THE WAGES OF FAILURE:

NEW EVIDENCE ON SCHOOL

RETENTION AND LONG-RUN

OUTCOMES

Philip Babcock

(corresponding author)

经济系

加州大学,

圣巴巴拉

圣巴巴拉, CA 93106-9210

babcock@econ.ucsb.edu

Kelly Bedard

经济系

加州大学,

圣巴巴拉

圣巴巴拉, CA 93106-9210

kelly@econ.ucsb.edu

抽象的
By estimating differences in long-run education and la-
bor market outcomes for cohorts of students exposed
to differing state-level primary school retention rates,
this article estimates the effects of retention on all stu-
dents in a cohort, retained and promoted. 我们发现
A 1 standard deviation increase in early grade retention
is associated with a 0.7 percent increase in mean male
hourly wages. 更远, the observed positive wage effect
is not limited to the lower tail of the wage distribution but
appears to persist throughout the distribution. 尽管
there is an extensive literature attempting to estimate
the effect of retention on the retained, this analysis of-
fers what may be the ﬁrst estimates of average long-run
impacts of retention on all students.

C(西德:2) 2011 Association for Education Finance and Policy

293

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THE WAGES OF FAILURE

介绍

1.
Both the Goals 2000: Educate America Act, signed into law by Bill Clin-
ton in 1994, and No Child Left Behind (NCLB), signed seven years later
by George W. 衬套, called for outcome-based reforms tying grade promo-
tion to student performance. Opponents of retaining underperforming stu-
dents argue that retention discourages students, destroys their conﬁdence,
delays exposure to the next year’s curriculum, and leaves them further be-
hind (Thompson and Cunningham 2000). Proponents of retention claim
that the “social promotion” of underperforming students teaches students
and teachers that effort and achievement are unimportant, forces teachers
to deal with a much wider range of student preparedness, and denies stu-
dents a second chance to learn what they missed (AFT 1997). Alleged costs
or beneﬁts of grade retention, 然后, have been used as a rationale for the
大规模, outcome-based education reforms of recent years and have just
as often been used to criticize these policies. But there would seem to be lit-
tle ground on which to make either judgment. Existing evidence is mixed,
suffers from methodological problems, and is limited in scope to a nar-
row subset of students. 尤其, most previous research on retention
explores the impact of retention on the retained but abstracts from any
possible impact on their promoted classmates. This is potentially a serious
omission, as the vast majority of students are promoted. By estimating dif-
ferences in long-run education and labor market outcomes for cohorts of
students exposed to differing state-level primary school retention rates, 这
article attempts to ﬁll that gap and shed some light on the potentially im-
portant effects of grade retention that may have been overlooked in previous
工作.

Our main ﬁnding is that a 1 standard deviation increase in retention
through grade 2 is associated with an increase of 0.7 percent in male work-
ers’ average hourly wages. This ﬁnding is robust to controls for changes in
school expenditures, early and delayed school entry, demographic composi-
tion of states, selective migration between states, and other potential con-
founding factors. 更远, the observed positive wage effect is not limited
to the lower tail of the wage distribution but appears to persist through-
out the distribution. Though there is an extensive literature attempting to
estimate the effect of retention on the retained, this analysis offers what
may be the ﬁrst estimates of average long-run impacts of retention on all
学生.

The remainder of the article is organized as follows. 部分 2 reviews the
previous literature and motivates the analysis; 部分 3 describes the data and
empirical strategy; 部分 4 reports results and discusses possible implications
of the ﬁndings; and section 5 summarizes and concludes.

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Philip Babcock and Kelly Bedard

2. THE IMPACT OF RETENTION
The Impact of Retention on the Retained
There is a vast literature examining the effect of retention on the retained. 这
following summary sketches the main ﬁndings but is by no means exhaustive.
The main areas of comparison are academic achievement and high school
completion. Several meta-surveys (Holmes and Matthews 1984; Holmes 1989;
Jimerson 2001) ﬁnd that in most early studies, retained students performed
less well academically and were more apt to drop out of high school than
were observationally similar promoted students.1 However, drawing inferences
from this body of research is difﬁcult because selection on unobservables is
a serious confounding factor. It is likely that decisions to retain one student
and promote a superﬁcially similar student hinge on student traits that the
educator observes but the researcher does not (例如, maturity, motivation, 这
ability to sit still). Retained students may therefore differ substantially from
comparison groups of promoted students.

Three recent studies employ regression discontinuity strategies to address
the selection problem. Jacob and Lefgren (2004) take advantage of an account-
ability policy in the Chicago public schools that tied summer school attendance
and grade retention to test score cutoffs. They ﬁnd that retained third graders
scored higher on math achievement tests two years later than their promoted
同行, while retained sixth graders scored lower on reading tests.2 In
a follow-up (Jacob and Lefgren 2007), the authors report a small increase in
the probability of dropping out for students retained in eighth grade but no
signiﬁcant effect on the dropout rate for sixth-grade retention. Greene and
Winters (2007), using a regression discontinuity design made possible by a
similar Florida policy, report increased reading gains for students retained in
third grade, relative to promoted students. These gains may have resulted from
retention itself or from speciﬁc interventions for retained students that were
also mandated by the Florida policy.

Potential Implications of Retention Policy for All Students
Is there a reason to believe that marginal increases in retention can have an
impact beyond the marginally retained? Previous work in applied economic
theory offers many. Economic theory predicts that retention policies inﬂu-
ence the effort, expectations, and practices of students and their teachers, 和

A few studies have found positive effects of retention in some settings (see Karweit 1991; 亚历山大,
Entwisle, and Dauber 1995; Eide and Showalter 2001; Lorence et al. 2002).

2. The authors do not draw strong conclusions from the latter ﬁnding on retained sixth graders because

promoted students faced high-stakes testing and retained students did not.

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295

THE WAGES OF FAILURE

in so doing inﬂuence the outcomes of both promoted and retained students.
Speciﬁcally, in the theoretical literature on education standards, altering a stan-
dard changes incentives for students and institutions. Neal and Schanzenbach
(2007) emphasize the allocation of resources by institutions: the modiﬁcation
of a standard causes institutions to direct resources toward the subgroup of
students nearest the cutoff and away from students at the top and bottom of
the distribution, yielding potential effects on all students. Betts (1996) 和
Costrell (1994) report that when a standard rises, students throughout the
distribution alter their effort choices, with relatively high-ability students in-
creasing effort to meet it and others (those who had been marginally willing
to meet the lower standard) giving up and reducing effort. To the extent that a
change in retention policy is an implicit change in the standard for promotion,
it may be expected to inﬂuence all students through these channels.3

A second strand of literature, the large body of theoretical and empirical
work on peer effects, also leads one to expect an impact of retention policy
on the promoted. Lazear’s (2001) model of peer effects may be particularly
相关的. In this model, a disrupting student prevents learning by all of his
classmates for the duration of the disruption. Thus any intervention (例如
a retention policy) that alters the behavior or allocation of disruptive students
is expected to alter outcomes for all of that student’s peers. 更普遍,
a broad literature argues that interventions targeting a subgroup of students
may alter outcomes of untreated classmates through imitation, mentoring,
and other modes of social interaction (看, 例如, Akerlof 1997; Mofﬁt 2001;
Glaeser, Sacerdote, and Scheinkman 2003). There has been little previous
work investigating peer effects associated with retention. Lavy, Paserman, 和
Schlosser (2008), in research that comes closest to this point, ﬁnd that the
proportion of delayed peers in a cohort (peers who are older than would be
expected for their cohort) has a negative effect on student performance. 这
authors use the term repeaters to describe the older students but emphasize that
they do so loosely: the vast majority of their repeaters delayed entry into ﬁrst
grade and were not retained. This research, 然后, yields results best interpreted
as estimates of ability-related peer effects rather than retention effects.

