THREE ESSAYS IN THE ECONOMICS OF EDUCATION
By
Quentin Owen Brummet

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
Economics – Doctor of Philosophy
2013

ABSTRACT

THREE ESSAYS IN THE ECONOMICS OF EDUCATION
by
Quentin Owen Brummet
This dissertation consists of three self-contained chapters. The ﬁrst chapter investigates
the eﬀects of school closings in Michigan on student achievement. Many school districts
across the country are shutting schools, but school closing policies remain a very controversial issue. This study investigates the eﬀects of school closing policies on student achievement
by examining over 200 school closings in Michigan. Relative to the previous literature, the
analysis uses a broader set of school closings to thoroughly investigate heterogeneity in treatment eﬀects based on the performance level of the closed school. The results indicate that, on
average, school closings in Michigan did no persistent harm to the achievement of displaced
students. Moreover, students displaced from relatively low-performing schools experience
achievement gains. The displacement of students and teachers creates modest negative
spillover eﬀects on the receiving schools, however. Hence, the closing of low-performing
schools may generate some achievement gains for displaced students, but not without imposing spillover eﬀects on a large number of students in receiving schools.
The second chapter examines the eﬀects of a shortened school year policy on student
achievement. Changing the length of the school year has dramatic potential eﬀects for
student achievement, but the magnitude of these eﬀects will depend on the extent to which
parents and teachers respond to the policy change. This study examines student achievement
in Hawaiian public schools, which furloughed teachers on 17 Fridays during the 2009-2010
school year. This policy was well-publicized in advance, allowing time for parents and teachers to adjust their behavior. Using multiple speciﬁcations and identiﬁcation strategies, the
study ﬁnds negative eﬀects from the school furlough policy on student achievement in el-

ementary school. The analysis ﬁnds no eﬀects on achievement in middle and high school,
however.
The ﬁnal chapter, co-authored with Seth Gershenson and Michael Hayes, looks at teacher
grade reassignments in elementary schools. While recent research suggests that grade-level
reassignments play an important role in fostering student achievement, the literature on
teacher turnover and attrition has largely ignored the reassignment of teachers within schools.
We seek to ﬁll this gap using teacher-level micro data from Michigan to document the
prevalence and distribution of grade-level reassignments across diﬀerent types of schools and
teachers. We ﬁnd that inexperienced teachers and teachers who are new to their school are
less likely to switch grades. The results also suggest that the disruptions associated with
within-school teaching reassignments are inequitably distributed across schools and students.
Urban schools, schools with higher attrition rates, and schools with higher concentrations of
minorities have signiﬁcantly higher rates of grade switching.

To Jennifer.

iv

ACKNOWLEDGMENTS

I would ﬁrst like acknowledge the help of my advisor, Gary Solon, who has provided essential
support for these projects. He has taught me and extraordinary amount about how to be
an economist, and I will be forever grateful for his guidance and mentorship. I am also
extremely grateful to my other advisors – Michael Conlin, Todd Elder, and David Arsen.
Each of them has consistently provided helpful feedback on my research, and I am indebted
to all of them for their advice.
I also am grateful for the valuable advice and feedback I received from other great faculty,
including Soren Anderson, Stacy Dickert-Conlin, Steven Haider, Scott Imberman, Leslie
Papke, and Jeﬀ Wooldridge. Special thanks are also due to Susan Dynarski, Kenneth Frank,
Brian Jacob, and Barbara Schneider. In addition to providing feedback on research projects,
these faculty members were instrumental in helping to obtain access to much of the data
used in chapters 1 and 3.
I am truly indebted to many friends for valuable conversations and helpful comments on
earlier drafts of these papers. There are too many to count, but a partial list includes Ot´vio
a
Bartalotti, Michael Bates, Paul Burkander, Steven Dieterle, Hassan Enayati, Steven Hemelt,
Joshua Hyman, Daniel Litwok, Seth Gershenson, Christina Plerhoples, Nathaniel Schwartz,
Brian Stacy, Paul Thompson, and Kelly Vosters. I have been blessed to have many great
friends in my graduate career, and I am grateful to all of them for their help.
I would also like to thank my family. In particular, without the love and support of my
parents Gary and Donna I would never have made it to graduate school in the ﬁrst place.
Most importantly, I acknowledge all of the support I have received from my wife Jennifer.
Not only has she supported me at every step in this process, but she also has provided
invaluable help with editing and revising drafts. I cannot adequately express my thanks to
her for all of her help, love, and support. None of this would have been possible without her.

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

CHAPTER 1 THE EFFECT OF SCHOOL CLOSINGS ON STUDENT
ACHIEVEMENT . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 School Closings in Michigan . . . . . . . . . . . . . . . . . . . . . . .
1.4 Conceptual Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.1 Baseline Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Possible Explanations for Changes in Student Achievement
1.6.3 Heterogeneity by Performance of the Closed School . . . .
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
4
6
8
11
14
17
21
25
30

CHAPTER 2 THE EFFECT OF FOUR-DAY SCHOOL WEEKS ON
STUDENT ACHIEVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL FURLOUGH
DAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Grades 4–5 . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Grades 6–10 . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Heterogeneity by School Characteristics . . . . . . . . . .
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 3 THE FREQUENCY AND CORRELATES OF
TEACHERS GRADE-LEVEL REASSIGNMENTS:
EVIDENCE FROM MICHIGAN . . . . . . . . . . . .
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 The Prevalence and Distribution of Grade Switching
3.4.2 The Correlates of Grade Switching . . . . . . . . . . .

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vi

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3.4.3
3.5

The Relationship between Grade Switching and Other
Types of Teacher Turnover . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59
60

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
APPENDIX A TABLES FOR “THE EFFECT OF SCHOOL CLOSINGS ON STUDENT ACHIEVEMENT” . . . . . . . . . . 64
APPENDIX B TABLES FOR “THE EFFECT OF FOUR-DAY SCHOOL
WEEKS ON STUDENT ACHIEVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL FURLOUGH
DAYS” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
APPENDIX C TABLES FOR “THE FREQUENCY AND CORRELATES
OF TEACHERS GRADE-LEVEL REASSIGNMENTS:
EVIDENCE FROM MICHIGAN” . . . . . . . . . . . . . . . 78
APPENDIX D FIGURES FOR “THE EFFECT OF SCHOOL
CLOSINGS ON STUDENT ACHIEVEMENT” . . . . . . . 86
APPENDIX E FIGURES FOR “THE EFFECT OF FOUR-DAY
SCHOOL WEEKS ON STUDENT ACHIVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL
FURLOUGH DAYS” . . . . . . . . . . . . . . . . . . . . . . 94
APPENDIX F APPENDICES FOR “THE EFFECT OF SCHOOL
CLOSINGS ON STUDENT ACHIEVEMENT” . . . . . . . 104
F.1 Baseline Analysis Separate by Closing Cohort . . . . . . . . . . . . 104
F.2 Results with Interactions for School Performance Diﬀerential . . . 106
APPENDIX G APPENDICES FOR “THE EFFECT OF FOUR-DAY
SCHOOL WEEKS ON STUDENT ACHIVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL
FURLOUGH DAYS” . . . . . . . . . . . . . . . . . . . . . . 109
G.1 Descriptive Statisitcs . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
G.2 Grade Level Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . 110
APPENDIX H APPENDIX FOR “THE FREQUENCY AND
CORRELATES OF TEACHERS GRADE-LEVEL
REASSIGNMENTS: EVIDENCE
FROM MICHIGAN” . . . . . . . . . . . . . . . . . . . . . . 112
H.1 Within-school Grade-level Reassignment Origins and Destinations 112
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

vii

LIST OF TABLES

Table A.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

Table A.2 Descriptives of Students in Closed Schools . . . . . . . . . . . . . . . . . .

65

Table A.3 Student and Teacher Movement after Closings . . . . . . . . . . . . . . .

66

Table A.4 Average Eﬀects of School Closings on Displaced Students in Michigan . .

67

Table A.5 Eﬀects of School Closings on Receiving Schools . . . . . . . . . . . . . . .

68

Table A.6 School Closings and Voluntary Student Mobility . . . . . . . . . . . . . .

69

Table A.7 Displaced Student Achievement Trajectories by Change in School Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

Table B.1 Comparison of HSA and NAEP Results . . . . . . . . . . . . . . . . . . .

71

Table B.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Table B.3 ITS Estimates – Grades 4 -5 . . . . . . . . . . . . . . . . . . . . . . . . .

73

Table B.4 DD Estimates – Grades 4-5 . . . . . . . . . . . . . . . . . . . . . . . . . .

74

Table B.5 ITS Estimates – Grades 6 -10 . . . . . . . . . . . . . . . . . . . . . . . . .

75

Table B.6 DD Estimates – Grades 6-10 . . . . . . . . . . . . . . . . . . . . . . . . .

76

Table B.7 Heterogeneity by School Demographics . . . . . . . . . . . . . . . . . . .

77

Table C.1 Self-contained Teachers’ Assignments the Following Year . . . . . . . . . .

79

Table C.2 Incidence of Grade-level Reassignments per Teacher . . . . . . . . . . . .

80

Table C.3 Average Characteristics by Teacher-year . . . . . . . . . . . . . . . . . . .

81

Table C.4 Logit Average Partial Eﬀects on Probability of Changing Grades . . . . .

82

Table C.5 Grade Switching as a Predictor of Teacher Turnover . . . . . . . . . . . .

84

Table C.6 Logit Average Partial Eﬀects on Teacher Turnover . . . . . . . . . . . . .

85

Table F.1 Eﬀects of School Closings by Closing Cohort . . . . . . . . . . . . . . . . 105
Table F.2 School Closings and School Performance . . . . . . . . . . . . . . . . . . . 106

viii

Table F.3 School Closings and School Performance using Value-Added Measures . . 108
Table G.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Table G.2 Heterogeneity in Eﬀects by Grade Level – ITS Estimates

. . . . . . . . . 110

Table G.3 Heterogeneity in Eﬀects by Grade Level – DD Estimates . . . . . . . . . . 111
Table H.1 Within-school Grade-level Reassignment Origins and Destinations . . . . 112

ix

LIST OF FIGURES

Figure D.1 Location of School Closings 2006-2009 . . . . . . . . . . . . . . . . . . .

86

Figure D.2 Distribution of School Performance Statewide . . . . . . . . . . . . . . .

87

Figure D.3 Achievement Trajectory of Displaced Students by Performance of Closed
School – Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Figure D.4 Achievement Trajectory of Displaced Students by Performance of Closed
School – Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

Figure D.5 Performance Trajectory at Schools Receiving Students by Performance
of Closed School – Mathematics . . . . . . . . . . . . . . . . . . . . . . .

90

Figure D.6 Performance Trajectory at Schools Receiving Students by Performance
of Closed School – Reading . . . . . . . . . . . . . . . . . . . . . . . . .

91

Figure D.7 Performance Trajectory at Schools Receiving Teachers by Performance
of Closed School – Mathematics . . . . . . . . . . . . . . . . . . . . . . .

92

Figure D.8 Performance Trajectory at Schools Receiving Teachers by Performance
of Closed School – Reading . . . . . . . . . . . . . . . . . . . . . . . . .

93

Figure E.1 Grades 4-5 Mathematics Trajectories . . . . . . . . . . . . . . . . . . . .

95

Figure E.2 Grades 4-5 Reading Trajectories . . . . . . . . . . . . . . . . . . . . . . .

96

Figure E.3 Grades 6-10 Mathematics Trajectories . . . . . . . . . . . . . . . . . . .

97

Figure E.4 Grades 6-10 Reading Trajectories . . . . . . . . . . . . . . . . . . . . . .

98

Figure E.5 Enrollment Trajectory by Furlough Status . . . . . . . . . . . . . . . . .

99

Figure E.6 Pupil-Teacher Ratio Trajectory by Furlough Status . . . . . . . . . . . . 100
Figure E.7 Fraction Asian/Paciﬁc Islander Trajectory by Furlough Status . . . . . . 101
Figure E.8 Fraction White Trajectory by Furlough Status . . . . . . . . . . . . . . . 102
Figure E.9 Per-Pupil Charter School Funding in Hawaii . . . . . . . . . . . . . . . . 103

x

CHAPTER

1

THE EFFECT OF SCHOOL CLOSINGS ON STUDENT ACHIEVEMENT

1.1

Introduction

Over 1800 public schools were shut in the United States after the 2008-2009 academic year
alone (Common Core of Data, 2011). School closings have become common nationwide, and
urban centers such as Chicago, Detroit, Kansas City, New Orleans, Oakland, Philadelphia,
and Pittsburgh have all recently closed schools. In addition, as policy discussions increasingly
focus on high-stakes accountability, some policymakers have suggested shutting the lowestperforming schools and shifting students to higher-performing schools as a way to increase
student achievement. Community leaders and teachers unions often vehemently oppose
these school closings, however. In fact, during the recent teacher strike in Chicago, the
president of the Chicago Teachers Union described the district’s desire to shut schools with
excess capacity as the “big elephant in the room” (Lah and Botelho, 2012). Given this
controversy, understanding how school closings inﬂuence student achievement is essential for
policymakers, because the extent to which districts should utilize closing policies depends
crucially on the eﬀect of closings on student achievement.
Theoretically, the eﬀect of shutting schools on student achievement is ambiguous. On
one hand, school closings may cause harm to students, because the closings disrupt peer
and teacher networks. This disruption may aﬀect the displaced students who are forced to
change schools as well as students at the receiving schools who experience an inﬂux of new
students and teachers. On the other hand, being displaced from low-performing schools may
expose students to higher-quality peer groups and teachers, generating achievement gains.
Hence, if students are systematically moved to higher-quality schools, the net eﬀect of the
displacement could very well be positive. Which of these eﬀects dominates and under what

1

circumstances is an open empirical question.
This paper provides evidence on the nature of these eﬀects by examining school closings
in Michigan. Michigan provides an excellent setting for examining school closings because
a large number of schools have shut in the past decade. Using statewide student-level
micro-data to follow students after displacement, the study estimates the eﬀects of school
closings on both displaced students and students in nearby receiving schools. Because schools
may be selected to close on the basis of their past test scores, the analysis examines the
achievement trajectories of these schools prior to closure. By documenting the magnitude of
the dip in test scores prior to closure, the analysis generates plausible bounds on the eﬀect
of closing schools. This bounding approach does not deliver point identiﬁed estimates, but
generates policy relevant conclusions while relying on less restrictive assumptions than an
approach that attempted to match closed schools to a control group of schools on the basis
of past test scores. In addition, the current study examines a wide range of school closings
and hence is better able than prior studies to estimate heterogeneous eﬀects based on the
performance level of the closed school. Identifying this heterogeneity is key for extrapolating
these results to other settings. In particular, understanding whether districts should adopt
policies of closing particularly low-performing schools will depend on the eﬀects that closing
low-performing schools generates on the achievement of both displaced students and students
in the receiving schools.
The results indicate that school closings in Michigan did no persistent harm to the
achievement of displaced students. For reading, students experience no signiﬁcant change
in test scores at the time of displacement. For mathematics, students in closed schools are
falling behind their peers in the district prior to closure, and this dip prior to displacement is
not the result of formal school closing announcements. Student achievement in mathematics remains low in the ﬁrst year in their new school, but improves markedly thereafter. In
the second year following displacement, student test scores in mathematics are substantially
higher than they were in the year prior to being displaced. This result suggests plausible

2

bounds on the eﬀect of school closings on student achievement. If the drop in test scores
prior to closure is driven by a multiple period transitory shock, then the results indicate no
long term eﬀect of school closings on student achievement. If instead the drop prior to closing
represents a declining trend in student achievement at the closed school, displacement has a
positive impact on mathematics achievement for displaced students. In either case, school
closings create modest negative spillover eﬀects onto students in receiving schools, however,
and these eﬀects persist for multiple years. All of these results are robust to controlling for
district-wide time trends and selective mobility of students out of schools prior to closure.
Intuitively, the eﬀect of displacement varies based on the performance level of the closed
school. In mathematics, students displaced from relatively low-performing schools experience
gains in achievement compared to their prior performance at the closed school. In addition,
the estimated eﬀects on receiving schools vary with respect to the performance level of the
closed schools. If students are displaced from relatively low-performing schools, the spillover
eﬀects are larger in magnitude.
These results imply that districts forced to close schools due to changing demographics
or ﬁnancial problems do no persistent harm to the achievement of displaced students, and
the spillover eﬀects onto students in receiving schools are modest in magnitude. In addition,
displaced students experience improvements in achievement if they are displaced from schools
that are low-performing relative to nearby schools. Hence, school closings can be eﬀective in
raising the achievement of students in low-performing schools while imposing only modest
negative spillover eﬀects. However, a large scale policy to close low-performing schools will
fail to improve average achievement district-wide because any gains from displaced students
will be oﬀset by achievement losses for students in receiving schools.
The paper proceeds as follows. Section 2.2 discusses the relevant literature, Section 1.3
describes the context and institutional details surrounding school closings in Michigan, and
Section 1.4 outlines a conceptual model of how school closings can be expected to aﬀect
student achievement. Section 2.3 then discusses the data used in the analysis and Section

3

2.5 presents the empirical speciﬁcation and results. Section 2.6 concludes, discussing policy
implications of the results.

1.2

Literature Review

The qualitative literature on school closings documents concern from both teachers and administrators that students displaced from closed schools would suﬀer from the displacement
(Lipman and Person, 2007; Steiner, 2009; Kirshner, Gaertner, and Pozzoboni, 2010). For
example, Kirshner et al. (2010) investigate the closing of one large urban high school. In
addition to documenting achievement losses, they report roughly 40% of students surveyed
reported that they felt a sense of loss or that friendships and relationships were disrupted by
the displacement. Whether this sort of disruption generates persistent achievement eﬀects
across a wide range of school closings is an empirical question.
The few quantitative studies to investigate school closing policies in particular districts
have found mixed results, however.1 Sacerdote (2012) examines the achievement of students
forced to leave school due to Hurricane Katrina. His results indicate that students experience
temporary sharp declines in test scores following displacement, but make up substantial
ground thereafter and in many cases experience long-run achievement gains as a result of
the displacement. The circumstances faced by Katrina evacuees are unique, however, and
it is impossible to understand whether these results are driven by changes in family and
residential circumstances due to the hurricane. In Chicago Public Schools, De la Torre
and Gwynne (2009) evaluate school closings aimed at chronically low-performing schools,
and ﬁnd that the closings led to transitory drops in test scores.2 The most comprehensive
1 A related literature that explores the eﬀects of school turnarounds and reconstitutions
(i.e., replacing school staﬀ without shifting students to other schools) ﬁnds mixed results for
student outcomes (Gill, Zimmer, Christman, and Blanc, 2007; Hess, Jr., 2003; Brady, 2003;
Malen, Croninger, Muncey, and Redmond-Jones, 2002).
2 Ongoing work by Barrow, Park, and Schanzenbach (2012) investigates a similar set of
school closings from Chicago and ﬁnds persistent drops in test scores for displaced students.

4

published study to date is Engberg, Gill, Zamarro, and Zimmer (2012), which investigates
the closing of approximately 20 schools in an anonymous urban school district. The authors
ﬁnd that displaced students are harmed substantially, but these eﬀects can be mitigated
by sending displaced students to higher quality schools. Due to data limitations, however,
they are unable to examine the achievement trajectory of students in closed schools prior to
displacement. In addition, the policy investigated by Engberg et al. (2012) displaced 25%
of the students in the school district in the same year. Because this large upheaval aﬀected
the majority of students in the district either directly or through spillover eﬀects, it may be
diﬃcult to apply these results to other settings.
This disagreement about the eﬀects of school closing policies is likely due to the fact
that these results pertain to speciﬁc school closing policies, and not to broad-base closing
policies such as those investigated in the present analysis. By examining a larger variety
of school closings, the current study seeks to add to this existing literature in three ways.
First, the study examines a broader set of closings than these previous studies, and uses
this large data set to investigate heterogeneity of school closing eﬀects on the basis of school
performance. Second, by using statewide micro-data, the analysis is able to account for
students who leave the district after a school closing. This allows the analysis to be robust
to non-random selection of students leaving the school district after a school closing. Last,
the study pays particular attention to the role of teachers in school closing policies. In many
school closings in Michigan, teachers are retained in the district after displacement. This
generates additional spillover eﬀects in a possibly distinct set of receiving schools.
The eﬀect of shifting students from one school to another has also been studied in a
variety of other contexts. For instance, a large literature documents achievement losses for
students who change schools voluntarily or as part of a structural transition from elementary
to middle school.3 As well, the school choice literature uses random lottery admissions to
3 Recent prominent papers in the voluntary student mobility literature include Hanushek,
Kain, and Rivkin (2004a), Xu, Hannaway, and D’Souza (2009), and Loeb and Valant (2011).
See Rockoﬀ and Lockwood (2010) for an examination of student mobility from elementary

5

examine the eﬀect of being admitted to school choice programs on a variety of student
outcomes, but students who apply to school choice programs are a select sample and hence
diﬀerent from students displaced by school closings.4 The literatures on desegregation and
peer eﬀects also investigate the eﬀect of shifting students from one school to another.5 All of
these policies diﬀer from school closings in that they do not include the mobility of teachers
that is typically generated by a school closing. In addition, the policy environments are
much diﬀerent. For instance, the peer eﬀects generated by Katrina evacuees in Houston,
as studied by Imberman et al. (2012), are likely diﬀerent than those generated by closing
schools and shifting students to another school within the same school district.

