Seth Gershenson

(corresponding author)

School of Public Aﬀairs

美国大学

华盛顿, 直流 20016

gershens@american.edu

Erdal Tekin

School of Public Aﬀairs

美国大学

华盛顿, 直流 20016

tekin@american.edu

THE EFFECT OF COMMUNITY TRAUMATIC

EVENTS ON STUDENT ACHIEVEMENT:

EVIDENCE FROM THE BELTWAY

SNIPER ATTACKS

抽象的
Community traumatic events such as mass shootings, terrorist
attacks, and natural disasters have the potential to disrupt stu-
dent learning. 例如, these events can reduce instructional
time by causing teacher and student absences, school closures,
and disturbances to classroom and home routines. 这张纸
uses a quasi-experimental research design to identify the eﬀects
的 2002 “Beltway Sniper” attacks on student achievement in
Virginia’s public elementary schools. To identify the causal im-
pact of these events, the empirical analysis uses a diﬀerence-in-
diﬀerences strategy that exploits geographic variation in schools’
proximity to the attacks. The main results indicate that the attacks
signiﬁcantly reduced school-level proﬁciency rates in schools
within ﬁve miles of an attack. Evidence of a causal eﬀect is most
robust for math proﬁciency rates in the third and ﬁfth grades,
and third-grade reading proﬁciency, suggesting that the shootings
caused a decline in school proﬁciency rates of about 2 到 5 百分.
Particularly concerning from an equity standpoint, these eﬀects
appear to be entirely driven by achievement declines in schools
that serve higher proportions of racial minority and socioeco-
nomically disadvantaged students. 最后, results from supple-
mentary analyses suggest these deleterious eﬀects faded out in
subsequent years.

https://doi.org/10.1162/edfp_a_00234

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513

Effect of Community Traumatic Events on Achievement

I N T RO D U C T I O N

1 .
In contrast to the signiﬁcant drop in crime in the United States over the last two
几十年, the frequency of community traumatic events, such as terrorist attacks, 大量的
shootings, and natural or man-made disasters, has increased during this time period.
例如, a study conducted by the U.S. Federal Bureau of Investigation identiﬁed
160 incidents involving active shooters, 其中 486 individuals were killed and 557
individuals were wounded between 2000 和 2013 (我们. 司法部 2013).1
The frequency of such events has increased signiﬁcantly during this time period, 作为
平均数 6.4 active shooter incidents occurred annually between 2000 和 2006 com-
pared with an average of 16.4 such incidents per year between 2007 和 2013. 其他
study focusing on the time interval between incidents reached a similar conclusion
(科恩, Azrael, and Miller 2014). This pattern has heightened awareness of the need
for eﬀective policies designed to protect children and communities from the direct and
indirect eﬀects of such violent acts.2

Accumulating evidence indicates that exposure to violent traumatic events, 这样的
as domestic violence, 恐怖主义, random school shootings, and community traumatic
events in general, harms the health and well-being of children, as measured by de-
压力, aggressive behavior, anxiety and stress, social and emotional problems, 和
impaired cognitive development and academic achievement (Fremont 2004; Hoven
等人. 2005; Danese et al. 2009; Wendling 2009; Currie and Tekin 2012; Daniels and
Haist 2012; Di Pietro 2015).

The potential eﬀects of community traumatic events on student learning can op-
erate through both direct and indirect channels. Direct channels can include school
absenteeism and poor academic performance at school due to a lack of focus associ-
ated with anxiety and fear, and indirect channels can include disruptions created by
parents and teachers who experience problems themselves. 而且, children do not
have to be direct victims or witnesses of community traumatic events to be harmed:
indirect exposure such as learning about a violent death or serious injury, the fear of
death to self or a family member, an increased sense of vulnerability or helplessness,
or repeatedly engaging with trauma-related stories via the media can also harm chil-
dren’s well-being (Pfeﬀerbaum et al. 2001; Saylor et al. 2003; Calderoni et al. 2006;
Becker-Blease, Finkelhor, and Turner 2008; Holman, Garﬁn, and Silver 2014).

This paper provides insights into the impact of community traumatic events on stu-
dent achievement using the 2002 “Beltway Sniper” attacks as a natural experiment.3 As
explained in section 2, the Beltway Sniper attacks were a series of coordinated shootings
of individuals targeted randomly but living in the Washington, 直流, metropolitan area

1. According to the FBI, “Active shooter is a term used by law enforcement to describe a situation in which a
shooting is in progress and an aspect of the crime may aﬀect the protocols used in responding to and reacting at
the scene of the incident. Unlike a deﬁned crime, such as a murder or mass killing, the active aspect inherently
implies that both law enforcement personnel and citizens have the potential to aﬀect the outcome of the event
based upon their responses” (我们. 司法部 2013).

2. One such example is the Investigative Assistance for Violent Crimes Act of 2012, which authorizes the Depart-

ment of Justice to investigate mass shootings in public places.

3. Our deﬁnition of community traumatic events refers to incidents that aﬀect entire communities by causing
physical, emotional, or psychological distress, or harm to persons living in them. Individuals exposed to these
events must experience changes in their daily lives to an extent that often overwhelms them and leads to condi-
tions beyond their control, often resulting in depression, post-traumatic stress disorder, and suicidality (Prae-
torius 2006).

514

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Seth Gershenson and Erdal Tekin

and along Interstate 95 (I-95) in Virginia. The attacks left ten people dead and three
people critically injured over a period of three weeks in October 2002. The question
considered in this paper is an important one because the relationship between com-
munity traumatic events and student achievement has implications for both proactive
and reactive policy making. Regarding the former, debates over the costs and beneﬁts
of policies to prevent community traumatic events or minimize their harmful conse-
quences for the public could be signiﬁcantly inﬂuenced by evidence that these events
have a negative impact on student achievement. 例如, if children who are indi-
rectly exposed to these events suﬀer signiﬁcant setbacks at school, this would motivate
eﬀorts to identify policy interventions designed to prevent these events from occurring
and to reduce exposure among children. Regarding the latter, the strength of the re-
lationship between community traumatic events and academic achievement, 和
types of students who are most aﬀected by the trauma associated with these events, 有
important implications for the optimal provision of school and community resources
following a traumatic incident.

Our analysis improves upon existing research along several dimensions. 第一的, 我们
carefully address the endogeneity of exposure to community traumatic events by ex-
ploiting schools’ geographic distances from the locations of each of the sniper attacks
as a measure of “intensity of treatment.” In other words, variation in the intensity of
exposure, as measured by the distance between schools and shooting sites, allows us to
identify the causal impact of these attacks on student achievement using a diﬀerence-
in-diﬀerences (DD) estimation strategy. 更具体地说, we compare the proﬁciency
levels of students attending schools that are located near one of the shooting sites before
and after the shooting incident to the proﬁciency levels of students attending schools
farther away from the shooting sites. Proﬁciency rates are an important, policy-relevant
measure of schools’ academic performance, as they are the measure by which schools
were graded by the federal No Child Left Behind Act (NCLB).

第二, unlike most of the extant literature that focuses on outcomes of psycho-
logical well-being, we consider academic achievement of children as the outcome mea-
sure. Psychological manifestations of traumatic events on children may sometimes be
latent or the symptoms may not be promptly recognized by parents. It is also pos-
sible that children and parents are reluctant to acknowledge and seek help for these
problems because of social stigma. Unlike psychological symptomology, academic out-
comes are arguably more objective and easily observable—by parents, 教师, 和
school administrators—measures of the consequences of psychological trauma asso-
ciated with exposure to community traumatic events. Because aﬀected students may
have negative spillovers on their classmates, a ﬁnding of any impact on academic out-
comes would also provide compelling justiﬁcation for the public and policy makers to
be concerned about how to best help aﬀected children (Carrell and Hoekstra 2010).

第三, our outcome measures are school-level proﬁciency rates obtained from of-
ﬁcial school records. 所以, they are not subject to the reporting error potentially
inherent in subjective parental reports of their children’s academic proﬁciency. 这
is potentially an important improvement because parental reports can be problematic
如果, 例如, trauma associated with these events impairs parents’ ability to report
or remember accurately. 或者, some parents may have a tendency to relate any
academic problems their children are experiencing to these tragic events.

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515

Effect of Community Traumatic Events on Achievement

最后, unlike most other human-action and natural disasters, 恐怖袭击, 和
school shootings, the beltway sniper attacks were prolonged and intermittent in na-
真实. 在这个意义上, the psychological manifestations caused by these attacks may more
closely resemble those caused by the chronic community violence that is endemic to
many inner-city neighborhoods in the United States.4 Millions of children—15 percent
到 43 percent of girls and 14 百分比到 43 percent of boys—experience at least one trau-
matic event while growing up (我们. Department of Veteran Aﬀairs 2014). Regardless of
the cause of the traumatic stressors, these children are likely to exhibit a wide range of
reactions that can aﬀect many facets of their lives, including educational achievement
and attainment. 所以, the results of the current study are likely to provide a reli-
able and representative assessment of the impact of childhood exposure to the type of
stress experienced by a large segment of the United States population.

Our results provide robust evidence in support of a causal relationship between
exposure to the sniper attacks and math and reading proﬁciency of students in third
and ﬁfth grades. Speciﬁcally, the results suggest that the shootings caused a decline
in school proﬁciency rates of about 2 百分比到 5 百分. These eﬀects are similar in
magnitude to those obtained in Marcotte and Hemelt (2008) of the impact of ten un-
scheduled snow-related school closures on math and reading assessments of students
in similar grades in Maryland. Our estimates are also large enough to have changed the
standing of a nontrivial number of schools’ Adequate Yearly Progress (AYP) designa-
tions in the ﬁrst year of the NCLB. These results are fairly robust to the operationalized
deﬁnition of “closeness” to a sniper attack, controlling for time-variant school charac-
teristics and school district linear time trends, and accounting for overlap in the schools
aﬀected by the attack on the Pentagon on 11 九月 2001, which occurred in the year
preceding the sniper attacks. Particularly concerning from an equity standpoint, 伤害
caused by the sniper attacks appears to be primarily driven by achievement declines in
schools that predominantly serve racial minority and socioeconomically disadvantaged
学生. 最后, we show that the reductions in school proﬁciency caused by the sniper
attacks were relatively short-lived, fading out in subsequent academic years.

