................................ 135

Table 4.6 Fixed Effects, First Differencing, and Random Trends Estimations:
Satisfactory Rate on the 4th grade Math Test .................................................. 138

Table 4.7 Fixed Effects, First Differencing, and Random Trends Estimations:
Satisfactory Rate on the 7‘h Grade Math Test ................................................. 143

Table 4.8 Fixed Effects, First Differencing, and Random Trends Estimations:
Satisfactory Rate on the 4th Grade Reading Test ............................................ 145

Table 4.9 Fixed Effects, First Differencing, and Random Trends Estimations:
Satisfactory Rate on the 7‘h Grade Reading Test ............................................ 146

xi

LIST OF FIGURES

Figure 3.1 Student Flow through School Choice Programs in Michigan ................. 62

xii

CHAPTER 1 INTRODUCTION

School choice has been one of the most prominent developments in elementary and
secondary education reform in the US. since the 19903. The choice movement has been
partly driven by the belief that parents and students should have the freedom to choose
schools. It has also been driven by concerns over the academic achievement of children
in public schools, particularly in many urban schools serving low—income and minority
students.

School choice has gained considerable political and academic support in recent years.
To date, two types of school choice policies have emerged in the US: private choices
such as education vouchers or tuition tax credits, and choice among public schools such
as intra- and inter -district choice and charter schools. Choice advocates argue that
traditional public schools (TPS) are bureaucratic and operate in a relatively monopolistic
market. Efﬁcient allocation of resources and maximization of students’ academic
learning are not their primary goals (Chubb & Moe, 1990; Friedman, 1962; 1980) and the
incentives for improvement or innovation are weak. Instead, proponents argue that the
introduction of school choice will transform the monopolistic public school system
through the application of competitive market pressures. Parents and students as
consumers are free to choose from multiple suppliers—schools. School choice policies
directly link school funding with enrollment and create a strong market incentive
mechanism for schools to attract students. Schools that improve educational quality at
lower costs thrive as they gain students and funding. Schools that fail to improve quality

will lose students and money, and will eventually close.

With the expansion of choice programs, concerns about their consequences have
arisen. These concerns generally fall into two categories. First, critics of choice argue that
the delivery of educational services is very different from allocation of private goods and
service. Are parents rational consumers? Do they have well—developed knowledge of
effective education so as to make informed choices among schools? Will free-market
competition provide the right kind of education that reﬂects the “public good” nature of
education? Second, critics of school choice policies are concerned that market
mechanisms in schooling will generate adverse distributional consequences. Will school
choice policies exacerbate the unequal distribution of educational resources among
schools and students? What kinds of students will choice schools attract? Will choice
schools be more segregated and stratiﬁed than TPSs? What are the impacts of choice
schools on student composition in TPSs? Do they lead to more segregation or
stratiﬁcation in TPSs? Will they create less cohesive communities? Do choice policies
have the same effect across the whole public school system or exert different effects on
different communities?

Although these questions are of great importance, the answers are still not conclusive.
It is important to evaluate the multiple effects simultaneously because different
educational goals are usually intertwined or in conﬂict with one another. For example,
efﬁciency is often achieved at the cost of equity. Past empirical studies often focused on
either one or some of the questions, and they provide only limited progress in addressing

these issues due to both data limitations and methodological issues.

Framing the Questions

This dissertation evaluates the impact of charter schools on various educational
outcomes. Although there are many forms of school choice, this dissertation focuses on
charter schools for two reasons. First, charter schools are the most rapidly expanding
form of school choice. In 1991 Minnesota passed the ﬁrst charter school law. By 2003,
more than 40 states had passed legislation allowing for the creation of charter schools.
Today, over one million students are enrolled in more than 3,500 charter schools
nationwide.1 Second, under the No Child Left Behind (NCLB) Act, charter schools have
become an important policy tool to turn around failing schools.

Charter school policy creates two mechanisms: a re-sorting of students among
schools and competition among schools. In order to study how student sorting and
competition jointly inﬂuence equity, school efﬁciency, and, more broadly, social
cohesion, I perform two types of empirical analysis in this dissertation. The ﬁrst part
examines patterns of student sorting (or re-sorting) associated with choice policies.
Speciﬁcally, I seek to answer questions such as: What kinds of students tend to choose to
go to charter schools? Are charter schools more stratiﬁed than TPSs by race,
socioeconomic status (SES), and performance level? How are students’ propensities to
select charter schools inﬂuenced by their own characteristics, as well as the
characteristics of their assigned public schools? How does charter school policy inﬂuence
the degree of racial or ethnic segregation and social stratiﬁcation in TPSs?

The second part examines the impact of charter competition on the efﬁciency of

nearby traditional public schools. Although the question of whether competition produces

 

' Source: US. Charter Schools website. Available at:
http://www.uscharterschools.org/pub/uscs_docs/o/history.htm

charter schools that are more efﬁcient than TPSs is important, I emphasize the impact of
competition on TPS efﬁciency. This is because the vast majority of students remain in
TPSs, and they have not been the center of attention of past research. For the empirical
analysis corresponding to these two major portions of the dissertation, I assembled two
different datasets and relied on different methodologies including Hierarchical Linear

Models (HLM) and estimating unobserved effects models through ﬁxed effect estimators.

Structure of Dissertation

The dissertation is organized into ﬁve chapters. In the next section of this chapter I
lay out the framework of the study, explain in detail how sorting and competition
mechanisms created by charter schools jointly inﬂuence various educational outcomes.
Since my empirical work focuses on Michigan, I ﬁirther describe the two school choice
programs in Michigan —a charter school program and inter-district choice, and how the
school ﬁnance system has facilitated the development of school choice.

In Chapters 2 and 3, I answer the questions about how students sort themselves across
different types of schools, and how the sorting process inﬂuences stratiﬁcation by race,
SES, and performance level. More speciﬁcally, in Chapter 2, I perform cross-sectional
comparisons of student composition in charter schools and TPSs, answering the question
of whether charter schools are more or less stratiﬁed than TPSs. In Chapter 3, I ask how
the sorting of students associated with Michigan’s charter school program inﬂuences
student composition in TPSs. Through an application of HLMs, the pattern of student
ﬂow between their assigned public schools and choice schools between two years is

studied at both the student and school level.

Chapter 4 investigates how competition induced by charter schools inﬂuences TPS
school efﬁciency. Using 11 years of school-level panel data, I estimate whether the
presence of charter school competition inﬂuences student achievement in nearby TP83,
and whether the inﬂuence in the long run might be different from the short-term inﬂuence.
The estimations rely on ﬁxed effect estimations and several other models to check for
robustness.

Conclusions drawn from the ﬁndings in Chapters 2, 3, and 4 are set forth in Chapter 5,

followed by implications for educational policy.

Theoretical Framework

School choice research has focused on its likely effects on various educational
outcomes, such as student performance and its efﬁcacy in expanding educational options
for low-income and minority families. Advocates and critics alike often frame their
arguments around only one or some dimensions of the effects, instead of evaluating all
aspects simultaneously. As Levin (2002) has pointed out, policy goals are often
intrinsically in conﬂict; advancement of one goal will probably hinder the fulﬁllment of
others. It is important to evaluate policies comprehensively from multiple dimensions.
Levin developed a framework to evaluate voucher programs which includes four
normative criteria or dimensions of evaluation: (1) freedom of choice; (2) productive
efﬁciency; (3) equity; and (4) social cohesion (Levin, 2002). According to Levin,
freedom of choice refers to the rights of families to choose schools for their children that
are consistent with their child-rearing practices. Equity refers to the quest for'fairness in
access to educational opportunities, resources, and outcomes by student characteristics

such as social class, race, disability, and geographical location. Productive efﬁciency

refers to the maximization of educational results for any given resource constraint. Social
cohesion refers to the provision of a common educational experience that will prepare
students for civic participation (Levin, 2002). Although the framework was originally
designed to evaluate voucher programs, it also applies to the evaluation of public school
choice policies such as charter schools and inter-district choice.

School choice policies increase the number of schooling options available to parents
that historically have been unavailable in the public school system where children have to
go to their assigned schools, usually located within the boundaries of their residing
districts. From this perspective, school choice, by deﬁnition, furthers the goal of freedom
of choice. Indeed, surveys from different states consistently have shown that choice
parents are very satisﬁed with the choices they make (McCully & Malin, 2003; Pioneer
Institute, 2000; Solmon, 2003). When evaluating school choice policies as an alternative
to the TPS system, researchers consequently tend to focus on the other three goals: equity,
efﬁciency, and social cohesion.

Increased freedom to choose under choice policies creates two mechanisms: a sorting
of students among schools and competition among schools. To evaluate the effectiveness
of school choice policies, one must understand how student sorting and competition

jointly inﬂuence the outcomes Levin has put forth.

Sorting Mechanism

School choice policies allow parents to choose from different schools for their
children and for schools to provide differentiated educational services, which in turn
inevitably create a re-sorting or redistribution process that rearranges students among

schools. This sorting process has implications for equity, efﬁciency, and social cohesion.

First, student sorting under school choice policies carries equity implications insofar
as it alters the overall degree of social stratiﬁcation in the public school system. It has the
potential to either decrease or increase equity, depending on who chooses and who stays.
Advocates for choice policies suggest that such policies enable students who are not well
served by TPSs to attend choice schools that better meet their needs (Chubb & Moe, 1990;
Finn, Manno, & Vanourek, 2000; Friedman, 1962). This hope is especially prominent for
students who are unable to afford switching to better public schools by moving to a
different residential district or paying tuition for private schools. Advocates argue that
these students tend to be from low-income and minority families, and possibly with low
levels of achievement (Mathews, 2004). From this perspective, supporters argue that
choice policies enhance equity by expanding educational opportunities for disadvantaged
students.

Critics of school choice policies, however, worry about the students remaining in
TPSs. On the demand side, they argue that all students are not equally able to take
advantage of newly available choice options. Disadvantaged students are more likely to
be left behind because their parents tend to be unprepared for making informed choices
(Gintis, 1995). These parents also tend to have greater difﬁculty in obtaining and
assessing information about choice programs or school quality and in arranging
transportation to choice schools (Arsen, Plank, & Sykes, 1999; Bell, 2005; Levin, 1998).
On the supply side they are concerned that schools enrolling high concentrations of
racially and socially disadvantaged students will be at a disadvantage in competition with
other schools for students (F iske & Ladd, 2000). Under this scenario, choice could

exacerbate inequity, with well-informed and higher-achieving students attending choice

schools, and truly disadvantaged students becoming more concentrated in high minority
and high poverty schools that lose both higher—achieving students and the ﬁnancial
resources that go with them.

Past research has shown that student composition in schools affects student outcomes.
Low-income students have higher levels of achievement and/or larger achievement gains
over time if they attend middle-class schools rather than high-poverty schools (Borman &
Dowling, 2003; Coleman, 1966; Hanushek et al., 2003; Levin, 1998; Summers & Wolfe,
1977; Zimmer & Toma, 2000). Reduced social stratiﬁcation in schools improves equity
through positive peer effects for disadvantaged students. So a high degree of social
stratiﬁcation exacerbates inequity because afﬂuent students beneﬁt from high-achieving
middle-class peers, and disadvantaged students are concentrated in high-poverty schools
with low-achieving peers. How the redistribution of children under school choice
influences racial segregation and social stratiﬁcation has therefore become the main
equity consideration in the choice debate.

Second, student sorting under school choice has potential implications for social
cohesion. Isolated students tend to have little ﬁrst-hand exposure to social or cultural
diversity and may therefore be inhibited in learning lessons of tolerance and acceptance
of differences, or perhaps be less willing to accept a common set of values and shared
base of knowledge. Students in integrated schools, on the other hand, are more likely to
live and work in interracial settings and to be better prepared for participation in
democratic life as adults (Braddock et al., 1984; Eaton, 2001; Hallinan, 1998; Wells &
Crain, 1994). While there is a longstanding view that racial and ethnic diversity within

schools can help to promote social cohesion, it is unclear whether choice policies increase

or decrease this diversity. School choice critics have argued that choice policies will
exacerbate segregation in schools, especially along racial and etlmic lines. Advocates,
however, expect choice policies to reduce school racial segregation, since most racial
segregation in public schools reﬂects segregation in the residential housing market, and
choice policies enable children to attend schools outside their neighborhood (Finn et al.,
2000; Friedman, 1962; Greene, 2005). The link between. school choice and social
cohesion remains an empirical issue that has produced only mixed results in past research.
In addition, student sorting is relevant to measuring school efﬁciency, but in an
indirect way. Improvements in student achievement at a school can be the result of it
improving teaching and learning in response to competitive pressures or as a result of it
enrolling more able students. School choice advocates typically maintain the former
competitive response hypotheses under which competition generates strong incentives for
schools to develop programs that better serve students’ needs. Efforts to test this
hypothesis empirically, however, must account for the self-selection of students into
choice schools. For example, suppose that students enrolled in choice schools are more
able or motivated than otherwise similar students remaining in TPSs. If the selection bias
is not controlled for, choice schools could appear to be more efﬁcient than TPSs even
though they are not. Likewise, a school can appear to be less efﬁcient when students
enrolled are less able or motivated. Efforts to measure the effect of choice policies on
school efﬁciency must therefore separate the competitive effect from the student
composition effect (selection bias). This requires not only sophisticated statistical tools,

but also the availability of detailed data.

Competition Mechanism

Understanding how competition inﬂuences school outcomes—especially efficiency—
is the other main issue in evaluating school choice. School choice advocates assert that
the US. public schools are inherently inefﬁcient, spending too much money while
producing poor student outcomes (Brandl, 1998; Chubb et al., 1990). Allowing parents
choice and connecting school ﬁnance directly to the number of students enrolled, school
choice creates a market incentive mechanism under which choice schools are motivated
to have high quality programs so that they can attract more students—their customers.
More importantly, all TPSs are motivated to improve their educational quality as well,
since excessive loss of students and resources to choice schools will lead to less funding
and even school closure. As a result, choice advocates suggest that both choice students
and the students remaining in the TPS system will enjoy more efﬁcient provision of
educational services.

Opponents, on the other hand, argue that school choice does not necessarily improve
efﬁciency because the concept of market competition and choice were borrowed from
other ﬁelds and can not be readily adapted to the delivery of public education (Fiske &
Ladd, 2000). Parents may not choose schools based on school quality, but rather on a
variety of other factors such as location and accessibility from their home or the school’s
football team, factors that have nothing to do with quality. Sometimes, parents make
rational decisions to choose failing schools for their children, because parents’
preferences are shaped by their social networks (Bell, 2005). On the other hand, TPSs can

respond the competition from school choice by a range of possible strategies, some of

10

which have little to do with improving school quality and becoming more efﬁcient
(Arsen & Ni, 2005).

Empirical work on the impact of competition on school efﬁciency is limited and
results from this line of inquiry are mixed. While the economic rationale for competition
and efficiency is conceptually clear, it remains empirically difﬁcult to establish the causal
relationship between the two because of the confounding effects of students sorting and
non-randomness of choice school location.

To summarize, the sorting and competition mechanisms created by school choice
simultaneously affect the efﬁciency, equity and social cohesion of the public school
system. Sorting inﬂuences racial segregation and social stratiﬁcation that have
implications for both social cohesion and equity. Competition directly inﬂuences school
efﬁciency, but the causal relationship between the two can only be established after
controlling for the sorting effects of students and endogenous location of choice schools.

With this study, I attempt to evaluate Michigan’s charter school program more
comprehensively. Applying Levin’s framework, 1 estimate the effects of charter schools
on efﬁciency, equity, and social cohesion by answering two broad questions. First, does
student sorting lead to more racial segregation and stratiﬁcation by student SES and
ability in charter schools and TPSs? Second, does charter competition increase school
efficiency for TPSs? Before examining these questions, I offer a brief history of school
choice and school funding in Michigan so as to provide context in which to situate the

data I will explore later.

School Choice Context in Michigan

Michigan provides an interesting setting for the study of school choice policies
because it gives parents a wide array of choices. In addition to the traditional choice
programs such as intra-district choice, home schooling, and magnet schools, Michigan
further expanded parents’ opportunities to select their children’s schools with the passage
of two state-level school choice programs in the 19905: a charter school program and an
inter-district choice policy that allows students to choose public schools located outside
their home district. In addition, the state’s school ﬁnance system, commonly designated
Proposal A, greatly facilitated the development of the two choice programs by allowing
per-pupil funding to follow students to the schools they attend. In short, it set up a
market-driven system of schooling in which public schools—both traditional and charter

schools—began to compete with one another.

Charter School Program

In 1993, Michigan became the eighth state to adopt a charter school law. A charter
school, ofﬁcially designated a public school academy (PSA) in Michigan, is a state-
supported public school that operates independently under charters granted by an
authorizing body. A PSA could be organized by educators, parents, or others (e.g., any
nonproﬁt organization) and authorized by a publicly elected body with an educational
mission, such as a local, intermediate, or state board of education or the elected
governing board of a public community college, college, or university. A charter school
is supposed to enjoy the operational autonomy of a private school while being held

accountable for meeting state performance standards and, as of 2001, standards under the

12

No Child Left Behind (N CLB) Act. All attendees are “active choosers” as all enrolled
students select the school and no one is compelled to attend. Charter schools have no
geographic boundaries as do TPSs. Students are free to choose to go to any of charter
schools in the state, on a space available basis. PSAs can serve any grades but most
charter schools in Michigan serve students only in the K-8 range.

Originally, no limit was imposed on the number of charters that could be issued by
any of the authorizing boards. However, in 1996, following a proliferation of charters
issued by the board of Central Michigan University, the legislature imposed a cap on the
total number of schools that may be chartered by the 15 public universities in the state.
This cap of 150 schools has limited new school development since 2000. However, there
is no cap on the number of schools chartered by other organizations. Thus, charter
schools in Michigan have developed steadily during the past decade. With the ﬁrst
charter school founded in Detroit in 1994, Michigan had 226 charter schools by 2005.
The majority of Michigan charter schools now contract for services with private, for-
proﬁt Educational Management Organizations (EMO). About 92,000 students (or ﬁve
percent of the state’s public school population) enrolled in charter schools in 2005. So far,
Michigan’s charter enrollment is the third largest in the nation after California and

Florida.2

Inter-district Choice Program

In 1996, the Michigan legislature created an inter-district choice program, commonly
known as “schools of choice” program. All local public school districts can determine

whether or not they will accept nonresident students in their schools. However, they

 

2 Source: http://www.publiccharters.org/section/states/mi

I3

cannot prohibit students who live within their boundaries from attending public schools
in another district that admit them.3 Districts are responsible for publishing the schools,
grades, and programs that are available for nonresident students and for accepting
applications. Random selection by lottery, with certain exceptions, must be used if the
number of applicants exceeds available space.

Under the provisions of Section 105, students may leave any resident district to enter
a choice school within the same intermediate school district (ISD), in most instances
deﬁned by county boundaries. A new component of the state’s inter-district choice policy
(Section 105C) was subsequently added, and it permits districts to enroll nonresident
students from local districts in contiguous ISDs. Up to 2004, about half of Michigan’s
555 local districts enrolled nonresident students under the inter-district choice program.
About 80,000 students enrolled in school of choices under the state’s inter-district choice

policy in 2004.

Proposal A

In 1994, Michigan voters approved Proposal A, a school ﬁnance reform movement
that shifted the funding responsibilities from local districts to the state. Local voters could
no longer increase taxes to support school operations. Under Proposal A, school districts
have received almost all their operational revenues from the state on a per-pupil basis.
Each student receives a foundation grant, which was approximately $6875 in 20064. That

money goes directly to the school district that the student attends.

 

3 Inter-district choice is a state program. School districts within an intermediate school district (ISD) may
develop their own inter-district plans that operate in place of the state’s policy.

A small set of hold-harmless districts, whose foundation in year 1993-94 was $6,500 or greater, are
eligible to levy additional local property taxes to sustain funding above the state basic foundation
allowance.

In addition to state and federal categorical aid, each charter school receives a per-
pupil allowance equal to the foundation allowance of the district in which the school is
located. For inter-district choice students, the revenue follows automatically to the
districts where they attend schools. Districts enrolling an inter-district choice student
receive the lesser of the foundation allowance of the resident district or the enrolling
district. Enrolling districts are prohibited from charging tuition in any form to make up
any revenue differences.

Proposal A creates ﬁscal incentives for schools to compete for students through
school choice program, because operating revenue that districts and charter schools
receive depends directly on the number of students that they enroll. The only way the
schools can increase their revenue is to attract more students.

Arsen et al. (2002) argued that charter schools and inter-district choice pose very
different kinds of challenges for Michigan’s public schools and school districts. Charter
schools are new entrants to the market for schooling. In order to survive and expand, they
have to compete aggressively with TPSs for students. Hence, charter school program
generates sharp and intense competition between charter schools and TPSs. By contrast,
Michigan’s inter-district choice is more controlled, unfolding almost entirely within ISDs
or among contiguous ISDs. In some cases, district superintendents within ISDs, have
cooperated or colluded with each other in order to manage competition among
themselves and protect individual districts from excessive enrollment losses (Arsen et al.,
2002)

In addition, Arsen et al. (2002) pointed out there are ﬁve dimensions of local context

that are important in determining the extent to which school choice policies affect the

 

schools and school districts: socioeconomic status, socioeconomic diversity, school
district enrollment size, population density, and population growth. Because school
districts in Michigan differ considerably in these ﬁve dimensions, charter schools and
inter-district choice create very different impacts on school districts in different parts of
the state. Generally speaking, urban districts and surrounding low-income suburban
districts tend to attract extensive competition from charter schools because they have high
student density, and have a large proportion of parents who are not satisﬁed with the
education their children receive. On the other hand, inter-district choice is less likely to
be available to students in urban districts, especially those with very high concentration
of minority and low-income students, due to supply-side restrictions on the openings for
transfer students established by suburban districts. Despite increasing ﬁnancial pressures,
many surrounding suburban districts are unwilling to accept nonresident students from
urban districts given community resistance and the political risks for local district
administrators and board members of altering the racial or social class composition of
local schools.

In suburban and rural areas, however, school districts are less likely to face
competition from charter schools. Low student population density in rural areas makes it
hard for charter schools to draw enough students. Also, as public education quality is
usually good in suburban areas, it is hard for charter schools to attract enough students
who seek for alternative educational options, unless they live in nearby central city
districts. On the other hand, inter-district transfers may be more attractive in low-density
areas because some children must travel much farther to their assigned public school than

they would to a school in an adjacent district. Students from suburban areas might be

l6

attracted to programs from neighboring districts and accepting nonresident students from
the neighboring suburban districts might not be an issue because perceived social
difference between neighboring districts are not large (Arsen et al., 2002).

Together, the school choice programs and the school ﬁnance system in Michigan
have created one of the most competitive markets for schooling among the ﬁfty states.
The inﬂuence of charter schools in Michigan consequently has signiﬁcant implications

for the larger debate about school choice policies in the nation.

CHAPTER 2 CHARTER SCHOOLS AND STUDENT SORTING

As noted in Chapter 1, charter school policy allows students to select from different
schools and for schools to provide differentiated educational services. This inevitably
creates a re-sorting or redistribution process that rearranges students among schools.
Years after the ﬁrst policies were put into place, one central issue concerning equity
persists: are all students provided equal opportunity to choose, and does choice lead to
greater racial and social integration of students across schools?

This chapter and the following chapter address some of these questions by analyzing
Michigan’s charter school program. This chapter is organized as follows. In the ﬁrst
section, I summarize the literature on how the introduction of charter schools inﬂuence
racial segregation and social stratiﬁcation. I also review the literature for inter-district
choice, since it is part of my empirical analysis. In the next section, I specify three
research questions related to charter schools and student sorting. Next, I describe my data
and methodology. After that, I present the results for my ﬁrst two research questions:
who participates in charter school programs and do charter schools differ from TPSs in
student composition? The third research question, the impact of charter schools on

student composition in TPSs, is analyzed in Chapter 3.

Previous Research: Consequences of Sorting under Public School Choice

Along with the fast development of charter school policy, there is a growing body of
literature studying how the sorting mechanism it created inﬂuences racial segregation and

social stratiﬁcation. My review of previous research is organized around three issues that

highlight whether the analysis focuses on individual students or schools, charter schools
or TPSs:

(1) How do rates of participation in charter schools vary across student groups by race,
SES, and achievement?

(2) Does the sorting of students generate increased or decreased homogeneity of
students within schools? That is, are charter schools more homogenous or diverse than
TPSs by race, SES, and achievement across schools?

(3) How does the sorting of students inﬂuence student composition in TPSS? Does it
generate an increased concentration of disadvantaged students in disadvantaged TPSs?

The ﬁrst two topics have been extensively studied, while the third remains mostly
untouched. Among the existing studies, I argue that the empirical evidence is not

conclusive and much of it is ﬂawed.

Who Chooses Charter Schools?

This question has been examined by a series of annual reports on charter schools
published by the US. Department of Education. Using national data collected from
National Center for Education Statistics (N CES) Common Core of Data (CCD), the
studies made cross-sectional statewide comparisons of the overall racial and social
composition of charter schools versus all public schools in the states with charter schools.
The reports consistently found that, nationwide, students in charter schools have similar
demographic characteristics to students in all public schools. However, it is critical to
note that in several states charter schools serve signiﬁcantly higher percentages of
minority or economically disadvantaged students (Colorado Department of Education,

2000; US. Department of Education, 1997; 1998; 1999; 2000).

Camoy et al. (2005) systematically examined whether charter schools attract more
socioeconomically disadvantaged students than do regular public schools within
otherwise similar demographic categories.5 Using NCES data, the authors performed
cross-tabulations of race and SES to examine the characteristics of all charter and regular
public school students nationally. The results show that within each racial category,
regular pubic schools have a greater share of low-income students than charter schools.
The authors also summarized 19 studies of charter school demographic characteristics
from 12 individual states and the District of Colombia and reached the same conclusion:
although charter schools tend to have higher percentages of minority students, the
average SES of those students is either equal to or more advantaged than the minority
students in TPSs.

Research on whether students choosing charter schools are higher or lower achievers
than students remaining in TPSs is very limited. In a recent study, Booker, Zimmer and
Buddin (2005b) compared individual test scores of charter students in the year before
their move and found that in Texas, students who move to charter schools are, on average,
lower performing than other students at the public schools they leave. However, little
evidence of ability sorting into charter schools was found in California in the same study.

Another study of Arizona’s charter schools also concluded that students had lower test

 

5The Economic Policy Institute (EPI)’s analysis on SES stratiﬁcation comes as a byproduct of statistical
debates over whether charter or TPSs are more effective. Since student achievement is correlated with
family SES, researchers have been obliged to control for family SES in making comparisons of student
achievement. Using NCES data, researchers at the American Federation of Teachers (AFT) showed that
charter school students performed signiﬁcantly behind students in TPSs (Nelson et al., 2004) However,
charter school proponents charged that the AFT study “fails to meet professional standards” because it only
controlled limited information on the family background. Proponents argued that many charter schools
enroll more disadvantaged students, “black students who attend charter schools may well come from poorer
families than black students in TPSs” (Mathews, 2004) If this is the case, the inability to control for student
SES makes the conclusion that charter schools are less effective than public schools implausible, even
though charter school students’ scores were lower on average. EPI’s analysis comes as a response to the
debate.

20

scores before they entered charter schools than did comparable students in regular public
schools (Solmon & Goldschmidt, 2004). However, the comparison was based on
students’ test scores at the end of their ﬁrst year in charter schools instead of scores
before they entered charter schools. This is ﬂawed because several studies have
suggested that in the ﬁrst year after students transfer to a new school, their achievement
tends to drop (Bifulco & Ladd, 2004; Hanushek et al., 2003). Therefore, the comparison
was downward biased for charter school students.

