## Abstract

This study investigates the effect of violent crime on school district–level achievement in English language arts (ELA) and mathematics. The research design exploits variation in achievement and violent crime across 813 school districts in the United States and seven birth cohorts of children born between 1996 and 2002. The identification strategy leverages exogenous shocks to crime rates arising from the availability of federal funds to hire police officers in the local police departments where the school districts operate. Results show that children who entered the school system when the violent crime rate in their school districts was lower score higher in ELA by the end of eighth grade, relative to children attending schools in the same district but who entered the school system when the violent crime rate was higher. A 10% decline in the violent crime rate experienced at ages 0–6 raises eighth-grade ELA achievement in the district by 0.03 standard deviations. Models that estimate effects by race and gender show larger impacts among Black children and boys. The district-wide effect on mathematics achievement is smaller and statistically nonsignificant. These findings extend our understanding of the geography of educational opportunity in the United States and reinforce the idea that understanding inequalities in academic achievement requires evidence on what happens inside as well as outside schools.

## Introduction

Recent work by Reardon et al. (2016b) reported large disparities in academic achievement levels and in racial/ethnic achievement gaps across school districts in the United States. Whereas the mean achievement in school districts such as Brookline, MA, and Cupertino, CA, is three grades above the national mean, the mean academic achievement in Camden, NJ, and Detroit, MI, is more than two grades below the country average. Similarly, the White-Black achievement gap ranges from virtually zero in places like Hillside, NJ, to more than 1 standard deviation in Cleveland, OH, and Atlanta, GA. Correlational evidence suggests that variation in mean achievement levels is highly related to the socioeconomic characteristics of the families living in the school district (Reardon 2016) and that racial/ethnic gaps are wider in school districts with higher levels of racial/ethnic segregation and larger racial/ethnic differences in parental income and education levels (Reardon et al. 2016b).

By themselves, these findings have made a groundbreaking contribution to understanding how geography shapes educational opportunity in the United States. However, our knowledge of the causal mechanisms underlying these patterns is more limited. Building on an extensive body of ethnographic and quantitative evidence showing that exposure to violent crime is a key pathway through which growing up in disadvantaged neighborhoods affects children’s developmental trajectories (Burdick-Will et al. 2011; Harding 2009; Harding et al. 2011; Sharkey 2018a), this study aims to fill this gap by examining how changes in violent crime in the school districts where children grow up shape their academic achievement.

The study combines multiple sources of aggregated school district–level data to estimate the impact of violent crime experienced in childhood (at ages 0–6) on English language arts (ELA) and mathematics eighth-grade achievement in 813 school districts in the United States and seven birth cohorts of children born between 1996 and 2002. During these seven years, the violent crime rate fell by 23% nationally (Federal Bureau of Investigation 2015); and in school districts like Chicago and New York City, the decline in violent crime over that period was greater than 35%. To produce causal estimates of the effect of violent crime on achievement, the research design leverages exogenous shocks to crime rates arising from the availability of funds to hire police officers in local police departments thorough the Community Oriented Policing Services (COPS) grants program. This program substantially increased the size of police departments that received the grants, which led to important reductions in violent crime rates (Evans and Owens 2007). Here, I extrapolate this finding to an instrumental variable setup in which I exploit the change in the violent crime rate induced by the COPS grants to estimate the causal effect of violent crime on achievement.

The findings show that birth cohorts who experienced lower levels of violence during childhood performed better in ELA by the end of eighth grade, relative to older birth cohorts of the same school district who experienced higher violent crime rates in childhood. A 10% decline in the violent crime rate raised the district-wide performance in ELA by 0.03 standard deviations. Analyses by race/ethnicity and gender show that the benefits of declining violence are larger among Black students and males. Models exploring the effect of violent crime on mathematics achievement also suggest performance improvements as crime rates fell, but those effects are smaller and concentrated among boys. Importantly, the effect of crime on achievement is not driven by compositional changes in school districts or by changes in school district revenue and spending after the receipt of the COPS grants.