2 . B AC K G RO U N D
A voluminous literature in psychology describes the relationship between childhood
exposure to traumatic events and psychological well-being. Many studies in this liter-
ature suggest an association between exposure to traumatic events and psychological
健康. 然而, these studies are mostly based on conceptual considerations and de-
scriptive empirical analyses that fail to adequately address the problem of endogenous
exposure to traumatic events. These investigations typically rely on information drawn
from samples of interviews of individuals who were exposed to traumatic events such as
九月 11, 2001 terrorist attack (Beauschesne et al. 2002; Halpern-Felsher and
Millstein 2002; Hoven et al. 2005; Neria, DiGrande, and Adams 2011), 这 1995 Okla-
homa City bombing (Pfeﬀerbaum et al. 1999, 2000), or Hurricane Katrina (Spell et al.

4. A recent article by Monteiro and Rocha (2017) considers drug battles between gangs that take place in favelas
[slums] in Rio de Janeiro. Using variation in violence that occurs across time and space when gangs battle over
territories, the authors ﬁnd that exposure to such violence reduces student achievement in math. To the extent
that drug-related gang violence constitutes an extreme episode of a community-wide traumatic event, this study
is informative for the purposes of our analysis.

516

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Seth Gershenson and Erdal Tekin

2008). Several empirical studies acknowledge the potential endogeneity of exposure
to community traumatic events, but attempt to address this problem by conditioning
on a minimal set of control variables in a multivariate regression framework. 这是
an important limitation of the literature because children are unlikely to be exposed
to these events exogenously. 换句话说, children who are exposed to community
traumatic events may have certain attributes that contribute to their poor outcomes re-
gardless of the traumatic events to which they are exposed. 例如, if these events
are more likely to take place in neighborhoods with high poverty and crime rates or in
communities lacking the necessary resources to cope with the aftermath of traumatic
事件, conclusions drawn from correlational studies may overestimate the true impact
of exposure to community traumatic events.

相似地, parenting style and speciﬁc behaviors adopted by parents in response to
community traumatic events can inﬂuence the extent of the harm caused to their chil-
dren.5 For example, some parents may attempt to minimize the harm of these events
to their children by limiting children’s exposure to news media or by spending more
time with them. 或者, rigid work schedules or their own stresses may limit the
amount of extra care and emotional support they are able to provide to their children
during these times. 更糟, the stress experienced by parents might lead to coun-
terproductive behaviors, which may further fuel anxiety and fear among children—for
例子, by following trauma-related news stories in front of their children. Failing to
account for these behavioral responses or changes in parenting styles would cause an
upward bias in the case of “negative” parenting style and a downward bias in the case
of “positive” parenting style.

Another limitation is that the extant literature largely relies on self-reported retro-
spective data drawn from interviews of parents about the exposure of their children
to these events or interviews of aﬀected older children. Because information on both
exposure and reactions come from the same source, these data may suﬀer from system-
atic measurement error. 例如, parents whose children are performing poorly at
school may attribute this problem to past exposure to a traumatic event. 相关地, 作为
a practical matter, the analysis samples are self-selected in the sense that researchers
only have data on individuals who agreed to be interviewed. 总之, credible es-
timation of the impact of community traumatic events on children’s well-being poses
numerous challenges that the extant literature has failed to systematically address. 我们
contribute to this literature by applying a DD method to statewide, objective data on
primary school proﬁciency rates that are immune to these concerns.

最近, studies examining the short-run eﬀects of acute, extreme violence have ad-
dressed many limitations of earlier research. Speciﬁcally, a series of papers by Patrick
Sharkey and coauthors (Sharkey 2010; Sharkey et al. 2012, 2014) exploit the arguably
random temporal variation in extreme violence (IE。, homicides) in inner city neighbor-
hoods in Chicago and New York to estimate the eﬀect of proximity to such incidents on
standardized tests and other developmental assessments. The authors identify arguably
causal eﬀects by noting that conditional on living in a neighborhood that experiences

5. There are studies emphasizing the importance of parental behaviors in inﬂuencing the consequences of trau-
matic events on children (Buka et al. 2001; Plybon and Kliewer 2001), which have been shown to vary by so-
cioeconomic status (Guryan, Hurst, and Kearney 2008; Kalil, Ryan, and Corey 2012).

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517

Effect of Community Traumatic Events on Achievement

extreme violence, whether incidents of extreme violence occur in the week before, 或者
week after, the educational assessment is as good as random. In both New York and
芝加哥, the authors ﬁnd robust evidence that acute exposure to violence in the week
preceding the assessment reduces performance on English Language Arts (ELA) 测试
scores, 注意力, and impulse control relative to a control group of children who were
acutely exposed to extreme violence in the week following the assessment. 相似地, 关于-
cent research on the impact of school shootings (IE。, homicides that occurred on school
理由) ﬁnds that fatal school shootings reduce high school proﬁciency rates by about
4 到 5 percentage points in both math and ELA (Beland and Kim 2016). The harmful
eﬀects are even larger in more severe incidents that resulted in multiple deaths. 这些
eﬀects are identiﬁed using a school-district ﬁxed eﬀects DD strategy, where the control
group is composed of schools that did not experience a school shooting but are in the
same district as a school that did. 相似地, Poutvaara and Ropponen (2018) exploit a
school shooting that occurred in Finland right before high school seniors took their
national matriculation exams, which is associated with a 7 percent nationwide decline
in male performance on the exam.

These studies represent important advances in our understanding of the causal re-
lationship between acute exposure to extreme violence and cognitive development. 铝-
though the present study constitutes a fresh contribution to the growing line of analyses
that take serious steps to address the endogeneity problem, it also extends the litera-
ture in a number of important dimensions. 例如, the other studies (例如, 那些
by Sharkey and coauthors) are limited to neighborhoods in large, urban centers that
have relatively little sociodemographic diversity, which may not be representative for
the impact of unpredictable and purely random tragedies that are increasingly taking
place in the United States. 此外, the identiﬁcation strategy used by Sharkey and
coauthors only allows for the identiﬁcation of impacts that manifest in the immediate
aftermath (例如, one week) of the events. 最后, all of the studies focus on incidents
of acute violence that do not necessarily generalize to broader, community-wide stres-
sors that play out over longer time horizons. Using an identiﬁcation strategy that can
examine the persistence of such eﬀects, the current study contributes to the literature
discussed above by considering the Beltway Sniper attacks, which created a high degree
of stress and uncertainty and took place over a period of three weeks across a large, 所以-
ciodemographically diverse section of the country.

A related literature studies the eﬀect of large-scale violent events (例如, civil wars)
using data from countries such as Guatemala (Chamarbagwala and Morán 2011), Is-
rael (Brück, Di Maio, and Miaari 2014), 秘鲁 (León 2012), Rwanda (Akresh and Walque
2008), and Tajikistan (Shemyakina 2011). These studies consistently ﬁnd that individu-
als exposed to such events experience worse educational outcomes. 然而, the types
of events analyzed in these studies often disrupt many aspects of life, including eco-
nomic and political systems, and destroy infrastructure. 相比之下, the Beltway Sniper
attacks investigated in the current study did not destroy physical infrastructure nor did
they create sociopolitical upheaval, suggesting that the mechanisms through which the
sniper attacks might have inﬂuenced educational outcomes were quite diﬀerent than
those in previous analyses of large-scale violent events. 在这个意义上, our paper more
closely resembles recent studies of the impact of episodes of violent conﬂict between

518

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Seth Gershenson and Erdal Tekin

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来源: Clark County Prosecutor, www.clarkprosecutor.org/html/death/US/muhammad1181.htm.

数字 1. Locations of the Beltway Sniper Attacks

drug gangs and security forces or among the gangs themselves in Mexico (Márquez-
Padilla, Pérez-Arce, and Rodriguez-Castelán 2015; Romano 2015) and Brazil (Monteiro
and Rocha 2017). 然而, none of these studies focuses on the United States. 那里-
fore, the generalizability of ﬁndings from these studies to other contexts is not straight-
向前, especially because the settings analyzed in those papers have substantially
higher baseline levels of violence than the United States.

3 . T H E B E LT W AY S N I P E R AT TAC K S
The Beltway Sniper attacks were a series of coordinated shootings carried out in Oc-
tober 2002 in the Washington, 直流, metropolitan area and along I-95 in Virginia. 这
locations of these shootings are marked in the map displayed in ﬁgure 1. 之间 2
和 24 十月, ten people were fatally shot and another three people were critically
injured by riﬂe bullets ﬁred from some distance with marksman accuracy. Five of the
shootings took place in Virginia, resulting in three fatalities and two serious injuries.
One of the shootings targeted a 13-year-old student, who was wounded by a single bul-
let that struck him in the chest “as he waited in front of the school for the doors to be
opened” (John Allen Muhammad v. Maryland 2007, p. 12). The shootings sparked one

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519

Effect of Community Traumatic Events on Achievement

of the largest criminal manhunts in U.S. history until the two suspects, who were later
found guilty of these shootings, were captured on 24 October.6

The shootings were sporadic in nature, as victims were shot while mowing grass,
reading on a bus station bench, walking in the parking lot of a grocery store, and pump-
ing gas at a gas station. The unexplained and random nature of the shootings inﬂicted a
tremendous deal of stress and fear among people living in and around the communities
where the shootings occurred. This stress and fear prompted many local residents to
modify behaviors, such as skipping work and school, running or weaving through park-
ing lots, canceling outdoor activities, and avoiding shopping centers and gas stations
nearby I-95 (Coppola 2004; Zivotofsky and Koslowsky 2005; 米切尔 2007). The shoot-
ings also occupied both local and national media attention during this period, 哪个
further contributed to public fear and anxiety (米切尔 2007). Media coverage was so
intense that 503 articles appeared in the Washington Post alone during the three-week
period of shootings (Muzzatti and Featherstone 2007).7

As fear quickly spread throughout neighboring communities, many parents re-
acted by preventing their children from taking the school bus or walking home alone
and instead driving children to school. Schools went on “lockdown” and canceled out-
door events such as soccer games and ﬁeld trips.8 Schools in Chesterﬁeld, Goochland,
Hanover, Henrico, and Powhatan counties in Virginia and the city of Richmond closed
for multiple days as a result of the shootings (Prothero 2002). The number of school
children aﬀected by school closings reached about 200,000 in Richmond alone (Shreve-
port Times 2002). 此外, many parents voluntarily kept their children home even
when schools remained open. 因此, there was a signiﬁcant increase in absen-
teeism with daily attendance rates falling as low as 10 percent at elementary schools
close to one of the shootings (Schulte 2002).