Most previous studies about who participates in charter schools are cross-sectional
comparisons of total charter and TPS students at the state level, and only a few conducted
comparisons at the school or district level. Highly aggregated analyses might mask the
variations within individual schools or districts because they do not take into account the
possibility that charter schools are not randomly distributed across local communities

with very different racial or social characteristics.

Student Composition in Charter Schools and TPSs

Realizing state averages can mask variations in the racial distribution of students
among schools, a study released by the Civil Rights Project at Harvard University
provides an alternate methodological approach (Frankenberg & Lee, 2003). The study
used more recent CCD from 16 states that had total statewide charter enrollments of at
least 5,000 students in 2000-01 to make cross-sectional state-level comparisons of the
racial composition of charter schools and non—charter public schools. The authors
calculate racial exposure indexes, and investigate the concentration of students of all
races in racially imbalanced and isolated schools. By this measure, the study concluded

that charter schools displayed higher levels of segregation than TPSs.

2l

A number of other researchers have compared the racial composition of charter
schools to that of all regular public schools in their host district or to geographically
adjacent schools (Ascher & Wamba, 2000; Cobb & Glass, 1999; Colorado Department of
Education, 2000; 2001; Miron & Nelson, 2002a; Miron et al., 2002b; Weiher & Tedin,
2002). A standard strategy is to determine the portion of charter schools that have
unusually high or low concentrations of a given racial group relative to district average or
nearby schools. These studies tend to ﬁnd that charter schools either are not racially
distinct from their surrounding districts or are less racially diverse than their surrounding
districts. In other words, charter schools are not more racially integrated compared to
nearby TPSs. The consistency of the ﬁnding is very surprising given the large inter-state
variation in charter school policies and the very different patterns of racial segregation in
TPSs.

Available evidence on whether charter schools are more homogeneous in terms of
student social class than TPSs is much more limited and inconclusive. Carol Ascher and
her colleagues (2000) analyzed data from more than 550 charter schools in twenty-six
states. When disaggregated to the district level, they found that only 35 percent of charter
schools were socio-economically diverse as compared to 72 percent of public schools in
surrounding districts. They conclude that charter schools are more homogeneous in
student SES than TPSs.

Studies found mixed evidence on whether charter schools “skim” high-performing
students. Using the National Assessment of Educational Progress (NAEP) data,
researchers at the American Federation of Teachers (AFT) found that, overall, charter

school students had test scores that were a half a grade lower than scores of students in

22

TPSs (Nelson et al., 2004). NCES’s own study also conﬁrmed the AF T’s ﬁndings (NAEP,
2005). Responding the AFT study, Hoxby (2004) reached the opposite conclusion. Using
state assessment data, she compared the reading and mathematics proﬁciency of charter
school students to that of their fellow students in the nearest regular public school with a
similar racial composition and found that charter students are 5 percent more likely to be
proﬁcient in reading and 3 percent more likely to be proﬁcient in math. Later, however,
researchers at EPI re-examined Hoxby’s study using the same data, and found that her
results of the higher math and reading proﬁciency in charter schools disappear when
racial composition and low-income status are directly controlled (Roy & Mishel, 2005).
Nevertheless, all these studies used cross-sectional comparisons and were unable to
determine whether the low test scores of charter school students were due to charter
schools disproportionately attracting students with lower academic achievement or to
charter schools being less effective in raising student performance. A possible way to
address this issue is to compare students’ pre-choice test scores to scores of students in
the TPSs they left. If choice students whose scores before they decided to choose were
lower than those of students they left behind, it can be inferred that choice students are

more academically disadvantaged than comparable students in the TPSs.

The Impact of Charter Schools on Student Composition in TPSs

Compared to the extensive study of the ﬁrst two questions—what kinds of students
participate in charter schools and whether charter schools are more stratiﬁed than TPSs,
the impact of charter schools on student composition in TPSs remains mostly untouched.
Cross-sectional comparisons of racial composition are not sufﬁcient to assess whether or

not charter schools are exacerbating racial segregation and social stratiﬁcation in TPSs

23

because factors other than choice programs may also affect student composition in TP85,
and children in choice schools would not necessarily attend TPSs in the absence of choice
programs.

One strategy for overcoming this impasse is to utilize panel data to measure changing
patterns of racial composition in TPSs caused by the introduction of charter schools. Dee
and F u (2004) utilize school-level panel data from Arizona and New Mexico, to
implement a “difference-in-differences” research design to study the inﬂuence of charter
schools on racial segregation in Arizona public schools. Using public schools in New
Mexico as the control group, the authors estimate the change in the percentage of White
non-Hispanic students in Arizona public schools before and after the charter school
policy was introduced relative to the change in New Mexico’s schools. The results
suggest that the introduction of charter schools in Arizona has signiﬁcantly reduced the
proportion of White non-Hispanic students in TP85, and therefore increased racial
segregation. This study contributes signiﬁcantly to our understanding of the impact of
school choice on TPSs. However, the study only addressed one dimension of the choice
policies’ potential impact. Important questions remain: what kinds of TPSs tend to lose
students to charter schools? After students are drawn away to charter schools, some
subsequently return to TPSs. We have no previous research that examines the net effect
of these transfer patterns on the racial, SES, and academic composition of students in
TPSs

To summarize, existing research has studied the impact of charter schools on racial
segregation and social stratiﬁcation from a variety of aspects. The question of who are

active choosers was studied by comparing the demographics of choosers and non-

24

choosers at the state and national level. Most studies show that, overall, minority and
low-income and low-performing students are slightly more active in choosing charter
schools. Studies regarding the second question whether charter schools are more
homogenous than public schools usually compare student characteristics of charter and
TPSs at school, district, or even state levels. Although consensus has not been reached
about stratiﬁcation by SES and performance, researchers tend to agree that charter
schools are either not racially distinct from or less diverse than surrounding district or
nearby TPSs. However, as the educational opportunities of disadvantaged students has
been the persistent concern, the third question, how the emergence of charter schools
inﬂuences the stratiﬁcation by race, SES, and performance level in TPSs, especially high
poverty schools, remains unaddressed by existing research.

One big challenge faced by researchers is that sorting is an inherent phenomenon of
school choice. Aggregated analyses and cross-sectional comparison mask the variation
among schools due to the endogeneity of charter school location. Comparisons of these
kinds will not answer whether charter schools draw the “better” students from a school or
draw students from “better” schools, and whether students left behind enjoy less
diversiﬁed learning environments compared to the choosers.

Using panel data at the student level to discern the dynamics of student ﬂows is one
possible approach to circumventing the endogeneity problem. In principle, we would like
to compare the characteristics of active choosers to the characteristics of their classmates
in both the schools they transferred from and to. By examining the characteristics of
students who move from a regular public school to a charter school (or move from a

charter to a regular public school) with their new and former peers, we can isolate the

25

social nature of the sorting process facilitated by choice policies. Data of this type would
enable researchers to discover both whether school choice increases racial segregation
and whether active choosers tend to be more or less disadvantaged relative to other
students in their schools. Unfortunately, panel demographic data at the student level are

usually unavailable for charter school research.

Inter-district Choice

Most of the conceptual and methodological issues discussed to this point regarding
the impact of charter schools also apply to the analysis of inter—district choice policy.
Many states have introduced open-enrollment policies under which students can attend
public schools outside their district of residence. Provisions vary across states, but as in
the case of charter schools, all or most of per-pupil funding typically transfers with a
student to the educating district. A key feature of inter-district choice policies is that
school districts can generally decide whether or not to open themselves to nonresident
students.

Compared to the research on the impact of charter schools, limited evidence exists
about inter-district choice policies. One of the most extensive studies of inter-district
choice was done in Massachusetts. Using data from multiple sources, mainly student
level data and the data collected from 20 districts with more than 100 transfers under
inter-district choice, Armor and Peiser (1997) showed that choice students tended to be
White and more afﬂuent than the overall demographic make-up of districts that they left.
Another study in Michigan found that students active in inter-district choice are generally
moving to districts with higher test scores, with higher family income, and lower

concentrations of Black students (Arsen et al., 1999). In Georgia, where school districts

26

can establish their own policies under which students are allowed to transfer, a study
(Doering, 1998) found that minorities were underrepresented in inter-district choice
programs. Choice students were primarily White students transferring from White school
districts to districts that were also primarily White.

All these studies indicate White and relatively afﬂuent students are more likely to
take advantage of inter-district choice. However, cross sectional district-level data are
insufﬁcient to explore the change of racial composition of participating districts resulting
from the policy. The lack of information on choice student makes it impossible to
compare choice students’ characteristics with those of students in either sending or
receiving districts.

A more recent study (N i & Donahue, 2004) on inter-district choice in Michigan used
student level data, and found that the program increases racial segregation and
socioeconomic stratiﬁcation in central city districts because more affluent and White
students attend schools outside their residing districts. Unfortunately, the study’s data
could only identify the resident districts of choice students, but not their assigned public
schools. As a result, the analysis could only discern the impact of sorting at the district
level instead of the school level. As in the case of charter schools, it would be desirable to
study this question with panel student-level data, with which one could track the ﬂows of
choice students among TPSs.

How sorting inﬂuences racial segregation and social stratiﬁcation is a complex issue.
The accuracy of measurement depends not only on the sophistication of methodologies,
but also on the availability of detailed data. In addition, choice policies vary widely in

terms of their ﬁnancial features, and regulations, as well as support service in different

27

states (Levin, 2002). Research ﬁndings in one state often cannot be easily generalized to
another state. On balance, given the different conditions under which choice policies
operate and the limitations of research methodologies and data,.we really do not know
much about the issue of racial segregation related to charter schools and inter-district

choice (Gill et al., 2001; Wells et al., 2000).

Research Questions

In order to study student sorting associated with charter schools, I use two years of
student-level data to study the impact of Michigan’s charter school policy on student
composition by race, SES, and student performance level from several different
perspectives. Speciﬁcally, I ask three sets of research questions:

(1) Who chooses to attend charter schools? Are they systematically different from the
students in TPSs by race, SES, and performance? Do the results vary across different
types of communities, including central city, suburban, and rural areas?

(2) Are charter schools more homogeneous or more diverse than TPSs by race, SES,
and performance level?

(3) How does the sorting of students inﬂuence student composition in TPSs? Does it
lead to more integration or segregation and stratiﬁcation?

In this chapter, I will focus on question (1) and (2), while in Chapter 3 I will answer
question (3). Students remaining in the public schools, especially those attending schools
in inner cities with high concentration of low-income and minority students are the main
concerns of researchers and policy makes as well. Although these schools are heavily

impacted by the introduction of charter schools, how sorting inﬂuences their situation has

28

not received much explicit attention from existing studies. Therefore, I will put more

emphasis on the third research question in my analysis.
Data and Empirical Strategies

Analyses in this chapter and chapter 3 draw on data from multiple sources. The
primary data are obtained from the State of Michigan’s Single Record Student Database
(SRSD) for 2002-03 and 2003-04.6 The SRSD contains detailed individual information
on each student in Michigan’s K-12 public schools, including student age, gender, race
and ethnicity, free and/or Reduced Lunch (FRL) eligibility, school attended and
participation in programs as Title 1, special education, and gifted/talented. SRSD is
collected three times a year, so the database tracks all students as they progress through
Michigan’s public school system.

Several variables from the SRSD for the year 2002-03 will be analyzed to discern
students’ probability to change schools in 2003-04. These variables include the student’s
race, eligibility for receiving FRL, which serves as a proxy student SES. Information
about individual student performance, the scores of the state’s Michigan Educational
Assessment Program (MEAP) tests come from the ofﬁce of School Assessment and
Accountability at the Michigan Department of Education (MDE). Not all Michigan
students were tested annually on each subject. Each year, only students in certain grades
were tested in certain subjects. In this study, I focus on math and reading scores. During
2002-03 and 2003-04, reading was tested only in grades 4, 7, and 11, and math in grades

4, 8, and 11. School level data in this analysis are aggregated from student level data.

 

6 For more detailed information about SRSD, please visit the website of by the Center for Educational
Performance and Information (CEPI) of Michigan at www.michigan.gov/cepi.

29

For the ﬁrst research question of who attends charter schools in Michigan, I conduct
statewide descriptive comparisons of characteristics of students attending charter schools
and attending TPSs, in terms of race, SES, and student performance. I then further
disaggregate the comparisons according to where the students are from, in order to
explore how locations of charter schools matters inﬂuence what kinds of students they
attract.

For the second question of whether charter schools are more homogeneous than TPSs,
I compare student composition in PSAs and TPSs at district—level. I ﬁrst categorize all
charter schools into three types depending on where they draw their students. Then, I
compare their student composition with their comparing TPSs. In addition, I group TPSs
into four quartiles according to their racial diversity, SES composition, and performance
level to further investigate whether the effects of charter schools differ based on the
degree of homogeneity in the schools of nearby local school district.

The third question about the impact of student sorting on TPSs under charter school
policy raises the most interesting issues. I address this question separately in Chapter 3.
Using two years of student-level data, I am able to look at the distribution of students in
2002—03, knowing where students live and their social and educational characteristics,
and examine where they go to school in 2003-04. So, I trace all students in the state who
move from one school to another (under both charter school and inter-district choice
policies), and examine how that movement is related to student, school and community
characteristics. The analyses rely on a set of Multinomial Hierarchical Generalized Linear

Models (HGLM), which incorporate data for individual students nested in schools so as

30

to discern the dynamics of student ﬂows at two levels: the individual student level and

the school level.

Descriptive Analyses

School choices in Michigan have developed very fast during the past decade. As
Table 2.1 shows, by 2004, Michigan had 218 charter schools that enrolled roughly 73,000
students, or about 4.2 percent of the state’s public school students. 26,000 other students
participated in the state’s inter-district choice program, attending public schools outside
the district in which they lived. In total, choice students make up 7% of all Michigan’s
public K-12 students.

Table 2.1 Aggregate Participation in Michigan’s School Choice Policies in Selected Years

 

 

School Year 96-97 98-99 00-01 02-03 03-04
Number of PSAs 79 138 184 206 218
Number of PSA Students 12,047 34,319 56,417 66,567 73,039
PSA Students As 3 Percentage

Of K-IZ Students 0.8 2.2 3.5 3.8 4.2
Number of Inter-district 7,836 14,723 25,553 39,923 48,837

Choice Students
Inter-district Choice Students

As a Percentage of All K-12 0.5 ()_9 1.6 2,3 2.8
Students

Choice and PSA Students

As a Percentage of K-12 1.3 3.1 5.1 6.1 7.0
Students

 

In the following sections, I will focus on charter schools, answering the questions of
who attends charter schools and whether charter schools are more stratiﬁed than TPSs in

terms of race, social class, and performance.

31

Who Participates in Charter School Program in Michigan?

One central debate about charter school policy revolves around what kinds of students
charter schools serve—whether they serve the most disadvantaged or instead “cream” the
best students that are easier to educate. What kinds of students do charter schools attract?
Compared with TPSs, are charter schools more or less likely to enroll minority students?
Are charter students more or less likely to be poor? Do they perform better or worse than
students in TPSs?

In this section, the characteristics of students attending charter schools and TPSs in
Michigan are compared by race, SES, and academic achievement, as well as by
combinations of these characteristics. In addition, because charter schools are not evenly
distributed among different types of communities, charter and traditional school student
characteristics are also compared according to where students live: central cities, suburbs,
or rural areas. Comparing charter students to other students in the local area where they
reside instead of where they attend school is important because students are free to attend
a charter school anywhere in the state. In fact, many students in Michigan attend charter
schools outside their resident districts.

Racial/Ethnic Distribution of Charter and TPS Students

The data show that Michigan’s charter schools, or PSAs, are indeed serving a
disproportionate share of the state’s Black students. As shown in Table 2.2, Black
students made up 54 percent of all PSA students in Michigan, a ﬁgure that is three times
the percentage of Black students in TPSs. By contrast, White students represented 37
percent of PSA students, only half the percentage of White students in the TPSs. The

high percentage of Black in PSAs is primarily a function of charter school location.

32

About half of Michigan’s PSAs are located in Detroit and other central cities, attracting
students from these cities and their surrounding low-income suburbs where Black
students are concentrated (See Appendix A for the deﬁnition of community type).

Table 2.2 Percentages of Students in PSAs and TPSs by Race/ethnicity, 2003-04

 

 

 

 

. Percentage
gomemunity Total enrollment White Black Asian Hispanic
yp PSA TPS PSA ES PSA TPS PSA TPS PSA ﬂ
Detroit 29,882 153,706 6 4 89 90 0.4 1 4 5

Othercem‘al 17,371 168,532 41 44 47 41 1 2 7 11

cities
Low'mcome 3,105 43,641 22 51 71 39 2 3 3 5
suburb
M‘ddle‘mcome 15,090 680,110 74 85 17 9 2 2 3 3
suburb
H‘gh'mcome 2,492 269,068 81 88 7 4 6 5 2 2
suburb
Rural 5,099 356,639 84 93 2 1 1 1 2 3
Total 73,039 1,671,696 37 75 54 18 1 2 4 4

 

Students are organized by districts of residence.
In 2003-04, 399 out of 555 school districts had students attending PSAs, excluding the districts without
PSA students did not change the ﬁgures in the tables much.

Table 2.2 also compares the racial composition of PSA and TPS students by
community type of their residence. With the exception of Detroit, the data demonstrate
two opposing trends for White and Black students. For each community type, the
percentage of Black students in PSAs is higher than the percentage in TPSs, while the
share of White students is consistently lower in PSAs than in TPSs. The most dramatic
difference in the racial composition occurs in the low-income suburbs where the share of
Black students enrolled in PSAs is more than doubled the share in TPSs, and the share of

White students attending PSAs is almost 50 percent lower than in TPSs. By contrast, the

33

racial composition of students in Detroit’s charter schools and TPSs is very similar,
because students throughout Detroit are predominantly Black.

There are relatively few Hispanic and Asian students in Michigan schools, making up
only six percent of all students. The share of students who are Hispanic is slightly higher
in PSAs than in TPSs, while the percentage of Asian students is nearly double in TPSs as
compared to PSAs. When breaking into different communities, there is no signiﬁcant
distribution difference between PSA and TPS students among these two racial groups.
Comparison ofPSA and TPS Students by SES

As Table 2.3 shows, 42.6 percent of PSA students statewide were eligible for FRL in
2003-04, almost 10 percentage points higher than TPS students. This is consistent with
the conventional argument that PSAs serve more disadvantaged students than TPSs.
However, it is important to note that when this indicator of family poverty is
disaggregated by community type and racial group, PSA students within each racial
group are less likely to be poor than TPS students in most parts of Michigan.

Of course, the percentages of FRL students vary by community type. Disaggregating
the statewide data yields surprising results: In school districts where poor families are
concentrated, including Detroit, other central cities, and low-income suburbs, charter
school students are actually less likely to come from low-income families than are TPS
students. By contrast, in relatively afﬂuent middle- and high-income suburbs, PSA
students are generally more likely than TPS students to be eligible for the FRL program.

These patterns hold for both White and Black students, but to a greater extent for

Black students. In particular, the difference in poverty status is very big for Black

34

students from Detroit, indicating that Black PSA students from Detroit are much less
likely than their counterparts attending TPSs to come from low-income families.

In relatively afﬂuent suburban areas, however, charter school students are slightly
more likely to come from poor families than traditional public school students. Since
White students are more likely to reside in these suburban areas in Michigan, White PSA
students statewide are more likely to be eligible for FRL than White students in TPSs.

Table 2.3 Percentages of Students Eligible for Free/reduced Lunch by Race/ethnicity and
Community Type, 2003-04

 

 

 

% of FRL
PSA TPS Difference
(1) (2) (2)-(1)
Total - Statewide 42.6 32.9 -9.7
‘ Detroit 53.8 71.8 18.0
Other Central City 50.9 55.4 4.5
Low-income Suburb 52.1 54.3 2.1
Middle-income Suburb 24.7 23.3 -1.4
High-income Suburb 13.5 8.5 -5.0
Rural 30.6 35.0 4.4
White - Statewide 28.6 23.2 -5.4
Detroit 62.1 65.9 3.8
Other Central City 35.3 36.8 1.5
Low-income Suburb 42.7 44.9 2.2
Middle-income Suburb 22.3 19.9 -2.4
High-income Suburb 12.7 7.3 -5.3
Rural 25.9 33.6 7.6
Black — Statewide 53.7 63 .7 10.0
Detroit 51.6 71.2 19.6
Other Central City 63.7 70.2 6.5
Low-income Suburb 55.5 63.2 7.7
Middle-income Suburb 34.3 43.7 9.4
High-income Suburb 35.0 28.2 -6.8
Rural 54.8 61.8 7.0

 

MEAP Scores Comparison between PSA and TPS Students

35

While only students in certain grades took the MEAP tests in Michigan during 2003-
04, Table 2.4 shows that TPS students in those grades score higher on average than PSA
students in both mathematics and reading. This is not necessarily evidence, however, that
TPSs are more effective than PSAs. Such a comparison at one point in time does not
account for the possibility that charter schools attract lower-performing students on
average, nor does it capture gains in achievement over time.

Table 2.4 Average MEAP Scores of TPSs and PSAs at Certain Grades, 2003-04

 

 

PSA TPS Difference
(1) (2) (2)-(1)
Grade
Math
4 537 550 13
8 529 547 18
1 1 495 537 42
Reading
4 541 554 13
7 527 543 16
1 1 535 548 13

 

Table 2.5 presents more detailed information on 4th grade math MEAP score
comparisons. It shows that TPS students consistently have higher test scores than PSA

students for each community type, race, and SES subcategory.7

 

7 Results are similar for other grades and subject areas.

36

Table 2.5 Grade 4 Math MEAP Scores by Race/ethnicity and Community Type, 2003-04

 

 

PSA TPS Difference

Al) (2) (2)-(1)
Community type
Detroit 532 536 4
Other Central City 535 542 7
Low income Suburb 526 538 12
Middle income Suburb 544 552 8
High income Suburb 554 562 8
Rural 543 549 6
Race/ethnicity
White 541 549 8
Black 518 527 9
Hispanic 522 532
Asian 547 560 13
Socioeconomic Status
FRL 529 540 11
Non-FRL 543 555 12

 

Difference between PSA and TPS Students

The data show that the characteristics of students attending PSAs differ
systematically by race, SES, and achievement levels from students attending TPSs. First,
PSAs serve disproportionately more Black students than TPSs. One reason is that charter
schools are more likely to be located in central cities and attract students from central
cities and surrounding low-income suburbs, where Black students are more concentrated.

Second, charter school students are more likely to be socially disadvantaged than
traditional public school students at the state level. Further analysis of the data by
community type, however, suggests that charter schools “cream” the more socially
advantaged students in high-poverty areas, while serving more disadvantaged students

from affluent areas. This is true for both White and African American students. Since

37

White students are much less likely be from low-income areas than African American
students, on average White students attending charter schools are more
socioeconomically disadvantaged than White students in TPSs, while Aﬁican American
charter school students tend to be much less disadvantaged than Aﬁican American
students in TPSs.

Third, on average, charter school students have signiﬁcantly lower MEAP scores than
TPS students. The cross-sectional comparisons presented in this chapter do not attempt to
determine whether the low test scores of PSA students are because charter schools
disproportionately attracting students with lower academic achievement or because
charter schools are less effective in raising student performance. This issue will be further
explored in Chapter 3.

However, the claim that charter school students earn lower test scores than traditional
public school students because they serve a socioeconomically disadvantaged student
population is not valid for two reasons. First, this analysis shows that low-income PSA
students have signiﬁcantly lower scores than low-income TPS students. In addition, in
relatively less-afﬂuent communities, PSAs actually serve a more socially advantaged
student population than TPSs. This pattern is especially evident for Black students.
Except for the afﬂuent suburban areas, Black charter school students are much less likely

to be from low-income families than Black students in TPSs.

Are Charter Schools More Racially Segregated Than TPSs?

Whether charter schools lead to racial segregation or diversity remains an empirical
issue. Previous research has compared the characteristics of students in charter schools

and TPS, and found that charter schools tend to be less racially diversiﬁed than TPSs

38

(Cobb et al., 1999; Frankenberg et al., 2003; Wells et al., 2000). However, most of the
past research has tended to seek overall judgments on the effect of charter schools on
racial segregation. Yet it is quite likely that this effect will vary across local contexts. For
example, choice might decrease diversity in racially heterogeneous districts, but have
limited effect on the diversity of very homogeneous districts.

Any assessment of the degree of diversity in charter schools relative to TPSs requires
an appropriate speciﬁcation of the TPSs to which charter sschools are compared. Some
existing studies compare charter schools with the nearest TPS, based on the implicit
assumption that this is the school from which charters are most likely to draw their
students (Cobb et al., 1999; Hoxby, 2004). However, charter schools do not always
attract students from the nearest TPS. It is possible that charter schools draw students
from multiple districts, each with very different racial compositions thus complicating
any determination of the effect of charters on school racial diversity. One corollary of this
is that the effect of charter schools on diversity may vary systematically across central
city, suburban, and rural communities. Empirical evidence on patterns of this sort is very
limited. This section explores the following questions:

0 Are most charter schools more racially segregated than TPSS?

- Under what local circumstances are charter schools more racially segregated or

diversiﬁed than TPSs?

In order to address the limitation of previous research, charter schools in this section
are categorized according to the racial diversity of their comparison TPSs. In addition,
charter schools are grouped based on whether they draw students from a single or

multiple districts. The purpose of the categorization and grouping is to explore whether

39

the effects of charter schools on the racial diversity differ based on the degree of racial
diversity in the schools of nearby local school districts.

As Table 2.6 shows, in 2003-04, among the 218 charter schools in Michigan, 104
PSAs were located in central cities and 82 in suburban areas, the majority of which were
middle-income suburbs. The remaining 32 PSAs were located in rural areas. On the one
hand, all the PSAs were concentrated in 92 of the state’s 555 school districts. On the
other hand, PSAs drew students from districts all over the state. The majority of districts
(339) had resident students attending PSAs, no matter whether the PSAs were located
inside or outside their jurisdictions.

Table 2.6 Number of PSAs in Michigan, by Location, 2003-04

 

Districts Districts Sending

PSAS Districts Hosted PSAs Students to PSAs

 

Central city 104 15 15 15
Low-income Suburb 10 21 5 19
Middle-income Suburb 59 186 39 173
High-income Suburb 13 35 8 35
Rural 32 298 25 157
Total 218 555 92 399

 

Two methodological issues must be addressed in order to answer the question of
whether PSAs are more racially integrated or segregated than TPSs. First, what is the
proper measure for the degree of racial segregation? Second, what are the appropriate
TPSs to compare PSAs to?

Measure of Racial Diversity
There are many different approaches to measuring school racial diversity. A simple

method is to calculate the proportion of White students in the total enrollment, or

40

alternatively, Black students in the total enrollment. As the proportion of White students
(or Black students) declines from a very high value and by deﬁnition the proportion of
students of other racial groups increases, the student body necessarily becomes more
diverse. The major shortcoming of this measure is that it only measures one racial group
and ignores other groups.

A more reﬁned measure, Diversity Range (DR), is deﬁned as the reciprocal of the
difference between the enrollment shares of the largest and smallest racial groups.

DR=1——( % racial group with largest share -°/o racial group with smallest share)

In Michigan, the vast majority of students are from two racial groups: White and
Black. Therefore, instead of using the difference between the racial groups with the
largest and the smallest share, it is reasonable to use the range between White and Black.
The modiﬁed DR is deﬁned as:

DR= 1-——- | ( % White—% Black) |

DR ranges from 0 to 1. A high value implies more racial diversity, while a low value
means less racial diversity. For example, if a school has 60 percent White and 40 percent
Black students, the DR would be the 1 — (.60—.40) = .80, which implies high racial
diversity.

C omparison School Districts

Comparing a charter school’s student composition to that of a neighboring TPS would
be a sound method so long as the charter school attracts its students from the
neighborhood. However, in Michigan, this comparison is not appropriate because on
average, a typical charter school draws students from nine different school districts. More

than half of all PSAs draw students from more than ﬁve districts, and 19 schools draw

41

students from more than 20 school districts. This means that the neighboring TPS in the
districts where a charter school is located is frequently not the primary school of origin
for charter school students.

