HOLD BACK TO MOVE FORWARD? - IA de Investigación especializada en el MIT

DETÉNGASE PARA AVANZAR?

EARLY GRADE RETENTION AND

STUDENT MISBEHAVIOR

Umut ¨Ozek

American Institutes for

Investigación

1000 Thomas Jefferson St. NW

Washington, corriente continua 20007

uozek@air.org

Abstracto
Test-based accountability has become the new norm in
public education over the last decade. In many states
and school districts nationwide, student performance on
standardized tests plays an important role in high-stakes
decisiones, such as grade retention. This study examines
the effects of grade retention on student misbehavior
in Florida, which requires students with reading skills
below grade level to be retained in the third grade. El
regression discontinuity estimates suggest that grade re-
tention increases the likelihood of disciplinary incidents
and suspensions in the short run, yet these effects dis-
sipate over time. The ﬁndings also suggest that these
short-term adverse effects are concentrated among eco-
nomically disadvantaged and male students.

350

doi:10.1162/EDFP_a_00166
© 2015 Asociación para la política y las finanzas educativas

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Umut ¨Ozek

1. INTRODUCCIÓN
Accountability remains at the forefront of the education policy debate more
than a decade after the No Child Left Behind Act of 2001 was signed into
law. The last decade has witnessed the nationwide implementation of an
educational system where student test performance plays an important role
in high-stakes decisions, such as school closures and teacher retention and
compensación. All states have established test-based performance benchmarks
for students and meeting these standards is a prerequisite for high school
graduation and grade promotion in many states.

Grade retention has been a long-standing and highly debated intervention
for low-performing students. The biggest point of contention is the academic
beneﬁts of grade retention—that is, whether holding back students who are not
ready for more challenging course content translates into higher achievement
in the following years.1 The overarching conclusion of the earlier literature is
that retained students perform signiﬁcantly worse than their promoted peers
in the years that follow. Por otro lado, more recent studies, which better
address the identiﬁcation challenges by using the nonlinearities in retention
políticas, show that grade retention, especially in early grades, has a positive
impact on test scores in the short term.2

Equally contentious are the possible adverse effects of grade retention
políticas. Critics of these policies commonly argue that grade retention imposes
signiﬁcant emotional burdens on students because they are stigmatized as
failing and they face the challenges of adjusting to new peers, which might in
turn lead to student disengagement from schooling. De hecho, two recent studies
have found evidence that grade retention in eighth grade reduces the likelihood
of high school graduation under some conditions (Jacob and Lefgren 2009),
whereas early grade retention has no signiﬁcant impact on student attendance
in the following years (Schwerdt and West 2012).

This study explores another way this emotional burden might manifest
sí mismo, by examining the possible adverse effects of early grade retention on
student disruptive behavior in the years that follow. Using the test-based third-
grade promotion policy in Florida, regression discontinuity estimates suggest
that “just-retained” students are signiﬁcantly more likely to have disciplinary
problems and receive suspensions in the two years that follow, yet these ef-
fects vanish in the long run. Más, subgroup analyses reveal this adverse
effect is mostly concentrated among economically-disadvantaged and male
estudiantes. These ﬁndings might help better assess the costs and beneﬁts of

1. holmes (1989) and Jimerson (1999) provide excellent meta-analysis of the earlier grade retention

investigación.

2. Some examples are Jacob and Lefgren (2004, 2009), Greene and Winters (2007, 2012), and Schwerdt

and West (2012).

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351

GRADE RETENTION AND STUDENT MISBEHAVIOR

grade retention in an era where test-based accountability is becoming the new
norm.

The remainder of the paper is organized as follows. Sección 2 proporciona
background on the Florida early grade retention policy. Sección 3 describes the
data and details the empirical strategy, sección 4 presents the ﬁndings, y
sección 5 concluye.

2. POLICY BACKGROUND
The Just Read, Florida! Initiative, enacted in 2001, uses frequent progress
supervisión, intensive instructional assistance, and grade retention to ensure
all students meet the reading benchmarks described in Florida’s Sunshine
States Standards before they reach the fourth grade, when students tradition-
ally begin to “read to learn” rather than “learn to read.” Since 2002, all third
graders in Florida are categorized into “achievement levels” based on their
reading performance in the curriculum standards-based Florida Curriculum
Assessment Test (FCAT-SSS). If a student fails to perform at achievement
nivel 2 or higher, the law requires that they should not be promoted to the
fourth grade. This discontinuity in grade promotion is the key element of my
identiﬁcation strategy described subsequently.

The legislation requires that schools provide development strategies for
retained students. These include proven effective teaching strategies, assign-
ing retained students to high-performing teachers, participation in summer
reading camps, and at least ninety minutes of reading instruction each day.
If the retained student can demonstrate the required reading level before the
beginning of the following school year or during the school year, they might
be eligible for mid-year grade promotion.

There are several “good cause exemptions” under which students can be
promoted to fourth grade even though they fail the high-stakes reading test.
Por ejemplo, if a student can demonstrate an acceptable level of performance
on an alternative standardized test approved by the State Board of Education,
the student is promoted to the next grade. Más, limited English proﬁciency
(LEP) students with less than two years in the English for Speakers of Other
Languages program, special education students with certain disabilities, estu-
dents who show through a teacher-developed portfolio that they can read at
grade level, and students who have received intensive reading remediation for
two years and who have already been retained twice between kindergarten and
third grade are granted the good cause exemption.3

3. For more information, see www.justreadﬂorida.com/docs/read_to_learn.pdf.

352

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Umut ¨Ozek

3. DATA AND EMPIRICAL STRATEGY
Datos

To examine the consequences of grade retention, I utilize student-level ad-
ministrative data and track seven cohorts of students in Florida entering third
grade for the ﬁrst time between 2003–04 and 2009–10. The data set includes
demographic information on students such as race, género, free or reduced-
price lunch (FRPL) elegibilidad, LEP status, LEP program entry and exit dates,
exceptional student education status, and FCAT-SSS scores in reading and
matemáticas.

More importantly for the purposes of this study, the data set contains de-
tailed information about student disciplinary incidents. En particular, for each
incident, I observe the type of disciplinary/referral action taken and the dura-
tion of the suspension (if applicable) for at least two years after the students in
the sample ﬁrst enter third grade. These incidents can be triggered by a wide
array of student misbehavior, ranging from disruptive behavior in the class-
room to gang involvement.4 Based on the severity of the incident, profesores y
principals have full discretion over the type of action taken, which may include
corporal punishment, in-school or out-of-school suspension, placement in a
different program, and expulsion.

Mesa 1 breaks down by grade the incident rates, types of disciplinary action,
and days suspended. There are several ﬁndings worth highlighting. Primero, inci-
dent rates increase monotonically as grade increases, with a signiﬁcant jump
between elementary and middle school, which might be driven by differences
in teacher and principal tolerance toward student misbehavior between grade
niveles. This trend is also observed in the average suspension days. Segundo,
punishment types differ considerably across grade levels, with more frequent
use of corporal punishment and out-of-school suspensions in earlier grades.
Finalmente, suspension is the most frequent form of student punishment, con
almost all students involved in disciplinary incidents (80 a 90 por ciento) receiv-
ing in-school or out-of-school suspensions. In the analyses that follow, I am
interested in the likelihood of student misbehavior (as measured by the inci-
dent indicator), and the severity of the misbehavior (as measured by whether
the student received an in-school or out-of-school suspension), noting that the
results are similar when the number of suspended days is used as an indicator
of severity.

