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An Empirical Analysis of Racial Di↵erences in Police Use of Force

⇤

Roland G. Fryer, Jr.

†

July 2017

Abstract

This paper explores racial di↵erences in police use of force. On non-lethal uses of force,

blacks and Hispanics are more than ﬁfty percent more likely to experience some form of force

in interactions with police. Adding controls that account for important context and civilian

behavior reduces, but cannot fully explain, these disparities. On the mos t extreme use of f or ce –

oﬃcer-involved shootings – we ﬁnd no racial di↵erences in either the raw data or when contextual

factors are taken into account. We argue that the patterns in t h e data are consistent with a

model in which police oﬃcers are utility maximizers, a fraction of which have a preference for

discrimination, who incur r el at ively high expected costs of oﬃcer-involved shootings.

Keywords: discrimination, decision making, bias, police use of force

⇤

This work has beneﬁtted greatly from discussions an d debate with Chief William Evans, Chief Charles McClelland,

Chief Martha Montalvo, Sergeant Stephen Morrison, Jon Murad, Lynn Overmann, Chief Bud Riley, and Chief

Scott Tho m so n . I am grateful to David Card, Kerwi n Charles, Christian Dustmann, Michael Greenstone, James

Heckman, Richard Holden, Lawrence Katz, Steven Levitt, Jens Ludwig, Glenn Loury, Kevin Murphy, Derek Neal,

John Overdeck, Jesse Shapiro, Andrei Shleifer, Jorg Spenkuch, Max Stone, John Van Reenan, Christopher Win sh i p ,

and seminar participants at Brown University, University of Chicago, London School of Economics, University College

London, and the NBER Summer Insti t u te for helpful comments and suggestions. Brad Allan, Elijah De La Ca mp a ,

Tan aya Devi, William Murdock III, and Hannah Ruebeck provided truly phenomenal project management and

research assistance. Lukas Altho↵, Dhru va Bhat, Sa m a rth Gupta, Julia Lu, Mehak Malik, Beatrice Masters, Ezinne

Nwank wo, Charles Adam Pfander, Sofya Shchukina an d Eric Yang provided excellent research as sis t an c e. Financial

support from EdLabs Advisory Grou p and a n anonymous donor is grateful ly acknowledged. Correspondence can be

addressed to the au t h or by email at rola n d [email protected]ard.edu. The usual caveat applies.

†

Department of Economics, Harvard University, and the NBER, (rfry[email protected]ard.edu);

“We can never be satisﬁed as long as the Negro is the victim of the unspeakable hor ror s

of pol i ce brutality.” Mart i n Luther King, Jr., August 28, 1963.

I. Introduction

From “Bloody Sunday” on the Edmund Pettus Bridge to the public beatings of Rodney King,

Bryant Allen, and Freddie Helms, the relationship between African-Americans and police has an

unlovely history. The images of law enforcement clad in Ku Klux Klan regalia or those peaceful

protesters being attacked by canines, hi gh pressure water hoses, and te ar gas are an in d el i bl e part

of Am er i can history. For much of the 20th century, law enforcement chose to brazenly enforce the

status quo of overt discrimination, rather than protect and serve all citizens.

The raw memories of these injustices have been resurrected by several high proﬁle incidents of

questionable uses of force. Michael Brown, unar me d, was shot twelve times by a polic e oﬃcer in

Ferguson, Missouri, after Brown ﬁt the description of a robbery suspect of a nearby store. Eric

Garner, unarmed, was approached because oﬃcers believed he was selling single cigarettes from

packs without tax stamps and in the process of arresting him an oﬃcer choked him and he died.

Walter Scott, unarmed, was stopped because of a non-functioning third brake light and was shot

eight times in the back wh i le attempting to ﬂee. Samuel Du Bose, unarmed, was stopped for failu re

to displ ay a front license plate and while trying to drive away was fatally shot once in the head.

Rekia Boy d , unarmed, was killed by a Chicago police oﬃcer who ﬁred ﬁve times into a group of

people from inside his police car. Zachary Hammond, unarmed, was driving away from a drug deal

sting operat ion when he was shot to death by a Seneca, South Carolina, police oﬃcer. He was

white. And so are 44% of police shooting subjects.

