MOVING MATTERS: THE CAUSAL EFFECT

OF MOVING SCHOOLS ON STUDENT

PERFORMANCE

Amy Ellen Schwartz

Maxwell School of Citizenship

and Public Aﬀairs

Syracuse University

Syracuse, NY 13244

amyschwartz@syr.edu

Leanna Stiefel

Robert F. Wagner Graduate

School of Public Service

and Institute for Education

and Social Policy

New York University

New York, NY 10012

leanna.stiefel@nyu.edu

Sarah A. Cordes

(corresponding author)

College of Education

Temple University

Philadelphia, PA 19122

sarah.cordes@temple.edu

Abstract
Policy makers and analysts often view the reduction of student
mobility across schools as a way to improve academic perfor-
mance. Prior work indicates that children do worse in the year
of a school move, but has been largely unsuccessful in isolating
the causal eﬀects of mobility. We use longitudinal data on stu-
dents in New York City public elementary and middle schools to
isolate the causal eﬀects of school moves on student performance.
We account for observed and time-invariant diﬀerences between
movers and non-movers using rich data on student sociodemo-
graphic and education program characteristics and student ﬁxed
eﬀects. To address the potential endogeneity of school moves aris-
ing from unobserved, time-varying factors, we use three sets of
plausibly exogenous instruments for mobility: ﬁrst-grade school
grade span, grade span of zoned middle school, and building sale.
We ﬁnd that in the medium term, students making structural
moves perform signiﬁcantly worse in both English language arts
(ELA) and math, whereas those making nonstructural moves ex-
perience a signiﬁcant increase in ELA performance. In the short
term, there is an additional negative eﬀect for structural moves in
ELA. These eﬀects are meaningful in magnitude and results are
robust to a variety of alternative speciﬁcations, instruments, and
samples.

doi:10.1162/EDFP_a_00198

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419

Effect of Moving Schools on Performance

I N T RO D U C T I O N

1 .
Policy makers and analysts often view the reduction of student mobility across schools
as a way to improve academic performance. Indeed, the preponderance of existing re-
search indicates that children do worse in the year of a school move (Rumberger 2003,
2015; GAO 2010), although in many respects the empirical base for this conclusion is
lacking. Much of the existing work is best viewed as correlational rather than causal,
with the observed lower performance of movers confounding the impact of mobility
with unobserved determinants of moves. Moreover, most current work tends to ig-
nore many nuances of school moves, despite the likelihood that the impact will de-
pend on the timing and context of the move. Perhaps most importantly, moves that are
structurally mandated when a student reaches the terminal grade of his current school
and that take place only in the summer, are likely to have diﬀerent eﬀects than non-
structural moves which are made because of residential relocations, family dissolution,
acceptance into preferred programs, and so forth, and which can occur either in the
summer or middle of a school year. With one notable exception, much of the prior
research fails to separate structural from nonstructural moves, ignoring their very dif-
ferent genesis and potential diﬀerence in impacts. Conversely, research that examines
them separately—focusing on one and ignoring the other—is also problematic because
the two types of moves are likely related, as parents consider both prior and anticipated
mobility when making decisions about whether to change schools. Thus, studying one
type of move to the exclusion of the other will not fully illuminate the eﬀects of either
type of move and may yield biased impact estimates. Finally, existing mobility research
focuses on short-term impacts—typically on performance in the year of the move—
providing little insight into medium-term eﬀects that may aﬀect learning several years
later. If the medium-term eﬀects of mobility on student performance are negative (pos-
itive), changes in policy may well be warranted to reduce (increase) mobility and/or to
ameliorate the eﬀects. If, however, short-term eﬀects do not persist, then policy eﬀorts
may be better focused on facilitating adjustment and acclimation.

In this paper, we use longitudinal data on students in New York City (NYC) public
elementary and middle schools to isolate the causal eﬀects of school moves on stu-
dent academic performance. Using student-level regression models, we account for
observed and time-invariant diﬀerences between movers and non-movers with rich de-
mographic data on student sociodemographic and education program characteristics
as well as student ﬁxed eﬀects. To address the potential endogeneity of school moves
arising from unobserved, time-varying factors, we use three sets of plausibly exogenous
instruments for mobility in order to provide suﬃcient sources of exogenous variation
for our multiple endogenous school move variables.

First, we exploit the relationship between grade span and mobility. Drawing on
Rockoﬀ and Lockwood (2010) and Schwerdt and West (2013), we construct instruments
for mobility (both structural and nonstructural) using the grade span of a student’s ﬁrst-
grade school. The underlying intuition is as follows. School grade span implies a future
transition point at which a student must move to another school. This ultimately shapes
decisions about the timing of both structural and nonstructural moves because parents
balance the costs and beneﬁts of making a move at a non-mandated time versus allow-
ing their child to remain in the school until the next mandated move. The implication

420

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

is that the grade span of a student’s ﬁrst-grade school can serve as an instrument for
later mobility, both structural and nonstructural.

Second, we use the grade span of a student’s zoned middle school with the reason-
ing that parents may be more likely to have their child make a structural move if there
is a seamless transition between elementary and zoned middle schools (i.e., a student
in a K–5 elementary school zoned for a grades 6–8 middle school), whereas they may
be more likely to have their child make a nonstructural move if there is overlap in the
grades oﬀered by a student’s zoned middle school and his current school (i.e., a student
in a K–6 elementary school is zoned for a grades 6–8 middle school).1

Third, we use indicators of the sale of the building in which a student lives, and fo-
cus our analysis on the roughly 80 percent of public school students who live in renter
households. Because building sale reﬂects characteristics or decisions of a building’s
owner, the timing of sale is plausibly random for renters living in those buildings. Thus,
the sale creates an exogenous, unanticipated shock to residential stability that may in-
duce school mobility as families relocate to housing farther away from their child’s
current school. To be clear, students in rental housing are, on average, more likely to
be disadvantaged and experience housing instability than students in owner-occupied
housing, so that our empirical work will shed light on the impacts of mobility for a large
population of urban students.2

Our paper adds to the growing literature on student mobility by (1) directly address-
ing the endogeneity of mobility using student ﬁxed eﬀects and three diﬀerent sets of
credible instrumental variables to derive causal estimates of mobility’s eﬀects; (2) es-
timating the diﬀerential impact of mobility across timing and context, distinguishing
between summer and mid-year moves, and (within the category of summer moves) fur-
ther distinguishing structural from nonstructural moves, and articulated moves (made
into the new school’s lowest grade served) from nonarticulated moves (made into the
middle of the grade span); (3) examining the medium-term impacts of mobility on stu-
dent performance at the end of middle school; and (4) estimating the eﬀects of mobility
on students in rental housing in a large urban school district. Drawing together the sep-
arate literatures on mobility (i.e., nonstructural moves) and grade span (i.e., structural
moves), we explore and exploit the relationship between structural and nonstructural
moves, past moves and anticipated moves, and housing and schools, in order to shed
new, nuanced insight into the impact of mobility on academic performance.

To preview the results, we ﬁnd that mobility has signiﬁcant and heterogeneous ef-
fects in both the short and medium term. In the medium term, students making struc-
tural moves perform signiﬁcantly worse in both English language arts (ELA) and math,
whereas those making nonstructural moves experience a signiﬁcant increase in ELA

1. There is a wide variety of grade spans in NYC, including many where an elementary school is not perfectly
aligned with a zoned middle school. A little over 35 percent of students in our sample attended a ﬁrst-grade
school whose terminal grade was not aligned with the zoned middle school’s lowest grade (see table A.3 in the
online appendix, which is available on the Education Finance and Policy Web site at www.mitpressjournals.org
/doi/suppl/10.1162/EDFP_a_00198).

2. A large share of renters is also found in other large U.S. cities. For example, in the Miami metropolitan area
63 percent of family households are renters; in Los Angeles, it’s 55 percent. These numbers understate the
share of public school students in renter households if children of owner-occupants disproportionately attend
private schools.

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421

Effect of Moving Schools on Performance

performance only. In the short term, there is an additional negative eﬀect for structural
moves in ELA but not math, whereas nonstructural moves have no additional short-
term eﬀect in either subject. Finally, our ﬁndings suggest that articulated moves, made
to start a destination school in its lowest grade, are driving the positive eﬀect of non-
structural moves for ELA. Thus, our estimates indicate that the type of mobility most
commonly ignored in the literature (structural) has long-term negative consequences
for both math and ELA performance, and articulated, nonstructural moves have signiﬁ-
cant positive consequences for ELA. These eﬀects are meaningful in magnitude and the
results are robust to a variety of alternative speciﬁcations, instruments, and samples.
Importantly, they speak to the eﬀects of mobility among some of the most vulnera-
ble populations of students—those living in rental housing who are disproportionately
poor and underperforming.

The rest of the paper is organized as follows. Section 2 provides a review of the
literature, followed by a framework for understanding mobility in section 3. Section
4 describes the identiﬁcation strategy and empirical models, and data are discussed
in section 5. Results are presented in section 6. We conclude with a discussion and
consideration of implications for policy and future research.

2 . P R E V I O U S L I T E R AT U R E
Early literature is practically unanimous in ﬁnding that school moves are associated
with dips in academic performance. (See Mehana and Reynolds 2004 for a meta-
analysis of quantitative studies from 1975 to 1994; Reynolds, Chen, and Herbers 2009
for a meta-analysis of quantitative studies from 1990 to 2008; and Rumberger 2015 for
a more recent overview of the mobility literature.) These ﬁndings, however, are based
primarily on cross-sectional data, lack reﬁnement in their measurement of mobility,
omit controls for important covariates, and are not based on an empirical approach
that addresses unobserved student and family characteristics that lead to some school
moves. Thus, the results are best viewed as correlational, establishing that students who
move also tend to have lower performance.