Mesa 2 presents the descriptive statistics for the entire sample (ﬁrst col-
umn) along with the promoted students with scores below cutoff (segundo

4. The data also contain indicators for severe misbehaviors, such as use of alcohol, drogas, or weapons,
involvement in a hate crime, and involvement in a gang. Because the prevalence of these incidents
is very low at the grade levels in which I am interested in this study, I do not use these indicators as
outcomes in the analysis that follows.

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353

GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 1. Disciplinary Incidents and Punishment Types by Grade

All Students

Students Involved in Disciplinary Incidents

Incident
Rate

Corporal
Punishment

In-School
Suspension

Out-of-School
Suspension

Days
Suspended

0.024
(0.152)

0.033
(0.177)

0.040
(0.196)

0.053
(0.223)

0.062
(0.242)

0.076
(0.265)

0.217
(0.412)

0.253
(0.435)

0.256
(0.436)

0.271
(0.445)

0.260
(0.439)

0.174
(0.379)

0.151
(0.358)

0.065
(0.246)

0.042
(0.201)

0.032
(0.177)

0.027
(0.161)

0.024
(0.153)

0.020
(0.139)

0.007
(0.085)

0.007
(0.082)

0.006
(0.077)

0.003
(0.058)

0.004
(0.065)

0.005
(0.071)

0.006
(0.078)

0.236
(0.424)

0.289
(0.454)

0.306
(0.461)

0.320
(0.467)

0.326
(0.469)

0.493
(0.500)

0.497
(0.500)

0.495
(0.500)

0.543
(0.498)

0.552
(0.497)

0.549
(0.498)

0.540
(0.498)

0.570
(0.495)

0.526
(0.499)

0.521
(0.500)

0.527
(0.499)

0.524
(0.499)

0.526
(0.499)

0.385
(0.487)

0.386
(0.487)

0.389
(0.487)

0.360
(0.480)

0.339
(0.473)

0.337
(0.473)

0.338
(0.473)

1.524
(2.497)

1.591
(2.473)

1.663
(3.051)

1.746
(3.185)

1.826
(4.005)

1.959
(4.301)

2.696
(6.774)

2.908
(8.234)

3.103
(9.151)

3.131
(10.33)

3.035
(10.15)

2.963
(9.992)

2.816
(9.269)

Calificación

Notas: Standard deviations are given in parentheses.

columna) and retained students below cutoff (third column). During this time
marco, apenas 16 percent of all third graders scored below the retention cutoff
y 8 percent were retained, with signiﬁcantly higher retention rates in the
earlier cohorts (apenas 11 percent in the ﬁrst cohort versus 6 percent in the
last). Compared with their promoted peers, retained students are signiﬁcantly
more likely to have disciplinary issues during the third grade, more likely to
come from economically disadvantaged families, more likely to belong to a
racial/ethnic minority group (other than Asian), less likely to have English
as their native language, and more likely to be ﬁrst generation immigrants.
Conditional on low performance on the high-stakes reading test in the third

354

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Umut ¨Ozek

Mesa 2. Estadísticas descriptivas

Below Cutoff: Below Cutoff:

Todo

Promoted

Retained

Third grade

Retained

Disciplinary incident

In-school suspension

Out-of-school suspension

FCAT math score

Age (in months)

Limited English proﬁciency

Special education

FRPL eligible

Male

Blanco

Negro

Hispano

asiático

Foreign born

English not native

0.081
(0.273)

0.051
(0.22)

0.021
(0.143)

0.032
(0.175)

0.035
(1.002)

104.718
(6.039)

0.087
(0.282)

0.150
(0.357)

0.552
(0.497)

0.510
(0.5)

0.460
(0.498)

0.223
(0.416)

0.249
(0.432)

0.023
(0.151)

0.079
(0.27)

0.261
(0.439)

0.107
(0.309)

0.041
(0.198)

0.074
(0.262)

−1.079
(0.934)

109.169
(8.056)

0.238
(0.426)

0.450
(0.497)

0.782
(0.413)

0.591
(0.492)

0.284
(0.451)

0.337
(0.473)

0.331
(0.471)

0.013
(0.115)

0.139
(0.346)

0.363
(0.481)

0.117
(0.322)

0.045
(0.206)

0.081
(0.273)

−1.276
(0.88)

105.699
(6.621)

0.188
(0.39)

0.301
(0.459)

0.802
(0.398)

0.588
(0.492)

0.247
(0.431)

0.409
(0.492)

0.302
(0.459)

0.010
(0.1)

0.086
(0.281)

0.333
(0.471)

norte

1,298,460

110,373

98,746

Nota: Standard deviations are given in parentheses.

calificación, these differences seem to subside considerably, yet the promoted low
performers are signiﬁcantly more likely to be LEP and/or special education
students because of the exemption clauses in the policy.

The biggest challenge in revealing the causal impact of grade retention is
that the retention decisions are typically made by teachers and principals based

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355

GRADE RETENTION AND STUDENT MISBEHAVIOR

on student attributes that are not necessarily observable to the researcher,
such as parental involvement and student motivation, which in turn affect
future student outcomes. Por lo tanto, regression-adjusted differences based
on observable student attributes between promoted and retained students are
likely to yield biased inferences. en este estudio, I utilize the non-linearity created
by the retention policy and compare students who scored right below and right
above the promotion cutoff in a regression discontinuity framework. In what
follows, I detail this empirical approach.

Empirical Framework
Let Si denote the difference between the third-grade reading score of student
i and the retention cutoff, with negative values indicating scores below cutoff.
Deﬁning treatment, Ri , as being retained at the end of third grade, a common
regression model representation of this evaluation problem would become:

Di = α + β Ri + εi ,

(1)

where Di is the disciplinary outcome of student i. Because students on both
sides of the retention cutoff can be promoted or retained under the Florida
política, I utilize a fuzzy regression discontinuity (RD) design where the causal
impact of retention on disciplinary problems is given by:

β =

lim
S↑0
lim
S↑0

mi [D|S] − lim
S↓0
mi [R|S] − lim
S↓0

mi [D|S]

mi [R|S]

(2)

β will yield an unbiased estimate of the causal impact of retention provided
that there is a signiﬁcant jump in retentions at the cutoff (large denominator
in equation 2) y eso

lim
S↑0
lim
S↑0

mi [ε|S] − lim
S↓0
mi [R|S] − lim
S↓0

mi [ε|S]

mi [R|S]

= 0.