总之, economic theory offers many reasons to believe that retention
policy has the potential to inﬂuence both the retained and the promoted.
更远, large and far-reaching education reforms have been motivated in part

Because our data predate the broad standards-based reforms of recent years, we do not argue that
changes in retention policies are due strictly to test-based standards. 然而, while the theoretical
work cited above takes test-based standards as a point of departure, an identical logic holds for
implicit modiﬁcations of informal standards of the sort that would yield changes in retention rates
during the eras we study.

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Philip Babcock and Kelly Bedard

by alleged effects of retention on all students. But despite extensive research
attempting to quantify the impact of retention on the subgroup of retained
学生, there is little or no existing evidence on the effect of retention policy
on all students.4 Below we describe the data and empirical strategy that we
employ to investigate this broader effect.

3. EMPIRICAL STRATEGY
Speciﬁcation
We model the response of adult labor market outcome, Yibc y, for individual
i from state of birth b and year of birth cohort c, observed in the census or
the American Community Survey (ACS) in year y, to the state of birth level
retention rate, Rbc , as follows:

Yibc y = α0 + α1 Rbc + Xibc yα2 + Aibc yα3 + Bbα4 + Tzc α5 + εibc y,

(1)

where X is a vector of personal characteristics,Aibc y is a quadratic function of
年龄,5 Bb is a vector of state of birth indicators, Tzc is a vector of region z speciﬁc
birth cohort indicators, and ε is the usual error term.6 Equation 1 不
hold educational attainment constant because retention practices may alter
labor market outcomes by changing highest grade attained or within-grade
(cognitive or noncognitive) human capital accumulation.7 Educational attain-
ment and other intermediate outcomes are treated as endogenous, 潜在的
channels through which retention practices may affect labor market outcomes.
Identiﬁcation in this model comes from within-state changes in retention rates
that predict within-state deviations from region-level trends in the dependent
variable.8 This model allows estimation of reduced form effects of grade reten-
tion for an entire cohort but does not separately identify the effect of retention
on the subgroup of retained students. All regressions are population weighted,
and the standard errors are clustered at the state of birth level.

Quantifying Retention Policies
One approach to studying the effects of retention policies is to look for
within-state changes in relevant laws or other explicitly articulated polices.

4. There is also some research investigating the overall impact of school accountability on student
结果 (例如, Carnoy and Loeb 2002; Hanushek and Raymond 2004). 然而, these articles do
not speciﬁcally investigate grade retention.

5. All results are similar if a vector of age indicators is used instead. Under the speciﬁcation with age

指标, one age indicator from each birth cohort is excluded.

6. We assume that individuals are educated in their state of birth. All retention measures are deﬁned

in the next section. Nonrandom migration is discussed in section 4.
In section 4 we also report results of a model that features educational attainment as the dependent
variable.
部分 4 also presents results for models expanded to include current marital status, region and
state of residence characteristics, and region of birth and region of residence interactions.

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297

THE WAGES OF FAILURE

This approach is problematic because the content of retention-related laws
varies greatly across states and over time, and the speciﬁc manner in which
laws are translated into practice is often ambiguous. 20世纪70年代开始,
many states passed laws that mandated minimum competency testing (MCT).
Some of these laws may have inﬂuenced retention by tying grade promotion
to test scores. 然而, early MCT laws were often simplistic one-page bills
that left the crucial details of implementation to be worked out later (Pipho
2002). Beginning in 1985, and in several later periods, data on state-level
MCT mandates were collected by the Education Commission of the States.
States speciﬁed the grade levels tested and whether (and in which grades) 这
tests were to be used for grade promotion decisions. But most of the avail-
able data are too recent to allow a panel analysis of long-run outcomes, 和
the speciﬁc tests and test score cutoffs used in promotion decisions were not
speciﬁed. 而且, evidence suggests that retention rates often change in
grade levels not speciﬁcally targeted by stated grade promotion policies. 更多的
具体来说, educators appear to alter early promotion practices in anticipa-
tion of promotional gates on later grades (see Jacob 2002; Hauser, Frederick,
and Andrew 2005). The diverse MCT laws, 然后, do not map to school reten-
tion practices in a coherent way. 由于这些原因, we argue that what states
actually do is a better measure of their retention practices than their stated
政策.

Because no national database of promotion and retention statistics exists,
researchers often calculate retention rates from differences in age-grade re-
tardation across consecutive years.9 The rate of age-grade retardation, as used
这里, is the fraction of students below modal grade for a given age. For pur-
poses of exposition, we focus on the complementary measure, the fraction of
students who are “on time.” More formally, we deﬁne the fraction of on-time
students as the fraction of students in a birth cohort who have reached or
exceeded the modal grade for that age. If Oa
bc is the fraction of students born
in state b in cohort c observed to be on time when they reach the modal age a
associated with a given grade, the inferred retention rate is:

Ra
bc

= Oa
bc

− Oa+1
bc

(2)

This measure captures the decrease over a year in the fraction of students in
a cohort who are on time. When fewer students are on time, it is assumed

9. Some researchers do not use differences in age-grade retardation across years to infer retention
rates but take age-grade retardation itself as a proxy for retention. See Cascio 2005 for an analysis
of the biases involved in such an approach. Also see Deming and Dynarski 2008 for evidence on
changes over time in delayed entry (redshirting).

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Philip Babcock and Kelly Bedard

that retention accounts for the difference. We reﬁne this measure in several
方法.

We use the 1960, 1970, 和 1980 Public Use Microdata to calculate re-
tention rates. Thus we use three cohorts in the analysis, spaced at ten-year
intervals. The censuses have three distinct advantages over other data sources.
第一的, the samples are large enough to allow construction of precise state-
year retention measures.10 Second, the 1960–80 censuses also have the added
advantage of including data on quarter of birth; the importance of this infor-
mation will be clear shortly. 第三, combining retention measures from the
1960–80 censuses and wage data from the 2000 census and the 2001–7 ACSs
facilitates a panel analysis in which the effect of retention rates on long-run
outcomes is estimated from within-state variation over time. But in order to
infer retention rates, we must modify equation 2 to account for the fact that
we do not observe a given birth cohort in consecutive grades and thus must
compare on-time rates between consecutive cohorts in consecutive grades to
estimate retention rates:

Ra
bc

= Oa
bc

− Oa+1
bc−1.

(3)

We label a student’s cohort by the year he turned six, the modal age for ﬁrst
年级. 在里面 1980 人口普查, age is reported as of 1 四月 1980, so the majority of
six-year-olds turned six in 1979. 例如, the on-time measure O6
MO 1979 是
the fraction of six-year-olds in 1979 in Missouri who were in (or had completed)
年级 1. Because we do not observe this cohort in grade 2, we calculate the grade
2 on-time rate for students who were seven years old in 1979 (and thus six
years old in 1978.) The grade 1 retention rate is the difference between the 1979
cohort’s grade 1 on-time rate and the 1978 cohort’s grade 2 on-time rate. 这
approximation assumes smoothness of retention policy between these pairs
of consecutive cohorts. For simplicity, we label this as the retention rate for
1979, although the retention rate applies to a two-year 1978–79 cohort.

An additional reﬁnement of the on-time measure is warranted, given dif-
fering school age-entry laws in different states over time. The standard method
for calculating retention rates from on-time status (例如, Hauser 1999) is to de-
ﬁne six-year-olds as on time if they are in ﬁrst grade or higher, seven-year-olds
if they are in second grade or higher, 等等. But this ignores age-entry laws
and the census reporting date. 例如, the age-entry cutoff for kinder-
garten in Missouri in 1979 曾是 1 十月 (IE。, state law required that students
who turned ﬁve after 1 October defer entering kindergarten until the following
年). By this rule, any student who was reported in the 1980 census to be

10.