This article also contributes to the literature on the consequences of the decline in violence in America. The study is situated in the late 1990s and early 2000s, a period when community violence fell sharply across the country. Between 1991 and 2015, the property crime rate fell by 50%, the violent crime rate fell by 51%, and the homicide rate fell by 54% across the nation (Federal Bureau of Investigation 2015).1 In cities like New York City or Los Angeles, the decline in the murder rate between the highest record in the 1990s and the level in 2015 was larger than 75%. Even cities that still today struggle with severe problems of community violence, such as Chicago and Detroit, experienced reductions in their murder rates of at least 30% between 1991 and 2015 (Federal Bureau of Investigation 2015).2 This progress in making cities safer represents one of the most remarkable improvements in the quality of life in urban America in recent history (Sharkey 2018b), and although the literature has made significant progress in documenting the causes of this decline (Levitt 2004; Zimring 2006), much less is known about its consequences for individuals and communities. This study aims to fill this gap by documenting how the school achievement of children who lived through the decline in violence changed as their communities became safer.

## Neighborhood Violence and Educational Outcomes

A long tradition of scholarship in criminology, economics, and sociology has documented the negative consequences of growing up in violent neighborhoods (Aizer 2007; Burdick-Will 2013; Burdick-Will et al. 2011; Harding 2009; Harding et al. 2011; Sharkey 2018a). Studies examining the acute short-term effects of exposure to neighborhood violence have found that when children take cognitive assessments in the days after a homicide has occurred in their neighborhood, their performance declines relative to other children from the same neighborhood who were not exposed to violence in the days before the assessments were given (Sharkey 2010; Sharkey et al. 2014). Evidence on noncognitive outcomes among children has shown that concentration, self-regulatory behaviors, cortisol levels, and sleeping patterns are severely affected in the aftermath of a violent crime (Heissel et al. 2018; McCoy et al. 2015; Sharkey et al. 2012).

In addition to the consequences of direct exposure to violent crime, ethnographic studies have shown that children living in disadvantaged neighborhoods are forced to develop strategies to navigate threatening public spaces and change their daily routines and patterns of social interaction in a way that may negatively affect their educational development (Shedd 2015). Adolescents from disadvantaged and violent neighborhoods interact more frequently with older peers who provide them not only with street wisdom and safety but also with alternative scripts and frames that shape their attitudes toward schooling (Harding 2010). Boys and girls living in dangerous neighborhoods are forced to develop a reputation for being “tough” (Anderson 2000; Jones 2009), and although earning this reputation may prevent them from being victimized in the streets, it may complicate their interactions with teachers and school staff and affect their academic performance (Devine 1996).

Beyond these effects on individuals, an extensive literature in criminology and urban sociology has documented the negative effects that crime has at the community level. Neighborhood violence undermines the quality of life in entire communities, transforms the sociodemographic composition of neighborhoods, and leads to public and private disinvestment (Morenoff and Sampson 1997; Sampson 2012; Skogan 1986). Recent evidence on these community-level effects of crime has shown that children born to low-income families experience lower levels of economic mobility if violent crime is higher in the county where they spend their adolescence (Sharkey and Torrats-Espinosa 2017).

One of the most distinct features of neighborhood violence in the United States is its degree of spatial concentration in low-income and minority neighborhoods. Evidence from crime trends in micro-places within neighborhoods in Boston has shown that the majority of robberies and gun violence incidents across the city take place in a very small fraction of street segments and intersections (Braga et al. 2010, 2011). This high degree of spatial concentration and the high levels of residential racial segregation that characterize American cites generate large disparities in exposure to violence across different racial groups. Using data from the FBI’s Uniform Crime Reports (UCR) program, Sharkey (2018a) estimated that the homicide victimization rate is 6.6 times higher for Blacks than for Whites. Estimates from the National Crime Victimization Survey (NCVS) also show large Black-White gaps in self-reported violent victimization and nonfatal firearm victimization. The UCR and NCVS data also reveal large gender disparities in exposure to violence. The homicide victimization rate is 3.9 times higher for males than for females, and the rates of self-reported violent victimization and nonfatal firearm victimization are also much higher among males (Sharkey 2018a).