Therefore, I have grouped all 218 charter schools in Michigan into three categories
based on where the students they enroll come from. As Table 2.7 shows, Type I includes
133 PSAs that draw more than half of their students from the local public school district
in which the PSAs are located. Type 11 includes 44 PSAs that draw the majority of their
students from a district other than the one in which they are located. The remaining 41
PSAs, representing Type III, draw students from multiple districts, none of which
contributing more than 50 percent of the PSA’s enrollment.

When grouping charter schools by geographical features of the district in which they
are located, it is clear that the majority of PSAs located in central cities are Type I PSAs
that draw their students mainly from their host districts, while many suburban and rural
charter schools are Type II and Type III PSAs attracting their students from districts
outside the one in which they are located.

Table 2.7 PSAs and Comparing TPSs in Michigan, 2003-04

 

Number of PSAs in different communities

 

Other Low- Middle- High-
Total Detroit central income income income Rural
cities suburb suburb suburb

 

Type 1: Draw 50% or

more of their students 133 54 40 2 15 4 18
from host district

Type 11: Draw 50% or

more of their students 44 1 1 8 23 4 7

from a non-host district
Type III: Draw
students from multiple
districts, each less than
50%

41 2 6 0 21 5 7

42

Depending on where they are located and where they attract their students, student
composition of three types of PSAs systematically differs. Table 2.8 shows that compared
with the Type I PSAs, Type II PSAs tend to be more racially diverse, have a more
afﬂuent student body and higher average MEAP test scores. Type III PSAs are the most
racially diverse among the three types, and tend to enroll more afﬂuent students with
higher test scores than the other two types of PSAs.

Table 2.8 Student Compositions of PSAs, 2003-04

 

 

Diversity 0 Math MEAP Reading
Types Of PSA Range /0 FRL score MEAP score
Type I .36 52.0 522 529
Type II .45 37.6 526 534
Type III .72 21.8 531 542
Total .45 43.3 525 532

 

I compare the racial diversity of charter schools to that of the district where most of
their students live. For Type I PSAs, their primary sending districts are also their host
districts. For type II PSAs, the primary sending districts are not the host districts, but the
districts where most of their students would have attended school in the absence of choice.
Type III PSAs draw students more evenly from multiple districts. Therefore, they are
compared with their host districts, even though they might not be sending a signiﬁcant
share of students to the PSAs.

Racial Composition of TPSs and PSAs Statewide

As shown in Table 2.9, a large share of Michigan’s public schools, both TP85 and
PSAs, are racially segregated. Statewide, PSAs are more likely to be Black segregated,
and TPSs are more likely to be White segregated. This is hardly surprising, since students

in the vast majority of the state’s school districts are predominantly White and PSAs are

43

disproportionately located in central cities where Black students are concentrated. On
average, PSAs have a larger DR (are more racially diverse) than TPSs. In addition, PSAs
are 10% less likely to have very small DR (<.10) than TPSs. Both measures indicate that
when viewed from the level of the state as a whole, Michigan’s charter schools are more
racially diverse than TPSs.

Table 2.9 Racial Diversity Measures of PSAs and TPSs, 2003-04

 

 

PSA TPS
Average % of White 44.6 75.2
Average % 0 Black 45.1 16.8
% of schools with White>80% 28.9 66.9
% of schools with Black>80% 33.0 9.4
Average DR .28 .20
% of schools with DR<.10 41.7 51.1

 

In order to examine this issue further, PSAs are classiﬁed into three types, and their
DRs are compared with that of corresponding comparable districts. Each type of PSAs is
further disaggregated into four groups according to the racial diversity of their
comparable districts. This is because TPSs are not homogeneous. For example, rural
districts are usually highly White segregated, while districts in some central cities present
great racial diversity because of the large minority population. The racial diversity of
suburban district is generally between rural and central cities, but not always. Depending
on where their students come from, PSAs also vary largely in racial diversity. Classifying
the comparison districts into categories with different racial diversity help us to explore
whether the effects of PSAs on the racial diversity differ in school districts that were

more segregated or diverse.

44

 

I analyze Detroit separately for two reasons. First, Detroit is home to a quarter of
Michigan’s charter schools. Second, students in Detroit are predominantly Black, while
other Michigan central cities are more racially diverse. So patterns of charter school
diversity may differ in these urban settings.

PSAs Located in Detroit or Drawing Students Primarily from Detroit

In the 2003-04 school year, Detroit hosted 57 PSAs, 54 of which are Type I PSAs,
drawing students mainly from Detroit. The city hosted one Type II PSA, which drew
students primarily from a middle-income suburban district. The remaining two Detroit
charter schools are Type III, drawing students from multiple districts. Furthermore, 19
charter schools located outside of Detroit in middle-income suburbs drew a majority of
their students from Detroit.

As Table 2.10 shows, the racial diversity in the largest group of Detroit charter
schools (Type I) is very low and similar to that of Detroit Public Schools”. The racial
composition of the only Type II PSA located in Detroit is very similar to its sending
district—a neighboring middle-income suburb district that is also highly White

segregated.

 

8 All these PSAs are predominately Black, except that one is predominantly White and three others are
predominantly Hispanic.

45

Table 2.10 Racial Diversity of PSAS located in Detroit or Drawing Students Primarily
from Detroit and Their Sending Districts

 

 

#psa. PSA 11518;“ DR £5381. 63:18.1)...
(2)

Type 1 Detroit PSAS 54 .13 .12 -.01
Type 11 Detroit PSAS 1 .15 .10 -.05
Type II suburban PSAS

drawing students primarily 19 .32 .12 -.20
from Detroit

Type 111 Detroit PSAS 2 .40 .12 -.29

 

Interestingly, the 19 PSAs located outside Detroit drawing students primarily from
Detroit are signiﬁcantly more diverse than the TPSs in Detroit, mainly because they draw
disproportionately more White students from Detroit. In these PSAS, students enjoy more
diverse environment than TPS students in Detroit. Furthermore, the two Type III PSAs
located in Detroit draw a much more diverse student body from multiple surrounding
districts, which also show positive evidence of racial integration.

Type I PSAS Drawing the Majority of Students ﬁ'om Their Host Districts

Table 2.11 compares the diversity of Type I PSAS outside Detroit to that of their host
districts.9 These 79 Type I charter schools are grouped into four quartiles according to the
racial diversity of their host districts. The most segregated districts are in the 1St quartile,
while the most racially diverse districts fall in the 4th quartile. Columns two and three
show the mean DRs of charter schools and TP88 and their differences are displayed in

column three.

 

9 Median DR was tried as well, and was similar to those for mean DR.

46

Table 2.11 Racial Diversity of Type I PSAS and Host Districts, by Host District DR

 

School District PSA mean DR District mean DR Difference

 

(1) (2) (2)-(1)
1st quartile (most segregated) .07 .05 -.01
2nd quartile .30 .29 -.01
3rd quartile .48 .54 .06
4th quartile (least segregated) .49 .92 .43
Total .33 .47 .14

 

Lower DR value implies more racial segregation. Type 1 includes PSAS that draw more than 50% of their
students from the district where the PSA is located.

Table 2.11 shows that charter schools that draw most of their students from the
district in which they are located display a range of racial diversity. As one would expect,
PSAS located in racially diverse districts are more diverse than PSAS located in racially
segregated districts. On the other hand, charter schools are much less racially diverse than
TPSs in the most racially diverse school districts. Among all Type I charter schools
outside Detroit, the mean DR is signiﬁcantly lower (less diverse) than the mean of their
host districts. This difference is primarily caused by schools in the 4th quartile, where
PSAS are almost 50% less diverse than their host districts, all of which are located in
racially diverse central cities, such as Jackson, Grand Rapids, and Lansing. In these
racially mixed school districts, charter schools appear to constitute a much less racially
diverse learning environment.

In the 1st and 2nd quartile, comprised of the least racially diverse districts, PSAS are
about as segregated as their host districts. Most of these were predominantly White rural
and suburban districts, such as Charlevoix and Petoskey in the northern Lower Peninsula,
and Spring Lake in the western Michigan. For the 3rd quartile, where the districts are

more racially diverse, PSAS are slightly less diverse than TPSs. This difference, however,

47

is not statistically signiﬁcant. Included in this 3lrd quartile are racially diverse yet mostly
Black districts like Pontiac and diverse, yet mostly White districts like Ann Arbor.

The above analysis shows that overall Type I PSAS were signiﬁcantly more
segregated than the districts where they are located, but this is primarily a function of
charter schools being much less diverse than TPS in the most diverse public school

districts, since PSAS located in highly segregated districts are also racially segregated.

Type II PSAS Drawing the Majority of Students from a District Other Than the Host
M61

Most of the 25 Type II PSAS are located in suburban areas and attract their students
from central cities, while a few are in rural areas drawing students from other rural
districts.10

Table 2.12 shows that charter schools drawing students mostly from a very racially
homogeneous outside districts (1St quartile) are themselves very racially homogeneous,
although slightly less so than the outside district. PSAs in the 1St quartile were mostly
located in predominantly White districts in Michigan’s northern Lower Peninsula such as
Boyne City, Traverse City, and Marquette. PSAS in the 2"d quartile were actually more
racially diverse than schools in the primary sending district. When charter schools draw
their students primarily from the most racially diverse outside districts, they are much
less diverse than those districts. PSAS in the 3rd and 4th quartiles were mostly located in
suburban districts and drew students from nearby racially diverse central cities such as

Flint and Grand Rapids.

 

'0 This does not include 19 Type II PSAs drawing students primarily from Detroit.

48

Table 2.12 Racial Diversity of Type II PSAS and Sending Districts, by DR of Sending
Districts

 

Sending District

 

PSA mle)an DR Mean DR Digeraqce
(2)
1St quartile (most segregated) .08 .06 -.02
2nd quartile .44 .21 -22
3rd quartile .34 .57 .23
4’h quartile (least segregated) .47 .97 .50
Total .33 .47 .14

 

Type II PSAS refer to PSAS drawing students mainly from a district other than the district in which they are
located.

Type III PSAS Drawing Students from Multiple Districts

More than half of the Type III PSAS are located in middle-income suburbs or central
cities, where population density is high enough to attract enough students from multiple
districts. As Table 2.13 indicates, similar to Type II PSAS, Type III PSAS appear to be
more diverse than host districts when the districts are relatively segregated, while they

appear to be more segregated than the districts with greatest racial diversity.

Table 2.13 DR of Type III PSAS and Host Districts, by DR of Host District

 

PSA mean DR District mean DR Difference

 

(1) (2) (2)-(1)
1St quartile (most segregated) .28 .06 -.22
2nd quartile .22 .14 -.08
3rd quartile .49 .30 -.19
4th quartile (least segregated) .40 .78 .37
Total .36 .31 -.05

 

Note: Type III PSAs refer to PSAs drawing student from multiple districts, none of which contributed to a
signiﬁcant share of the enrollment of the PSA.

This section compares the Racial Diversity of the three types of PSAS that of TPSs in

Michigan. Several key conclusions emerge from this analysis. First, although statewide,

49

PSAS were more racially diverse than TPSs, not all PSAS are more diverse than TPSs in
Michigan. In fact, depending where their students come from, PSAS had very different
effects on racial segregation. PSAS drawing students mainly from .the districts in which
they are located tended to be more racially segregated than their host districts. The
evidence is even stronger when PSAS are divided by racial diversity of their host district:
PSAS located in racially segregated districts remained racially segregated and PSAS in
more racially diverse districts were signiﬁcantly less diverse than their host districts.

Second, charter schools drawing students from one district other than the host
districts show some positive evidence toward racial integration. Further disaggregated
analysis shows that PSAs drawing students from segregated districts are more racially
diverse than the districts, while PSAS drawing students from diverse districts are less
diverse than these districts.

Third, PSAS drawing students from multiple districts also show racial integration in
more segregated host districts, but not in districts that are racially diverse. However, as
mentioned earlier, their host districts might not be the best comparison group because the
PSAS do not draw a large share of students from their host districts.

In sum, the effects of PSAS on racial segregation vary across districts depending upon
the degree of racial segregation of the districts. Generally speaking, PSAS drawing
students from segregated districts, such as predominantly White rural or suburban
districts or predominantly Black Detroit, show no further racial segregation, and in some
cases show evidence of slight racial integration. However, where charter schools draw
their students from racially diverse districts—mostly central cities—they are less diverse

than these districts.

50

Are Charter Schools Serving More Socioeconomically Advantaged Students Than T PSs?

As shown earlier, the percentage of FRL students in PSAS is much higher than in
TPSs statewide in Michigan. However, PSA students from central cities and low-income
suburban areas are more socially advantaged than TPS students from their own racial
groups. Will this conclusion hold when compare SES composition of PSAS with their
host districts or sending districts? Do PSAS have lower share of low-income students in
high-poverty communities? Do they serve a relatively low SES student population in
relatively afﬂuent areas? In this section, the percentage of FRL students in PSAS is
compared with that of TPSs in their comparable districts. Similar to the analysis of racial
diversity, all the comparisons will be disaggregated according to two criteria: the types of
PSAS and the share of F RL students in their comparable school districts.

PSAs Located in Detroit or Drawilg Students Primarily from Detroit

Table 2.14 indicates that the Type I PSAS located in Detroit have smaller share (about
7 percentages lower) of FRL students than Detroit Public Schools. The one Type II PSAS
that located in Detroit draws a majority of its students from a neighboring middle-income
suburb district. Recalling that the racial composition of the PSA is very similar to its
sending districts, it is interesting to note that it has a much higher share (about 31
percentages higher) of FRL students than its sending district.

The percentage of F RL students in the 19 Type II PSAS located outside Detroit are
only half of that of its sending district—Detroit, indicating these PSAS are drawing
disproportionately non-poor students from Detroit. Furthermore, the two Type III PSAS
located in Detroit also have a much lower share of students eligible for FRL than Detroit

Public Schools.

51

Table 2.14 Percentages of F RL of PSAS Located in Detroit or Drawing Students
Primarily from Detroit and Their Sending Districts

 

PSA mean District mean Difference

 

(1) (2) Q)-(1)
Type I Detroit PSAS .67 .74 .07
Type II Detroit PSAS .74 .43 -.31
Type II suburban PSAS drawing 39 74 3 5
students primarily from Detroit ' ' '
Type III Detroit PSAS .45 .74 .29

 

Type I PSAS Drawing the Majority of Students from Host Districts

Table 2.15 compares the percentage of FRL students in Type I PSAS to that of their
host district means. The districts are divided into four quartiles according to the degree of
concentration of FRL students in the host districts of all Type I PSAS. According to Table
2.15, all Type I PSAS enroll a relatively lower share of FRL students than their host
districts in all quartiles but ﬁrst quartile, where the districts on average have a lower share
of FRL students. These districts include some middle- and high-income suburban, and a
few relatively afﬂuent rural districts. The difference in the 4th quartile is remarkable. The
mean percentage of F RL students is only 45 in PSAS located in high-poverty districts,
where 80 percent of all students in these districts are eligible for FRL. Most of the
districts in the 4th quartile are central city districts, including Lansing, Benton Harbor,

and Saginaw.

52

Table 2.15 Percentages of FRL of Type I PSAS and TPSs in Host Districts, by Percentage
of FRL of Host Districts

 

 

PSA mean TPS mean Difference
(1) (2) (2)-(1)
1St quartile (most afﬂuent) .35 .20 -.15
2'“1 quartile .41 .44 .03
3rd quartile .55 .61 .06
4th quartile (poorest) .45 .80 .35

 

Type II PSAS Drawing the Majority of Students from a District Other Than Host District

An examination of Type II PSAs reveals a similar trend as Type I PSAS. As
illustrated in Table 2.16, PSAS drawing students from districts with high percentages of
F RL students tend to have lower shares of F RL students than their sending districts. By
contrast, PSAS tend to have larger percentages of students eligible for FRL than TPSs
when the districts have lower shares of FRL students. However, the difference between
Type II PSAS and TPSs are not as big as between Type I PSAS and TPSs in high-poverty
districts.

Table 2.16 Percentages of FRL of Type II PSAS and TPSs in Sending Districts, by
Percentage of FRL of Sending Districts

 

PSA mean TPS mean Difference
(1) (2) (2)-(1)
1St quartile (most afﬂuent) .31 .11 -.20
2nd quartile .36 .27 -.09
3rd quartile .25 .44 .19
4th quartile (poorest) .60 .71 .12

 

Type III PSAS Drawing Students from Multiple Districts
As shown in Table 2.17, most of the Type III PSAS attract lower shares of FRL

students than their host districts. PSAS located in districts with relatively high

53

percentages of FRL students have lower shares of F RL students than their host districts.
Although in the 2nd quartile where districts have relatively low concentration of FRL
students, the share of F RL students in PSAS is higher than their host district mean. It is
only a difference of two percentage points.

Table 2.17 Percentages of F RL of Type III PSAS and TPSs in Host Districts, by
Percentage of FRL of Host Districts

 

 

PSA mean TPS mean Difference
(1) (2) (2)-(1)
1St quartile (most afﬂuent) .08 .10 .01
2"" quartile .24 .22 -.02
3rd quartile .24 .39 .14
4th quartile (poorest) .34 .59 .24

 

This section analyzes the SES composition of three types of PSAS with the mean SES
composition with their host or sending districts. In most cases, PSAS tend to attract
proportionately more afﬂuent students than TPSs in their comparing districts, no matter
whether they draw their students from a single district or multiple districts. The data
show that in districts with high concentration of low-income students, PSAS have
signiﬁcantly lower shares of low-income students. The only exception is that when
districts have a relatively low share of low-income students, PSAs located in or drawing
students primarily from these districts tend to have a higher percentage of FRL students.
For example, PSAS located in central cities attracting students from suburban areas tend
to have more poor students than their sending districts, which usually have small
enrollment rates of low-income students.

The comparisons of SES composition between TPSs and PSAS reinforce the

conclusion that PSAS “cream” more non-poor students from districts with high

54

concentration of low-income students, while attract more low-income students from

relatively afﬂuent districts.

Comparison of Performance Level in Charter Schools and TPSs

Aggregated analysis in the earlier section shows that, statewide, students attending
PSAS have signiﬁcantly lower MEAP scores than TPS students. In this section, I
compare student performance levels in PSAS with TPSs in their comparing districts. Do
PSAS differ from TPSs regarding to their students’ academic performance? If yes, do
they have academically less successful students than neighboring TPSs?

Following the same approaches for the comparisons of racial and SES composition of
PSAS and TPSs, I compare the mean MEAP scores, both math and reading, for the three
types of PSAS with TPSs in comparing districts, and disaggregate the comparisons
according to the mean achievement level of comparable school districts. The analysis
shows, in most cases, the three types of PSAS have lower MEAP scores in both math and
reading than TPSs in their host districts or primary sending districts. This is more evident
in districts that have high performance levels: the higher the mean district MEAP scores,
the larger the difference between district means and PSA means. PSAS do not always
have lower test scores than TPSs, however. In districts with very low levels of
performance, PSAS have similar or even slightly higher MEAP scores than mean TPS
scores. PSAS located in suburban areas that draw students from central cities also tend to

have higher test scores than TPSs in their sending districts.

55

Discussion

This chapter answers ﬁrst two research questions I posed in the beginning of this
chapter: who participates in charter schools and how charter schools differ from TPSs in
student composition. Both questions are analyzed through three dimensions: race, SES,
and academic performance. In answering question one, aggregated analysis of all
students attending charter schools and all students in TPSs are compared. For question
two, PSAs are grouped into three types according where they draw their students, and
compared with TPSs in their host districts or primary sending districts—schools that
charter school students would have attended in the absence of choice.

The analysis shows that charter schools in Michigan enroll disproportionately more
Black students than TPSs. This partly reﬂects the fact that half of the Michigan’s charter
schools are located in central cities, where minority students are more concentrated.
Further comparisons between charter schools and nearby comparing TPSs reveal that
most charter schools are more racially segregated than TPSs: PSAS located in or
primarily drawing students from racially segregated districts remains racially segregated
and PSAS located in or primarily drawing students from more racially diverse districts
tend to be relatively less diverse than TPSs. There are a few exceptions. PSAS located in
racially segregated districts yet drawing students from multiple districts are usually more
racially diverse than TPSs in their host districts. The number of these kinds of PSAs is
relatively small, however.

Racially diverse schools promote social cohesion. As pointed out in Chapter 1, many
studies have found evidence that racial integration in K-12 schools is important in

fostering more tolerant and open-mind adults. Students attended racially diverse K-12

56

schools are more likely to attend diverse colleges, live in integrated neighborhoods, work
in diverse ﬁrms, and have friends from another racial group. Indeed, the earlier the
students experience diverse learning environments, the greater the positive impact in
social cohesion (Orﬁeld & Lee, 2005). In Michigan, charter schools are largely serving
grades K-8. Many students in the racially segregated charter schools are experiencing
isolated learning environment in their early stage of education. This undermines
prospects for the development of understanding, respect, and tolerance across racial lines.
Second, the analysis reveals that charter schools attract more socially advantaged
students in high-poverty areas, while serving more disadvantaged students from afﬂuent
areas. There are a small number of PSAS located in or close to afﬂuent districts and draw
students from these districts. These PSAS tend to have a much higher share of low-
income students than TPSs from the districts. It is especially true for a few PSAS located
in central cities yet drew students from neighboring suburban districts. They usually have
relatively higher enrollment rates of low-income students than TPSS in their primarily
sending districts. In these areas, charter schools are expanding new educational
opportunities for low-income students. However, from a policy perspective, the concerns
arose in relatively poor school districts, where the majority of PSAS tend to have a
relatively more afﬂuent student body than TPSS in these school districts. This is
consistent with the claim of critics that charter schools “skim the cream” of higher SES
better-off students, although in my analysis, the skimming is limited to poor districts.
Third, almost all charter schools tend to have lower student achievement, MEAP test
scores in this case, than TPSS in their comparison districts. It is still too early from this

analysis to decipher whether the low test scores of charter schools is due to charter

57

schools attracting lower-performing students or to charter schools being less effective in
raising student performance than TPSS. If the low test scores result from a “composition
effect”—students with low-performing student choosing charter schools, this is positive
evidence that charter schools provide new opportunities for students who were poorly
served by TPSS. If, however, the low scores are results of poor performance of charter
schools in raising student achievement, we should worry about the validity of the
argument that competition will produce effective choice schools. We also need to worry
about the assumption that parents are rational consumers, choosing charter schools
because of their high quality as measured by student achievement. Although this
dissertation will not directly answer whether charter schools are more or less effective
than TPSS in raising student test scores, the student composition effect is further explored
in Chapter 3. Through a series of HLM models, the chapter explicitly examines whether
the likelihood of individuals’ choice to attend charter schools is related to their previous
academic performance.

In sum, while the ﬁndings in the chapter are largely consistent with conclusions from
previous studies in this area, it offers a much more nuanced picture than most pervious
studies. Charter school policy in Michigan redistributes students among PSAS and TPSS.
There is some positive evidence toward more racial integration and expansion of
educational opportunities for socioeconomically disadvantaged students. For example,
charter schools drawing students from multiple districts show some positive evidence
toward racial integration. A small number of charter schools drawing students from
afﬂuent districts tend to have higher share of low-income students than TPSS. However,

in most cases, charter schools tend to be more racially segregated, have a lower share of

58

low-income students, and tend to have lower performing levels than TPSS in comparison
districts.

TPSs in central cities usually have higher concentration of minority students than
TPSs from suburban and rural areas. Many TPSs in these districts are racially diverse,
except for Detroit and Benton Harbor Schools that are predominantly Black. Charter
schools in central cities districts not only increase racial segregation or remain highly
segregated; they further exacerbate socioeconomic stratiﬁcation among minority students.
Although the reasons for low performance level in charter schools are not entirely clear,
if PSAS unifome perform worse than TPSS, we should worry about the possibility that
charter schools exacerbate stratiﬁcation by student performance.

This chapter provides a static comparison of student composition between charter
schools and TPSS. In next chapter I start to model the dynamics of student ﬂow between
charter schools and TPSS, and answer the question how the student ﬂow changes student

composition in TPSS over time.

59

CHAPTER 3 THE IMPACT OF SCHOOL CHOICE ON STUDENT COMPOSITION

IN TRADITIONAL PUBLIC SCHOOLS

Most research about the impact of school choice policies on racial segregation and
social stratiﬁcation focuses on deciding what kinds of students become active choosers
and whether choice schools or TPSS tend to be more segregated or stratiﬁed. However,
the evidence on what kinds of TPSS tend to lose students to choice schools and the impact
of school choice on the student composition in TPSS, especially in predominantly
minority schools in high poverty communities, is very limited. Few existing studies have
combined analysis at both the student and the school level, which would allow us to
detect any systematic differences in sorting patterns among students from different
backgrounds across different schools, and therefore how school choice policies inﬂuence
student compositions in TPSS with different characteristics.

There are two signiﬁcant challenges in this research. First, sorting is an inherent
phenomenon of school choice. Aggregated analyses usually mask the variation among
schools due to the endogeneity of charter schools’ locations. Charter schools are not
randomly distributed across local communities with very different racial or social
characteristics. State or district level comparisons of student composition do not tell us
much about the impact at the student and school level. Second, student sorting initiated
by school choice is inﬂuenced simultaneously by the characteristics of individual
students and their families as well as the characteristics of the schools they attended.
Analysis focusing on either level alone will not create a comprehensive understanding of

the sorting process.

60

In order to address these limitations, this chapter utilizes multilevel regressions to
model student ﬂows initiated by Michigan’s two school choice policies—charter school
and inter-district choice—to evaluate their effect on the composition of students in TPSS.
Using two years of student-level data nested in schools, the dynamics of student ﬂows are
modeled at both the individual student level and the school level. The individual level
examines the student characteristics that inﬂuence their decision to move from their
assigned public school to a charter school (or move from a charter to an assigned school).
The school level explores characteristics of schools that that inﬂuence students’ decision
to switch schools. Taken together, the multilevel regressions tell us who participates in
school choice and how the sorting of students changes student composition in TPSS.

The ﬁrst section of this chapter explains possible directions of student movement
under Michigan’s two school choice programs. Section 2 describes three research
questions corresponding to the three different directions of student ﬂow. Section 3
discusses empirical methods including the speciﬁcations of the multilevel regression
models. The following section presents the empirical analysis and a concluding section

discusses the implications of the ﬁndings.

Student Flow under School Choice Programs

In 2004-05, about 82,000 students, or four percent of Michigan’s public school
students, were enrolled in charter schools. Michigan’s charter enrollment is currently the
third largest nationally after California and Florida. Another 80,000 students attended
TPSS outside their district of residence through the state’s inter-district schools of choice
policy. In total, approximately seven percent of all public school students currently

participate in one of the state’s two school choice programs.

61

Figure 1 illustrates student ﬂows under Michigan’s choice policies. First, the vast
majority of students attend schools in their home districts, or the assigned schools.ll A
relatively small proportion of these students choose to transfer from their assigned
schools to charter schools or inter-district schools of choice, that is, TPSS in a
neighboring district. Second, some students who formerly attended charter schools or
inter-district choice schools return to their assigned schools every year for a variety of
reasons. Finally, a very small number of students shift between the two choice programs.
For example, some charter school students might choose to switch to another public
school through inter-district choice, or inter-district choice students might transfer to a
charter school. It is necessary to study the full array of student ﬂows in order to ﬁnd out
how choice policies inﬂuence student composition in TPSS.

Figure 3.1 Student Flow through School Choice Programs in Michigan

 
  
   
 

  

Assigned
Public School

 
  

  
   
 

Inter-district
School of Choice

Charter ............... >
School <. ...............

 

” Traditionally, Michigan students can attend different schools within their resident school district through
intra-district choice. However, this is not the focus of this research. Thus, I treat all the schools in the home
district as the assigned schools even though parents can choose different schools within their home district.