(3)

There are several ways to estimate β in this context. First is to estimate equa-
ción 2 nonparametrically using kernel-weighted local polynomial smoothing
initially as proposed by Hahn, Todd, and van der Klaauw (2001) and later de-
veloped by Porter (2003) to include higher-order polynomial estimators. Este
method reduces the possibility of misspeciﬁcation bias in parametric models
and achieves the optimal rate of convergence. When the selection variable is
discreto, sin embargo, as in this case, a nonparametric estimator might lead to bi-
ased estimates as it is not feasible to compare averages within arbitrarily small
neighborhoods around the cutoff (Lee and Card 2008). Por lo tanto, following

356

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Umut ¨Ozek

Cifra 1. Retention and Third-Grade Reading Scores. Notas: The ﬁgure presents the local linear
smoothing of the retention indicator on relative reading score of the student separately for the left
of the cutoff date and the right. The triangle kernel and a bandwidth of 5 points are used in the
estimation. The solid circles represent raw cell means.

Lee and Card (2008), I estimate equation 2 parametrically using the following
two-stage least squares framework:

Ri = φ + δ Bi + k(Y ) + k(Y ) ∗ Bi + υi ,

Yi = α + β ˆRi + k(Y ) + k(Y ) ∗ Bi + εi ,

(4a)

(4b)

where k(Y ) is a polynomial function of the relative reading score and Bi is an
indicator for students below the cutoff. In the preferred speciﬁcation, I limit
the analysis to students within a bandwidth of 5 puntos, because increasing
bandwidth is expected to produce biased estimates in situations such as the
case examined here, where the selection variable is correlated with the outcome
conditional on treatment status. I check the robustness of this speciﬁcation
using different bandwidths (1, 10, 15, y 20) and polynomial orders (0, 1, 2,
3, y 4), and cluster the standard errors at the relative reading score level as
suggested by Lee and Card (2008).

4. RESULTADOS
I ﬁrst check to make sure there is a signiﬁcant discontinuity in the treatment
variable at the cutoff. Cifra 1 presents the local linear smoothing of the
retention indicator on the relative reading score, calculated separately for each

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357

GRADE RETENTION AND STUDENT MISBEHAVIOR

side of the cutoff using the triangle kernel and the bandwidth of 5 puntos, con
the solid circles representing the retention rate for each test score. This ﬁgure
shows that students who score just below the retention cutoff are approximately
30 percentage points more likely to be retained compared with their peers who
scored right at the cutoff. This is true for each cohort with slightly larger
discontinuities observed for the third graders in the earlier cohorts.

Cifra 2 presents a graphical inspection of the effects of retention on
student discipline, replacing the retention indicator in ﬁgure 1 with whether
the student was involved in a disciplinary incident in the next two years (en
the upper panel) or in the past two years (lower panel). Whereas the third
graders who scored right below the promotion cutoff were no more likely to
have disciplinary issues during the previous two school years than their peers
on the other side, they are signiﬁcantly more likely to be involved in incidents
in the following two years. Using the jump in the retention rate at the cutoff
displayed in ﬁgure 1, the simple Wald estimator given in equation 2 indicates
the magnitude of this difference is roughly 4–5 percentage points. This gap
approximately corresponds to one fourth of the control mean at the cutoff.

Mesa 3 presents the short-term effects of grade retention on disciplinary
incidents and suspensions in the years following the retention. In the ﬁrst two
columnas, I estimate equations 4a and 4b using a bandwidth of 5 points and a
linear k(Y ), and the last two columns use 20 points and a quartic polynomial.
In all speciﬁcations, I include cohort ﬁxed-effects to take differences between
cohorts into account, although the results are robust to the exclusion of these
efectos fijos.

The estimated effects reported in columns labeled as (I) align well with
the earlier graphical analysis. Grade retention increases the likelihood of dis-
ciplinary incidents by about 3 a 5 puntos de porcentaje (30 a 50 por ciento de la
control mean of 0.107 at the cutoff) in the following year, and roughly by 5 a 6
puntos de porcentaje (40 a 50 percent of the control mean of 0.132 at the cutoff)
in the second year that follows. Just-retained students are also signiﬁcantly
more likely to receive suspensions in the following two years. The estimated
effects are positive for both in-school and out-of-school suspensions, pero el
point estimates are only statistically signiﬁcant for out-of-school suspensions
in the ﬁrst year and in-school suspensions in the second year. One possible
explanation behind this discrepancy is that the retained students are involved
in more severe incidents in the ﬁrst year after they are retained, y por lo tanto
receive out-of-school suspensions, compared with the second year.

Mesa 4 explores the effects of grade retention beyond the ﬁrst two years. En
this analysis, I restrict the sample to earlier cohorts (ﬁrst-time third graders be-
entre 2003 y 2006) that are observed for at least six years after third grade.
The estimates presented in columns (I) indicate that there are no signiﬁcant

358

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Cifra 2. Retention and Disciplinary Incidents. Notas: The two panels examine the disciplinary
incidents in the two years following (upper panel), and in the two years prior to (lower panel), el
ﬁrst time students enter the third grade. Both panels present the local linear smoothing of the
corresponding incident indicator on relative reading score of the student, separately for the left and
the right of the retention cutoff score.

discontinuities at the retention cutoff in the long-run, except for the signiﬁ-
cant negative discontinuity during the third year after retention. Important to
note here, sin embargo, is that during that year the majority of the just-promoted

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359

GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 3.

Early Grade Retention and Misbehavior Same Age Comparisons, Short-Term Effects

Score Range

1 year later

Disciplinary incident

In-school suspension

Out-of-school suspension

2 años después

Disciplinary incident

In-school suspension

Out-of-school suspension

First-stage discontinuity

Lineal

Quartic

(I)
5

(II)
5

(I)
20

(II)
20

0.031∗∗∗
(0.008)

0.009
(0.009)

0.037∗∗∗
(0.012)

0.050∗∗∗
(0.010)

0.034∗∗∗
(0.003)

0.025∗∗
(0.007)

0.313∗∗∗
(0.007)

0.039∗∗∗
(0.009)

0.009
(0.009)

0.045∗∗∗
(0.013)

0.055∗∗∗
(0.011)

0.033∗∗∗
(0.004)

0.028
(0.009)

0.319∗∗∗
(0.006)

0.046∗∗∗
(0.014)

0.013
(0.011)

0.046∗∗∗
(0.016)

0.048∗∗∗
(0.017)

0.040∗∗∗
(0.009)

0.018
(0.012)

0.314∗∗∗
(0.008)

0.064∗∗∗
(0.012)

0.016
(0.011)

0.062∗∗∗
(0.016)

0.054∗∗
(0.020)

0.040∗∗∗
(0.009)

0.025∗
(0.014)

0.322∗∗∗
(0.007)

norte

Cohort FE

Student covariates

Within-school peer average

43,793

178,248

Sí

Notas: Robust standard errors, clustered at the relative reading score level, are given
entre paréntesis. Discontinuity estimates are obtained parametrically using the speciﬁed
polynomial order and the score range. Columns labeled as (I) presentar las estimaciones
from the base speciﬁcation in equations 4a and 4b, with the addition of cohort ﬁxed
efectos, and the columns labeled as (II) add student covariates and within-school peer
averages to the estimation.
∗Statistical signiﬁcance at 10%; ∗∗statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁ-
cance at 1%.

students attend middle school whereas their just-retained peers are in ele-
mentary school. It is possible, por lo tanto, that the observed discontinuities are
reﬂections of the aforementioned jump in the incident and suspension rates
between elementary and middle grades.