In sum, the literature on neighborhood violence reviewed above shows that crime is a salient attribute of children’s environment that reaches beyond individuals who are directly victimized (Sharkey 2018a). The spatial concentration of crime disrupts the functioning of communities, lowers the quality of institutions such as schools, and erodes the quality of resources that facilitate academic success. Building on this body of evidence, this study pushes the literature forward and takes a national perspective in the study of the long-term effect of crime on children’s academic performance.

## Data Description

The selection of school districts begins with the 1,000 school districts with the largest student enrollment in grades 3–8 in school year 2008–2009. Districts included in the sample are those that have data on academic achievement in eighth grade for Black, Hispanic, and White children as well as crime data when children of each birth cohort were 0–6 years old. The analytic sample includes 813 unique school districts that yield an unbalanced panel of 4,255 school district-cohort observations.3

Data on academic achievement are obtained from the Stanford Education Data Archive (SEDA). The SEDA data include estimates of the average test scores of students in virtually all public school districts in the United States (Reardon et al. 2016a). The estimates are obtained from approximately 300 million state accountability tests taken by approximately 45 million students in grades 3–8 attending public and charter schools between school years 2008–2009 and 2014–2015, which represents most of all third to eighth graders attending public and charter schools at that time.4 Test scores are placed on a common scale that allows performance to be compared across school districts, states, grades, and years. The achievement measures in the SEDA data are disaggregated by grade (3–8), school year (2008–2009 to 2014–2015), subject (ELA and mathematics), race/ethnicity (Asian, Black, Hispanic, and White), and gender.5 This study focuses on the overall achievement in the district, achievement by race and ethnicity (Black, Hispanic, and White students), and achievement by gender (females and males). All measures of achievement are in standard deviation units of the national distribution.

The SEDA data are repeated cross-sections of achievement by grade and school year, thus enabling the possibility of studying the trajectory of several birth cohorts. Given that the data include achievement measures in grades 3–8 for school years 2008–2009 to 2014–2015, 12 birth cohorts are represented in the SEDA data, although not all cohorts have achievement measures in all grades. Assuming that children begin first grade at age 6, children born in 1996 were in eighth grade in school year 2008–2009, and children born in 2007 were in third grade in school year 2014–2015. Under this assumption, eighth-grade estimates from school years 2008–2009 to 2014–2015 in the SEDA data can be used to characterize the educational achievement of children born between 1996 and 2002.

As Reardon (2018) noted, this operationalization of cohorts does not ensure that a consistent pool of students is followed over time. Students in eighth grade in school year 2014–2015 in a given district are not the exact same ones who were in third grade in school year 2009–2010 in the same district. Students moving to other school districts or being retained in a grade will change the pool of students between third and eighth grade. Without access to longitudinal student-level data, this limitation is impossible to address. In additional analyses included in the online appendix, I show that enrollment figures and the racial composition of schools in the districts in the sample did not change in a way that threatens the validity of the results reported here.

Crime data are obtained from the FBI’s UCR program, which contain crimes known or reported to local police agencies. The main analyses will focus on the impact of changes in violent crimes (murders, aggravated assaults, and robberies). Crime is measured as the average crime rate in the school district when children of a given birth cohort were 0–6 years old.6 To obtain school district crime rates, I assign crime reports from local police agencies to municipalities (i.e., cities and towns) using the 2012 Law Enforcement Agency Identifiers Crosswalk (U.S. Bureau of Justice Statistics 2018), and I crosswalk places to school districts by identifying the city or town whose centroid falls inside the boundaries of a given school district.