Porter (2010) provides an in-depth qualitative analysis of the experiences of school
personnel and the emergency response by school district administrators to the shoot-
ings in Montgomery County, Maryland. Although Porter does not provide any insights
into the potential impact of the attacks on student achievement, the analysis is help-
ful in understanding the psychological ordeal experienced by various actors involved in
the lives of children aﬀected by the shootings, including parents, 教师, and school
管理员. Aside from this qualitative study, most of our knowledge about the im-
pact of the sniper attacks comes from reviews of newspaper articles and a few studies
based on interviews of a small number of parents and children who had lived near
shooting sites. These studies suggest that geographic proximity to the attack sites was
an important contributor to psychological symptomology exhibited by children such as
increased vulnerability and stress (管家, Panzer, and Goldfrank 2003; 米切尔 2007;
Becker-Blease, Finkelhor, and Turner 2008).

Becker-Blease, Finkelhor, and Turner (2008) analyzed data from the Develop-
mental Victimization Survey, which was conducted between December 2002 和

6. One of the perpetrators was sentenced to death and his execution was carried out in 2009. The other was

sentenced to six consecutive life sentences without the possibility of parole.

7. 因此, 超过 70 percent of citizens reported that they had followed the news more than usual during the
weeks of the sniper attacks, which highlights the role of media in shaping the public perceptions during the
时期 (Coppola 2004; 米切尔 2007).

8. See www.crimemuseum.org/crime-library/the-washington-dc-sniper.

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Seth Gershenson and Erdal Tekin

二月 2003. Focusing on the sample of respondents from Maryland (N= 30), 为了-
吉尼亚 (N= 49), and Washington, 直流 (N= 2), the authors found increased stress and
worry among children, with more apparent signs among minority children and those
from low-income households. 相似地, these children were also more likely to change
their daily routines during the period of shootings. 此外, children living in
neighborhoods near the shooting locations were likely more severely aﬀected than chil-
dren elsewhere in Virginia and Maryland, as well as the rest of the United States, 不是
only because the snipers were only targeting people in that area, but also because these
children had likely been exposed to more intense local media coverage (Becker-Blease,
Finkelhor, and Turner 2008).

在五月 2003, Self-Brown et al. (2011) studied the psychological responses of children
to the sniper attacks through telephone interviews with 355 parents who had children
2 到 27 years old and had lived in Washington, 直流, or its surrounding counties during
the sniper attacks. 关于 32 percent of parents participating in the interviews reported
that their children had experienced at least one psychological stress symptom related
to the sniper attacks.

There is also evidence to suggest that the shootings took a toll on the psychologi-
cal well-being of parents and teachers (Schulden et al. 2006; Porter 2010). 使用数据
from a survey of 1,205 adults who had lived in the communities aﬀected by the shoot-
ings in October 2002, Schulden et al. (2006) 表明 44 percent of parents had
experienced at least one traumatic stress symptom and 7 percent reported symptoms
consistent with a diagnosis of post-traumatic stress disorder. 此外, 作者
found that women who lived within 5 miles of any sniper attack were at greatest risk
for traumatic stress.

总之, there is widespread evidence to suggest the sniper attacks of October
2002 had a negative impact on the psychological well-being of citizens, especially chil-
dren and those from socioeconomically disadvantaged backgrounds, and those living
in neighboring communities. Given the well-documented relationship between psycho-
logical well-being and school outcomes (例如, Carrell and Hoekstra 2010), exposure to
these attacks might have also aﬀected student achievement, although this question has
not been studied to date. The goal of the present study is to ﬁll this gap in the literature.

4 . 数据
Academic performance is measured annually at the school level in the form of proﬁ-
ciency rates. These rates measure the percentage of students who score at or above a
predetermined “proﬁciency score” on Standards of Learning (SOL) standardized tests
administered each spring in Virginia’s public schools. These school-level proﬁciency
rates are made publicly available by the Virginia Department of Education and are based
on student performance on SOL tests that are typically administered each May.9 We fo-
cus on third- and ﬁfth-grade proﬁciency in mathematics and ELA, as these SOL tests
have been administered annually by the state since the spring of 1998. 重要的,
although the tests themselves have evolved over time, the basic reporting of schools’
proﬁciency rates has not.

9. See www.pen.k12.va.us/testing/achievement_data/archived/index.shtml.

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Effect of Community Traumatic Events on Achievement

Our primary analysis focuses on the academic years 1997–98 through 2002–03.
Henceforth, we refer to academic years by the spring semester (when the tests were
管理的), so the impact of the sniper attacks on test scores would appear in 2003.
The DD identiﬁcation strategy exploits variation in schools’ geographic proximity to
the attack locations. We argue this is a plausible measure of the intensity of treatment
(IE。, exposure to the sniper attacks), though arguably all children in the state might
have been aﬀected via exposure to intense media coverage. 所以, there may have
been spillover eﬀects on the “control” schools that were farther away from the attacks.
然而, it is important to note that such a bias would work against ﬁnding signiﬁcant
eﬀects of these attacks on school proﬁciency rates, and thus our estimates may be in-
terpreted as lower bounds of the “true” treatment eﬀects. Sensitivity analyses consider
various deﬁnitions of schools’ treatment statuses, or “closeness,” to the attacks, 并找到
that the main results are robust to the operationalized deﬁnition of “closeness.”

Closeness can be deﬁned by either the “commute” or “crow ﬂies” distance between
each school’s street address and that of the nearest sniper shooting.10 The results are
quite robust to which of these deﬁnitions is used to construct measures of “closeness,”
so we focus on the “crow ﬂies” distance for simplicity. After choosing how to measure
the distance between each school and its nearest sniper attack, we then must assume a
functional form through which distance enters the econometric model. The preferred
baseline model uses a simple binary indicator for “within 5 miles” of at least one shoot-
英. 然而, as shown in Appendix table A.1, the main results are fairly robust to using
alternative deﬁnitions using alternative thresholds, multiple categorical indicators (IE。,
之内 5 miles, 5 到 10 miles, 以及超过 10 miles), and a continuous quadratic func-
tion of miles to the nearest attack. These alternatives yield qualitatively similar results,
so we use the “within 5 miles” binary treatment for simplicity.

Our identiﬁcation strategy assumes that sniper attacks had either no or little im-
pact on children who attended schools relatively far from the attacks. 这个假设
does not require the proﬁciency levels of these students to be similar to those of their
counterparts who attended schools located in proximity to the shootings. 反而, 它是-
quires the proﬁciency levels to be trending similarly between the two groups of students
in the pre-attack period. 的确, schools that are farther away from the shooting sites
are mostly located in rural counties. 因此, the composition of students attending
these schools diﬀers in several dimensions from those in schools close to shooting sites,
including race, socioeconomic status, and academic achievement. There are also cor-
responding diﬀerences in school characteristics such as school enrollment (尺寸) 和
student–teacher ratio. While this does not necessarily constitute a problem for our anal-
分析, we exclude schools that are outside a 50-mile radius of all sniper shootings from
the analytic sample in an attempt to create a control group that more closely resembles
the treatment group. Exclusion of these schools amounts to a conservative approach,
if anything, as it would bias our analysis against ﬁnding an eﬀect given the likelihood
of spillover eﬀects on the control group; 然而, this turns out to be a moot point, 作为
the main results are robust to the deﬁnition of the control group. 最后, eliminating

10. Both types of distances were generated by the Web site freemaptools.com/how-far-is-it-between.htm, 哪个
uses an algorithm that evaluates potential driving routes to identify the shortest route between two geocoded
addresses for the “commute” distance and latitude and longitude geocodes to compute straight line “as the
crow ﬂies” distances.

522

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桌子 1. Description of Sniper Attacks’ Proximities to Virginia (VA) 学校

日期

Fatal

城市

状态

2 十月

3 十月

4 十月

7 十月

9 十月

11 十月

14 十月

19 十月

22 十月

是的

不

是的

不

是的

银泉

Rockville

Silver spring

Kensington

华盛顿

Fredericksburg

Bowie

Manassas

Fredericksburg

Falls Church

Ashland

银泉

医学博士

直流

医学博士

笔记: Distances are measured in miles “as the crow flies.”

Distance
to Nearest
学校 (mi)

VA Schools
之内 5 mi

VA Schools
之内 10 mi

9.88

7.08

7.07

4.49

7.07

1.20

18.76

0.28

1.02

0.71

0.97

10.24

170

these schools guards against the possibility that proﬁciency levels of students in rural
schools were trending diﬀerently than those of relatively more urban schools in the
华盛顿, 直流, suburbs, perhaps due to diﬀerences in district-level policies. 这是
not an implausible scenario since district policies may reﬂect in part the political and
cultural preferences of citizens, which are likely to diﬀer signiﬁcantly between rural and
urban communities. 尽管如此, the main results are robust to using alternative cut-
oﬀs, 例如 40 miles or 60 miles, and to including all Virginia schools in the analytic
sample.

We augment the school-level proﬁciency and “closeness to sniper attack” data with
information on time-variant school-level characteristics that are publicly provided in
the National Center for Education Statistics’ Common Core of Data.11 Speciﬁcally, 这些
variables include total enrollment, percent black, percent Hispanic, percent eligible for
free or reduced-price lunch, number of full-time equivalent teachers (FTE), and pupil–
teacher ratio. All but the last two variables have been collected since 1998, 然而
FTE and pupil–teacher ratios are only available from 1999 向前. We therefore im-
puted 1998 values of FTE and pupil–teacher ratio, though we also consider models that
exclude these two imputed variables and the main results are robust.12 Importantly,
controlling for these time-variant school characteristics in the DD regression models
increases the precision of the DD estimates and controls for potentially confounding
changes in schools’ student and teacher characteristics.

桌子 1 shows that although only ﬁve of the thirteen sniper shootings occurred in
弗吉尼亚州, the shootings that occurred in Maryland and in Washington, 直流, plausibly
aﬀected Virginia’s public school students as well, given the proximity and overlap in
media coverage between Northern Virginia and the areas outside Virginia in which

11. 参见http://nces.ed.gov/ccd/.
12. Values were imputed as the ﬁtted values of linear regressions containing school ﬁxed eﬀects, linear time trends,
observed total enrollment, percent black, percent Hispanic, and percent eligible for free or reduced-price lunch.
Results are robust to only controlling for the four school-level characteristics that are observed starting in 1998.