The estimates presented so far have relied on the same-age comparisons be-
tween retained and promoted students. The primary concern in this approach
is that the estimated differences in disciplinary incidents might be caused by
the differences in incident rates across grades. Nota, sin embargo, that the incident
rates increase with grade, as reported in table 1. Más, mesa 5 presenta el
same-grade comparisons between retained and promoted students around the

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Mesa 4.

Early Grade Retention and Misbehavior Same Age Comparisons, Long-Term Effects

Score Range

3 años después

Disciplinary incident

In-school suspension

Out-of-school suspension

4 años después

Disciplinary incident

In-school suspension

Out-of-school suspension

5 años después

Disciplinary incident

In-school suspension

Out-of-school suspension

First-stage discontinuity

norte

Cohorts

Cohort FE

Student covariates

Within-school peer average

Lineal

Quartic

(I)
5

(II)
5

(I)
20

(II)
20

−0.092∗∗
(0.045)

−0.108∗∗∗
(0.020)

−0,042
(0.028)

0.016
(0.028)

0.007
(0.018)

0.020
(0.030)

−0,009
(0.013)

0.006
(0.013)

−0,017
(0.012)

0.012
(0.036)

−0.012
(0.014)

−0,042
(0.028)

0.028
(0.027)

0.021
(0.015)

0.020
(0.030)

−0,008
(0.018)

0.0001
(0.012)

−0,017
(0.012)

−0.122∗∗∗
(0.051)

−0.137∗∗∗
(0.021)

−0.047
(0.033)

0.033
(0.036)

0.027
(0.026)

0.021
(0.037)

−0,007
(0.026)

−0.005
(0.019)

−0,004
(0.020)

−0,021
(0.039)

−0.037∗∗
(0.018)

−0.047
(0.032)

0.042
(0.036)

0.035
(0.026)

0.021
(0.037)

−0,011
(0.028)

−0.018
(0.016)

−0,004
(0.020)

0.347∗∗∗
(0.009)

0.356∗∗∗
(0.010)

0.345∗∗∗
(0.009)

0.356∗∗∗
(0.010)

21,712

87,924

2003–2006

Sí

Notas: Robust standard errors, clustered at the relative reading score level, are given in
parentheses. Discontinuity estimates are obtained parametrically using the speciﬁed polyno-
mial order and the score range. Columns labeled as (I) present the estimates from the base
speciﬁcation in equations 4a and 4b, with the addition of cohort ﬁxed effects, and the columns
labeled as (II) add student covariates and within-school peer averages to the estimation.
∗∗Statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.

cutoff. Eso es, I compare promoted students with their retained peers around
the cutoff when they reach the same grade level. Una vez más, I restrict the
sample to the 2003–06 cohorts who are old enough to reach eighth grade by
the end of my sample. The ﬁndings reinforce the conclusion that the retained

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361

GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 5.

Early Grade Retention and Misbehavior Same Grade Comparisons

Score Range

4th grade

Disciplinary incident

In-school suspension

Out-of-school suspension

5th grade

Disciplinary incident

In-school suspension

Out-of-school suspension

6th grade

Disciplinary incident

In-school suspension

Out-of-school suspension

7th grade

Disciplinary incident

In-school suspension

Out-of-school suspension

8th grade

Disciplinary incident

In-school suspension

Out-of-school suspension

First-stage discontinuity

norte

Cohorts

Lineal

Quartic

(I)
5

(II)
5

(I)
20

(II)
20

0.045∗∗∗
(0.016)

0.009
(0.008)

0.044∗∗
(0.020)

0.055∗∗∗
(0.021)

0.046∗∗∗
(0.014)

0.023∗∗
(0.011)

0.051
(0.042)

0.008
(0.020)

0.055∗∗
(0.025)

−0,004
(0.022)

−0,002
(0.012)

−0,008
(0.024)

0.005
(0.023)

0.004
(0.026)

−0.0003
(0.013)

0.329∗∗∗
(0.002)

0.046∗∗∗
(0.009)

0.005
(0.007)

0.046∗∗∗
(0.015)

0.056∗∗∗
(0.016)

0.047∗∗∗
(0.013)

0.026∗∗∗
(0.008)

0.059∗∗
(0.030)

0.016
(0.020)

0.060∗∗∗
(0.016)

0.013
(0.024)

0.005
(0.011)

0.004
(0.028)

0.024∗
(0.013)

0.022
(0.019)

0.012
(0.018)

0.046∗∗
(0.021)

0.004
(0.012)

0.050∗∗
(0.022)

0.065∗∗∗
(0.026)

0.053∗∗∗
(0.020)

0.018
(0.016)

0.025
(0.046)

−0.027
(0.019)

0.056∗∗
(0.027)

0.017
(0.033)

0.014
(0.020)

0.009
(0.031)

0.017
(0.029)

−0,016
(0.022)

0.035
(0.026)

0.319∗∗∗
(0.006)

0.314∗∗∗
(0.008)

21,712

87,924

0.050∗∗∗
(0.014)

0.002
(0.010)

0.054∗∗∗
(0.016)

0.063∗∗∗
(0.020)

0.053∗∗∗
(0.018)

0.021∗
(0.012)

0.031
(0.034)

−0.019∗
(0.011)

0.062∗∗∗
(0.019)

0.037
(0.033)

0.022
(0.020)

0.028
(0.034)

0.032
(0.020)

0.003
(0.019)

0.044∗
(0.024)

0.322∗∗∗
(0.007)

87,924

2003–2006

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Mesa 5. Continuado.

Score Range

Cohort FE

Student covariates

Within-school peer average

Lineal

Quartic

(I)
5

Sí

(II)
5

Sí

(I)
20

Sí

(II)
20

Sí

Notas: Robust standard errors, clustered at the relative reading score level, are given in paren-
tesis. Discontinuity estimates are obtained parametrically using the speciﬁed polynomial order
and the score range. Columns labeled as (I) present the estimates from the base speciﬁcation
in equations 4a and 4b, with the addition of cohort ﬁxed effects, and the columns labeled as (II)
add student covariates and within-school peer averages to the estimation.
∗Statistical signiﬁcance at 10%; ∗∗statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.

students are signiﬁcantly more likely to have disciplinary problems in the short
run, yet these differences dissipate in middle school.

Identiﬁcation Checks

Other than the causal effect of retention, there are several alternative scenarios
that might explain the observed discontinuities in disciplinary problems. Uno
of these explanations is the differences in student attributes (p.ej., prior dis-
ciplinary problems, logro, demographics, family characteristics, y
other observed and unobserved traits) between retained and promoted stu-
dents around the cutoff. I investigate this possibility by replacing the disci-
plinary outcomes in equation 4b with student characteristics and check for
possible discontinuities. The ﬁndings presented in table 6 reject this explana-
tion and show that the students on the two sides of the retention cutoff are
comparable along these observed traits. To further examine whether differ-
ences in student attributes explain the gaps in disciplinary outcomes at the
cutoff, columns labeled as (II) in tables 3, 4, y 5 present the parametric esti-
mates controlling for observed student attributes listed in table 6, junto con
cohort ﬁxed-effects and within-school average peer outcomes. Tables A.1 and
A.2 in the Appendix present the full ﬁrst- and second-stage results for column
II in table 2. The inclusion of these covariates does not seem to signiﬁcantly
change the estimated impact of retention, except for the discontinuities in the
third year after retention.