62

Research Questions

In this chapter, I utilize student level data for the 2002-03 and 2003-04 school years
to track student movement among assigned and choice schools between the two years, in
order to investigate how student and school characteristics in 2002-03 predict attendance
patterns in 2003-04, and the impact of this sorting of students among schools on student
compositions in TPSS.

To comprehensively model the student ﬂow across different types of schools as
shown in Figure 1, I employ three sets of two-level Multinomial Hierarchical Generalized
Linear Models (HGLM). Each model addresses one of the following component
questions:

(1) For all students attending assigned schools in 2002-03, which students moved to
charter schools or inter-district schools of choice in 2003-04? And how do they compare
to students in their former school, in terms of their race, SES, and academic performance?
What kinds of TPSS tend to have more students transfer to charter schools or inter-district
schools of choice? Do school characteristics inﬂuence the likelihood of transfer
differentially among students with different racial or SES backgrounds?

(2) For all charter school students in 2002-03, who returned to their assigned schools
in 2003-04? What kinds of charter schools tend to have students returning to their
assigned schools?

(3) For all students attending inter-district schools of choice in 2002-03, who returned
to their assigned schools in 2003 -04? What kinds of TPSS tend to have nonresident

students return to their assigned schools?

63

The analyses of the above three questions present full information about the
individuals who actively choose or return and the organizational information about the
schools they choose to leave. While each question itself does not provide complete
information on the impact on TPSS, the net effect of student ﬂow can be assessed to see if
the sorting process changes the student composition in TPSS in terms of race, SES, and

performance level.

Methodology

As mentioned in Chapter 2, this analysis draws on data from multiple sources,
including SRSD for 2002-03 and 2003-04, and math and reading MEAP scores for 2002-
03. As noted, a series of multinomial HGLMs are utilized to analyze the student
movement initiated by school choice. All of these models have two levels, with similar
explanatory variables at both student level and school level. The outcome variable in the
level-1 models is a categorical variable, describing students’ transfer status. All the
explanatory variables at both levels are for 2002-03, while the outcome variable describes

the change of attendance status from 2002-03 to 2003-04.

Explanatory Variables

Student level:

At level-1, several student background variables are included to capture demographic
characteristics of students in 2002-03. Race/ethnicity is measured through a series of
dummy variables associated with minority status (Black, Asian, and Hispanic). SES is
measured by the eligibility for F RL. It is a binary variable, where students who are

eligible for F RL are deﬁned as low-income students, otherwise as non-low-income

64

students. A set of interactions between SES and each of the minority dummies are also
included to detect any differential effects of SES on transfer decisions for students from
different racial groups. Standardized MEAP scores in two subjects, math and reading,
measure student performance. It should be noted Michigan students do not take the
MEAP test every year. In 2002-03, Math was tested in grades 4, 8, and 11, and reading
tested in grades 4, 7, and 11. When test scores are added to the student level model, only
students in the tested grade are included in the model. In other words, in addition to the
model for all students, I estimate three additional models, each for grade 4, 7, and 8
students, with their MEAP scores for 2002-03 added in the student level models along
with other control variables.12 Two additional variables were also included in the level-1
model as controls: special education status and language proﬁciency status, measured as
whether the student is Limited English Proﬁcient (LEP) or not. Although a gender
variable was included throughout the preliminary analysis, it proved to have no
signiﬁcant effect and was eliminated.

School level:

At level-2, the unit of analysis is schools. The regression coefﬁcients in the level-

1 model for each school are conceived as outcome variables that are hypothesized to
depend on speciﬁc school characteristics. On the basis of the theoretical framework,
several school characteristics are supposed to inﬂuence students’ choice decision. First,
two types of student composition variables are aggregated for all the students to the
school level. They are percentage of students who are eligible for FRL, and the

proportion of Black, Hispanic, or Asian students. Furthermore, a school effectiveness

 

12 High school students are not analyzed due to the small sample sizes.

65

index is constructed as the difference between the actual average school MEAP score and
the predicted MEAP score, adjusting for differences in student background and other
characteristics that are outside a school’s control.13 This variable is standardized for the
convenience of interpretation.

Other variables such as educational level, school size, and location are also controlled.
Given the fact that in Michigan, students in elementary schools are more likely to
participate in school choice than middle and high school students, two dummies, each
reﬂecting the level of education, are included. The variable reﬂecting school size is
expressed in logarithmic notation to allow for diminishing marginal effects. This variable
captures possible different transfer trends in small schools versus large schools. School
location is very relevant to the opportunity of attending a charter school because the
availability of charter schools greatly differs by community type. Two dummy variables,
urban and rural, are introduced relative to the reference group, suburban districts.

Some other variables such as percentage of adults who are high school graduates, the
poverty rate, and the racial composition of school districts were considered, but were
eliminated because they were either highly correlated with each other or with variables

already included in the models.

Multinomial HGLM Descriptions

Using HLM to analyze the student sorting process induced by charter schools has
several advantages. First, both student characteristics and school characteristics inﬂuence
students’ decision to participate in a charter school program. Models focusing on either

student level or school level would lose information on the other level and induce

 

'3 The predictors included to predict school MEAP are: % of Black students, % of Hispanic students, % of
Asian students, % of F RL students, school size and urbanicity of schools.

66

estimation bias and inefﬁciency. HLM overcomes this limitation by incorporating data
from multiple levels (students nested within schools) to determine the impact of
individual as well as school factors upon individual level outcomes. The coefﬁcients at
the student level will reﬂect the difference in probabilities of transfer for students with
different SES, race, and performance within schools. The estimated coefﬁcients for the
student level models are allowed to vary across schools and any observed differences can
be modeled with school level variables (Raudenbush & Bryk, 2002).

Second, in order to examine whether certain organizational features of schools have
differential impacts on the likelihood of students from various backgrounds to transfer,
HLM also allows for the “slope-as-outcome” model at the school level (Raudenbush et al.,
2002). For example, if the coefﬁcient of the “BLACK” variable is found signiﬁcant at
level-l, it indicates that the likelihood of Black students to transfer to a charter school is
different from that of non-Black students. In order to determine whether this racial
difference in transfer propensity is associated with school factors, we can use the
coefﬁcient (or the BLACK slope) as an outcome variable and model it with school level
variables at level 2, which is referred to as the “slope-as-outcome” model. For instance,
the model helps to answer the question: are Black students from White-predominant or
Black- predominant schools more likely to transfer to charter schools?

To explain how the multinomial HGLMs are speciﬁed, return to my research question
(1): who actively participates in school choice? As mentioned earlier, only the students
who attended their assigned schools in 2002-03 are relevant in answering question (1),
which means that students who attended charter schools or inter-district schools of choice

in 2002-03 are excluded here. Taking all students who attended their assigned schools in

67

2002-03, I modeled their attendance status in 2003-04 as a function of their own
characteristics and the characteristics of the school that they attended in 2002-03 through
a two-level multinomial HGLM.

There are 3 possible options for the attendance status of each student, which takes on
the value of m with probability Prob (R=m) = (pm, for m = 1, 2, and 3, where 1 indicates

the student attends a charter school, 2 an inter-district school of choice, and 3 the
assigned public school. The level-l sampling model for the outcome variable is
multinomial, such that the three possible attendance choices of a student follow the

multinomial distribution. The link function is the multinomial logit link. The dependent
variable at level 1, nmij, is the log-odds of student i who attended school j in year 2002-03

transferring to a charter school (m=1) or an inter-district school of choice (m=2) in year
2003-04 relative to staying in the assigned public school (m=3), the reference group.
Speciﬁcally, for category m=1 and 2,
11ml] = log (rpm-j llp3,-j ) = log (Prob (R,-J=m)/Prob (Ry- =3)
There are two separate level-1 structural models, one for charter schools (category 1)
and the other for inter-district schools of choice (category 2), both relative to assigned

school (category 3). Predicted log-odds can be converted to an odds ratio by taking exp
(11m). The probability of transferring is expressed as 1 / (1 + exp (41mg) ).

The level-2 models have a parallel form for the two categories, charter schools and
the inter-district schools of choice. For each set of level-2 equations, the coefﬁcients in
the level-1 structural models are conceived as outcome variables that are hypothesized to

depend on speciﬁc school characteristics.

68

H m}: B 0,0,.) + sz B 6(le q.) for m=1,2 and q=1, ...,Q ,,,
q=1

Moreover, two slope-as-outcome models are speciﬁed at the school level to estimate
whether school characteristics have differential inﬂuences on the attendance choice of
students with different racial or SES backgrounds.

Similar to question (1), the models involved in answering questions (2) and (3) are
also multinomial HGLMs. Explanatory variables included in the student and school
levels are similar, but the outcome variables are different in terms of the categories. The
students included in analyzing question (2) are all students in charter schools in 2002-03,
and their transfer status in 2003-04 is a categorical variable that takes value of I (returned
to their assigned school), 2 (transferred to an inter-district school of choice), or 3
(remained in a charter school). Likewise, for question (3), all students in an inter-district
school of choice in 2002-03 are included, and their attendance status is a categorical
variable that takes value of I (returned to assigned school), 2 (transferred to a charter
school), or 3 (stayed in an inter-district school of choice).

Each set of models is built sequentially in a process started with a fully unconditional
model, with no predictors at either level. The predictors’ ﬁxed effects, signiﬁcance of
variance components and reliabilities of coefﬁcients are evaluated.'4 If the variance
components are not signiﬁcant, the random effects are constrained to zero in the interest

of parsimony. Such constraints are likely to be especially useful in multinomial models

since there are multiple outcome categories.

 

'4 Variance components are calculated only for level-2 models. Multinomial HGLM does not give
information on level-1 variance, so the ratio of level-l or level-2 variance to the total variation cannot be
calculated. Nevertheless, this measure is less informative in Multinomial HGLM because the level-1 link
functions are nonlinear, and the variance becomes heteroskedastic.

69

After the evaluation of the unconditional models, conditional models are built with
student characteristics (except for the academic performance variables) added only at
level-1. The intercepts for the student level models are allowed to vary across schools.
The variance of the error term can then be examined to see if there are signiﬁcant
differences between schools. If the variance term is not signiﬁcant, then the coefﬁcient is
“ﬁxed” so that the effect of the student level coefﬁcient is constrained to be the same for
all schools.

Next, conditional models are speciﬁed. In addition to the fully speciﬁed level-1
models, level-2 predictors are introduced to the level-1 intercept equations. Finally,
slope-as-outcome equations are introduced at level-2 to explore the different impact of
school characteristics on the likelihood of transfer for students with different racial and
social backgrounds, if the slope coefﬁcients at level-1 are signiﬁcant. The same sets of
multinomial HGLMs are built sequentially for students in grade 4, 7, or 8, with student
performance variables added at the student level.

In order to control for differences in student compositions between schools, all
student level variables were centered around their grand means. Thus, the intercept term
from the student level model represents the adjusted mean log-odds for schools assuming
that each school enrolled students who had mean characteristics for the entire population

of students.

Sampling Strategies
In the 2002-03, there were 1.7 million students in Michigan’s public schools.

However, only about 1.45 million students were found remaining in the system in 2003-

04. The 0.25 million students who were no longer in the system had either graduated,

70

moved out the state, dropped out of school, attended a private school, or were home
schooled in 2003-04. Among the students remaining in the system for the two
consecutive years, about 1.35 million students attended assigned public schools, 54,000
attended charter schools and 31,000 attended inter-district schools of choice in 2002-03.

As Table 3.1 shows, in 2003-04, the vast majority of students who attended their
assigned schools in 2002-03 remained in their assigned schools, only 0.8 percent
transferred to charter schools and 0.9 percent transferred to inter-district schools of
choice. Many TPSS did not have any students transfer to a charter school or an inter-
district school of choice. In order to have a reasonable transfer rate, only schools that had
more than 5 students transferring to charter schools or inter-district schools of choice in
2003-04 are included in answering question (1). According to this criterion, about 95
percent of transferring students are included in the analysis. In total, 1291 schools, or
about one third of all TPSS, are included in the analysis.

Table 3.] Attendance Status of Michigan Public School Students, 2002-03 and 2003-04

 

School Attended in 2003-04

 

 

Schoozlorgét-eorgded 1n Assigned Charter Inter-district Total
school school School of choice
Assigned school 1,328,950 10,797 1 1,769 1,351,516
(98.3%) (0.8%) (0.9%) (100%)
10,091 42,530 712 53,333
Charter ““001 (18.9%) (79.7%) (1.3%) (100%)
Inter-district 5,626 208 25,23 1 3 1,065
School of choice (18.1%) (0.7%) (81.2%) (100%)
Total 1,352,984 53,873 40,458 1,447,315

 

In contrast to the tiny portion of students who transferred from their assigned public
schools to charter schools or inter-district schools of choice, a much higher share of

charter school and inter-district choice students returned to their assigned schools

71

between the two years. As indicated in Table 3.1, among the 54,000 charter school
students in 2002-03, 19 percent returned to a TPS in their resident district in 2003-04.
Among the 31,000 students who attended inter-district schools of choice in 2002-03, 18
percent returned to their assigned school. Since the numbers of students transferring back
to assigned schools are fairly big, all the students in charter schools and inter-district
schools of choice in year 2002-03 with valid data are included in the analysis of questions
(2) and (3) analyses, respectively. In addition, student movement between charter schools
and inter-district schools of choice is very small and negligible. From 2002-03 to 2003-04,
among about 1.5 million students, only about 700 students transferred from charter
schools to inter-district schools of choice and about 200 students transferred from inter-
district schools of choice to charter schools. Although they represent a small component
of the entire sorting process and were analyzed in the HGLMs, these results are not

reported.

Findings

Question (1 ) .° Transferring from Assigned Schools to Choice Schools

A description of variables at both student and school levels is presented in Table 3.2.
A fully unconditional model is formulated where the log-odds of choice relative to
attending assigned schools are predicted via a two-level model with no predictors at
either level. The equations contain no error terms in the level-1. However, error terms are
included in the two level-2 intercept models to gauge the extent of between-school
variation on the two outcomes: my, the log-odds of attending a charter school (relative to

the assigned school), and 112,], the log-odds of transferring to an inter-district school of

72

choice (relative to the assigned school). The results are presented in Table 3.3. The
predicted grand mean log-odds of attending charter schools is =-4.72 (se=0.041), which
means for students in a typical school, the expected odds of choosing a charter school
versus staying in their assigned school is 0.009. In other words, the mean probability for
them to transfer to a charter school is estimated to be 0.88%. '5 Similarly, the predicted
grand mean log-odds of transferring to an inter-district school of choice is =-4.70
(se=0.03 5), which means the expected odds of students transferring to an inter-district
school of choice versus staying in the assigned school is 0.015, corresponding to a
probability of 0.9% of transfer. Estimated variances between schools for both categories
are signiﬁcant, which suggests sufﬁcient variation and the inclusion of these error terms
in the subsequent models. In addition, the reliabilities for both models at level-2 are 0.78

and 0.84 respectively, which are both within the range of satisfactory magnitude.

 

'5 Calculated as l/(l+exp 4.72)).

73

Table 3.2 Variables and Description, All Students in the Assigned Schools in 2002-03

 

 

Description N Mean SD Min. Max.
Student level
ATTENDANCE Categorical (1= charter; 2= Inter- 570926 2.95 0.28 1 3
STATUS district school of choice; 3=
assigned school)
WHITE Dummy (1=White; 0= no) 570926 0.59 0.49 0 1
BLACK Dummy (1=Black; 0= no) 570926 0.33 0.47 0 1
HISPANIC Dummy (1=Hispanic; 0: no) 570926 0.04 0.20 0 1
ASIAN Dummy (1=Asian; 0= no) 570926 0.01 0.12 0 1
FRL“ Dummy (1=Eligible for F RL, 570926 0.43 0.47 0 1
=no)
BLACK F RL Interaction between Black and 570926 0.21 0.41 0 1
FRL
ASIAN FRL Interaction between Asian and 570926 0.01 0.08 0 1
FRL
HISPANIC F RL Interaction between Hispanic and 570926 0.03 0.16 0 1
FRL
SPECED Dummy (1=special education, 570926 0.10 0.30 0 1
0=no)
LEP Dummy (1=limited English 5 70926 0.02 0.15 0 l
proﬁciency, 0=no)
MATH, G4 Standardized MEAP score 46654 0 1 -6.12 4.91
READING, G4 Standardized MEAP score 46493 0 1 -5.71 5.34
READING, G7 Standardized MEAP score 29457 0 l -4.69 6.90
MATH, G8 Standardized MEAP score 26982 0 1 -5.63 5.18
School level
SCH_BLK % Black within a school 1291 0.32 0.39 0 l
SCH_HIS % Hispanic within a school 1291 0.05 0.11 0 0.87
SCH_ASIAN % Asian within a school 1291 0.01 0.03 0 0.29
SCH_FRL % eligible for F RL within a school 1291 0.44 0.26 0 l
SCHEFF Adjusted performance measure of 1291 0.01 0.88 -3.67 3.83
school effectiveness
LN(FTE) Logarithm of school size 1291 6.12 0.61 0.59 7.87
MIDDLE Dummy (1=middle school, 0=no) 1291 0.17 0.37 0 1
HIGH Dummy (1=high school, 0=no) 1291 0.15 0.35 0 1
URBAN Dummy (1=Urban, 0=others) 1291 0.40 0.49 0 1
RURAL Dummy (1= Rural, 0=others) 1291 0.23 0.42 0 1

 

*About 13% students failed to report their eligibility of F RL. This variable is imputed using
information on other variables by way of multivariate regression, sometimes known as
conditional mean imputation. This method imputes missing values with predicted values derived
from a regression equation based on variables in the data set that contain no missing values.

74

Table 3.3 Unconditional Models on the Likelihood of Transfer, from Assigned Schools to
Choice Schools

 

 

 

 

 

 

 

 

Fixed Effect gtgﬂiaent Odds ratio P-value
For category (1)—charter school
Intercept (1) -4.72 0.009 0.000
(0.041)
For category (2)—Inter-district school of choice
Intercept (2) -4.20 0.015 0.000
(0.035)
Variance components at level-2
Coefficient )C P-value
Variance Category (1) 1.76 20731.4 0.000
Category (2) 1.40 18027.2 0.000
Reliability Estimate
Intercept (1) 0.784
Intercept (2) 0.843

 

Note: the coefﬁcients are from HGLMs with multinomial logit link function. The signiﬁcance of
coefﬁcients is assessed based on the robust standard errors.

a) The Fixed Effects of Student Characteristics on the Likelihood of Transfer

Table 3.4 presents the estimation results for the two conditional multinomial
regression models (See Appendix B for model equation descriptions). For each model,
the predictors’ ﬁxed effects of both categories (charter schools and inter-district schools
of choice) are shown. The ﬁrst column of each category shows the coefﬁcient, or log
odds, of each predictor and its standard error in parenthesis, followed by the odds ratio,
the exponential values of the estimated regression coefﬁcients allowing for interpretation.

The results for category 1, charter schools, are the focus of interest. The coefﬁcients
of level-1 student variables for model 1 remain relatively stable in model 2 when school
level variables were added. The results of model 1 indicate that Black students and low-

income students are more likely to transfer to charter schools. The coefﬁcient of Black

75

students is 0.64 (p<0.001), indicating that on average, Black students are 1.9 times more
likely to transfer to charter school than non-Black students. The coefﬁcients of Asian and
Hispanic students show different signs, but neither is signiﬁcant.

On average, being a low-income student raises the odds of transfer to 1.4 times the
odds for non-low-income student (coefﬁcient = 0.34, p<0.01). Interestingly, the three
interactions between F RL and race dummies are all negative and signiﬁcant, and the
magnitudes of the three coefﬁcients are all bigger than the coefﬁcient of F RL. This
means that although low-income White students are more likely to transfer to charter
schools than non-low-income White students, for minority students, coming from low-
income families lowers the odds of transferring to a charter school. Being a special
education student decreases the likelihood of moving to a charter school, while being a
LEP student does not signiﬁcantly alter the odds of transferring relative to a non-LEP
student.

The level-1 coefﬁcients for category 2, inter-district schools of choice, indicate
similar patterns. Minority students are more likely to transfer to inter-district schools of
choice. Although low-income White students are more likely to transfer than non-low-
income White students, low-income minority students are less likely to transfer than non-

low-income minority students.

76

Table 3.4 Estimated Effects of Student and School Characteristics on the Likelihood of
Transfer from Assigned Schools to Choice Schools

 

 

 

 

Model 1 Model 2
Inter-district School Inter-district
Charter SChOOl of Choice Charter SChOOI School of Choice
Coeff. Odds Coeff. Odds Coeff. Odds Coeff. Odds
(SE) ratio (SE) ratio (SE) ratio (SE) ratio
Fixed eﬂect of student characteristics
Intercept -4.74 ** 0.009 -4.22 ** 0.015 -4.72 ** 0.009 -4.18 ** 0.015
(0.04) (0.04) (0.04) (0.03)
BLACK 0.64 ** 1.888 0.42 ** 1.523 0.64 ** 1.904 0.42 ** 1.524
(0.13) (0.09) (0.13) (0.09)
HISPANIC 0.21 1.231 0.32 ** 1.376 0.23 1.254 0.32 ** 1.374
(0.13) (0.09) (0.14) (0.09)
ASIAN -0.04 0.964 -0.01 0.986 -0.03 0.970 -0.02 0.984
(0.20) (0.13) (0.21) (0.13)
FRL 0.34“ 1.408 0.42 ** 1.516 0.36 ** 1.439 0.41 ** 1.514
(0.06) (0.04) (0.07) (0.04)
BLACK FRL -0.58** 0.559 -0.66 ** 0.516 -0.60 ** 0.551 -0.66 ** 0.515
(0.07) (0.07) (0.08) (0.07)
ASIAN FRL -0.58 * 0.558 -0.97 ** 0.381 -0.58 * 0.559 -1.00 ** 0.369
(0.29) (0.29) (0.29) (0.30)
HISPANIC -0.35 * 0.705 -0.53 ** 0.586 -0.37 * 0.692 -0.53 ** 0.587
FRL (0.15) (0.14) (0.15) (0.14)
SPECED -0.37 ** 0.693 -0.02 0.981 -0.36 ** 0.695 -0.02 0.981
(0.06) (0.04) (.06) (0.04)
LEP 02] 0.814 -0.29 0.751 -0.21 0.813 -0.29 0.750
(0.11) (0.15) (0.11) (0.15)
Fixed eﬂect at school characteristics
% BLACK 1.54 ** 4.649 -0.23 0.797
(0.13) (0.17)
% HISP 1.25 ** 3.501 0.08 1.079
(0.25) (0.34)
% ASIAN 1.89 * 6.589 -2.54 * 0.079
(0.81) (1.22)
% FRL 0.47 * 1.607 -0.61 ** 0.543
(0.19) (0.19)
SCH_EFF -O.13 ** 0.875 -0.10 * 0.906
(0.03) (0.04)
Ln(FTE) -0.36 ** 0.694 -0.81 ** 0.447
(0.12) (0.09)
MIDDLE -0.31 ** 0.736 0.01 1.014
(0.09) (0.09)
HIGH -0.25 * 0.780 0.59 ** 1.803
(0.12) (0.10)
URBAN 0.42 ** 1.516 -0.44 ** 0.643
(0.09) (0.13)
RURAL -0.41 ** 0.666 -0.04 0.965
(0.12) (0.07)
Variance at level-2 0.66 0.94
% eylained compared to the unconditional model 62.5% 32.9%

 

*p<.05, *"'p<.01.

77

b) Inﬂuence of School Characteristics on the Likelihood of Transfer

Model 2 in Table 3.4 estimates the effects of school characteristics on the likelihood
of students to transfer. At the school level, the coefﬁcients of the demographic variables
are all positive and signiﬁcant for students transferring to charter schools. This means
that after controlling for individual student’s background variables, the likelihood of them
transferring to a charter school increases if he/she attends a school with high percentages
of minority and low-income students. For instance, the expected odds of a student
transferring to a charter school would increase to 2.1 times if the proportion of Black
students in a school was one standard deviation above the mean (coefﬁcient = 1.54, SE =
0.13).16 Students attending schools with high concentration of low-income students are
more likely to transfer out than students in schools with low concentration of low-income
students (coefﬁcient = 0.47, p < 0.01).

School effectiveness has a negative effect on the likelihood of student transfers,
which indicates that parents rationally choose to leave poorer performing schools.l7 If a
school raises its effectiveness one standard deviation above the mean, the odds of its
students transferring to a charter school would decrease by 12%. In addition, school size
has a negative effect, which means that the larger the school is, the less likely the students
are to transfer. This seems strange at ﬁrst sight because there are more students

transferring to charter schools from larger schools than from smaller schools. However,

 

'6 This is calculated as exp (0.47“ 1 .54), where 0.47 is the standard deviation of percentage of Black (Table
3.2) and 1.54 is the coefﬁcient of % Black estimated from model 2, as shown in Table 4.
‘7 The actual school mean MEAP scores have been used for the analysis and similar results were obtained.

78

the proportion of students transferring to charter schools is larger in smaller schools than
in bigger schools.18

As expected, the mean probability of transfer of students in middle schools or high
schools is smaller than that of elementary school students, even after controlling for
school size. School location also matters in students’ choice. The estimated coefﬁcients
are 0.42 for urban and -0.41 for rural, which imply that compared to students in suburban
schools, students in urban schools are 1.5 times more likely to transfer to charter schools,
while students in rural areas are only 0.66 times as likely to transfer to charter schools.
This is not surprising because half of Michigan’s charter schools are located in urban
districts. The density of charter schools in Michigan’s rural areas is much lower.

Interestingly, in the case of inter-district school of choice, most of the school level
coefﬁcients are either insigniﬁcant or have different signs than those of the charter school
models. The percentages of students who are Black or Hispanic in a school have no effect
on its students’ likelihood to transfer through inter-district choice, although the
percentage of Asian students is negative and signiﬁcant. We should not stress this result
too much because the average percentage of Asian students among Michigan public
schools is only about one percent. The coefﬁcient of the share of students who are low-
income is negative, indicating that students in more afﬂuent schools are more likely to
transfer to an inter-district school of choice than students in schools with high
concentration of low-income students. The location of schools also has the opposite
effect compared to the transfer to charter schools. Students in urban areas are less likely

to transfer through inter-district choice than suburban and rural students.

 

'8 Assuming there are two schools. The big school has 2000 students and the small school has 200 students.
If 20 students transfer out the big school, the transfer rate is 1%. But if there are only 3 students transferring
out the small school, the transfer rate would be 1.5%, higher than that of the big schools.

79

The contrast of coefﬁcients between the two equations implies that charter schools
and schools of choice draw students from very different sets of TPSS. Urban schools with
high percentages of minority and low-income students and with low school effectiveness
are more likely to lose students to charter schools, while relatively more affluent
suburban and rural schools with low school effectiveness are more likely to lose students
to other TPSS through inter-district choice.

It also reﬂects the fact that the market for inter-district choice is signiﬁcantly
constrained on the supply side. Although students desire to leave ineffective schools, this
option is frequently unavailable to them. As mentioned earlier, in Michigan, a school
district has discretion as to whether to open up to receive nonresident children. In making
this decision, district ofﬁcials may rationally make an assessment of who will come if
they open up. School boards’ concern about the prospect of nonresident students
changing their district’s social or racial composition has been reported in Michigan
(Arsen et al., 2002). This concern appears to be particularly relevant in suburban districts
that border central city districts. Such suburban districts appear reluctant to open up even
if they are experiencing declining enrollment and expect that they would be able to attract
nonresident urban students. In Michigan, minority students are disproportionately
concentrated in a small set of urban districts. Once urbanicity is held constant, race is not
an issue anymore. The SES of neighboring districts still appears to operate as an element
in districts’ decision about whether to open up to nonresident students. In interviews with
intermediate school district superintendents, Arsen et al. (2002) found that even in rural

areas where students are overwhelmingly white, districts are reluctant to attract

80

nonresident students from poorer districts nearby who would lower the SES composition
of their schools.