1.3

School Closings in Michigan

The current study examines the closing of 246 elementary and middle schools in Michigan
between 2006 and 2009.6 School closings in Michigan are driven almost exclusively by
declining district enrollments. In addition to well-documented statewide population declines,
an increase in school choice policies has led to further enrollment declines in some districts.7
Figure D.1 displays the location of closed elementary and middle schools in Michigan between
2006 and 2009.8 As can be seen, the Detroit Metropolitan Area had a large number of school
closings over this time period. This includes many schools in the city of Detroit, but also
to middle school.
4 Prominent examples of the school choice literature include Rouse (1998), Cullen, Jacob,
and Levitt (2005), Abdulkadiro˘lu, Angrist, Dynarski, Kane, and Pathak (2011) and Deming
g
(2011).
5 See Guryan (2004) or Reber (2010) for studies on the eﬀects of desegregation policies and
student outcomes. Imberman, Kugler, and Sacerdote (2012) and Angrist and Lang (2004)
are prominent examples of studies that use exogenous movement of students to estimate the
magnitude and structure of peer eﬀects.
6 This paper will adopt the convention of referring to academic years by the spring, i.e.,
the 2005-2006 academic year will be referred to as 2006.
7 Toma, Zimmer, and Jones (2006) ﬁnd that in Michigan around 80% of students who
enroll in charter schools were previously enrolled in traditional public schools.
8 These 246 closed schools include 18 charter schools.

6

schools in suburban areas. In addition, other urban centers such as Flint, Saginaw, and
Grand Rapids have closed schools recently. Hence, while a number of rural districts closed
schools between 2006 and 2009, the analysis presented below is primarily representative of
urban and suburban school closings.
While some districts make plans for school closures years in advance, the vast majority
of districts do not decide on which school to close until the spring of the last year the school
is open. The choice of which school to close is very complex, and the schools chosen for
closure are often not the lowest-performing schools in the district. In addition to test scores,
district oﬃcials examine factors such as school condition, enrollment, and location when
making their decision. Nonetheless, because district oﬃcials take into account test scores
when making their decision, closed schools are on average lower performing than neighboring
schools.
After closure, students are assigned to a new school within the district. While parents can
choose to move or have their children utilize a school choice program, the shutting of a school
does not alter parents’ choice set. Displaced teachers also move within the district after a
school closes. In fact, the fraction of teachers leaving the teaching profession is no larger
after a closing than in a normal year.9 While the majority of displaced students are usually
transferred to the same nearby schools, displaced teachers can be shuﬄed throughout the
district. Hence, schools that receive displaced teachers may be quite diﬀerent from students
in schools that receive displaced students, and both groups of schools may be aﬀected by the
closing.
9 A small number of districts have placement policies based on teacher preferences, but the
majority of displaced teachers are reassigned using standard district transfer policies that
weigh school needs and administrator preferences in addition to the teacher’s own stated
preferences.

7

1.4

Conceptual Model

Consider the following stylized model of student achievement:
Yist = Xit β + Mit αit + ψst + µi + eist

(1.1)

Here, Yist represents the achievement of student i in school s at time t. Xit is a vector
of student observable characteristics, ψst is a school quality component of student achievement, µi represents ﬁxed student-level inﬂuences, and eist is an idiosyncratic error. Given
that student mobility may aﬀect student achievement for more than one year, Mit is a
vector of indicators indicating that the student moved schools k years ago. In particular,
Mit αit =

k αit,k mi,t−k where mi,t−k is an indicator that the student moved schools in

year t − k. Note that αit varies both across students and within students over time. This
allows for the fact that diﬀerent students respond heterogeneously to moving schools, and
the same student may respond diﬀerently to diﬀerent moves. For example, students may experience less disruption when moving to new schools with many of their previous classmates
or teachers.
For ease of exposition, assume that mobility has no eﬀect on Xit and future values of mit .
This rules out scenarios where being displaced by a closing makes the student more likely
to either move schools in the future or be placed in programs such as special education.10
Letting Titk be an indicator that the student was displaced due to a school closing k years
ago, the causal eﬀect of moving schools due to a school closing can be written as follows:
E[Yist |Titk = 1]−E[Y

|T
= 0] = αit,k +(E[ψst |Titk = 1]−E[ψ |Titk = 0]) (1.2)
i,s ,t itk
s ,t

Similar to the model of student mobility discussed in Hanushek et al. (2004a), this eﬀect
consists of two components. The ﬁrst component represents the direct eﬀect of changing
schools on student achievement. Again, this eﬀect may be heterogeneous among students
10 The model can be readily extended to incorporate these eﬀects, but their inclusion does
not change the conclusions of the model.

8

depending on the circumstances surrounding the displacement. In addition to this direct
eﬀect, students will on average experience a change in school quality.
Note that the quality of the receiving school may change due to the inﬂux of new peers
and teachers. Hence, school closings may aﬀect students in receiving schools as well as
displaced students. In particular, consider the following decomposition of school quality:
T
P
ψst = (Fst ΠP + Fst ΠT ) + SQst + ust

(1.3)

P
T
The ﬁrst group of terms consists of Fst and Fst , which represent the fraction of students
and teachers in a school who are new to the school, respectively. This captures that new
students and teachers in the school may cause disruption to the learning environment. As
with student mobility, disruption to the school environment may aﬀect schools dynamically.
P
Therefore, Fst ΠP =

P P
T T
j πj fs,t−j and Fst Π =

T T
P
T
j πj fs,t−j , where fst and fst repre-

sent the fraction of students and teachers at school s in year t, respectively. SQst captures
both school-level factors that are ﬁxed in the school over time such as school facilities and administration, as well as aspects of school quality that may ﬂuctuate within a school over time,
such as the quality of the peer and teacher composition in the school. ust is a school*year
level error term.
In this framework, the change in school quality following a displacement can be written
as follows:
T
P
ΠT )
ψst − ψs ,t−k = (Fst ΠP − F P
ΠP ) + (Fst ΠT − F T
s ,t−k
s ,t−k
+ (SQst − SQs ,t−k ) + (ust − us ,t−k )

(1.4)

The ﬁrst two terms reﬂect that the receiving school experience disruption due to the inﬂux of
new students and teachers. Hence, it is possible that students who might have been expected
to move to a much better school as a result of displacement do not actually experience this
improvement in school quality because the inﬂux of teachers and students from the closed
school reduced the quality of the receiving school. The last two terms will be important in the

9

empirical analysis. In particular, consider two cases. On one hand, if student achievement
improved after displacement because students were displaced to higher-quality schools, then
SQst > SQs ,t−k , which represents a causal eﬀect of school closings on displaced students.
On the other hand, if student achievement increased because ust > us ,t−k , this would not
represent a causal increase in student achievement. For example, if schools were selected to
be closed on the basis of their latest test scores, displaced students would have particularly
low draws of u

s ,t−k
detail in Section 2.5.

, leading ust − u
to be positive. This issue is discussed in greater
s ,t−k

Students in receiving schools also experience a change in school quality due to the disruption from new students and teachers and the change in peer and teacher quality. This
eﬀect may diﬀer from that experienced by displaced students, however, because students at
receiving schools do not experience changes in some aspects of school quality. For example,
a school’s curriculum is likely not changed by the inﬂux of new students. Hence, the displacement of students would expose them to potentially better curriculum without changing
the curriculum experienced by students who were already attending the receiving school.
While being displaced by a school closing is a type of student mobility, it is important
to note that the eﬀect of moving schools due to a school closing is distinct from eﬀects that
have been estimated in other literatures on student mobility. In particular, these eﬀects are
likely to diﬀer for at least three reasons.
First, the circumstances surrounding mobility may be diﬀerent between displaced students and other movers. This will result in αit,k being diﬀerent on average for students
displaced by closings compared to other forms of student mobility. For instance, students
in closed schools often attend school post-displacement with many of their previous classmates. If the mobility eﬀect is due to disruption in student peer networks as a result of
the move, one might expect student achievement to be lower in the case of students who
move by themselves when compared to students displaced by school closings. In addition,
the discussion of the impending closure may create disruption in the school prior to closure.

10

This disruption in student achievement would not occur prior to most other student moves
and might alter the eﬀect of the move on student achievement.
Next, as discussed in the voluntary mobility literature, diﬀerent types of student moves
will result in diﬀerent changes in school quality. In the context of the current model, this
implies that (SQst − SQ
) is diﬀerent depending on the setting of the study. These
s ,t−k
diﬀerences in school quality may potentially be very diﬀerent for school closings compared
to other forms of student mobility because students are typically reassigned after closings.
With other forms of student mobility, students are often explicitly making the decision to
change schools, implying that they may be more likely to make their schooling decisions on
the basis of school quality.
P
Last, the inﬂow of students following school closings is typically very large. Hence, Fstj
T
and Fstj are greater in the context of school closings compared to other types of mobility.
In addition, because the inﬂux of new students and teachers into the receiving schools will
often be much larger than inﬂuxes of other movers, school closings have the potential to
fundamentally alter the quality of the receiving schools. In the context of the model, this
implies that changes in SQst are potentially much larger for receiving schools after closings
than typically would occur in the case of other forms of student mobility.

1.5

Data

This study uses student-level administrative data maintained by the Center for Educational
Performance and Information (CEPI) and the Michigan Department of Education (MDE).
A detailed description of the data can be found in an online data appendix.11 Brieﬂy, the
sample includes all students in grades 3-8 over the 2006-2010 academic years. In total, this
represents 1,252,101 students and 3,416,174 student*year observations. Of these students,
39,205 were displaced by a school closing, with some students being displaced multiple times.
11 Online material can be found on the author’s website at https://sites.google.com/site/
quentinbrummet.

11

Student achievement scores are taken from the Michigan Educational Assessment Program (MEAP) exams, which are administered to students in grades 3-8 in early to midOctober. Therefore, displaced students usually take their last test in the closed school prior
to the formal announcement of the school closing. The fall administration of the MEAP
slightly changes the interpretation of the results. MDE designs the tests so that test scores
in year t are the result of instruction in year t − 1 (Michigan Department of Education,
2005). Nonetheless, it is possible that extensive MEAP preparation prior to taking the tests
may aﬀect MEAP scores. If test scores represent knowledge gained the current year, interventions should have an immediate impact. However, if test scores reﬂect knowledge gained
the previous year, interventions should have a lagged eﬀect on student achievement. The
current study takes the approach of assuming that achievement in year t is the result of
instruction in year t. This contrasts with the approach taken by Hoxby (2000), who assumes
achievement in year t is not aﬀected by school inputs in year t. As will be seen later, treating
achievement in year t as being the result of instruction in year t − 1 only strengthens the
results.
Table A.1 presents descriptive statistics for the sample used in the analysis. The sample
includes signiﬁcant portions of minority and disadvantaged students. In particular, 42.9% of
the sample is eligible for free or reduced-price lunch and 24.1% of the sample is either black
or Hispanic. Over 1.2% of the sample attend a school that will close that year, corresponding
to over 40,000 observations. In addition, 7.0% of the sample attends school in a district that
closed a school the previous year, and may themselves be aﬀected by closings due to spillover
eﬀects. Due to the limited time frame of the study, there are fewer observations in the sample
for students who are many years away from closure. Nonetheless, over 10,000 student*year
observations exist on students three or more years after displacement. In addition, there is
substantial variation in the fraction of students at a school that were just displaced by a
school closing. Most students in the sample do not attend school with any displaced students,

12

but in some schools up to 74.0% of students were previously displaced by a school closing.12
Table A.2 presents descriptive statistics for students in closed schools in Michigan and
compares them to all students in Michigan and students within their district. Compared to
other schools in their district, closed schools enroll almost 100 fewer students. This is not
an artifact of diﬀerent grade conﬁgurations between open and closed schools, because closed
schools have lower enrollment even comparing among schools with K-5 grade conﬁgurations.
This evidence supports statements by district oﬃcials, who often cite declining enrollments as
one of the key factors in deciding which schools to close. While students in closed schools are
similar in terms of gender and Limited English Proﬁciency status compared to other students
in the state, districts that close schools have much diﬀerent demographics than districts
that do not. Almost 50 percent of students displaced by school closings attend schools in
urban areas. Compared to the average student in Michigan, these students are more likely
to be African-American, participate in special education programs, and be economically
disadvantaged as measured by eligibility for free or reduced-price lunch. These diﬀerences
are largely due to diﬀerences between districts that close many schools and districts that
do not. In terms of student achievement, students in closed schools tend to perform 0.4–0.5
standard deviations worse than the state average, but also a little over 0.1 standard deviations
worse than students within their district. Hence, while the majority of poor performance
by students in closed schools can be attributable to district-level diﬀerences, the fact that
students in closed schools perform worse than peers in their own district supports anecdotal
evidence from district oﬃcials that school performance is considered when making their
decision of which school to close.
Table A.3 displays statistics on the movement of students and teachers after closings. For
the majority of school closings, the median student in that closed school attends a school
less than 1.5 miles away from their previous school after being displaced. However, for some
12 These instances where many students were previously displaced are the result of school
consolidations.

13

closings the median student attends school almost ﬁve miles away from their previous school
after displacement. As a result of remaining in the same school district, students often attend
the same receiving school after closure. As can be seen, the fraction of students attending
the modal receiving school after closure is often less than the fraction of teachers attending
the modal receiving school, underscoring the point that displaced teachers are often more
widely dispersed after closure than displaced students. Table A.3 also shows that for the
majority of school closings, non-trivial fractions of students either leave the school district or
attend a charter school after displacement. This highlights one advantage to using state-wide
administrative data to study school closings – it is much easier for parents to move out of
district in response to school closings than to leave the Michigan public and charter school
system.

1.6

Empirical Analysis

Given the complex decision process for deciding which school to close, school closings are not
likely to be randomly assigned conditional on student ﬁxed eﬀects and observable characteristics. Most importantly, district administrators often take student test scores into account
when deciding what school to close, creating a pattern where student test scores in schools
decline prior to closure. This dip could be due to either a systematic decline in student
test scores prior to closure or a transitory decline in test scores, similar to the “Ashenfelter
Dip” that has been observed in job training programs (Ashenfelter, 1978; Ashenfelter and
Card, 1985). If the dip is transitory, it may lead conventional program evaluation techniques
to overestimate the impact of school closings due to mean reversion in student test scores
(Chay, McEwan, and Urquiola, 2005). Note that there could also be a causal eﬀect of school
closings on student achievement prior to closure. Closed schools are often in danger of being closed for years before they are eventually closed, which could lower student test scores
through additional disruption in the schools.
Because of these concerns, it is important to consider the pattern of test scores prior to
14

closure when investigating school closings. Consider the following model:
3
Yist =

3
δk Titk +

k=−2

P P
T T
1[Titj = 0](πj,l fs,t−j+1 + πj,l fs,t−j+1 )

j=1

+ Xist β + µi + θgdt + ist

(1.5)

The treatment speciﬁcation for displaced students mirrors that found in research on displaced workers and includes dummy variables indicating how many years the student is from
displacement (Jacobson, LaLonde, and Sullivan, 1993; Stevens, 1997). Speciﬁcally, for k < 0,
Titk is a dummy variable indicating that the student attends a school that will close in |k|
years. If k is positive, Titk takes a value of 1 if the student was displaced by a school closing
k years ago.13
P
T
The variables fst and fst represent the fraction of students and teachers at school s in
year t who were displaced j years ago, respectively. Note that these variables can also be
deﬁned at the grade level as opposed to the school level. School-level disruption measures
are preferred for two reasons. First, they capture potentially important spillover eﬀects
P
T
across grade levels, which would bias the results if fst and fst were deﬁned at the grade
level. In addition, the fall administration of the MEAP means that multiple teachers may
P
T
be responsible for student achievement in year t, implying that grade level fst and fst
P
T
measure would miss spillover eﬀects across grade levels.14 Both fst and fst are interacted
with an indicator for whether the student was displaced k years ago.15 Yist represents the
achievement of student i in school s, year t. Xist is a vector of student controls containing free
or reduced-price lunch eligibility, Limited English Proﬁciency status, and special education
13 For example, if a school closes after the 2008 academic year, students attending that
school in 2007 have Ti,2007,−1 = 1, Ti,2008,0 = 1, and Ti,2009,1 = 1.
14 Results using grade-level variation are qualitatively similar, and can be found in Online
Appendix Table C.1.
15 If a student moves into a school for a reason other than being displaced by a closing, they
are counted as a student at the receiving school. The results are not sensitive to changes in
this deﬁnition.

15

status.16 All test scores are standardized within grade and year to have mean 0 and variance
1. µi and θgdt are student and grade*district*year ﬁxed eﬀects, respectively.
While school closings are potentially endogenous, the dynamic speciﬁcation allows the
researcher to identify separate eﬀects of school closings based on what assumptions are made
about the decline in test scores prior to displacement. If the drop in achievement prior to
closure is caused by the closing itself or is transitory in nature, then the eﬀect of school
closings on student achievement k years after closure is δk . To the extent that drops in
test scores represent a systematic decline in the quality of the closed schools, the eﬀect of
the school closure is at least as large as δk − δ0 . In particular, under the assumption that
student achievement would have remained the same had the school not closed, the eﬀect of
displacement is exactly δk − δ0 . If the school was trending downwards, then δk − δ0 is a
lower bound for the eﬀect of the displacement on student achievement.
As shown in Table A.2, districts that closed many schools are much diﬀerent than the
average district in the state. The inclusion of grade*district*year ﬁxed eﬀects makes the
analysis robust to any district-level time trends that may diﬀer between districts that did
or did not close schools. In addition, because a given test is administered to students in
a particular year*grade, this analysis compares students displaced by closure only to their
peers within the district who took the same test.17 These ﬁxed eﬀects makes the estimation computationally demanding, however. As a result, the analysis uses a computational
algorithm developed by Guimar˜es and Portugal (2010).18 Standard errors are adjusted for
a
16 Student mobility history, average school demographics, and average rates of student
mobility in the school are excluded as they are possible outcomes from school closings. The
results are not sensitive to the inclusion of these variables.
17 While not shown here, results are qualitatively similar using district*year ﬁxed eﬀects as
opposed to grade*district*year ﬁxed eﬀects. Note that the inclusion of district*grade*year
ﬁxed eﬀects also that this makes the speciﬁcations similar to much of the school closing literature using district-level administrative data, which often includes either year or year*grade
ﬁxed eﬀects.
18 Brieﬂy, this algorithm alternates between estimating the coeﬃcients on the variables of
interest and the ﬁxed eﬀects, holding one set of parameters ﬁxed while estimating the other
set.

16

clustering at the district level.19
Equation (1.5) is similar to value-added models used to estimate teacher quality, which
often condition on lagged student outcomes. However, recent simulation evidence by Guarino, Reckase, and Wooldridge (2011) shows that the decision of whether to condition on a
lagged test score or student ﬁxed eﬀect should depend largely on the mechanism for assigning
students to treatment. In the context of estimating teacher eﬀects, estimators that condition on lagged test scores often perform well if students are tracked into classrooms on the
basis of past test scores. However, the relevant assignment mechanism in the current study
is how students are assigned to schools, which is likely to be based primarily on relatively
time-invariant characteristics of students such as residential location. As such, a student
ﬁxed eﬀects approach is preferred for the current study.
Given these concerns, the analysis is broken up into three parts. Section 1.6.1 estimates
the average eﬀect of school closings in Michigan, and Section 1.6.2 examines possible explanations for the patterns observed in the data. Last, Section 1.6.3 examines heterogeneity
based on the performance level of the closed school.