The next generation of studies takes a more nuanced approach, using longitudi-
nal data to more ﬁnely characterize moves, explore the number of moves made over a
student’s academic career, and control for a multitude of family and individual charac-
teristics, including pre-move academic performance. These studies suggest there may
be greater heterogeneity in the impact of mobility than described by previous work,
ﬁnding that reductions in performance are cumulative with the number of moves. In a
study of Baltimore’s ﬁrst through ﬁfth graders, Alexander, Entwisle, and Dauber (1996)
ﬁnd that controlling for student background and ﬁrst-grade test scores, there is a signif-
icant negative relationship between the number of school moves and ﬁfth grade read-
ing (but not math) performance. In their study of Chicago low-income, black seventh
graders, however, Temple and Reynolds (2000) ﬁnd that both math and reading scores
decline with each additional move even when controlling for student characteristics
and kindergarten performance.

A second set of longitudinal studies uses nationally representative data (NELS:88)
collected by the National Center for Education Statistics to analyze the relationship be-
tween mobility and high school students’ performance and graduation outcomes. These

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

data include richly detailed characteristics of students and their families as well as infor-
mation on school and residential moves. These studies ﬁnd that moves involving both
residential and school changes are associated with large reductions in math (but not
reading) performance (Pribesh and Downey 1999) and also with a decreased probabil-
ity of graduation (Rumberger and Larson 1998; Swanson and Schneider 1999). Swan-
son and Schneider (1999) ﬁnd that the relationship varies with the timing of the move,
with early moves (before tenth grade) having a positive association with math score
gains between tenth and twelfth grades and late moves (between grades 10 and 12) hav-
ing a negative association. Critically, this generation of longitudinal studies does not
distinguish mid-year mobility, include student ﬁxed eﬀects to minimize the inﬂuence
of unobserved characteristics associated with moving, or address possible endogeneity
of moves. Further, because the data are drawn from high school students, these studies
focus almost exclusively on nonstructural mobility.

In the most recent wave of longitudinal studies, researchers include student ﬁxed
eﬀects to mitigate potential bias due to unobserved time invariant diﬀerences between
movers and non-movers. Hanushek, Kain, and Rivkin (2004) model annual gains in
math scores using three cohorts of Texas elementary school students to examine the
relationship between various types of nonstructural moves made within and across dis-
tricts and regions in Texas. Using a single aggregated measure of mobility, they ﬁnd
a negative and signiﬁcant coeﬃcient on gain scores, but estimates are sensitive to the
speciﬁcation of the model and to controls for school quality.3 Most relevant to our study,
they ﬁnd that within-district moves decrease score gains on the order of 0.024 to 0.088
standard deviation (SD), but this study fails to consider the impacts of structural mobil-
ity, such that the comparison group is composed of both movers and non-movers.

In another study, Grigg (2012) uses longitudinal data on elementary and middle
school students in Metropolitan Nashville Public Schools to examine the relationship
between various kinds of moves (between-year compulsory, between-year noncom-
pulsory, within-year compulsory, and within-year noncompulsory) and achievement
growth. Exploiting a policy change that created an exogenous shock to the timing of
structural moves, Grigg ﬁnds that all types of moves are associated with lower achieve-
ment growth in the year immediately following the move. Furthermore, the ﬁndings
suggest that the move itself, net of other factors, may inﬂuence achievement. Although
the Grigg study makes a substantial contribution to the literature by exploring whether
impacts of school mobility vary by the timing and context of the move and includes
student ﬁxed eﬀects to lessen bias from time-invariant diﬀerences between movers and
non-movers, it does not directly address the endogeneity of school moves arising from
unobserved, time-varying factors. This suggests that the ﬁndings, particularly those re-
garding the impacts of between-year noncompulsory moves, may be biased.

Most school mobility literature focuses exclusively on nonstructural moves, yet
there is a separate body of work on the relationship between grade span and academic
achievement that focuses almost exclusively on structural moves. In the grade span
literature, authors consistently ﬁnd that academic performance dips as students move

3. Speciﬁcally, they ﬁnd that students who move within a district have lower gains in math achievement than
students who change districts. Students who change districts, but stay within a geographic region, also have
lower gains but the magnitude of the estimated eﬀect is smaller.

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423

Effect of Moving Schools on Performance

from lower schools (elementary schools) to upper-level schools (i.e., middle or junior
high schools; see Rockoﬀ and Lockwood 2010; Schwartz et al. 2011; and Schwerdt and
West 2013, for recent examples). More generally, Schwartz et al. (2011) ﬁnd a negative re-
lationship between school transitions—whether structural or nonstructural—and aca-
demic performance.4

Taken together, these ﬁndings indicate that both nonstructural and structural moves
may matter for student performance. Thus, although the grade span and mobility lit-
eratures have been remarkably separate in considering these diﬀerent moves, fully un-
derstanding the eﬀects of student mobility likely requires simultaneous consideration
of structural and nonstructural moves, which we do here.

3 . A F R A M E WO R K F O R M O B I L I T Y : W H Y D O S T U D E N T S M A K E

N O N S T RU C T U R A L M OV E S A N D H OW D O E S M O B I L I T Y
A F F E C T P E R F O R M A N C E ?

Why Do Students Make Nonstructural Moves?
Students make nonstructural moves for either voluntary reasons, where the timing and
destination of the move are chosen by the family, or involuntary reasons, where the
timing and destination are largely determined by shocks to the household (see Grigg
2012 and Rumberger 2015 for detailed discussion of typology of moves).

To understand why parents and families would choose to move, we draw on an eco-
nomic approach to parent (family or student) decision making. In this approach, par-
ents decide whether (and when) to move their student from one school to another by
weighing the present value of the costs and beneﬁts of available schooling options. Par-
ents choose to move their child from school A to school B if the gain in the student’s
performance (or utility, human capital, etc.) is suﬃcient to oﬀset the costs of moving.5
In our discussion below, we focus on the mobility decision made at the family level, and
therefore focus on costs to mobile students and their parents. There are also costs of
mobility to schools (i.e., processing and acclimating new students) and to classmates
(i.e., negative consequences of exposure to high levels of churn in their schools and
classrooms), which we do not consider here.

Costs of moving arise from a variety of sources including the following: (1) admin-
istrative costs, which might include ﬁlling out new forms, providing documentation,
and taking placement exams; (2) logistical costs, which might include making arrange-
ments for transportation, after-school activities, and so on; and (3) psychic costs, which
might arise from adjusting to new routines, adapting to a new physical space, and so
forth. In addition, there may be a loss of social capital among both students and par-
ents, which is likely to decrease student performance. For example, school mobility
may disrupt a student’s peer network, and at the same time reduce parents’ informa-
tion about school policies and culture. After the disruption of peer networks, mobile

4. There are, of course, many other forms of induced mobility: school closings, school reorganizations, student
reclassiﬁcations into special education, student suspensions, program closings, and so forth, and many of
these have a separate literature. These forms of induced mobility are far less common than the other forms of
mobility that are the focus of this paper, however, thus we do not review them here.

5. The model we outline is primarily for expository purposes. There is extensive work in the school choice litera-
ture that examines the topic of how parents choose schools and whether they choose high-performing schools
(see, e.g., Kleitz et al. 2000; Hastings and Weinstein 2008; Rich and Jennings 2015).

424

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

students may be more likely to associate with lower-performing and/or more deviant
peers (Phelan, Davidson, and Yu 1998; South and Haynie 2004; Haynie, South, and
Bose 2006; Dupere et al. 2015) and suﬀer both socially and psychologically (Rumberger
et al. 1999; Dupere et al. 2015). Finally, there may be a cost due to diﬀerences between
the academic programs and curricula in the old and new schools (curricular mismatch),
which could also aﬀect performance. As an example, if two schools cover mathemati-
cal topics diﬀerently, students who move may ﬁnd themselves either over or underpre-
pared for the material being taught at the destination school.

Potential beneﬁts are also myriad—the new school may oﬀer a higher achieving
peer group which in turn may increase a student’s own performance (Hanushek et al.
2003) or a curriculum better matched to a student’s learning (or just one that is more
preferred). It may oﬀer access to better transportation, after-school options, and so
on. The disruption to peer groups and friendship networks may, indeed, be a good
thing if, for example, the student had been bullied or fallen in with a bad crowd at the
origin school. Thus, mobility may, in principle, yield net positive eﬀects on student
performance.6

Because the costs and beneﬁts of mobility depend upon the length of time a student
spends (or would spend) in each alternative school, this suggests that parents will con-
sider both prior and anticipated future moves when making their decision. Put simply,
the beneﬁt of attending a better school is likely to be increasing in the number of years
a student attends that school and the cost of remaining in a worse school will similarly
increase with the number of years he stays in that school.7 Thus, the probability that a
student will move to a better school is increasing in the number of years until the next
structural move at both the origin and destination schools. As an example, parents will
be more likely to move their child from a mismatched or low-quality K–5 elementary
school at the end of third grade than at the end of fourth grade because the fourth grader
will enjoy the beneﬁts of any new school for less time than the third grader will, other
things constant. Similarly, parents will also consider the grade span of nearby middle
schools. For example, parents will be more likely to move their children at the end of
ﬁfth grade than at the end of fourth grade if the closest middle school starts in grade
six because moving their child in fourth grade would result in multiple moves over a
short period of time.