As for the adequacy of the multinomial models, the estimated variance components
for both categories are shown in Table 3.4. In model 2, about 62.5% of the variation
among schools in the log-odds of charter school transfers (relative to staying in assigned
schools) is explained, while 32.9% of the variation between schools in the log-odds of
inter-district schools of choice transfers (relative to assigned schools) is explained. This
indicates that a fair amount of variance is explained by school level covariates, especially
among schools losing students to charter schools.

c) Iﬁferential School Effects on the Likelihood of Transfer for Students with Various

Backgrounds: Estimation of “Slope-as-Outcome ” Models

In model 2 of Table 3.4, level-2 variables are only introduced in the level-2 intercept
models representing both school choice policies. In other words, the school
characteristics are only used to explain how school factors affect the mean probability of
transfer, but not to explain whether the effects of school factors might differ among
White and Black students, and among low-income and non-low-income students. In this
section, for both choice policies I expand the school level models to incorporate school
factors in two slopes: BLACK and F RL. School factors are not added to Asian and
Hispanic slopes because of the small sample sizes. In order to avoid multicolinearity
among slope models caused by the high correlation between race and F RL, 1 estimate the
two multinomial regressions by introducing only one slope at a time (See Appendix C for

model equation descriptions). For each model, the coefﬁcients of the slope-as-outcome

81

model represent the differential school effects on students with speciﬁc race or SES
background.

The estimation of school ﬁxed effects for the two slope-as-outcome models is
presented in Table 3.5. Other ﬁxed effects at both levels are not presented since the level-
1 models and intercept-as-outcome models at level 2 remain the same as in model 2, and
the estimated coefﬁcients at both levels are essentially unchanged.

Table 3.5 Slope-as-outcome Models: School Fixed Effects on the Likelihood of Transfer

from Assigned Schools to Choice Schools, Students with Different Race and SES
Backgrounds

 

 

 

 

BLACK Slope FRL Slope
Inter-district Inter-district

Charter SChOOl School of Choice Charter SChOOl School of Choice

Coeff. Odds Coeff. Odds Coeff. Odds Coeff. Odds

(SE) ratio (SE) ratio (SE) ratio (SE) ratio

Intercept 0.67** 1.961 -0.13 0.88 0.37** 1.447 0.11** 1.121
(0.08) (0.07) (0.05) (0.03)

%BLACK -0.30 0.738 -0.63 ** 0.531 -0.81** 0.444 -0.31* 0.737
(0.25) (0.23) (0.15) (0.15)

% HISPANIC -0.50 0.604 -0.51 0.601 -0.96** 0.381 -0.48 0.617
(0.46) (0.64) (0.34) (0.42)

% ASIAN 3.17 * 23.91 3.24 * 25.51 -0.11 0.893 -4.34** 0.013
(1.53) (1.48) (1.20) (1.55)

% FRL -0.97 ** 0.378 -0.47 0.626 -0.26 0.770 -0.58 * 0.557
(0.29) (0.27) (0.25) (0.26)

LN(FTE) 0.13 1.140 -0.08 0.919 -0.06 0.946 0.00 0.997
(0.14) (0.11) (0.12) (0.11)

SCHEFF 0.07 1.077 -0.10 0.905 0.09 1.094 0.03 1.032
(0.07) (0.06) (0.05) (0.05)

MIDDLE -0.03 0.967 0.04 1.040 0.16 1.174 0.04 1.045
(0.18) (0.15) (0.10) (0.10)

HIGH -0.45 * 0.636 0.41 * 1.511 -0.04 0.956 -0.01 0.990
(0.22) (0.17) (0.14) (0.12)

URBAN -0.55** 0.580 -0.57 ** 0.566 -0.15 0.857 -0.58 *"' 0.558
(0.16) (0.14) (0.13) (0.11)

RURAL 0.07 1.070 -0.43 0.650 -0.15 0.860 -0.22 * 0.799
(0.28) (0.24) (0.15) (0.09)

 

* p<.05, ** p<.01.

82

I ﬁrst consider the results for the charter school equations because they are the focus
of interest. For the BLACK slope-as-outcome model, the coefﬁcients for the race
dummies reveal that the proportion of minority students in a school has no substantially
differential effect on log-odds of Black student transferring as compared to non-Black
students, except for the percentage of Asian students. The estimated coefﬁcient for
percentage of Asian is 3.17 (p = 0.013), indicating that if the proportion of Asian students
increases by one standard deviation, a Black student in the school will be 1.1 times likely
to transfer to a charter school than a non Black student, which is a very small differential
effect."

All other things being equal, a one standard deviation increase in a school’s
percentage of low-income students reduces the odds for a Black student to move to a
charter school to 0.65 times the odds for a non-Black student. The coefﬁcient of % F RL
is estimated to be -0.97 ( p<0.01) and is larger than the magnitude of the intercept, 0.67,
which means that Black students are less likely to transfer to charter schools than non-
Black students, mostly White students, in high poverty schools. This result is noteworthy
when compared to the results of model 2 in Table 3.4, that on average, non-Black
students are less likely to go to charter schools than Black students. This means, although
in a typical school, Black students are more likely to transfer to charter schools than
White students, in schools with high concentration of low-income students, Black
students are less likely to transfer than White students.

School effectiveness and school size do not seem to have any differential impact on

Black and non-Black students. However, school location matters. Being in an urban

 

’9 Calculated as exp (3.83*0.03) where 0.03 is the standard deviation of the percentage of schools’ students
who are Asian.

83

school decreases the odds for a Black student to choose a charter school. Although the
odds of them to choose is still slightly bigger than for non-Black students, the difference
is much smaller than in suburban or rural areas. The difference of the odds is estimated to
be exp(0.67+(-0.55)) = 1.13, which means Black students are 0.13 times more than non-
Black students to transfer in urban areas, while in suburban or rural areas, the odds for
Black students to transfer are 1.96 times the odds for non-Black students.

The estimation of the FRL slope model is shown in the last four columns in Table 3.5.
It evaluates the differential school effects on low-income and non-low-income students.
The odds of low-income students, regardless of race and other characteristics, to transfer
to a charter school decrease along with the increase in the percentages of minority
students in a school. Indeed, the likelihood of a low-income student transferring to a
charter school is substantially smaller than a non-low-income student, if the student was
in a school with very high proportion of Black or Hispanic students. For example, in an
all-Black school, low-income students are only .64 times likely to transfer than their non-
low-income classmates.20 However, after controlling for individual SES, whether the
school a student attended had high proportion of low-income students does not seem to
have a differential effect on the probability of transfer for low-income and non-low-
income students. Nor do school location, school effectiveness, or school size has a
differential effect on low-income and non-low-income students.

Table 3.5 also shows the results of slope models for inter-district transfers. Strong
differential school effects are also found reﬂecting similar patterns as in the charter
school equations that disadvantaged students in disadvantaged schools are less likely to

choose. For example, the odds of Black students transferring through inter-district choice

 

2° Calculated as exp[0.37+(-0.81)].

84

greatly decreases if they are in schools with high concentration of Black students or in
urban schools. In schools with high concentrations of minority and poverty students,
students from low-income families, regardless of their racial background, are less likely
than their more afﬂuent classmates to participate in inter-district choice. In addition, the
odds for poor students in urban schools to choose through inter-district choice is much
lower than poor students in suburban schools.

d) Inﬂuence of Previous Student Performance on the Likelihood of Charter School
QLOL'QQ

As indicated earlier, only students at certain grades took the MEAP tests in certain
subjects during 2002-03. In order to include performance variables in the level-1 models,
three separate models are estimated, each for grades 4, 7, and 8, the grades where the
math or reading was tested in 2002-03. All the speciﬁcations remain the same as in the
models for all students, except that individual test scores are added to the level-1 models.
All the test scores are standardized for the convenience of interpretation.

For each grade, the unconditional model with no predictors at either level is estimated
ﬁrst. The results are shown in Table 3.6. Fixed effects for both categories are signiﬁcant
at each grade level. For instance, for 4th graders the expected mean odds are 0.015 of
choosing a charter school (relative to staying in the assigned school), and 0.014 of
transferring to an inter-district school of choice (relative to staying in the assigned
school). There is little difference in the likelihood of choice among these grades, although
the probability of transferring to an inter-district school of choice is slightly larger than

that of transferring to a charter school at each grade. Variations at school level are all

85

found signiﬁcant and the reliabilities are reasonably large, implying enough variance that
allows for inclusion of school variables at level-2.

Table 3.7 contains the results of estimating the ﬁrlly speciﬁed models for the three
grades, including the coefﬁcients, standard errors, and odds-ratios. Consider only the
results for the charter school equations. At level 1, neither the coefﬁcients of math and
reading scores is signiﬁcant for the grade 4 model. However, both the grade 7 and 8
models indicate that students with higher test scores are less likely to transfer to charter
schools. In 7th grade, holding all other characteristics constant, the odds of a student
transferring to a charter school declines to 0.81 when his/her reading score increases a
standard deviation (coefﬁcient = -0.22, p< 0.001). In 8th grade, the odds of transfer to a
charter school falls to .69 when math scores increase a standard deviation (coefﬁcient = -
0.38, p<0.001). This indicates that parents care about their children’s academic

achievement only at a later stage of their education.

86

 

 

 

 

 

 

 

 

 

 

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89

The estimation of other student and school level variables for the three grade-speciﬁc
models show similar patterns with the models including students in all grades. At the
student level, Black students are more likely to transfer to charter schools. On average,
low-income students are more likely to transfer than non-low-income students. However,
among Black students, those who are low-income are less likely to transfer than non-low-
income students.

At the school level, students in schools with high concentration of poverty and
minority students, especially Black students, are more likely to choose charter schools.
After controlling for individual students’ performance, school effectiveness fails to have
a signiﬁcant effect on students’ decision to choose charter schools. However, there are
some discrepancies in the magnitude and signiﬁcance in the coefﬁcients across models.
For example, in the grade 8 model, Black students fail to show different patterns from
non-Black students in the likelihood of transfer. And low-income students in grades 4 and
8 do not show signiﬁcantly different patterns from non-low-income students. This is
partly because test scores are highly correlated to a student’s family background as well
as the student’s ability and motivation, especially in higher grades. Inclusion of test
scores in the models might have captured many of these characteristics so that race and

SES variables are not signiﬁcant anymore.

Question (2): Transferring from Charter Schools to Assigned Schools

In this section, I took all charter school students in 2002-03, and analyzed their
attendance status in 2003-04 through a similar set of multinomial HGLMs as in question

(1). The main goal is to understand who transfers from charter schools back to their

90

assigned public schools, and what kind of charter schools are more likely to have students
return to their assigned schools.

As in the analysis of question (1), the outcome measure is a categorical variable
describing student attendance status in 2003-04, which takes the value 1 if a student
transferred back to the assigned school, 2 if he/she transferred to an inter-district school
of choice, and 3 if he/she stayed in a charter school. Four sets of multinomial regression
models are estimated. The ﬁrst set of models includes all charter students in 2002-03. The
other three models are for students in grade 4, 7, and 8, respectively. The explanatory
variables at both levels remain the same across models, except that the models for
speciﬁc grades include performance variables. School level variables are measured based
on all students of schools, not the just the students in the grades taking the relevant
MEAP tests. Descriptive statistics for the variables in the model including all charter
school students are presented in Table 3.8.

Table 3.8 Variables and Description, All Charter School Students in 2002-03

91

 

Standard

 

 

 

N Mean . . Min. Max.
Dev1atlon

Student level
ATTENDANCE 52220 2.61 0.78 1.00 3.00
STATUS
BLACK 52220 0.52 0.50 0.00 1.00
HISPANIC 52220 0.04 0.20 0.00 1.00
ASIAN 52220 0.01 0.09 0.00 1.00
F RL 52220 0.45 0.44 0.00 1.00
BLACK F RL 52220 0.30 0.41 0.00 1.00
ASIAN FRL 52220 0.00 0.04 0.00 1.00
HISPANIC FRL 52220 0.03 0.16 0.00 1.00
SPECED 52220 0.05 0.22 0.00 1.00
LEP 52220 0.01 0.10 0.00 1.00
MATH, G4 5485 0.04 1.00 -4.43 5.36
READING, G4 5485 0.03 1.00 -4.55 5.67
READING, G7 4344 0.03 1.00 -4.77 4.01
MATH, G8 3077 0.00 1.00 -3.61 4.50
School level
SCHBLACK 188 0.45 0.42 0.00 1.00
SCHHISPA 188 0.04 0.10 0.00 0.84
SCHASIAN 188 0.01 0.03 0.00 0.43
SCH_FRL 188 0.44 0.28 0.00 0.99
SCHEFF 188 5.55 0.82 2.94 7.63
LN(FTE) 188 0.00 0.90 -3.59 3.17
URBAN 188 0.15 0.36 0.00 1.00
RURAL 188 0.51 0.50 0.00 1.00
ELEMENT 188 0.35 0.48 0.00 1.00
MIDDLE 188 0.65 0.48 0.00 1.00
HIGH 188 0.54 0.50 0.00 1.00

 

Note: Attendance status is categorical: l = Assigned school, 2 = inter-district school of choice, 3
= stay

Unconditional models are estimated ﬁrst. The results are shown in Table 3.9. The
ﬁxed effects for both categories are signiﬁcant in all the models, and the expected mean
odds for charter school students transferring back to their assigned schools (relative to
staying in charter schools) are far bigger than the odds transferring to another school
through inter-district choice (relative to staying in charter schools). For example, for 4th

graders, the odds of switching back to the assigned schools are 0.182, while the odds to

92

transfer to an inter-district school of choice are only 0.01. The magnitudes of the
expected mean odds to transfer are similar for all models except for the 8th grade model,
where the odds are far larger. The estimated 8th grade mean log-odds for category 1 is
0.75 (p<0.01), corresponding to very high odds of transfer back to the assigned school of
2.12, or probability of transfer of .68. This indicates that 68 percent of Michigan’s 8th
grade charter school students in 2002-03 transferred back to their assigned schools the
following year, if each school enrolled students with mean characteristics of all charter
school students. This is mainly because there are fewer charter schools available at the
high school level in Michigan and the majority of middle-school charter students have no
other options but to return to TPSS.

All level-2 variance components are signiﬁcant at the 0.001 level, except in grade 7
there is no signiﬁcant variation across charter schools in the log-odds of transferring to
inter—district schools of choice (relative to staying in a charter school). So, in the

following analysis I constrained the random effect to zero in the interest of parsimony.

93

 

 

 

 

 

 

 

 

 

 

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94

a) Student Fixed Effects on the Likelihood of Transfer Back to the Assigned Schools

The results for the four fully speciﬁed two-level intercept-as-outcome multinomial
regression models are presented in Table 3.10. The table only presents the estimation
results for charter school students’ movement back to their assigned schools. The
equations for charter students moving to inter-district choice schools were estimated but
not shown in the table because almost all the coefﬁcients were insigniﬁcant. The main
reason is that the portion of charter students transferring to schools of choice is so small
that there is not much variability in several explanatory variables to ensure valid

estimations.

95

Table 3.10 Fixed Effects of Student and School Characteristics on the Likelihood of
Transfer from Charter Schools to Assigned Public Schools

 

 

 

 

All Grade4 Grade7 Grade8
Coeﬁf Odds Coeﬂ Odds Coeﬂ Odds Coeﬂ Odds
(SE) ratio (SE) ratio (SE) ratio (SE) ratio
Fixed effect at student characteristics
Intercept —l.44** 0.237 -1.66** 0.190 -1.48** 0.228 0.65** 1.918
(0.06) (0.06) (0.08) (0.17)
BLACK -0.04 0.995 -0.01 0.994 -0.11 0.896 -0.14 0.871
(0.11) (0.19) (0.18) 0.22)
HISPANIC 0.15 1.159 -0.09 0.910 0.11 1.118 0.18 1.196
(0.12) (0.3 8) (0.39) (0.42)
ASIAN 0.25 1.293 0.70 2.01 l -- -- -- --
(0.17) (0.56)
FRL 0.16 * 1.168 0.49 ** 1.629 0.23 1.262 -0.22 0.802
(0.08) (0.16) (0.17) (0.23)
BLACK FRL -0.13 0.880 -0.60 ** 0.548 -0.26 0.775 0.35 1.423
(0.09) (0.21) (0.22) (0.24)
ASIAN FRL -0.12 0.863 -0.62 0.536 -- -- --
(0.35) (1.04)
HISPANIC -0.47 ** 0.626 -0.26 0.771 0.14 1.153 -0.41 0.661
FRL (0.17) (0.50) (0.51) (0.52)
SPECED 0.15 * 1.156 -0.16 0.856 -0.27 0.766 0.11 1.114
(0.07) (0.17) (0.33) (0.27)
LEP -0.22 0.803 0.10 1.108 -0.85 0.426 -0.57 0.567
(0.22) (1.65) (0.50) (0.53)
MATH -- -- -0.21** 0.810 -- -- 0.22M 1.251
(0.06) (0.07)
READING -- -- -0.05 0.956 -0.21** 0.81 1 -- --
(0.05) (0.05)
Fixed effect of school characteristics
SCH_BLAC 0.11 1.113 0.29 1.336 -0.27 0.761 0.07 1.070
K (0.20) (0.21) (0.33) (0.45)
SCH_HIS -0.34 0.714 -0.78 0.456 -l.03 0.357 0.01 1.014
(0.59) (0.78) (1.00) (1.23)
SCH_ASIA -8.16 0.000 -8.98 0.000 -- -- -1.81 0.164
(3.85) (4.82) (1.29)
SCH_FRL 0.22 1.243 -0.19 0.828 0.09 1.099 -0.20 0.822
(0.26) (0.29) (0.42) (0.71)
LNFTE -0.22 0.803 -0.39 ** 0.676 -0.10 0.905 0.42* 1.523
(0.11) (0.10) (0.13) (0.16)
SCHEFF -0.02 0.977 -0.26 ** 0.770 -0.16 0.853 0.29 1.339
(0.07) (0.08) (0.10) (0.17)
RURAL -0.07 0.929 0.24 1.269 -0.04 0.963 -0.86* 0.422
(0.14) (0.18) (0.25) (0.38)
URBAN -0.17 0.843 -0.12 0.889 0.02 1.021 -0.31 0.731
(0.14) (0.14) (0.21) (0.35)

 

Note: For grade 7 and 8, there is essentially no variability found in Asian. Therefore, the variable

is excluded. *p<.05, **p<.01.

 

96

At the student level, none of the coefﬁcients for Black, Hispanic, or Asian is
signiﬁcant for all four models. This implies that, on average, the likelihood of charter
students transferring back to their assigned schools does not signiﬁcantly differ among
students with different racial/ethnic backgrounds.

In the model including all charter school students, being a low-income student
increases the odds of returning to the assigned school to 1.17 times the odds for a non-
low-income student, holding other predictors constant (coefﬁcient = 0.156, p<0.001).
This is true for the grade 4 model, too, where the odds of transfer is 1.6 times for low-
income students (coefﬁcient = 0.49, p<0.001). However, the effect of FRL disappears in
grade 7 and 8. In addition, the coefﬁcients of interactions between race and FRL are
mostly insigniﬁcant in all the models. It is only signiﬁcant with Hispanic FRL for the
model with all charter students, where the estimation is based on a very small sample size
of low-income Hispanic students transferring back to their assigned schools.

As for the effect of student performance, the estimation results of the grade 4 model
show that both the coefﬁcients for math and reading are negative (coefﬁcient of ma = -
0.21, p<0.01, coefﬁcient of reading = -0.05, p>0.05), indicating that high performing
charter school students are less likely to return to their assigned schools, although the
coefﬁcient of reading is not statistically signiﬁcant. Similarly, the grade 7 model shows
that students with higher reading achievement were also less likely to switch to their
assigned schools (coefﬁcient = -0.21, p<0.01). By contrast, for the grade 8 model, the
estimated coefﬁcient for math is positive (coefﬁcient = 0.22), indicating a one standard
deviation increase in student achievement for 8th graders in charter schools raises the

odds of transferring back to the assigned schools to 1.20 times. Interestingly, although the

97

8th graders who returned performed better than the students remaining in the charter
schools, they still perform more poorly than their TPS counterparts.
b) Inﬂuence ofSchool Characteristics on the Likelihood of Transfer

As the bottom panel of Table 3.10 shows, the movement of charter students back to
their assigned schools is not well predicted by school characteristics. The coefﬁcients of
percentages of minority and low-income students are all insigniﬁcant, indicating student
movement back to the assigned schools is not associated with these aspects of charter
school student composition. Moreover, with the exception of 4th graders, charter schools’
effectiveness is not signiﬁcantly related to the likelihood of charter school students

transferring back to their assigned schools.

Question (3 ) .° Transferringfrom Inter-district Schools of Choice Back to Assigned Public

Schools

In this section, I repeat the sequence of analyses as for question (2). The students
included in the question (3) analysis all attended inter-district schools of choice in 2002-
03. The descriptive information is shown in Table 3.11. Four sets of multinomial HGLMs
are analyzed, with the ﬁrst model including all students attended inter-district schools of
choice, and second to fourth models including only students in grade 4, 7, and 8
respectively. Again, the focus of interest is the student movement from inter-district

schools of choice back to their assigned schools.

98

Table 3.11 Variables and Description, All students in Inter-district Schools of Choice in
2002-03

 

 

 

N Mean Standard Min. Max.
Devratron

Student level
Dependent variable 27096 2.63 0.77 1.00 3.00
BLACK 27096 0.17 0.38 0.00 1.00
HISPANIC 27096 0.04 0.19 0.00 1.00
ASIAN 27096 0.01 0.09 0.00 1.00
FRL 27096 0.36 0.45 0.00 1.00
BLACK FRL 27096 0.09 0.28 0.00 1.00
ASIAN FRL 27096 0.00 0.04 0.00 1.00
HISPANIC FRL 27096 0.02 0.14 0.00 1.00
SPECED 27096 0.09 0.29 0.00 1.00
LEP 27096 0.00 0.07 0.00 1.00
MATH, G4 2142 0.25 0.65 -l.73 3.50
READING, G4 2142 0.12 0.70 -2.47 4.09
READING, G7 2334 0.02 0.99 -4.94 4.13
MATH, G8 2061 0.00 1.00 -3.61 5.19
School level
SCHBLACK 1342 0.09 0.20 0.00 1.00
SCHHISPA 1342 0.03 0.05 0.00 0.61
SCHASIAN 1342 0.01 0.02 0.00 0.45
SCH_FRL 1342 0.33 0.21 0.00 0.99
SCHEFF 1342 5.93 0.69 1.56 7.63
LN(FTE) 1342 0.02 0.78 -5.89 3.43
URBAN 1342 0.10 0.30 0.00 1.00
RURAL 1342 0.41 0.49 0.00 1.00
ELEMENT 1342 0.50 0.50 0.00 1.00
MIDDLE 1342 0.21 0.41 0.00 1.00
HIGH 1342 0.23 0.42 0.00 1.00

 

Note: Attendance status is categorical: l = Assigned school, 2 = charter school, 3 = stay

99

Following the method of answering questions (1) and (2), I started with the
unconditional models. The estimations for both assigned school and charter school
options are shown in Table 3.12. The expected odds for inter-district choice students
transferring back to their assigned schools are relatively high. For example, for 7th
graders in 2003, the expected mean odds of returning to the assigned schools (relative to
staying) are .214, or about 1 out of 5. This corresponds to a probability of 1/(1 + exp
(1.543)) = 0.18. For 8th graders, the expected odds are even higher. For all four models,
the variability across schools is signiﬁcant for the log-odds of return to assigned schools,
but not signiﬁcant for transfers to charter schools. In fact, the number of students who
transferred from an inter-district choice school to a charter school is so small that no
patterns could be found through the estimation and the reliabilities for category 2
equations are extremely low. Therefore, although transfers to charter schools were

included in the analysis, the results are not reported.

100

 

 

 

 

 

 

 

 

 

 

 

 

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Table 3.13 Fixed Effects of Student and School Characteristics on the Likelihood of
Transfer from Inter-district Schools of Choice to Assigned Schools

 

 

 

 

A11 Grade4 Grade7 Grade8
Coeﬂ Odds Coeﬂ Odds Coeﬂ Odds Coeﬂ Odds
(SE) ratio (SE) ratio (SE) ratio (SE) ratio
Fixed eﬂect at student characteristics
BLACK -0.05 0.954 -0.39 0.675 0.31 1.361 -0.13 0.878
(0.10) (0.33) (0.26) (0.27)
HISPANIC 0.18 1.195 -- -- -- -- -1.13 0.323
(0.14) (0.73)
ASIAN -0.04 0.959 -- -- -- -- -- --
(0.22)
FRL 0.64 ** 1.905 0.49 ** 1.635 0.73** 2.069 0.56 ** 1.754
(0.05) (0.15) (0.16) (0.16)
BLACK FRL -0.25 * 0.776 -0.11 0.893 -0.61 0.543 0.13 1.138
(0.10) (0.37) (0.32) (0.32)
ASIAN FRL 0.69 1.985 -- -- -- -- -- --
(0.46)
HISPANIC -0.42 * 0.660 -- -- -- -- 1.23 3.407
FRL (0.19) (0.87)
SPECED 0.12 * 1.129 -0.15 0.858 0.40 1.490 0.07 1.075
(0.06) (0.25) (0.19) (0.20)
MATH -- -- -0.13 0.881 -- -- 0.03 1.032
(0.12) (0.07)
READING -- -- -0.005 0.995 -0.04 0.963 -- --
(0.11) (0.07)
Fixed effect of school characteristics
Intercept -1.41** 0.243 -1.57 0.207 -1.59** 0.205 -1.26** 0.283
(0.03) ** (0.08) (0.09)
(0.07)
SCH_BLAC 0.12 1.132 0.60 1.821 0.10 1.108 0.77 2.149
(0.18) (0.42) (0.50) (0.52)
SCH_HISP 1.51 4.518 -- -- -0.35 0.704 2.33 10.323
(0.61) (2.10) (1.92)
SCH_ASIA -0.10 0.906 -- -- 1.27 3.555 9.52 13608
(2.14) (4.87) (5.04)
SCH_FRL -0.08 0.925 0.16 1.171 -0.40 0.670 -0.36 0.701
(0.18) (0.38) (0.51) (0.53)
LNFTE -0.02 0.979 0.02 1.021 -0.11 0.899 -0.33* 0.717
(0.06) (0.15) (0.15) (0.17)
SCHEFF -0.11 * 0.900 0.04 1.046 -0.17 0.842 -0.21 0.814
(0.04) (0.13) (0.13) (0.13)
URBAN 0.35 ** 1.422 -- -- 0.58 1.793 0.24 1.271
(0.12) (0.33) (0.34)
RURAL 0.08 1.080 -- -- -0. 12 0.891 -0.06 0.942
(0.07) (0.21) (0.21)
MIDDLE -0. 13 0.877 -- -- -- -- -- --
(0.08)
HIGH -0.37 ** 0.692 -- -- -- -- -- --
(0.08)

 

Note: In grade speciﬁc models, some variables are excluded because there is essentially no variability

found. ‘p<.05, ** p<.01.

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Table 3.13 contains the results of the four conditional models in which variables at
both level-1 and level-2 are included. The estimation results for the model including all
choice students are shown in the ﬁrst and second columns, and results for the grade 4, 7,
and 8 models are in the next six columns.

For the model containing all inter-district choice students, some patterns are found to
be consistent with the patterns of the movement from charter schools to the assigned
schools. At level-1, among the demographic factors, low-income students had
signiﬁcantly higher odds of return than non-low-income students, while students from
different racial groups did not show different patterns. The coefﬁcients of interactions
between race and FRL show that although for Black and Hispanic students, low-income
students are more likely to return than non-low-income students from the same racial
group, the gap of odds between low-income and high-income students are smaller than
that for White and Asian students.