1.6.1

Baseline Analysis

Table A.4 contains estimates of the speciﬁcation shown in Equation (1.5). For mathematics,
student test scores drop in the years prior to closure, stay low in the ﬁrst year at their new
school, and then improve in the years after closure. In particular, students perform 0.061
standard deviations worse during the last year the school is open compared to three years
prior to closure. Student performance is even lower in the year after closure, and drops to
0.074 standard deviations below their performance three years prior.20 Student achievement
19 Adjusting for clustering at the district level is preferred since that is the level on which the
decision to close a school is made. In practice, standard errors clustered at the district level
are larger than those clustered at the school level, and hence the standard errors reported
in the analysis can be viewed as conservative.
20 Given that there are ﬁve years of data and six treatment indicators, it is clear that
diﬀerent cohorts of displaced students identify diﬀerent subsets of the δk coeﬃcients. If
17

improves thereafter and, two years after closure, is similar to levels two years prior to closure
and signiﬁcantly better than in the last year in the closed school.21 Note again that because
the MEAP is given during the fall, much of the poor student performance in the ﬁrst year
after displacement could be the result of knowledge that was gained the year before. Hence,
the estimated coeﬃcient for one year after displacement may overstate any potential negative
eﬀects from the displacement.
As discussed previously, this analysis provides plausible bounds for the eﬀect of school
closings on the achievement of displaced students. If the drop in student test scores prior to
closure is transitory in nature, school closings have short-run negative eﬀects on displaced
students, but no long-run eﬀects. Hence, at the very least the results imply that school
closings in Michigan had no sustained negative impacts on displaced students. To the extent
that drops in mathematics scores prior to displacement represent a declining trend not caused
by the school closing itself, the eﬀect of the closing is positive, and over the long run student
achievement in mathematics improved as a result of the displacement. Section 1.6.2 will
return to this and present evidence about the nature of the dip in student performance prior
to displacement.
For reading scores, the pattern is less clear. On the whole, the estimated achievement
trajectories are similar for mathematics and reading. Student achievement drops prior to
displacement and in the ﬁrst year at the new school, but improves moderately thereafter.
There are some important diﬀerences between reading and mathematics, however. In particular, the dip in test scores prior to displacement is not signiﬁcant, and the results are
not estimated with enough precision to rule out that student achievement does not change
after displacement.22 Hence, while these estimates are imprecise, the results indicate the
the composition of school closings diﬀers substantially from year to year, then the dynamic
pattern of the pooled results will not accurately reﬂect the true eﬀect of school closings.
Appendix F.1 displays the results of speciﬁcations like those shown in Section 1.6.1, but
where treatment is deﬁned separately for each cohort. The results are qualitatively similar.
21 The t statistic for a Wald test testing that mathematics achievement two years after
displacement is the same as mathematics achievement the year prior to displacement is 1.86.
22 The t statistic for a Wald test testing that reading achievement two years after displace18

potential for only modest eﬀects of displacement on student achievement in reading.
Both Sacerdote (2012) and De la Torre and Gwynne (2009) similarly ﬁnd fadeout in displacement eﬀects, but these patterns contrast with those presented in Engberg et al. (2012),
who ﬁnd sustained detrimental eﬀects from displacement. There are multiple possible explanations for this diﬀerence in results. For one, these studies only analyze data from single
school districts and therefore are unable to account for dynamic attrition of students out
of districts after closure. If the students selecting out of the district were students whose
achievement was trending upwards, estimates will be biased towards estimating overly negative eﬀects of school closings. In addition, it is possible that displaced students experienced
diﬀerent changes in school quality between the two settings. The only other study to attempt to estimate heterogeneity in closing eﬀects on the basis of the performance level of the
closed school is Engberg et al. (2012), who use a measure of school quality developed by the
school district, which is diﬃcult to extrapolate to other settings. This point is returned to in
Section 1.6.3, which attempts to estimate this heterogeneity in school closing eﬀects.23 Also,
Engberg et al. (2012) examine a policy that displaced 25% of students in the school district
in a single year. Hence, the disruption studied in this district may not be representative
of school closing policies where a smaller fraction of students in the district were displaced.
Whether these explanations account for the diﬀerences in results is a question for future
research.
Students in schools that receive the displaced students are also aﬀected by the closing. Table A.5 displays results from speciﬁcations as described by Equation (1.5), with the
fraction of displaced students in the receiving school also interacted with treatment for displaced students.24 Both displaced students and students previously attending the receiving
ment is the same as reading achievement the year prior to displacement is -0.87.
23 In addition, the model estimated by Engberg et al. (2012) does not include student ﬁxed
eﬀects, but controls instead for student’s baseline test scores. As explained in Todd and
Wolpin (2003), if the baseline scores measure student achievement with error, the estimated
model under-adjusts for student ﬁxed eﬀects. The resulting omitted-variables bias is likely
to generate overly negative estimates of displacement eﬀects.
24 Refer to Online Appendix Table C.3 for full estimates of this speciﬁcation, where the
19

schools are negatively aﬀected by the inﬂux of new students. To interpret the size of these
coeﬃcients, consider that the standard deviation of the fraction of displaced students in a
receiving school is roughly 0.035, so the -0.218 coeﬃcient for mathematics represents a 0.008
standard deviation decline in student achievement for a one standard deviation increase in
the fraction of students in the school who were just displaced by a school closure. Likewise,
the -0.280 coeﬃcient on reading can be interpreted as a 0.010 standard deviation drop in student achievement for each standard deviation increase in the fraction of displaced students
in the school. These results could potentially be biased if students were sent to schools that
were trending up or down prior to receiving the displaced students. While not shown here,
P
T
leads of the fst and fst variables are close to zero, providing support for the assumption
that students were not dynamically sorted into receiving schools.25
These ﬁgures are of the same magnitude as those reported in Hanushek et al. (2004a)
for the fraction of students who voluntarily move into the school. While this estimate is
very small, it is important to note that, unlike voluntary moves studied in Hanushek et al.
(2004a), school closings aﬀect concentrated geographic areas, and most receiving schools are
likely to experience a much larger than one standard deviation increase in the fraction of
displaced students when nearby schools close. In fact, the median displaced student attends
a school in which roughly 20% of the student body was just displaced the previous year.
In this case, student achievement at the receiving school declines by roughly 0.044 standard
deviations in math and 0.056 standard deviations in reading as a result of the inﬂux of new
students.26
main treatment speciﬁcation for displaced students is estimated for those students attending
receiving schools with mean levels of fraction of displaced students and teachers in their
receiving school after displacement.
25 Online Appendix Table C.2 contains the estimates of regressions including these leads
of the treatment variables.
26 One might expect that larger schools have more resources to shift around, and hence
are better able to accommodate the same percentage change in new students compared to
smaller schools. If this were the case, then there would be heterogeneity in spillover eﬀects
with regards to school size. This does not appear to be the case, however, as the spillover
eﬀects do not vary with the size of the receiving school.
20

Receiving schools are also aﬀected by an inﬂux of displaced teachers. Similar to previous
results, both displaced students and students at the receiving school are aﬀected similarly by
the disruption. In particular, the fraction of displaced teachers in a receiving school tends to
have a negligible negative eﬀect in the ﬁrst year, and is signiﬁcantly larger in magnitude two
or more years afterwards for both mathematics and reading. This pattern could be explained
by the fall administration of the MEAP, as instruction in year t may not have its full impact
until year t + 1. The implied negative impact is very small, however. The median school
receiving displaced teachers has 16.7% of its teaching force composed of displaced teachers.27
This implies that for students in these receiving schools, the drop in mathematics test scores
due to the new teachers would be small in ﬁrst year and rise to 0.014 the year after. The
eﬀect on reading scores is similar. In the ﬁrst year there is a negligible 0.005 drop in test
scores, but the year after student achievement is 0.022 lower than before the inﬂux of new
teachers. While these estimates are smaller in magnitude than those presented previously
for the fraction of displaced students entering a school, they are not statistically diﬀerent.

1.6.2

Possible Explanations for Changes in Student Achievement

The interpretation of the results may change substantially depending on the explanation
of the dip in mathematics test scores prior to displacement. One possible explanation is
that announcements of school closings caused a drop in student and teacher morale which
drove the decrease in test scores prior to closure. This is unlikely though, because the
vast majority of closings in Michigan were announced during the spring of the last year
the school was open, after students had taken the MEAP exams.28 In particular, these
closings contain over 90% of all students who were displaced. This implies that the drop in
27 The median displaced student attends a school where 5.3% of the teachers were displaced
one year prior.
28 Data on date of announcement of school closings were obtained from internet searches of
newspaper articles and personal communication with district oﬃcials. There is substantial
missing data on when school closings were announced, however, corresponding to 19.5% of
displaced students.
21

student achievement prior to closure is not driven by disruption resulting from the formal
announcement that the building would be closed.29 This does not rule out the possibility
that the discussion of impending closure caused disruption in the learning environment prior
to the formal announcement of the closure, but it is unlikely that the formal announcements
of the school closings are driving the decline in test scores prior to closure.30
Another possible explanation is that students were selectively moving out of schools
prior to closure. Because the treatment speciﬁcation in Equation (1.5) deﬁnes all students
attending schools prior to closure as treated, students switching into or out of schools prior to
closure help to identify the model, implying that dynamic selection of these students may bias
the results. In addition, the analysis above ignores other student mobility patterns that may
be correlated with school closings. To address both these concerns, Table A.6 displays results
based on speciﬁcations such as that shown in Equation (1.5), with a separate treatment
speciﬁcation estimated both for students who move schools voluntarily and for students who
move out of schools prior to the closing. The estimated mathematics trajectory for displaced
students is very similar to that shown in Table A.4, implying that the drop in test scores prior
to displacement is not driven by selective mobility out of schools prior to closing. For reading,
the drop in student achievement appears to be slightly larger than in Table A.4. Nonetheless,
students still recover substantially in the two to three years after displacement and the results
are not statistically diﬀerent from those presented previously. In addition, achievement
trajectories for displaced students and voluntary movers are statistically diﬀerent in both
mathematics and reading. This underscores the fact that moving schools voluntarily is
29 Online Appendix Table C.4 contains results of speciﬁcations estimated just on the set
of school closings not announced in advance.
30 Another possible way to investigate whether the anticipation of the closing had a negative eﬀect is to examine whether displacement eﬀects were much less for students in the
highest grade at the school. This is highly suggestive however, as prior work has documented
achievement losses for students who change schools due to grade progressions (Rockoﬀ and
Lockwood, 2010). Nonetheless, as documented in Online Appendix Table C.5, results for students in their terminal grade at the time of closure are qualitatively very similar to students
in younger grades.

22

a diﬀerent treatment from being displaced by a school closing. Note also that voluntary
movers experience a decline in test scores in the last year in their old school, suggesting that
voluntary moves are endogenous to student achievement.
Given these results, it is unlikely that either formal announcements of closings or selective
mobility of students out of closed schools drove the drop in mathematics scores prior to
displacement. This still leaves open the possibility that the drop was the result of a transitory
shock in student test scores, and schools were selected to be closed on the basis of these
negative shocks. However, the fact that the shock is present for multiple periods rules out
a story that the school simply had one bad year and students rebounded afterwards due to
simple mean reversion.31 One explanation that cannot be ruled out is that discussion of the
impending closure harmed closed schools relative to other schools in the district. While this
is possible, a potentially more likely explanation is that district administrators shut schools
that were systematically losing ground prior to closure. If this latter explanation is true, the
increase in mathematics scores after displacement is not simply a statistical artifact but a
causal increase in student test scores. In either case, the substantive conclusions for reading
scores are unchanged. There is no detectable dip in achievement prior to displacement and
student achievement does not change signiﬁcantly after displacement. These results are
unchanged accounting for selective mobility of students out of schools prior to closure and
do not appear to be driven by formal announcements of school closings.
One potential explanation for the increase in student achievement after displacement is
that school closings occurred as part of a district-wide plan to upgrade facilities, as previous
research has found that upgrading facilities can produce moderate student achievement gains
(Cellini, Ferreira, and Rothstein, 2010). Given the current ﬁscal environment in Michigan,
however, very few of the school closings currently studied are a result of these sorts of plans.32
31 In addition, if the fall MEAP test does measure knowledge gained in prior periods as it
was designed, this implies that the shock would have needed to be present for three years in
a row to explain the results.
32 Districts are classiﬁed as upgrading facilities if they have obtained a qualiﬁed bond to

23

In fact, only a little over ten percent of the displaced students considered in the analysis
attended school in a district that was upgrading facilities, and results are qualitatively similar
when limiting the analysis to just those districts without such plans.33 One might also think
that by closing schools, districts are able to devote more expenditures towards students as
opposed to building maintenance. However, results available from the author suggest that
the distribution of district-level per-pupil expenditures do not change signiﬁcantly when
districts close buildings.34
One might also worry that the increase in test scores after closure was driven entirely by
selective attrition of displaced students from the Michigan public school system. While the
analysis is robust to attrition based on time-constant factors, dynamic attrition of displaced
students out of the Michigan public and charter school system would bias the results. Only
2.25% of students displaced by closure leave Michigan public schooling compared to 2.11% of
all other students, however.35 As previously documented in Table A.3, it is much more likely
for students to either leave the school district or attend a charter school after displacement.
Hence, while it is possible for students to leave the state or attend private schools after closure, these ﬁgures suggest that bias resulting from dynamic selection of students moving out
of Michigan or to private schools is likely not a ﬁrst-order concern for the current analysis.36
The next section will examine another possible explanation for the increase in mathematics achievement after displacement. In particular, it will examine the role of school
performance in the eﬀect of school closings on student achievement and whether increases
renovate or construct a new elementary or middle school over the previous ﬁve years. These
data is publicly available from the Michigan Department of Treasury and can be found at
https://treas-secure.state.mi.us/apps/ﬁndschoolbondelectinfo.asp.
33 The estimates of these regressions are available in Online Appendix Table C.6.
34 Expenditure information is publicly available from Bulletin 1014, which is published
by the Center for Educational Performance and Information and can be found at http:
//www.michigan.gov/mde/0,1607,7-140--21514--,00.html.
35 The corresponding ﬁgure for students in receiving schools is 2.70%.
36 Data from the 2010 Private School Universe Survey indicate that on the order of 6 − 7%
of Michigan students attend private schools. This is roughly half the size of the fraction of
students who utilize school choice programs such as charter schools or inter-district choice.

24

in school performance can explain the estimated gains in mathematics after displacement.

1.6.3

Heterogeneity by Performance of the Closed School

As discussed in Section 1.4, the eﬀect of school closings on student achievement can be
expected to vary based on the performance of closed schools relative to nearby receiving
schools. Hence, estimating heterogeneity in the eﬀects of school closings with respect to the
performance of the closed school is essential to evaluating the eﬀects of a potential school
closing policy. It is important to note that there are two possible eﬀects of interest. One eﬀect
of interest is the eﬀect of moving from a low- to high-performing school. This is the question
that is answered if students are randomly assigned to receiving schools after displacement.
However, a question of greater policy interest is the eﬀect of closing a low-performing school,
taking into account that districts cannot forcibly assign students to receiving schools after
displacement.37 Because no school closing policy can force students to attend their assigned
school after displacement, the eﬀect of shutting a low-performing school will include the
location and schooling choices that are made by parents after the closing. Hence this study
investigates heterogeneity in eﬀects based on the diﬀerence in performance between the closed
school and nearby schools.
The current study uses the average of 4th and 7th grade proﬁciency rates from 2000-2005
as a measure of school performance.38 This contrasts with Engberg et al. (2012), who use
a value-added index generated by the anonymous school district to measure the quality of
the closed school. Proﬁciency rates are preferred for the current study because value-added
measures attempt to partial out aspects of school performance that are out of the school’s
37 Engberg et al. (2012) instrument for the quality of school that a student attends postdisplacement with the quality of the school to which the student was assigned to attend,
which estimates the eﬀect of school quality on student achievement for students who attend
their assigned school after displacement.
38 To ensure comparability across years, these measures are normalized within year to have
mean zero and standard deviation one. As a frame of reference, in the current sample one
standard deviation in proﬁciency rates corresponds to roughly a 0.4–0.5 standard deviation
diﬀerence in student test scores.
25

control, including peer eﬀects.39 The eﬀect of shutting a low-performing school will depend
on all components of school performance, however. Average school proﬁciency measures
capture peer inputs in addition to school and teacher quality. This is important because the
eﬀect of shutting schools will depend on these changes in peer composition.40
As with the main results presented in Section 1.6.1, the speciﬁcation examines the achievement trajectory of displaced students prior to closure. In particular, it interacts the treatment
variables from Equation (1.5) with the diﬀerence in school performance between the closed
school and nearby schools that remained open:
3
Yist =

3
δk Titk +

P P
T T
1[Titj = 0](πj fs,t−j + πj fs,t−j )

j=1
k=−2
3
3
3
P P
T T
¯ 3,P
¯ 3,T
+
γk Titk ∆is,t−k +
1[Titj = 0](πj fs,t−j ∆s,t−j + πj fs,t−j ∆s,t−j )
j=1
k=−2
+ Xist β + µi + θdgt + ist

(1.6)

¯
is the diﬀerence between the performance of the closed school
where ∆3 = P
−P3
ist
i,s ,t
i,s ,t
¯ 3,P
and average performance of all schools within three miles of the closed school. ∆s,t and
¯ 3,T
∆s,t represent school-level averages of ∆3
i,s,t for displaced students and teachers in a receiving school, respectively.41 Note that the coeﬃcients of the model are only identiﬁed using
variation across diﬀerent school closings and do not use within-closing variation of which
39 Depending on the speciﬁcation of the value-added model, school quality may be deﬁned
to include peer quality or teacher quality in addition to ﬁxed school-speciﬁc components.
Nonetheless, as the estimates in the current study are estimated using within-student variation, any diﬀerences in the results when using value-added compared to average performance
measures would more likely be due to diﬀerences in the measurement of peer and teacher
quality than diﬀerences in student ability.
40 While average proﬁciency rates are preferred for the current study, it is possible to
construct out-of-sample value-added measures for the sample of schools used in the analysis.
Results from speciﬁcations as shown in Equation (1.6) using these value-added measures are
available in Appendix Table F.3. The results are qualitatively similar.
41 One could also interact P
¯
and P 3
separately with the treatment. This
i,s ,t−1
i,s ,t−1
produces qualitatively similar results to what is presented in Table A.7, and hence the
current speciﬁcation is preferred for ease of exposition.
26

schools students attend after displacement. Hence, the estimates reﬂect long-run locational
choices of parents that are arguably exogenous conditional on student ﬁxed eﬀects, and are
not biased by parental decisions about where to send their children after displacement.
In the current sample, the average displaced student attends a school that is 0.66 standard deviations below the state average in terms of school performance the year prior to
displacement, and 0.30 standard deviations below the average of schools within three miles.
There is substantial heterogeneity in performance of the closed school, however. Figure D.2
shows the distribution of standardized math proﬁciency statewide, and plots separate densities for both closed and open schools. The density for schools that were closed is shaded
black and the density for schools that remained open is shaded white. Examining Figure
D.2, it is clear that the average closed school was below average for the state, but there
is substantial variation in the performance level of closed schools and in some cases closed
schools were above the state average.
Table A.7 displays three achievement trajectories based on estimates of Equation (1.6).42
The ﬁrst column displays the achievement trajectory for students who attended a closed
school that was 0.5 standard deviations worse in terms of school performance than nearby
schools. The middle column displays the same trajectory for students who attended a closed
school of the same quality as nearby schools, and the ﬁnal column contains students who
attended a closed school that was 0.5 standard deviations better than nearby schools. The
results show that students who attended poor-performing closed schools experience sharp
increases in test scores after displacement, and two or more years after displacement are
performing better than they ever did in the closed school. Students displaced from schools
of the same quality as nearby schools experience a drop in achievement prior to closure and
into their ﬁrst year after displacement, but recover and perform no diﬀerently two or three
years after displacement than they did two or three years prior to displacement. Students
displaced from higher-performing schools are hurt by displacement, though, and never recover
42 The parameter estimates of Equation (1.6) can be found in Appendix Table F.2.

27

in their new school. Hence, while shutting low-performing schools generates achievement
gains, shutting high-performing schools does persistent harm to student achievement.43
For reading, the pattern is again less clear. While students are trending similarly prior
to displacement, there is no clear pattern in achievement after displacement. This can be
explained by a story that mathematics scores are more heavily inﬂuenced by factors within
school control, while reading scores are more heavily inﬂuenced by other factors such as
parental involvement. Both mathematics and reading trajectories are plotted out in Figure
D.3 and Figure D.4, respectively. Prior to displacement students in these three groups have
similar achievement trajectories. The year after displacement, students displaced from lowperforming schools experience slight increases in mathematics scores relative to their peers.
Two or more years after displacement, these students continue to improve and are performing
signiﬁcantly better in mathematics than they ever did in the closed school. For reading, there
is no distinct pattern between the three lines, again suggesting that reading scores may be
less inﬂuenced by school-level factors.
The relative performance of the closed school aﬀects not only the magnitude of the eﬀects
on displaced students, but also the magnitude of the eﬀects on students in receiving schools.
Figures D.5 and D.6 plot out the diﬀerential impacts of closed school performance for schools
that contain 20% displaced students, while Figures D.7 and D.8 plot out trajectories for
schools that contain 20% displaced teachers. Unsurprisingly, spillover eﬀects are larger in
magnitude if displaced students come from relatively low-performing schools. For displaced
teachers, heterogeneous eﬀects for mathematics are signiﬁcant at the .10 level in the ﬁrst year
after teachers are displaced, but become imprecise thereafter. These results are consistent
with a story that spillover eﬀects from displaced students are due to negative peer eﬀects
from displaced students, while spillover eﬀects from displaced teachers are due to disruption
43 Since the policy idea of shutting down failing schools is often targeted at schools in urban
settings, it is important to examine the eﬀects of shutting down low-performing schools in
these areas. Online Appendix Table C.7 contains the results of speciﬁcations such as shown
in Table A.7, limiting the sample to only Detroit Public Schools.