相比之下, the small state-year samples in the October supplement of the Current Population
Survey yield extremely noisy state-year retention rates by grade.

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299

THE WAGES OF FAILURE

seven years old in grade 1 would be classiﬁed as behind. But if a Missouri
ﬁrst grader’s birthday fell between 1 October and 31 March and he had turned
seven by the census reporting date (1 四月 1980), he would have been six on
1 十月 1979 and on time for grade 1. 在这种情况下, 然后, the standard rule
incorrectly assigns about half of all students.11 Using data on the student’s
quarter of birth and data on school age-entry laws (Bedard and Dhuey 2009),
we are able to modify the on-time measure to account for state-level age-entry
laws and the census reporting date.12 Speciﬁcally, given the Missouri cutoff,
we deﬁne seven-year-olds born in quarters 4 和 1 to be on time if they are in
年级 1 or higher, those born in quarters 2 和 3 to be on time if they are in
年级 2 or higher, and so on for other age cohorts. 当然, age-entry cutoffs
do not always occur on the boundary between quarters (as was the case in this
convenient example). When cutoffs are not in the boundary between quarters,
we map students born in a speciﬁc quarter to the on-time status that most
accurately characterizes the majority of students born in that quarter.

Changes in school entry cutoff dates also require that we exclude obser-
vations for which the age-entry law changes in the year we observe a cohort
or during the previous or following year. This is important for at least two
原因. 第一的, the difference in on-time rates between consecutive cohorts in
consecutive grades is not a valid estimate of retention rates when the cutoffs
change between the two cohorts, because the difference no longer nets out
the misallocation of students in states with cutoffs that do line up exactly with
reported quarter of birth information. 第二, there may be some leading or
lagging of cutoff changes in terms of early and late enrollment in the years
immediately surrounding cutoff changes. This again invalidates differencing
across consecutive years as a means of estimating retention.

A third reﬁnement of the retention measure is warranted because some
types of retention are not captured by equation 3. Students who moved from
being on time to behind over consecutive grades would be accounted for in
方程 3. 然而, some students move from being ahead to being (strictly)
on time or from being behind to being further behind. To account for retention
of these types, we let A denote the fraction of students in the cohort who are
ahead and D the fraction of those who are two years behind, and modify
方程 3 as follows:

(西德:2)

Ra
bc

Oa
bc

− Oa+1
bc−1

(西德:3)

(西德:2)

氨基酸
bc

− Aa+1
bc−1

(西德:2)

(西德:3)

Da+1
bc−1 − Da

(西德:3)
.

(4)

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11.

If the ﬁrst-grade student’s birthday fell between 1 April and 1 十月, and he were seven at the time
of the census, he would have been seven on 1 October of his grade 1 school year and behind. 这些
students would be correctly assigned by the standard rule.

12. Appendix table A.1 reports school age-entry laws used to construct the retention rates.

300

Philip Babcock and Kelly Bedard

桌子 1. Retention Rates

Grade 1 retention

Grade 2 retention

Grade 3 retention

笔记: Population weighted.

1959

0.083
(0.041)

0.073
(0.050)

0.054
(0.039)

Cohort

1969

0.072
(0.036)

0.050
(0.022)

0.039
(0.026)

1979

0.055
(0.023)

0.045
(0.017)

0.054
(0.016)

The retention measure we use, 然后, consists of the decrease in the fraction
of students on time, the decrease in the fraction of students ahead, 和
increase in the fraction of students who are two years behind.13 Measures that
consider age-grade retardation alone do not account for retention of the latter
类型.

桌子 1 reports summary statistics for retention rates in grades 1, 2, 和
3 calculated from 1960, 1970, 和 1980 census samples, as described above.
Note that the expression “grade g retention” is a simpliﬁcation for brevity.
The measure actually captures some retention in neighboring grades. 成为
precise, grade g retention refers to retention occurring over the age range
associated with grade g, based on age-entry laws. 换句话说, this mea-
sure captures the treatment received by a legally deﬁned age-entry cohort.
Consistent with previous research, we ﬁnd that the retention rate is higher in
ﬁrst grade. Previous research also suggests that policy interventions generate
strong responses in early grades. 雅各布 (2002) notes that retention rates in
grades 1 和 2 increased after the introduction of the Chicago public schools
outcome-based policy initiative, even though the policy targeted later grades.
And Hauser, Frederick, and Andrew (2005) observe that with the introduction
of outcome-based reforms, early grade retention rates have responded more
than later grades.14 Early grade retention may be a preventative action, 在-
tended to address any observed problems prior to the time when performance
becomes a binding determinant of promotion. Because early grade retention
is most common and appears responsive to policy, we focus on retention over

13. Multigrade retention rates are calculated similarly: Ra
bc

− Oa+s
bc ), where s is the span of years over which retention is estimated.

= (Oa
bc

(Da+s
bc−s

− Da

bc−s ) + (氨基酸

− Ag +s

bc−s ) +

14. Previous research suggests that retention is also common in kindergarten. 然而, estimates of
retention in kindergarten are not easily inferred from on-time rates. This is because a subset of
students does not attend kindergarten and thus appears on time in ﬁrst grade without having been
on time in kindergarten. This makes it impossible to estimate kindergarten retention using on-time
费率.

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301

THE WAGES OF FAILURE

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数字 1. Retention Rates through Second Grade across School Entry Cohorts

grades 1 和 2 in the main regressions. 数字 1 displays retention rate time
trends for the ten states with the largest student enrollments in 1959. A com-
plete tabulation of estimated retention rates by state and year can be found in
appendix table A.2.

Calculating on-time status from the census is an indirect way of estimating
retention rates. Before moving to the main regressions, it is worth pausing to
check our measure against a direct and independent measure to make sure
that it is informative. Retention rates are reported directly by some states in
some years (see Shepard and Smith 1989; Hauser, Frederick, and Andrew
2005). These data are sparse and do not go back far enough to allow for a full-
scale panel analysis of long-run outcomes. 然而, the state-reported data on
retention rates do have some overlap with the census sample we use. Specif-
ically, there are grade 1 and grade 2 retention data from both sources for nine
states in 1979. 数字 2 is a scatter plot of the two retention measures plotted
互相对抗. The correlation between the census retention measure and
the state-reported measure is 0.93, and sample means are 0.12 和 0.14, 关于-
spectively. To the extent that we are able to compare, retention rates calculated
from census on-time rates match very well with state-reported retention rates.

Long-Run Outcomes and Controls
For the dependent variables in the regressions that follow, we use log hourly
wage and educational attainment outcomes for adult males in the 2000 5

302

Philip Babcock and Kelly Bedard

数字 2. Retention Rates Derived from the Census versus Reported by States

Percent Public Use Microdata Sample and the 2001–7 ACS. The retention rate
over grades 1 和 2 is calculated from the observed age and grade outcomes of
birth cohorts covering three years.Thus adult respondents in three-year birth
cohorts are mapped to the retention rate associated with the year (and birth
状态) in which they would have been in ﬁrst or second grade.15 Table 2 报告
descriptive statistics for the sample of males between the ages of 25 和 54
whose labor market outcomes are observed in the census or ACS between 2000
和 2007. All models reported in section 4 include controls for the fraction of
students who are on time in grade 1, ahead as of grade 1, the youngest age at
which school entry is legally allowed, kindergarten subsidization, expenditure
per student, pupil-teacher ratio, average daily attendance, relative salary of
教师, compulsory school-leaving age, a quadratic age function, and state of
birth, 种族, and region of birth speciﬁc cohort indicators.16

15. Results are robust to other mappings. In all speciﬁcations, ﬁndings are similar whether two-, three-,
or four-year cohorts are used. This speaks to concerns about our inability to perfectly map census
and ACS wage data, as well as cohort-speciﬁc control variables, to retention cohorts. Results of these
auxiliary regressions are available from the authors upon request.