At level-2, the coefﬁcient for school effectiveness is signiﬁcant. If a school was one
standard deviation more effective above average, the odds of its students returning to
their assigned school declined to 0.9 times. School location and level of education also
matter. Urban schools have more students transferring back than suburban and rural
schools. High school students are less likely to return to their assigned schools than
elementary or middle school choice students.

Models for speciﬁc grades show that students’ individual performance seems to have
no inﬂuence in determining whether they return to their assigned schools. The effect of

school effectiveness also disappears when individual performance is controlled. In

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addition, most of the student and school level effects disappear in the grade speciﬁc
models. Only low-income students show persistently higher odds of return than non-low—
income students.

Overall, the student and school variables fail to predict very much about the
transfer patterns for inter-district choice students back to their assigned public schools.
There could be two explanations for this. First, choice students were scattered in so many
schools (more than 1,000 TPSs) that the sample ratio between level-1 and level-2 models
are relatively small and defy accurate estimation. Second, the number of choice students
who switched back to their assigned schools is so small that there is not much variability
among the many variables. This indicates that student ﬂow back from inter-district

schools of choice has not signiﬁcantly inﬂuenced student composition in the TPSS.

Discussion

This chapter analyzes student sorting initiated by Michigan’s school choice programs.
Three sets of multinomial HGLMs were estimated to investigate how student and school
factors inﬂuence students’ choice among their assigned schools, charter schools, and
TPSS outside their district of residence. Here I assess the net effect of student sorting on
student composition across the state’s TPSs.

Charter schools do provide new opportunities for students who struggled
academically in their assigned schools, regardless of race and SES. However, the students
they attract tend not to be the most disadvantaged students. Rather the process of student
sorting initiated by charter schools tend to leave the most disadvantaged students behind
in the most disadvantaged schools. While Black students are more likely to choose

charter schools than White students, low-income minority students are less likely to

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choose charters than low-income White students. Moreover, special education students
are shown to have a smaller likelihood of attending charter schools than general
education students.

Charter schools attract students from low-performing schools with high concentration
of minority and poverty students, which are most likely to be located in urban areas. This
can be regarded as a positive and intended result of choice policy. However, my analysis
also shows that charters attract relatively “better-oft” students from these schools. For
example, in high-poverty urban schools, White students have higher odds of switching to
charter schools than Black students. In minority concentrated schools, relatively afﬂuent
students are more likely to take advantage of charter schools than low-income students.

Meanwhile, students who returned to their assigned schools from charter schools
were more likely to be low-income and have lower academic performance than their
classmates who stayed in charter schools. In addition, special education students are more
likely to return from charter schools to their assigned schools. Thus, this analysis
concludes that charter schools tend to attract moderately disadvantaged students, while
the most disadvantaged students are left behind in the most disadvantaged schools.

My analysis of student sorting under inter-district choice suggests that students in
urban districts face supply-side restrictions on their choice of traditional schools outside
their district of residence. My results are consistent with the notion that suburban districts
neighboring urban areas are less likely to open up to accept nonresident students because
they worry that the incoming choice students from urban districts would change the racial

and SES composition of their own schools.

105

The net effect of student movement initiated by charter school policy is that the truly
disadvantaged students—low-income minority students with low performance—remain
concentrated in ineffective urban schools with high concentrations of minority and low-
income students. The percentage of minority students in these school tend not to increase
because Black students are more likely to go to charter schools, and they show the same
inclination as students from other racial groups to return to TPSS. However, charter
school choice tends to further increase the concentration of low-income and low-
performing students in urban schools because charter school students who are from low-
income families and have lower performance than their classmates are more likely to
return to their assigned schools.

Taken as a whole, Michigan’s charter school program still has limited impact on the
overall composition of students in the state’s TPSs, because charter schools only enroll a
small fraction of public school students. Yet the ﬁnding that charter schools exacerbate
social and academic stratiﬁcation within the state’s lowest-performing schools in
predominantly minority and high-poverty urban areas is cause for concern. After all,
these are the students who have been most poorly served by TP83 and who charter school
policy was meant to help.

In general, the results of this chapter fail to support the claim from school choice
advocates that charter schools attract the most disadvantaged students. Rather, charter
schools help to promote choice for the moderately disadvantaged students. The truly
disadvantaged students have not beneﬁted as much under Michigan’s school choice

policies as they are currently designed and implemented, since these students have

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become increasingly concentrated in public schools with other similarly disadvantaged
students.

This chapter does not address why charter schools in Michigan fail to reach the most
disadvantaged students. However, some possible reasons have emerged from the
literature. First, minority, low-income parents do not necessarily devalue school quality;
rather, their social networks and customary attendance patterns limit their capacity for
choice (Bell, 2005). Second, charter schools might use speciﬁc marketing strategies and
admission requirements that potentially limit access for racially and economically
disadvantaged applicants. Transportation is another potential factor that may limit the
choice of disadvantaged students. Usually charter schools do not provide bus
transportation. Parents of disadvantaged students are less able to arrange the
transportation for their kids (Henig & MacDonald, 2002).

Some have argued that charter schools exercise greater latitude in formally or
informally encouraging some students to return to their assigned schools (Miron et al.,
2002a; Wells, 1998). Students with behavior problems, special needs, or low test scores
may be more likely to be counseled out. Such claims are disputed by charter school
advocates, and indeed charter schools’ poorest performing students might be more likely
to return to their assigned schools on their own accord. While this chapter offers no
evidence on such charter school practices, it does appear that there is a systematic pattern
for charter schools’ most poorly performing students to return to TPSs. Moreover, charter
schools often do not have adequate staff to provide programs for students with special
needs. Special need students are discouraged to choose charter school and are more likely

to get sent back from charter schools (Miron et al., 2002a).

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School choice offers opportunities for students who are dissatisﬁed with their
assigned schools to choose a school that might better meet their needs. Parents are
making sensible choices because the schools they left usually have lower performance.
However, by doing that, choice policy creates external costs on students who remain in
the most disadvantaged schools. Therefore, policy makers should aware that choice
policy creates losers, among both schools and students.

Students who remain in the most disadvantaged schools experience a turbulent and
unstable learning environment because the student mobility and possible teacher mobility
induced by school choice. In addition, it is reasonable to assume that as potentially more
motivated classmates depart for alternative schools through choice policies, the students
who remain will have a less motivated peer group and this will continue the downward
spiral of low performance.

The parents of students who leave their assign school for choice schools are most
likely to be those who care more about their children’s education and who might be best
positioned to help to improve schools. Once those parents are gone, the school has a less
“alert” consumer base and business continues as usual with fewer informed demands for
change from its clients (Hirschman, 1970).

In addition, schools losing students through choice policies are likely to be the ones
that have already experienced signiﬁcant loss of students and faced harsh education
challenges. Choice policy accelerates the rate of their enrollment decline which in tum
may initiate a self-reinforcing cycle of declining revenues, program cuts, and further
enrollment loss. Regardless of the competitive pressure for improvement generated by

choice policy, schools may lack the capacity to reverse the downward spiral.

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Michigan school choice policies are intended to beneﬁt all public school children—
not simply those who take advantage of choices. The challenge for policy makers is to
have a response strategy in place to address the problems facing these truly

disadvantaged students who are left behind in the mostly disadvantaged schools.

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CHAPTER 4 THE IMPACT OF CHARTER SCHOOLS ON EFFICIENCY OF

TRADITIONAL PUBLIC SCHOOLS

Recent research on school choice focuses not only on the impact of choice policies on
the redistribution of students and resources among schools, but also on the competitive
effect of choice policy on school productive efﬁciency. Some research focuses on the
interactions between the two issues as well, because equity and efﬁciency are often in
conﬂict: economic competition oﬁen generate unequal distribution of educational
resources. On the other hand, equal distribution of educational resources does not
necessarily improve educational productivity.

In the previous two chapters 1 addressed the sorting or redistribution of students
associated charter school policy. In this chapter I turn to estimate the second mechanism
of charter schools—the competitive effect. Does charter competition improve the
efﬁciency of TPSS and thereby beneﬁt the vast majority of students who remain in the
TPS system? Microeconomic theory predicts that charter school policy will improve the
effectiveness of all schools. First, it creates effective charter schools because they have to
attract students and revenue from existing pubic schools. Moreover, the introduction of
charter schools will spur competition among TPSS, since they have to compete with the
newly established charter schools for students. TPSS will become more responsive to
parents’ demands and improve school quality. Therefore, competition will not only
beneﬁt active choosers but also the majority of students who remain in TPSS (Finn et al.,
2000; Kolderie, 2004; Nathan, 1998).

Opponents, however, argue that the concept of market competition and choice were

borrowed from other ﬁelds and cannot be readily adapted to the delivery of public

110

 

education (F iske et al., 2000). Choice schools will not necessarily be more effective or
efﬁcient. On the demand side, parents might not choose schools based on school quality,
but on other school attributes, such as convenience, or the racial or social class
composition of a school. On the supply side, choice schools might choose to admit high
achieving students or those who are easy to educate, which makes choice schools appear
to be more effective or efﬁcient because of a student composition effect instead of a
competitive effect (Arsen et al., 1999; Wells et al., 2000).

Further, critics also argue that TPSs will not necessarily be more effective or efﬁcient
when they face competition from school choice. For instance, charter competition creates
ﬁscal constrains for TPSs facing competition because of the loss of students, which make
it harder for them to continue providing the same quality programs, let alone improving
educational services. Since revenues decline faster than costs in TPSS losing students, it
is likely that TPSS will cut programs, which could spur the loss of further students and
resources (Arsen et al., 1999; Fiske et al., 2000).

Whether charter school policy creates efﬁcient charter schools is an important
question. However, the impact of charter school competition on the efﬁciency of TPSS
may be of greater importance, because the large majority of students remain in TPSS. Past
research has produced mixed results on the impact of charter schools on TPS
effectiveness and efﬁciency. Although the connection between competition and student
outcome is conceptually clear, it is hard to establish the causal relationship between the
two because of the confounding effects of student transfers between charter schools and

TPSs and non-randomness of charter school location.

111

Using 11 years of school level panel data in Michigan, my analysis in this chapter is
based on a series of models by ﬁxed effect and other estimations, which not only
implicitly control for the unobserved school heterogeneity, but also explicitly control for
the changing student composition and other factors induced by the charter school policy.
The models also separate the competition effect of charter schools from that of inter-
district choice—the other school choice program in Michigan. My results fail to show
any positive competitive effect on student achievement in TPSS. Indeed, in areas with
high charter school density I found a negative impact on school performance.

This chapter is organized as follows. First, I conceptualize the causal relationship
between charter competition and school effectiveness / efﬁciency. In section 2, I
summarize the previous studies estimating the competitive effect of school choice on
school effectiveness and identify several methodological challenges in the research. In
section 3, I describe my research questions. Section 4 discusses the data and econometric
approaches including how to handle the possible endogeneity of charter competition. In

section 5, I present the analysis results. Discussions and conclusions follow.

Conceptualization of Competition and School Efﬁciency

In microeconomic theory, school effectiveness and efﬁciency are related to the
production process of schools, which transform “inputs” into “outputs.” Inputs include
students with certain characteristics as well as ﬁnancial and material supports. Output
refers to student achievement after a period of formal schooling. The transformation
process within a school can be understood as the instruction, curricula, and organizational
arrangements that make it possible for students acquire knowledge. School effectiveness

can be described as the extent to which the desired level of outputs is achieved. High

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school effectiveness indicates high levels of educational outcomes, such as high test
scores. School efﬁciency, sometimes also referred to productivity, means the extent to
which educational inputs produce desired student outcomes. Increased efﬁciency means
achieving better student outcomes with the same combinations of inputs, or the same
student outcomes with fewer inputs.

School choice advocates argue that the allocation of resources in TPSs is not efﬁcient,
because families made residential and schooling choices simultaneously and schools
served only those who lived within jurisdictions of the school districts. Consequently,
TPSs operate in a relatively monopolistic market, with weak incentives for improvement
or adoption of new teaching technologies. The introduction of school choice, however,
links school ﬁnance to school popularity and creates a direct market incentive mechanism,
which motivates TPSS to become more productively efﬁcient. According to school choice
advocates, if a school becomes more efﬁcient, it would become more attractive and
popular, and should gain more students (Hoxby, 2003a). Meanwhile a school that fails to
become more productive or efﬁcient will lose students. This will give incentives for the
school to improve its productivity; otherwise it would go out of business in the long run.
From this perspective, long-term effects on efﬁciency are even more substantial than
short-term effects. As economists argue, an administrator who wants to raise school
productivity has only certain options in the short term, such as inducing his staff to
worker harder, getting rid of unproductive staff and programs, and allocating resources
away from non-achievement oriented activities. However, in the long term, some general
equilibrium mechanisms are available to an administrator. For instance, the ﬁnancial

pressure of choice would bid up the wages for high quality teachers, and thus draw

113

people into teaching who would otherwise pursue other careers. This long term effect
would be more substantial on school enrollment and even the existence of schools
(Hoxby, 2003a).

However, school choice critics are not convinced by the microeconomic model of
competition resulting in greater school effectiveness and efﬁciency. They argue that ﬁrst,
highly motivated students might be more active in choosing to attend choice schools; less
motivated students would then be clustered in increasingly disadvantaged TPSS. These
schools in turn would have difﬁculty responding to the competitive challenge because of
negative peer effects over which they have limited control. Second, losing students to
choice schools will ordinarily decrease TPSs’ educational revenue. Expenditure, however,
cannot be readily decreased. Teachers cannot be easily laid off, and capital input or
overhead costs are largely ﬁxed. Cutting programs is the necessary response, which will
lead to less popularity of schools and could possibly trigger further loss of students.

The resolution of these contrasting viewpoints is clearly signiﬁcant. Whether school
choice competition can raise the effectiveness and efﬁciency of TPSs is even more
important than whether competition can create effective and efﬁcient choice schools,
since — for the foreseeable future — the majority of students still remain in the TPS system.

However, the existing literature fails to provide consistent evidence on this issue.

Existing Research

There is a substantial body of research on the impact of competition on educational
outcomes. In most of this research, however, the competition analyzed is generated by

private schools or neighboring public schools. In their comprehensive review of cross-

114

sectional research in the US, Belﬁeld and Levin (2002) concluded from more than 41
studies that competition has only modest positive effects on student achievement.

There are fewer studies about the effects of competition speciﬁcally resulting from
school choice, and most of them have focused on the impact on choice schools rather
than TPSs. There has been relatively little research on the impact of school choice
competition on TPSS. So far, studies about this issue have focused on states such as
Florida, California, Arizona, Michigan, Texas, and North Carolina, where charter school
laws have been in place long enough and enrollments in charter schools are sufﬁcient to
generate signiﬁcant competitive pressure on TPSS. Among these few studies, the results
are surprisingly mixed.

To establish a causal relationship between competition and school effectiveness or
efﬁciency, several methodological issues are involved. First, the location of charter
schools is not randomly determined. It is reasonable to expect charter schools choose to
locate in areas where students are not satisﬁed with the educational services they receive.
Alternatively, charter schools might attract students whose parents tend to be more
motivated and more informed. It is likely that this unobserved heterogeneity of schools
will introduce positive or negative bias in estimation if not controlled for. Second, the
student self-selection problem might confound the effect of competition on TPS
effectiveness. Students who move to charter schools probably differ systematically from
the students who do not exercise their option to do so. They might differ in past
performance and family background, which are observable, as well as in motivation and
innate ability, which are unobservable. If this was the case, the composition of students in

TPSS facing competition will be different from that of TPSS facing no competition. The

115

analysis in Chapter 2 and 3 shows that in Michigan, students are redistributed across
charter schools and TPSS by race, SES, and performance. The sorting does inﬂuence the
student composition of students in TPSS, especially in schools in central cities.

Several strategies have emerged in the empirical studies to address these problems.
To control for the bias caused by the endogeneity of charter location, researchers usually
rely on longitudinal data and use a ﬁxed-effect strategy or they introduce instrumental
variables, which ideally will be correlated with where charter schools choose to locate,
but not related to neighboring TPS outcomes. To correct for the student self-selection
problem, scholars usually include lagged dependent variables to control for students’ past
performance, incorporate schools’ student composition as additional explanatory
variables, or control for student ﬁxed effect when data are available.

Drawing on an eight-year panel of data on individual student test scores for public
schools students in Texas, Booker et al. (2005a) evaluated the achievement impact of
charters schools on TPSS. The authors included school ﬁxed effects and student ﬁxed
effects in the model to control for student background, and found that the emergence of
charter schools had a positive impact on student performance for students remaining in
TPSS. But the effect was relatively small, less than 0.1 standard deviations of test scores.

In Florida, competition from charter schools appeared to have a modest positive
impact on student achievement in Florida’s TPSS (Sass, 2006). Using student-level
longitudinal data and relying on student ﬁxed effect models, the author found that the
positive results were quite robust under several measures of charter competition
penetration: presence of nearby charter schools, the number of competition charters, or

the enrollment share of charter schools. By contrast, a study in California which also

116

relied on student-level longitudinal data and ﬁxed effect models found that charter
competition, measured in a variety of ways, failed to improve the performances of TPSs
in California (Buddin & Zimmer, 2005)

Using longitudinal data on school-level achievement in North Carolina, Holmes et a1
(2003) investigated the competition effect of charter schools on TPSs. Applying a wide
set of models, including cross-sectional OLS and IV panel models, they found that the
introduction of charter schools improved the performance in TPSS. Overall, they reported
that TPSs facing competition gained approximately a one percent increase in the test
scores, or about one quarter of the average yearly growth. In another study, Bifulco and
Ladd (2004) also examined North Carolina charter schools. Unlike the Holmes et al.
study, Bifulco and Ladd used individual panel data and controlled for individual student
ﬁxed effects. The authors found that competition of charter schools had no substantially
positive impacts on effectiveness of TPSS. The authors attribute the different results
between the two studies as that Holmes and his colleagues did not use a full student-level
panel to account fully for potential differences between students in schools located near
charter schools and those in schools located elsewhere.

North Carolina is not the only state where contradictory results about the impact of
charter school competition on TPS effectiveness have emerged. Studies based on
Michigan have also produced mixed conclusions. Bettinger (2005) estimated charter
schools’ impact on TPS effectiveness in 1999, shortly after Michigan’s charter school
program had been introduced. The author used distance from a charter school to develop
indicators of whether or not schools face competition from charter schools. In order to

correct the bias caused by endogeneity of charter location, Bettinger (2005) introduced an

117

instrumental variable, the proximity of a public school to one of state universities. This
was based on the fact that in Michigan, the majority of charter schools are authorized by
universities. It could be expected that universities are more likely to authorize charter
schools nearby. Ideally, charter location would be related to proximity to state
universities, but not related to neighbor public school outcomes. Bettinger (2005) also
included the lagged dependent variable to control for students’ past performance and
other school-level covariates, including percentage of Black and students receiving
free/reduced lunch to address the student self-selection problem. The study shows that
charter schools had little or no effect on test scores in neighboring public schools.

In contrast, a study by Hoxby (2003b) reached different conclusions, namely that
public schools subject to charter school competition raised their productivity and
achievement in response. The increase was largest in the 4th grade, about 2.40 scale
points a year in reading and 2.5 scale points in mathematics of Michigan’s MEAP tests.
Hoxby deﬁned that a school faces charter competition if charter schools account for at
least 6 percent of total enrollment inside the district’s boundaries. To estimate the effects
of charter competition, Hoxby used a detrended difference-in-difference strategy to
control for each school’s initial productivity. This method was based on the assumption
that the public schools close to charter schools have different preexisting level of
productivity and different of productivity trends than schools not facing competition from
charter schools. Detrended difference-in—difference estimates can control for each
school’s initial productivity level and trend, and identify changes that occurred in schools
facing competition as compared to other public schools that did not face equivalent

competition. On the other hand, Hoxby fails to control for changes in student

118

 

composition in her models. Her detrended difference-in-difference strategy only controls
for schools’ unobservable characteristics that are constant over the time. However, the
composition of students in schools may well change with the entry of charter schools,
which would also inﬂuence peer effects on student learning. If changes in the
composition of students are different between TPSS that face charter competition and
those that do not, then the estimation of the causal effect will be biased.

So far, past research has produced mixed results about the inﬂuence of choice
competition on TPS effectiveness, even when it is based on charter schools in the same
state. There are several other potential reasons for this besides the different methods used.
First, the measurement of competition from charter schools varies in different studies.
Some researchers use the number of charter schools within a given radius of public
school to measure the intensity of competition (Bettinger, 2005; Bifulco et al., 2004).
Others use the distance of a public school from a charter school to measure competition
(Bifulco et al., 2004). Still others identify a certain percent of a school district’s
enrollment in charter schools as the threshold of competition (Hoxby, 2003b). There is no
consensus about which measure is better than the others. While school-level competition
measures can reﬂect within district variations in the intensity of charter school
competition, school districts might be the appropriate unit for competition measures,
since the revenue loss due to choice and most decisions about resource allocation are
made at the district level.

A related issue is that the units of analysis are different in different studies. For this
research question that focuses on the organizational effectiveness of schools, it is

reasonable to take schools rather than individual students are the unit of analysis.

119

 

Although students can decide how much time and energy to devote to studying, they have
no discretion in allocating educational resources and have no responsibility to care about
the performance of their peers. Instead, schools or school districts are the decision-
making organizations that allocate resources to different programs and to different groups
of students so as to collectively respond to charter competition. However, researchers
increasingly use students as the unit of analysis when student-level data are available.
This is also desirable because students who choose to attend charter school might differ

systematically from students in unobserved ways. Controlling for student ﬁxed effects

 

can successfully reduce some sources of heterogeneity bias.

Third, studies have been conducted in different stages of state charter school
development. For example, when Bettinger (2005) studied Michigan’s charter schools in
1999, only 33 charter schools were established and had been in operation only for two
years. This is probably not long enough for TPSS to react to the competition from charter
schools. It is also possible that the long—term impact of charter schools will be different

than short-term impact.

Research Questions

This chapter aims to address some of the limitations of past research and establish a
causal relationship between charter competition and TPS efﬁciency. School choice not
only inﬂuences student achievement but also signiﬁcantly inﬂuences educational
expenditure in TPSS. In this chapter, I will estimate the change of student achievement
while controlling for the educational expenditure. In other words, I will to focus on
estimating school efﬁciency by separating the effect of charter competition and the effect

of educational spending. Speciﬁcally, I ask two questions: (1) how has competition from

120

charter schools inﬂuenced TPSS efﬁciency, and (2) does charter market penetration have
different impacts on TPS efﬁciency in the short-term or long-term?

Like Hoxby (2003b) and Betinger (2005), my analysis focuses on Michigan’s charter
school program. However, my research differs from these studies in several respects.
First, the availability of more recent data allows me to evaluate both short-term and long-
terrn policy effects of charter school policy. Second, more detailed data allow me to
capture other systematic changes induced by school choice, including changes in student
demographics, school expenditure, and school size. Third, my models explicitly control
for the competition from Michigan’s other choice program—inter—district choice—which
might confound the effect of charter competition if not controlled. Fourth, I measure
charter competition confronted by each district as the percentage of that district’s students
who have transferred to charter schools. This is different from using charter enrollment as

a percentage of charter host district, which I will later elaborate.

Data and Methodology

Data Sources

This analysis utilizes a school-level panel dataset of Michigan schools from 1994 to
2004. The data were assembled from three main sources: the K-12 databases of the
Michigan Department of Education (MDE), Data and Reports from the State of
Michigan’s Center for Educational Performance and Information (CEPI), and Common
Core Data (CCD) from the National Center of Educational Statistics (N CES). The
merged dataset includes information by schools for school choice enrollment, student

demographics, school ﬁnance, and other school level factors over the 11 years.

121

Information about student achievement—the scale scores and percent of students
attaining satisfactory performance levels on the Michigan Educational Assessment
Program (MEAP) tests—come from the MDE’s Ofﬁce of School Assessment and
Accountability. As noted in earlier chapters, not all Michigan students were tested
annually in the same subjects. During the years included in this study, only students in
certain grades were tested in certain subjects. These include grades 4 and 7 reading and
math. Grade 7 math was no longer tested after 2000. As a result, student level
longitudinal achievement data are not available. However, as noted, from a policy
perspective, it is probably more interesting to see how schools as organizations respond

to charter competition.

Measure of Competition

Competition from charter schools is measured by the charter school enrollment as a
percentage of total district enrollments. This measure is a district-level measure because
the loss of students to charter schools inﬂuences district revenues directly, and they must
in turn decide how to adjust their resource allocation. In this sense, school districts
instead of schools should be the primary organization that responds to the ﬁnancial
pressure introduced by choice competition.

This measure of competition improves upon the one introduced by Hoxby (2003b).
Hoxby deﬁned whether or not a district faces strong charter school competition as
whether or not the charter school enrollment reach 6% of the total enrollment of the
district. However, the measure is based on the assumption that students attend charter
schools in the district in which they reside. This assumption is not true in Michigan’s case.

As mentioned in chapter 2, in 2003 and 2004, half of Michigan’s charter schools draw

122

students from districts other than their host district. Consequently, the percentage of
students transferred to charter schools in a district rather than the percentage of charter
enrollment of total enrollment inside the district’s boundaries should be a more accurate
measure of charter competition. To construct the measure, I ﬁrst identiﬁed the primary
sending district for each charter school, i.e., the district in which most students in each
charter school lived. Then for each district, I added up the total enrollment of charter
schools that primarily draw students from the district. Finally, I computed the charter
enrollment as the percentage of the total enrollment of the district. Although this measure
does not reﬂect the exact percentage of students that each district loses to charter schools,
it is undoubtedly a more accurate measure than the charter enrollment as a percentage of
the total enrollment of the school district where the charters schools are located.“

The main limitation of the measure is that there is no way to identify primary sending
districts of charter schools before 2002 since student-level data were unavailable then. So,
my measure of charter competition is based on 2003 estimation, assuming that a charter
school has always attracted students primarily from the same district since its
establishment.”

Furthermore, I initially used two different approaches for the competition
measurement. One is a continuous variable reﬂecting the percentage of charter

enrollment. The other is the dummy variable following the deﬁnition of Hoxby (2003b)

 

2' I also constructed the same measure of charter school competition as Hoxby used in her study. The two
measures are highly correlated. The estimation bases on the alternative measure generated similar results
but in a smaller magnitude. The possible reason is that the alternative measure underestimates the charter
competition in some districts. For example, many charter schools draw students from central cities, but
located in surrounding suburban districts. As a result, the estimation of the alternative measure is biased
toward 0.

22 For instance, if charter school A drew a majority of its students from school district B in year 2003, I
assume it did so since the year it was established. Although I have found it is fairly consistent for 2003 and
2004, there is no way to test this for previous years.

123

and Bettinger (2005), which takes the value of 1 if the percentage of charter enrollment
reaches 6 percent, and 0 otherwise. In my analysis, I have used both and found the effects
are more dramatic using the dummy variables, but otherwise similar. Theoretically, the
impact of competition should not be linear, but negligible at ﬁrst and then becoming
more observable when the share of charter enrollment reaches a certain point or threshold.
So I decide to use the dummy variable in my analysis. Following Hoxby (2003b), 1 also
deﬁned the dummy variable using other out points such as 3%, 5% and 10%, similar
results emerged. Bettinger (2005) made the same observation in his study.

In order to distinguish the effect of charter competition in short-term, mid-term, and
long-term, I also created three dummy variables that reﬂect the duration of charter
competition. For instance, if a district consistently lost more than 6% of its students to
charter schools for less than 4 years, I identify the charter competition as short-term.
Likewise, the loss of more than 6 percent of students for 4 to 6 years is deﬁned as mid-
term competition, and for greater than 6 years is long-term competition.