Data on the COPS program are obtained from the U.S. Department of Justice.7 They include the number of full-time police officers hired through the grants program in each year. The instrument is constructed by computing the number of full-time officers per 100,000 residents that each local police department had received up to the year when a given birth cohort was 0–6 years old. Additional details about the instrument are provided in the next section.

Figure 1 shows the average eighth-grade achievement by birth cohort and racial/ethnic group in the districts in the sample. The bars reveal large achievement gaps across racial/ethnic groups. White students scored between 0.1 and 0.2 standard deviations above the eighth-grade national mean, Hispanic students scored between 0.3 and 0.5 standard deviations below the national mean, and Black students scored between 0.4 and 0.5 standard deviations below the national mean.

Table 1 shows means and standard deviations for violent crime rates at ages 0–6 for each of the seven birth cohorts in the study. The oldest cohort was 0–6 years old between 1996 and 2002 and experienced an average violent crime rate for that period of 879 crimes per 100,000 residents. The youngest birth cohort was 0–6 years old between 2002 and 2008 and experienced an average violent crime rate for that period of 800 crimes per 100,000 residents.

Table 1 also shows how COPS grants grew over time. On average, 16 police officers were hired, and 2.37 million dollars (in 2015 USD) were awarded for each 100,000 residents in the district when the 1996 birth cohort was 0–6 years old. When the 2002 birth cohort was 0–6 years old, these figures had increased to 28 police officers and 4.04 million dollars (in 2015 USD) for each 100,000 residents in the district. Figure A1 in the online appendix shows that in relative terms, more police officers were hired through the COPS program than outside the program between 1996 and 2008, suggesting that the COPS program played an important role in increasing the size of police departments during the time considered in this study.8

## Empirical Strategy

### Ordinary Least Squares Estimation

The empirical strategy exploits geographic variation in achievement and crime across 813 school districts and temporal variation across seven birth cohorts in a difference-in-differences framework. The estimating equation takes the following form:
$Ysc=δOLSCrimesc+Ss′+Cc′+εsc.$
1

In Eq. (1), Ysc is the eighth-grade ELA and mathematics achievement in school district s for birth cohort c (measured in standard deviations of the national distribution), Crimesc is the log average violent crime rate in school district s measured when birth cohort c was 0–6 years old, $Ss′$ is a set of school district fixed effects, $Cc′$ is a set of birth cohort fixed effects, and εsc is an stochastic error term. Standard errors are clustered by school district.9

The parameter δOLS characterizes the association between changes in crime rates at ages 0–6 and changes in achievement by the end of eighth grade. The two sets of fixed effects, $Ss′$ and $Cc′$, account for time-invariant attributes of the school district and time trends that are common to all districts. Although this difference-in-differences specification represents an improvement on cross-sectional designs, causal identification will not be possible if within-district changes in crime rates over this period are endogenous. The next section discusses the implications of such a scenario and proposes a strategy to address these endogeneity concerns.

### Two-Stage Least Squares Estimation

Estimating the impact of exposure to violent crime on academic achievement presents empirical challenges that are difficult to overcome without an experimental design. Neighborhood violence is highly correlated with other attributes of neighborhoods that may also have an impact on academic achievement, such as poverty and labor force participation (Aizer 2007). One possibility would be to control for as many of these factors as the data allow, but the threat of having omitted one or more confounders would still be present. Another threat is the residential selection of families into school districts on the basis of socioeconomic attributes that are predictive of academic performance (Sampson and Sharkey 2008). If more affluent families have the ability to forecast changes in crime rates in their school district and decide to relocate to a safer school district, higher achievement levels in low-crime school districts could be a reflection of this sorting process.

## Discussion

Although violent crime rates in America still remain higher than in most developed countries (United Nations Office on Drugs and Crime 2019), the decline in violence that began in the early 1990s represents a major improvement in the quality of life of Americans. Much has been written about the causes of the crime decline (Levitt 2004; Zimring 2006), but an understanding of its consequences for individuals and communities is more limited. This study is an attempt to fill this gap by estimating the impact of declining crime rates on the educational achievement of seven birth cohorts who entered the school system when the violent crime rate in their school districts was markedly different.