Unlike test scores, disciplinary outcomes are not standardized measures
across educational settings. Eso es, given two identical student behaviors,
different disciplinary outcomes might emerge based on factors such as the
principal attitude or the school environment. To see whether such differences

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363

GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 6.

Early Grade Retention and Student Characteristics

Score Range/Bandwidth

Current year

Disciplinary incident

In-school suspension

Out-of-school suspension

Prior year

Disciplinary incident

In-school suspension

Out-of-school suspension

Limited English proﬁciency

Special education

FRPL eligible

Male

Age in 3rd grade (in months)

FCAT Math score: 3rd grade

Blanco

Negro

Hispano

asiático

Foreign born

English not native

Peer incident rate

1 year later

Lineal
5

Quartic
20

−0.012
(0.023)

0.002
(0.011)

−0,011
(0.015)

−0.005
(0.007)

−0.015∗
(0.009)

−0,004
(0.005)

0.019
(0.012)

0.002
(0.012)

0.003
(0.017)

−0.050∗∗∗
(0.013)

0.572∗∗∗
(0.220)

0.006
(0.022)

−0.020
(0.029)

−0,009
(0.009)

0.033
(0.030)

−0.034
(0.023)

−0,006
(0.011)

−0,021
(0.018)

−0,007
(0.010)

−0.019
(0.016)

−0.005
(0.006)

0.025
(0.015)

−0.014
(0.021)

−0,004
(0.018)

−0.043∗∗∗
(0.015)

0.392
(0.282)

0.070
(0.045)

0.001
(0.035)

−0.020
(0.020)

0.022
(0.042)

−0.016∗∗∗
(0.004)

−0.023∗∗∗
(0.005)

0.027
(0.021)

0.035
(0.022)

0.004
(0.021)

0.027
(0.027)

−0.0003
(0.002)

0.0009
(0.003)

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Mesa 6. Continuado.

Score Range/Bandwidth

2 años después

3 años después

4 años después

5 años después

Lineal
5

−0.0002
(0.003)

−0.110∗∗∗
(0.007)

−0,007
(0.005)

0.001
(0.008)

Quartic
20

0.0005
(0.003)

−0.101∗∗∗
(0.006)

−0,008
(0.006)

−0,004
(0.009)

Notas: Robust standard errors, clustered relative reading score
nivel, are given in parentheses. Discontinuity estimates are ob-
tained parametrically using the speciﬁed polynomial order and
the score range. Both speciﬁcations include the cohort ﬁxed ef-
efectos.
∗Statistical signiﬁcance at 10%; ∗∗∗statistical signiﬁcance at 1%.

explain the differences between retained and promoted students, I calculate
the percentage of peers involved in disciplinary incidents at the school-year
level for each student. Si, por ejemplo, retained students are attending schools
with stricter principals, one would expect to observe higher peer incident
rates for these students. The last ﬁve rows of table 5 present the discontinuity
estimates along this dimension and show that students on the two sides of the
cutoff are attending similar schools. This is not the case for the third year after
retention, sin embargo, which presents evidence justifying the earlier explanation
for the third-year discontinuity in disciplinary problems. De hecho, when peer
differences are accounted for in column II of table 4, the estimated differences
at the cutoff in the third year are no longer statistically signiﬁcant.

Another concern regarding identiﬁcation in the RD design in this context,
as noted in McCrary (2008), is the possibility of selection variable manipulation
(es decir., the reading scores in this case) by teachers and/or principals. Under this
scenario, one would expect to see an unusual discontinuity in the test score
distribution around the promotion cutoff. It is important to note here that
this is very unlikely, because FCAT scores are assessed without any teacher
or principal involvement. Regardless, I present graphical evidence to dismiss
this possibility, because the formal test developed by McCrary (2008) is not
appropriate in this case as it relies on local linear regressions, which might
lead to incorrect inferences when the running variable is discrete (Card and
Sotavento 2008). Cifra 3 provides the reading score distribution around the cutoff.
The number of students in each bin seems to be increasing as the retention
cutoff falls on the left tail of the normally distributed reading scores, pero el

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365

GRADE RETENTION AND STUDENT MISBEHAVIOR

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Cifra 3. Selection Into/Out of Treatment. Notas: The ﬁgure presents the number of students in
each reading score bin between 20 points below and above the retention cutoff, which is shown by
the vertical line.

results present no unusual discontinuity at the cutoff and hence no evidence
of strategic sorting around the cutoff.

Finalmente, differential attrition might lead to biased estimates if retained
students leave the sample at higher rates than their promoted peers or if
retained stayers differ from the promoted stayers in the following years. I
ﬁrst check the attrition rates around the cutoff. The discontinuity estimates
presented in table 7 suggest retained students are equally likely to leave the
Florida public school system as the promoted students around the cutoff.
Segundo, I compare the just-retained stayers with just-promoted stayers along
observable student characteristics. Conditional on staying in the sample during
the following two years, comparisons reported in table 8, combined with the
results in table 6, suggest the retained leavers are quite similar to promoted
students who left the sample in the years that follow.

Robustness Checks

To check the robustness of these ﬁndings, mesa 9 repeats the main analysis
using various bandwidths and polynomial orders, ranging from a bandwidth
de 1 and order zero, under which the RD design is equivalent to the traditional
instrumental variable framework, to a bandwidth of 15 points and quartic poly-
nomial. In all speciﬁcations, I include the aforementioned student covariates,
average peer outcome at the school-level, and cohort ﬁxed-effects to improve

366

Umut ¨Ozek

Mesa 7.

Early Grade Retention and Attrition

Score Range/Bandwidth

Left at the end of the

Current year

First year after

Second year after

Third year after

Lineal
5

Quartic
20

0.0006
(0.005)

0.009
(0.008)

0.008
(0.013)

0.009
(0.008)

−0,006
(0.005)

0.011
(0.009)

0.011
(0.012)

0.021∗∗∗
(0.007)

the precision of the estimates. The estimated discontinuities are positive and
statistically different from zero in all but two speciﬁcations. The impact sizes
are comparable to the ones in the original speciﬁcations, que van desde 3 a 7
percent in the ﬁrst year and 4 a 10 percent in the second year.

I also conduct additional robustness checks using different covariates in
el modelo. Table A.3 presents estimates from regression models where (1) I
also control for special education and limited English proﬁciency indicators
interacted with being below the cutoff to account for the exemption clauses in
the policy (in column I); y (2) I use school ﬁxed-effects to eliminate time-
invariant across-school differences in disciplinary outcomes. The ﬁndings are
almost identical to the estimates presented in table 3, reinforcing the previous
conclusions.