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Effect of Community Traumatic Events on Achievement

桌子 2. Descriptive Statistics for School Pass Rates

All Schools

Schools within 50 miles

英语 3

英语 5

数学 3

数学 5

全部

(1)

63.36
(17.19)
[6,312]

72.29
(16.45)
[6,284]

73.23
(16.68)
[6,310]

60.84
(21.85)
[6,283]

Outside 5 miles

之内 5 miles

(2)

63.02
(17.37)
[5,837]

72.04
(16.65)
[5,809]

72.91
(16.94)
[5,836]

60.39
(22.08)
[5,810]

(3)

67.58***
(14.09)
[475]
75.38***
(13.44)
[475]
77.19***
(12.39)
[474]
66.37***
(17.87)
[473]

全部

(4)

67.25
(17.31)
[2,882]

74.86
(16.76)
[2,913]

76.09
(16.70)
[2,879]

65.09
(21.49)
[2,909]

Outside 5 miles

之内 5 miles

(5)

67.19
(17.88)
[2,407]

74.76
(17.33)
[2,438]

75.87
(17.42)
[2,405]

64.84
(22.12)
[2,436]

(6)

67.58
(14.09)
[475]

75.38
(13.44)
[475]

77.19
(12.39)
[474]

66.37
(17.87)
[473]

Notes: Standard deviations are reported in parentheses. Sample sizes are reported in brackets. “Within ‘x’ miles”
refers to schools’ proximity to the nearest sniper attack.
***Statistically significant differences between treated (之内 5 miles) and control groups at the 99 percent confi-
dence level.

sniper attacks occurred. 例如, 这 3 October sniper shooting in Kensington,
Maryland, was within 5 miles of two Virginia public schools and within 10 miles of
seventy-two Virginia public schools. 相似地, all but two of the Maryland attacks were
之内 10 miles of at least one Virginia public school and four of the Maryland attacks
were within 10 miles of more than ten Virginia public schools. 因此, 桌子 1 suggests the
earlier attacks that occurred in Maryland and in Washington, 直流, potentially aﬀected
residents of Virginia and contribute to the geographic variation in “treatment status.”
桌子 2 summarizes the proﬁciency rates both for the overall sample and separately
by distance to the nearest sniper attack. Proﬁciency rates ranged from about 60 每-
分至 80 百分. To put these numbers in perspective, the thresholds for making
AYP in Virginia in the ﬁrst two years of NCLB were 61 in ELA and 59 in mathematics
(Virginia Board of Education 2010). 有趣的是, columns 2 和 3 show that there are
statistically signiﬁcant diﬀerences between “treated” and “control” schools in average
proﬁciency rates. This suggests that there were some systematic diﬀerences between
schools by schools’ proximities to an attack, which is unsurprising as the attacks were
relatively close to the Washington, 直流, metropolitan area. These diﬀerences further
motivate our decision to restrict the sample to schools within 50 miles of at least one
attack and highlight the importance of accounting for preexisting diﬀerences between
“treated” and “control” schools in the econometric model via school ﬁxed eﬀects.

Columns 4–6 of table 2 present the same summary statistics for the analytic sample
of schools within 50 “as the crow ﬂies” miles of at least one sniper attack. It is imme-
diately obvious that these control schools more closely resemble the treated schools, 作为
proﬁciency gaps between treated and control schools tend to be smaller and lose their
statistical signiﬁcance. This is the analytic sample used in the main analyses.

桌子 3 similarly summarizes schools’ distances to the sniper attacks and the time-
variant school characteristics observed in the Common Core of Data. A nontrivial num-
ber of Virginia public schools were proximate to at least one sniper attack. The average

524

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桌子 3. Descriptive Statistics for School Characteristics

全部

(1)

15.73
(11.88)

0.16

0.37

566.53
(195.16)

0.25
(0.27)

0.08
(0.12)

0.29
(0.24)

37.89
(13.51)

15.65
(9.32)

2,878

Treated

(2)

2.93
(1.15)

1.00

控制

(3)

18.23***
(11.42)

0.00***
0.25***

544.18
(163.43)

570.88
(200.49)

0.16
(0.11)

0.21
(0.17)

0.33
(0.21)

40.90
(13.13)

13.34
(2.67)

460

0.26***
(0.28)
0.06***
(0.08)
0.28*
(0.24)
37.31***
(13.51)
16.10***
(10.06)

2,418

Miles

之内 5 miles

之内 10 miles

Enrollment

% 黑色的

% Hispanic

% FRPL

FTE

Pupil-teacher ratio

氮

Notes: Standard deviations are reported in parentheses. Sample re-
stricted to schools within 50 miles “as the crow flies” of at least one
攻击. FRPL: free or reduced-price lunch eligible; FTE: full time equiva-
lent teachers.
***Statistically significant differences between treated (之内 5 miles)
and control groups at the 99 percent confidence level.

school in the analytic sample (之内 50 miles of at least one sniper attack) was about
16 miles from at least one sniper attack. 关于 16 percent of elementary schools were
之内 5 miles “as the crow ﬂies” of a sniper attack and 37 percent were within 10 miles.
There are several diﬀerences between treated and control elementary schools, as de-
ﬁned by the “ﬁve-mile” treatment. Treated schools have smaller enrollments, 但是这个
diﬀerence is not signiﬁcantly diﬀerent from zero. 种族, 种族的, and socioeconomic dif-
ferences in enrollments are statistically signiﬁcant, 然而, because treated schools’
enrollments are less black, more Hispanic, and more disadvantaged. 尽管是
较小, 一般, treated elementary schools have signiﬁcantly more FTE teachers
and signiﬁcantly lower pupil–teacher ratios.

5 . E C O N O M E T R I C M O D E L
Our goal is to estimate the impact of exposure to the Beltway Sniper attacks on academic
achievement. We do so by specifying the following reduced-form empirical model:

yst = β0 + β1Xst + β2Closes × d2003 + λt + δs + γ tDistricts + εst,

(1)

where yst is the proﬁciency rate of school s in academic year t in a particular grade and
subject.13 The time-varying school characteristics described in the previous section are
represented by the vector Xst. The variable Closes is a binary indicator equal to 1 如果

13. We estimated equation 1 using the natural logarithm of the outcome variables instead of levels. These results

are similar to those presented in our paper and are available from the authors upon request.

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Effect of Community Traumatic Events on Achievement

school is within 5 miles of any shooting location, and zero otherwise.14 The binary indi-
cator d2003 equals 1 in the academic year 2003, which is the treatment year in which the
sniper attacks occurred, and zero otherwise. Year ﬁxed eﬀects (λt) control for any secu-
lar time trends in the outcome variables and year-speciﬁc statewide shocks to academic
achievement associated with, 例如, national- or state-level policies. School ﬁxed
eﬀects (δs) account for any unobserved time-invariant heterogeneity between schools
in Virginia. We estimate equation 1 by ordinary least squares.15 In all analyses, 标准
errors are robust to clustering at the school level, making statistical inference robust
to arbitrary forms of both heteroskedasticity and serial correlation within schools over
time.16

The coeﬃcient of interest is β2, which represents the average eﬀect on school pro-
ﬁciency of being within 5 miles of a sniper attack. A causal interpretation of the esti-
mate of β2 in equation 1 hinges on the “parallel trends” assumption required by the
DD method. 直观地, this means that although there may be pre-existing diﬀerences
between “treated” and “control” schools, there are no pre-existing diﬀerential trends
between “treated” and “control” schools. We address this assumption in two ways.
第一的, we follow Marcotte and Hemelt (2008) in explicitly relaxing the “parallel trends”
assumption by controlling for school district–speciﬁc linear time trends (γ tDistrict).
所以, our empirical speciﬁcation controls for any unobservable district-level char-
acteristics and policies that are trending linearly over time and predict proﬁciency rates,
which is potentially important given that policies and decisions regarding school clo-
sures are typically made at the district level (Marcotte and Hemelt 2008).17 第二,
we directly test the “parallel trends” assumption by estimating an event-study speciﬁ-
cation that allows the treatment to have an eﬀect in years prior to the sniper attacks.
If these placebo eﬀects are statistically signiﬁcant, particularly in the year before the
sniper attacks, we would worry that the “parallel trends” assumption fails and that sig-
niﬁcant estimates of β2 in the baseline equation 1 are spuriously driven by pre-existing

14. Appendix table A.1 shows the main ﬁndings are robust to using alternative speciﬁcations of “closeness,” such as
a continuous quadratic function of the school’s distance to the closest attack site, using alternative thresholds
to deﬁne a binary “closeness” indicator, and using a pair of mutually exclusive categorical indicators for “within
ﬁve miles” and “ﬁve to ten miles,” with the omitted reference category being “more than ten miles from an
attack.”

15. We also estimate the models by weighted least squares using schools’ grade-speciﬁc enrollments as weights
(Solon, 海德尔, and Wooldridge 2015). These estimates are qualitatively similar to, and reported alongside, 这
unweighted estimates in table 4.

16. Clustering at the district level yields nearly identical statistical inference, which is unsurprising because schools
are nested in districts and all models condition on school ﬁxed eﬀects and district-speciﬁc time trends. We prefer
clustering at the school level because the treatment varies at the school level.

17. Allowing for quadratic district-speciﬁc time trends yields qualitatively similar results. Note that an alternative
approach could be to estimate models with school-speciﬁc linear trends. 然而, 与约 540 elementary
schools in the analytic sample and only 6 years of data, we lose a commensurate number of degrees of freedom
by doing so. 因此, estimates of β2 in models that condition on school-speciﬁc linear trends are less precise,
though generally of the same sign as those obtained from the estimation of equation 1 and its district trend
analog. As an alternative attempt to account for the possibility of diﬀerential trends at the school level, we also
estimate our models controlling for two-way interactions of each of our school-level control variables and year
指标. If the year-to-year changes in test scores at the school level are highly correlated with changes in
school level characteristics such as enrollment, pupil–teacher ratio, and the racial composition of the schools,
then these interactions may capture the changes in school level trends in a ﬂexible way. The results from this
speciﬁcation are similar to the main results presented in the paper and are available from the authors upon
request.

526

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Seth Gershenson and Erdal Tekin

diﬀerential trends in the treated schools. It is reassuring, 然后, that in the results pre-
sented below event-study estimates provide evidence that is consistent with the sniper
attacks having a causal eﬀect on schools’ math and ELA proﬁciency rates.