The oldest cohort of children in this study was born in 1996, when the national violent crime rate was at 636 crimes per 100,000 residents. The youngest cohort was born in 2002, when the national violent crime rate was 494 per 100,000 residents, a 23% decline from the 1996 level (Federal Bureau of Investigation 2015). Being only seven years apart meant living through childhood and adolescence with a lower risk of being victimized in the streets and experiencing the trauma and stress associated with living in violent environments. When comparing the achievement at the end of eighth grade of children born between 1996 and 2002, experiencing a 10% decline in violent crime raised the district-wide performance in ELA of an entire birth cohort by 0.03 standard deviations. Analyses by race/ethnicity show that the district-wide improvement in achievement that followed the fall in violence is driven by the gains that accrued to Black children. These findings are consistent with evidence from studies documenting that the acute effect of exposure to homicides on students’ performance is larger among Black students and in predominantly Black schools (Gershenson and Tekin 2017; Sharkey 2010; Sharkey et al. 2014). The larger effects among Black and Hispanic students make sense when considering that their neighborhoods, which have higher average levels of concentrated violence (Morenoff and Sampson 1997; Peterson and Krivo 2010; Sampson et al. 1997), experienced the largest declines in crime in the 1990s and 2000s (Friedson and Sharkey 2015).

An important finding emerging from this study is the larger effect of violence among boys. On the basis of the 2SLS estimates in Table 6, the achievement gap between female and male students closed by 0.03 standard deviations in mathematics for a 10% decline in the violent crime rate. Although girls are also exposed to community violence and forced to develop strategies to navigate threatening school and street environments (Jones 2009), ethnographic accounts show that young minority men experience the most severe consequences of neighborhood violence (Anderson 2000; Harding 2010). From this perspective, it makes sense that the alleviation of the stress and trauma associated with having to navigate violent spaces translated into larger gains among boys.

Focusing on the coefficient magnitudes, the size of these effects may appear small. However, it is worth remembering that these improvements in achievement are averaged over all students in the school district. These estimates imply that the effect might be larger for children living in neighborhoods where crime was more concentrated and where the crime drop was felt more intensely (Friedson and Sharkey 2015). Similarly, data limitations do not allow taking a longer-term view and comparing, for example, the achievement of children born in the late 1980s to that of children born in the early 2000s. These two sets of children lived through school years in vastly different neighborhood and school environments in terms of levels of violence. Extrapolating the 2SLS estimates obtained here to the 20-year period 1992–2012, the average change in the homicide rate during that time—approximately a 50% decline—represents that children born in 2012 will benefit from the equivalent to five to eight months of additional instruction by the end of eighth grade because of the drop in neighborhood violence.

The evidence on ELA achievement is clear and strong, but the effect of violent crime on mathematics is inconclusive. All point estimates for mathematics are in the same direction as those in ELA models, but their magnitudes are smaller and in some models are statistically nonsignificant. This pattern is consistent with findings from other studies of violence and student outcomes (Sharkey 2010; Sharkey et al. 2014). These studies have suggested that performance in mathematics and reading assessments may be explained by different self-regulatory mechanisms that interact differently with violence-related stressors (Liew et al. 2008). Children suffering from the trauma and stress associated with neighborhood violence may find it harder to maintain the level of attention and concentration necessary in reading assessments in which the different parts of the test are often interconnected, but they may find it easier to stay focused during mathematics assessments in which test items can be tackled individually. One additional explanation for the difference in ELA and mathematics estimates is that the learning of literacy skills relies more on the support and resources that children find at home than the learning of mathematics skills does (Griffin and Morrison 1997). The disruption that violence causes in the neighborhood is likely to enter the home environment if parents become anxious about their children being victimized or if children are exposed to the constant sound of sirens, for example, hindering the learning of reading skills at home.