16. Data on expenditures per student, pupil-teacher ratios, and average daily attendance are from the
Statistical Abstract of the United States. Relative teacher salaries are deﬁned as the average wage of
teachers divided by the average wage of male 30–49-year-old bachelor of arts degree holders in
the 1950–2000 U.S. censuses (intercensus years are linearly interpolated). The aforementioned
variables are thirteen-year averages while the cohort is in school. The beginning of state-subsidized
kindergarten is an indicator variable for whether publicly subsidized kindergarten existed (这
information is from Dhuey 2009). School entry age laws (which enter linearly into all speciﬁcations)
are measured at age ﬁve and are from Bedard and Dhuey 2009; see appendix table A.1 for more
细节. School-leaving laws (speciﬁed linearly) are measured at age fourteen and are from the Digest

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303

THE WAGES OF FAILURE

桌子 2. Summary Statistics

Ln hourly wage

Retention through grade 2

Percent on time or ahead as of grade 1

Percent ahead as of kindergarten

Expenditure per student (1,000s)

Average daily attendance (1,000s)

Pupil-teacher ratio

Relative teacher wage

Minimum school exit age (in years)

Publicly provided kindergarten

Youngest legal school entry age (in months)

年龄

黑色的

Hispanic

Other race

Sample size

Employed Men

All Men

意思是

3.054

0.127

0.887

0.093

3.684

1,689

21.288

0.619

16.314

0.750

57.542

40.560

0.091

0.064

0.028

标准
Deviation

0.708

0.059

0.060

0.042

1.302

1,219

3.043

0.075

0.667

0.433

1.517

8.112

0.288

0.246

0.165

意思是

–

0.128

0.888

0.093

3.672

1,700

21.343

0.619

16.313

0.744

57.542

40.587

0.105

0.067

0.030

标准
Deviation

–

0.060

0.042

1.310

1,230

3.067

0.075

0.676

0.436

1.512

8.206

0.307

0.251

0.172

590,517

788,968

Notes: Population weighted. “Employed men” sample is restricted to employed men who earn positive
工资, are not in school, and are not in prison.

4. 结果
Wages
桌子 3 reports the results from regressions of log hourly wages on retention
through grade 2 (IE。, total fraction retained in grade 1 或者 2). The ﬁrst row re-
ports the results for all men aged 25–54. Using the baseline speciﬁcation from
方程 1, 柱子 1 indicates that a 0.1 change in the fraction of students re-
tained through grade 2 in the respondent’s state-year birth cohort is associated
与一个 2.3 percent increase in wages. This is a large effect, but it is associated
with an extreme change in retention rates. The within-state standard deviation
of retention rates is 0.03. This change, which we argue is a reasonably sized
震惊, is associated with an increase in wages of about 0.7 百分.

The model in column 1 allows that intermediate choices (例如, 教育,
state of residence, marital status) may be endogenous—potentially inﬂuenced

of Education Statistics (http://nces.ed.gov/Programs/digest/). Information not provided by the Digest
of Education Statistics regarding the oldest age required by compulsory schooling comes from state
statutes and corresponding historical session laws.

304

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桌子 3. The Impact of Retention Policy on ln Hourly Wages: Sampling and Speciﬁcation Sensitivity

Speciﬁcation

Sample Size

(1)

(2)

(3)

(4)

All men

White men

Excluding southern states (all men)

1957–59 and 1967–69 cohorts only

1967–69 and 1977–79 cohorts only

Including additional controls (all men)

Additional Controls:

State of residence

Region of residence ∗ Age

State of residence GDP & unempl. 速度

Marital status

Region of birth ∗ Region of residence

0.2321∗∗
(0.0838)

0.2743∗∗
(0.1000)

0.2974∗∗
(0.1084)

0.2674∗∗
(0.0885)

0.1843∗
(0.0949)

0.2396∗∗
(0.0512)

不

0.2361∗∗
(0.0762)

0.2881∗∗
(0.0929)

0.2840∗∗
(0.1041)

0.2321∗∗
(0.0878)

0.2246∗∗
(0.1024)

0.2461∗∗
(0.0505)

是的

不

0.2342∗∗
(0.0760)

0.2894∗∗
(0.0919)

0.2833∗∗
(0.1028)

0.2188∗∗
(0.0881)

0.2311∗∗
(0.1046)

0.2452∗∗
(0.0504)

是的

590,517

507,254

410,697

450,853

363,820

590,517

Notes: All models are population weighted and the standard errors are heteroskedasticity-consistent
and clustered at the state of birth level. All models also include controls for the fraction of students
who are on time in grade 1, ahead as of grade 1, the youngest age at which school entry is legally
allowed, kindergarten subsidization, pupil teacher ratio, relative salary of teachers, compulsory
school leaving age, a quadratic age function, and state of birth, 种族, and region of birth speciﬁc
cohort indicators. The models reported in the last row also control for the percent of children aged
5–9 who are black, Hispanic, and other races, family size, the number of children siblings (包括
个人), the poverty rate, cohort size (measured by the size of the ﬁrst grade cohort), 和
fraction of men aged 25–29 who immigrated to the state from Central America (including Mexico),
immigrated from somewhere other than Central America, and migrated from another state.
∗signiﬁcant at 10%; ∗∗signiﬁcant at 5%.

by the state-level retention rate. This is the preferred speciﬁcation, as it does not
impose arbitrary limits on the mechanism by which retention rates may affect
工资. 然而, it is worth investigating the robustness of the ﬁndings to other
speciﬁcations. Speciﬁcally, there may be a concern that the results are driven
by omitted variables correlated with state of residence economic conditions
and state of birth retention rates. Column 2 reports estimates from a speciﬁ-
cation that includes controls for state of residence, state of residence GDP and
unemployment rates, region of residence interacted with a quadratic function
年龄, 和婚姻状况. The coefﬁcient on the retention rate changes only
very slightly in this speciﬁcation. Column 3 further adds region of birth by
region of residence interaction terms to control for nonrandom migration of

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305

THE WAGES OF FAILURE

workers between regions.17 Regressions from all models yield statistically and
economically signiﬁcant effects of the retention rate on hourly wages. All point
estimates are similar, showing about a 0.7 percent wage increase in response
to a standard deviation change in the retention rate.

A major concern, given the methodology used, is that changes in retention
policy may be confounded with changes in other state policies that occurred
同时地. One could imagine that state-level changes in retention policy
are sometimes implemented in a package that includes other reforms. In all
回归, we have controlled for available and relevant education policy vari-
埃布尔斯, including education expenditure per student, kindergarten subsidiza-
的, pupil-teacher ratio, relative salary of teachers, compulsory school-leaving
年龄, and youngest legal school entry age. Changes in these education policies
do not account for the observed association between retention rates and wages.
School age-entry laws merit close attention. They have been shown to inﬂu-
ence student outcomes (Bedard and Dhuey 2009) and may also inﬂuence re-
tention policy. We have controlled for this in several ways. 第一的, as described in
部分 3, we use age-entry cutoffs in the construction of the retention measure
and exclude observations for which the age-entry law changes in the year we ob-
serve a cohort or during the preceding or following year. This reduces the like-
lihood that age at entry is confounded with the retention measure and ensures
that the measure is attached to a meaningful cohort of students, those grouped
together by state law. 第二, we control directly for youngest legal school entry
年龄, as described above. 第三, to capture any additional effects of within-state
changes in delayed or accelerated entry into schooling, we also include control
variables for the fraction of students on time and the fraction of students ahead
when they enter grade 1. These controls are included in all speciﬁcations.18

Wage effects of retention are robust to the inclusion of controls for edu-
cation policies, which would suggest that retention is not a proxy for other
改革. To go a step further, one could also investigate whether retention
rates and other education policies do, 实际上, tend to move in tandem. 为了
例子, do expenditures per pupil rise when the retention rate rises? 状态
ﬁxed effects regressions (with region-speciﬁc cohort indicators) of education
policies on the retention rate reveal no signiﬁcant correlation between the re-
tention rate and expenditures per pupil, kindergarten subsidization, relative
salary of teachers, compulsory school-leaving age, youngest legal school entry
年龄, and the fractions of students ahead and on time when they enter grade 1.