These incidents, some captured on video and viewed widely, have generated prot est s in Ferguson,

New York City, Washington, Chi c ago, Oakland, and several other citie s and a national movement

(Black Lives Matter) and a much needed national discourse about race, law enforcement, and

policy. Police precincts from Houston, TX, to Camden, NJ, to Tacoma, WA, ar e beginning to issue

body worn cameras, engaging in community policing, and enrolling oﬃcers in training in an e↵ort

to purge racial bias from their instinctual decision making. However, for al l the eerie similarities

Author’s calculations bas ed on ProPublica research that analyzes FBI data between 1980 and 201 2 .

between the current spate of police interactions with African-Americans and the historical injustices

which remain unhealed, the current debate is virtually data free. Understan di n g the extent to which

there are racial di↵erences in police use of force and (if any) wh et h er those di↵erences might be due

to discrimination by police or exp l ain ed by other factors at the tim e of the incident is a q ue st i on

of trem en dou s social importance, and the subject of this paper.

A primary obstacle to th e study of police use of force has been the lack of readily available data.

Data on lower level uses of force, which happen more frequently than oﬃcer-involved shootings, are

virtually non-existent. This is due, in part, to the fact that most police precincts don’t explicitly

collect data on use of force, and in part, to the fact that even when the data is hidden in plain

view within pol i ce narrative accounts of interactions with civilians, it is exceedingly d i ﬃcu l t to

extract. Moreover, the task of compiling rich data on oﬃcer-i nvolved shootings is burdensome. Until

recently, data on oﬃcer-involved shootings were extremely rare and contained little information on

the d et ai l s surroun d in g an incident. A simple count of the number of police shootings that occur

does little to explore whether rac ial di↵erences in the frequency of oﬃcer-involved shootings are

due to police malfeasance or di↵erences in suspect behavior.

In this paper, we estimate the extent of racial di↵erences in p ol ic e use of force using four separate

datasets – two constructed for t he purposes of t hi s study.

Unless otherwise noted, all results are

conditional on an interaction. Underst an d in g p ot ential selection into police data sets due to bias in

who police interacts with is a diﬃcult endeavor. Sect i on 3 attempts to help get a sense of potential

bias in police interact ion s. Put simply, if one assumes police simp ly stop whomever the y want for

no particular reason, there seem to be large racial di↵erences. If one assumes they are tryi n g to

prevent violent crimes, then evidence for bias is exceed i ngl y small.

Of the four dat as et s, the ﬁrst comes from NYC’s Stop, Question, and Frisk program (hereafter

Stop and Frisk). Stop and Frisk is a practice of the New York City police department in which

police stop and que st i on a ped est r i an, then can frisk them for weapons or contraband. The dataset

contains roughly ﬁve million observations. And, important for the purposes of this paper, has

Newspapers su ch as the Washington Post estimate that there were 965 oﬃcer-invo lved sh ootings in 2015. Web-

sites such as fatal encounters estimate that the number of annual shootings is approximately 704 between 2000 and

2015.

Throughout the text, I depart from custom by using the terms “we,” “our,” and so on. Althoug h this is sole-

authored work, it took a large team of talented individuals to collect the data necessary for this projec t . Using “I”

seems disingenuous.

detailed information on a wide range of use s of force – from putting hands on ci vi l i ans to striking

them wit h a baton. The secon d dataset is the Police-Public Contact Survey, a triennial survey

of a nationally r ep re se ntative sample of civilians, which contains – from the civilian point of view

– a description of interactions with pol i ce, which includes uses of force. Both these datasets are

public-use and re adi ly available.

The other two datasets were assembled for the pur poses of this research. We use event sum-

maries from al l incidents in which an oﬃcer discharges his weapon at civilians – including b ot h hits

and misses – from three large cities in Texas ( Au st i n , Dallas, Houston), six large Florida counties,

and Los Angeles County, to construct a dataset in which one can investigate racial di↵erences in

oﬃcer-involved shootings. Because all individuals in these data have been involved in a poli ce

shooting, analysis of these data alone can only estimate racial di↵ere nc es on the intensive margin

(e.g., did the oﬃcer discharge their weapon before or after the suspect attacked).