28

as the school accommodates the new teachers.44 Another possible explanation is that the
disruption is due to teachers who are not accustomed to dealing with new students. If this
were the case, one might expect the lowest grade at the new school to not experience as
much disruption, because the teachers in these grades are accustomed to accommodating
new students. While not shown here, spillover eﬀects do not vary between the lowest grade
and older grades in receiving schools.45
Given the estimates presented above, it is unlikely a policy to systematically close lowperforming schools would be able to generate substantial achievement gains without imposing
widespread spillover eﬀects on receiving schools. For instance, consider a hypothetical policy
that shut a school that was 0.5 standard deviations below the average for nearby schools.
A simple back-of-the-envelope calculation based on the above estimates would suggest that
student achievement three years after displacement will be 0.116 standard deviations higher
on average than it was during their last year in the closed school. However, spillover eﬀects
may mitigate many of these gains. For instance, suppose that the closed school was half
the size of the nearby schools and the displaced students were distributed evenly over four
diﬀerent schools, resulting in a relatively small 11% of the receiving school population being
new to the school. Given the estimates presented above, students at the receiving school
would have their achievement lowered by around 0.02 standard deviations. If displaced
teachers were to be retained within the district, this would be even larger. In addition, the
spillover eﬀects will be larger due to the inﬂux of low-performing peers. In this example,
this implies that the spillover eﬀects will be roughly .01 larger in magnitude due to the
low-performing peers. Hence, even in this optimistic scenario, displaced students would only
experience a positive gain in achievement of 0.096 compared to a 0.03 decline for students
44 An alternative explanation for the negative spillover eﬀects on receiving schools is that
receiving schools were near capacity and had diﬃculty accommodating the new students who
entered the school. As documented in Online Appendix Table C.8, the results are qualitatively similar when controlling for capacity of the school, using the maximum enrollment in
the school since 1990 as a crude proxy for capacity.
45 These results may be found in Online Appendix Table C.9

29

in receiving schools. While this loss is smaller in magnitude than the gain in achievement
for displaced students, students in receiving schools constitute a much larger segment of the
district population. Hence, average achievement district-wide will not improve.
This calculation does not rule out all justiﬁcations for school closing policies. First, the
results from Section 1.6.1 suggest that even when there are negative eﬀects from closings, they
tend to be modest. Hence, if there are large ﬁnancial gains from shutting down schools then
closings may be an eﬀective cost-saving tool for school district administrators to undertake.
As well, the above calculation focuses on average district-wide student achievement. It may
be that districts wish to maximize the minimum level achievement in the district, in which
case school closing policies may be justiﬁed because they have the potential to substantially
raise achievement for the subset of students in very low-performing schools. Nonetheless,
this analysis does point to the limitations of targeted school closing policies as a large-scale
policy tool to improve student achievement. Any policy will have to balance the costs of
achievement losses at receiving schools against any potential achievement gains for displaced
students.

1.7

Conclusion

Given the prevalence of school closings, understanding the eﬀects of shutting schools on
student achievement is crucial for policymakers. The results show no signiﬁcant change in
reading scores in the two to three years before and after displacement. For mathematics,
students in closed schools are falling behind their counterparts in the district prior to displacement. After closure, students continue to perform at a low level in the ﬁrst year in
a new school but improve signiﬁcantly within two to three years after displacement. In
both reading and mathematics, the inﬂux of new students and teachers negatively impacts
students in receiving schools, but the losses tend to be modest. The results vary based on
the performance of the closed school. If the closed school was low-performing relative to
nearby schools, displaced students perform relatively better after displacement and students
30

in receiving schools perform relatively worse.
These results have important implications for policymakers. First, the fact that school
closings in Michigan did no persistent harm to student achievement suggests that school
closings may be an eﬀective policy tool for districts that need to cut costs. In addition,
because students displaced from low-performing schools experience increases in test scores
after closure, there is the potential for increases in achievement for displaced students by
shutting low-performing schools. This increase in achievement comes at the expense of
additional disruption due to the inﬂux of previously low-performing new students in receiving
schools, however. Moreover, these spillover eﬀects are even larger if teachers from the lowperforming school are reassigned within district. Hence, while closing low-performing schools
may generate some achievement gains for displaced students, it is unlikely that these policies
can improve average student achievement district-wide.
There are other potential consequences associated with school closing policies that are
outside the scope of the current study. In addition to the impact on the the achievement
of students immediately aﬀected by the policy, school closings will have longer-run impacts
that are outside the context of the current analysis. In particular, school closings have
lasting eﬀects on quality of schools that future cohorts of students attend. Closings may
also fundamentally alter the way in which students are distributed throughout the district,
changing the structure of peer eﬀects. In addition, closings create potentially important
eﬀects on teacher labor markets. When schools close, teachers are shuﬄed throughout the
district, often on the basis of seniority. This reshuﬄing changes both teacher-school matches
and the structure of teacher peer eﬀects, both of which have the potential to signiﬁcantly
aﬀect student achievement (Jackson and Bruegmann, 2009; Jackson, forthcoming). Hence,
the welfare eﬀects of closing schools may go beyond immediate achievement eﬀects on the
displaced students and receiving schools. While these issues are still very much unresolved,
understanding the immediate impacts on student achievement due to school closings provides
policymakers with valuable information to consider when weighing the costs and beneﬁts of

31

shutting down schools.

32

CHAPTER

2

THE EFFECT OF FOUR-DAY SCHOOL WEEKS ON STUDENT
ACHIEVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL FURLOUGH DAYS

2.1

Introduction

Changing the length of the school year is one of the most natural policy levers for aﬀecting
student achievement. Because changing how much time students spend in school has such
dramatic potential consequences, policies that alter school year length garner much attention. On one hand, many observers have called for longer school years to improve student
achievement, citing the fact that American schools have on average shorter school years than
similar developed countries (Lee and Barro, 2001). On the other hand, some school districts
across the country have shortened their school years to ease budget deﬁcits, generating much
controversy. Because these policies may have profound eﬀects on student learning, understanding the relationship between length of school year and student achievement is imperative for policymakers. While less instructional time theoretically harms student achievement,
teachers may respond by covering more material in the school day or parents may respond
by obtaining after-school tutors. These behavioral responses may work to oﬀset the negative
eﬀects of lost instructional time, and the magnitude of their eﬀects is an empirical question.
The few quasi-experimental studies to examine the eﬀect of school year length in modern
educational settings use variations in instructional time that may not have been entirely
salient to parents and teachers. The current study ﬁlls this void by investigating a school
furlough day policy in Hawaii, which reduced the 2009-2010 school year for all public school
students from 180 to 163 instructional days. This policy was well-publicized in advance and
very salient to parents and teachers. In fact, while the furlough days were originally intended
to be in place for two years, the government reached a deal with the teachers union and a

33

coalition of banks to eliminate furlough days for the 2010-2011 academic year. While charter
schools saw reductions in funding, they were not mandated to take the furlough days and
the majority of charter schools took no school furlough days.
The analysis uses two identiﬁcation strategies to isolate the eﬀect of the furlough days
on student achievement in Hawaiian public schools. First, the study uses variation within
furloughed public schools over time in an “interrupted time series” (ITS) design, comparing
student performance in academic year 2010 to the trend in test scores before and after the
furlough day policy. This approach is unable to control for test-period eﬀects that aﬀected
all studentsi in 2010, however. Hence, the study also performs a “diﬀerence in diﬀerence”
(DD) analysis, using unfurloughed charter schools as a control group. This design is able
to control for test-period eﬀects, but charter schools are an imperfect control group because
they saw reductions in funding in the 2010 school year. Hence, the DD analysis is biased
towards ﬁnding positive eﬀects of the furlough days on student achievement.
The results indicate that school furlough days had negative eﬀects on mathematics
achievement in elementary school. The magnitude of these eﬀects is well in line with prior
literature, indicating that reductions in school year length hurt student achievement even in
a scenario where the policy is well-publicized in advance and salient to teachers and parents.
The results for middle and high school indicate that there were no negative impacts from
the school furlough days, however. This may indicate that teachers in these grade levels had
an easier time adjusting the content of their material or that students in these grade levels
are less susceptible to educational interventions. All of these results are robust to a number
of diﬀerent speciﬁcations, and unobserved test-period eﬀects are likely not large enough to
substantially alter the results.
The remainder of the paper is organized as follows. Section 2.2 discusses the relevant
literature on school year length, Section 2.3 discusses sources of data used for the analysis,
and Section 2.4 discusses the estimation strategies employed in this analysis. Section 2.5 then
presents the results, and Section 2.6 concludes and discusses potential policy implications of

34

the results.

2.2

Literature Review

A large literature correlates school year length and student achievement,1 but only a few
studies use quasi-experimental variation to examine the eﬀects of school year length. Marcotte (2007) and Marcotte and Hemelt (2008) use variation in the amount of snow days
taken by schools in Maryland to identify the impact of instructional time. Their results
indicate that students who took exams in years with relatively more snow days performed
signiﬁcantly worse on mathematics exams. In addition, Marcotte and Hemelt (2008) show
that more than half the schools that failed to meet Adequate Yearly Progress (AYP) in a
given year would have met AYP had they been open for all scheduled school days. While
snow days provide credibly exogenous variation, the reduction in instructional time may not
be entirely salient to parents and teachers. Moreover, even if the reduction is salient, snow
days are not announced in advance and hence there is less time for parents and teachers to
adjust their behavior.
Sims (2008) uses variation induced by a 2001 policy change in Wisconsin that forced
schools to start the school year after Labor Day, and ﬁnds that reductions in classroom time
lead to lower average math scores for 4th graders, but have no eﬀect on average for reading
scores. Hansen (2011) further explores using both law changes and snow days to examine
the eﬀect of school year length on student achievement, and ﬁnds similar results to both
Marcotte and Hemelt (2008) and Sims (2008). While potentially more salient than snow
days, changes in school start dates change the number of instructional days before an exam
while often leaving total instructional time unaltered. Hence, the results of such studies
may be diﬃcult to extrapolate to scenarios where a policy to shorten the school year was
announced in advance.
1 For examples, see Card and Krueger (1992), Eide and Showalter (1998), Lee and Barro
(2001), Woessmann (2003), or Eren and Millimet (2007).

35

Pischke (2007) examines shortened school years in West Germany from 1966-1967, where
students were exposed to school years that were about 1/3 shorter than the typical year.
He ﬁnds that the short school years led to increased grade retention among the aﬀected
students, but had no eﬀect on later labor market outcomes. While this policy was very
salient to both parents and teachers, it is hard to extrapolate the results of this analysis to
modern educational settings.
A related literature examines four-day school weeks where instructional time was extended on the four days in which school was in session. In particular, Anderson and Walker
(2012) and Sagness and Salzman (1993) investigate four-day school week policies in rural
Colorado and Idaho, respectively. They both ﬁnd that student achievement improved after the implementation of the four-day school week policy. Other related work investigates
the eﬀects of multi-track year-round calendars, where students in diﬀerent tracks attend
school year round, but at least one track is always on break.2 For example, Graves (2010)
and Graves (2011) ﬁnd negative eﬀects of these calendars on student achievement, while
McMullen and Rouse (2012) ﬁnd no impact on student achievement.3 While these studies
investigate similar policies to Hawaiian school furlough days, the policies they investigate
alter the distribution of instructional time in a much diﬀerent manner than furlough days.
Hence, their results are not directly comparable to the current study.

2.3

Data

The study uses school characteristics from the Common Core of Data (CCD) and proﬁciency
rates from the Hawaii State Assessment (HSA) for years 2007-2012.4 The HSA is a computer
2 For a survey of this literature, see Cooper, Valentine, Charlton, and Melson (2003).
3 Another strand of literature uses discontinuities in assignment to estimate the causal
eﬀect of mandatory summer school for low-performing students. See Jacob and Lefgren
(2004) or Matsudaira (2008) for prominent papers in this literature.
4 HSA data is available for years prior to 2007, but is not used for the current study
because the HSA was redesigned in 2007 and hence scores prior to 2007 are not directly
comparable to scores from 2007 onwards.
36

adaptive test administered to all students in grades 3-8 and grade 10, and results are made
publicly available by the Hawaii Department of Education.5 The current study will not
explicitly examine scores from grade 3 because they are the product of multiple years of
instruction instead of a single year. The exams are administered every spring between
late March and early April, and 13 of the 17 furlough days in 2010 occurred prior to the
administration of the HSA exams. Hence, the reduction in instructional days prior to the
administration of the exam was roughly 10%.
To assess the validity of the HSA exams, Table B.1 compares proﬁciency rates from the
HSA to the commonly used proﬁciency rates from the National Assessment of Educational
Progress (NAEP).6 While the proﬁciency results for the tests are very diﬀerent in terms
of levels, both tests show increases in proﬁciency rates over time. In fact, the correlation
between the HSA and NAEP scores in mathematics is 0.945. While this calculation is based
only on six data points, it does give some weight to the validity of the HSA results, indicating
that the increase in test scores over the sample period was most likely due to an increase in
content knowledge and not a lowering of standards.
In total, the sample consists of 31 charter schools and 260 traditional public schools in
Hawaii.7 Table B.2 displays descriptive statistics for the sample of schools used in the analysis, broken apart by time period and number of furlough days that the school took in 2010.8
Note that 22 of the 31 charter schools in Hawaii took zero furlough days, and only 2 charter
schools took the entire 17 furlough days that were taken by Hawaiian public schools.9 As
5 Students in grades 4, 8, and 10 take a science exam as well. Students in grades 3 and 4
who are in the Hawaiian Language Immersion Program can take the exam in the Hawaiian
language. HSA results can be found at http://doe.k12.hi.us/myschool/sat-hcps-terranova.
htm.
6 NAEP scores can be found at http://nces.ed.gov/nationsreportcard.
7 In 2008, a larger than average number of schools did not report testing data. Because
data from year 2008 is not central to the identiﬁcation of the eﬀects of school furlough days,
this issue is not considered a ﬁrst-order concern. Results available from the author show
results with year 2008 excluded, which are qualitatively similar.
8 Refer to Appendix G.1 for descriptive statistics for the entire sample.
9 Data on number of furlough days taken by charter schools was collected through phone
37

seen in Table B.2, schools that took less than 17 furlough days look slightly diﬀerent in terms
of demographic characteristics. These schools serve similar populations in terms of fraction
eligible for free/reduced-price lunch compared to their furloughed counterparts. However,
they are lower performing in terms of mathematics proﬁciency, enroll fewer Asian/Paciﬁc
Islander students, and tend to have lower pupil-teacher ratios than their furloughed counterparts. While these groups of schools are very diﬀerent, Table B.2 also shows that there were
only slight changes in the demographic makeup of these schools after the school furlough
days, particularly for furloughed schools. In particular, the racial and free/reduced-price
lunch composition of the schools remained relatively ﬂat, and public schools experienced
only modest enrollment declines. Hence, it does not appear that the furlough policy caused
a dramatic shift in the composition of Hawaiian public schools.

2.4

Empirical Model

In order to estimate the eﬀect of Hawaii’s furlough days on student achievement, one must
estimate what the counterfactual achievement of Hawaiian students would have been in the
absence of school furlough days. Consider the following model where student achievement
in school i, grade g, year t can be written as:
Yigt = τ Tit + uigt

(2.1)

where Yigt is the fraction of children proﬁcient in year t, Tit is an indicator that the school was
“treated” (i.e., took school furlough days), and uigt is an error term. Let uigt = ξigt + igt
be a decomposition of uigt , where by construction Cov(Tit , ξigt ) = 0 and Cov(Tit , igt ) = 0.
Hence,
E[Yigt |Tit = 1] − E[Yigt |Tit = 0] = τ + E(ξigt |Tit = 1) − E(ξigt |Tit = 0)

(2.2)

As previously stated, the current study uses two diﬀerent designs to estimate τ . First,
an ITS design uses trends in student achievement in other years to construct an estimate
conversations with charter school oﬃcials.
38

of what student achievement in Hawaiian public schools would have been in the absence of
school furlough days. In practice, this restricts the model so that ξigt = µig + f (t), and
estimates the following equation on the subset of schools that experienced school furlough
days:
Yigt = f (t) + τ · 1[t = 2010] + Xit β + µig + eigt

(2.3)

The clear drawback to this approach is that identiﬁcation relies on the functional form
speciﬁcation of f (·).
The second strategy uses a DD design, and compares furloughed schools to unfurloughed
schools in the same year. This implies that ξigt = µig + γt , and hence there is allowed to be
a separate test-period eﬀect for each year. In particular, consider the following model where
F Daysit is the number of furlough days the school took divided by 17:
Yigt = γt + τ F Daysit + Xit β + µig + igt

(2.4)

This approach allows for test-period eﬀects, and does not rely on the functional form of f (·)
for identiﬁcation. Identiﬁcation instead relies on variation in student performance between
schools that did and did not take furlough days. The resulting estimates will be robust to
any time-constant unobserved heterogeneity that may be correlated with F Daysit .
While this approach allows for test-period eﬀects, it maintains the assumption that
E(γt |Tit = 0) = E(γt |Tit = 1). This assumption is violated in the current scenario because charter school funding cuts in 2010 likely harmed student achievement. Hence, the
estimated eﬀect of the furlough policy is expected to be biased towards ﬁnding positive effects of the furlough days, and the magnitude of the bias will depend on the magnitude of
the negative eﬀect of the funding cuts. Section 2.5 returns to this issue further, and discusses
the potential magnitude of eﬀects from charter school funding cuts. This speciﬁc problem is
not a problem for the ITS analysis because it compares the set of schools that took furlough
days to their projected performance. Hence, the two designs are viewed as complementary.

39

2.5

Results

Prior to placing restrictions on the empirical model, Figures E.1-E.4 display test score trajectories over the sample period. Schools are divided into groups based on the number of
furlough days that they took in the 2009-2010 academic year. Figure E.1 shows the trajectory of scores for the HSA mathematics exam in grades 4 and 5. Schools that took furlough
days perform below their trend in year 2010, indicating that there may have been a negative eﬀect from the furlough days. In addition, unfurloughed schools made up ground in
2010 compared to 2009, again indicating the potential for a negative eﬀect from the furlough days. Nonetheless, it is noteworthy that furloughed and unfurloughed schools followed
roughly similar trajectories over the time period, lending support to the idea that unfurloughed charter schools serve as a comparable control group for the DD analysis. Figure E.2
shows the trajectory of reading scores for grades 4-5. As can be seen, there is almost no
distinguishable deviation from trend in achievement in year 2010. Figures E.3 and E.4 show
the same graphs for grades 6-10. Neither math nor reading scores for furloughed schools
dip in 2010. Hence, these graphs present suggestive evidence that the furlough day policy
negatively impacted mathematics achievement for students in elementary school, but eﬀects
on students in grades 6-10 were likely small in magnitude.
Figures E.5-E.8 display the trajectory of school composition variables over the time period. As can be seen by examining Figure E.5, unfurloughed schools experienced increases in
enrollment in 2010 relative to their previous trajectory. If this increase represents selective
mobility of students from one school to another, the results will be biased. Students who
selected out of furloughed schools were likely relatively high-achieving, however. If this is the
case, selective mobility leads to overly-negative estimates of school furlough days on student
achievement and any negative eﬀects from the furlough days would tend to be overstated.
Hence, the analysis can be viewed as a conservative estimate of the impact of school furlough
days.
Figure E.6 shows the trajectory of pupil-teacher ratios over the time period, which in40

crease only slightly in the 2010 academic year. Hence, increases in pupil-teacher ratio are an
unlikely explanation for the results shown below.10 Figures E.7 and E.8 also show that the
racial composition of schools did not change in year 2010. Note that the CCD changed it’s
racial categorization of students in the 2011 academic year and hence 2011 is not comparable
to other years.11 While this recoding aﬀects the descriptive pattern of student composition
in Hawaiian schools, it is not a concern for the empirical analysis presented below.