17. See Heckman, Layne-Farrar, and Todd 1995.
18. The results are robust to the exclusion of these controls. 例如, the retention coefﬁcient
reported in column 1 在表中 3 changes from 0.2321 到 0.2327 when all education controls are
excluded.

306

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Only one policy appears to covary with the retention rate: increases in the
retention rate are associated with a small, statistically signiﬁcant increase in
pupils per teacher (suggestive of larger class sizes and less teacher time per
student). There would appear to be little or no evidence that increased reten-
tion rates proxy for increased investment in education or other human capital
enhancing education reforms.19

One might further be concerned that other, noneducation system, 政策
and/or socioeconomic changes may be confounding factors. 例如,
institutional changes within states, concurrent with retention rate changes,
may have altered labor market outcomes for nonwhite workers. 桌子 3, 排 2,
restricts the sample to white males. Findings are robust to this restriction,
suggesting that main results are not driven by external policies that altered
labor market outcomes for nonwhite workers.

Retention in the southern states was much higher than in the rest of the
country in the 1940s and 1950s. Brown v. 教育委员会, and the ensuing
transformation of educational institutions in the South, may have ushered in
pervasive changes in retention policy. To discern whether apparent effects of
retention policy are driven by these broader policy changes, we drop southern
states from the regressions in table 3, 排 3. The results are robust to the
exclusion of southern states.

Different external policy changes may have occurred in different subperi-
ods covered by the data. In table 3, rows 4 和 5, point estimates appear similar
for both of the ten-year subperiods across which we can observe changes
in retention rates between cohorts, though smaller sample sizes lessen the
precision of the estimates.

A remaining concern is that within-state changes in the demographic com-
position and characteristics of the school-age population may be confounded
with retention. 排 6 在表中 3 checks for this by including a broad range
of additional controls. These include the percent of children aged 5–9 who
are black, Hispanic, and other races; family size; number of children (在-
cluding the individual); poverty rate; cohort size (measured by the size of
the ﬁrst-grade cohort); and fraction of men aged 25–29 who immigrated to
the state from Central America (including Mexico), immigrated from some-
where other than Central America, and migrated from another state. 这
estimated effect of retention is largely unaffected by the inclusion of these
variables.20

19. Results of these supporting regressions are available from the authors upon request.
20. 更远, state ﬁxed effects regressions of these variables on the retention rate reveal no signiﬁcant
correlation between changes in retention rates and demographic composition or characteristics for
the school-age population. Supporting regressions are available upon request.

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307

THE WAGES OF FAILURE

As is always the case, unobservables remain a possible confounding inﬂu-
恩斯. 例如, changes over time in average unobserved ability of cohorts,
within a state, may inﬂuence results. 然而, more able cohorts would likely
feature lower retention rates and higher wages, 其他条件相同. Thus it
is likely that effects of this type would work against ﬁnding a positive effect
of retention on wages. Standard stories about unobserved changes in cohort
composition would suggest, if anything, that the coefﬁcients on retention in
桌子 3 may be biased downward.

总之, regressions from all models yield statistically and econom-
ically signiﬁcant effects of the retention rate on hourly wages. All point esti-
mates are similar, showing about a 0.7 percent wage increase in response to a
standard deviation change in the retention rate.

Timing: Retention Impacts by Grade
The analysis so far has focused on overall retention through grade 2, 但
it may also be informative to examine retention by speciﬁc grades. 桌子 4,
panel B, repeats the exercise of table 3, using grade 1 and grade 2 retention
rates as separate regressors. The effects of grade 1 和 2 retention appear
very similar. Panels C and D repeat the exercises of panels A and B but
examine retention through grade 3. The wage effect of early grade retention
appears to be driven by changes in grade 1 和 2 retention; panel D shows
little or no effect of third-grade retention.21 Panels E, F, and G, which contain
results from separate regressions of log wages on grade 1, 年级 2, and grade
3 retention, 分别, show the same pattern: positive wage effects for
ﬁrst-grade retention, imprecisely estimated positive effects for second-grade
retention, and little or no effect of third-grade retention. Taken as a whole,
the estimates reported in table 4 suggest that wage effects are strongest for
retention in the earliest grades.

Educational Attainment
Educational attainment is one mechanism that could generate the observed as-
sociation between grade retention rates and hourly wages later in the life cycle.
Are changes in the retention rate associated with changes in educational at-
tainment? 桌子 5 indicates that the answer is no. Under all speciﬁcations, 这
association between increased retention rates and educational attainment is

21. Kindergarten retention is not included as a covariate in table 4 because construction of kindergarten
retention rates from the census is problematic (see note 14). If increased grade 1 retention were
associated with decreased kindergarten retention, it would be difﬁcult to infer whether stricter reten-
tion policy or weaker retention policy drove wage results above. 然而, state-reported retention
data indicate that this is not the case and thus mitigate the concern: state-level changes over time
in the kindergarten retention rate are positively associated with changes in the ﬁrst-grade retention
速度.

308

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桌子 4. The Impact of Retention Policy on ln Hourly Wages

Speciﬁcation

(1)

(2)

(3)

Panel A: Base Case
Rentention through grade 2

Panel B
Grade 1 retention

Grade 2 retention

Panel C
Rentention through grade 3

Panel D
Grade 1 retention

Grade 2 retention

Grade 3 retention

Panel E
Grade 1 retention

Panel F
Grade 2 retention

Panel G
Grade 3 retention

Additional Controls:
State of residence
Region of residence ∗ Age
State of residence GDP & unempl. 速度

Marital status
Region of birth ∗ Region of residence

0.2321∗∗
(0.0838)

0.2895∗∗
(0.0769)

0.1988∗
(0.1064)

0.1288∗∗
(0.0574)

0.2541∗∗
(0.0797)

0.1669
(0.1229)

0.0263
(0.0868)

0.2530∗∗
(0.0662)

0.1653
(0.1024)

0.0080
(0.0586)

不

0.2362∗∗
(0.0762)

0.2913∗∗
(0.0728)

0.2043∗∗
(0.0987)

0.1446∗∗
(0.0549)

0.2483∗∗
(0.0785)

0.1840
(0.1122)

0.0569
(0.0909)

0.2534∗∗
(0.0687)

0.1705∗
(0.0948)

0.0311
(0.0624)

是的

不

0.2343∗∗
(0.0760)

0.2930∗∗
(0.0734)

0.2002∗∗
(0.0984)

0.1422∗∗
(0.0556)

0.2531∗∗
(0.0788)

0.1780
(0.1136)

0.0504
(0.0912)

0.2559∗∗
(0.0694)

0.1662∗
(0.0945)

0.0279
(0.0620)