Under this framework, students will make voluntary nonstructural moves if and
only if parents decide that the beneﬁts of the move ultimately outweigh the costs. That
is, if they expect their child to be better oﬀ even after the disruption of a nonstruc-
tural move. Therefore, one would expect children making such voluntary, nonstructural
moves to perform better or no diﬀerently than their peers, on average. Conversely, in-
voluntary moves will tend to be precipitated by unforeseen events where parents are un-
able to weigh the costs and beneﬁts of a mobility decision, such that these involuntary

It should be noted that mobility is also likely to aﬀect not only the mobile student but also his peers. Examining
the spillover eﬀects of mobile students on their nonmobile peers is beyond the scope of this paper but has been
investigated by others (see, e.g., Whitesell, Stiefel, and Schwartz 2016).

7. Similarly, the beneﬁts and costs of moving to a new school will depend upon the number of years until the next
mandated structural move out of that school—that is, the number of years a student will be able to attend the
new school until the next structural move mandated at that school. The shorter the time until an anticipated
structural move in the next school, the shorter the period to amortize the cost of the move to the new school.

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Effect of Moving Schools on Performance

structural moves might well harm performance. The implication is that eﬀects of mo-
bility are likely to be heterogeneous, with some moves improving student outcomes
and others proving harmful. Although the mobility literature does acknowledge this
potential heterogeneity (Rumberger 2015), as noted previously, there is only one other
study of which we are aware that attempts to empirically diﬀerentiate the impacts of
mobility across timing and context (Grigg 2012).

How Might Mobility Affect Performance?
Given that every move is accompanied by a diﬀerent set of costs and beneﬁts, the eﬀect
of mobility on performance is likely to depend, at least in part, on the context of the
move. Structural moves may be less costly than nonstructural moves if schools pro-
vide supports or processes to ease transitions (e.g., orientation programs, freshman
social events) and/or design instruction to stem losses in student performances due
to curricular mismatch. Similarly, articulated nonstructural moves (made to start in
the destination school on time) may be less costly than nonarticulated moves (where
students join a new school in the middle of its grade span). Following a similar logic,
involuntary nonstructural moves made in response to a shock may be more harmful
than voluntary nonstructural moves where parents are able to optimize the timing and
context.

In the end, decisions about whether, and when, to move schools are clearly com-
plicated, reﬂecting multiple motivations that are beyond the scope of this paper to
speciﬁcally identify. Rather, we draw the following key insights from our conceptual
framework, which informs our empirical eﬀorts to estimate causal eﬀects of moves:
(1) the eﬀects on performance are likely to vary with the timing and context of mo-
bility; (2) structural and nonstructural moves are related to one another and should
be considered simultaneously, rather than in isolation; (3) anticipated mobility shapes
the likelihood of mobility in any year and, because both the terminal grade of a stu-
dent’s ﬁrst-grade school and the entry grade of a student’s middle school determine
anticipated future mobility, they also predict mobility each year; and (4) unanticipated
mobility is related to changes in life circumstances, such as changes in housing.8 We
use these insights in the empirical strategy below.

4 . E M P I R I C A L S T R AT E G Y
The primary challenges to identifying the causal eﬀects of school moves on student per-
formance are that (1) movers are likely to be diﬀerent from non-movers and (2) moves
may be endogenous. We propose, in turn, solutions to each of these challenges.

First, movers are likely to be diﬀerent from non-movers in many ways. For example,
households/children who move may be more ambitious and forward-looking (poten-
tially leading to upwardly biased estimates) or more irresponsible and transient (poten-
tially leading to downwardly biased estimates). To address this, we use student ﬁxed
eﬀects to capture time-invariant diﬀerences between students and families, such as

8. Although changes in housing are likely related to school moves, the focus of this particular analysis is on the
impact of school mobility. We examine the impacts of residential mobility and concurrent residential and school
moves in other work (see Cordes, Schwartz, and Stiefel 2017 and Cordes et al. 2016).

426

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

general propensity to move schools, supplemented by a variety of time-varying student
characteristics.

Second, mobility may reﬂect factors that change over time, including those that re-
late directly to schooling (e.g., ﬁt or opportunity) and those that relate only indirectly
(e.g., housing or employment). Without accounting for these factors, any observed
relationship between mobility and student performance may be spurious, reﬂecting
changes in life circumstances rather than the impact of mobility per se. We address
this concern with instrumental variables. In particular, we use three alternative sets
of instruments representing three diﬀerent sources of variation: a set based upon the
grade span of a student’s ﬁrst-grade school, a set based on the entry grade of a student’s
zoned middle school, and a set based on the sale of the building where a student lives,
which are credibly exogenous for our sample of students living in rental housing.

As described earlier, the grade span variables will predict both structural and non-
structural moves—the terminal grade of a student’s ﬁrst-grade school will be highly
correlated with the year in which that student makes a structural move. It will also
capture, in some part, the potential net beneﬁt (or net cost) of making a nonstructural
move and, thus, the probability of making a nonstructural move in any given year. Sim-
ilarly, the grade span of a student’s middle school is correlated with the year in which a
student will make a structural or nonstructural move. If the entry grade of a student’s
middle school is one grade higher than the terminal grade of his elementary school,
this will increase the probability that a student makes a structural move. Conversely, if
the entry grade of a student’s zoned middle school is the same as the terminal grade
of his ﬁrst-grade school, he might be more likely to make a nonstructural move in or-
der to begin middle school on time. Put diﬀerently, the likelihood of a nonstructural
move increases when grade spans of elementary and middle schools overlap than if
they align.

For these instruments to be valid, it is only required that shocks to student achieve-
ment are not anticipated by families, conditional on student controls and ﬁxed eﬀects,
and are therefore not reﬂected in the choice of grade conﬁguration of either a student’s
ﬁrst-grade elementary school or the middle school of that student’s ﬁrst-grade ZIP code.
Similar instruments have been used in other work examining the impacts of grade con-
ﬁguration and middle school entry grade (see Rockoﬀ and Lockwood 2010; Schwerdt
and West 2013).

The building sale variables will predict nonstructural moves, as they capture shocks
to family housing that may precipitate more unanticipated, reactive moves made with
little regard to schooling per se. Because our analysis focuses on a sample of students
living in rental units, and building sale reﬂects the characteristics of owners, this should
meet the exclusion restriction.9

Long-term Effects of Mobility on Academic Performance
We begin with a simple diﬀerence-in-diﬀerence analysis to compare the medium-term
performance of summer and within-year movers to that of their stable peers. To do so,

9. To eliminate concerns that building foreclosure or sale is related to characteristics of tenants in small rental
buildings, we also perform a robustness test, including the exclusion of students who live in buildings that
house two to four families (2–4 family buildings).

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Effect of Moving Schools on Performance

we estimate models that link the performance of student i in academic year t to a series
of variables capturing his school mobility as well as a vector of individual characteristics
and a series of ﬁxed eﬀects. Our baseline model can be written as:

Yit = γ PostSummerrit + θ PostMidYrit + βXit + αi + αt + αg + (cid:6)it,

(1)

where Yit represents performance on standardized tests in ELA or math, given in grades
3 through 8, PostSummer takes a value of 1 if student i made a summer move in year t
and remains 1 in all years after, PostMidYr takes a value of 1 if student i attends a diﬀer-
ent school in March or June of year t than in October of that same year and remains 1
in all years after, Xit represents a set of time-varying student characteristics, including
English proﬁciency, poverty status, and so on, αi are student ﬁxed eﬀects, αt are year
eﬀects that capture common macro factors such as changes in New York City Depart-
ment of Education (NYCDOE) personnel and policies that aﬀect all public students,
and αg are grade eﬀects that capture diﬀerences in policies, programs, and other id-
iosyncrasies speciﬁc to students in a particular grade.10 As is usual, α, β, γ , and θ are
vectors of parameters to be estimated and ε is an error term. In this model, γ captures
the average yearly post-move impact on the academic performance of mobile students
compared with their stable peers.11 We ﬁrst estimate these models using ordinary least
squares (OLS) with robust standard errors and student ﬁxed eﬀects.12 We then turn to
instrumental variables (IV) models.

Instrumental Variables
We begin with a set of variables that captures the number of years until the student
reaches the terminal grade of his ﬁrst-grade school (YearsPre) or after (YearsPost), and
a dummy variable that takes a value of 1 in the year a structural move is anticipated
(Terminal).13 In an alternative speciﬁcation, we include the squares of YearsPre and
YearsPost as instruments; in another, we use a nonparametric form, replacing YearsPre
and YearsPost with a full set of terminal grade indicator variables interacted with student
grade, ϕgT, where g is student i’s current grade and T is student i’s ﬁrst-grade school
terminal grade. To summarize, our ﬁrst set of instruments uses the grade span of a stu-
dent’s ﬁrst-grade school to predict school mobility, exploring diﬀerent functional forms.
In the analysis below, we show results from both the quadratic and nonparametric ter-
minal grade span speciﬁcations.

Our second set of instruments mirrors the ﬁrst, using the entry grade of a student’s
zoned middle school (as of ﬁrst grade) rather than the terminal grade of his ﬁrst-grade
school. To be speciﬁc, we identify a student’s zoned middle school as the middle school
located closest to the centroid of his ﬁrst-grade residence ZIP code. We then construct a
set of variables capturing the number of years until the student reaches the entry grade

10. We can include both grade and year eﬀects because we have multiple cohorts of students, each of which is in

diﬀerent grades in diﬀerent years.