2.5.1

Grades 4–5

Table B.3 displays the results of regressions based on the speciﬁcation shown in Equation
(2.3) for grades 4 and 5.12 These regressions are estimated only on the subset of schools that
were furloughed.13 Column (1) presents results setting f (t) = δ1 t, and column (2) includes
controls for fraction of students eligible for free or reduced-price lunch, African-American,
Hispanic, Asian/Paciﬁc Islander, and American Indian. Note that columns including controls
have fewer observations because controls are not available for 2012. Column (3) examines
whether the trend in test scores changed after year 2010 by setting f (t) = δ1 t + δ2 t · 1[t ≥
2010]. If the trend diﬀers before and after 2010, this reﬂects either a persistent eﬀect from
the school furlough days or misspeciﬁcation of f (t). Column (4) sets f (t) = δ1 t + δ3 t2 .
The quadratic speciﬁcation allows for the most ﬂexible functional form of f (t) while not
10 In particular, pupil-teacher ratios in charter schools went up by only 0.3 percent in 2010.
Even given the large eﬀects of class size on student achievement found in studies such as
Krueger (1999) and Angrist and Lavy (1999), this diﬀerence is not large enough to predict
sizeable drops in student achievement.
11 Starting in 2011, the CCD categorized multiracial students as a separate racial category.
This had the eﬀect of causing both white and Asian/Paciﬁc Islander populations to decline.
The current study imputes multiracial students to a single race category using data on the
schools past populations of students, but this procedure still leaves the rates incomparable.
12 While not shown here, all results are robust to setting the dependent variable equal
to log[Yit /(1 − Yit )] or using a fractional probit speciﬁcation as in Papke and Wooldridge
(2008).
13 Refer to Appendix Table G.2 for results by individual grade level. The results indicate
that there was no eﬀect of the furlough days on achievement in third grade.

41

overﬁtting the data, and hence is the most preferred speciﬁcation out of the four columns.
The results are very consistent across all speciﬁcations. In particular, the estimates
indicate a roughly 4-6 percentage point drop in the fraction of students proﬁcient as a result
of the furlough days. Given that proﬁciency in 2010 was roughly 50%, a 4-6 percentage point
drop represents a 8-12% decline in test scores for an almost 10% reduction in school days.14
This result is well in line with previous work by Marcotte and Hemelt (2008), Sims (2008),
and Hansen (2011), who all ﬁnd similar declines for elementary school. Also, as shown in
column (3), there is little diﬀerence in the trend of scores pre- and post-2010. This indicates
that achievement continues along the pre-2010 trend line in the years following the furlough
policy. Taken literally, this would indicate that there was no persistent eﬀect of the furlough
days. However, as discussed previously, any misspeciﬁcation in f (t) would bias these results.
Hence, this result is only suggestive evidence that the negative eﬀects of the furlough days
were transitory. As shown in Panel B, the results for reading are diﬀerent from the math
results, and indicate that furlough days had no signiﬁcant eﬀect on student achievement
in reading. This result ﬁts with a story that reading achievement is less susceptible to
educational interventions than mathematics achievement.
Table B.4 displays the results from the DD speciﬁcations, based on speciﬁcations as shown
in Equation (2.4).15 Columns (1)-(3) present results with year ﬁxed eﬀects, columns (4)-(6)
present results with group-speciﬁc trends, and columns (7)-(8) present results with schoolspeciﬁc trends. In addition, columns (2) and (5) include a lead of the treatment variable
while columns (3), (6), and (8) include control variables for racial and free or reduced-price
lunch eligible composition in the school. In contrast to the results presented in Table B.3, the
results are always positive and typically statistically insigniﬁcant. Note that the estimates of
leads of the furlough day policy in columns (2) and (5) indicate that furloughed schools had a
14 It is diﬃcult to convincingly map these ﬁgures into student standard deviation units,
but a rough conversion can be obtained if one assumes that underlying test scores are normal
and the policy change resulted in a mean shift to the underlying normal distribution. Under
these assumptions, the eﬀect was in the range of 0.126-0.151 student standard deviations.
15 Refer to Appendix Table G.3 for DD results by individual grade level.
42

spike in performance relative to unfurloughed schools in the year prior to the furlough policy.
While this result is not statistically signiﬁcant, it gives some indication that the estimates are
potentially upward biased. Columns (7) and (8) present the preferred speciﬁcations, where
school-speciﬁc trends are included in the empirical model. The estimates are very imprecise,
and the lower bounds of the 95% conﬁdence intervals are -0.039 and -0.060, respectively.
As discussed before, these results are biased upwards and the magnitude of the bias will
depend on the magnitude of the eﬀect of charter school funding cuts. While evidence on the
relationship between school expenditures and student performance is mixed,16 the conﬁdence
intervals presented above are very wide and even small negative eﬀects from funding cuts
would put the DD estimates in line with those presented in Table B.3. Nonetheless, the fact
that public schools did not fall behind their charter counterparts in 2010 indicates that testperiod eﬀects are likely not substantially biasing the results presented in Table B.3 towards
zero.
Taken as a whole, these results indicate that students in elementary school were negatively
aﬀected by the shortened school year. They also present suggestive evidence that this eﬀect
was transitory and student achievement recovered in the years following the furlough policy.
Hence, while Hawaiian school furlough days represent a much diﬀerent policy from those
studied by previous literature, the eﬀects of the policy on students in grades 4-5 were very
similar to what was has been found in other settings.

2.5.2

Grades 6–10

Table B.5 displays ITS results for students in grades 6-10. For math scores, students in
grades 6-10 perform at or above their trend in math scores in 2010, contrasting with the
results shown for grades 4-5 in Table B.3. The trend line ﬁts the achievement trajectories of
furloughed schools quite well, and hence it is unlikely that test-period eﬀects are substantially
16 Hanushek (2003) and Krueger (2003) provide surveys of the literature on the relationship
between school resources and student achievement.

43

biasing these estimates. In fact, the largest average observed deviation from trend in a given
year is 0.001, which is much smaller in magnitude than the diﬀerence between the grade 4-5
and grade 6-10 results. While the trend of math test scores appears to increase after 2010,
this trend in test scores became steeper after 2010 and hence is unlikely to be the result of
persistent eﬀects from the furlough day policy. As with the results for students in grades
4-5, reading scores change very little in year 2010 relative to their trend, with the exception
of column (3), which is heavily inﬂuenced by one unusual year of reading scores in 2012. The
result of no eﬀect from the furlough days contrasts with results in prior studies, which ﬁnd
signiﬁcant eﬀects of shortened instructional time on achievement in eighth grade.
Table B.6 presents the results of DD speciﬁcations such as those shown in Table B.4,
but estimated for grades 6-10. As shown for grades 4-5, the results for reading are not
statistically diﬀerent from zero. However, the DD estimates for math are consistently positive
and statistically signiﬁcant. Note also that, unlike the results presented for grades 4-5, the
estimates of leads of the furlough policy presented in columns (2) and (5) are extremely
close to zero. This result indicates for grades 6-10, charter schools performed no diﬀerently
the year prior to the policy relative to their prior trajectory. The lower bounds of the
95% conﬁdence intervals for the preferred estimates presented in columns (7) and (8) are
-0.002 and -0.003, respectively. For these conﬁdence intervals to overlap with the results
presented in Table B.3, the eﬀect of the expenditure cuts on charter school students would
need to be roughly 0.05 percentage points. While an eﬀect of this magnitude is theoretically
plausible,17 it is hard to reconcile this large of an eﬀect with the trend in charter school
achievement observed over the sample period. To examine this, Figure E.9 displays the per17 For instance, Papke (2005) ﬁnds that a 10% increase in funding led to between a 1-2
percentage point increase in proﬁciency rates. Applying these results to the current setting,
this implies that the observed decrease in proﬁciency rates would have been on the order of
.025 to .050 percentage points. While taken literally, the high end of this estimate implies
that the 95% conﬁdence interval overlaps with some of the point estimates shown in Table
B.3, this calculation makes clear that the DD estimates are diﬃcult to reconcile with prior
studies.

44

pupil funding of charter schools in Hawaii over the sample period. Note that charter schools
experienced consistent cuts in funding over this time period, not just a single cut in 2010.
In addition, Figure E.1 shows that charter schools were not systematically falling behind
their counterparts in traditional public schools over the time period.18 Because charter
schools neither experienced a single drop in funding in 2010 nor fell steadily behind their
furloughed counterparts over the time period, it is unlikely that funding cuts had a large
enough negative eﬀect on student achievement to explain the diﬀerence between the grade
4-5 and grade 6-10 results.
For the grade 6-10 results to align with previous literature, two facts must be true. First,
an unobserved positive shock would need to have aﬀected all test scores in 2010, and the
positive test-period eﬀect would have to be larger than any observed deviation from trend.
Second, unfurloughed charter schools would need to have had large drops in achievement
from funding cuts. This is unlikely because charter schools saw similar drops in funding
in many other years while not falling behind regular public schools in terms of student
achievement. Hence, the most plausible explanation is that students in middle and high
school were less aﬀected by the change in instructional time.

2.5.3

Heterogeneity by School Characteristics

As discussed previously, parents and teachers may have oﬀset some of the damage of the
furlough days by changing lesson plans or by oﬀering out-of school tutoring. If this were the
case, one might expect the eﬀect of furlough days to vary based on the composition of the
school. To explore this possibility, Table B.7 contains the results of ITS speciﬁcations such
as those in column (4) of Table B.3 broken apart by quartiles of both percent of students
eligible for free or reduced-price lunch and average achievement in 2007. Panels A and B
present results for grades 4-5, while Panels C and D present results for grades 6-10. For
18 Also note that the results are qualitatively similar if the model conditions on charter
school funding while assuming that public school funding remained unchanged.

45

students in grades 4-5, the eﬀects appear to diﬀer by school-level achievement, with higherachieving schools being less aﬀected by the policy. These diﬀerences are slightly imprecise,
however. In particular, the analysis rejects the hypothesis that the sum of the eﬀects in the
ﬁrst two quartiles is diﬀerent from the sum of the eﬀects in the second two quartiles, but just
fails to reject the hypothesis that all estimated eﬀects are identical.19 The results do not
diﬀer by the fraction of students eligible for free or reduced-price lunch, however, and none
of the estimated eﬀects are statistically diﬀerent from one another.20 These results indicate
that parents and teachers in high-achieving schools may have been able to oﬀset some of the
negative impacts of the furlough days.
The results from grades 6-10 display little heterogeneity by school composition, however.
In particular, the estimated eﬀects of the furlough policy are almost identical across both
quartiles of achievement and quartiles of free or reduced-price lunch eligibility. On one hand,
this result could reﬂect that teachers in these grades are better able to adjust to the shortened
school year and therefore students in all types of schools were unaﬀected by the policy. On
the other hand, these results could simply reﬂect that there was little eﬀect of the furlough
days on students in these grades, and hence teachers and parents did not need to adjust their
behavior. This explanation ﬁts with a story that students in these grades are less susceptible
to interventions, and hence were not harmed by the shortened school year. Which of these
explanations is more relevant is a question for future research.

2.6

Conclusion

Hawaii’s school furlough days present an excellent opportunity to study the eﬀects of school
year length on student achievement. This policy decreased the length of the school year
for all public school students by 17 days and was announced in advance, allowing parents
and teachers time to adjust their behavior. The results indicate no detectable eﬀect of
19 The p-values for these two tests are 0.037 and 0.105, respectively.
20 The p-value for a test that all eﬀects are identical is 0.849.

46

the furlough day on reading achievement. For mathematics achievement, the shortened
school year negatively impacted achievement in elementary school, and the analysis presents
suggestive evidence that high-performing schools were less aﬀected by the policy. This latter
evidence highlights the potential for responses on the part of parents and teachers to oﬀset
some of the damage of diminished instructional time. The analysis indicates no eﬀects in
middle and high school, however. This result may be explained by diﬀerences in the teaching
environment in middle and high school, or diﬀerences in the receptiveness of these students to
educational interventions. All of these results are robust to multiple identiﬁcation strategies
and speciﬁcation checks.
The total eﬀect of shortening the school year goes beyond eﬀects on student learning.
School year length may profoundly aﬀect parental labor supply, teacher classroom behavior,
or even crime rates as shown in Jacob and Lefgren (2003). Understanding how school year
length relates to these outcomes is important for future research. Nonetheless, understanding
what eﬀect a highly publicized and controversial shortened school year policy had on student
achievement is a major step towards understanding the eﬀects of school year length.

47

CHAPTER

3

THE FREQUENCY AND CORRELATES OF
TEACHERS GRADE-LEVEL REASSIGNMENTS:
EVIDENCE FROM MICHIGAN

3.1

Introduction

Teacher turnover, whether measured by attrition from the profession or mobility across
schools, can disrupt the functioning of schools in a myriad of ways. For example, high rates
of teacher turnover may reduce instructional quality, destabilize schools, and disrupt schools
curriculums and course oﬀerings (Shields, Humphrey, Wechsler, Riehl, Tiﬀany-Morales,
Woodworth, Young, and Price, 2001). Within-school teaching reassignments (i.e., gradelevel and subject changes) and initial classroom assignments have similar consequences, as
recent research suggests that teachers returns to experience are greater when experience is
accrued in the same grade and that the composition of teachers initial classroom assignments
signiﬁcantly impacts subsequent mobility decisions (Ost, 2011; Feng, 2010). This evidence
has led observers such as Jacob and Rockoﬀ (2011) to argue that principals should think
carefully about how to best allocate teachers to grades and subjects, as such decisions are
typically non-controversial yet may have substantial eﬀects on student achievement.
However, the large literature on teacher turnover generally ignores the within-school
sorting of teachers into grade levels. This is a glaring omission, as student achievement is
aﬀected not only by the number of teachers new to the school, but also by the number of
teachers who are teaching in a new assignment. In addition, within-school rates of grade
switching are similar in magnitude to both rates of attrition from the profession and mobility
across schools. Well-documented higher rates of teacher turnover in low-performing and
impoverished schools suggest that such schools may necessarily experience more shuﬄing

48

of teachers across grade levels and subjects.1 An inequitable distribution of within-school
turnover in teaching assignments presents an additional challenge that students, teachers,
and administrators in disadvantaged schools must overcome. The current study contributes
to the literature on teacher turnover by investigating the teacher- and school-level predictors
of grade switching and the relationship between grade switching and other types of teacher
turnover.
We use rich administrative panel data on the universe of self-contained kindergarten
through ﬁfth-grade Michigan public school teachers during the 2003-04 through 2008-09
school years. These data are well suited for the analysis, as Michigan is home to a large
demographically and socioeconomically diverse student population, the panel nature of the
data allows individual teachers to be tracked over several years, and the large sample size
provides suﬃcient power with which to identify the predictors of grade switching. In addition,
we verify that the phenomenon of grade switching is not unique to Michigan by showing that
rates of grade switching and other types of teacher turnover in the nationally representative
Schools and Staﬃng Survey (SASS) are similar to those in Michigan.
We ﬁnd that grade switching is more prevalent in schools in urban areas, schools serving
minority student populations, and schools with higher attrition rates. In addition, less
experienced teachers switch grades more often, particularly those teachers who are new to
their school. Grade switching strongly predicts future grade switching, but not other types
of turnover. Interestingly, there is signiﬁcantly less grade switching in charter schools and no
relationship between grade switching and schools academic performance. These results imply
that in addition to higher rates of teacher turnover, urban schools with high concentrations of
minority students also experience signiﬁcantly higher rates of grade-level reassignments. This
is true even after conditioning on school-level turnover rates and suggests that policymakers
concerned with problems of teacher turnover in disadvantaged schools should pay similar
1 For example, see Hanushek, Kain, and Rivkin (2004b) or Lankford, Loeb, and Wyckoﬀ
(2002).

49

attention to the inequitable distribution of grade-level reassignments.
Section 2 proceeds with a brief review of the relevant literature. Section 3 describes
the data and methods used to perform the empirical analysis of grade switching. Section
4 presents the results and section 5 concludes with a summary and discussion of the main
ﬁndings.

3.2

Literature Review

Two studies tangentially touch on the frequency of within-school grade-level reassignments
of self-contained classroom teachers. Chingos and West (2011) use administrative data from
Florida to show that teachers in tested grades who have low value-added scores are more
likely to move to non-tested positions within their current school and exit teaching than
their higher-achieving counterparts. Of Floridas 24,475 self-contained tested-grade (4th–8th
grade) teachers in 2001-02, 84% remained in a tested-grade classroom the following year
and 52% remained in a similar position seven years later (excluding retirements). These
ﬁgures represent a lower bound for the percentage of tested-grade teachers who changed
grades, however, as the analysis does not consider switches between tested grades (and does
not consider teachers initially teaching in non-tested grades). Notably, 7% of the 2001-02
cohort taught in self-contained, non-tested classrooms the following year. Male, Hispanic,
and experienced teachers were more likely to transition from tested to non-tested grades.
Ost (2011) is primarily concerned with identifying grade-speciﬁc returns to teaching experience. Ost shows that of North Carolina teachers who taught in self-contained classrooms
in consecutive years between 1995 and 2007, about 70% remained in the same grade, most reassignments were to an adjacent grade, moving to higher and lower grades was equally likely,
and that within-school grade switching is weakly related to students current performance.
More generally, the current study is related to the literatures on teacher attrition and
teacher sorting, as grade-level reassignments are a type of teacher turnover. Guarino, Santibanez, and Daley (2006) thoroughly review the literature on teacher attrition and mobility,
50

which generally ﬁnds higher rates of teacher turnover in urban and low-performing schools,
schools comprised of low-income or minority students, and amongst inexperienced, female,
white, and highly-credentialed teachers. Loeb, Darling-Hammond, and Luczak (2005) ﬁnd
good working conditions and higher pay to be associated with reduced rates of turnover.
However, the existing literature largely ignores within-school changes in teaching assignments as a type of teacher turnover.
An exception to this critique is Boyd, Lankford, Loeb, and Wyckoﬀ (2008), who investigate the eﬀect of a newly-implemented fourth-grade test in New York State on fourth-grade
teacher turnover, where turnover is deﬁned as either leaving the fourth grade or leaving the
public-school system. Using administrative data, the authors ﬁnd that teachers were more
likely to remain in the newly-tested fourth grade and that this change was primarily driven
by a decrease in the grade-level reassignments of fourth-grade teachers (as opposed to attrition from the profession). The Boyd et al. (2008) study exempliﬁes the potential importance
of grade-level reassignments in operationalized deﬁnitions of teacher turnover.
Similarly, Cohen-Vogel (2011) investigates the extent to which principals in ten Florida
elementary schools use student-performance data to reassign teachers across grade levels and
make staﬃng decisions more generally. The author presents qualitative evidence that principals felt free to make grade-level reassignments and typically considered both teachers preferences and performance when making such decisions. Cohen-Vogel and Osborne-Lampkin
(2007) analyze the collective-bargaining agreements of 66 Florida school districts and ﬁnd
that while teachers seniority matters, administrators retain a reasonable amount of discretion
in changing teachers assignments. Furthermore, the authors ﬁnd that collective-bargaining
agreements are not more rigid in low-performing, poor, or minority schools.
We contribute to the existing literature by examining patterns in the frequency of grade
switching and documenting the distribution of grade switching across diﬀerent types of
schools and teachers. We further test whether grade switching predicts other types of teacher
turnover and compare the predictors of grade switching to those of other types of teacher

51

turnover. By providing a more comprehensive picture of the distributions of diﬀerent types
of teacher turnover, the current analysis furthers our understanding of the functioning of
teacher labor markets and the equity of teacher quality.

3.3

Data and Methods

The primary analysis examines teachers grade-level assignments in the Registry of Educational Personnel (REP) database, an administrative employee-level panel data set maintained
by Michigans Center for Educational Performance and Information (CEPI). The REP contains information on all public-education employees in Michigan, but the sample is restricted
to teachers in self-contained classrooms for the 2003-04 through 2008-09 school years. This
leaves a ﬁnal sample of 113,978 observations on 33,390 unique teachers.
We augment the REP data with publicly available school- and district-level information
from two additional sources. First, data on school type, student demographics, and locale
are taken from the National Center for Education Statistics Common Core of Data. Second,
we use grade-level math proﬁciency rates, publicly provided by the Michigan Department
of Education.2 Proﬁciency rates indicate the fraction of the schools students who tested
as proﬁcient on the Michigan Education Assessment Program (MEAP) standardized test.3
Proﬁciency rates increased statewide throughout the sample period. To ensure comparability
across years and grades, we standardize proﬁciency rates to have a mean of zero and a
standard deviation of one within each year and grade. Because the external validity of
state-level analyses is always a concern, we also compute a variety of teacher turnover rates
using data from the nationally representative 1999 and 2003 Schools and Staﬃng Surveys
(SASS) and corresponding Teacher Follow-Up Surveys (TFS).4 The SASS and TFS are
conducted by the U.S. National Center for Education Statistics (NCES) and are publicly
2 See: http://www.michigan.gov/mde/0,4615,7-140-22709 31168 31530---,00.html.
3 See Michigan Department of Education (2005) for an overview of the MEAP tests.
4 We are unable to use the 2007 SASS, as the 2008 TFS does not record current grade.