是的

Notes: All models are population weighted, and the standard errors are heteroskedasticity-consistent
and clustered at the state of birth level. All models also include controls for the fraction of students
who are on time in grade 1, ahead as of grade 1, the youngest age at which school entry is legally
allowed, kindergarten subsidization, pupil-teacher ratio, relative salary of teachers, compulsory
school-leaving age, a quadratic age function, and state of birth, 种族, and region of birth–speciﬁc
cohort indicators. The sample size is 590,517, except for models that include third-grade retention.
The sample size for these models is 586,415 due to missing retention data for Nevada and Iowa in
the late 1970s.
∗signiﬁcant at 10%; ∗∗signiﬁcant at 5%.

statistically insigniﬁcant and economically small. In the baseline speciﬁcation
of column 1, a reasonably sized policy shock of 0.03 to the fraction of students
retained is associated with a decrease of 0.1 percentage point in the high
school graduation rate. The observed association between retention and some
college or college completion is likewise small and statistically insigniﬁcant,
but marginally positive. There would appear to be little or no clear evidence

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THE WAGES OF FAILURE

桌子 5. The Impact of Retention Policy on Educational Attainment

Grade 10 或者更多

Grade 11 或者更多

High school graduation or more

Some college or more

BA or more

Sample size

Additional Controls:

State of residence
Region of residence ∗ Age

State of residence GDP & unempl. 速度

Marital status
Region of birth ∗ Region of residence

(1)

−0.0126
(0.0293)

−0.0123
(0.0291)

−0.0345
(0.0342)

0.0454
(0.0749)

0.0477
(0.0504)

Speciﬁcation

(2)

(3)

−0.0108
(0.0306)

−0.0086
(0.0319)

−0.0283
(0.0368)

0.0594
(0.0761)

0.0503
(0.0512)

−0.0109
(0.0306)

−0.0088
(0.0320)

−0.0292
(0.0368)

0.0533
(0.0776)

0.0453
(0.0516)

788,968

不

是的

不

是的

that changes in the retention rate generate economically signiﬁcant changes
in the years of schooling a worker completes. 清楚地, 然而, 人类
capital acquisition depends on both the quantity and the quality of schooling
received, and the dependent variables in table 5 capture only the former.

Potential Mechanisms and Distributional Effects
The analysis thus far has focused on the effect of early grade retention on all
学生. This leaves open the question of whether observed wage gains ac-
crue primarily to retained or promoted students.22 Because we do not observe
retention histories for respondents in the 2000 census and the 2001–7 ACSs,
we cannot sort students by early grade retention status and identify separately
the wage effects on each subgroup. Even if this were possible, we would face

22. 更确切地说, when we discuss promoted students in the following analysis, we explore possible
effects of retention policy on students who were not marginally retained. Most of these students
were in fact promoted, so we use the term for simplicity of exposition.

310

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桌子 6. The Impact of Retention Policy on ln Hourly Wages across Quantiles

10th quantile

25th quantile

50th quantile

75th quantile

90th quantile

Additional Controls:

State of residence
Region of residence ∗ Age

State of residence GDP & unempl. 速度

Marital status
Region of birth ∗ Region of residence

(1)

0.2294∗
(0.1184)

0.1908∗∗
(0.0621)

0.1370∗∗
(0.0575)

0.1822∗∗
(0.0685)

0.2544∗∗
(0.1105)

不

Speciﬁcation

(2)

(3)

0.2533∗∗
(0.0968)

0.1463∗∗
(0.0747)

0.1872∗∗
(0.0600)

0.2642∗∗
(0.0713)

0.1798∗
(0.1035)

是的

不

0.2583∗∗
(0.1036)

0.1335∗∗
(0.0660)

0.1805∗∗
(0.0531)

0.2196∗∗
(0.0656)

0.1656
(0.1128)

是的

Notes: All models are population weighted, and the standard errors are heteroskedasticity-consistent
and clustered at the state of birth level. All models also include controls for the fraction of students
who are on time in grade 1, ahead as of grade 1, the youngest age at which school entry is legally
allowed, kindergarten subsidization, pupil-teacher ratio, relative salary of teachers, compulsory
school-leaving age, a quadratic age function, and state of birth, 种族, and region of birth–speciﬁc
cohort indicators. The sample size is 590,517.
∗signiﬁcant at 10%; ∗∗signiﬁcant at 5%.

serious endogeneity issues. 相似地, because we do not observe socioeco-
nomic status in childhood for adult respondents, we cannot parse out effects
by socioeconomic status (SES) in early grades. 然而, we can examine some
indirect evidence on mechanisms and distributional effects.

例如, one might expect that the long-run effects of retention policy
would be concentrated in the lower part of the wage distribution, since it
seems reasonable to think of retention as disproportionately affecting low-skill
孩子们. We employ quantile regressions to investigate this possibility and
summarize the results in table 6. Though coefﬁcients vary by speciﬁcation
and are not always precisely estimated, the retention coefﬁcient is positive
throughout the distribution. 而且, in no speciﬁcation is it possible to
reject a uniform distribution of effects across the quantiles. The average wage
effect reported in table 3, 然后, does not appear to be driven entirely by effects
of early grade retention on low-wage earners. 有趣的是, what it means to
be in the top quartile of wage earners also appears to rise with the strictness
of the retention policy to which a cohort was exposed.

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311

THE WAGES OF FAILURE

桌子 7. Retention Patterns across SES Groups

Retention Rate for:

全面的

(1)

Lowest

Middle Two
SES Quartile SES Quartiles SES Quartile

Highest

(2)

(3)

(4)

Panel A

Average

0.1295
(0.0596)

0.2242
(0.0920)

0.1107
(0.0421)

0.0584
(0.0448)

Panel B: First differences

Overall change < −0.03 −0.0610 (0.0318) Overall change > +0.03

0.0567
(0.0249)

−0.0840
(0.0620)

0.0764
(0.1036)

−0.0490
(0.0384)

0.0401
(0.0479)

−0.0317
(0.0603)

0.1111
(0.0782)

Sample
尺寸

(5)

111

Notes: State-level census data from 1960–1980. Weighted by cohort size. Standard deviations are
in parentheses.

The observed effects in the upper quantiles are suggestive of an effect on the
promoted because it is hard to imagine that a great many students who failed
grades 1 或者 2 would end up high in the wage distribution. For such spillovers
to exist, 然而, it must be the case that students in the upper quantiles
are exposed to students who are retained in early grades. One might question
whether this is true. Speciﬁcally, if high-wage workers attended schools for the
advantaged that featured little or no retention—or, more to the point, little or no
change in the retention rate over time—the upper quantile estimates reported
在表中 6 would be implausible. Below we investigate whether workers with
high wages were likely to have been exposed to retained peers in early grades
and whether there were changes over time in the intensity of that exposure.

桌子 7 reports retention rates across childhood SES categories. Panel A
reports state-level grade 1 retention rates by family income quartile for the
1960, 1970, 和 1980 census samples used in the previous tables. 尽管
there is more retention among children from the lowest family income quartile
(0.22), retention is common among the middle 50 percent of children (0.11)
and among the top quartile of the family income distribution (0.06).23 自从
the analysis in this article is based on within-state changes rather than levels,
panel B reports changes in retention rates. Speciﬁcally, it indicates that when
overall retention rates change between censuses by at least 1 标准差,
the retention rates for children from families with low, 中间, and high
incomes all move in the same direction. 简而言之, we observe similar changes
in retention policy or practice among all SES subgroups and ﬁnd no evidence

23. 为了我们的目的, the family income distribution is the distribution of family income observed

among our school entry cohorts, as deﬁned in section 3.