11. This comparison group of stable students includes not only those who never move, but also those who will

move in the future but have not yet made a move.

12. Notice that our models include student ﬁxed eﬀects rather than lagged test scores. Similar results are obtained

in a value-added speciﬁcation.

13. Note that YearsPre, YearsPost, and Terminal are perfectly collinear within-student and so in models containing

student ﬁxed eﬀects, we omit YearsPost.

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of that middle school (YearsPreMS) or after (YearsPostMS), and a dummy variable that
takes a value of 1 in the year that the student’s current grade is equal to the entry grade of
his zoned middle school (Entry).14 In an alternative speciﬁcation, we include the squares
of YearsPreMS and YearsPostMS as instruments; in another, we replace YearsPreMS and
YearsPostMS with a full set of entry grade indicator variables interacted with the stu-
dent’s current grade, ηgE, where g is student i’s current grade and E is the entry grade
of student i’s zoned middle school. As with the ﬁrst-grade terminal grade instruments,
in the results below we show results using both the quadratic and nonparametric forms
of middle school entry grade.

Our third set of instruments exploits building sale for students living in rental hous-
ing. We create indicators for whether a student’s rental housing building in t was sold
between t − 2 and t − 1, interacting this variable with a set of building type dummies
(2–4 family, 5-plus family, and other building type) to allow for diﬀerent eﬀects across
building types, as building sale is likely to be more immediately disruptive for families
in buildings with fewer residential units. We use these indicators as instruments fol-
lowing the logic that building sale might induce residential, and hence school, mobility,
but because the student’s family is a renter and not an owner, the sale will be unrelated
to student performance except through its eﬀect on mobility.

Heterogeneity in Medium-term Impacts: Structural and Nonstructural Moves
We next turn to exploring the heterogeneity in impacts, separating moves into structural
and nonstructural moves:

Yit = γSPostStructit + γNPostNonStructit + θ PostMidY rit + βXit + αi

+ αt + αg + (cid:6)it,

(2)

where PostStruct is an indicator equal to 1 if a student made a structural move in year
t and equal to 1 in all subsequent years, PostNonStruct is an indicator equal to 1 if a
student made a nonstructural move in year t and equal to 1 in all subsequent years, and
all other variables are as previously deﬁned.15

Parsing Short-term and Medium-term Effects
Thus far, we have estimated the medium-term impact on academic performance from
moving schools, but what remains unclear from these models is whether the entire
impact occurs in the year of the move or whether mobility has lasting eﬀects on perfor-
mance. We next turn to parsing the short-term and medium-term eﬀects of mobility by
estimating the following:

Yit = γPSPostStructit + γPNPostNonstructit + γSStructuralit + γNNonStructit

+ θPMPostMidyrit + θMMidyrit + βXit + αi + αt + αg + (cid:6)it,

(3)

14. Note that YearsToMS, YearsPostMS, and Entry are perfectly collinear within-student. Thus in models containing

student ﬁxed eﬀects, we omit YearsPostMS.

15. For students making multiple structural or nonstructural moves, PostStruct and PostNonstruct take a value of 1
in the year of the ﬁrst such move. This is a relatively small fraction of our sample, however, with only 4 percent
of students making more than one structural move and 7 percent making more than one nonstructural move.

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429

Effect of Moving Schools on Performance

where Structural is an indicator equal to 1 if a student makes a structural move in year
t and equal to zero in all years after, NonStruct is an indicator equal to 1 if a student
makes a nonstructural move in year t and equal to zero in all years after, and all other
variables are as deﬁned in equation 2.16 In these models, the coeﬃcients on the Struc-
tural and NonStruct reﬂect any diﬀerential impacts of mobility experienced in the year
of the move itself. That is, the total eﬀect of structural mobility in the year of the move
is represented by γPS + γS and the total eﬀect of nonstructural mobility in the year of
the move is γPN + γN. If the main eﬀects of mobility are short-lived, then we would
expect large and signiﬁcant coeﬃcients on Structural and NonStruct and small, pos-
sibly insigniﬁcant coeﬃcients, on PostStruct and PostNonstruct. Other models further
diﬀerentiate Nonstructural moves to include Articulated moves, which take a value of 1
when a student joins the destination school in the lowest grade served, and NonArticu-
lated moves, which take a value of 1 when a student enters the destination school in the
middle of a grade span.

5 . DATA , M E A S U R E S, A N D D E S C R I P T I V E S TAT I S T I C S
Data and Measures
We use richly detailed student-level administrative data from the NYCDOE for three
cohorts of eighth grade students living in rental units (i.e., excluding students in single-
family homes, condos, and cooperatives, who number slightly more than 23,000) and
making standard academic progress (SAP) from ﬁrst grade through middle school,
allowing us to construct a complete school mobility history. These cohorts are deﬁned
as those students in eighth grade in academic years 2008–10 who progressed through
grades annually (e.g., in ﬁrst grade in 2002, second grade in 2003, third grade in 2004
… and eighth grade in 2009). These SAP students represent over 80 percent of all
students who are continuously enrolled since ﬁrst grade.17 We exclude those students
who enter NYC public schools after ﬁrst grade or exit before eighth grade because we
are unable to observe mobility patterns or performance during years in which these
students were not enrolled in NYC public schools. We focus our analysis on students
in grades 5–8 in order to include information on building sale. Overall, the sample has
more than 88,000 unique students (or about 29,000 students per cohort) attending
roughly 1,044 diﬀerent schools.

Student-level data include information on gender, race/ethnicity, nativity, poverty
(measured as eligibility for free or reduced-price lunch or attendance in a universal free
meal school), English proﬁciency, home language, receipt of special education services,

16. For students making multiple structural or nonstructural moves, Structural and NonStruct take a value of 1 in

each of the years that the student makes such a move.

17. The SAP students are a particularly attractive group of students to study for at least three reasons. First, there
is a long history of their mobility, with potential for heterogeneity in types of moves and for large numbers
of moves, and consistent longitudinal data on their schools and performance. Second, SAP students remain
in one school district (NYC), thus removing the possibility of confounding eﬀects of policies, practices, and
cultures that diﬀer across districts. Third, SAP students exclude students who have experienced signiﬁcant
changes in their academic placements—such as classiﬁcation into self-contained, full time (“ungraded”) spe-
cial education programs—which might obscure the impact of mobility and complicate the interpretation of
conclusions. The result is that SAP students are slightly higher achieving at any point in time than the cross
section of NYC students which may mean that any estimated eﬀects sizes are lower than would be found for
other students. See online Appendix table A.1 for characteristics of other NYC students who are not included
in the sample.

430

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

residence borough, and performance on standardized ELA and math exams adminis-
tered statewide in grades 3–8. Test scores are measured in z-scores, which are standard-
ized to have a mean of zero and a standard deviation of 1 across all students for each
grade–year combination. Each student has a unique identiﬁer enabling us to follow
him over time during his tenure in NYC public schools. These data also include infor-
mation on the school attended at three points of the academic year (October, March,
and June), allowing us to identify students changing schools in the summer (June to
October) and during the academic year (October to March or March to June). We use
this information to construct mobility measures.

For academic years 2005–10, NYCDOE data also contain student address informa-
tion, which we link to information on building characteristics and property transactions
to identify students living in rental units and construct our sale instruments.18 We fo-
cus on renters for four reasons. First, we expect renters as a group to be more mobile
and therefore we are particularly interested in the eﬀects of school mobility on this
population. Second, compared with students in owner-occupied housing, renters are
disproportionately more likely to be poor (82 versus 56 percent), less likely to be white
(13 versus 36 percent), and tend to be lower performing. Therefore, this is the group of
students for whom mobility is most likely deleterious. Third, while the building sale
instruments meet the exclusion restriction for students living in rental housing, they
are almost certainly endogenous for students in owner-occupied units. Focusing on
students in rental housing allows us to examine the impacts of unanticipated school
mobility, which is understudied in the current literature. Finally, because the majority
of NYC public school students (79.6 percent) are renters, this group provides insight
about most of the public school student population in NYC. Our main analysis includes
students living in any rental unit in year t, but we also estimate with two alternative
samples: students who are always renters and excluding students in small (2–4 family)
rental buildings where sale could be endogenous.

Descriptive Statistics
Despite popular notions of “typical” elementary school conﬁgurations, the timing of
mandated moves actually varies signiﬁcantly in NYC; there is simply no single standard
grade span for elementary schools. Although the majority of students in our sample
(63.5 percent) attended a K–5 school in ﬁrst grade, a substantial fraction (19.1 percent)
attended a K–6 school, 7.9 percent attended a K–8 school, and the remaining 9.5 percent
of students attended a school with some other grade conﬁguration. Taken from another
perspective, 58.0 percent of the schools attended by ﬁrst graders in our sample are
K–5, 22.2 percent are K–6, 8.8 percent are K–8, and the remaining 11 percent of schools
serve other grade spans. Therefore, although the vast majority of students will make
at least one structural move before grade 8, there is variation in the timing of when
such moves occur. Similarly, there is quite a bit of variation in when students enter
middle school. For example, whereas 76.5 percent of students are zoned for a middle
school that begins in sixth grade, 14 percent are zoned for a middle school that begins in

18. We deﬁne “owner occupied units” as all single-family homes, condos, and cooperatives. This is a conservative
deﬁnition of “owner occupied,” as some families living in condos are renters. Without unit-level data, however,
we are unable to separate owner-occupants from renter-occupants in condo buildings.