最后, we estimate equation 1 separately by school type to test for heterogeneous
eﬀects, as there are several reasons why schools serving diﬀerent student populations
might be diﬀerentially aﬀected by community traumatic events. Speciﬁcally, 因为
the aggregate data do not distinguish between proﬁciency rates of diﬀerent student
subgroups, we divide schools into terciles based on the percentage of total 2003 enroll-
ment that is black, and the percentage of total 2003 enrollment that is eligible for free or
reduced-price lunch (FRPL). There are at least two reasons to expect that the academic
achievement of socioeconomically disadvantaged and racial minority students was dis-
proportionately harmed by the disruptions and stress caused by the sniper attacks. 第一的,
as discussed in section 2, parental behaviors have the potential to mitigate the impact
of community traumatic events on children (Buka et al. 2001; Plybon and Kliewer
2001). Given the large research literature documenting the diﬀerences by socioeco-
nomic status (SES) in both the quality and quantity of time parents spend with school-
age children (例如, Guryan, Hurst, and Kearney 2008; Kalil, Ryan, and Corey 2012), 这是
plausible that high-SES parents had the resources necessary to provide support at home
and outside the traditional school day to help children cope with the trauma. 第二,
recent research on the eﬀects of weather-induced school closures and student absences
on academic achievement ﬁnds, at least in certain subjects and grade levels, the harm-
ful eﬀects of lost instructional time are greater in poorer schools (Marcotte and Hemelt
2008; 古德曼 2014). Given that school closures and student absences are potential
mechanisms through which the sniper attacks aﬀected achievement, the harmful ef-
fects of sniper-induced absences and school closures might be greater in disadvantaged
学校, if such schools are less able to provide the appropriate counseling and, 更多的
一般来说, struggle to solve the coordination problem inherent in public education (IE。,
Lazear 2001). 而且, given that absenteeism rates are higher among disadvantaged
学生 (Gershenson, Jacknowitz, and Brannegan 2017), another potential source of
heterogeneity in the sniper attacks’ eﬀects on academic achievement is through larger
eﬀects of the attacks on student absences in low-SES schools.

6 . R E S U LT S
Our main results are presented in table 4. Each cell in table 4 contains the estimate
of β2 in a unique regression, which measures the eﬀect of being within 5 miles of a
sniper attack. We present estimates separately for both the ELA and math proﬁciency
rates for each of grades 3 和 5. Columns 1 和 2 report estimates of β2 from equation
1 without and with time-variant school characteristics, 分别. If our identiﬁcation
strategy is valid, then controlling for exogenous determinants of academic test scores
should not inﬂuence the estimate of β2.

Column 1 of table 4 shows that being within a 5-mile radius of a sniper attack is
associated with lower pass rates in both subjects for both grade levels. 此外,
the estimated eﬀects are statistically signiﬁcant for three of the four models and the
magnitudes are sizeable, ranging from about 1.5 到 3 百分点. Taking the mean
pass rates in schools outside the 5-mile radius presented in column 5 of table 2 作为一个

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Effect of Community Traumatic Events on Achievement

桌子 4. Estimates of Effect of Proximity to Sniper Attacks on School Pass Rates

不
Controls

(1)

−2.100
(1.114)*

2,851
−1.423
(1.155)

2,881
−2.309
(1.019)**

2,848
−2.945
(1.336)**

Baseline

(2)

−1.924
(1.087)*

2,851
−1.376
(1.167)

2,881
−2.624
(0.964)***

2,848
−2.974
(1.350)**

2,878

是的

不

是的

Baseline
Weighted

(3)

−1.265
(1.242)

2,816
−1.160
(1.103)

2,806
−2.078
(1.051)**

2,816
−2.591
(1.386)*

2,807

是的

英语 3

氮

英语 5

氮

数学 3

氮

数学 5

氮

Trends

Controls

I-95
Sample

(4)

−1.110
(1.064)

2,243
−1.726
(1.190)

2,269
−2.744
(0.958)***

2,242
−3.703
(1.384)***

Common
支持
Sample

(5)

Nearest-
Neighbor
Sample

(6)

Pentagon
Sample

(7)

−3.303
(0.959)***

−3.732
(1.041)***

−2.640
(1.071)**

2,263
−1.012
(1.044)

2,500
−2.521
(0.858)***

2,471
−2.522
(1.265)**

1,372
−1.166
(1.117)

1,316
−1.705
(0.949)*

1,360
−3.000
(1.340)***

2,264

2,372

1,377

是的

不

2,880
−1.205
(1.224)

2,911
−2.258
(0.848)***

2,877
−2.183
(1.257)*

2,907

是的

Notes: Each cell reports the interaction term (treatment effect) from a distinct regression. Standard errors are reported in paren-
theses and are robust to clustering at the school level. School controls in columns 2—4 include full-time equivalent teachers,
student—teacher ratio, total school enrollment, percent black, percent Hispanic, and percent free or reduced-price lunch eligible.
All models control for school and year fixed effects. Columns 1—4 and 7 include linear district time trends. Sample contains data
从 1998 到 2003 school years (6 年). Observations in 2002 for schools within 5 miles of the Pentagon are excluded from
the analytic samples in all columns except for column 7. The treatment term indicator in column 7 equals one if the school was
之内 5 miles of the Pentagon in 2002 or was within 5 miles of a sniper attack in 2003. The samples in columns 5 和 6 是
restricted based on predicted propensity scores that reflect the propensity to be within 5 miles of a shooting. Propensities were
estimated by fully flexible logit models that included lagged proficiency rates. In column 5, the analytic sample is restricted to the
area of common support. In column 6, the analytic sample is restricted to the set of treated schools and five nearest-neighbor
control school matches.
***Statistically significant at the 99 percent confidence level; **statistically significant at the 95 percent confidence level;
*statistically significant at the 90 percent confidence level.

基础, these estimates translate into eﬀect sizes of about 2 percent for ﬁfth-grade ELA
和 4.5 percent for ﬁfth-grade math.

Column 2 shows that the estimates are robust to controlling for time-variant school
特征. This supports the validity of our identiﬁcation strategy, as it suggests the
other known determinants of academic proﬁciency are orthogonal to the within-school
variation in exposure to sniper attacks. 此外, Appendix table A.1 shows that the
patterns observed in table 4 are fairly robust to how “closeness” to a sniper attack is
测量的, because using alternative thresholds, as well as continuous and nonpara-
metric speciﬁcations, suggests schools closer to sniper attacks experienced signiﬁcant
declines in proﬁciency rates in 2003, particularly in math, relative to schools that were
farther away.

As suggested by Solon, 海德尔, and Wooldridge (2015), weighted least squares es-
timates of the baseline model that weight by schools’ grade-speciﬁc enrollments are
reported in column 3. These estimates are quite similar to the unweighted estimates
reported in column 2. Viewed as a diagnostic, this similarity suggests that the model
is correctly speciﬁed. In subsequent analyses we focus on the unweighted estimates
because grade-speciﬁc enrollments are missing for several schools and because the or-
dinary least squares estimates tend to be more precise. The latter is unsurprising, as it
suggests the underlying student-level error terms are correlated within schools (Solon,

528

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海德尔, and Wooldridge 2015). 因此, as discussed in section 5, all inference is
conducted using cluster-robust standard errors, which are also robust to arbitrary forms
of heteroskedasticity.

It is important to remember that the sniper shootings primarily occurred along the
I-95 corridor. One potential concern with our identiﬁcation strategy is that there was
something peculiar about schools located along the I-95 corridor that caused the pro-
ﬁciency rates in these schools to decrease in the year of the sniper attacks. 到目前为止,
control schools along I-95 are grouped together with other control schools that were
之间 5 和 50 miles of a sniper attack. 因此, we could be obtaining the par-
tial impact of some confounding event that aﬀected all schools along the I-95 corridor
that had nothing to do with the sniper attacks. Although we do not have a speciﬁc con-
founding event or factor that diﬀerentially aﬀected schools along I-95 in 2003 in mind,
we nevertheless guard against this possibility by estimating our main models using an
analytic sample restricted to schools in districts along the I-95 corridor. Doing so al-
lows us to conduct the analysis with a more homogenous sample of schools that is less
susceptible to potentially confounding factors that violate the parallel trends identify-
ing assumption. If the estimates obtained in column 2 of table 4 were indeed caused
by the sniper attacks, analyses of the I-95 sample should yield results similar to those
obtained in the full sample. 因此, we reestimate our baseline speciﬁcation us-
ing a restricted analytic sample of schools located along the I-95 corridor. Speciﬁcally,
the “I-95 sample” includes all schools in the twenty school divisions (districts) 通过
which I-95 passes and the city/town school divisions that are within 10 miles of I-95.18
As shown in column 4 of table 4, the estimates from this sample are very similar to
those in column 2. 尤其, the estimates for third- and ﬁfth-grade math exams are sta-
tistically signiﬁcant and similar in size to those for the baseline sample in column 2,
despite signiﬁcant reductions in the sample size. We interpret this ﬁnding as evidence
against an argument that our results are driven by some confounding factor related to
treated schools’ proximity to I-95.

或者, we could restrict the control group to observationally similar, 西米-
larly trending schools using a matching-on-observables procedure. We make two such
restrictions using propensity scores estimated by a ﬂexible logit model that includes
current school characteristics (the Xst in equation 1) and cubics in three lags of the
proﬁciency-rate outcomes. We use these estimated propensity scores to restrict the ana-
lytic sample to schools in the area of common support, and to the ﬁve nearest neighbors
of each treated school, in columns 5 和 6, 分别. We then estimate the baseline
model on these matched samples, without district trends and time-varying X, 作为
matching procedure explicitly matched on X and pre-existing trends in y. 再次,
the point estimates derived from the “matched sample” analyses in columns 5 和 6
closely resemble the baseline estimates reported in column 2. This is reassuring, 然而

18. The fourteen county school divisions are Greensville, Emporia, Sussex, Prince George, Dinwiddie, Chesterﬁeld,
Henrico, Hanover, Caroline, Spotsylvania, Staﬀord, Prince William, Arlington, and Fairfax. The six city/town
school divisions are Petersburg, Colonial Heights, Richmond, Fredericksburg, Falls Church, and Alexandria.
Because seven of the county school divisions contain schools with catchment areas that are more than ten miles
from I-95, we also verify that these results are robust to further restricting the “I-95 sample” to exclude such
学校.