312

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桌子 8. Distribution of Free Lunch Eligible Students across Schools

Fraction of Schools Reporting Speciﬁed
Percentage of Students Eligible for Free Lunch

Percentage of
Schools Reporting
0–10 10–20 20–40 40–60 60–80 80–100 Free Lunch Status∗

1988

0.034

0.181

0.213

0.273

0.122

0.072

0.106

1992

0.029

0.147

0.166

0.277

0.178

0.114

0.089

1996

0.019

0.126

0.148

0.276

0.191

0.130

0.111

2000

0.021

0.167

0.156

0.264

0.182

0.126

0.083

2004

0.041

0.129

0.133

0.261

0.199

0.143

0.094

31%

70%

81%

86%

89%

∗Percentage of schools in NCES with complete data and at least ﬁve ﬁrst graders reporting free
lunch percentage.

that increased retention for one SES subgroup is associated with decreased
retention for another.

Middle and high SES students are exposed to retention and to changes
over time in retention rates, within their own SES quartiles. 此外, 和
perhaps just as important, middle and high SES students are exposed to low
SES peers, and thus to changes in retention among this group. 桌子 8, 基于
on the Common Core of Data from the National Center for Education Statistics
(NCES), shows that in a majority of schools more than 20 percent of students
are eligible for free lunches.24 While the time period available from the NCES
postdates our last wave of census data by several years, the fraction of students
eligible for free lunch appears stable during the sixteen-year span for which we
have data. The main conclusion we draw from table 8 is that the vast majority
of children attend schools that include at least some children from low-income
家庭.

So far we have shown that children from all SES groups are subject to
retention and that almost all children attend schools that include low SES
学生, who are the most likely to be retained. One could still worry that
perhaps retention was uncommon at middle and high SES schools, 因此
students at these schools, though exposed to low SES students, 不是
exposed to failers. The ﬁnal piece to the puzzle is to show that children from
various SES groups are retained whether they attend low, medium, or high
SES schools. 桌子 9 shows the distribution of retention across SES groups
and school types using data from the 1998 kindergarten entry cohort from
the Early Childhood Longitudinal Survey (ECLS). We use ECLS data here

24. The sample includes all schools with complete data that have at least ﬁve ﬁrst-grade students and

report the fraction of students eligible for free lunch.

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313

THE WAGES OF FAILURE

桌子 9. Distribution of Retention across SES Groups and School Types

Lowest

Middle Two

Highest

SES Quartile SES Quartiles SES Quartile Overall

(1)

(2)

(3)

(4)

0.1808
(0.3849)
[2398]

0.0945
(0.2926)
[5650]

0.0695
(0.2543)
[3248]

0.1094
(0.3122)
[11296]

Panel A

All schools

Panel B

Lowest school free lunch quartile

(High SES)

Middle two school free lunch quartiles

(Middle SES)

Highest school free lunch quartile

(Low SES)

0.080
(0.272)
[95]

0.162
(0.368)
[659]

0.198
(0.399)
[724]

0.094
(0.292)
[940]

0.090
(0.286)
[2088]

0.135
(0.342)
[751]

0.072
(0.259)
[1221]

0.044
(0.205)
[791]

0.066
(0.250)
[127]

0.081
(0.274)
[2256]

0.097
(0.296)
[3538]

0.159
(0.366)
[1602]

Notes: Standard deviations are in parentheses, and sample sizes are in square brackets. ECLS data
restricted to children who entered kindergarten for the ﬁrst time in 1998. All estimates weighted
using panel weights. A student is deﬁned as retained if he or she repeated kindergarten, 年级 1,
or grade 2.

because it is the only source that reports both student-level and school-level
SES (deﬁned by the fraction of students eligible for free lunch). Although this
is a much more recent school entry cohort, retention is directly measured for
kindergarten through second grade, and ECLS-computed SES is used in place
of family income, the distribution of retention across SES quartiles is similar
to the corresponding rates shown for the census data used in the main analysis
(compare table 9, panel A, with table 7, panel A). As one might expect, retention
rates reported in table 9 are highest for low SES schools: 0.20, 0.14, 和 0.07
for low, 中间, and high SES students, 分别. More important for our
目的, while retention rates are lower at middle and high SES schools,
there is still substantial retention—the highest SES quartile schools feature
retention rates of 0.08, 0.09, 和 0.07 for low, 中间, and high SES students,
分别, and middle SES schools feature retention rates of 0.16, 0.09, 和
0.04, 分别, for low, 中间, and high SES students.

Taken as a whole, tables 7–9 indicate that advantaged students are exposed
to retention both in their own SES strata and through the presence of low
SES students in their school. This is particularly true for middle SES students
who are likely to attend schools that draw a fairly large fraction of low-income
学生. It is not implausible, 然后, that long-run wages of advantaged or

314

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Philip Babcock and Kelly Bedard

promoted students would respond to retention policy. As discussed in section
2, the effects of retention policy on advantaged or promoted students could be
the result of associated changes in the targeting of institutional resources, 这
optimal effort choices of students, or the dynamics and composition of peer
groups.25

5. SUMMARY AND CONCLUSION
Most previous research on retention explores the impact of retention on the
retained but abstracts from any possible impact on promoted students. 经过
estimating differences in long-run education and labor market outcomes for
cohorts of students exposed to differing state-level primary school retention
费率, this article estimates the effects of retention policy on all students in a
cohort, retained and promoted. The main ﬁnding is that a 1 标准差
increase in retention through grade 2 is associated with a 0.7 percent increase
in average male hourly wages. 更远, the observed positive wage effect is
not limited to the lower tail of the wage distribution but appears to persist
throughout the distribution.

Given the estimates above, we can approximate the costs and beneﬁts as-
sociated with changes in retention rates. While the beneﬁt-cost analysis here
is very simpliﬁed, it demonstrates the importance of considering effects on
all students. Similar to Cascio (2005) and Eide and Showalter (2001), we ap-
proximate large retention costs for the retained; 然而, our estimates also
suggest that these are more than offset by the gains to those not retained.
Assuming a 0.03 increase in retention and a rate of return to experience esti-
mated from the 2000 census for men aged 25–64,26 the cost for the average
retained man is approximately $34,000.27 然而, marginally retained men are greatly outnumbered by promoted men, for whom the average return is ap- 近似地 $5,700. 与一个 0.03 increase in retention, the average discounted
lifetime gain per man is $4,500. Clearly gains on average do not imply positive effects for every worker. Given the assumptions in this exercise, some workers 25. Lazear’s (2001) 模型, which emphasizes externalities associated with disruptive students, offers another interesting possibility. If increased retention allows for better handling of disruptive stu- 凹痕, one could imagine that schools with only a few disruptive students might actually beneﬁt more from increased retention (and an associated marginal reduction in the number of disrup- tive students) than schools with many disruptive students. In the latter case, there may be more instances in which multiple students disrupt simultaneously. 26. All calculations are for the average man who has fourteen years of education. The return to experience is estimated using ln yi = φ0 + φ1 expi + φ2 exp2 i 27. This includes a $5,000 direct cost for an extra year of schooling (recall that our estimates in table
4 show no evidence of altered educational attainment), the loss of a year of income while still in
学校, and the loss of a year of experience in every working year. These losses are counterbalanced
to some degree by the wage return associated with the retention policy. All values are discounted to
age twenty.

+ ui .

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315

THE WAGES OF FAILURE

bear very large costs, but small gains to the large majority swamp the losses to
the marginally retained.

These results, we conclude, argue for a data-driven policy discussion that
moves beyond a narrow focus on how retention inﬂuences the retained and ex-
plicitly takes into account effects of retention policy on both the promoted and
the retained. To the extent that these effects may work in opposite directions,
institutions will need to balance the gains and losses to the various groups.
While we hesitate to offer speciﬁc policy recommendations on the optimal
level of retention, we submit that the ﬁndings here, and continued research in
this vein, will assist policy makers in striking the balance.