To supplement, our fourth dataset contains a random sample of police-civilian interactions f r om

the Houston Police department from arrests codes in which lethal force is more likely to be justiﬁed:

attempted capital murder of a public safety oﬃcer, aggravated assault on a public safety oﬃcer,

resisting arrest, evading arrest, and interfering in arrest. S i mi l ar to the event studies above, these

data come from arrest narratives that range in length from two to one hundr ed pages. A team of

researchers was responsible for reading arrest reports and collecting almost 300 variables on each

incident. Combining this with the oﬃcer-involved shooting data from Houston allows us to estimate

both the extensive (e.g., whether or not a polic e oﬃcer decides to shoot) and intensive margins.

Further, the Houston arrests data contain almost 4,500 observations in which oﬃcers discharged

charged electronic devices (e.g., tasers). This is the second most extreme use of force, and in some

cases, i s a substitute for lethal use of force.

The results obtained using these data are informative and, in some cases, startling. Usi ng d at a

on police interactions from NYC’s Stop and Frisk program, we demonstrate that on non-lethal uses

of force – put t i ng hands on civil i an s (which includes sl app i ng or grabbing) or pushing individuals

into a wall or onto the ground, there are large racial di↵ere nc es. In the raw data, blacks and

The NYC Stop an d Frisk data has been used in Gelman et al. (2012) a n d Coviello and Persico (2015) to un-

derstand whether there is evidence of racial discrimination in proactive policing, and Ridgeway (2009) to develop a

statistical method to identify problem oﬃcers. The Police-Public Contact Survey has been used, mainly in criminol-

ogy, to study questions such as whether police treatment of citizens impacts the broa d er public opinion of the police

(Miller et al., 2004).

Hispanics are more than ﬁfty percent more likely to have an interacti on with police which involves

any use of force. Accountin g for 125 variables that represent baseline characteristics, encounter

characteristi cs , civilian behavior, p r eci n ct and year ﬁxed e↵ects, the odds-ratio on black (resp.

Hispanic) is 1.178 (resp. 1.122).

Interestingly, as the intensity of force incr eas es (e.g. handcuﬃng civ i li an s without arrest, draw-

ing or pointing a weapon, or using pepper spray or a baton), the probability that any civilian is

subjected to such treatment is small, but the raci al di↵erence remains surp ri s in gl y constant. For in-

stance, 0.26 percent of interact i on s between p ol i ce and civilians involve an oﬃcer drawing a weapon;

0.02 percent involve using a bat on . These are rare events. Yet , the results ind i cat e that they are

signiﬁcantly more rare for whites than blacks. With all controls, blacks are 21 percent more likely

than whites to be involved in an interaction with police in whi ch at l e ast a weapon is drawn and

the di↵erence is statistically signiﬁcant. Across all non-lethal uses of force, the odds-ratio of the

black coeﬃcient ranges from 1.175 (0.036) to 1.275 (0.131).

Data from the Police-Public Contact Survey are qualitatively similar to th e r e su lt s from Stop

and Frisk d at a, both in terms of whether or not any force is used and the intensity of force, though

the estimated rac i al di↵erences are signiﬁcantly larger. Blacks and Hispanics are approximately 1.3

percentage points more likely than whites to report any use of force in a police interaction, including

controls for civilian demographic e, civilian behavior, contact characteristics, oﬃcer characteristics

and year. The white mean is 0.7 percent. Thus, the odds ratio is 2.769 for blacks and 1.818 for

Hispanics.

There are several potential explanations for the quantitative di↵erences between our estimates

using Stop and Frisk data and those using PPCS data. First, we estimate odds -r at i os and the

baseline probability of force in each of t he datasets is substantially di↵erent. Second, the PPCS

is a nationally representative sample of a broad set of police-civi l ian interactions. Stop and Frisk

data is from a particular form of polici n g in a dense urban area. Third, the PPCS is gleaned from

the civilian perspective. Finally, granular controls for location are particularly important in the

Stop and Frisk dat a and unavailable in PPCS. In the end, the “answer” is likely somewhere in the

middle and, importantly, bot h bounds are statistically and economically important.