The findings from this study add to a growing body of work showing that economic opportunity varies substantially by location (Chetty et al. 2014), and they suggest that the effect of crime on economic mobility documented in previous studies operates partly through effects on educational achievement (Sharkey and Torrats-Espinosa 2017). If places, rather than people living in them, account for a large share of the differences in economic mobility across metropolitan areas (Chetty and Hendren 2018), making places safer can generate long-term social returns that extend beyond the most immediate and direct benefits of reducing community violence. More broadly, these findings provide additional evidence on the role that violence plays in shaping the developmental trajectories of children, and they reinforce the idea that understanding differences in academic achievement requires evidence on what happens inside schools as well as what happens outside schools.

The most important limitation of this study is that it provides no evidence on the mechanisms driving the improvement in achievement as crime rates fell. The supplementary analyses in the online appendix show that the COPS funds did not change school resources and that the effects are not driven by changes in the economic and racial composition of school districts over time. It is unclear, however, whether children born in the 2000s fared better because they were able to stay more focused on school as their surroundings became safer, or because safer streets meant that parents were more willing to enroll them in extracurricular activities that furthered their development, for example. Given the age when changes in crime rates are measured, at ages 0–6, it is likely that an important part of the explanation has to do with how parents responded to crime changes in the neighborhood. Future research that surveys children about their perceptions of safety and parents about their strategies to shield children from street crime can help unpack these mechanisms.

The discussion of the consequences of the crime decline cannot ignore the costs of such change. A shift toward more aggressive forms of policing and soaring incarceration rates have disrupted the lives of minority youth as much as street violence did in the 1980s and early 1990s. More police in the streets cannot be the only response to confront community violence, and the reduced-form findings do not mean that more police in the streets are needed to close achievement gaps. The use of the COPS grants as an instrumental variable is just a methodological tool to recover causal estimates from a policy shock that reduced crime rates. The policy debate should be around strategies to make neighborhoods safer. Giving more resources to police departments so that they can engage and partner with community organizations and provide effective responses to communities’ needs is just one of the many possibilities. Importantly, law enforcement agencies should be held accountable so that they carry their jobs with fairness and without engaging in discriminatory practices. This accountability requirement is of crucial importance in light of recent qualitative and quantitative evidence showing the negative effects of policing on minority youth (Legewie and Fagan 2019; Rios 2011).

## Acknowledgments

The author thanks Ingrid Ellen, Jennifer Hill, Mike Hout, Sean Reardon, Patrick Sharkey, Florencia Torche, and participants at the Furman Center Fellows Meetings and the Russell Sage Foundation conference “Improving Education and Reducing Inequality in the United States: Obtaining New Insights from Population-Based Academic Performance Data” for helpful comments. This research has been supported by a grant from the Russell Sage Foundation and the William T. Grant Foundation (RSF Award: 83-17-07).

## Notes

1

Work by Lauritsen et al. (2016) showed a discrepancy between crime trends in the FBI’s Uniform Crime Report (UCR) data and in the National Crime Victimization Survey (NCVS). Their findings suggest that NCVS data are more reliable indicators of the trends in violent crime from 1973 to the mid-1980s. Given the period being studied here, 1996 to 2008, the UCR data provide an accurate account of how crime rates changed over time and across space.

2

Baltimore and Milwaukee cannot join Chicago and Detroit on that list because of the spike in crime experienced in 2015, which brought the murder rate above the level in 1991. If changes are measured between 1991 and 2014, Baltimore and Milwaukee had reductions in their murder rates of 18% and 44%, respectively.

3

Among the 813 school districts, 59 have data on eighth-grade achievement for two birth cohorts; 85, for three birth cohorts; 100, for four birth cohorts; 148, for five birth cohorts; 205, for six birth cohorts; and 216, for seven birth cohorts. All findings remain qualitatively the same if the analyses are restricted to the 216 school districts for which data for the seven birth cohorts are available.