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529

Effect of Community Traumatic Events on Achievement

unsurprising, as the district trends in the baseline model already control for possible
diﬀerences between treated and control schools’ trends.

最后, the impact of traumatic events that occurred elsewhere in the country dur-
ing our analysis period would be captured by our year ﬁxed eﬀects. One potential ex-
ception is the terrorist attack on the Pentagon that occurred on 11 九月 2001.19
Given the proximity of the Pentagon to several of the Virginia communities aﬀected by
the sniper attacks that occurred almost one year later, it is possible that persistent psy-
chological symptomology of trauma associated with the 11 九月 2001 attacks, 和
with that on the Pentagon in particular, might confound our analysis of the 2002 sniper
attacks. 换句话说, the eﬀects of the sniper attacks documented herein might be
at least partly attributable to the Pentagon attack. To provide further insights into the
问题, we consider a version of equation 1 in which the treatment is redeﬁned as being
within a 5-mile radius of the sniper attacks in October 2002 or within a 5-mile radius
of the Pentagon in 2001. In addition to providing evidence on the sensitivity of our
main results, this analysis is interesting in its own right, as it provides evidence on
the average impact of both the Pentagon and sniper attacks. As shown in column 7 的
桌子 4, these estimates are quite similar in size and precision to our preferred baseline
估计.

总之, the evidence presented in table 4 indicates that being within a 5-mile
radius of a sniper attack site is associated with a statistically signiﬁcant decrease in
proﬁciency on third-grade ELA and third- and ﬁfth-grade math tests. This result is con-
sistent with previous research on the harmful eﬀects of disruptions to learning, 哪个
ﬁnds that weather-related school closures and exposure to acute incidents of extreme vi-
olence have relatively larger eﬀects on achievement in the elementary grades (马科特
and Hemelt 2008; Sharkey et al. 2014). 而且, it is important to emphasize that the
most robust estimates are obtained for math proﬁciency. This is consistent with the
previous literature on the eﬃcacy of school inputs that routinely shows math achieve-
ment scores are more sensitive than ELA scores to shocks to school environments (例如,
Hanushek and Rivkin 2010). Currie and Thomas (2001) speculate this may be because
children are more apt to learn reading skills at home, which suggests, to the extent that
the sniper attacks caused absences, school closures, and displaced instructional time
during school days, one would expect to see larger eﬀects on math achievement.

Next we estimate an event-study version of equation 1 to trace out the trends in
proﬁciency rates, separately for treated and control schools, year-by-year for the peri-
ods leading up to the year of the sniper shootings. As discussed in section 5, this pro-
vides a simple test of the “parallel trends” assumption required for consistency by the
DD speciﬁcation given in equation 1. 正式地, this is done by augmenting equation
1 to include interactions between each of the year indicators with the Close treatment
指标. Event study estimates of speciﬁcations that control for time-variant school

19. The attack on the Pentagon was part of a larger, coordinated terrorist attack by the terrorist group Al-Qaeda on
美国. 在 11 九月 2001, two planes crashed into the World Trade Center buildings in New York
城市. On the same day, a third plane crashed into the Pentagon causing a partial collapse of the headquarters.
A fourth plane, which was heading to Washington, 直流, crashed in a ﬁeld in Pennsylvania. A total of 2,996
individuals were killed in the attacks. The total number of casualties at the Pentagon crash was 189, 包括
59 passengers, 125 people who were in the building at the time, 和 5 terrorists. As the deadliest terrorist attack
ever carried out in the United States, the events of 11 九月 2001 caused a tremendous amount of fear and
anxiety.

530

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桌子 5. Event Study Estimates of Effect of Proximity to Sniper Attacks on School Pass Rates

Outcome

1998

1999

2000

2001

2002

2003

1998 × Close

1999 × Close

2000 × Close

2001 × Close

2002 × Close
2003 × Close

School-years (氮)

学校 (clusters)

ELA 3

(1)

−24.284

(0.815)***

−15.774

(0.617)***

−14.548

(0.547)***
−9.378
(0.568)***

—

1.954
(0.557)***
−0.237
(1.796)

0.693
(1.669)
−1.320
(1.485)

0.139
(1.268)

Omit
−2.097
(1.388)

2,851

513

ELA 5

(2)

−2.973
(0.677)***
−3.345
(0.602)***
−5.207
(0.514)***
−2.579
(0.552)***

—

4.496
(0.580)***

1.561
(1.643)

3.240
(1.598)**
−0.659
(1.349)

1.980
(1.265)

−0.478
(1.392)

2,881

546

数学 3

(3)

−19.877

(0.683)***

−15.176

(0.575)***
−9.824
(0.499)***
−4.174
(0.465)***

—

5.642
(0.508)***
−0.283
(1.443)

1.447
(1.275)
−0.381
(1.177)

0.305
(1.031)

−2.447
(1.095)**

2,848

511

数学 5

(4)

−23.008

(0.854)***

−19.807

(0.707)***
−5.997
(0.648)***
−3.829
(0.621)***

—

3.771
(0.684)***

1.142
(2.268)

2.695
(2.129)
−1.825
(1.729)
−1.250
(1.705)

−3.495
(1.531)**

2,878

541

Notes: Standard errors are reported in parentheses and are robust to clustering at the school
等级. Analytic samples are restricted to schools within 50 miles of at least one sniper shooting.
All models control for school and year fixed effects, district specific linear time trends, 和
the following time-variant school controls: full-time equivalent teachers, student—teacher ratio,
total school enrollment, percent black, percent Hispanic, and percent free or reduced-price
lunch eligible. Sample contains data from 1998 到 2003 school years (6 年). 观察结果
在 2002 for schools within 5 miles of the Pentagon are excluded from the analytic samples.
ELA: English language arts.
***Statistically significant at the 99 percent confidence level; **statistically significant at the
95 percent confidence level.

characteristics are presented in table 5. Consistent with our earlier ﬁndings, the es-
timates of the coeﬃcients on the interaction between the Close and 2003 (treatment
年) indicators are negative for all four tests and statistically signiﬁcant for math in
both grades. 此外, these treatment eﬀect estimates are larger in magnitude
than all of the other interaction terms. 直观地, the goal of the event study analysis
is to examine the diﬀerences between treatment and control schools in the years lead-
ing up to 2003, the academic year in which the sniper attacks took place. This is most
easily accomplished visually, so we plot the interaction terms reported in table 5, 沿着
with their 95 percent conﬁdence intervals, in ﬁgure 2. As illustrated in ﬁgure 2, 那里
is a clear overall pattern of a statistically signiﬁcant divergence in 2003 from the pre-
sniper attack period trends. The aforementioned pattern is most pronounced for third-
grade English and third- and ﬁfth-grade math scores. 此外, the estimates on
the year indicators suggest that average pass rates had been increasing consistently over
the analysis period. Interpreting the estimates on the interaction terms in conjunction

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531

Effect of Community Traumatic Events on Achievement

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Notes: The omitted year is 2002. Brackets represent 95 percent confidence intervals, robust to clustering at school level. The bars rep-
resent the estimated interaction terms reported in Table 5, from event study models that control for time-varying school characteristics
and school and year fixed effects.

数字 2. Event Study Estimates of the Impact of Sniper Attacks on Pass Rates

with the individual year indicators supports the hypothesis that the sniper attacks de-
creased proﬁciency rates in nearby schools.

Given the evidence presented to this point, which suggests that the sniper attacks
caused a statistically signiﬁcant decrease in school proﬁciency rates in third-grade ELA
第三个- and ﬁfth-grade math, natural questions to consider are whether the trauma
was ampliﬁed in schools that were close to multiple shootings and whether these ef-
fects persisted into subsequent school years. Regarding the former, eleven schools were
之内 5 miles of two sniper attacks. The treatment in these schools was likely particu-
larly intense. To formally test this hypothesis, we augment the baseline model to code
Close as a vector of categorical indicators for the number of nearby attacks, omitting
“zero attacks” as the reference category. These results are presented in table 6. 这里,
we see evidence of signiﬁcant dosage eﬀects for each subject: The eﬀect of being within
5 miles of two attacks is two to seven times as large as being within 5 miles of one at-
tack and is strongly statistically signiﬁcant in each case. The treatment indicators are
jointly signiﬁcant for each subject and the eﬀect of being within 5 miles of two attacks is
signiﬁcantly larger than the eﬀect of being within 5 miles of one attack in three of four
案例. The presence of such dosage results are consistent with the sniper attacks having
had a causal impact on student achievement and suggests that more severe community
traumatic events cause proportionally greater harm to student learning.

An analysis of the persistence of such eﬀects is possible because the SOL tests con-
tinued in a similar form for two additional years following the academic year in which

532

Seth Gershenson and Erdal Tekin

桌子 6. Dosage Effects of Sniper Attacks on School Pass Rates

英语 3

英语 5

主题

(1)

(2)

2003 × 1 攻击

2003 × 2 Attacks

Joint Sig. (p)

Difference (p)

氮

−1.196
(1.118)
−7.729
(2.104)***

−0.887
(1.214)
−5.427
(2.067)***

0.001

0.003

2,851

0.032

0.035

2,881

数学 3

(3)

−2.290
(1.019)**
−5.390
(1.545)***

0.001

0.060

2,848

数学 5

(4)

−2.690
(1.419)*
−5.301
(1.997)***

0.016

0.206

2,878

Notes: The omitted category is 2003 × 0 Attacks, where Attacks counts the number of
attacks that occurred within 5 miles of the school. Standard errors in parentheses are
robust to clustering at the school level. Analytic samples restricted to schools within 50
miles of at least one sniper shooting. School controls include full-time equivalent teach-
呃, student—teacher ratio, total school enrollment, percent black, percent Hispanic, 和
percent free or reduced-price lunch eligible. All models control for school and year fixed
effects as well as district-specific linear time trends. Sample contains data from 1998
到 2005 school years (8 年). Observations in 2002 for schools within 5 miles of the
Pentagon are excluded from the analytic samples.
***Statistical significance at the 99 percent confidence level; **statistical significance
在 95 percent confidence level; *statistical significance at the 90 percent confidence
等级.

the sniper attacks occurred. 因此, 桌子 7 presents estimates of augmented base-
line and dosage models that utilize data through 2005. These models include the usual
Close × d2003 interaction term and Close × Post interaction terms, where Post equals 1 如果
the academic year is 2004 或者 2005, and zero otherwise. The speciﬁcation estimated in
panel A of table 7 is otherwise identical to the baseline speciﬁcation estimated in table
4. These results are consistent with the sniper attacks having had a negative impact on
students’ academic achievement in 2003. 尤其, the estimated eﬀects of being
之内 5 miles of a sniper attack are uniformly negative and are statistically signiﬁcant
in three subjects: third-grade ELA and third- and ﬁfth-grade math. 然而, these ef-
fects do not persist, as the estimated eﬀects of proximity to a sniper attack in subsequent
years tend to be statistically indistinguishable from zero and small in magnitude. 这是
perhaps unsurprising that we detect no persistent eﬀects of the sniper attacks on proﬁ-
ciency rates in subsequent years across all schools—as the attacks occurred in October
的 2002 和 2004 tests were administered in May 2004, 多于 18 月
later—and the majority of treated schools were exposed to only one attack.