In stark contrast to non-lethal uses of force, we ﬁnd that, conditional on a police interaction,

there are no racial di↵erences in oﬃcer-involved shootings on either the exten si ve or intensive

margins. Using data from Houston, Texas – where we have both oﬃcer-involved shooti ngs and a

randomly chosen set of potential i nteractions with police where lethal force may have be e n justiﬁed –

we ﬁnd, after controlling for suspect demographics, oﬃcer demographics, encounter characteristics,

suspect weapon and year ﬁxed e↵ects, that blacks are 27.4 percent less likely to be shot at by police

relative to non-black, non-Hispanics. This coeﬃcient is meas ur ed with considerable error and not

statistically signiﬁcant. This resul t is remarkably r obu st across alter nat i ve empirical speciﬁcations

and subsets of the data. Partitioning the data in myriad ways, we ﬁnd no evidence of racial

discrimination in oﬃcer-involved shoot in gs. Investigating the intensive margin – the timing of

shootings or how many bullets were discharged in the endeavor – there are no detec t abl e racial

di↵erences.

Our r esu l t s have several important caveats. Fi r st , all but one dataset was provided by a select

group of police departments. It is possible that these departme nts only s up p li e d the d at a because

they are either enlightened or were not conc er ne d abou t what the anal ys i s would reveal. In essence,

this is equivalent to analyzing labor market discrimination on a set of ﬁrms willing to supply a

researcher with their Human Resources data! There may be import ant selection in who was wi ll i n g

to share their data. The Police-Public contact survey partially sidesteps this issue by including

a nationally representative sample of civilians, but i t does not contain data on oﬃcer-involved

shootings.

Relatedly, even police departments willing to supply data may cont ai n police oﬃcers who present

contextual factors at that time of an incident in a biased manner – making it diﬃcult to interpret

regression coeﬃcients in the s t and ard way.

It i s exceed ingl y diﬃcu l t to know how prevalent this

type of misreporting bias is (Schneider 1977). Accounting for contextual variabl es recorded by

police oﬃcers who may have an incentive to distort the truth is problemat i c. Yet, whether or n ot

we inc l ud e control s does not alter the basic qualitative conclusions. And, to the extent that there

are racial di↵erences in underreporting of non-lethal use of force (and police are mor e likely to not

report force u se d on blacks), our estimates may be a lower bound. Not reporting oﬃc er -i nvolved

shootings seems u n li kely.

In the Samuel DuBose case at the University of Cincinnati, the oﬃcer reported “Mr. DuBose pulled away and

his arm was caught in the car and he got dragged” yet b ody camera footage showed no such series of events. In

the Laquan McDonald case in Chicago, the police reported that McDonald lunged at th e oﬃc er with a knife whil e

dash-cam footage showed the teenager walki n g away from the police with a small knife whe n he was fatally shot 16

times by the oﬃc er.

Third, given the inability to randomly assign race, one can n ever be conﬁdent in the direct re-

gression approach when interpreting racial disparities. We partially address this in two ways. First,

we build a model of police-civili an interactions that allows for both statistical and taste-based dis-

crimination and use th e predictions of the model to help interpret the data. For instance, if police

oﬃcers are pure statistic al discriminators then as a civil ian ’ s signal to police regarding thei r likeli-

hood of compliance becomes increasingly determinis ti c , racial di↵erences should disappear. To t es t

this, we investigate racial di↵erences in use of f or ce on a set of police-civilian interactions in which

the police report the civilian was compliant on every measured d im en si on , was not arrested, and

neither weapons nor contraband were found. In contrast to the model’s predictions, racial di↵er-

ences on this set of inter act i ons is l ar ge and stat i s ti c all y si gni ﬁ cant. Additionally, we demonstrate

that the marginal returns to compliant behavior are the same for blacks and whites, but the aver-

age return to compliance is lower for blacks – suggestive of a taste-based, rather than statistical,

discrimination.

For oﬃcer-involved shoot i n gs, we employ a simple Beckarian Outcomes test (B ecker 1993) for

discrimination inspired by Knowles, Persico, and Todd (2001) and Anwar and Fang (2006). We

investigate the fraction of white and black suspects, separately, who are armed conditional upon

being involved in an oﬃcer-involved shooting. If the ordinal threshold of shooting at a black susp e ct

versus a white suspect is di↵erent acr oss oﬃcer races, then one could reject the null hypot h es is of

no dis cr i mi nat i on . Our results, if anything, are the opposite. We cannot reject the null of no

discrimination in oﬃcer-involved shootings.