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Effect of Moving Schools on Performance

Table 1.

Eighth Grade Student Characteristics by Mobility History, Renters Only

Summer Moves

Mid-year Moves

Female

Asian

Black

Hispanic

White

Foreign born

Limited English proficient

Non-English at home

Poor

Graded special education

Test scores

5th grade ELA

8th grade ELA

5th grade math

8th grade math

Average # summer moves

Average # structural moves

Average # nonstructural moves

Average # mid-year moves

Grade span of 4th grade school
K to 8+
K to 4

K to 5

K to 6

All others

Observations

Percent of total

None
(1)

0.53

0.08

0.40

0.39

0.12

0.08

0.02

0.36

0.85

0.06

0.005

0.146

0.020

0.132

0.00

0.13

0.59

0.00

0.17

0.07

5,829

6.7%

One
(2)

0.53

0.17

0.27

0.42

0.14

0.10

0.02

0.47

0.80

0.05

0.193

0.240

0.262

0.226

1.00

0.87

0.13

0.09

0.05

0.04

0.73

0.16

0.02

Two plus
(3)

None
(4)

0.53

0.13

0.34

0.45

0.08

0.11

0.02

0.43

0.84

0.07

0.034

0.095

0.073

0.051

2.24

1.05

1.19

0.30

0.06

0.62

0.16

0.10

0.53

0.16

0.29

0.42

0.13

0.10

0.02

0.47

0.81

0.05

0.160

0.218

0.224

0.206

1.22

0.87

0.35

0.00

0.09

0.04

0.67

0.16

0.04

Any
(5)

0.52

0.12

0.38

0.42

0.08

0.11

0.02

0.38

0.86

0.08

−0.031
0.025
−0.017
−0.073
1.65

0.83

0.82

1.25

0.09

0.05

0.63

0.18

0.05

57,403

23,533

76,134

10,631

66.2%

17.1%

87.7%

12.3%

Notes: Mobility history includes all moves made between grades 1—8. Summer moves are made
between June and October. Mid-year moves are made between October and June. Poverty is
defined by eligibility for free or reduced-price lunch, or attendance in a universal free meal
school. Foreign-born students have birthplaces outside the United States. Graded special ed-
ucation students include those receiving full- or part-time services. Test scores are measured
as z-scores (mean zero and standard deviation one for all tested students by grade and year).

ﬁfth grade and another 9 percent are zoned for middle schools with other entry grades
(see table A.2 in the online appendix). This variation in grade span is consistent with
signiﬁcant variation in both the timing and number of moves made by NYC public
school students over the course of their schooling career. Furthermore, this variation
is important for our identiﬁcation strategy, which leverages these diﬀerences in grade
conﬁguration to predict student mobility.

As expected, there are signiﬁcant diﬀerences between movers and non-movers
(table 1). Students who never make a summer move are overwhelmingly enrolled in
K–8 schools in fourth grade, disproportionately black (40 percent), poor (85 percent),
and relatively low scoring (0.005 ELA and 0.020 math, grade 5; and 0.146 ELA and 0.132
math, grade 8), and those making only one summer move are almost entirely enrolled
in K–5 or K–6 schools in fourth grade, disproportionately Asian (17 percent), white (14

432

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Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes

percent), and high scoring (0.193 ELA and 0.262 math, grade 5; and 0.240 ELA and
0.226 math, grade 8).19 Furthermore, of the 66.2 percent of students who make only
one summer move, the overwhelming majority make a structural move (87 percent)
rather than a nonstructural move (13 percent). That is, students with relatively low lev-
els of mobility appear less likely to make voluntary moves. Students making more than
one summer move have characteristics associated with traditionally at-risk students:
higher shares of black (34 percent), Hispanic (45 percent), and poor (84 percent) stu-
dents, and lower performance on ELA and math exams in both ﬁfth and eighth grades.
Moreover, students who make two or more summer moves also make more mid-year
moves than their peers who make zero or one summer move (0.30 compared with 0.13
and 0.09, respectively) and make roughly equal numbers of structural and nonstruc-
tural moves. Students who make at least one mid-year move are the lowest scoring of all
groups (–0.031 ELA and –0.017 math, grade 5; and 0.025 ELA and –0.073 math, grade
8) and are disproportionately black (38 percent) and poor (86 percent). The majority
of mid-year movers also experience at least one summer move during their academic
careers (for relationship between summer and mid-year mobility, see table A.3 in the
online appendix). Thus, movers and non-movers diﬀer in in a variety of ways.

6 . R E S U LT S
Difference-in-Difference Results
We begin with a simple summary analysis of the medium-term relationship between
mobility and academic performance, comparing movers with their stable peers. These
models are most similar to what has been estimated in the previous literature and there-
fore serve as a good starting point for the discussion. As shown in the ﬁrst two columns
of table 2, students who make summer moves earn lower scores in both ELA (0.041)
and math (0.072) in the years following a move, as do mid-year movers (0.031 and
0.045 in ELA and math, respectively), controlling for student characteristics and prior
performance only.20 Introducing student ﬁxed eﬀects and moving to the diﬀerence-
in-diﬀerence results (columns 3 and 4) substantially increases the magnitude of the
coeﬃcients: Summer movers perform 0.079 lower in ELA and 0.118 lower in math,
and mid-year movers perform 0.039 lower in ELA and 0.131 lower in math than their
stable peers. The ﬁnding that the negative relationship between mobility and perfor-
mance is larger with the inclusion of student ﬁxed eﬀects suggests that movers as a
whole are slightly better performing that non-movers (which is consistent with the de-
scriptive results in table 1).

Disentangling structural and nonstructural moves (columns 5 and 6) suggests that
there are likely heterogeneous medium-term eﬀects of mobility: Students who make
structural moves perform almost twice as poorly as students who make nonstructural
moves, and this result is statistically signiﬁcant. Even so, these results indicate that

19. Note, all z-scores are above zero because the sample is restricted to those students who are continuously en-
rolled and making standard academic progress—a group that tends to be higher performing, on average.
Therefore, we expect that any estimated eﬀects sizes for this group are lower than would be found for other
students.

20. Although direct comparisons with Hanushek, Kain, and Rivkin (2004) are diﬃcult because the outcome in
their models is gain scores whereas our outcome is in levels, our results are of the same sign and similar
magnitude to theirs, where they ﬁnd a decrease in gain scores of between 0.024 and 0.088 SDs among within-
district movers.

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433

Effect of Moving Schools on Performance

Table 2.

OLS Results, Relationship Between Mobility and Performance, ELA and Math Exams, Renters Only

ELA
(1)

Math
(2)

ELA
(3)

Math
(4)

ELA
(5)

Math
(6)

Post-summer move

−0.041***
(0.003)

−0.072***
(0.003)

−0.079***
(0.004)

−0.118***
(0.004)

Structural

Nonstructural

Post mid-year move

−0.031***
(0.003)

−0.045***
(0.003)

−0.039***
(0.011)

−0.131***
(0.011)

Student characteristics

Student fixed effects

−0.100***
(0.004)
−0.053***
(0.007)
−0.000
(0.012)

−0.159***
(0.004)
−0.076***
(0.006)
−0.078***
(0.012)

Observations

Unique students
R2

342,685

343,832

342,685

343,832

342,685

343,832

88,241

0.480

88,254

0.590

88,241

0.743

88,254

0.801

88,241

0.743

88,254

0.802

Notes: Robust standard errors in parentheses. Post-summer move is equal to 1 in all years after a student moves schools
between June and October. Post-summer move is equal to 1 in all years after a student moves schools between October
and June. Summer moves made after the completion of a terminal grade are structural moves. Summer moves made after
the completion of a non-terminal grade are nonstructural moves. All models include controls for poverty, English proficiency,
home language, participation in special education services, grade, residence borough, and year. Models in columns (1)
and (2) also control for gender, race, and prior test scores. Models in columns (3) through (6) include student fixed effects.
Sample excludes students living in single family homes, condos, or coops in year t.
***p < 0.01. all else equal, both types of mobility have a negative relationship with student perfor- mance. As previously noted, however, there are reasons to believe these results do not fully account for the endogeneity of school mobility. We therefore turn to IV estimates, which are our preferred speciﬁcation. In the results that follow, although we control for mid-year mobility, we do not report the results because no instruments suitable for the identiﬁcation of this variable are available and we cannot interpret the coeﬃcient estimates as causal.21 What Predicts Mobility? Before turning to the estimates from the IV models themselves, by examining results from the ﬁrst stage model we ﬁrst consider whether and to what extent our proposed instruments actually predict student mobility. If, as described in our conceptual frame- work, structural and nonstructural mobility are related, we should see evidence that grade span is a signiﬁcant predictor of both types of moves. As shown in table 3, columns 1 and 3, the probability of making a structural move is strongly predicted by both elementary and middle school grade span. The probability that a student makes a structural move decreases with YearsPre (but at a decreasing rate) and YearsPost, and increases by 12.3–12.5 percentage points at Terminal. That is, a student is signiﬁcantly more likely to make a structural move in the year after completing the terminal grade of his ﬁrst-grade elementary school and signiﬁcantly less likely to have made a structural move in any other year. For middle school entry grade, the probability 21. Although building sale was predictive of mid-year mobility in the ﬁrst stage, the point estimates and the F of the excluded instruments were quite small and deemed insuﬃcient for identiﬁcation. 434 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d . f / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes Table 3. First-stage Instrumental Variable Results, Summer Moves, ELA Exams ELA Math Post Structural (1) Post Nonstructural (2) Post Structural (3) Post Nonstructural (4) First-grade terminal grade YearsPre YearsPre2 Terminal (= 1 if current grade is terminal grade) YearsPost2 Middle school entry grade YearsPreMS YearsPreMS2 Entry (= 1 if current grade is entry grade) YearsPostMS2 Building Sale Sale of 2–4 family building Sale of 5+ family building Sale of other building type Observations Unique students F excluded (11, 8,150) Prob > F
R2