Subgroup Analysis

Having provided evidence that grade retention, on average, leads to disruptive
comportamiento, I now check to see whether the estimated effects of grade reten-
tion are heterogeneous by observed student characteristics. Mesa 10 presents
the estimated discontinuities in whether the student was involved in a disci-
plinary incident in the following two years by socioeconomic status in the ﬁrst
panel, by race/ethnicity in the second panel, and by gender in the third panel.
All regressions include student covariates, cohort ﬁxed effects, and within-
school average peer outcome. The most striking result is that the adverse ef-
fect of retention is primarily concentrated among economically disadvantaged

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GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 8.

Attrition and Student Characteristics

Score Range/Bandwidth

Current year

Disciplinary incident

In-school suspension

Out-of-school suspension

Prior year

Disciplinary incident

In-school suspension

Out-of-school suspension

Limited English proﬁciency

Special education

FRPL eligible

Male

Age in 3rd grade (in months)

FCAT Math score: 3rd grade

Blanco

Negro

Hispano

asiático

Foreign born

English not native

In Sample – Following
Año

In Sample – Two Years
Más tarde

Lineal
5

Quartic
20

Lineal
5

Quartic
20

−0,017
(0.023)

0.002
(0.011)

−0,013
(0.015)

−0,006
(0.006)

−0.016∗∗∗
(0.002)

−0.005
(0.006)

0.018
(0.011)

0.005
(0.012)

0.001
(0.015)

−0.051∗∗∗
(0.014)

0.585∗∗∗
(0.215)

0.020
(0.018)

−0,025
(0.028)

−0,011
(0.010)

0.038
(0.029)

−0.040∗
(0.022)

−0,006
(0.010)

−0,025
(0.018)

−0,008
(0.010)

−0.020∗∗∗
(0.007)

−0,006
(0.007)

0.026
(0.016)

−0,011
(0.021)

−0,006
(0.017)

−0.043∗∗
(0.016)

0.369
(0.274)

0.084∗∗
(0.040)

−0,004
(0.034)

−0,023
(0.019)

0.028
(0.041)

−0.019
(0.025)

0.002
(0.012)

−0,016
(0.016)

−0.005
(0.006)

−0.014∗∗∗
(0.003)

−0,006
(0.005)

0.010
(0.013)

0.004
(0.012)

−0,003
(0.013)

−0.061∗∗∗
(0.013)

0.596∗∗
(0.276)

0.016
(0.015)

−0,031
(0.027)

−0,004
(0.010)

0.036
(0.030)

−0.016∗∗∗
(0.004)

−0.023∗∗∗
(0.005)

−0.016∗∗∗
(0.004)

0.025
(0.021)

0.037∗
(0.021)

0.002
(0.021)

0.029
(0.027)

0.023
(0.020)

0.032
(0.022)

−0.046∗
(0.024)

−0,007
(0.012)

−0,029
(0.018)

−0,007
(0.009)

−0.017∗
(0.007)

−0,007
(0.006)

0.012
(0.017)

−0,007
(0.019)

−0,016
(0.018)

−0.053∗∗∗
(0.015)

0.321
(0.307)

0.094∗∗∗
(0.033)

−0,011
(0.032)

−0,011
(0.019)

0.021
(0.040)

−0.023∗∗∗
(0.005)

−0,001
(0.021)

0.016
(0.025)

Notas: Robust standard errors, clustered relative reading score level, are given in parentheses.
Discontinuity estimates are obtained parametrically using the speciﬁed polynomial order and the
score range. Both speciﬁcations include the cohort ﬁxed effects.
∗Statistical signiﬁcance at 10%; ∗∗statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.

368

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Mesa 9. Robustness Checks Using Different Bandwidths and Poly-
nomial Orders

Score
Range

Polynomial
Orden

Incident
Following Year

Incident Two
Years Later

0.035∗∗
(0.018)
[8,643]

0.049∗∗∗
(0.019)
[43,793]

0.028∗∗
(0.012)

0.035∗∗
(0.017)

0.074∗∗∗
(0.018)
[84,914]

0.013
(0.011)

0.043∗∗∗
(0.016)

0.071∗∗∗
(0.018)
[128,441]

0.008
(0.010)
[172,584]

0.051∗∗∗
(0.021)
[8,643]

0.089∗∗∗
(0.012)
[43,793]

0.042∗∗∗
(0.011)

0.038∗
(0.020)

0.106∗∗∗
(0.010)
[84,914]

0.026∗∗
(0.011)

0.050∗∗∗
(0.019)

0.085∗∗∗
(0.018)
[128,441]

0.021∗∗∗
(0.009)
[172,584]

Notas: Robust standard errors, clustered at the relative reading
score level, are given in parentheses. Discontinuity estimates
are obtained parametrically using the speciﬁed polynomial order
and the score range. All regressions control for the student co-
variates listed above, cohort ﬁxed effects, and within-school peer
averages. Sample sizes are given in square brackets.
∗Statistical signiﬁcance at 10%; ∗∗statistical signiﬁcance at 5%;
∗∗∗statistical signiﬁcance at 1%.

students as measured by their FRPL eligibility. Grade retention leads to a 7 a 9
percentage point increase in disciplinary incidents for economically disadvan-
taged students, whereas it has no statistically signiﬁcant effect on more afﬂuent
estudiantes. The estimated discontinuities are positive for all major racial/ethnic
groups in Florida, but the largest effect seems to be on African American
estudiantes. Similarmente, grade retention affects students of both genders, pero el
point estimates are larger for boys.5

Important to note here is that subgroup effects are not statistically different from each other, principalmente
because of smaller sample size and less precise estimates.

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GRADE RETENTION AND STUDENT MISBEHAVIOR

Mesa 10.

Early Grade Retention and Misbehavior Subgroup Analysis

Score Range/Bandwidth

Incident within two years

Todo

First-stage discontinuity

norte

Socioeconomic status

FRPL Eligible

First-stage discontinuity

norte

FRPL Ineligible

First-stage discontinuity

norte

Race/Ethnicity

Blanco

First-stage discontinuity

norte

Negro

First-stage discontinuity

norte

Hispano

First-stage discontinuity

norte

Gender

Male

First-stage discontinuity

norte

Female

Lineal
5

Quartic
20

0.053∗∗∗
(0.011)

0.320∗∗∗
(0.007)

44,247

0.062∗∗∗
(0.013)

0.329∗∗∗
(0.008)

32,991

0.026
(0.021)

0.295∗∗∗
(0.006)

11,256

0.048∗∗
(0.021)

0.288∗∗∗
(0.009)

13,250

0.076∗∗∗
(0.020)

0.353∗∗∗
(0.007)

15,718

0.027∗
(0.015)

0.322∗∗∗
(0.009)

13,007

0.065∗∗
(0.032)

0.328∗∗∗
(0.007)

23,891

0.039
(0.024)

0.071∗∗∗
(0.015)

0.322∗∗∗
(0.008)

180,066

0.081∗∗∗
(0.019)

0.329∗∗∗
(0.010)

132,875

0.044∗
(0.023)

0.303∗∗∗
(0.005)

47,191

0.079∗∗
(0.026)

0.290∗∗∗
(0.009)

54,858

0.101∗∗∗
(0.027)

0.352∗∗∗
(0.009)

62,613

0.031
(0.023)

0.328∗∗∗
(0.011)

53,135

0.100∗∗∗
(0.033)

0.331∗∗∗
(0.010)

96,815

0.037
(0.028)

370

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Mesa 10. Continuado.