Taken together, we argue that the results are most consistent with, but in no way proof of, taste-

based discrimination among police oﬃce rs who face convex costs of excessive use of force. Yet, the

data does more to provide a more compelling case t hat there is no discrimination in oﬃcer-i nvolved

shootings than it does to il l umi n at e the reasons behind racial di↵erences in non-lethal uses of force.

The rest of the paper is organized as follows. The next section describes and summarizes the four

data sets used in the analysis. S ec t i on 3 describes potential selection into police data sets. Section

4 presents esti mat es of racial di↵erences on non-lethal uses of force . Section 5 describes a similar

analysis for the use of l et h al force. Section 6 attempts to reconci le the new facts with a simple

model of police-civili an interaction that incorporates both statistical and taste-b ase d channels of

discrimination. The ﬁnal section concludes. Ther e are 3 online appendices. Appendix A describes

the data used in our analysis and how we coded variables. Appendix B describes the process of

creating datasets from event summaries. Appendix C p r ovides additional theoretical results.

II. The Dat a

We use four sources of data – none ideal – which together paint an empirical portrait of racial

di↵erences in police u se of force conditional on an interaction. Th e ﬁrst two data sources – NYC’s

Stop and Frisk program and the Police-Public Contact Survey (PPCS) – provide information on

non-lethal force fr om both the police and civilian perspectives, respectively. The other two datasets

– event summaries of oﬃcer-involved sho ot i ngs in ten locations across the US, and data on interac-

tions between civili ans and police in Houston, Texas, in which the use of lethal of force may have

been justiﬁed by law – allow us to investigate racial di↵erences in oﬃcer-involved shootings on both

the ex t en si ve and intensive margins.

Below, I brieﬂy discuss each dataset in turn . Appendix A provides further detail.

A. Ne w York City’s Stop-Question-and-Frisk Program

NYC’s Stop-Question-and-Frisk data consists of ﬁve million individual police stops in New York

City between 2003 and 2013. The database contains detailed information on the characteristics

of each stop (precinct, cross st re et s, time of day, inside/outside, high/low crime area), civilian

demographics (race, age, gender, height, weight, build, type of identiﬁcation provided), wheth er

or not the oﬃcers were in uniform, encounter characteristics (reason for stop, reason for frisk (if

any), reason for search (if any), suspected crime(s)), and post-encounter characteristics (whether

or not a weapon was eventually found or whether an individual was summonsed, arrested, or a

crime c omm it t e d) .

Perhaps the most novel component of the data is that oﬃcers are required to document which

one of the following seven uses of force was used, if any: (1) hands, (2) force t o a wall, (3) handcu↵s,

(4) draw weapon, (5) push to the ground, (6) point a weapon , (7) pepper spray or (8) strike with

a baton.

Oﬃcers are instructed to include as many uses of force as applicable. For instance, if

Police oﬃcers can also include “other” force as a type of force used against civilians. We exclude “other” forces

from our analysis. Appendix Table 4 calc u l a tes racial di↵erences in the use of “other” force and shows that including

these forces does not alter our results.

a stop results in an oﬃcer puttin g his hands on a civilian an d, later within the same interaction,

pointing his weapon, th at observation would have both “hands” and “point a weapon” as uses of

force. Unfortunatel y, oﬃcers are not requi re d to document the sequence in which they used force.

These data have important advantages. First, the Stop and Frisk program encompasses a

diverse sample of police-civilian interac ti on s.

Between the years 2003 and 2013, t h e same period

as the Stop and Frisk data, there were approximately 3,457,161 arrests in NYC – 26.3% fewer

observations than Stop and Frisk ex cl ud i ng stops that resulted in arrests.

Unfortunately, even

this robust dataset is incomplete – nowhere is the universe of all police interactions with civ i l ian s

– or even all police stops – recorded.

Second, lower level uses of force – such as the use of hands – are both r ec or de d in th es e data

and more freq u ently used by law enforcement than more intense use s of force. For instance, if

one were to use arrest data to glean use of force, many lower level uses of f orc e would simply be

considered standard operating procedure. Putting hands on a suspect, pushing them up against a

wall, and putting handcu↵s on them are so un-noteworthy in the larger context of an arrest that

they are not recorded in typi cal arrest descriptions. Yet, becau se proactive policing is a larger and

less con fr ontational port ion of police work, these actions warrant data entry.