−0.129***
(0.022)
0.073***
(0.003)
0.123***
(0.010)
−0.033***
(0.002)

−0.177***
(0.035)
0.072***
(0.013)

0.006
(0.012)

0.002
(0.002)

0.011***
(0.004)
−0.003
(0.005)
−0.008
(0.010)

342,685

88,241

203.26

0.000

0.849

0.002
(0.014)
−0.015***
(0.003)
−0.016***
(0.005)
0.003***
(0.001)

0.045***
(0.014)
−0.027***
(0.009)
0.006**
(0.003)
−0.001
(0.001)

0.016***
(0.003)
−0.002
(0.002)

0.005
(0.007)

342,685

88,241

23.40

0.000

0.912

−0.126***
(0.022)
0.073***
(0.003)
0.125***
(0.010)
−0.033***
(0.002)

−0.177***
(0.035)
0.072***
(0.013)

0.006
(0.012)

0.002
(0.002)

0.012***
(0.004)
−0.004
(0.005)
−0.008
(0.011)

343,832

88,254

205.79

0.000

0.849

0.001
(0.014)
−0.014***
(0.003)
−0.017***
(0.005)
0.003***
(0.001)

0.046***
(0.014)
−0.027***
(0.009)
0.007**
(0.003)
−0.001
(0.001)

0.015***
(0.003)
−0.001
(0.002)

0.004
(0.006)