52

available.5 The SASS is a nationally-representative random sample of approximately 43,000
elementary and secondary public school teachers in each survey year. The TFS follows up
with approximately 5,300 randomly sampled SASS respondents the following year to see if
and where they are still teaching. The SASS-TFS analysis is restricted to regular full-time
kindergarten through ﬁfth-grade self-contained classroom teachers who were surveyed by the
TFS. The ﬁnal sample excludes special education teachers and teachers who taught more
than one grade in the SASS survey year. These restrictions yield samples of 763 and 1,069
teacher observations for the 1999-00 and 2003-04 school years, respectively.
In the empirics we identify the predictors of grade switching and other types of turnover
in Michigan by estimating logit models of the form
P r(yigst = 1|·) = Λ β0 + β1 xit + β2 zst + ηg + τt

(3.1)

where y is a binary indicator of teacher turnover between years t and t+1, i indexes teachers,
g indexes grades, s indexes schools, x is a vector of possibly time-varying teacher characteristics, z is a vector of possibly time-varying school characteristics, η is a grade ﬁxed eﬀect
(FE), and τ is a year FE. Extensions of equation (3.1) are considered that add school, district, or grade-by-year FE to the model. The parameters of equation (3.1) are estimated by
maximum likelihood, from which we compute average partial eﬀects (APE) of each covariate on the conditional probability of turnover.6 Subsequent analyses report APE standard
errors that are adjusted for clustering at the district level. Adjusting for clustering at the
district level makes statistical inference robust to the presence of correlation within districts
and schools, as schools are nested in districts.7
5 See http://nces.ed.gov/surveys/sass/dataproducts.asp.
6 See Wooldridge (2010) for the deﬁnitions and estimation of APE for both continuous
and discrete explanatory variables in binary choice models such as logit.
7 See Angrist and Pischke (2009, p. 319) for a discussion of clustering at the highest
level. Technically, two-way standard errors that allow for correlation within both teachers
and districts are appropriate, as teacher sometimes change districts (Cameron, Gelbach, and
Miller, 2008). Changing districts is rare in the current data, however, and estimated two-way
standard errors are marginally smaller than one-way district clustered standard errors in the
53

3.4
3.4.1

Analysis
The Prevalence and Distribution of Grade Switching

Table C.1 displays the prevalence of teacher grade reassignments in relation to other types
of teacher turnover. In particular, the ﬁrst panel of table C.1 describes the overall and
year-speciﬁc turnover of Michigans self-contained kindergarten through ﬁfth-grade classroom
teachers between 2003-04 and 2008-09. Of teachers remaining in a self-contained classroom
in the same school the following year, 76% remained in the same grade. The percentage of
teachers who changed grades but remained in a self-contained classroom in the same school
is 6.7%. Notably, this ﬁgure is similar in magnitude to two commonly-used measures of
turnover: the percentages who changed schools (6.1%) and who exited the Michigan public
school system (5.3%). The frequency of within-school grade-level reassignments in Michigan
is fairly constant across years, ranging from 6% to 7%. Not reported in table C.1 is the
ﬁnding that grade switch rates are also similar across grades, ranging from 5% to 8%, and
that most grade changes are to an adjacent grade.8 Similarly, other types of turnover are
fairly constant over time and across grades. The second panel of table C.1 reports similar
average turnover rates derived from nationally representative SASS data. The SASS data
suggest that grade switching is a national phenomenon and that national rates of teacher
turnover, including grade switching, are similar in magnitude to those observed in Michigan.
Table C.2 examines the distribution of switching across individual teachers in Michigan.
Grade switching is not driven by a small number of serial switchers, as 63% of grade-level
reassignments were experienced by teachers who changed grades only once and another 24%
of reassignments involved teachers who changed grades twice. Overall, a non-trivial 18%
current application. Thus we report the more conservative (i.e., larger) district-clustered
standard errors.
8 Markov transition matrices reported in appendix table H.1 show that teachers are most
likely to move to adjacent grades and that moving to lower grades is slightly more common.
These patterns are similar to those documented by Ost (2011) using data from North Carolina
and do not vary by year.

54

of Michigans self-contained classroom elementary-school teachers experienced at least one
grade-level reassignment between the 2003-04 and 2008-09 school years.

3.4.2

The Correlates of Grade Switching

Table C.3 documents the unadjusted diﬀerences in average teacher and school characteristics
included by the number of teacher switches. The ﬁrst column reports overall averages for
the six-year sample. Each subsequent column of table C.3 reports the same average characteristics separately by the number of times that teachers changed grades between 2003-04
and 2008-09. A few diﬀerences emerge between the teachers who never changed grades and
those who did. For example, non-switchers were more likely to hold a Masters degree and
to have ten or more years of teaching experience. Similarly, teachers who experienced no
grade-level reassignments were less likely to be in urban and charter schools, and were more
likely to be in the highest-performing (fourth-quartile of proﬁciency rates) schools.9 In addition, teachers who switch grades are more likely to teach in urban schools and schools with
high proportions of students eligible for free or reduced-price lunch. The following section
examines these correlates in more detail, by conditioning on teacher and school observables
and focusing on teacher-years as the unit of analysis.
Table table C.4 reports logit-model APE of teacher and school characteristics on the
probability that self-contained classroom teachers changed grades, but remained in the same
school the following year. Column 1 of table C.4 contains a baseline speciﬁcation that
conditions on teacher and school characteristics, grade taught, and a full set of year dummies.
Teachers race and education are not signiﬁcant predictors of grade switching. A small,
marginally signiﬁcant eﬀect of gender is found, suggesting that female teachers are about
half of a percentage point more likely to be reassigned than male teachers. Teachers age and
9 The practice of looping (i.e., teachers changing grades in lockstep with a student cohort)
may cause certain schools to have multiple teachers who repeatedly change grades. However,
we ﬁnd no evidence of systematic looping in Michigan, and do not believe that this drives
the results.

55

experience are strongly statistically signiﬁcant predictors of grade switching, although only
the experience eﬀects are practically signiﬁcant: teachers with two to nine years of experience
are between one and two percentage points less likely to change grades than new teachers,
while those with ten or more years of experience are more than three percentage points
less likely to do so. Teachers in urban schools are signiﬁcantly more likely to experience
grade-level reassignments than their counterparts in rural and suburban schools. The most
important predictor of grade switching in column 1 is charter-school status, as teachers
in charter schools are more than four percentage points less likely to change grades than
teachers in traditional public schools, and this diﬀerence is strongly statistically signiﬁcant.
We include school-level attrition from the school, district or Michigan public education
in the model to test whether grade switching is more common in schools with high attrition
rates, or if grade switching is a substitute for other types of teacher turnover. The former
may result from principals shuﬄing teachers grade-level assignments in an eﬀort to ﬁll the vacancies created by teacher attrition when the availability of external replacements is limited.
Alternatively, the latter would occur if dissatisﬁed teachers change (or are asked to change)
grades before changing schools or leaving the profession to see if a diﬀerent grade provides a
better ﬁt. Attritions positive and statistically signiﬁcant APE suggests that grade switching
is more common in high-attrition schools, although the diﬀerence is practically small.10
An interesting non-ﬁnding regards the relationship between school achievement levels
and grade switching: the grade-level indicators of schools math-proﬁciency quartiles are
individually and jointly insigniﬁcant. In fact, the APE appear to be precisely-estimated zeros,
which suggest that grade switching is not concentrated in either high- or low-performing
schools. This non-ﬁnding is robust to instead measuring school quality with Michigan’s
School Report Card grades (Michigan Department of Education, 2007).
Relative to ﬁfth-grade teachers and the omitted group of kindergarten teachers, the
10 The results on teacher- and school-level predictors of grade switching are qualitatively
similar when controlling for higher-order polynomials of turnover or quartiles of turnover.

56

results in column 1 of table C.4 show that ﬁrst, second, third, and fourth-grade teachers are
between 1 and 2 percentage points more likely to change grades and that these diﬀerences
are strongly statistically signiﬁcant. This is likely because in the sample, kindergarten and
ﬁfth-grade teachers have only one adjacent grade switch to, and the majority of grade-level
reassignments are to an adjacent grade. Of course, the result for ﬁfth-grade teachers may
change if the analysis was extended to include sixth-grade teachers. The year dummies,
which omit 2003-04 as the base year, indicate no clear trends in the frequency of grade
switching.
Column 2 of table C.4 adds grade-by-year ﬁxed eﬀects (i.e., grade-year interaction terms)
to the baseline speciﬁcation of column 1. Doing so is potentially important, as the years
studied in the current analysis witnessed the implementation of high-stakes tests in certain
grades associated with the 2001 No Child Left Behind Act. As a result, pressures to change
grades potentially varied systematically by grade-year during this time period. However,
adding grade-by-year ﬁxed eﬀects (FE) does not change the estimated eﬀects of the teacher
or school characteristics in a meaningful way; nor does this addition explain a signiﬁcant
amount of variation in grade switching, as evidenced by the nearly identical pseudo-R2 in
columns 1 and 2.
Columns 3 and 4 of table C.4 add district and school FE to the baseline speciﬁcation, respectively. The estimates in columns 3 and 4 are nearly identical to one another, suggesting
that variation across schools is less important than variation across districts. The district
and school FE do explain a nontrivial amount of variation in within-school grade-level reassignments, as the pseudo-R2 increases by a factor of 3 when district FE are added to the
baseline model and by a factor of 4 with the addition of school FE.11
With two exceptions, the estimates in columns 3 and 4 are remarkably similar to those
11 It is also reasonable to condition on principal FE. Unfortunately, reliable principal data
is missing for more than 20% of school-year observations, so we do not report these results.
However, estimates of such models using observations for which principal data are available
yield qualitatively similar results to those that include school FE.

57

of the baseline speciﬁcation in column 1, suggesting that the main results are not driven by
unobserved diﬀerences between districts. First, when looking at within-district (or withinschool) variation, teachers holding a masters degree become signiﬁcantly less likely to change
grades. This result is interesting despite the relatively small eﬀect size, as it suggests that
some combination of the distribution of teachers and the functioning of internal (withinschool) teacher labor markets vary by unobserved district characteristics. Second, the estimated APEs of the schools black population and school-level attrition rate lose statistical
signiﬁcance, which is likely the result of these variables exhibiting little within-district variation between 2003 and 2008.
Finally, we attempt to better understand the relationship between teachers experience
and grade switching, as experience is consistently one of the most important predictors of
grade switching in columns 1 through 4 of table C.4. We distinguish between total teaching
experience and tenure in the current school, as the predictive ability of experience may vary
by type of experience. Such diﬀerences may arise because teachers within-school seniority or
relationships with school administrators matter more than general teaching experience, or
because teachers with substantial teaching experience have identiﬁed their preferred grade
level, regardless of their tenure at their current school.
Speciﬁcally, the model estimated in column 5 of table C.4 adds a “new to school” indicator
to the school-FE speciﬁcation of column 4.12 The results suggest that all else equal, teachers
in their ﬁrst year in a school are about one percentage point more likely to change grades than
teachers with more school-speciﬁc experience. The overall eﬀect of experience diminishes
slightly, but remains strongly statistically signiﬁcant for teachers with more than ten years
of experience; estimated eﬀects of the other teacher and school characteristics are unchanged.
This basic ﬁnding is robust to either removing the school FE or replacing them with district
FE.
12 We lose one year of data in the process, as the administrative data records total experience in the school district, but not in any particular school.

58

3.4.3

The Relationship between Grade Switching and Other Types of Teacher
Turnover

This section considers the relationship between grade switching and other types of teacher
turnover. We begin by testing grade switchings ability to predict future teacher turnover, as
grade switching may be indicative of teachers unease in the classroom or schools instability.
In table C.5 we extend table C.4’s baseline speciﬁcation (column 1) to include a year-speciﬁc
count of teachers previous grade-level reassignments and examine the eﬀect of previous grade
changes on the probability of remaining in the same teaching assignment, changing grades,
changing schools, and leaving Michigan public education in four separate logit models.13 As
in column 5 of table C.4, one year of data is lost when creating this variable.
Column 1 of table C.5 shows that past switches signiﬁcantly lower the probability of
teachers remaining in the same grade and school in consecutive years. Column 2 suggests
that most of this decrease is due to the 5 percentage point increase in the probability of
changing grades associated with each past switch. However, columns 3 and 4 of table C.5
suggest that grade switching does not strongly predict other sorts of teacher turnover.
It is also of interest to compare the predictors of grade switching reported in table C.4
to those of other types of teacher turnover, as the optimal design and targeting of policies
aimed at decreasing teacher turnover may vary by turnover type. Accordingly, columns 1
and 2 of table C.6 report logit-model APE of select covariates on the probability of changing
schools and of leaving teaching, respectively. The speciﬁcations estimated in table C.6 are
otherwise identical to the baseline speciﬁcation of column 1 in table C.4. Again, adding
district or school FE to the logit models estimated in table 6 does not change the qualitative
results.
A comparison of the estimated APE in table C.6 to those in column 1 of table C.4
yields several similarities: teachers experience and the racial makeup of schools similarly
13 We estimate separate logits rather than a multinomial logit (MNL) to avoid making
the strong Independence of Irrelevant Alternatives assumption, though MNL results are
qualitatively similar.

59

inﬂuence the probability of all three types of teacher turnover. There are some notable
diﬀerences, however, especially among the school characteristics. For example, teachers in
charter schools are signiﬁcantly less likely to change grades or schools, but are more likely
to leave the teaching profession. Similarly, school performance (as measured by grade-level
proﬁciency quartiles) is not associated with changing grades or leaving the profession, but is
signiﬁcantly negatively correlated with changing schools. This may be reﬂective of teachers
systematically moving from lower- to higher-performing schools throughout as their careers
progress.

3.5

Discussion

This study examines the frequency and predictors of teachers within-school grade-level reassignments using rich administrative data from Michigan between 2003-04 and 2007-08.
This time period witnessed a nontrivial number of such grade changes, as in any given year
about 7% of the states self-contained kindergarten through ﬁfth-grade teachers experienced
a grade-level reassignment. The phenomenon of grade switching is not unique to Michigan,
as a similar rate of about 9% is found in nationally representative data over a similar time
period. In Michigan, and nationally, the rate of grade switching is similar in magnitude to
rates of attrition from the profession and mobility across schools.
Grade switching is more common in schools with high attrition rates, which may be the
result of principals responses to vacancies created by teachers departures. Urban schools
with higher fractions of minority students are found to have higher levels of grade switching,
even conditional on the amount of teacher turnover in the school. While grade switching
does not appear to vary by schools achievement levels, charter schools have signiﬁcantly fewer
grade-level reassignments than their traditional public school counterparts. This suggests
that charter school principals may be following the advice of researchers such as Jacob and
Rockoﬀ (2011) by minimizing grade-level reassignments.
Teachers with more experience, both overall and in the current school, are found to be
60

signiﬁcantly less likely to change grades, as are teachers in charter schools. The negative
correlation between grade switching and teachers experience likely results from some combination of experienced teachers having relatively more input in their teaching assignments
and having learned which grade(s) they are most comfortable in. Importantly, grade switching predicts future grade switching but no other types of teacher turnover, suggesting that
grade switching is not an early indicator of teachers dissatisfaction with the profession.
A limitation of the current study is its inability to diﬀerentiate between teacher- and
principal-induced reassignments. While nearly 90% of teacher mobility across schools is
at teachers, as opposed to administrators, discretion (Keigher, 2010), it is diﬃcult to determine the corresponding percentage of grade-level or subject reassignments initiated by
teachers. Indeed, Cohen-Vogel (2011) suggests that such reassignments are initiated by both
teachers and principals. Furthermore, some reassignments may be determined by mutual
agreement or compromise. Future iterations of nationally representative surveys of teachers
and/or principals might consider adding items that ask the reason for grade and subject
reassignments.
Nonetheless, the general ﬁnding that grade switching is non-random has several implications for administrators, principals, and policy makers seeking to improve student outcomes. That the predictors of teacher turnover vary by turnover type suggests that principals, policymakers, and analysts must think carefully about the operationalized deﬁnition of
teacher turnover and recognize grade (and potentially subject) reassignments as a nontrivial
type of within-school turnover when devising and implementing teacher-retention programs
and investigating the impact of high-stakes accountability on teacher turnover (Boyd et al.,
2008).14
Finally, the ﬁnding that new teachers are more likely to change grades following their ﬁrst
14 The frequency and non-random distribution of grade switching may also have implications for value-added modeling. For instance, omitting grade-speciﬁc experience from
value-added models may contribute to the time instability frequently observed in rankings
of estimated teacher eﬀects (e.g., McCaﬀrey, Sass, Lockwood, and Mihaly (2009).

61

year in a new school, even after controlling for total years of teaching experience, suggests
that the within-school politics of seniority play an important role in determining grade-level
reassignments. This is not to say that all schools should adjudicate teaching assignments in
the same manner, as the optimal level of grade switching will depend on the speciﬁc school
and district context. Rather, the results of the current analysis underscore the potential
beneﬁts of paying greater attention to teachers grade-level and subject reassignments. The
relatively high rates of grade switching observed in Michigan and nationally suggest that
there are potentially large gains in student performance to be had by reconsidering the
frequency with, and reasons for, which teachers change grades.

62

APPENDICES

63

APPENDIX

A

TABLES FOR “THE EFFECT OF SCHOOL CLOSINGS ON STUDENT
ACHIEVEMENT”

Table A.1: Descriptive Statistics
Variable
Student Characteristics
Grade
Free/Reduced-Price Lunch Eligible
African-American/Hispanic
Mathematics Score
Reading Score

Mean

SD

Min

Max

5.540
0.429
0.240
0.006
0.003

School Characteristics
School Enrollment
2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year After Closure
2 Years After Closure
3+ Years After Closure
Fraction of Students Displaced 1 Year Prior
Fraction of Students Displaced 2 Years Prior
Fraction of Students Displaced 3+ Years Prior
Fraction of Teachers Displaced 1 Year Prior
Fraction of Teachers Displaced 2 Years Prior
Fraction of Teachers Displaced 3+ Years Prior
District Characteristics
District Closed School Previous Year
Number of Observations
Number of Students
Number of Schools
The level of observation is the student*year.

64

1.711 3.000
0.495 0.000
0.427 0.000
0.998 -4.631
0.999 -4.288

8.000
1.000
1.000
3.381
2.222

538.5
0.006
0.010
0.012
0.009
0.004
0.003
0.006
0.003
0.002
0.007
0.004
0.004

233.9
0.076
0.098
0.107
0.092
0.066
0.056
0.035
0.021
0.016
0.055
0.042
0.044

0.0
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

1793.0
1.000
1.000
1.000
1.000
1.000
1.000
0.740
0.613
0.618
1.000
1.000
1.000

0.070
3,416,174
1,252,101
2,926

0.254

0.000

1.000

Table A.2: Descriptives of Students in Closed Schools
Variable
Students in Closed Schools District Mean Entire Sample
Female
0.488
0.497
0.493
African-American
0.536
0.496
0.187
Hispanic
0.053
0.079
0.053
Special Education
0.151
0.137
0.127
Limited English Proﬁcient
0.036
0.066
0.039
Free/Reduced Price Lunch Eligible
0.671
0.651
0.429
School Enrollment (K-5 Schools Only)
287.9
387.4
425.1
School Enrollment
430.8
524.4
538.5
Elementary School*
0.285
0.282
0.272
Rural School
0.032
0.055
0.244
Urban School
0.500
0.662
0.247
Mathematics Score**
-0.506
-0.390
0.006
Reading Score**
-0.436
-0.318
0.003
N
40,141
364,794
3,416,174
*An elementary school is deﬁned as any school with highest grade less than or equal to 5.
**Test scores standardized by grade*year to have mean zero, variance 1.

65

Table A.3: Student and Teacher Movement after Closings
Percentile
N
10
25
50
75
90
Mean
Fraction of Students Attending a New School District
246 0.015 0.031 0.056 0.104 0.169 0.093
Fraction of Students Attending a Charter School
246 0.000 0.000 0.025 0.077 0.160 0.064
Median Distance to New School for Student
239 0.441 0.825 1.370 2.043 4.846 2.117
Fraction of Students Attending the Modal Receiving School 246 0.197 0.275 0.350 0.487 0.632 0.389
Fraction of Teachers Attending the Modal Receiving School 246 0.115 0.167 0.250 0.438 0.714 0.339
Each observation represents a single closed school. The modal school is deﬁned separately for students and
teachers as the receiving school that receives the largest number of students or teachers from closed schools,
respectively.

66

Table A.4: Average Eﬀects of School Closings on Displaced Students in Michigan
Math
-0.004
[0.029]
-0.041***
[0.014]
-0.061**
[0.030]
-0.074**
[0.033]
-0.016
[0.020]
-0.010
[0.016]

2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year after Closure
2 Years after Closure
3+ Years after Closure

Reading
-0.010
[0.010]
-0.013
[0.011]
-0.026
[0.017]
-0.053
[0.033]
-0.041
[0.029]
-0.033
[0.021]

N
3,416,174 3,416,174
The unit of observation is the student*year. Standard
errors are adjusted for clustering at the district level.
*** indicates signiﬁcance at the 0.01 level, ** at the
0.05 level, and * at the 0.1 level.