I then obtained a vector of dummy variables by interacting the charter enrollment
dummy variable and the three duration dummy variables. So, the measure of charter
competition used in this analysis is a vector of dummy variables measuring the
competition from two dimensions, one is the magnitude of the competition, and the other

is the duration of the competition.

Estimation Strategies

As mentioned earlier, although the connection between charter competition and
effectiveness is conceptually clear, it is hard to establish the causal relationship between

the two mainly because of two reasons. First, charter schools are not randomly located.

124

As chapter 3 shows, in Michigan, charter schools tend to locate in urban areas where
minority and low-income students are concentrated. It is possible that charter location is
inﬂuenced by unobservable factors which may be related to achievement in either
positive or negative ways if not controlled. Second, charter schools tend to attract
students with certain characteristics which in turn change the composition of students in
TPSS. Such changes over time in student composition would confound the estimated
competitive effect of charter schools if not controlled.

In order to address the challenges, this chapter utilizes ﬁxed effect estimation that not
only implicitly control for the unobservable time invariant school characteristics that
inﬂuence its likelihood of facing charter competition, but also explicitly control for
changing student composition and other factors induced by school choice. It also tries to
separate the competition effect of charter schools from that of inter-district choice—the
other school choice program in Michigan. Several other models are also included for
robustness checks. The unit of analysis of this chapter is the school. However, the
competition measure is a district-level measure.

For the analysis, I rely on educational production function approach, where student
achievement is a function of charter competition and other school level controls. The

equation can be written as
Y,-,=CS,-,B1+SCH,-,B2+‘YIC,-,+I,5+ Vi: (1)
where Y i, is the percentage of students passing the MEAP test at a satisfactory level. I

estimate several models, each with a different dependent variable that reﬂects the
satisfactory rate in reading and math at grades 4 and 7, respectively. The satisfactory rate

measures the school effectiveness when per-pupil expenditure is not controlled. After

125

controlling inputs such as expenditure and student demographics, the satisfactory rate
measures school efﬁciency or productivity which reﬂects achievement per dollar spent.
Scale scores for both subjects were initially used but replaced by satisfactory rates mainly
for two reasons. First, it is difﬁcult to interpret the results because the score itself is not
meaningful, and the cut score varies for each year.23 In addition, the reading scale scores
before 2003 are not comparable to the reading scores after 2003, due to changes in the
test and content standards since that year.

The variables of interest in this analysis are included in CS, a vector of dummy
variables that reﬂect both the magnitude and the duration of charter competition. SCH“ is

a vector of characteristics of school i at time t, including the percentage of students
eligible for free/reduced lunch, percentage of students who are minority, pupil-teacher
ratio, per-pupil expenditure in logarithmical form to impose a diminishing effect of
spending on performance, and the percentage of instruction expenditure in the total
expenditure. 1C indicates the competition that districts face through inter-district choice
policy, the other state-wide choice program in Michigan. As with the charter competition
measure, 1C is a dummy variable reﬂecting the strength of competition from nearby

school districts. If the percentage of students transferring out of a district exceeds 6, 1C
takes the value of 1, otherwise 0. A set of year dummies, 1,, is also included to capture
any systematic inﬂuence not accounted for by the observable inputs that vary over time
but are common to all schools. V,-, is the unobserved error for school i at time t.

I start to estimate equation (1) with simple ordinary least squares (OLS) by pooling

data across schools and over the years, in order to identify the association between

 

23 If the cut score changes every year, it is possible that the same scale score may be deﬁned as satisfactory
in one year, but not in other years.

126

student achievement and charter competition. Pooled OLS estimation assumes all school-
level variables not controlled in the model are uncorrelated with charter competition,
which is unlikely to be true in this analysis, because the location of charter schools might
be inﬂuenced by unobserved features of TPSS.

To address the limitation of the Pooled OLS in estimating equation (1), 1 decompose

the error term V i, in equation (1) into an unobserved school effect and an idiosyncratic

error that changes over time (Wooldridge, 2000). The same set of school factors is
included to capture the possible change of students caused by choice-induced student
mobility. The model is written as follows:
Yi,=CS,-,B1+SCH,~,B2+yIC,-,+I,6+6,-+u,-, (2)
where 6?; is an unobserved school ﬁxed effect that will pick up all the unobserved

characteristics of a school that are stable over time. u,-, is the idiosyncratic error term that
changes across time for each school.
One way to estimate model (2) is through ﬁxed effects (FE) transformation. FE can

readily eliminate the unobserved ﬁxed effect, 9,, and allows for arbitrary correlation

between (9,- and CS”, which means that the location of charter school are allowed to be

related to historical differences among schools and factors.

Estimating model (2) through FE estimation might account for most of the
endogeneity of charter competition. However, it is possible that the future charter
competition is correlated with the idiosyncratic error in schools today. In other words,
how schools respond to charter competition in time period one might inﬂuence the

magnitude of charter competition in the future. If this is the case, the strict exogeneity

127

 

assumptions will be violated, and the general FE estimator will be biased. For robustness
checks on the strict exogeneity assumption, 1 estimate equation (2) through ﬁrst
difference (FD) method, where I ﬁrst difference the equation over time and estimate it by
pooled OLS and robust standard errors.

Estimating random trend models provides another way for robustness check. As

written in equation (3), a random trend model allows each school to have its own time
trend, g,-, in addition to the level effect, 6,- (Wooldridge, 2002). There are many ways to
estimate random trend models. In this chapter, I estimate it by ﬁrst differencing the

equation to eliminate 6, and then applying ﬁxed effects to the differences, which
eliminate the school-speciﬁc trend, g,-.
Y i, = CS ,-, B1 +SCH,-,Bz+ 71C ,-, + [,5 + 6,- + git + u” (3)
In addition to estimating model (2) through both FE and FD, and estimating model

(3), the random trends model, I have also tried other ways for robustness check, which I

will elaborate later.

Findings

Descriptive Statistics

Table 4.1 provides information on the charter competition over the 11 years. The
percentage of charter school enrollment statewide increased almost every year. In 2004, it
reached 4.2%. Although the ﬁrst charter school in Michigan was founded in 1994, no
TPS faced strong charter competition before 1996. By 2004, about 2.6% of all TPSS in
Michigan have been facing long-term charter competition. Further, Table 4.2 shows that

most of TPSS facing strong charter competition are located in urban school districts.

128

Indeed, about 80% of all schools in central cities are facing signiﬁcant charter
competition, and most of these schools had faced long-term charter competition for more
than 6 years.

Table 4.1 Numbers of TPSS Facing Strong Charter Competition, by Year and Duration

 

 

 

% of state Number of schools experiencing
Year enrollment in strong charter competition Total
charter schools short-term mid-term long-term
1994 0.02 0 0 0 2,497
1995 0.03 0 0 0 2,502
1996 0.33 12 0 0 2,497
1997 0.86 87 0 0 2,499
1998 1.39 164 10 0 2,505
1999 2.19 116 356 0 2,508
2000 3.09 155 416 0 2,507
2001 3.77 76 391 8 1,844
2002 3.92 92 179 304 2,552
2003 3.67 93 144 358 2,712
2004 4.24 1 18 95 382 2,685

 

Table 4.2 TPSS Facing Strong Charter Competition in 2004, by Community Type

 

C . Number of schools facing charter Universe % of schools
ommunrty

 

 

t e competition of facing strong

yp short-term mid-term long-term schools competition
Urban 70 62 337 595 78.8%
Suburban 39 19 28 1364 6.3%
Rural 9 14 1 7 726 5.5%

 

Table 4.3 provides MEAP satisfactory rates for both math and reading at grades 4 and
7. The satisfactory rates increased every year before 1998 and then vary across the
subsequent years. This indicates that there are systematic ﬂuctuations in the MEAP tests
among years, including cut scores, difﬁculty, and new curricular requirements. Although

the analysis compares schools facing charter competition with schools facing no

129

competition in the same year—and thereby the change of cut scores and difﬁculty levels
across years should not inﬂuence the analysis results—it is important to include year
dummies in the analysis in order to control for changes in the tests or ratings. TPSs facing
signiﬁcant charter competition have consistently lower satisfactory scores than the

schools facing no charter competition with a few exceptions.24

 

2‘ In 1996, only a few middle schools faced signiﬁcant charter competition and they had satisfactory rates
above average. The satisfactory rates in these schools dropped in the subsequent years. It would be
interesting to see whether the drop is caused by charter competition.

130

Table 4.3 Summary Statistics of Satisfactory Rates, by Year, Charter Competition, and

 

 

Subjects
Math Reading
No CC* CC Difference No CC CC Difference
Grade 4
1994 48.5 -- 48.5 43.0 -- --
1995 61.2 -- 61.2 42.9 -- --
1996 63.1 62.1 1.0 49.7 51.7 -2.0
1997 60.9 51.2 9.7 49.0 38.2 10.8
1998 75.1 62.6 12.5 59.1 45.7 13.4
1999 75.2 61.5 13.7 62.5 48.6 13.9
2000 79.9 64.7 15.2 61.7 49.6 12.2
2001 78.1 60.0 18.1 66.0 48.5 17.4
2002 70.3 49.4 20.8 63.1 39.2 23.9
2003 70.5 49.4 21.0 80.0 60.3 19.7
2004 77.7 59.4 18.4 83.9 68.7 15.2
91%
1994 40.9 -- -- 38.5 -- ~-
1995 48.3 -- -- 34.8 -- --
1996 54.1 63.0 -8.8 41.6 52.6 -11.0
1997 50.9 45.3 5.6 39.3 33.4 5.9
1998 61.2 51.3 10.0 47.9 42.2 5.7
1999 65.8 47.6 18.2 54.7 41.5 13.2
2000 66.8 44.3 22.6 50.1 37.2 12.9
2001 -- -- -- 60.5 40.4 20.1
2002 -- -- -- 55.3 31.7 23.6
2003 -- -- -- 65.6 39.8 25.9
2004 -- -- -- 64.1 46.0 18.1

 

 

Note: No CC refers to schools facing no signiﬁcant charter competition.
CC refers to schools facing signiﬁcant charter competition.
7th graders were no longer tested in math since 2001.

Table 4.4 displays the descriptions of variables used in the models, along with their
means and standard deviations. Inter-district choice is a district-level measure. On
average, about six percent of schools are in districts that have more than 6 % of their
students transferring out of the district through inter-district choice. Since the mean is

calculated cross all years, the percentage of students transferring through inter-district

131

 

 

increased is much bigger in recent years. As a matter of fact, in 2004, about 17.6 percent
of schools are in districts that have more than 6% students transferring to other districts.
On average, schools spend about 63% of their educational expenditure on the instruction.
The standard deviation is fairly small, only about 4 percent, indicating there is not much
variation in this variable. The average percentage of FRL students is 32% over the 11
years. This number increased every year. In 2004, about 40% of students statewide were
eligible for FRL. Black students comprise the largest minority group in Michigan public
schools. Hispanic and Asian students combined account only for about 6% of all students.
Statewide, the racial and ethnic composition of Michigan schools changed slightly over
the years, with a six percentage point increase in minority students between 1994 and
2004. The pupil-teacher ratio is about 19.1 :1 on average, which decreased slightly over

the years.

132

Table 4.4 Description of Explanatory Variables

 

 

 

Variable Description :3: Mean IS): Min Max
Dummy variable (l—at
Inter-district least 6% students
. transferring out through 28043 0.06 0.24 0 1
ch01ce . . . .
1nter-drstr1ct chorce;
0—otherwise)
Log (per-pupil Per-pupil expenditure 28184 8 90 0 17 8 22 10 88
exp) in logarithm form ' ' ' '
o . . .
Instr/exp (%) /° “wimcnm’ 1“ ““31 28184 0.63 0.04 0.36 0.92
expenditure
Log(enroll) Log °fS°h°°l 26911 6.05 0.65 0.69 11.93
enrollment
o . .
% FRL /o of students eligible 26926 0.32 0.2 6 0 1
for free lunch
% Black % of black students 27031 0.17 0.31 0 1
% Asian % of Asian students 27031 0.02 0.03 0 0.85
% Hispanic % of Hispanic students 27031 0.03 0.07 0 0.90
P/T Ratio Pupil-teacher ratio 26669 19.10 3.67 0.1 49.1
Pooled OLS

I ﬁrst pooled the data and estimated the satisfactory rate as a function of charter
competition and other observable controls by OLS. I use robust standard errors clustered
on schools which allow for serial correlation and heteroskedasticity. A set of year
dummies are added to allow for secular changes in student performance over time, such
as the difﬁculty level of the test. Estimates of the model are presented in Table 4.5. For
both math and reading in grades 4 and 7, two sets of models of the association between
charter competition and student achievement are estimated. For each subject and grade,
the ﬁrst column shows results with no control variables, while the following column
shows the results of the model including the full set of control variables, including per-

pupil expenditure in log form.

133

Looking at the pooled OLS results with no controls, it is clear that there is a negative
association between charter competition and satisfactory rates for math and reading for
both grades 4 and 7. For example, the results in column (1) show that, once a school faces
strong charter competition, its satisfactory rate for 4’h grade math decreases about 15.7
percentage points, or 0.8 standard deviations.25 If the strong charter competition persists,
the satisfactory rate drops further to 20.5 percentage points lower compared to schools
facing no substantial charter competition. The negative association between charter
competition and student achievement becomes much smaller in magnitude when the full
set control variables is included. For instance, column (2) shows that math satisfactory
rate for 4‘h grade only decreases 4.14 percentage points under charter competition. This
further supports the ﬁndings in chapter 3 that charter schools tend to draw higher-
perforrning students from low-performing schools and schools with high concentration of
low-income and minority students. Once student demographic and ﬁnance factors
variables are controlled, the effect of the charter school enrollment became much smaller.
The subsequent columns show similar patterns for 4th grade reading, and 7’h grade math

and reading.

 

25 The standard deviation of 4th math satisfactory rates is 20.52.

134

 

 

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135

Educational expenditure is positively associated with achievement in both subjects
and grades. Results in column (1) show that a 10% increase in expenditure increases the
satisfactory rate by about 1.9 percentage points. The estimated effects of other control
variables are also consistent with expectations: if a school spends a larger share of its
current operating funds on instruction, the satisfactory rate increases. High concentrations
of low-income, Black, and Hispanic students are associated with lower satisfactory rates.
However, high percentages of Asian students are associated with higher satisfactory rates
in each subject in both grades. School size and percentage of students transferring out
through inter-district choice do not seem to be related to satisfactory rates.

Taking the results at face value, the estimates suggest negative impact for student
achievement in schools facing more competitive markets. However, Pooled OLS
estimates do not remove unobserved school effects, which might be correlated with the
degree of charter competition. If so, the pooled OLS estimates would be biased. To

address this possibility, next I employ ﬁxed effect and other models.

Fixed Effect Estimations and Potential Source of Bias

Table 4.6 shows estimates of the impact of charter competition on 4th grade math
satisfactory rate by FE estimations, followed by two other estimations to check for
robustness. Column (1) of Table 4.6 contains the FE estimates. The estimated effect of
charter competition in both the short- and mid-term is insigniﬁcant. However, the long-
term charter competition is negative and signiﬁcant: a school facing strong charter
competition for more than 6 years is estimated to realize a decline in its 4th grade math

satisfactory rate by about 4.21 percentage points, or about .25 standard deviations. The

136

fully robust t-statistic that allows for serial correlation and heteroskedasticity is quite
large (t = 3.92).

Once the school ﬁxed effects and aggregate time effects are controlled for, other
variables become much less signiﬁcant. This is not surprising as student composition and
expenditure vary much less within schools over time than across schools. Schools with a
high percentage of Black students exhibit lower levels of satisfactory rates than schools
with a lower percentage of Black students. The coefﬁcient on expenditure remains
positive, indicating higher level of spending leads to higher student achievement. The
percentage of students transferring out through inter-district choice has a positive effect
on the satisfactory rate, about half the size of charter competition but in opposite
direction. This is somewhat surprising, but can be explained by the different designs of
the two choice policies. Charter school program generates sharp and intense competition
between charter schools and TPSS because charter schools have no pre-existing claims on
students or resources. In order to survive and expand, they have to compete aggressively
with TPSS for students. By contrast, Michigan’s inter-district choice is more controlled,
and sometimes induces more cooperation and more collusion among districts within a
local ecology (Arsen et al., 2002). In addition, while districts lose some students through
inter-district choice, they might as well take nonresident students in through inter-district
choice. With the revenue brought in through incoming students, the ﬁscal constraints the

districts face should not be as acute as under charter competition.

I37

Table 4.6 Fixed Effects, First Differencing, and Random Trends Estimations: Satisfactory
Rate on the 4‘h grade Math Test

 

 

(1 ) Fixed Effects (2) First (3) Random
(FE) Differencing (FD) Trends M°d°1
(FD+FE)
Charter competition
Short-term 0.56 -0.95 -1.19
(0.81) (1.11) (1.14)
Mid—term -095 -092 -1.34
(0.80) (1.25) (1.38)
Long-term -4.21* * -3.51* -4.61 *
(1.08) (1.76) (2.09)
. . . 2.73** 1.02 1.26
Inter-distrlct ch01ce (0.80) (1.16) (124)
L0 (pep u 11 ex ) 17.34** 3.36 1.69
g P P P (2.43) (4.24) (4.35)
0.08 0.17 0.16
0

MSU/ex" (A) (0.06) (0.08) (0.09)
LO (enroll) -020 -O.68 0.15
g (0.99) (1.39) (1.74)
-003 0.02 0.02

0
/° FRL (0.02) (0.03) (0.03)
-023" -0.21* 027*

0
/° mac“ (0.05) (0.09) (0.11)
0/ Asian -005 -0.06 -002
° (0.06) (0.12) (0.14)
(y His mic -0.19** -013 027*
° 1’ (0.07) (0.12) (0.13)
. -0.07 -0.03 -0.05
m Rat“) (0.05) (0.07) (0.08)
Obs. 193999 16482 16482
R2 0.33 0.10 0.10

 

The R-squareds are net of school ﬁxed effects.
See Table 4.5 for other notes.

Consistency of FE estimator requires that charter competition is strictly exogenous
after accounting for the school ﬁxed effects (which means, charter competition, CS”,
must be uncorrelated with the idiosyncratic errors, u,,, in all time periods r). But if future

movements in charter competition depend on current unexplained changes in test

I38

performance, the strict exogeneity is violated and the FE estimator is biased. For example,
suppose student achievement in a TPS changes because charter schools draw some
students away from the TPS and the students are systematically different in unobserved
ways from the students remaining in the TPS. If the school draws more charter
competition or less charter competition in next year because of its changed student
composition and achievement, the FE estimator is not accurate anymore. It is usually
hard to tell which way the bias will go. My analysis in chapter 3 shows that students with
lower performance tend to choose to go to charter schools. If these students happen to
have lower academic abilities, the FE estimator will bias upward because the students
remaining in TPSs have higher abilities then before. However, low-performing charter
students are also more likely to return to TPSS, which might indicate bias in the other
direction. To add to the complication, although students who are actively switching
schools program (either from TPS to charter school or from charter school to TPS) are
low-performing than the students who stay, they might be as a group more motivated or
whose parents care more about their education. This suggests the opposite direction of
bias from the ability sorting.

I use FD estimators to check whether FE is biased and which direction the bias might
be. If the strict exogeneity assumption fails, the magnitude of heterogeneity bias of the
FD estimator is c, and it remains essentially the same as the length of time, T, grows. By
contrast, the heterogeneity bias of the FE estimator is of order UT, and the magnitude of
bias decreases to c/T. This means that although we do not know the value of c, the
magnitude of the bias of the ﬁxed effect estimator is substantially decreased for large T.

In this study, T is 11, it is useful to compare the FE and FD estimators and to have a

139

sense of whether the estimates are biased, and what direction and what magnitude of the
bias might be.

The FD estimator results are presented in column (2) of Table 4.6. The sample size is
smaller in this estimation because one year of data is lost under the ﬁrst differencing of
the data. The estimated charter competition remains insigniﬁcant in short- and mid-term.
The long-term charter competition is negative and signiﬁcant, indicating persistent
charter competition decreases satisfactory rates by 3.51 percentage points. By comparison
to the FE estimator, the FD estimator is 4.14-3.51=0.7 percentage points bigger. This
might indicate that there is small heterogeneity bias toward zero in the FE estimator, but
the magnitude is not substantial.

In the ﬁxed effect estimations, the unobserved effect is deﬁned to have the same
partial effect on passing rates in all 11 time periods. This assumption might be too strong
for this study, because it is a relatively long time. A random trend model allows us to
control for an additional source of heterogeneity. That way, charter competition is not
just a function of initial historical factors of schools, but also a function of how quickly a
district is responding to the charter competition. For instance, if a TPS quickly responds
to charter competition and improve its student achievement by innovations in instruction,
the random trend model allows the time trend of this school to be different from TPSS
having no response when facing charter competition. Column (3) in Table 4.6 presents
the random trend model estimates. Again, the sample size is smaller than the FE
estimation because by ﬁrst differencing, one year of data is lost. The estimated long-term
charter competition decreases the 4th grade math satisfactory rate by 4.61 percentage

points, which is pretty much consistent with the FE and FD estimators, which also

140

indicates that there is no evidence that undermines the strict exogeneity assumption of
charter competition after controlling for school heterogeneity. Interestingly, the positive
effects of inter-district choice and expenditure disappear in the FD estimator and random
trend model estimation. One possible explanation is that these variables are endogenous,
in which case the FE and FD estimators are both probably biased. For example, the future
spending or magnitude of inter—district choice might depend on current, unexplained
changes in satisfactory rate.

In addition to the heterogeneity bias, the second source of potential bias arises if
charter competition is contemporaneously correlated with unobserved time-varying,
idiosyncratic variables that affect student achievement. For example, parental motivation
or other factors that might be correlated with charter competition are still in the time-
varying error term, which could cause charter competition to be endogenous. In this study,
this is less a concern because I am able to control for other school variables such as
student composition, expenditure, and class size. By explicitly controlling for these
variables, there should be much less variation leﬁ over in the time-varying error term.
Further, the consistent estimates by the three different estimations—FE, FD, and random
trends model estimations—suggest that my results are reliable, which also indicate after
controlling for unobserved school heterogeneity and other variables, the problem
associated with what is remaining in the idiosyncratic error is negligible.

Moreover, there is an empirical consideration to rely on the consistent estimation
results of the different approaches. If charter competition is still considered to be
endogenous after netting out school ﬁxed effects and controlling for other variables, the

methods of instrumental variables (IV) would be ideal in obtaining consistent estimates.

141

Such IVs should be related to charter competition, but do not have a signiﬁcant impact on
student achievement. However, truly external IVs are very hard to ﬁnd in the charter
school research. And using weak IVs that are not strictly exogenously tends to inﬂate the
bias. More than often, slight correlation between the IVs and the variables that they are
instrumented for could cause larger bias than estimators using no IVs (Wooldridge,
2002).26 From a policy perspective, we need to be cautious about the potential inﬂation of
bias and put more weight on the conventional estimation of FE or FD transformations.

Table 4.7 through Table 4.9 show estimates of how charter competition inﬂuences the
satisfactory rates for the 7th grade math, 4th grade reading, and 7‘h grade reading,
respectively. These tables are organized in a similar fashion as Table 4.6. According to
Table 4.7, charter competition seems to have no substantial effects on 7th grade math
satisfactory rate. One main reason is that as mentioned earlier, 7th math was no longer
tested after 2000. This further supports the conclusion that the effect of charter

competition is negligible at ﬁrst, but becomes more visible in the long run.

 

26 I have tried to estimate the impact of charter competition using lagged charter competition as [Vs.
The methods produced very large point estimates. Sine the [Vs are not strictly exogenous, it is very likely
that the endogeneity of IVs have translated into large biases.

142

Table 4.7 Fixed Effects, First Differencing, and Random Trends Estimations: Satisfactory
Rate on the 7th Grade Math Test

 

 

(1 ) Fixed Effects (2) First (3) Random Trends
(FE) Differencing (FD) Model (FD+FE)
Charter competition
Short-term -2.33 -3.81 -5.70*
(1.37) (2.31) (2.82)
Mid-term -2.06 -025 -3.48
(1.76) (3.11) (3.93)
. . . -1.39 -057 0.86
Inter-drstrrct chorce (1.60) (3.38) (3.59)
Log(per-pupil exp) 7.57 -6.13 -6.59
(3.99) (8.05) (10.21)
0.00 0.14 0.13
0
Insu/exl’ W (0.10) (0.18) (0.22)
Log(em0m -0.31 -413 -3.28
(1.71) (3.87) (4.57)
0.05 0.04 -0.01
0
/° FRL (0.03) (0.05) (0.06)
-0.06 -0.06 0.30
0
/° mac“ (0.18) (0.33) (0.35)
0/ Asian -0.79* -1.14 -1.03
° (0.40) (0.62) (0.70)
% Hispanic -O.18 -0.42 -032
(0.14) (0.25) (0.31)
. -019 0.06 0.07
m Rat“) (0.13) (0.15) (0.18)
Obs. 4921 2523 2523
R2 0.40 0.15 0.16

 

 

 

See Table 4.6 for notes.

Column (1) of Table 4.8 contains the ﬁxed effects estimates of 4th grade reading. It
shows that the estimated charter competition has a small negative impact on reading in
the short-term. Once facing the charter competition, the satisfactory rate of 4th grade
reading decreases about 2.78 percentage points. The magnitude of the impact becomes

larger in the mid-term. And in the long run, charter competition decreases the satisfactory

I43

rate by 11.25 percentage point, or 0.5 standard deviations.27 As in the 4th grade math
models, other variables such as expenditure, inter-district choice, and percentage of Asian
students signiﬁcantly inﬂuence the satisfactory rate in the FE estimation, but the effects
disappear in the estimations of FD and random trends models presented in column (2)
and (3) respectively. However, instructional expenditure as a percentage of total
expenditure continues to show a positive inﬂuence on reading. In the FE estimation, a
one percentage point increase in the instructional expenditure share results in a .24
percentage points increase in the 4th grade reading satisfactory rate. It is surprising to get
consistent results, because there is not much variation in the variable across schools and
over the years. A possible explanation is that schools that had extra resources might have

devoted them mostly on reading programs, which made the reading achievement go up.

 

27 The standard deviation of 4th reading satisfactory rates is 20.94.

144

Table 4.8 Fixed Effects, First Differencing, and Random Trends Estimations: Satisfactory
Rate on the 4‘h Grade Reading Test

 

 

(1) <2) (3)
. First Differencing Random Trends
Frxed Effects (FE) (FD) Model (FD+FE)
Charter competition
Short-term -2.78** -1.78 -204
(0.73) (1.11) (1.14)
Mid-tenn -4.76** -3.18* -3.8l**
(0.75) (1.23) (1.34)
Long-term -10.03** -10.13** -11.77**
(1.03) (1.70) (2.01)
. . . 3.82** 1.49 1.87
Inter-district chorce (0' 64) (1.22) (132)
L0 (per- u H ex ) 17.71** 6.93 5.34
g P p p (2.23) (4.24) (4.56)
0.24** 0.29** 0.30**
0
mgr/ex" V") (0.05) (0.09) (0.09)
L0 (enroll) 090 051 0.69
g (0.94) (1.42) (1.71)
0.00 0.02 0.02
0
/° FRL (0.02) (0.02) (0.03)
009 014 024*
0
/° Blac“ (0.06) (0.08) (0.10)
0/ Asian 018* 002 0.02
° (0.07) (0.13) (0.14)
0/ His mic 015 017 029*
° 1’ (0.08) (0.11) (0.12)
. 0.05 002 004
m Rat“) (0.05) (0.07) (0.07)
Obs. 19386 16461 16461
R2 0.51 0.24 0.24

 

See Table 4.6 for notes.

The results in table 4.9 also show a large negative effect of charter competition on 7‘h
grade reading achievement. In the FE estimation presented in column (1), charter
competition shows a small negative effect on satisfactory rates in TPSs in the short term.
This adverse effect continues to grow in the mid-term, and in the long-term charter

competition is estimated to decrease the satisfactory rate by 11.25 percentage points.