然而, the dosage results reported in table 6 suggest that if the impacts persisted
任何地方, it would likely have been in the most intensely treated schools that were
close to multiple sniper attacks. Panel B of table 7 tests this hypothesis by allowing
the persistence eﬀects to vary with intensity of treatment. 的确, these results show
some evidence that the eﬀects did persist in subsequent years, particularly in math,
in the most intensely treated schools. Like in panel A, the dosage-persistence results
reported in panel B show no evidence of persistent eﬀects in schools that were close
to only one shooting, and the persistent eﬀects of exposure to two shootings are less
precisely estimated than those in the year of the attacks.

再次, the results presented in table 7 are consistent with the sniper attacks
having had a causal eﬀect on student achievement immediately following the attacks

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533

Effect of Community Traumatic Events on Achievement

桌子 7. Persistence in Effect of Sniper Attacks on School Pass Rates

主题

2003 × Close

2004/5 × Close

Difference (p)

氮

2003 × 1 攻击

2003 × 2 Attacks

2004/5 × 1 攻击

2004/5 × 2 Attacks

Joint Sig. of 2004—05 interactions (p)

Difference in 1A (p)

Difference in 2A (p)

氮

英语 3

英语 5

数学 3

(1)

(2)

(3)

数学 5

(4)

Panel A: Exposure Model

−2.609
(1.003)***

−1.518
(1.067)

−2.341
(0.898)***

1.318
(1.133)

0.001

3,835

2.370
(1.202)**

0.0001

3,877

0.663
(1.152)

0.001

3,835

Panel B: Dosage Model

−1.774
(1.036)*
−9.085
(1.974)***

1.580
(1.163)
−1.471
(1.948)

0.183

0.005

0.0002

3,835

−1.215
(1.119)
−4.521
(1.904)**

2.932
(1.243)**
−3.151
(1.756)*

0.002

0.0001

0.499

3,877

−2.244
(0.949)**
−3.772
(1.580)**

1.254
(1.167)
−4.966
(2.174)**

0.019

0.0003

0.574

3,835

−2.802
(1.255)**
−0.348
(1.333)

0.054

3,876

−2.657
(1.330)**
−4.532
(1.944)**

0.162
(1.348)
−5.342
(3.032)*

0.183

0.033

0.808

3,876

Notes: In panel A, Close is a binary indicator for being within 5 miles of at least one attack. In panel B, 这
omitted category is 2003 × 0 Attacks, where Attacks counts the number of attacks that occurred within
5 miles of the school. Standard errors in parentheses are robust to clustering at the school level. Analytic
samples restricted to schools within 50 miles of at least one sniper shooting. School controls include full-
time equivalent teachers, student—teacher ratio, total school enrollment, percent black, percent Hispanic,
and percent free or reduced-price lunch eligible. All models control for school and year fixed effects as well
as district-specific linear time trends. Sample contains data from 1998 到 2005 school years (8 年).
Observations in 2002 for schools within 5 miles of the Pentagon are excluded from the analytic samples.
***Statistical significance at the 99 percent confidence level; **statistical significance at the 95 百分
confidence level; *statistical significance at the 90 percent confidence level.

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that persisted in subsequent school years for the subset of schools that were nearby
two attacks. That the eﬀects were not universally persistent is a comforting ﬁnding in
the sense that the negative impacts associated with the sniper attacks were relatively
short-lived for the majority of students. Even though it may be possible to reverse the
harmful impacts of community traumatic events on student achievement, doing so
would still come at a cost given the private parental and public resources that need to
be reallocated toward remedying these problems. 所以, eﬃciency losses associated
with these attacks should not be overlooked. 还, while the eﬀects on test scores may
have faded out, eﬀects on socioemotional outcomes might persist. Chetty et al. (2011)
ﬁnd that although eﬀects of primary school classroom quality on test scores “fade out”
迅速地, eﬀects on noncognitive measures in later grades, and on earnings in adulthood,
persist.

Heterogeneity in the Sniper Effects
最后, we conclude our analysis with an investigation of potential heterogeneity in the
eﬀects of the community trauma on school proﬁciency rates associated with the 2002

534

Seth Gershenson and Erdal Tekin

桌子 8. Heterogeneity in Effects of Proximity (5 miles) to Sniper Attacks on School Pass Rates

Sample

Outcome

英语 3

英语 5

数学 3

数学 5

School Level controls

学校 & year FE

District trends

Bottom Tercile
FRPL Enrollment

Top Tercile
FRPL Enrollment

Bottom Tercile
Black Enrollment

Top Tercile
Black Enrollment

(1)

−1.570
(1.511)

1.026
(1.279)
−1.248
(1.313)
−1.044
(1.700)

是的

(2)

−3.107
(2.129)
−3.803
(2.456)
−3.965
(2.157)*
−5.336
(2.823)*

是的

(3)

−0.206
(1.422)

0.424
(1.216)

0.855
(1.408)
−0.779
(1.470)

是的

(4)

−2.391
(1.689)
−3.989
(2.013)**
−4.044
(1.680)**
−4.787
(2.270)**

是的

Notes: Each cell reports the interaction term (treatment effect) from a distinct regression. Standard errors
are reported in parentheses and are robust to clustering at the school level. Sample sizes are reported in
brackets. Analytic samples restricted to schools within 50 miles of at least one sniper shooting. 学校
controls include full-time equivalent teachers, student-teacher ratio, total school enrollment, percent black,
percent Hispanic, and percent free or reduced-price lunch (FRPL) eligible. All models control for school and
year fixed effects (FE) as well district-specific linear time trends. Sample contains data from 1998 到 2003
school years (6 年). Observations in 2002 for schools within 5 miles of the Pentagon are excluded from
the analytic samples. The percent-FRL terciles are 18 和 47. The percent-black terciles are 9 和 34.
**Statistical significance at the 95 percent confidence level; *statistical significance at the 90 percent con-
fidence level.

sniper attacks. As discussed above, this analysis is motivated by the common ﬁnding in
the literature on the psychological eﬀects of community traumatic events that signs of
trauma are disproportionately concentrated among racial minority and socioeconomi-
cally disadvantaged children (Shannon et al. 1994; Becker-Blease, Finkelhor, and Turner
2008; Neria, Nandi, and Galea 2008). To answer this question, we sorted schools by
the percentage of students in 2003 who were eligible for FRPL and the percentage of
students who were black. Then we divided each distribution into three equal parts and
estimated the baseline model separately for schools in the bottom and top terciles. 这
bottom terciles contain relatively advantaged schools and the top terciles contain rela-
tively disadvantaged schools.

Columns 1 和 2 of table 8 report baseline estimates for schools in the bottom and
top terciles of the FRPL distribution, 分别. Based on previous research, we ex-
pect the eﬀects of the sniper attacks on proﬁciency rates to be more pronounced among
the relatively poorer schools in column 2. 的确, this is exactly what we see: Point es-
timates for the bottom tercile sample in column 1 are relatively small in magnitude and
indistinguishable from zero whereas those for the top tercile of the FRPL distribution
reported in column 2 are negative, larger in magnitude, and more precisely estimated.
Reductions in the poorer (top tercile) schools’ proﬁciency rates caused by the sniper
attacks are large—about twice the size of the baseline estimates that restricted the ef-
fect to be homogeneous for all schools—at about 5 percentage points for each ELA and
math test.

The estimates reported in columns 3 和 4 of table 8 reinforce the notion that the
adverse eﬀects of trauma caused by the sniper attacks fell disproportionately on chil-
dren from historically disadvantaged backgrounds. 尤其, the harmful eﬀects

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535

Effect of Community Traumatic Events on Achievement

of proximity to the sniper attacks are signiﬁcantly larger in schools that serve predomi-
nantly black student populations, which are similar in size to the eﬀects observed in the
relatively poor schools. None of the estimates in column 3, which shows estimates for
schools at the bottom tercile in black enrollment, are meaningful either economically
or statistically. 相比之下, the eﬀects are much larger in magnitude and statistically sig-
niﬁcant in three out of four outcome models in column 4, which shows the estimates
for schools that predominantly serve black students. 再次, this result is consistent with
the extant literature that predicts racial minority children to be more adversely aﬀected
by community traumatic events.

重要的, the results presented in table 8 indicate that the October 2002 sniper
attacks signiﬁcantly harmed academic achievement in schools serving disadvantaged
人口, and these eﬀects were not driven by districtwide trends in performance.
相当, these eﬀects represent negative deviations from trends and suggest that the
ﬁndings documented throughout much of this paper—the 2002 Beltway Sniper at-
tacks reduced academic achievement in Virginia’s public schools—were largely driven
by declines in student achievement in schools serving socioeconomically disadvantaged
and racial-minority students. This is unsurprising, as these students, 社区, 和
schools are regularly subjected to numerous other stressors and have relatively fewer
resources with which to cope with unanticipated shocks (such as the sniper attacks),
which presented yet another hurdle to overcome for students, 教师, and adminis-
trators in these schools.

7 . D I S C U S S I O N
The increased frequency of school shootings and community traumatic events in the
United States places a large and rising number of children at an enormous risk for psy-
chological problems. The current study documents that these types of events not only
undermine the psychological well-being of children, but can also disrupt their cognitive
发展, especially in the short run. Diﬀerence-in-diﬀerence estimates that lever-
age the natural experiment created by the October 2002 Beltway Sniper attacks indicate
that children who attended schools close to the shooting locations experienced lower
academic achievement than their counterparts who attended schools farther away. 这
estimates are most robust for proﬁciency in third- and ﬁfth-grade math, suggesting that
shootings caused a decline in school proﬁciency rates of about 3 到 5 百分点.
Particularly concerning from an equity standpoint, these eﬀects appear to be entirely
driven by achievement declines in schools that enroll large numbers of racial minority
and socioeconomically disadvantaged students.