67

Table A.5: Eﬀects of School Closings on Receiving Schools
Math
Displaced Students:
Fraction of Displaced Students

Reading

-0.246*
-0.266**
[0.132]
[0.113]
Fraction of Displaced Students (lagged)
-0.113
-0.208**
[0.103]
[0.083]
Fraction of Displaced Students (twice lagged) -0.200*
-0.064
[0.111]
[0.068]
Fraction of Displaced Teachers
-0.071***
-0.035
[0.019]
[0.030]
Fraction of Displaced Teachers (lagged)
-0.145***
-0.101***
[0.042]
[0.034]
Fraction of Displaced Teachers (twice lagged) -0.133***
0.025
[0.033]
[0.059]
Students At Receiving Schools:
Fraction of Displaced Students
-0.218*
-0.280**
[0.112]
[0.133]
Fraction of Displaced Students (lagged)
-0.189***
-0.249
[0.073]
[0.153]
Fraction of Displaced Students (twice lagged) -0.184**
-0.257*
[0.092]
[0.145]
Fraction of Displaced Teachers
0.003
-0.032*
[0.031]
[0.019]
Fraction of Displaced Teachers (lagged)
-0.082***
-0.134***
[0.029]
[0.032]
Fraction of Displaced Teachers (twice lagged)
-0.046
-0.114**
[0.032]
[0.047]
N
3,416,174
3,416,174
The unit of observation is the student*year. Standard errors are adjusted
for clustering at the district level. *** indicates signiﬁcance at the 0.01
level, ** at the 0.05 level, and * at the 0.1 level.

68

Table A.6: School Closings and Voluntary Student Mobility

Displaced
Students
Panel A: Mathematics Achievement
2 Years Prior to Move
1 Year Prior to Move
Year of Move
1 Year after Move
2 Years after Move
3+ Years after Move

Voluntary
Movers from
Closed Schools

Other
Voluntary
Movers

-0.005
[0.050]
-0.046*
[0.026]
-0.052
[0.035]
-0.075*
[0.044]
-0.022
[0.028]
-0.013
[0.021]

–
–
0.057***
[0.020]
-0.033*
[0.019]
-0.005
[0.016]
0.036**
[0.017]
0.058**
[0.025]

0.002
[0.004]
-0.002
[0.005]
-0.027**
[0.011]
-0.036***
[0.005]
-0.022***
[0.005]
-0.015***
[0.004]

Panel B: Reading Achievement
2 Years Prior to Move

-0.012
–
-0.002
[0.035]
–
[0.004]
1 Year Prior to Move
-0.024
0.024*
-0.003
[0.021]
[0.013]
[0.004]
Year of Move
-0.020
-0.013
-0.026***
[0.027]
[0.017]
[0.007]
1 Year after Move
-0.072*
0.004
-0.019***
[0.042]
[0.020]
[0.005]
2 Years after Move
-0.060
-0.010
-0.009**
[0.039]
[0.023]
[0.004]
3+ Years after Move
-0.036
-0.012
-0.012***
[0.029]
[0.021]
[0.005]
N=3,416,174. All coeﬃcients for a given dependent variable are estimated in the
same regression. Standard errors are adjusted for clustering at the district level.
*** indicates signiﬁcance at the 0.01 level, ** at the 0.05 level, and * at the 0.1
level.

69

Table A.7: Displaced Student Achievement Trajectories by Change in School Performance
Closed School
.5 s.d. below
Nearby Schools
Mathematics:
2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year After Closure
2 Years After Closure
3 Years After Closure
N
Reading:
2 Years Prior to Closure

-0.018
[0.023]
-0.048***
[0.013]
-0.073**
[0.032]
-0.078**
[0.038]
0.010
[0.056]
0.043**
[0.018]

Closed School
Same as
Nearby Schools
0.004
[0.028]
-0.034**
[0.013]
-0.048
[0.034]
-0.075**
[0.035]
-0.031
[0.023]
-0.019
[0.017]
3,257,564

-0.021
[0.019]
-0.036***
[0.013]
-0.053***
[0.016]
-0.068**
[0.032]
0.036
[0.087]
-0.045
[0.039]

Cloised School
.5 s.d. above
Nearby Schools
0.027
[0.036]
-0.019
[0.017]
-0.023
[0.036]
-0.071**
[0.035]
-0.073
[0.048]
-0.081***
[0.021]

-0.009
0.004
[0.011]
[0.032]
1 Year Prior to Closure
-0.009
0.019
[0.015]
[0.021]
Year of Closure
-0.019
0.015
[0.011]
[0.016]
1 Year After Closure
-0.057*
-0.047
[0.030]
[0.032]
2 Years After Closure
-0.054**
-0.144
[0.027]
[0.115]
3 Years After Closure
-0.047**
-0.048
[0.021]
[0.034]
N
3,292,314
Reported trajectories based on a linear combination of coeﬃcients shown in Appendix F.2. Standard errors are adjusted for clustering at the district level. ***
indicates signiﬁcance at the 0.01 level, ** at the 0.05 level, and * at the 0.1 level.

70

APPENDIX

B

TABLES FOR “THE EFFECT OF FOUR-DAY SCHOOL WEEKS ON
STUDENT ACHIEVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL FURLOUGH DAYS”

Table B.1: Comparison of HSA and NAEP Results

Grade
Mathematics:
4
4
4
8
8
8
Reading:
4
4
4
8
8
8

Year

HSA
Level Change

NAEP
Level Change

Diﬀerence
Level Change

2007
2009
2011
2007
2009
2011

0.478
0.507
0.610
0.258
0.391
0.539

0.029
0.103
0.133
0.148

0.330
0.370
0.400
0.210
0.250
0.300

0.040
0.030
0.040
0.050

-0.148
-0.137
-0.210
-0.048
-0.141
-0.239

0.011
-0.073
-0.093
-0.098

2007
2009
2011
2007
2009
2011

0.537
0.612
0.674
0.599
0.663
0.681

0.075
0.062
0.064
0.018

0.260
0.260
0.270
0.200
0.220
0.260

0.000
0.010
0.020
0.040

-0.277
-0.352
-0.404
-0.399
-0.443
-0.421

-0.075
-0.052
-0.044
0.022

71

Table B.2: Descriptive Statistics
17 Furlough Days
Less than 17 Furlough Days
Variable
2007-2009
2010
2011-2012 2007-2009
2010
2011-2012 Total
Math Proﬁciency
0.313
0.349
0.455
0.426
0.482
0.578
0.474
Reading Proﬁciency
0.632
0.690
0.700
0.603
0.648
0.695
0.645
Enrollment
280.953
299.000
317.391
686.412
684.749
678.198
652.907
Pupil-Teacher Ratio
12.705
12.883
12.952
15.536
15.608
15.710
15.323
Fraction African-American
0.014
0.013
0.017
0.022
0.021
0.024
0.022
Fraction Hispanic
0.028
0.028
0.027
0.047
0.046
0.049
0.045
Fraction Asian/Paciﬁc Islander
0.705
0.683
0.635
0.730
0.733
0.755
0.731
Fraction Free/Reduced-Price Lunch
0.415
0.428
0.502
0.436
0.470
0.503
0.454
Title I School
0.655
0.690
0.586
0.587
0.615
0.641
0.608
Charter
1.000
1.000
1.000
0.008
0.008
0.008
0.108
N
215
97
210
1782
622
1247
4173
The unit of observation is the school*grade*year, excluding grade 3. Schools that took less than 17 furlough
days are grouped with schools that took no furlough days. Refer to Appendix G.1 for full descriptive statistics
of sample. CCD data for year 2012 is not available yet.

72

Table B.3: ITS Estimates – Grades 4 -5
(1)
Panel A: Mathematics
Year 2010
Year
Year*Post2010
Year Squared
Panel B: Reading
Year 2010
Year
Year*Post2010
Year Squared
Linear Trend
Controls
Slope Shift in 2010
Quadratic Trend
Observations
Clusters
Years

(2)

(3)

(4)

-0.056***-0.051***-0.078***-0.044***
(0.006) (0.006) (0.011) (0.006)
0.041*** 0.037*** 0.022*** 0.016*
(0.002) (0.003) (0.004) (0.008)
0.008
(0.008)
0.004**
(0.001)
-0.011* -0.008 -0.006 -0.005
(0.005) (0.005) (0.011) (0.005)
0.030*** 0.027*** 0.022*** 0.016*
(0.002) (0.002) (0.003) (0.007)
0.012
(0.007)
0.002*
(0.001)
x

x
x

x

x

x
x
2052
180
6

1691
179
5

2052
180
6

2052
180
6

Sample restricted to only grades 4 and 5. The unit of observation is the school*grade*year. Year is coded so that the
2007 school year is year 1. Standard errors in parentheses adjusted for clustering at the school level. * denotes signiﬁcance
at the 0.10 level, ** at the 0.05 level, ** at the 0.01 level.

73

Table B.4: DD Estimates – Grades 4-5
(1)
Panel A: Mathematics
(Furlough Days)/17

(2)

(3)

(4)

(5)

(6)

(7)

(8)

0.022
(0.033)

0.032
(0.037)
0.055
(0.031)

0.027
(0.033)

0.022
(0.033)

0.018
(0.035)
0.055
(0.031)

0.010
(0.034)

0.028
(0.034)

0.010
(0.036)

0.016
(0.030)

0.025
(0.031)
-0.008
(0.038)

0.039
(0.023)

0.014
(0.030)

0.029
(0.035)
-0.009
(0.038)

0.043
(0.025)

0.033
(0.026)

0.039
(0.027)

x

x

x
x

Lead of (Furlough Days)/17
Panel B: Reading
(Furlough Days)/17
Lead of (Furlough Days)/17
Group Speciﬁc Trends
School Speciﬁc Trends
Controls
Year FE
Observations
Clusters
Years

x

x

x
x

x

x

x
x

x

x
x
x

2228
203
6

1839
201
5

1823
200
5

2228
203
6

1839
201
5

1823
200
5

2228
203
6

1823
200
5

Sample restricted to only grades 4 and 5. The unit of observation is the school*grade*year. Standard
errors in parentheses adjusted for clustering at the school level. * denotes signiﬁcance at the 0.10 level,
** at the 0.05 level, ** at the 0.01 level.

74

Table B.5: ITS Estimates – Grades 6 -10
(1)
Panel A: Mathematics
Year 2010
Year
Year*Post2010
Year Squared
Panel B: Reading
Year 2010
Year
Year*Post2010
Year Squared
Linear Trend
Controls
Slope Shift in 2010
Quadratic Trend
Observations
Clusters
Years

(2)

(3)

(4)

0.003
0.007
0.016
0.012
(0.006) (0.006) (0.011) (0.006)
0.043*** 0.039*** 0.033*** 0.024**
(0.002) (0.003) (0.004) (0.008)
0.020*
(0.008)
0.003**
(0.001)
-0.005 -0.013* 0.036** -0.011
(0.006) (0.006) (0.012) (0.006)
0.025*** 0.030*** 0.040*** 0.038***
(0.002) (0.002) (0.003) (0.006)
0.008
(0.007)
-0.002*
(0.001)
x

x
x

x

x

x
x
1599
185
6

1305
182
5

1599
185
6

1599
185
6

The unit of observation is the school*grade*year. Year is
coded so that the 2007 school year is year 1. Standard errors
in parentheses adjusted for clustering at the school level. *
denotes signiﬁcance at the 0.10 level, ** at the 0.05 level, **
at the 0.01 level.

75

Table B.6: DD Estimates – Grades 6-10
(1)
Panel A: Mathematics
(Furlough Days)/17

Observations
Clusters
Years

(4)

(5)

(6)

(7)

(8)

0.035* 0.037* 0.029
(0.016) (0.015) (0.016)
-0.004
(0.024)

0.035* 0.030* 0.029
(0.017) (0.015) (0.016)
-0.004
(0.025)

0.029
(0.016)

-0.020
(0.018)

-0.006
(0.021)
0.004
(0.017)

-0.023
(0.017)

-0.018
(0.019)
0.002
(0.018)

-0.025
(0.018)

-0.017
(0.018)

-0.025
(0.021)

x

x

x
x

Lead of (Furlough Days)/17
Group Speciﬁc Trends
School Speciﬁc Trends
Controls
Year FE

(3)

0.030
(0.016)

Lead of (Furlough Days)/17
Panel B: Reading
(Furlough Days)/17

(2)

-0.014
(0.020)

x

x

x
x

x

x

x
x

x

x
x
x

1945
213
6

1603
213
5

1567
209
5

1945
213
6

1603
213
5

1567
209
5

1945
213
6

1567
209
5

Sample restricted to only grades 6-10. The unit of observation is the school*grade*year. Standard errors in parentheses adjusted for clustering at the school level. * denotes signiﬁcance at the 0.10 level, **
at the 0.05 level, ** at the 0.01 level.

76

Table B.7: Heterogeneity by School Demographics
Panel A: Quartiles of Percent FRL in 2007 (Grades 4-5)
Quartile
(1)
(2)
(3)
Mathematics
Reading

−0.037***
(0.011)
−0.037***
(0.011)

−0.048***
(0.010)
−0.000
(0.007)

−0.034**
(0.012)
−0.008
(0.010)

(4)
−0.056***
(0.014)
−0.012
(0.014)

Panel B: Quartiles of Percent Proﬁcient in 2007 (Grades 4-5)
Quartile
(1)
(2)
(3)
(4)
Mathematics
Reading

−0.054***
(0.014)
−0.054***
(0.014)

−0.063***
(0.014)
−0.021
(0.012)

−0.041***
(0.010)
−0.008
(0.008)

−0.026**
(0.009)
0.009
(0.008)

Panel C: Quartiles of Percent FRL in 2007 (Grades 6-10)
Quartile
(1)
(2)
(3)
(4)
Mathematics
Reading

0.017
(0.013)
0.017
(0.013)

0.012
(0.010)
−0.017
(0.012)

0.022
(0.013)
−0.002
(0.011)

0.000
(0.013)
−0.010
(0.015)

Panel D: Quartiles of Percent Proﬁcient in 2007 (Grades 6-10)
Quartile
(1)
(2)
(3)
(4)
Mathematics
Reading

0.018
(0.011)
0.018
(0.011)

0.018
(0.010)
−0.003
(0.010)

−0.020
(0.017)
−0.032*
(0.015)

0.028*
(0.013)
−0.020
(0.010)

Higher quartile schools are schools with higher proportions of
free/reduced price lunch eligible students or proﬁcient students, respectively. Dependent variable is school*grade*year math proﬁciency rate. Estimates are based on speciﬁcations such as those presented in column (4) of Table B.3 and Table B.5. Standard errors
in parentheses adjusted for clustering at the school level. * denotes
signiﬁcance at the 0.10 level, ** at the 0.05 level, ** at the 0.01 level.

77

APPENDIX

C

TABLES FOR “THE FREQUENCY AND CORRELATES OF TEACHERS
GRADE-LEVEL REASSIGNMENTS: EVIDENCE FROM MICHIGAN”

78

Table C.1: Self-contained Teachers’ Assignments the Following Year

Year(s)

2003/04
2004/05
2005/06
2006/07
2007/08
All

Same selfcontained
grade
1

76.40%
73.80%
75.80%
75.80%
78.30%
76.00%

New selfcontained
grade
2

6.00%
7.00%
6.30%
7.30%
6.80%
6.70%

Changed
school
3

Changed
district
4

Left selfcontained
Left
classroom teaching
5
6

In Michigan (REP Administrative Data)
5.80%
0.90%
3.60%
0.50%
6.60%
1.20%
4.10%
1.50%
6.50%
1.00%
3.90%
1.50%
6.30%
0.90%
3.60%
1.30%
5.20%
1.00%
3.10%
1.50%
6.10%
1.00%
3.60%
1.30%

Left MI
public
education
7

N
8

6.80%
5.80%
5.10%
4.80%
4.00%
5.30%

22,933
22,250
23,018
22,905
22,872
113,978

In U.S. (SASS Nationally Representative Sample)
1999/00
72.70%
8.20%
3.60%
3.00%
6.80%
.
5.60%
760
2003/04
70.80%
9.50%
3.50%
2.50%
8.00%
.
5.60%
1,070
Both
71.70%
8.90%
3.60%
2.70%
7.50%
.
5.60%
1,830
The deﬁnitions of columns 1 – 7 are mutually exclusive and sum to 100%. “By year” refers to the
initial self-contained year (e.g., the 2003-04 row reports the 2004-05 destination of teachers who were
self-contained in 2003-04). SASS means are weighted to account for unequal probabilities of sample
selection. SASS sample sizes are unweighted and are rounded to nearest ten.

79

Table C.2: Incidence of Grade-level Reassignments per Teacher
Switches per
teacher
1
2
3
4
5

Teacher-year
switches
% of switches
4,761
62.60%
1,834
24.10%
660
8.70%
200
2.60%
150
2.00%

Teachers
4,761
917
220
50
30

Total
7,605
100%
5,978
Michigan REP data. 5,978 teachers constitute 17.9% of the
33,390 teachers who taught in a self-contained kindergarten
through ﬁfth-grade classroom in Michigan between 2003-04 and
2007-08.

80

Table C.3: Average Characteristics by Teacher-year
All
teachers

Switches per teacher
0
1
>1

Teacher Characteristics
Black
Age
Female
Masters degree
No prev. experience
1 year experience
2 years experience
3-4 years experience
5-9 years experience
10+ years experience
New to school
2nd Year in School
3rd Year in School

4.00%
43.2
89.60%
51.90%
4.00%
4.70%
5.10%
10.70%
25.00%
50.50%
34.70%
24.50%
17.90%

3.80%
43.9
89.30%
52.50%
4.10%
4.50%
4.80%
9.90%
23.50%
53.30%
36.20%
24.40%
17.40%

4.80%
40.7
90.50%
50.20%
4.10%
5.60%
6.40%
13.30%
30.50%
40.30%
30.50%
25.10%
19.50%

4.50%
40.5
90.20%
48.50%
3.20%
4.80%
5.70%
13.90%
31.70%
40.60%
25.80%
23.60%
20.80%

School Characteristics
Urban
Rural
Suburban
Title 1
% free/reduced reduced lunch
% black
Charter

21.10%
32.40%
31.60%
37.20%
14.10%
6.80%
22.70%

20.00%
33.40%
31.10%
36.80%
13.30%
6.90%
22.50%

24.70%
28.80%
33.00%
38.70%
17.10%
6.90%
23.10%

25.80%
27.30%
34.60%
38.30%
16.80%
4.70%
26.40%

Proﬁciency Quartile
1st (lowest)
2nd
3rd
4th (highest)

24.50%
25.80%
21.10%
32.40%

24.60% 24.20% 25.10%
26.00% 25.20% 23.60%
20.00% 24.70% 24.90%
33.40% 28.80% 25.80%

N
113,978 89,354 19,155
5,469
Michigan REP data. Grade-level reassignments refer to the total
number of reassignments experienced by each teacher during the
six-year period.

81

Table C.4: Logit Average Partial Eﬀects on Probability of Changing Grades
1
Teacher Characteristics
Black
0.0014
(0.0045)
Age
-0.0011***
(0.0001)
Female
0.0057*
(0.0034)
Masters degree
(0.0036)
(0.0025)
1 year experience
(0.0060)
(0.0044)
2 years exp.
-0.0129***
(0.0047)
3-4 years exp.
-0.0134***
(0.0044)
5-9 years exp.
-0.0170***
(0.0046)
10+ years exp.
-0.0322***
(0.0056)
New to school
.

School Characteristics
Urban

0.0115**
(0.0055)
Rural
(0.0033)
(0.0039)
Title 1
0.0016
(0.0041)
% free/reduced lunch
(0.0031)
(0.0083)
% black
0.0261***
(0.0080)
Charter
-0.0425***
(0.0066)
Attrition
0.0238**
(0.0110)

2
0.0014
(0.0045)
-0.0011***
(0.0001)
0.0057*
(0.0034)
(0.0036)
(0.0025)
(0.0060)
(0.0044)
-0.0129***
(0.0047)
-0.0133***
(0.0044)
-0.0170***
(0.0046)
-0.0321***
(0.0056)
.