145

Although the FE estimator shows a negative inﬂuence of charter competition on student
achievement in short- and mid-term, it disappears in the FD estimator and random trend
model estimation in columns (2) and (3). However, the long-term negative effect of
charter competition persists throughout all the estimations. The charter competition is
estimated to cause more than a 0.5 standard deviation drop in the satisfactory rate.28

Table 4.9 Fixed Effects, First Differencing, and Random Trends Estimations: Satisfactory
Rate on the 7th Grade Reading Test

 

 

. . (3) Random
(1 ) I“($313313 ﬂeets Diﬁeiih;:;t(FD) Trends M°del
(FD+FE)
Charter competition
Short-term -3 .01 * -1 .53 -2.42
(1.19) (1.63) (1.73)
Mid-term -5.86** 1.41 -1.08
(1.08) (1.99) (2.39)
Long-term -11.25** -9.56** -16.88**
(1.68) (2.92) (3.74)
. . . 0.34 412* 458*
Inter-district chorce (0.80) (1.70) (199)
L0 mer- u 11 ex ) 12.30** -1.26 -3.05
g p p p (2.98) (5.96) (6.72)
0.39** 0.24 0.18
0
mgr/“P (4’) (0.07) (0.13) (0.14)
LO (enroll) 031 088 -1.45
g (1.07) (2.14) (2.12)
0.03 0.01 0.01
0
/" FRL (0.02) (0.04) (0.04)
027** 0.26 0.22
0
/° mac“ (0.10) (0.18) (0.21)
0/ Asian 029* 0.10 0.04
° (0.12) (0.26) (0.28)
% Hispanic 010 0.00 005
(0.13) (0.21) (0.22)
. -0.19** 010 010
m Ran" (0.06) (0.10) (0.11)
Obs. 6978 4874 4874
R2 0.48 0.25 0.26

 

See Table 4.6 for notes.

 

28 The standard deviation of 7‘h reading satisfactory rates is 18.31.

I46

Discussion

This chapter’s analyses indicate that charter competition has had a negative impact on
student achievement in Michigan’s TPSS. The effect is small or negligible at ﬁrst, but
becomes more substantial in the long run. The negative effect of charter competition is
consistent across grades in both math and reading tests, and robust across a range of
econometric models and estimations. In the long run, for schools in districts where
charter schools have drawn away a signiﬁcant share of students, the estimated charter
competition decreases their satisfactory rate about 0.2 standard deviations in math, and
0.5 standard deviations in reading.

Compared to the signiﬁcant negative effect of charter competition, the share of
students who transferred out through inter-district choice generally shows either no effect
or a small positive effect on student achievement. One possible explanation is that in
Michigan, inter-district choice is more disciplined and controlled than charter school
program. Most inter-district choice happens within ISD and contiguous ISDs, coordinated
by the ISD superintendents. In many cases, districts have agreement about enrollment
exchanges. Moreover, while one district loses students to other districts, it could gain
students from other districts at the same time. These kinds of cooperative or controlled
competition appear less likely to negatively impact student achievement than charter
competition.

The evidence in this chapter does not support the positive competitive effect typically
predicted by market theory, which presumes that charter schools spur competition among
regular public schools which in turn forces them to improve their quality. Instead, my

results are more consistent with the conception of choice triggering a downward spiral in

147

the most heavily impacted schools. School choice is not a “rising tide” that lifts all boats.
Rather, it produces gains and losses from reallocation of students and resources.

My ﬁnding is not necessarily contradictory to Bettinger’s study (2005), where he
found either no effects or very small negative effect from charter competition on the test
scores of students in the TPSs, because his Michigan data pertained to a period in which
only the short-term effect of charter competition could be captured. However, my results
are contradictory to Hoxby’s ﬁndings (2003b), where she found signiﬁcant positive
effects of charter competition on student achievement in TPSS. It is somewhat puzzling
given that I use a modiﬁed measure of charter competition based on her study, and
similar estimation strategies. Possible reasons for the contradictory ﬁndings stem from
both data and methods. First, her study relied on the data before 2001. Instead, I am able
to obtain more recent and more detailed data, so that besides the charter competition, I
also can control for other school characteristics such as student composition and
expenditure. Second, her measure of charter competition generates a very different list of
districts that face charter competition from my measure.

It is also worthwhile to think why some studies have found charter schools in other
states to have no substantial effects (such as North Carolina, California) or slight positive
effect (such as Florida and Texas) on student achievement in TPSS, while this study ﬁnds
signiﬁcant negative effects. At this stage, it is still too early to draw any conclusions
without further research. However, several unique features of Michigan might helps to
explain this difference. First, charter schools might operate differently in settings with
overall growing or declining enrollment. For example, in states with a growing

enrollment, TPSS may be overcrowded. Charter schools could serve as a “release valve”

148

for these schools. In this environment, TPSS are less likely to feel much competitive
pressure created through charter schools. By contrast, the population in Michigan has
been declining steadily for decades, thus reducing the student population. The charter
school movement is a zero-sum game between charter schools and TPSs, since any
increase enrollment in charter schools equals the reduction in enrollment in TPSs. Second,
local districts have no ability to increase taxes to support their school operations in
Michigan. In addition, the state aid for K-12 education almost remained the same level
over the past ﬁve years. The only way to obtain more educational revenue is to compete
aggressively for more students. In such an adverse competition environment, it is possible
that charter schools could have a more dramatic and negative effect.

In Michigan, about half of the charter schools are located in Detroit and other central
cities, attracting students from these areas and their surrounding low-income suburbs. As
a result, many schools in urban districts have experienced great charter competition and
faced acute ﬁnancial pressure due to the loss of students to charter schools. For example,
according to the Detroit News, about 42,000 students who live in Detroit attend charter
schools. Together with the students attending suburban schools through inter-district
choice, Detroit Public Schools has lost about one third of its students, or about $380
million educational revenue each year, to both choice programs (Wilkinson, 2007). By
contrast, the vast majority schools in rural and suburban areas are facing little
competition from charter schools.

Although this study does not try to identify the sources of the decrease in student
achievement due to charter competition, there are some possible explanations. First, when

students leave TPSS to charter schools, the loss of revenue is likely to exceed the

I49

associated decline in operational costs. Per-pupil administrative and instructional costs
increase when enrollment declines. In that sense, the marginal cost of losing one student
is smaller than the average cost a district bears to educate the remaining students. A large
decline in enrollment could greatly increase the average cost in educating students that
remain in TPSS.

Second, charter schools are not obliged to provide the full array of educational
services that TPSs offer. Enrollments at Michigan’s charter schools are largely
elementary because the relatively low cost of educating students at the elementary level
has made charters at this level a more viable ﬁnancial proposition than at the high school
level. Charter schools receive the same per-pupil allowance for both elementary and
secondary level students, thereby creating a ﬁnancial incentive for Offering only
elementary programs. Charter schools also tend to avoid providing high-cost service,
including special education services. After charter schools taking away low-cost students,
the concentrations of high-cost students in the TPSs increase. The more the charter
competition exists, the higher the average cost for educating the remaining students in
TPSs

Third, the high student mobility and possible high teacher turnover induced by
charter schools, often during the school year, creates a turbulent learning environment for
students remaining in these schools. Excessive turnover in school personnel and among
students can hinder attempts to nurture a shard culture and sense of community. Bryk and
Schneider (2002) argue that it is important to develop relationships of trust among
members of the school community, because high level of relational trust among school

personnel and between school personnel and parents improve children's academic

150

achievement. Trust, however, often takes time to develop, which can be impeded by high
student and staff mobility. In addition, teacher morale in these schools might drop
because of the exodus of their students. Regular daily instruction routine maybe disrupted.
With the anxiety of potentially being laid off, it is reasonable to expect that teachers
probably will focus less of their time and energy in instruction, which greatly inﬂuences
student achievement.

Analysis in this chapter largely reﬂects an urban phenomenon in Michigan. Charter
competition reinforces the vicious circle of enrollment loss, revenue decline, program
cuts, lower educational quality, and further enrollment loss. With the large decline of
enrollment and educational resources at such a fast pace, TPSs in these districts do not

have enough time and resources to react so as to improve their effectiveness.

15]

CHAPTER 5 CONCLUSIONS AND POLICY IMPLICATIONS

The ﬁrst charter school law was passed in Michigan thirteen years ago. Both the
number of charter schools and the enrollment in charter schools have increased steadily,
especially in central cities. Charter school policy created two mechanisms that may
inﬂuence the effectiveness and efﬁciency of charter schools and TPSs: a re-sorting
mechanism that redistributes students across schools and a competition mechanism
among schools. After the passage of many years, the effects of charter schools on the
Michigan educational system have become noticeable in many ways. Chapters 2, 3, and 4
in my dissertation evaluated the effects of Michigan’s charter schools by asking: How are
students systematically sorted into charter schools? How has the redistribution of students
inﬂuenced racial segregation and social stratiﬁcation in charter schools as well as in TPSS?
How has charter competition inﬂuenced student achievement in TPSS? In this chapter I
will ﬁrst review the ﬁndings in the preceding chapters within the context of Levin’s
analytic framework, ﬁrst introduced in Chapter 1 (Levin, 2002). I will then discuss what

can be learned from Michigan’s experience with choice and competition.

Summary and Analysis of Findings

Levin’s analytic framework suggests that since the policy goals of school choice are
inherently in conﬂict with each other, it is important to analyze how charter schools have
inﬂuenced freedom of choice, equity, productive efﬁciency, and social cohesion
simultaneously. Since school choice is by its nature designed to advance the goal of

freedom of choice, I will focus on the effect of charter schools on the other three values.

152

 

Equity

Do children of different racial or social class backgrounds, or those from different
geographical location have equal access to school choice options? Charter schools in
Michigan are more likely to be located in central cities so as to attract enough students to
survive and thrive. Since students in central cities historically had few options other than
attending their assigned TPSS—schools usually have high concentration of low-income
and minority students and are less likely to perform well in statewide standardized tests—
school choice policies have provided them more schooling opportunities. In Chapter 2, I
performed comparisons of student composition between charter schools and TPSs and
found a more complicated picture of who chooses and who stays. In suburban and rural
areas, many charter schools draw students from multiple districts and show more positive
signs of racial integration compared to TPSS. In central cities, however, charter schools
tend to enroll disproportionably more minority students—mostly Black students—than
TPSS, and display more racial segregation than nearby TPSS. In addition, in charter
schools, the percentages of low-income students are usually smaller than in TPSs in
central cities. Given the large percentages of minority students in Michigan’s central
cities, the presence of charter schools further stratify minority students by SES across
charter schools and TPSs.

In addition to the analysis of how student compositions in charter schools and TPSs
differ, the patterns of student ﬂow between their assigned public schools and charter
schools were studied in Chapter 3, in order to see how student sorting induced by charter
school policy inﬂuences the student composition in TPSs. The results show that charter

schools promote choice for some disadvantaged students, including low-income White

153

students, non-poor Black students, and students who struggled academically in their
assigned schools. However, the net effects of the process of student sorting—both the
movement of students from assigned public schools to charter schools and from charter
schools back to assigned schools—tends to leave the most disadvantaged students in the
most disadvantaged schools. In particular, low-performing, low-income, and/or special
needs students become increasingly concentrated in failing urban public schools with
other similarly disadvantaged students.

The analysis may not reﬂect the ﬁrll impact of student sorting over the past thirteen
years since the passage of Michigan’s charter school law, as it relies on only two years of
student ﬂow because of limitations in the data. In some suburban or rural areas, the
consequences of sorting on TPS student composition might be small since the enrollment
in charter schools only accounts for 1.7 percent in suburban areas and 1.3 percent in rural
areas. However, in central cities, sorting has caused more dramatic unequal distribution
of students across TPSs and charter schools. In addition, many charter schools have
existed more than ten years. Since the students going out to charter schools and students
coming back from charter schools are systematically different in their characteristics, the
accumulated effects of the continuing sorting over all the years is likely to have greatly
exacerbated the preexisting segregation and stratiﬁcation by race, SES, and ability in
central cities.

Take Detroit as an example for it is home to about 10% of all Michigan public school
students. It hosted about 57 charter schools in 2004, or about one fourth of all charter
schools in Michigan, many of which have existed for more than 10 years. In 2004 alone,

about 3.3 percent of students who attended Detroit Public Schools in 2003, or about 4000

154

 

students, transferred to charter schools. In addition to its resident students who were
already in charter schools, the total PSA enrollment from Detroit was 16 percent of its
resident students. This number continues to grow each year. Among all the Detroit
resident students attending charter schools, one ﬁfth returned to Detroit Public Schools in

2004, indicating a very high level of turnover between charter schools and TPSs.

Social Cohesion

The sorting mechanism of charter schools changes the racial and SES composition of
charter schools as well as that of TPSS. This implies that charter school policy could
inﬂuence social cohesion through two ways. One is to change the learning environment
of active choosers in charter schools. The other is to change the learning environment of
non-choosers remaining in TP88 and choosers who returned to TPSs.

The concern about the impact on social cohesion focuses on schools in central cities,
since sorting happens much more frequently in central cities than in suburban and rural
areas. The analysis in Chapter 2 shows that charter schools in Michigan are largely more
racially segregated than TPSs in central cities. The racially isolated learning environment
in these charter schools limits students’ opportunities to directly interact with students
from other racial groups, and hence hampers the learning of the values of tolerance and
respect for differences (Eaton, 2001; Hallinan, 1998; Wells et al., 1994). Evidence in
Chapter 3 suggests that student sorting does not intensify racial segregation in central city
TPSs since minority students are more likely to go to charter schools and yet show no
higher propensities to return to their assigned schools than White students. However,
since more non-poor students and general education students are choosing charter schools,

it leaves the TPSs with a higher concentration of low-income students and students with

155

special needs. This decreases the opportunities of the remaining students to interact with
students from middle-class backgrounds, an effect shown to improve their performance

(Hanushek et al., 2003; Zimmer et al., 2000).

Productive Eﬂiciency

In the context of school choice, improved efﬁciency is referred to as increased
educational results for any given resource constraint under market competition of
schooling (Levin, 2002). The analyses in Chapter 5 indicate that emergence of charter
competition has a negative impact on student achievement in Michigan’s TPSS. The
effect is small or negligible at ﬁrst, but becomes more substantial when the charter
competition persists. For schools in districts where charter schools have drawn away a
signiﬁcant share of their students for more than six years, the estimated charter
competition decreases their satisfactory rate about 0.2 standard deviations in math tests,
and 0.5 standard deviations in reading tests.

This is the ﬁrst study that ﬁnds charter schools have signiﬁcant large negative effects
on student achievement in TPSS. Other studies in the US have found either positive or
no signiﬁcant effects (Bettinger, 2005; Bifulco et al., 2004; Buddin & Zimmer, 2005;
Hoxby, 2003b; Sass, 2006; Solmon et al., 2001). As I argued in Chapter 4, although the
reason for this is not entirely clear, there are some possible explanations. First, Michigan
has one of the strongest educational markets in this country because the full amount of
educational revenue follows the students to whatever schools they attend and local
districts have no ﬁscal discretion to increase their educational revenue. It is also possible
that in Michigan’s current context of a depressed economy, stagnant or declining (real)

state education funding, and long-term population decline that school choice policies

l56

generate harmful impacts on schools at the bottom of the social hierarchy where the
impact of these broader economic forces is most pronounced.

Again take Detroit as an example; it loses more than $200 million annually to charter
schools because nearly 20 percent of its resident students are enrolling in charter schools.
The loss of educational revenues has imposed great ﬁscal pressure on the district’s
budget. As the charter schools tend to take low-cost students in elementary grades or
those without special education needs, the marginal costs of losing one student exceed the
revenue loss associated with the state funds for that one student. With the growing
number of students attending charter schools every year, Detroit has continually been
faced with making signiﬁcant cuts in stafﬁng and programs and to close schools. Such
cuts are always difﬁcult, but in the context of school choice they also raise the prospect
of spurring additional children to leave the district. In addition, schools in central cities
that lose students to charter schools are likely to be the ones that have already
experienced signiﬁcant loss of students and faced harsh education challenges. Despite the
strong incentives imposed by competition for them to improve, the educational
challenges they face by loss of students and ﬁrnding—and in turn, loss of staff and
closure of school buildings—appear to have been too formidable to overcome.

In sum, charter school density in suburban and rural areas is much lower than in
central city districts and they have not created systematic adverse effects on TPSS. In
central cities, however, charter schools have exacerbated the problems of TPSs that serve
disadvantaged students. They intensify the unequal distribution of educational resources

and negatively affect the student achievement in TPSS.

157

 

Inter-district Choice

Inter-district choice has not been the focus of this dissertation. However, being a part
of school choice development in Michigan, it was included in the analysis. Inter-district
choice has some interesting features that are distinctive from charter schools, and
therefore has different impact on student outcomes from charter schools.

First, unlike charter schools that tend to attract students from the central cities, inter-
district choice is more likely to occur among school districts in suburban and rural areas.
The opportunity for choice, however, is limited to students, especially those in central
cities, for several reasons. From the demand side, distance is a constraint. Central cities
are usually big and neighboring suburban schools are far away from the students who live
in the middle of central cities. Parents often have to choose based on trade-offs between
school quality and distance, transportation cost, and time.

From the supply side, participation in inter-district choice is voluntary for school
districts. Districts’ school boards have to vote as to whether or not they want to admit
choice students from other districts, and can specify the number of openings by grade
level and school. In fact, about one third of Michigan districts do not accept students
from other districts. Some suburban districts are experiencing residential population
growth, and do not like to take in nonresident students from other districts. Other
suburban districts are concerned about the potential adverse consequences of incoming
choice students on the racial and SES composition of their schools. They often opt out of
participating in inter-district choice even when they are experiencing declining

enrollments (Arsen et al., 2002; Ruehlen, 2007).

158

Second, inter-district choice poses very different challenges on TPSs than charter
schools. For example, if a TPS loses students to charter schools, the loss is a net loss.
However, when a TPS loses students to other TPSS through inter-district choice, it can
also gain students from other school districts, resulting in no net loss or even a net gain.
However, this is not always the case, especially in central cities. For instance, although
Detroit lost about 5 percent of its resident students to nearby suburban schools through
inter-district choice, the district did not gain any nonresident students from other districts.
The loss of students to suburban district is a net loss to Detroit Public Schools. So, to
some extent, inter-district choice reinforced the negative competitive effect of charter

schools in central cities.

Policy Implications

As charter schools and other forms of choice policies become more and more popular
in the US, Michigan’s experience with choice and competition over the last decade has
signiﬁcant implications for the larger debate about school choice policies and their
impacts elsewhere.

Charter school policy in Michigan was designed to beneﬁt not only the active
choosers but also the non-choosers who stay in TPSS through competitive market effects
that should, over time, increase the quality in all schools. The analysis in my dissertation
shows that although charter schools beneﬁt choosers in some ways, choice policies also
harm non-choosers in other ways. Not all students have equally access to school choice
options. Although some students take advantage of choice, many students are left in more
racially segregated and socially stratiﬁed schools. Schools that are heavily impacted by

charter schools failed to raise their productive efﬁciency as predicted by choice advocates.

159

Instead, they appear to have experienced a vicious cycle of student loss, declining
resources, cutting programs, and further loss of students.

Although the design of choice policy assumes that some schools will be successful
and others unsuccessful, it is not desirable to leave the unsuccessﬁrl ones to market forces
to determine whether the schools should eventually go out of business because all
children, including the children in the unsuccessful schools, should be guaranteed a
quality public education. Therefore, it is imperative for policy makers to have strategies
to ensure that the damage to students in these schools can be minimized without
signiﬁcantly reducing the beneﬁts to students who take advantage of school choice. This
might imply changes in choice policies in order to ensure more equity and diversity while,
at the same time, provide comprehensive assistance including professional development

and ﬁnancial support to improve the sinking schools in central cities.

I60

APPENDICES

Appendix A
The classiﬁcation of school district types is borrowed from David Arsen’s and

David Plank’s report, Michigan School Finance under Proposal A: State Control, Local
Consequences which deﬁnes school districts as follows:

[The authors’] classiﬁcation utilized National Center for Education
Statistics (N CES) data. The NCES classiﬁes school districts using Metropolitan
Statistical Areas (MSA) deﬁned by the US. Ofﬁce of Management and Budget.

[The authors’] “Central city” classiﬁcation includes school districts that
the NCES classiﬁes as primarily serving “Large Cities” and “Mid-size Cities.”
The NCES classiﬁes a few suburban districts with extensive employment as
“Mid-sized Cities” (e.g., East Lansing, Dearbom, and Kearsley).

[The authors] classiﬁed these districts as suburban. [The authors’]
suburban district classiﬁcations are based on two criteria: (1) the NCES classiﬁes
them as “serving an MSA but not primarily its central city” and (2) they have
population density of at least 20 people per square mile. The second condition is
necessary because MSAs follow county boundaries which may include outlying
rural areas. [The authors’] “High income suburb” classiﬁcation includes suburban
districts with median home value in 1990 greater than $95,000. [The authors’]
“Low-income suburb” classiﬁcation includes suburban districts with median
home value in 1990 of less than $42,000. [The authors’] “Middle-income suburb”

group includes suburban districts with median home value in 1990 greater than or

161

equal to $42,000 and less than or equal to $95,000.29

[The authors’] “Rural” district group includes those classiﬁed by the

NCES as “outside an MSA” plus those within an MSA with population density of

less than 20 people per square mile. which includes school districts that the NCES

classiﬁes as primarily serving “Large Cities” and “Mid-size Cities.”

Appendix B:

Model 1 is the multinomial HGLM estimates who tend to transfer from the assigned

public schools to charter schools or inter-district schools of choice. It only includes

student level variables, while no school level variables are included.

Level-1

Level-2

Prob[Y(1)= IIB] = (Piij
Prob[Y(2) = IIB] =¢21j
Prob[Y(3) = llB] =(l’31j = 1 Wm 102i)

L0g(¢11j /¢31j) = BOj(I) + Blj(1)*(BLACK) + 32m) *(HISPANIC) +
B3j(/) *(ASIAN) + B4111) *(FRL) + B5171) *(BLK_FRL) + B61”)
*(AS_FRL) + B 71(1) *(HIS_FRL) + 1381),) *(SPECED) + 391),) *(LEP)

L0g(¢2ij / (0311') = 3 0(2) + 1311(2) *(BLACK) + 321(2) *(HISPANIC) +
B3j(2) *(ASIAN) + B4j(2) I"(FRLJ + B5j(2)* (BLK_FRL) + B6j(2) *
(AS_FRL) + B7j(2) *(HIS_FRL) + ng-(z) I"(SPI’ECE‘ZD) + 391-(2) *(LEP)

307(1) = G000) + U010)
B1”) = 610(1) i=1 t0 9

 

29 Based on 2000 Census Bureau Data, we changed “high income suburb,” “middle income suburb,” and
“low income suburb,” to the latest median home value:

Classiﬁcation Range

High income suburb $170,000-356,500
Medium income suburb 575,000-170,000
Low income suburb $32,500-75,000

I62

B0j(2) = (300(2) + U002)
B02) = (5,00) l: 1 t0 9

Model 2 is the full multinomial HGLM with the full set of student and school level

variables, estimating who tend to transfer from the assigned schools to charter schools or

inter-district schools of choice.

Level-1

Level-2

Appendix C:

Prob[Y(l) = HR] = (Prij
Prob[Y(2) = llB] =¢2ij
Prob[Y(3) = 1|B] =00)- = 1 "Plij «#211

LOg((0iij /(03ij) = B 0,71) + B 11(1) *(BLACK) + B 21(1) *(HISPANIC) +
B 31(1) *(ASIAN) + B .11-(1) *(FRL) + B 5]“) *(BLK_FRL) + B 6j(l)
I"(AS_FRL) + B 7j(1) *(HIS_FRL) + B 8j(l) *(SPECED) + B 911])
*(LEP)

L0g((p2ij “03“) = B 01(2) + B 11le I%BLACK) + B 210) ll‘(HISPANICD +
B 3j(2) *(ASIAN) + B 4j(2) *(FRL) + B 510) *(BLK_FRL) + B 6j(2)
*(AS_FRL) + B 71(2) *(HIS_FRL) + B 8172) *(SPECED) + B 91-0)
*(LEF)

B0([) = (300(1) + G0/(1)*(SCH_BLAC) + G02(])*(SCH_HISP) +
G03(1)*(SCH_ASIA) + G04(])*(SCH_FRL) + ng([)*(SCHEFF) +
GO6(I)*(LNFTB) + G07(I)*(URBAN) + G08(I)*(RURAL) +
(309(1)*(MIDDLB) + G010(1)*(HIGH) + U00)

Bi(/) = (350(1) i=1t0 9

B0(2) = (300(2) + G01(2)*(SCH_BLAC) + G02(2)*(SCH_HISP) +
G03(2)*(SCH_ASIA) + G04(2)*(SCH_FRL) + G05(2)*(SCHEFF) +
G06(2)*(LNFTE) + G07(2)*(URBAN) + 008(2)*(RURAL) +
G09(2)"‘(1\/HDDLB) + G010(2)"‘(HIGH) + U00)

BIL?) = (310(2) i=1t0 9

I63

Totally there are two slope-as-outcome multinomial HGLMs are estimated, each for
slope BLACK and FRL. Here I only describe the model for slope BLACK.

Black Slope-as-outcome HGLM Model:

Level-l
Prob[Y(l) = IIB] = 9111
Prob[Y(2) = llB] =(02ij
Prob[Y(3) = 113] =90)- = 1 -(011j'¢2ij

L0g((pjij /(/’3ij) = B01”) + B [11]) *(BLACK) + B 2j(1) *(HISPANIC) +
B 3,), )*(ASIAN) + B410 )*(FRL) + B 5,), )*(SPECED) + B6j(,)*(LEP)

L08(¢2ij / (0311' ) = B010) + B1j(2)*(BLACK) + B2j(2)*(HISPANIC) +
B 3j(2)*(ASIAN) + B4j(2)*(FRL) + B 5j(2)*(SPECED) + B6j(2)*(LEP)

Level-2
130(1) = (300(1) + G0](])*(LNFTE) + 002(1)*(SCHEFF) +
G03(,)*(SCH_BLAC) + G04(,)*(SCH_HISP) + Gg5(,)*(SCH_ASIA) +
G06(])*(SCH_FRL) + G07(1)*(URBAN) + G08(1)*(RURAL) +
G09(1)*(MIDDLB) + G010(1)"‘(HIGH) + U00)

B1“) = 620(1) + G21(1)*(LNFTE) + G22(1)*(SCHEFF) +
G23(1)*(SCH_BLAC) + G24(])*(SCH_HISP) + G25(1)*(SCH_ASIA) +
026(])*(SCH_FRL) + G27(1)*(URBAN) + G28(1)*(RUR.AL) +
G29(0*(MIDDLB) + G210(1)"‘(HIGH) + an)

B1“) = (310(1) l: 2, 3,4...9

130(2) = (300(2) + G0/(2)*(LNFTE) + G02(2)*(SCHEFF) +

G0 3(2)*(SCH_BLAC) + G04(2)*(SCH_HISP) + 005(2)*(SCH_ASIA) +
(306(2)*(SCH_FRL) + G07(2)*(URBAN) + G08(2)*(RURAL) +
009(2)*(MIDDLB) + 0010(2)*(HIGH) + U00)

B1(2) = (320(2) + G21(2)"‘(LI‘IFTB) + G22(2)"'(SCHBFF) +
G23(2)*(SCH_BLAC) + G24(2)*(SCH_HISP) + 625(2)*(SCH_ASIA) +
626(2)*(SCH_FRL) + G27(2)*(URBAN) + G 23(2)*(RURAL) +
329(2)*(MIDDLB) + G210(2)"'(HIGH) + U00)

Bi(2) = 6,00) l: 2, 3,4...9

164

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