Score Range/Bandwidth

First-stage discontinuity

norte

Time spent in current school

Different school in 2nd grade

First-stage discontinuity

norte

Same school in 2nd grade

First-stage discontinuity

Lineal
5

0.310∗∗∗
(0.007)

20,356

0.051
(0.032)

0.334∗∗∗
(0.010)

10,722

0.053∗∗∗
(0.020)

0.315∗∗∗
(0.009)

Quartic
20

0.312∗∗∗
(0.008)

83,251

0.035
(0.037)

0.343∗∗∗
(0.005)

43,227

0.083∗∗∗
(0.021)

0.315∗∗∗
(0.009)

norte

33,525

136,839

Number of retained peers in school

Fewer than 5 colegas

First-stage discontinuity

norte

Más que 10 colegas

First-stage discontinuity

norte

0.097∗∗∗
(0.013)

0.177∗∗∗
(0.007)

13,737

0.021∗∗∗
(0.008)

0.433∗∗∗
(0.010)

20,129

0.164∗∗∗
(0.051)

0.173∗∗∗
(0.007)

56,741

0.036∗∗
(0.023)

0.443∗∗∗
(0.011)

80,361

Notas: Robust standard errors, clustered at the relative reading
score level, are given in parentheses. Discontinuity estimates are
obtained parametrically using the speciﬁed polynomial order and
the score range. All regressions control for the student covariates
listed above, cohort ﬁxed effects, and within-school average peer
resultados.
∗∗Statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.

Understanding the Mechanisms behind the Retention Effect

There are several mechanisms that might explain the adverse effect of grade
retention on student behavior. Por ejemplo, the observed discontinuity at the
retention cutoff might arise if the students who are old for their grade are
more likely to misbehave. Controlling for relative age, sin embargo, would lead
to misleading inferences in the framework outlined herein, because retention
is highly correlated with relative age in the years following retention. Allá-
delantero, to see if relative age is associated with student misbehavior, I conduct an

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371

GRADE RETENTION AND STUDENT MISBEHAVIOR

exploratory analysis where I restrict the sample to all fourth and ﬁfth graders
in the sample, the grades during which the negative effects of retention are
observado. To account for the possibility that relative age is correlated with un-
observed student characteristics, I also restrict the sample to students born in
August and September and use the “September-born” indicator as an instru-
ment for relative age (in months), taking advantage of Florida’s school starting
age policy.6 Hence, I exploit the variation in relative age created by the policy,
which is presumably exogenous to unobserved student attributes.

The results, which are available upon request, suggest a strong ﬁrst-stage
(students born in September, on average, are six months older than their peers
in the same grade), and a second stage estimate of 0.0008, which is statistically
signiﬁcant at the 1 nivel porcentual. This indicates that a twelve-month increase
in relative age, such as the one created by grade retention, would increase
the likelihood of disciplinary incident by 1 percentage point. Although not
necessarily conclusive, these ﬁndings provide evidence that the increase in
relative age caused by retention might be playing a role in the retention effect.
Another possible explanation is the emotional distress associated with loss
of friends and stigma caused by being left behind. Although it is not possible to
directly test for these hypotheses using administrative data, I present indirect
evidence using subgroup analysis. Primero, I break down the regression disconti-
nuity estimation by how much time the student has spent in the same school
before the third grade. The idea here is that the longer the student has spent in
the same school, the larger the emotional burden of loss of friends will be. El
estimates provided in the second-to-last panel in table 10 somewhat support
this hypothesis. For students who entered the school during the third grade,
the effect of retention is not statistically different from zero, whereas for the
“stable” students, the effects are negative and statistically signiﬁcant.

I also check to see whether retention effects are larger for students in
schools with fewer retained students. The idea in this exercise is that the
stigma associated with being held back is presumably less severe for students
if most of their peers are also retained. The last panel in table 10 presenta el
discontinuity estimates using schools with fewer than ﬁve retained students
in a given year and schools with more than ten retained third graders. El
estimated effects seem to support this hypothesis, with larger effect sizes for
the former subgroup of schools. Por ejemplo, for schools with fewer than
ﬁve retained students, the retained students are 10 a 16 puntos de porcentaje
more likely to be involved in a disciplinary incident, whereas that number is 2

6. In Florida, children who have attained the age of ﬁve years on or before 1 September of the school
year are eligible for admission to public kindergarten. In the regressions, I also control for student
covariates such as FRPL eligibility, raza/etnicidad, special education status, measures of English
proﬁciency, and school, año, and grade ﬁxed effects.

372

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Umut ¨Ozek

a 4 percentage points for schools with high retention rates. En general, all three
explanations seem to be playing a role on the adverse effects of grade retention.

5. CONCLUDING REMARKS
Test-based accountability has become the new norm in public education over
the last decade, with demands for greater accountability intensifying in the
wake of recent initiatives such as the Race to the Top. In many states and school
districts nationwide, not only schools and teachers are held accountable for
the performance of their students but low performance in standardized tests
also carries signiﬁcant implications for students. One of these implications is
grade retention for low performers.

en este estudio, I examine the effects of grade retention on student mis-
behavior using the non-linearity created by the Just Read, Florida! programa,
a reading initiative that requires students with reading skills below grade
level to be retained in the third grade. The regression discontinuity estimates
suggest grade retention increases the likelihood of disciplinary incidents and
suspensions among just-retained students who are otherwise comparable to
their peers on the other side of the retention cutoff. The ﬁndings also suggest
these adverse effects are concentrated among the economically disadvantaged,
African Americans, and boys.

The overarching conclusion in the recent literature is that grade retention,
especially in early grades, leads to signiﬁcant achievement gains in the short
run. The ﬁndings presented in this study reveal that these short-run beneﬁts
come with the burden of higher rates of student misbehavior. Si, sin embargo,
early grade retention policies gradually lead to improved learning in grades
before the third grade, and hence lower retention rates (as retention policies
typically intend to accomplish), then these adverse effects might become less
signiﬁcant in the long run. Eso es, despite the fact that the adverse effects of
grade retention on misbehavior persist, these effects might become less
concerning over time if reading achievement improves and fewer students are
retained. De hecho, this seems to be the trend in Florida, with signiﬁcantly more
students scoring above grade level in third grade and fewer students being
retained (12 percent retention rate in 2003 comparado con 7 por ciento en 2011).
Finalmente, it is important to note that the estimated effects in this study reﬂect
the combined effects of the grade retention and the instructional support com-
ponents of the Florida policy. Por lo tanto, the ﬁndings presented here might
not be generalizable to other grade retention policies. Sin embargo, este estudio
might help better assess the costs and beneﬁts associated with increasingly
popular test-based retention policies that are commonly tied to support mech-
anisms for the retained students.

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373

GRADE RETENTION AND STUDENT MISBEHAVIOR

This research was supported by the National Center for the Analysis of Longitudinal
Data in Education Research (CALDER) funded through grant R305A060018 to the
American Institutes for Research from the Institute of Education Sciences, A NOSOTROS. De-
partment of Education. The opinions expressed are those of the author and do not
represent views of the Institute or the U.S. Departamento de Educación. I would like to
thank Tiffany Chu and Kennan Cepa for excellent research assistance. All errors are
mío.