We thank Olivier Deschenes, Caroline Hoxby, Brian Jacob, Peter Kuhn, Heather Royer,
Jon Sonstelie, and seminar participants at the UCSB labor lunch and NBER Education
Working Group Spring 2009 for helpful comments.

参考
Akerlof, 乔治. 1997. Social distance and social decisions. Econometrica 65(5): 1005–
27.

亚历山大, Karl, Doris R. Entwisle, and Susan L. Dauber. 1995. On the success of failure:
A reassessment of the effects of retention in the primary grades. 纽约: 剑桥
大学出版社.

American Federation of Teachers (AFT). 1997. Passing on failure: District promotion
policies and practices. Available www.eric.ed.gov/PDFS/ED421560.pdf. Accessed 19 七月
2010.

Bedard, 凯莉, and Elizabeth Dhuey. 2009. Is September better than January? 这
effect of school entry age laws on skill accumulation. Unpublished paper, 大学
加利福尼亚州, 圣巴巴拉.

Betts, Julian R. 1996. The impact of educational standards on the level and distribution
of earnings. American Economic Review 88(1): 266–75.

Carnoy, 马丁, and Susanna Loeb. 2002. Does external accountability affect student
结果? A cross-state analysis. Educational Evaluation and Policy Analysis 24(4): 305–
31.

Cascio, Elizabeth U. 2005. School progression and the grade distribution of students:
Evidence from the Current Population Survey. IZA Discussion Paper No. 1747.

Costrell, Robert M. 1994. A simple model of educational standards. American Economic
审查 84: 956–71.

Deming, 大卫, and Susan Dynarski. 2008. The lengthening of childhood. 杂志
Economic Perspectives 22(3): 71–92.

Dhuey, Elizabeth. 2009. Who beneﬁts from kindergarten? Evidence from the intro-
duction of state subsidization. Unpublished paper, 多伦多大学.

316

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乙
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G
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e
s
t

哦
n
0
8
S
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p
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米
乙
e
r
2
0
2
3

Philip Babcock and Kelly Bedard

Eide, Eric R., and Mark H. Showalter. 2001. The effect of grade retention on educational
and labor market outcomes. Economics of Education Review 20: 563–76.

Glaeser, Edward L., Bruce I. Sacerdote, and Jose A. Scheinkman. 2003. The social
multiplier. Journal of the European Economic Association 1(2–3): 345–53.

Greene, Jay P., and Marcus A. Winters. 2007. Revisiting grade retention: An evalua-
tion of Florida’s test-based promotion policy. Education Finance and Policy 2(4): 319–
40.

Hanushek, Eric A., and Margaret E. 雷蒙德. 2004. The effect of school accountability
systems on the level and distribution of student achievement. Journal of the European
Economic Association 2(2–3): 406–15.

Hauser, Robert M. 1999. Should we end social promotion? Truth and consequences.
Unpublished paper, University of Wisconsin–Madison.

Hauser, Robert M., Carl B. Frederick, and Megan Andrew. 2005. Grade retention in
the age of accountability. Unpublished paper, University of Wisconsin–Madison

赫克曼, James, Anne Layne-Farrar, and Petra Todd. 1995. Does measured school
quality really matter? An examination of the earnings-quality relationship. NBER Work-
ing Paper No. W5274.

Holmes, C. 托马斯. 1989. Grade-level retention effects: A meta-analysis of research
学习. In Flunking grades: Research and policies on retention, edited by Lorie A. Shepard
and Mary Lee Smith, PP. 16-33. 伦敦: Falmer Press.

Holmes, C. 托马斯, and Kenneth M. Matthews. 1984. The effects of non-promotion
on elementary and junior high school pupils: A meta-analysis. Review of Educational
研究 54(2): 225–36.

雅各布, Brian A. 2002. Accountability, incentives and behavior: The impact of high-
stakes testing in the Chicago public schools. NBER Working Paper No. 8968.

雅各布, Brian A., and Lars Lefgren. 2004. Remedial education and student achieve-
蒙特: A regression-discontinuity analysis. Review of Economics and Statistics 86(1): 226–
44.

雅各布, Brian A., and Lars Lefgren. 2007. The effect of grade retention on high school
completion. NBER Working Paper No. W13514.

Jimerson, Shane R. 2001. Meta-analysis of grade retention research: Implications for
practice in the twenty-ﬁrst century. School Psychology Review 30(3): 420–37.

Karweit, Nancy L. 1991. Repeating a grade: Time to grow or denial of opportunity? 中心
for Research on Effective Schooling for Disadvantaged Students Report No. 16, Johns
Hopkins University.

Lavy, Victor M., Daniele Paserman, and Analia Schlosser. 2008. Inside the black of
box of ability peer effects: Evidence from variation in low achievers in the classroom.
NBER Working Paper No. 14415.

Lazear, Edward P. 2001. Educational production. Quarterly Journal of Economics 116(3):
777–803.

我

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3
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317

THE WAGES OF FAILURE

Lorence, Jon, A. Gary Dworkin, Laurence A. Toenjes, and Antwanette N. 爬坡道. 2002.
Grade retention and social promotion in Texas, 1994–1999: Academic achievement
among elementary school students. In Brookings Papers on Educational Policy: 2002,
edited by Diane Ravitch, PP. 13–52. 华盛顿, 直流: 布鲁金斯学会.

Mofﬁtt, 罗伯特. 2001. Policy interventions, low-level equilibria, and social interactions.
In Social dynamics, edited by Steven N. Durlauf and H. Peyton Young, PP. 45–82.
剑桥, 嘛: 与新闻界.

Neal, Derek, and Diane Whitmore Schanzenbach. 2007. Left behind by design: Proﬁ-
ciency counts and test-based accountability. NBER Working Paper No. W13293.

Pipho, Chris. 2002. Seven lessons learned from minimum competency testing. Avail-
able www.ecs.org/clearinghouse/32/67/3267.htm. Accessed 19 七月 2010.

Shepard, Lorrie A., and Mary Lee Smith. 1989. A review of research on kindergarten re-
注意力. In Flunking grades: Research and policies on retention, edited by Lorie A. Shepard
and Mary Lee Smith, PP. 64–78. 伦敦: Falmer Press.

汤普森, Charles L., and Elizabeth K. 坎宁安. 2000. Retention and social
promotion: Research and implications for policy. 纽约: ERIC Clearinghouse on Urban
教育. Available www.eric.ed.gov/PDFS/ED449241.pdf. Accessed 14 七月 2010.

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THE WAGES OF FAILURE

Table A.2. Retention through Second Grade

1959

1969

1979

伊尔

这

医学博士

明尼苏达州

公吨

纽约

或者

标清

0.18

0.24

0.19

0.12

0.10

0.11

0.18

0.02

0.10

–

0.16

0.10

0.21

0.25

0.16

0.14

0.00

0.13

0.43

–

0.23

0.11

0.10

0.30

0.31

0.24

0.08

0.21

0.11

0.15

0.25

0.23

0.09

0.26

0.08

0.11

0.07

0.06

0.11

0.17

0.15

0.10

0.15

–

0.15

0.09

0.08

0.12

0.10

0.02

0.19

0.18

0.26

0.09

0.04

0.08

0.22

0.12

0.16

0.18

0.05

0.16

0.20

0.09

0.10

0.16

0.11

0.10

0.18

–

0.20

0.05

0.16

0.14

0.09

0.08

0.01

0.08

0.15

0.14

0.09

0.13

0.14

0.16

0.04

0.08

0.09

0.06

0.07

–

0.16

0.10

0.08

0.07

0.05

0.08

–

0.11

0.12

–

0.04

0.11

0.08

0.10

0.11

0.09

0.07

–

0.13

0.03

–

0.13

–

0.05

322

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3 THE WAGES OF FAILURE: 图像

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