The plausibility and practical signiﬁcance of these results can be interpreted in a
couple of ways. 第一的, we put our ﬁndings into context by comparing them to those
from several studies that consider similar sources of traumatic experiences or toxic
stress. 例如, Sharkey et al. (2014) use data from a sample of New York City
public schools to explore the impact of exposure to community violence on children’s
test scores. Consistent with our results, they ﬁnd that the impact of violence is most
pronounced among African American students, who experience a 2.8 percentage point
decrease in the likelihood of passing the ELA exam. This eﬀect size is within the range
(2.4–4 percentage points) obtained in our analysis. 相似地, Beland and Kim (2016)

536

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Seth Gershenson and Erdal Tekin

桌子 9. Schools whose Adequate Yearly Progress Proficiency Status Was Affected by Sniper Attacks

Treated Schools (Would Have Passed)

Control Schools (Would Have Failed)

All Schools

Top
Tercile FRPL

Top
Tercile Black

All Schools

Top
Tercile FRPL

Top
Tercile Black

英语 3

数学 3

英语 5

数学 5

全部的

百分比

(1)

(2)

—

(3)

—

(4)

—

(5)

—

(6)

—

1.5%

18.5%

7.0%

1.3%

19.8%

17.1%

Notes: Based on baseline estimates from column 2 of table 4 and columns 2 和 4 and table 8. Numbers
are only reported for tests on which there were statistically significant effects. FRPL: free or reduced-price lunch
eligible.

ﬁnd that deadly high school shootings reduce school proﬁciency rates in math and ELA
经过 4 到 5 百分点.

Gershenson and Hayes (2018) show that the unrest experienced in Ferguson, 米斯-
微笑, 在 2014 in the aftermath of the police shooting of an unarmed black teenager
led to 15 和 8 percentage point increases in the fraction of students who scored “be-
low basic” in math and reading, 分别. The estimates obtained in that study are
larger than those found here. 然而, unlike the sniper shootings, the civic unrest
experienced in Ferguson aﬀected already disadvantaged communities and caused a
disruption over the course of the entire academic year. Our estimates also compare
reasonably well with respect to studies that consider relatively milder shocks to learn-
ing environments. 例如, Carrell and Hoekstra (2010) show that exposure to
a peer from a household associated with domestic violence leads to a 1.6 percentage
point reduction in the likelihood of college enrollment. 相似地, Marcotte and Hemelt
(2008) estimate the impact of unscheduled school closings on school proﬁciency rates
in Maryland by exploiting the natural experiment created by temporal and geographic
variation in snowfall. The authors ﬁnd that ten unscheduled, weather-related school
closings reduced third- and ﬁfth-grade math proﬁciency rates by between 5 和 7 每-
centage points. These eﬀects are remarkably similar in magnitude to the eﬀects of the
sniper attacks documented in the current study.

第二, one dimension of the policy relevance of our ﬁndings can be inferred by
considering how the sniper-induced reductions in proﬁciency rates aﬀected schools’
standing under the NCLB accountability policy, which was ﬁrst implemented in the
same school year that the sniper shootings occurred. 重要的, math and ELA proﬁ-
ciency rates determined whether schools made AYP under NCLB. To make AYP, 之中
other things, schools’ overall proﬁciency rates must meet or exceed a threshold prede-
termined by the state. 在 2003 the ELA and math proﬁciency thresholds were 61 和
59, 分别 (Virginia Board of Education 2010). Under NCLB, failing to make AYP
in two consecutive years subjected schools to potentially severe sanctions.

桌子 9 reports tabulations from a simple back-of-the envelope calculation of the
number of schools whose proﬁciency rating would have crossed the AYP threshold had
他们 (不是) been within 5 miles of the sniper attacks. Speciﬁcally, we use the baseline

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537

Effect of Community Traumatic Events on Achievement

estimates reported in tables 4 和 8 to compute two counterfactuals: 的数量
treated schools that failed but would have passed had they been outside the 5-mile ra-
dius of the nearest sniper shooting, and the number of control schools that passed but
would have failed had they been inside a 5-mile radius of the nearest sniper shooting.
全面的, the sniper shootings changed between 1 和 2 percent of schools’ positions rel-
ative to the AYP threshold. 然而, this ﬁgure is signiﬁcantly higher for schools in the
top terciles of the distributions of the percentage of students eligible for FRPL and the
percentage of black students. In these relatively disadvantaged schools, 之间 7 和
20 percent of elementary schools’ positions relative to the AYP threshold changed as a
result of the sniper attacks. This is consistent with results presented in table 8, 哪个
show that disadvantaged schools were particularly harmed by the sniper attacks, but is
also driven by the fact that many disadvantaged schools were initially closer to the AYP
thresholds due to their relatively lower proﬁciency rates. 因此, 这很重要
that state and federal consequential K–12 accountability policies recognize the impacts
that community traumatic events can have on the student test scores that determine
sanctions, as failing to do so might expand existing inequities between schools.

更普遍, these ﬁndings suggest that local and state education systems might
respond to community traumatic events by providing additional resources, 支持,
and guidance to aﬀected schools and communities. 例如, Weems et al. (2009)
describe a school-based intervention that signiﬁcantly reduced test anxiety among racial
minority students who were exposed to Hurricane Katrina. 而且, targeted support
would be justiﬁed, given that disadvantaged schools and communities appear to bear a
disproportionate burden of the harmful eﬀects. There are also implications for proac-
tive policies designed to eliminate or minimize the proclivity of manmade community
traumatic events, as doing so in an eﬃcient manner requires equating the marginal
cost and marginal beneﬁt of such eﬀorts. The results presented here suggest that the
costs of random shooting incidents may be larger than previously thought, as the psy-
chic and emotional costs recognized by previous research spill over into schools and
aﬀect students’ cognitive development and exam performance some ﬁve months after
the event.

最后, our auxiliary analysis suggests that the main deleterious impact of the sniper
shootings on student achievement did not persist into the subsequent academic year,
at least as measured by SOL proﬁciency rates. When we repeated our analysis with
data extending to the end of the academic years 2004 和 2005, estimated treatment
eﬀects in these later years are smaller in magnitude and less precisely estimated than
those in the academic year 2003. 一方面, this ﬁnding can be interpreted as a
glimpse of positive news because there might have been a correction to the disruption
caused by the sniper attacks that brought achievement trends back to their pre-attack
轨迹. 然而, this should not lessen concerns over the impact of community-
wide traumatic events on student development for at least three reasons. 第一的, 任何
public and private eﬀorts expended to counter the harmful eﬀect of these attacks on
student achievement would still represent an eﬃciency loss for society in light of the
scarcity of educational resources. 第二, educational interventions that aﬀect both test
scores and noncognitive skills often have long-run impacts on socioeconomic outcomes
(例如, labor market success) even when their eﬀects on test scores fade out relatively

538

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Seth Gershenson and Erdal Tekin

迅速地 (Chetty et al. 2011). 最后, the dosage models reported in table 7 suggest that
eﬀects may have persisted in some of the most intensely treated schools.

致谢
We thank two anonymous referees; participants at the 2015 annual conferences of the Associa-
tion for Education Finance and Policy, European Society for Population Economics, and Western
Economic Association; and seminar participants at American University and Auburn University
for comments and suggestions. Ashlyn Holeyﬁeld, Stephen Holt, Ly Le, and Catherine Bampoky
provided excellent research assistance. We are responsible for all opinions and errors.

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A P P E N D I X A

表A.1. Sensitivity of Baseline Estimates to Functional Form of Distance

英语 3

英语 5

数学 3

主题

(1)

(2)

(3)

数学 5

(4)

Panel A: Alternative Thresholds to Define Binary ‘Closeness’ Treatment
(each cell is a unique regression)

3 miles

4 miles

5 miles (Baseline)

6 miles

7 miles

−2.276
(1.375)*
−2.744
(1.190)**
−1.924
(1.087)*
−1.381
(1.045)
−1.567
(0.955)

−1.153
(1.576)
−0.885
(1.351)
−1.376
(1.167)
−0.227
(1.162)
−0.882
(1.020)

−2.639
(1.268)**
−2.736
(1.100)**
−2.624
(0.964)***
−2.552
(0.943)***
−2.196
(0.895)**

−1.566
(1.784)
−1.118
(1.502)
−2.974
(1.350)**
−2.426
(1.374)*
−1.652
(1.257)

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Effect of Community Traumatic Events on Achievement

表A.1. Continued.

英语 3

英语 5

数学 3

主题

(1)

(2)

(3)

数学 5

(4)

Panel B: Continuous Quadratic Function of Distance to Attack

Miles

Miles2

APE

Joint (p)

0.178
(0.136)
−0.004
(0.003)

0.067
(0.061)

0.40

0.207
(0.147)
−0.003
(0.003)

0.115
(0.063)*

0.16

0.325
(0.131)**
−0.006
(0.003)**

0.142
(0.056)**

0.04

Panel C: Multiple Discrete Distance Categories

0 到 5 miles

5 到 10 miles

Joint (p)

Difference (p)

氮

−1.934
(1.175)
−0.027
(1.059)

0.21

0.13

2,851

−1.819
(1.219)
−1.166
(1.070)

0.26

0.63

2,881

−2.800
(1.039)***
−0.465
(1.045)

0.02

0.04

2,848

0.264
(0.187)
−0.005
(0.004)

0.116
(0.070)

0.30

−2.770
(1.457)*

0.540
(1.397)

0.08

0.04

2,878

Notes: The omitted category in panel C is (>10 mi. from attack). 标准
errors in parentheses are robust to clustering at the school level. Analytic
samples restricted to schools within 50 miles of at least one sniper shoot-
英. All models control for school and year fixed effects, district-specific linear
time trends, and time-variant school controls including full-time equivalent
教师, student—teacher ratio, total school enrollment, percent black, 每-
cent Hispanic, and percent free or reduced-price lunch eligible. Sample con-
tains data from 1998 到 2003 school years (6 年). Observations in 2002
for schools within 5 miles of the Pentagon are excluded from the analytic
样品.
***Statistical significance at the 99 percent confidence level; **统计
significance at the 95 percent confidence level; *statistical significance at
这 90 percent confidence level.