The key limitation of the data is th ey only capture the police side of the story. There have

been several high -p r oﬁl e case s of pol i ce st or y t el l in g th at i s not con gr ue nt with v i de o evi d en ce of the

interaction. Another important limitation for inf er en ce is that the data do not provide a way to

identify oﬃcers or indiv id u als . Ideally, one would simply cluster standard errors at the oﬃcer level

to account for the fact that many data points – if driven by a few aggressive oﬃcers – are correlated

and classic inference treats them as independent. Our typical regressions c l us t er standard errors at

the precinct level. Appendi x Table 10 explores the robustness of our results for more disaggregate d

clusters – precinctˆtime of day, block-level, and even bl ockˆtime of day. Our conclusions are

una↵ected by any of these alternative ways to cluster st and ar d errors.

Summary statistics for the Stop and Frisk data are displayed in Appendix Table 2A. There are

Technically, NYC police are only required to record a stop if some force was used, a civil ia n was frisked or

searched, was arrest ed , or refused to provide identiﬁcation. Nonetheless, roughly 41 percent of all stops in the

database appear to be reported despite not resulting in any of the outcomes th a t legally trigger the requirement to

record the stop.

This number was calculated from the Division of Criminal Justic e Services’ record of adult arrests by counties

in New York City between 2003 and 2013.

six panels. Panel A contains baseline characteristics. Fifty eight percent of all stops recorde d were

of black civi l ian s. If police were stopping individuals at random, th i s number would be closer to 25.5

percent (the fraction of black civilians in New York City according to US Census 2010 records).

Hispanics make up twenty-ﬁve percent of the stops. The dat a are comprised predominantly of

young males; the median age is 24 years old. The median age in NYC is roughly 11 years older.

Panel B describes encounter characteristics for the full sample and then separately by race.

Most stop s occur out s id e after the sun has set in high-crime ar eas . There is a surprisingly small

number of stops – about th r ee percent – where the police report ﬁnding any weapon or contraband.

Panel C displ ays variables that describe civilian behavior. Approximately 50 per cent of stops were

initiated because a civilian ﬁt the relevant description of a person of interest, were assumed to be

a lookout for a crime, or the oﬃcers were casing a victim or location.

Panel D contains a series of alternati ve outcomes such as whether a civil ian was frisked, sum-

monsed, or arrested. Panel E provides descriptive statistics for the seven forms of force available

in th e data. Panel F provides the frequency of missing variab l es .

B. Th e Police-Public Contact Survey

The Police-Public Contact Survey (PPCS) – a nationally r ep r es entative sample – has been collected

by the Bureau of Justice Statistics every three years since 1996. The most recent wave publicly

available is 2011. Across all years, there are approximately 426,000 observations.

The main advantage of the PPCS data is that, u n li ke any of our other datasets, it provides the

civilian’s interpretation of interactions with police. The distinction between PPCS data and almost

any other data collected by the police is similar to the well-known di↵erences between certain data

in the Uniform Crime Reports (UCR) and the National Cri me Victimization S ur vey (NCVS).

One

explanation for these di↵erences given in the literature is that individu als are embarrassed or afraid

to report certain crimes to police or believe that reporting such crimes have unclear beneﬁts and

potential costs. Reporting police use of force – in partic ul ar for young minority males – may be

According to the US Department of Justice, UCR and NCVS measure an overlapping but nonidentical set of

crimes. The UCR Prog ra m’ s primary objective is to provide a reliable set of cri mi n a l justice statistics by compiling

data from monthly law enfo rcem ent reports or individual crime incident reports transmitted directly to FBI or to

centralized state agencies that then report to FBI. The BJS, on the other hand, established the NCVS t o provide

previously un availa b l e information about crime (including cri me not reported to police), v ic t im s and o↵enders.

Therefore, there are discrepanci es in victimization rates from the two reports, like the UCR which reports 89,000

forcible rapes in 2010 while th e NCVS rep o rt s 203,830 rapes and sexual assault s in 2010.

similar.