343,832

88,254

23.33

0.000

0.912

Notes: Robust standard errors, clustered by first-grade school by cohort, in parentheses. Coefficients displayed are for
the excluded instruments. Model also includes controls for poverty, English proficiency, participation in special education
services, whether a student made a mid-year move, grade, residence borough, year, and student fixed effects.
**p < 0.05; ***p < 0.01. of making a structural move decreases with YearsPreMS at a decreasing rate. Structural moves are weakly predicted by the sale of 2–4 family homes. Nonstructural moves are predicted by all sets of instruments (columns 2 and 4). For example, the probability that a student makes a nonstructural move decreases 1.6–1.7 percentage points at Terminal and increases with YearsPreMS, at a decreasing rate. That is, a child is less likely to make a nonstructural move the closer he is to the terminal grade of his elementary school and is more likely to make a nonstructural move if he has a longer time until he is eligible to attend his zoned middle school. Again, this is consistent with our intuition that parents are less likely to make a nonstructural move to a school where their child would be nearing the terminal grade (and have to make another move soon) and are more likely to make a nonstructural move if their child will not be eligible to attend the nearby middle school for multiple years. Finally, the probability of a nonstructural move increases 1.5–1.6 percentage points with sale of a l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d / . f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 435 Effect of Moving Schools on Performance 2–4 family building, which is consistent with renters experiencing unanticipated shocks when owners sell buildings. Overall these estimates show that our three sets of instruments are signiﬁcant pre- dictors of both structural and nonstructural moves. Many coeﬃcients are individually signiﬁcant, and the F statistics are large (all greater than 20). We ﬁnd similar results using other speciﬁcations of grade span and a more parsimonious set of instruments, excluding middle school entry grade.22 IV Results As shown in table 4, once we account for the endogeneity of moves, a very diﬀerent picture of mobility emerges. Structural moves continue to have a signiﬁcant negative impact on performance in the years after the move, decreasing performance by 0.096– 0.113 in ELA and 0.182–0.200 in math, depending on the parameterization of the grade span instruments. This is similar to but slightly larger than the results with student ﬁxed eﬀects alone. In contrast to the ﬁxed eﬀects results, however, IV results show nonstructural moves have no signiﬁcant medium-term impact in either ELA or math. Thus, it seems that estimates of the impact of nonstructural mobility from the student ﬁxed eﬀects models may be biased due to the endogeneity of nonstructural mobility. In particular, the compliers who are contributing to the estimated eﬀect in the IV model are likely to be making more “strategic” moves based on the cost–beneﬁt logic described previously, such that OLS estimates did not accurately capture the impact of nonstruc- tural mobility for this group. These estimates conﬂate the short- and medium-term eﬀects of mobility, however. Although it could be that all eﬀects of mobility are due to the disruption in the year of the move itself, it is also possible that eﬀects of mobility due to changes in curriculum or peers take longer to materialize and are therefore only observed in the medium term, or it could be that mobility had both short-term and medium-term eﬀects. To gain a further understanding of when mobility matters relative to the year of the move itself, we parse the short-term and medium-term eﬀects of mobility. As shown in table 5, we see that structural moves have signiﬁcant negative impacts on student performance for both ELA and math in the medium term, and an additional negative impact on short-term ELA performance.23 In ELA, students perform an additional 0.052–0.059 worse in the year of the move itself with small negative eﬀects in the years following the move. In math, there is no diﬀerential impact in the year of the move itself but students perform signiﬁcantly worse in all years following a structural move (0.176–0.186). By contrast, nonstructural moves appear to have lasting positive eﬀects in ELA (0.156–0.275) with no additional impact experienced in the year of the move itself. Nonstructural moves have no signiﬁcant impact on math performance, however. Thus, these estimates provide consistent evidence that structural moves harm student math and ELA performance in the medium-term, and nonstructural moves appear to have a positive eﬀect in ELA in 22. First-stage results from alternative grade span speciﬁcations and a more parsimonious set of instruments are available from authors upon request. Note that because there are only two endogenous variables in this model (structural and nonstructural moves), only two sources of exogenous variation are needed, thus including the third set is not required for estimation. 23. First-stage IV estimations for the results in table 5 are shown in tables A.4 (ELA) and A.5 (math) in the online appendix. 436 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d . / f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes Table 4. ELA and Math Exams Instrumental Variable Results, Effects of Structural and Nonstructural Moves, ELA Math (1) (2) (3) (4) Post-summer move Structural Nonstructural Instruments Building sale Terminal and entry grade Quadratic Nonparametric Observations Unique students −0.113*** (0.017) −0.096*** (0.014) −0.200*** (0.023) 0.020 (0.091) 0.043 (0.069) 0.089 (0.125) −0.182*** (0.019) −0.025 (0.089) Y Y N Y N Y Y Y N Y N Y 342,685 88,241 342,685 88,241 343,832 88,254 343,832 88,254 Notes: Robust standard errors, clustered by first-grade school and middle school by cohort, in parentheses. Post-summer move is equal to 1 in all years after a student moves schools between June and October. Summer moves made after the completion of a terminal grade are structural moves and summer moves made after the completion of a nonterminal grade are nonstructural moves. All models include controls for poverty, English proficiency, home language, participation in special education services, mid-year moves, building type, resi- dence borough, grade, and year. Models in columns (1) and (3) use the number of years between a student’s grade in t and the completion of the terminal grade of his first-grade school (YearsPre) and this number squared, the number of years between the beginning of a student’s grade in year t and the completion of the grade after the terminal grade of a student’s first-grade school (YearsPost), and an indicator equal to one in the summer following the completion of the terminal grade of a student’s first-grade school (Terminal) as grade span instruments. These models also include the number of years between a stu- dent’s grade in t and the entry grade of his closest ZIP code (YearsPreMS) and this number squared, the number of years between a student’s current grade and when he would have entered the lowest grade of his middle school (YearsPostMS), and an indicator equal to one in the summer before a student would enter the closest middle school if he started on time (Entry). Models in columns (2) and (4) use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school (ϕgT) and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school (ηgE). All models use the interaction between an indicator of whether a student’s current building of residence was sold between t − 2 and t − 1 and an indicator for the building type as instruments for school moves. ***p < 0.01. the medium-term. Furthermore, these results highlight the importance of separating the short-term versus medium-term impacts of mobility, as table 4 masks the result that the impacts of nonstructural mobility may take longer to appear. Articulated versus Nonarticulated Moves As noted in our conceptual framework, nonstructural moves include a set that is vol- untary and strategic (likely to improve performance) and another set that is involun- tary and unplanned (likely to harm performance). Although we have no direct data on parental motivation, we further probe the hypothesis that strategic moves are likely to diﬀer from unplanned moves by dividing nonstructural moves into (1) articulated moves, made to allow a student to begin his next school on time, which are arguably more likely to reﬂect strategic behavior, and (2) nonarticulated moves, where a student joins the new school mid–grade span, which are arguably more likely to be made in l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d . f / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 437 Effect of Moving Schools on Performance Table 5. tural and Nonstructural Moves, ELA and Math Exams Instrumental Variable Results, Short-Term and Medium-Term Effects of Struc- ELA Math (1) (2) (3) (4) −0.033 (0.024) 0.275** (0.109) −0.059*** (0.019) −0.005 (0.113) −0.047*** (0.018) 0.156* (0.083) −0.052*** (0.015) −0.024 (0.067) −0.186*** (0.034) 0.115 (0.149) −0.176*** (0.024) −0.040 (0.107) 0.022 (0.022) 0.242* (0.127) −0.001 (0.015) 0.074 (0.071) Y Y N Y N Y Y Y N Y N Y 342,685 88,241 342,685 88,241 343,832 88,254 343,832 88,254 Post-summer move Structural Nonstructural Move in year t Structural Nonstructural Instruments Building sale Terminal and entry grade Quadratic Nonparametric Observations Unique students Notes: Robust standard errors, clustered by first-grade school and middle school by cohort, in parentheses. Post-summer move is equal to 1 in all years after a student moves schools between June and October. Summer moves made after the completion of a terminal grade are structural moves and summer moves made after the completion of a nonterminal grade are nonstructural moves. Move in t is equal to 1 in the year that a student makes a partic- ular type of move and 0 in all other years. All models include controls for poverty, English proficiency, home language, participation in special education services, mid-year moves, building type, residence borough, grade, and year. Models in columns (1) and (3) use the number of years between a student’s grade in t and the completion of the terminal grade of his first-grade school (YearsPre) and this number squared, the number of years between the beginning of a student’s grade in year t and the completion of the grade after the ter- minal grade of a student’s first-grade school (YearsPost), and an indicator equal to one in the summer following the completion of the terminal grade of a student’s first-grade school (Terminal) as grade span instruments. These models also include the number of years be- tween a student’s grade in t and the entry grade of his closest ZIP code (YearsPreMS) and this number squared, the number of years between a student’s current grade and when he would have entered the lowest grade of his middle school (YearsPostMS), and an indicator equal to one in the summer before a student would enter the closest middle school if he started on time (Entry). Models in columns (2) and (4) use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school (ϕgT) and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school (ηgE). All models use the interaction between an indicator of whether a student’s current building of residence was sold between t − 2 and t − 1 and an indicator for the building type as instruments for school moves. *p < 0.1; ***p < 0.01. reaction to some sudden change in circumstance. Using multiple speciﬁcations, we ﬁnd results consistent with these predictions (see table 6). Articulated moves appear to have large, positive, medium-term eﬀects in ELA (0.173–0.229) and no eﬀects in math. Further, students experience no diﬀerential impact in the year of the articulated move itself. Nonarticulated moves, by contrast tend to have little signiﬁcant eﬀect on perfor- mance (and in fact many of the coeﬃcients are large and negative, although insignif- icant). This suggests that there is a particular set of nonstructural moves (articulated moves) that is likely to be beneﬁcial to student performance, and, importantly, this is the set of moves most likely to reﬂect strategic behavior on the part of parents. 438 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d f . / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes Table 6. ulated Moves, ELA and Math Exams Instrumental Variable Regression Results, Robustness, Articulated versus Nonartic- ELA Math (1) (2) (3) (4) −0.046* (0.027) −0.048*** (0.018) −0.136*** (0.048) −0.177*** (0.024) 0.229** (0.102) −0.128 (0.611) 0.173** (0.084) −0.236 (0.386) 0.063 (0.170) 2.590*** (0.998) 0.022 (0.113) −0.564 (0.466) −0.072*** (0.023) −0.051*** (0.015) 0.062* (0.034) −0.000 (0.015) −0.202 (0.212) 0.281 (0.202) −0.036 (0.073) 0.145 (0.162) 0.888** (0.347) −0.584** (0.284) 0.052 (0.076) 0.226 (0.168) Y Y N Y N Y Y Y N Y N Y 342,685 88,241 342,685 88,241 343,832 88,254 343,832 88,254 Post-summer move Structural Non-structural Articulated Nonarticulated Summer move in year t Structural Nonstructural Articulated Nonarticulated Instruments Building Sale Terminal and entry grade Quadratic Nonparametric Observations Unique students Notes: Robust standard errors, clustered by first-grade school and middle school by cohort, in parentheses. Post-summer move is equal to 1 in all years after a student moves schools between June and October. Summer moves made after the completion of a terminal grade are structural moves and summer moves made after the completion of a nonterminal grade are nonstructural moves. Move in year t is equal to 1 in the year that a student makes a particular type of move and 0 in all other years. All models include controls for poverty, English proficiency, home language, participation in special education services, mid-year moves, building type, residence borough, grade, and year. Models in columns (1) and (3) use the number of years between a student’s grade in t and the completion of the terminal grade of his first-grade school (YearsPre) and this number squared, the number of years between the beginning of a student’s grade in year t and the completion of the grade after the terminal grade of a student’s first-grade school (YearsPost), and an indicator equal to one in the summer following the completion of the terminal grade of a student’s first-grade school (Terminal) as grade span instruments. These models also include the number of years between a student’s grade in t and the entry grade of his closest ZIP code (YearsPreMS) and this number squared, the number of years between a student’s current grade and when he would have entered the lowest grade of his middle school (YearsPostMS), and an indicator equal to one in the summer before a student would enter the closest middle school if he started on time (Entry). Models in columns (2) and (4) use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school (ϕgT) and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school (ηgE). All models use the interaction between an indicator of whether a student’s current building of residence was sold between t − 2 and t − 1 and an indicator for the building type as instruments for school moves. *p < 0.1; **p < 0.05; ***p < 0.01. Other Considerations and Robustness Tests We explore the robustness of our results by controlling for school quality, trends in performance before moves, and alternatives to our renter sample. Results are qualita- tively unchanged. The results from alternative speciﬁcations discussed below use the l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d f / . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 439 Effect of Moving Schools on Performance Table 7. Robustness Checks, Instrumental Variable Specifications, School Quality, and Move Pre-trends ELA Math Main results (1) School Quality (2) Pre-trends (3) Main results (4) School Quality (5) Pre-trends (6) −0.047*** (0.018) 0.156* (0.083) −0.052*** (0.015) −0.024 (0.067) −0.042** (0.017) 0.121 (0.082) −0.039** (0.015) 0.000 (0.069) Y Y Y Y −0.037* (0.021) 0.249 (0.167) −0.176*** (0.024) −0.040 (0.107) −0.140*** (0.023) −0.063 (0.102) −0.148*** (0.029) −0.257 (0.196) −0.052*** (0.016) −0.054 (0.065) −0.001 (0.015) 0.074 (0.071) 0.031** (0.014) 0.077 (0.067) 0.029 (0.017) 0.141* (0.075) Y Y Y Y Y Y 0.016 (0.015) 0.126* (0.072) 0.058*** (0.020) −0.039 (0.085) Y Y 342,685 88,241 342,685 88,241 342,685 88,241 343,832 88,254 343,832 88,254 343,832 88,254 Post-summer move Structural Nonstructural Summer move in year t Structural Nonstructural 1 Year Prior to Structural move Nonstructural move Instruments Building sale Terminal & entry grade Nonparametric Observations Unique students Notes: Robust standard errors, clustered by first-grade school and middle school by cohort, in parentheses. Post-summer move is equal to 1 in all years after a student moves schools between June and October. Summer moves made after the completion of a terminal grade are structural moves and summer moves made after the completion of a nonterminal grade are nonstructural moves. Move in t is equal to 1 in the year that a student makes a particular type of move and 0 in all other years. All models include controls for poverty, English proficiency, home language, participation in special education services, mid-year moves, building type, residence borough, grade, and year. All models use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school. All models use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school (ϕgT) and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school (ηgE). School quality is the regression adjusted average ELA performance in that school-grade the prior year. Pre-trends are captured through a series of indicators controlling for one year pre-move. *p < 0.1; **p < 0.05; ***p < 0.01. nonparametric grade span speciﬁcations as instruments for mobility, although results using the quadratic grade-span speciﬁcation are qualitatively similar (see table A.6 in the online appendix). Further, although the results discussed below focus on structural and nonstructural moves, results regarding articulated and nonarticulated moves are similarly robust (see tables A.7 and A.8 in the online appendix). School Quality It is possible that moves are disproportionately made to better (or worse) schools, in which case our estimate of the impact of mobility may, in part, reﬂect changes in school quality such that isolating the impact of mobility (as distinct from improvements in school quality) requires controlling for these changes. Thus, we add a measure of school quality to our regression models (see table 7, columns 2 and 5). Speciﬁcally, we use the average, regression-adjusted value added for each school/grade in the previous year 440 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d / . f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes as a measure of school quality.24 Overall, results are robust. Signs and signiﬁcance of coeﬃcients generally remain, with the exceptions that the medium-term eﬀects of nonstructural moves in ELA are no longer signiﬁcant and the eﬀect of structural moves on math performance is small, positive, and signiﬁcant in the year of the move itself. This slight attenuation suggests that uncontrolled impacts may have been due, in part, to school quality improvements in the case of nonstructural moves and due to decreases in school equality in the case of structural moves. This ﬁnding is entirely consistent with the notion of parents making strategic, nonstructural moves in an eﬀort to improve their child’s outcomes. Prior Performance Another potential concern is that our estimates may capture trends in student perfor- mance in the years leading up to a move. If, for example, movers perform worse in the year before they move, then the negative relationship between structural moves and performance could be an artifact of this pre-existing trend in performance. Thus, we augment our models with a series of indicators for one year prior to structural move and one year prior to nonstructural move, which will capture students’ performance in the year preceding a particular type of move. Our results (see table 7, columns 3 and 6) are generally unchanged and, importantly, we see that students actually perform better or no diﬀerently in the year before a structural move (which is the opposite of what we would expect if our ﬁndings regarding the negative impact of structural moves were in- stead capturing pre-existing dips in student performance). Further, this does not appear to reﬂect a regression to the mean because when student performance is regressed on three years before and three years after a move there is a very obvious structural break in performance in the year of the move (see ﬁgures A.1 and A.2 in the online appendix). While nonstructural moves no longer appear to have a signiﬁcant eﬀect on ELA perfor- mance, the coeﬃcient remains large and positive but imprecisely estimated.25 Alternative Samples Next, we explore sensitivity to alternative samples of students. First, we limit our sample to those SAP students who always live in rental units between grades 5 and 8, to explore the possibility that results are at least partly driven by students moving into and out of rental housing for reasons not accounted for in this model. Results are robust to this change in sample—structural moves result in a signiﬁcant decline in both medium- term ELA and math performance, with a signiﬁcantly larger negative eﬀect on ELA in the year of the move (table 8, columns 1, 2, 5, and 6). Also similar to our main results, we ﬁnd that among students who never live in owner-occupied housing, nonstructural moves have positive impacts in ELA performance in all years following the move, with no eﬀects in math. Second, we exclude students living in small (2–4 family) rental buildings from our sample. The concern with including students in small rental buildings is that sale may, 24. These are calculated as the school/grade ﬁxed eﬀect from a conventional education production function model estimated for the year prior. That is, for year t models we use the t − 1 school ﬁxed eﬀect. 25. Because the sample focuses on students in grades 5–8, we do not have enough years of data to include “trends” in our model. The estimates in online appendix ﬁgures A.1 and A.2 represent coeﬃcient estimates from student ﬁxed eﬀects models estimated on our sample beginning in third grade. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d . f / f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 441 Effect of Moving Schools on Performance Table 8. Robustness, Always-Renter and No 2–4 Family Home Occupant Samples ELA Math Always-Renter No 2–4 Family Homes Always-Renter No 2–4 Family Homes (1) (2) (3) (4) (5) (6) (7) (8) Post-summer move Structural Nonstructural Summer move in year t Structural Nonstructural Instruments Building sale Terminal and entry grade Quadratic Nonparametric Observations Unique students −0.032 (0.024) 0.283*** (0.109) −0.043** −0.055* (0.018) (0.028) 0.165** (0.083) 0.229 (0.146) −0.048** −0.189*** −0.174*** −0.163*** −0.167*** (0.024) (0.020) −0.035 (0.107) (0.026) −0.026 (0.126) 0.199 (0.198) 0.119 (0.101) 0.107 (0.149) (0.040) (0.034) −0.059*** −0.054*** −0.102*** −0.067*** (0.019) −0.004 (0.114) (0.016) −0.092 (0.089) (0.031) −0.389 (0.267) (0.015) −0.039 (0.068) 0.020 (0.021) 0.197 (0.127) −0.002 (0.015) 0.050 (0.071) 0.051 (0.039) 0.588* (0.348) 0.003 (0.017) 0.171* (0.095) Y Y N Y N Y Y Y N Y N Y Y Y N Y N Y Y Y N Y N Y 328,496 328,496 214,290 214,290 329,619 329,619 215,238 215,238 82,698 82,698 57,097 57,097 82,700 82,700 57,146 57,146 Notes: Robust standard errors, clustered by first-grade school and middle school by cohort, in parentheses. Post-summer move is equal to 1 in all years after a student moves schools between June and October. Summer moves made after the completion of a terminal grade are structural moves and summer moves made after the completion of a nonterminal grade are nonstructural moves. Move in t is equal to 1 in the year that a student makes a particular type of move and 0 in all other years. All models include controls for poverty, English proficiency, home language, participation in special education services, mid-year moves, building type, residence borough, grade, and year. Models in columns (1), (3), (5), and (7) use the number of years between a student’s grade in t and the completion of the terminal grade of his first-grade school (YearsPre) and this number squared, the number of years between the beginning of a student’s grade in year t and the completion of the grade after the terminal grade of a student’s first-grade school (YearsPost), and an indicator equal to one in the summer following the completion of the terminal grade of a student’s first-grade school (Terminal) as grade span instruments. These models also include the number of years between a student’s grade in t and the entry grade of his closest ZIP code (YearsPreMS) and this number squared, the number of years between a student’s current grade and when he would have entered the lowest grade of his middle school (YearsPostMS), and an indicator equal to one in the summer before a student would enter the closest middle school if he started on time (Entry). Models in columns (2), (4), (6), and (8) use a vector of indicators that are the interaction between a student’s current grade and the terminal grade of his first-grade school (ϕg), and a vector of indicators that are the interaction between a student’s current grade and the entry grade of his closest middle school (ηgE). All models use the interaction between an indicator of whether a student’s current building of residence was sold between t − 2 and t − 1 and an indicator for the building type, as instruments for school moves. The always renter sample excludes students who ever live in a single- family home, condo, or cooperative between grades 5 and 8. The no 2–4 family home sample exclude students living in 2–4 family homes in year t. *p < 0.1; **p < 0.05; ***p < 0.01. in fact, reﬂect the characteristics of tenants (see table 8, columns 3, 4, 7, and 8). Again, sign and signiﬁcance of most coeﬃcients are largely unchanged—structural moves ap- pear to have negative eﬀects on both ELA and math performance in the medium term, with a signiﬁcantly more negative impact on ELA in the year of the move, and non- structural moves have no impact on performance in either subject. Consistent with other ﬁndings, however, coeﬃcients are large and positive, but imprecisely estimated. 7 . C O N C L U S I O N S The vast majority of students in the United States change schools at least once be- fore reaching ninth grade, and many move multiple times (GAO 2010). As policy mak- ers and educators consider interventions addressing school mobility, it is critical to be aware of several factors: (1) the organization of schools induces student mobility; 442 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d / . f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Amy Ellen Schwartz, Leanna Stiefel, and Sarah A. Cordes (2) there is a relationship between mandated articulation points and the timing of school moves; and (3) structural and nonstructural moves are related. Importantly, dif- ferences in the expected costs, beneﬁts, and motivation of structural and nonstructural moves imply that the consequences for students are likely heterogeneous and disen- tangling these diﬀerences is essential in crafting eﬀective policy. In this paper, we use longitudinal data on NYC public elementary and middle school students to estimate the causal eﬀects of heterogeneous school moves on stu- dent academic performance. Student ﬁxed eﬀects control for time-invariant diﬀerences between movers and non-movers, such as diﬀerences in ability and family circum- stances. Following the logic that the grade span of a student’s ﬁrst-grade elementary and zoned middle schools shapes subsequent mobility, and changes in housing may induce school moves, we use instrumental variables based on the conﬁguration of the ﬁrst-grade school, zoned middle school, and building sales as instruments for school mobility among a sample of students in rental housing. Our results are intuitively appealing. We ﬁnd that the impact of school moves on academic performance is, indeed, heterogeneous. Structural moves have negative con- sequences in both the short and medium terms, while the impact of nonstructural moves is more ambiguous, producing no eﬀects in the short term and either positive or no eﬀects in the medium term. When we disaggregate nonstructural moves into articulated and nonarticulated moves, we ﬁnd evidence to suggest that nonstructural moves made to start the destination school on time (and that are most likely to reﬂect strategic behavior) have positive eﬀects. These results are robust to alternative speciﬁ- cations, instruments, and samples. Perhaps most importantly, we uncover what appear to be permanent eﬀects of structural mobility that have gone unrecognized in previous literature. These results raise questions about the eﬃcacy of the policies followed by most U.S. districts that build structural moves into their school organizations. These struc- tural moves have negative short-term and medium-term consequences, and systems that minimize them have the potential to increase performance. For example, mov- ing to a system of all K–8 schools would eliminate structural mobility, which would increase performance. But a K–8 system also might have the unintended eﬀect of in- creasing nonstructural mobility. In particular, if all schools were K–8 schools, then any student moving schools would make a nonarticulated, nonstructural move. Although our results regarding nonarticulated moves are not signiﬁcant, many point estimates are large and negative (but imprecisely estimated). The net eﬀect of shifting to a K–8 system is, then, unclear a priori and would depend on the increased numbers of non- structural movers compared with the reduced numbers of structural movers. If stu- dents mostly remain in the K–8 school in which they ﬁrst enroll, performance would likely improve. It should be noted, however, that the results presented here are based on a system where the majority of students do, in fact, make structural moves. Therefore, our ability to extrapolate results to a system of K–8 schools where the majority of stu- dents do not make structural moves is limited. It would be worth examining mobility in urban school districts with K–8 systems, such as Chicago, as well as the impacts of reforms, such as those in Philadelphia, that have attempted to change districts over to K–8 systems. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 2 4 4 1 9 1 6 9 2 0 3 7 e d p _ a _ 0 0 1 9 8 p d / . f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 443 Effect of Moving Schools on Performance In the current system where districts often have a variety of grade spans, our results indicate that articulated, nonstructural moves, improve performance. Our estimates likely reﬂect the dominance of the strategic Tiebout-type moves, especially because we control for mid-year moves when many of the reactive moves likely occur.26 Thus dis- tricts may want to provide information that helps parents understand diﬀerences across schools and encourage such moves. Although the mobility and grade span literatures have remained largely separate, our work argues that they should be better integrated, and understanding the impact of mobility on academic performance requires recognizing the relationship between structural and nonstructural moves and between past and anticipated moves. Important directions for future research include more deeply probing underlying mechanisms of school mobility, including contemporaneous residential mobility, and exploring the externalities of mobility on nonmobile students. We look forward to the results of this work. 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