4

School districts are defined according the geographic catchment areas that include students in traditional public schools and local charter schools. Test scores from charter schools are included in the public school district in which they are chartered. For charter schools that are not chartered by a district, their test scores are included in the district in which they are physically located (Reardon 2018).

5

For additional details on the construction of aggregate measures from student test score data, see Ho and Reardon (2012) and Reardon and Ho (2015).

6

The choice of focusing on exposure to crime at ages 0–6 is motivated by the research design, which exploits the availability of funds to hire police officers through the COPS program. The first phase of the COPS program—the one considered in this study—ended in 2008, which is the year when the 2002 birth cohort was 6 years old. After 2008, the COPS program changed its rules for adjudicating grants, making the use of post-2008 data inadequate for the estimation strategy proposed here (for an analysis of the COPS program under the new grant allocation rule, see Mello 2019). Another reason to average crime rates over ages 0–6 is to obtain more stable crime rates. These multiyear averages also help in the 2SLS estimation by yielding a stronger first stage. Figure A8 in the online appendix shows OLS results when the violent crime rate is measured in one-year windows from age 0 to age 13.

7

The COPS data were collected by William Evans and Emily Owens, who generously shared them for this project.

8

The minimum, median, and maximum number of police officers per 100,000 residents at ages 0–6 for the 1996 birth cohort were, respectively, 0, 15.15, and 145.2. For the 2002 birth cohort, these figures were, respectively, 0, 24.75, and 431.84.

9

In a set of robustness tests, all OLS and 2SLS models are estimated including a vector of interpolated demographic controls, $Xsc′$, measured for school district s when birth cohort c was 0–6 years old. These controls include percentage non-Hispanic White, percentage non-Hispanic Black, percentage Hispanic, percentage foreign-born, percentage unemployed, percentage of families with income below the poverty line, and median household income (in 2000 USD). All these demographics are computed by linearly interpolating between census years. All results remain the same when these controls are included.

10

Prior studies of the COPS program have shown that most police officers hired through the grants remained in the police force over the long run (Evans and Owens 2007). Given that this study is focused on long-term impacts on achievement, I use the cumulative number of police officers who had been hired and retained up to the time when a birth cohort was 0–6 years old.

11

One could be concerned about a potential violation of the exclusion restriction in light of prior work that has documented a correlation between crime and the residential choices of families of different groups (Dugan 1999; Ellen et al. 2017; Xie and McDowall 2014). These studies relied on correlational data, and it is difficult to extract any benchmarks from them. It is also important to keep in mind that my sensitivity analyses in Fig. A6 in the online appendix do not focus on changes in crime rates; rather, they focus on changes in the COPS grants and the extent to which they changed student composition of the school district. I find no clear evidence of that being the case.

12

These controls are obtained from the 2000 census and include percentage non-Hispanic White, percentage non-Hispanic Black, percentage Hispanic, percentage foreign-born, percentage unemployed, percentage families with income below the poverty line, and median household income (in 2000 USD).

13

In the SEDA data, the measure of achievement for all students combined is constructed from the test scores of students of all racial and ethnic groups in the school district, which include more groups than the three being considered here. I report disaggregated results for Black, Hispanic, and White children (but not for others) because in some districts, the number of students of other racial/ethnic minorities is too low to yield reliable estimates of their achievement.

14

The SEDA data include estimates of racial/ethnic gaps for each school district and birth cohort. In Table A2 in the online appendix, I use these racial/ethnic gaps as outcomes in the 2SLS regressions. Results from these models suggest a positive impact of changes in crime rates (i.e., gaps narrowed as crime rates declined), but these effects are statistically nonsignificant.

15

In models that use SEDA estimates of gender gaps as outcomes (Table A2 in the online appendix), the female-male gap in mathematics is statistically significant.

16

The range of 0.3–0.5 standard deviations in growth per school year captures most of the estimates that the literature in education has generated up to this point. School years are assumed to have nine months of instruction.

17

This figure corresponds to the average enrollment per grade in years 1994–2008 in the set of 813 school districts included in the sample.

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