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APPENDIX

Cuadro A.1.

Early Grade Retention and Misbehavior First Stage Estimates

Score Range

Below cutoff

Incident one year before

Incident current year

LEP

Special education

FRPL eligible

Male

Age in 3rd grade

3rd grade FCAT Math score

Blanco

Negro

Hispano

asiático

Foreign born

English not native

Cohort FE

Student covariates

norte

Lineal
5

0.319∗∗∗
(0.006)

0.012
(0.008)

0.012∗
(0.007)

−0.016∗∗∗
(0.006)

−0.057∗∗∗
(0.004)

0.017∗∗∗
(0.004)

0.024∗∗∗
(0.003)

−0.004∗∗∗
(0.0001)

−0.067∗∗∗
(0.002)

0.0001
(0.009)

0.001
(0.009)

−0,007
(0.01)

−0.018
(0.016)

−0.026∗∗∗
(0.007)

0.002
(0.006)

Sí

Quartic
20

0.322∗∗∗
(0.007)

0.009∗∗
(0.004)

0.016∗∗∗
(0.003)

−0.021∗∗∗
(0.003)

−0.061∗∗∗
(0.002)

0.013∗∗∗
(0.002)

0.022∗∗∗
(0.002)

−0.005∗∗∗
(0.0001)

−0.061∗∗∗
(0.001)

0.01∗∗
(0.004)

0.007
(0.004)

0.002
(0.004)

0.002
(0.007)

−0.025∗∗∗
(0.003)

0.0001
(0.003)

Sí

42,393

178,248

Notas: Robust standard errors, clustered at the relative reading score
nivel, are given in parentheses. The results present the full ﬁrst stage
estimates for columns labeled (II) in table 3.
∗Statistical signiﬁcance at 10%; ∗∗statistical signiﬁcance at 5%;
∗∗∗statistical signiﬁcance at 1%.

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GRADE RETENTION AND STUDENT MISBEHAVIOR

Tabla A.2.

Early Grade Retention and Misbehavior Second Stage Estimates

Incident One Year Later

Incident Two Years Later

Score Range

Retained

Incident one year before

Incident current year

LEP

Special education

FRPL eligible

Male

Age in 3rd grade

3rd grade FCAT Math score

Blanco

Negro

Hispano

asiático

Foreign born

English not native

Cohort FE

Student covariates

Within-school peer average

Lineal
5

0.039∗∗∗
(0.009)

0.219∗∗∗
(0.01)

0.262∗∗∗
(0.006)

−0,004
(0.003)

−0,004
(0.004)

0.031∗∗∗
(0.003)

0.055∗∗∗
(0.003)

0.002∗∗∗
(0.0003)

−0.005∗∗
(0.002)

−0.019∗∗∗
(0.006)

0.033∗∗∗
(0.005)

−0.021∗∗∗
(0.006)

−0.028∗∗∗
(0.008)

−0.014∗∗∗
(0.005)

−0.019∗∗∗
(0.004)

Sí

Quartic
20

0.064∗∗∗
(0.012)

0.201∗∗∗
(0.005)

0.264∗∗∗
(0.003)

−0,003
(0.002)

−0,001
(0.002)

0.029∗∗∗
(0.002)

0.056∗∗∗
(0.001)

0.003∗∗∗
(0.0001)

−0.003∗∗
(0.001)

−0.009∗∗∗
(0.003)

0.042∗∗∗
(0.003)

−0.011∗∗∗
(0.004)

−0.024∗∗∗
(0.004)

−0.011∗∗∗
(0.002)

−0.018∗∗∗
(0.002)

Sí

Lineal
5

0.055∗∗∗
(0.011)

0.181∗∗∗
(0.01)

0.234∗∗∗
(0.011)

0.0001
(0.005)

−0,006
(0.004)

0.044∗∗∗
(0.004)

0.074∗∗∗
(0.004)

0.003∗∗∗
(0.0002)

−0.007∗∗∗
(0.001)

−0.01
(0.008)

0.043∗∗∗
(0.007)

−0.018∗∗
(0.008)

−0.032∗∗∗
(0.011)

−0.013∗∗
(0.005)

−0.031∗∗∗
(0.003)

Sí

Quartic
20

0.054∗∗∗
(0.022)

0.191∗∗∗
(0.005)

0.24∗∗∗
(0.004)

0.002
(0.002)

−0.01∗∗∗
(0.002)

0.04∗∗∗
(0.002)

0.067∗∗∗
(0.002)

0.003∗∗∗
(0.0001)

−0.007∗∗∗
(0.002)

−0.013∗∗∗
(0.004)

0.042∗∗∗
(0.004)

−0.023∗∗∗
(0.004)

−0.034∗∗∗
(0.006)

−0.019∗∗∗
(0.002)

−0.026∗∗∗
(0.002)

Sí

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178,248

43,793

178,248

Notas: Robust standard errors, clustered at the relative reading score level, are given in parenthe-
ses. The results present the full second stage estimates for columns labeled (II) in table 3.
∗∗Statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.

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Table A.3.

Early Grade Retention and Misbehavior: Alternative Speciﬁcations

Score Range

1 year later

Disciplinary incident

In-school suspension

Out-of-school suspension

2 años después

Disciplinary incident

In-school suspension

Out-of-school suspension

First-stage discontinuity

Lineal

Quartic

(I)
5

(II)
5

(I)
20

(II)
20

0.036∗∗∗
(0.010)

0.013
(0.010)

0.040∗∗∗
(0.014)

0.050∗∗∗
(0.013)

0.030∗∗∗
(0.005)

0.025∗∗∗
(0.009)

0.347∗∗∗
(0.008)

0.039∗∗∗
(0.009)

0.009
(0.007)

0.037∗∗∗
(0.011)

0.054∗∗∗
(0.013)

0.032∗∗∗
(0.004)

0.027∗∗∗
(0.005)

0.319∗∗∗
(0.006)

0.058∗∗∗
(0.013)

0.017
(0.010)

0.056∗∗∗
(0.015)

0.054∗∗∗
(0.018)

0.039∗∗∗
(0.008)

0.024∗∗
(0.012)

0.358∗∗∗
(0.008)

0.062∗∗∗
(0.013)

0.017
(0.011)

0.044∗∗∗
(0.015)

0.052∗∗∗
(0.022)

0.037∗∗∗
(0.010)

0.017
(0.011)

0.323∗∗∗
(0.007)

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Cohort FE

Student covariates

Peer incident rate at school

School FE

Includes LEP and SPED interacted

with the below-cutoff indicator

43,793

178,248

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Notas: Robust standard errors, clustered at the relative reading score level, are given in paren-
tesis. Discontinuity estimates are obtained parametrically using the speciﬁed polynomial
order and the score range. All regressions control for the student covariates listed above,
cohort ﬁxed effects, and within-school average peer outcomes.
∗∗Statistical signiﬁcance at 5%; ∗∗∗statistical signiﬁcance at 1%.