0.0115**
(0.0055)
(0.0033)
(0.0039)
0.0017
(0.0041)
(0.0031)
(0.0083)
0.0262***
(0.0080)
-0.0424***
(0.0066)
0.0237**
(0.0110)

82

3

4

5

(0.0009)
(0.0028)
(0.0007)
(0.0041)
(0.0042)
(0.0052)
-0.0011*** -0.0012*** -0.0012***
(0.0001)
(0.0001)
(0.0001)
0.0055
0.0068*
0.0068
(0.0035)
(0.0036)
(0.0043)
-0.0055** -0.0053** -0.0078***
(0.0023)
(0.0024)
(0.0027)
(0.0062)
(0.0055)
0.0048
(0.0046)
(0.0052)
(0.0064)
-0.0139*** -0.0139**
(0.0070)
(0.0050)
(0.0055)
(0.0071)
-0.0128*** -0.0122**
(0.0048)
(0.0047)
(0.0053)
(0.0065)
-0.0171*** -0.0171***
(0.0050)
(0.0050)
(0.0053)
(0.0066)
-0.0337*** -0.0374*** -0.0269***
(0.0059)
(0.0062)
(0.0074)
.
.
0.0117***
(0.0031)

0.0047
(0.0065)
(0.0041)
(0.0049)
0.0032
(0.0042)
0.0048
(0.0112)
(0.0025)
(0.0111)
.
0.0143
(0.0125)

.

.

.

.

0.0072
(0.0055)
(0.0076)
(0.0219)
(0.0591)
(0.0531)
.

0.0145**
(0.0065)
(0.0011)
(0.0240)
(0.0706)
(0.0676)
.

0.0240
(0.0147)

0.0189
(0.0188)

Table C.4 (cont’d)
1
Proﬁciency Quartiles
2nd
3rd
4th (highest)

2

3

4

5

0.0048
(0.0037)
0.0025
(0.0041)
(0.0007)
(0.0048)

0.0048
(0.0037)
0.0025
(0.0041)
(0.0007)
(0.0048)

(0.0017)
(0.0037)
(0.0015)
(0.0043)
(0.0025)
(0.0046)

(0.0049)
(0.0050)
(0.0055)
(0.0056)
(0.0057)
(0.0063)

(0.0041)
(0.0064)
(0.0028)
(0.0070)
(0.0080)
(0.0080)

.

0.0165***
(0.0035)
0.0241***
(0.0037)
0.0167***
(0.0035)
0.0127***
(0.0040)
-0.0074*
(0.0040)
0.0115**
(0.0058)
0.0047
(0.0058)
0.0161***
(0.0053)
0.0115**
(0.0052)

0.0163***
(0.0040)
0.0243***
(0.0041)
0.0161***
(0.0040)
0.0130***
(0.0046)
(0.0021)
(0.0046)
0.0121*
(0.0063)
0.0051
(0.0060)
0.0173***
(0.0056)
0.0124**
(0.0053)

0.0207***
(0.0047)
0.0284***
(0.0047)
0.0189***
(0.0046)
0.0174***
(0.0052)
0.0002
(0.0054)
0.0017
(0.0056)
(0.0072)
(0.0051)
0.0056
(0.0044)
-

Classroom Characteristics
First grade
0.0152***
(0.0035)
Second grade
0.0226***
(0.0037)
Third grade
0.0156***
(0.0034)
Fourth grade
0.0119***
(0.0040)
Fifth grade
-0.0074*
(0.0040)
2005.00
0.0110**
(0.0056)
2006.00
0.0045
(0.0057)
2007.00
0.0153***
(0.0052)
2008.00
0.0113**
(0.0053)

.
.
.
.
.
.
.
.

Fixed Eﬀects
None
Grade-year District
School
School
Log likelihood
-27335
-27327
-25857
-24400
-19520
Pseudo R2
0.0214
0.0217
0.0660
0.0941
0.0996
Districts
692
692
597
598
588
Schools
2158
2158
2029
1603
1513
Observations
113978
113978
110406
100408
77317
Michigan REP data. ∗ ∗ ∗p < 0.01, ∗ ∗ p < 0.05, ∗p < 0.1. The dependent variable is
an indicator of within-school grade switching. Parentheses contain standard errors that
are robust to clustering at the district level. Omitted categories include 0 years of prior
experience, suburban school, proﬁciency quartile 1, kindergarten teacher, and 2004. In
column 3, each charter school is coded as a unique district and receives its own ﬁxed
eﬀect.

83

Table C.5: Grade Switching as a Predictor of Teacher Turnover

Outcome
Prev. Switches

Leave school, district,
or self-contained
Stay Put Switch Grades
classroom
1
2
3
-0.0697***
0.0506***
0.0009
(0.0060)
(0.0030)
(0.0030)

Leave teaching
or state
4
-0.0044*
(0.0025)

N
91045
91045
91045
91045
Pseudo R-2
0.0391
0.0457
0.0511
0.0748
Log-Likelihood
-48279
-21699
-29611
-20029
Michigan REP data. ∗ ∗ ∗p < 0.01, ∗p < 0.1. Parentheses contain standard errors that
are robust to clustering at the district level. In addition to the “number of previous
switches”, the logit models estimated in this table include the same set of covariates as
the model estimated in column 1 of table C.4. One year of data was lost in creating the
“previous switches” variable. Adding school FE to the model produces qualitatively
similar results.

84

Table C.6: Logit Average Partial Eﬀects on Teacher Turnover
Type of turnover:
Teacher Characteristics
Masters degree
1 year experience
2 years experience
3-4 years exper.
5-9 years exper.
10+ years exper.

School Characteristics
% free/red. lunch
% black
Charter
Quartile 2
Quartile 3
Quartile 4 (highest)

Leave school/district
1

Leave teaching/state
2

0.0058*
(0.0031)
-0.0231***
(0.0057)
-0.0344***
(0.0070)
-0.0428***
(0.0066)
-0.0586***
(0.0074)
-0.0883***
(0.0082)

-0.0113***
(0.0017)
-0.0177***
(0.0046)
-0.0178***
(0.0049)
-0.0359***
(0.0051)
-0.0728***
(0.0050)
-0.0606***
(0.0049)

0.0480***
(0.0146)
0.0379***
(0.0102)
-0.0551***
(0.0084)
-0.0197***
(0.0049)
-0.0289***
(0.0059)
-0.0395***
(0.0069)

0.0067
(0.0053)
0.0117**
(0.0047)
0.0620***
(0.0040)
(0.0042)
(0.0026)
(0.0033)
(0.0026)
(0.0020)
(0.0028)

Pseudo R-squared
0.0490
0.0730
Log Likelihood
-36925
-25643
Michigan REP data. N = 113,978. ∗∗∗p < 0.01, ∗∗p < 0.05, ∗p <
0.1. Parentheses contain standard errors that are robust to clustering at the district level. Only selected variables are reported;
the speciﬁcations estimated in this table are identical to that estimated in column 1 of table 4, less attrition. Adding school FE
to the models produces qualitatively similar results.

85

APPENDIX

D

FIGURES FOR “THE EFFECT OF SCHOOL
CLOSINGS ON STUDENT ACHIEVEMENT”

Figure D.1: Location of School Closings 2006-2009

For interpretation of the references to color in this and all other ﬁgures, the
reader is referred to the electronic version of this dissertation.

86

Figure D.2: Distribution of School Performance Statewide

87

Figure D.3: Achievement Trajectory of Displaced Students by Performance of Closed School – Mathematics

88

Figure D.4: Achievement Trajectory of Displaced Students by Performance of Closed School – Reading

89

Figure D.5: Performance Trajectory at Schools Receiving Students by Performance of Closed School – Mathematics

90

Figure D.6: Performance Trajectory at Schools Receiving Students by Performance of Closed School – Reading

91

Figure D.7: Performance Trajectory at Schools Receiving Teachers by Performance of Closed School – Mathematics

92

Figure D.8: Performance Trajectory at Schools Receiving Teachers by Performance of Closed School – Reading

93

APPENDIX

E

FIGURES FOR “THE EFFECT OF FOUR-DAY
SCHOOL WEEKS ON STUDENT ACHIVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL
FURLOUGH DAYS”

94

Figure E.1: Grades 4-5 Mathematics Trajectories

Fitted lines represent linear regressions of average achievement on year.

95

Figure E.2: Grades 4-5 Reading Trajectories

Fitted lines represent linear regressions of average achievement on year.

96

Figure E.3: Grades 6-10 Mathematics Trajectories

Fitted lines represent linear regressions of average achievement on year.

97

Figure E.4: Grades 6-10 Reading Trajectories

Fitted lines represent linear regressions of average achievement on year.

98

Figure E.5: Enrollment Trajectory by Furlough Status

Year 2008 excluded. Racial composition categories in year 2011 are not comparable to previous years.

99

Figure E.6: Pupil-Teacher Ratio Trajectory by Furlough Status

Year 2008 excluded. Racial composition categories in year 2011 are not comparable to previous years.

100

Figure E.7: Fraction Asian/Paciﬁc Islander Trajectory by Furlough Status

Year 2008 excluded. Racial composition categories in year 2011 are not comparable to previous years.

101

Figure E.8: Fraction White Trajectory by Furlough Status

Year 2008 excluded. Racial composition categories in year 2011 are not comparable to previous years.

102

Figure E.9: Per-Pupil Charter School Funding in Hawaii

Data taken from Charter School Administrative Oﬃce (CSAO) Testimony to Senate Committee
on Ways and Means at http://www.capitol.hawaii.gov/session2012/testimony/Info Testimony WAM
01-17-12 CHARTER.pdf.
103

APPENDIX

F

APPENDICES FOR “THE EFFECT OF SCHOOL
CLOSINGS ON STUDENT ACHIEVEMENT”

F.1

Baseline Analysis Separate by Closing Cohort

Table F.1 displays the results of speciﬁcations like those shown in Table A.4, but where
treatment is deﬁned separately for each cohort of displaced students. All coeﬃcients shown
are relative to student achievement in 2006.

104

Table F.1: Eﬀects of School Closings by Closing Cohort

2006

Year of Displacement
2007
2008

Panel A: Mathematics Achievement
2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year after Closure
2 Years after Closure
3 Years after Closure

-0.035
[0.029]
-0.017
[0.029]
-0.023
[0.026]

-0.033***
[0.011]
-0.021
[0.015]
0.038*
[0.020]
0.045**
[0.018]

0.012
[0.037]
0.004
[0.021]
-0.013
[0.038]
0.037
[0.038]

Panel B: Reading Achievement
2 Years Prior to Closure
1 Year Prior to Closure

-0.010
[0.027]
-0.029
[0.023]
-0.007
[0.021]
0.003
[0.019]

Year of Closure

2009
-0.008
[0.029]
-0.046***
[0.018]
-0.084***
[0.032]
-0.095**
[0.043]

-0.012
[0.008]
-0.013
[0.020]
-0.031
[0.020]
-0.073
[0.047]

-0.027
[0.019]
1 Year after Closure
-0.036
-0.023
[0.028]
[0.015]
2 Years after Closure
-0.062*
-0.008
[0.033]
[0.024]
3 Years after Closure
-0.082**
0.018
[0.038]
[0.016]
Number of Displaced Students
9,942
11,063
5,613
13,523
N
3,416,174 3,416,174 3,416,174 3,416,174
The treatment speciﬁcation is set to 0 for all displaced students except for students
displaced following the given academic year. Standard errors are adjusted for clustering at the district level. *** indicates signiﬁcance at the 0.01 level, ** at the
0.05 level, and * at the 0.1 level.

105

F.2

Results with Interactions for School Performance Diﬀerential

The following table displays estimates of the speciﬁcation shown in Equation (1.6).
Table F.2: School Closings and School Performance
Math
Main Eﬀect Interaction
Displaced Students:
2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year After Closure
2 Years After Closure
3 Years After Closure

0.004
[0.028]
-0.035***
[0.013]
-0.049
[0.034]
-0.077**
[0.035]
-0.033
[0.022]
-0.020
[0.017]

Students At Receiving Schools:
Frac. of Disp. Students

0.044*
[0.023]
0.030**
[0.014]
0.050***
[0.009]
0.007
[0.016]
-0.083
[0.094]
-0.123***
[0.018]

Reading
Main Eﬀect Interaction
-0.009
[0.011]
-0.009
[0.015]
-0.019*
[0.011]
-0.057*
[0.030]
-0.054**
[0.027]
-0.047**
[0.021]

0.025
[0.048]
0.055***
[0.021]
0.069***
[0.024]
0.020
[0.023]
-0.179
[0.197]
-0.003
[0.059]

-0.145
0.201***
-0.232*
0.090***
[0.131]
[0.067]
[0.140]
[0.034]
Frac. of Disp. Students (lag)
-0.073
0.230
-0.228
0.006
[0.063]
[0.158]
[0.148]
[0.094]
Frac. of Disp. Students (2 lags)
-0.171*
0.207
-0.250
0.199
[0.092]
[0.309]
[0.175]
[0.244]
Frac. of Disp. Teachers
-0.069***
0.051*
-0.006
0.047**
[0.020]
[0.030]
[0.022]
[0.023]
Frac. of Disp. Teachers (lag)
-0.135***
0.050
-0.120***
-0.004
[0.063]
[0.061]
[0.045]
[0.022]
Frac. of Disp. Teachers (2 lags)
-0.124***
0.007
-0.108**
0.024
[0.028]
[0.052]
[0.048]
[0.023]
N
3,257,564
3,292,314
All coeﬃcients for a given dependent variable are estimated in the same regression.
Standard errors are adjusted for clustering at the district level. *** indicates
signiﬁcance at the 0.01 level, ** at the 0.05 level, and * at the 0.1 level.

106

The following table displays estimates of the speciﬁcation shown in Equation (1.6), with
value-added measures used in place of average school proﬁciency rates. Value-added measures are constructed by taking the Ordinary Least Squares estimate of ψ from the regression
equation Yist = Xist β +ψs +uist using data from years 2001-2005, where Xist includes controls for race, gender, Limited English Proﬁciency, migrant student status, free or reducedprice lunch status, and lags of both math and reading test scores. These measures are then
standardized to have mean zero, standard deviation one.

107

Table F.3: School Closings and School Performance using Value-Added Measures
Math
Main Eﬀect Interaction
Displaced Students:
2 Years Prior to Closure
1 Year Prior to Closure
Year of Closure
1 Year After Closure
2 Years After Closure
3 Years After Closure

0.003
[0.027]
-0.035***
[0.012]
-0.049*
[0.028]
-0.077**
[0.036]
-0.031
[0.022]
-0.014
[0.018]

Students At Receiving Schools:
Frac. of Disp. Students

0.049***
[0.016]
0.030**
[0.012]
0.052***
[0.009]
0.009
[0.015]
0.054
[0.147]
-0.091***
[0.020]

Reading
Main Eﬀect Interaction
-0.007
[0.011]
-0.005
[0.018]
-0.010
[0.018]
-0.051*
[0.031]
-0.052*
[0.029]
-0.049**
[0.024]

0.021
[0.014]
0.034**
[0.016]
0.044*
[0.025]
0.022
[0.021]
-0.032
[0.150]
-0.034
[0.042]

-0.153
0.198***
-0.187*
0.112***
[0.103]
[0.062]
[0.110]
[0.038]
Frac. of Disp. Students (lag)
-0.121**
0.208
-0.215*
0.106*
[0.056]
[0.135]
[0.123]
[0.064]
Frac. of Disp. Students (2 lags) -0.216***
0.372**
-0.243**
0.309*
[0.081]
[0.160]
[0.123]
[0.174]
Frac. of Disp. Teachers
-0.094***
-0.002
-0.019
0.012
[0.023]
[0.039]
[0.023]
[0.023]
Frac. of Disp. Teachers (lag)
-0.130*
0.044
-0.113**
-0.031
[0.067]
[0.034]
[0.044]
[0.026]
Frac. of Disp. Teachers (2 lags)
-0.109***
-0.006
-0.101**
-0.005
[0.034]
[0.043]
[0.044]
[0.025]
N
3,257,564
3,292,314
All coeﬃcients for a given dependent variable are estimated in the same regression.
Standard errors are adjusted for clustering at the district level. *** indicates
signiﬁcance at the 0.01 level, ** at the 0.05 level, and * at the 0.1 level.

108

APPENDIX

G

APPENDICES FOR “THE EFFECT OF FOUR-DAY
SCHOOL WEEKS ON STUDENT ACHIVEMENT:
EVIDENCE FROM HAWAIIAN SCHOOL
FURLOUGH DAYS”

G.1

Descriptive Statisitcs
Table G.1: Descriptive Statistics

Variable
N
Mean
Grade
4,173 5.803
Title I School
3,427 0.614
Charter School
4,173 0.137
Enrollment
3,362 595.1
Pupil-Teacher Ratio
3,393 15.32
Fraction Free/Reduced-Price Lunch Eligible 3,400 0.458
Fraction American Indian
3,412 0.008
Fraction Asian/Paciﬁc Islander
3,402 0.723
Fraction Hispanic
3,402 0.045
Fraction African-American
3,402 0.022
Math Proﬁciency
4,173 0.474
Reading Proﬁciency
4,171 0.646
Urban
4,173 0.204
Suburban
4,173 0.311
The unit of observation is the school*grade*year. CCD data
available yet.

109

S.D. Min
Max
1.739 4.000 10.000
0.487 0.000 1.000
0.344 0.000 1.000
377.3 101
2,639
2.37 4.33 20.93
0.209 0.014 0.961
0.010 0.000 0.125
0.193 0.062 1.000
0.035 0.000 0.288
0.036 0.000 0.258
0.189 0.000 1.000
0.158 0.000 1.000
0.403 0.000 1.000
0.463 0.000 1.000
for year 2012 are not

G.2

Grade Level Heterogeneity

This appendix presents results fully broken apart by grade level.
Table G.2: Heterogeneity in Eﬀects by Grade Level – ITS Estimates

Mathematics

Reading

3
0.0127*
(0.0075)

4
-0.0446***
(0.0071)

5
-0.0433***
(0.0077)

Grade
6
0.0098
(0.0089)

0.0425***
(0.0067)

-0.0076
(0.0059)

-0.0117*
(0.0065)

-0.0485***
(0.0077)

7
0.0261**
(0.0109)

8
0.0062
(0.0114)

10
0.0088
(0.0087)

0.0469***
(0.0120)

0.0451***
(0.0100)

0.0192*
(0.0108)

Estimates are based on ITS speciﬁcations including a quadratic time trend, directly comparable to
those presented in column (4) of Table B.3. The unit of observation is the school*grade*year. Standard errors in parentheses adjusted for clustering at the school level. * denotes signiﬁcance at the
0.10 level, ** at the 0.05 level, ** at the 0.01 level.

110

Table G.3: Heterogeneity in Eﬀects by Grade Level – DD Estimates
3
Mathematics -0.0749
(0.0485)

4
0.0275
(0.0350)

5
0.0280
(0.0353)

Grade
6
0.0233
(0.0182)

7
0.0409**
(0.0200)

8
0.0293
(0.0198)

10
0.0326*
(0.0177)

Reading

0.0347
(0.0266)

0.0307
(0.0266)

-0.0711***
(0.0194)

0.0367
(0.0223)

0.0381**
(0.0187)

0.0034
(0.0201)

-0.0385
(0.0392)

Estimates are based on DD speciﬁcations including school-speciﬁc linear trends, directly
comparable to those presented in column (7) of Table B.4. The unit of observation is the
school*grade*year. Standard errors in parentheses adjusted for clustering at the school
level. * denotes signiﬁcance at the 0.10 level, ** at the 0.05 level, ** at the 0.01 level.

111

APPENDIX

H

APPENDIX FOR “THE FREQUENCY AND
CORRELATES OF TEACHERS GRADE-LEVEL
REASSIGNMENTS: EVIDENCE
FROM MICHIGAN”

H.1

Within-school Grade-level Reassignment Origins and Destinations
Table H.1: Within-school Grade-level Reassignment Origins and Destinations
In Michigan (REP Administrative Data Universe)
Grade in year t + 1
Grade in year t
K1
2
3
4
5
K
75.20% 3.10% 1.20% 0.80% 0.40%
0.30%
1
1.60% 77.10% 3.60% 1.10% 0.50%
0.30%
2
0.80% 2.90% 76.00% 2.70% 0.90%
0.40%
3
0.40% 0.90% 2.10% 75.50% 2.60%
1.00%
4
0.30% 0.50% 0.80% 2.10% 76.00% 3.00%
5
0.20% 0.40% 0.50% 1.30% 2.70% 75.90%
In U.S. (SASS Nationally Representative Sample)
Grade in year t
Grade in year t + 1
K1
2
3
4
5
K
83.50% 1.60% 0.60% 0.00% 0.00%
0.50%
1
1.70% 67.60% 6.30% 3.80% 0.00%
0.50%
2
0.50% 5.90% 68.70% 1.40% 2.20%
0.00%
3
0.60% 0.00% 5.10% 74.10% 3.00%
2.60%
4
0.00% 0.70% 0.30% 0.70% 73.10% 2.00%
5
0.00% 1.00% 1.40% 0.10% 5.20% 71.30%
Rows do not sum to 100% because the table is restricted to self-contained
teachers who remained in a self-contained classroom in the same school
in subsequent years.

112

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