Another key advantage is that it approximates the universe of potential interactions with police

– rather than limited to arrests or police stops.

If a police oﬃcer is investigating a crime in a

neighborhood and they discuss it with a civilian – this type of interaction would be r ecor d ed in the

PPCS. Or, if a police oﬃcer used force on a civilian and did not report t h e interaction – this would

not be recorded in police data but would be included in the PPCS.

The PPCS also has important limitations. First, data on individ ual ’ s locations is not available to

researchers. There are no geographi c indicators. Second, the data on cont ex t ual factors surrounding

the interaction with police or the oﬃcer’s character i st i cs are limited. Third, the survey omits

individuals wh o are currently in jail. Fourth, the PPCS only includes the civilian ac cou nt of the

interaction which could be biased in its own way. In this vein, according to individuals in the PPCS

data, only 3.28% of them have resisted arrests and only 11.07% of c i vi l i ans argue d when they were

searched despite not being guilty of carrying alcohol, drugs or weapons.

Appendix Tab l e 2B presents summary statistics for PPCS sample with at least one interaction

with polic e. There are six panels. Panel A contains civilian demographics. Blacks comprise roughly

ten percent of the sample, women are 50 percent. The average age is approximately 13 years older

than the St op and Frisk data. Over 72 percent of the sam pl e reports being employed in the previous

week – average income category in the samp l e is 2.09. Income is recorded as a categorical variable

that is 1 for income levels below $20,000, 2 for income levels between 20, 000 and 49, 999, and 3 for

income l e vels greater than $50,000.

Panel B describes self-rep or t ed civilian beh avior. According t o all PPCS survey respondents,

only 1.93 percent of civili an s disobey police ord er s, try to get away, resist , argue or threaten oﬃcers

when t he y have some interaction with the police.

Panel C of Appendi x Table 2B includes summary data on the types of contact and oﬃcer

characteristi cs . Almost half of the interactions between the public and police are traﬃc stops, 0.35

percent are from street interactions – including the types of street i nteraction that may not appear

in our Stop and Frisk data – and 44.73 percent are “other” w hi ch include being involved in a traﬃc

accident, reporting a crime, being provided a service by the police, participating in block watch

Contacts exclude encounters with private sec u rity guards, police oﬃcers se en on a social basis, police oﬃce rs

related to the survey respondents, or any contacts that occurred outside the United States.

or other anti-crime programs, or being suspected by the police of something or as part of a police

investigation. Panel D contains alternative outcomes and Panel E describes the ﬁve uses of force

available in the data. Panel F provides the frequency of missin g variables.

C. O ﬃc er -Involved Shootings

There are no systematic datasets which include oﬃcer -i nvolved shootings (OIS) along with demo-

graphics, encounter characteristics, and suspect and police behavior.

For the purposes of this

project, we compile a dataset on oﬃce r- i nvolved shootings from ten locations across Ame r ic a.

To begin, ﬁfteen police departments across the country were contacted by the author: Boston,

Camden, NYC, Philadelphia, Austin, Dall as, Houston, Los Angeles, six Florida counties, and

Tacoma, Washington.

Importantly for thinking about the representativeness of the data – many

of these cities were a part of the Obama Administration’s Police Data Initiative.

We received

data from all but thre e of these police departments – NYC, Ph il ad el p hi a, and Tacoma, Washington

– all of which have indicated a willingness to participate in our data collection e↵orts but have not

yet provided data.

This is likely not a representative set of cities. Append i x Table 17 investigates

di↵erences between the cities that provided us data and other Metropolitan Statistical Areas on a

variety of dimensions such as pop u lat i on demographics and crime rates.

In most cases, OIS data begins as event summari e s from all incidents i n which a police oﬃcer

discharged their ﬁrearm at civilians (including both hits and misses). These summari e s, in many

cases, are more than ﬁfty page descriptions of the factors surrounding an oﬃcer-involved shooting.

Below is an extract from a “typical” summary:

“As I pointed my riﬂe at the vehicle my pr i mar y focus was on the male passenger

based on the information p r ovided by the dispatcher as the person who had been armed

Data constructed by the Washington Post has civilian demographic identiﬁers, weapons carried by civilian, signs

of mental illness and an indicator for threat level but no other contextual information.

Another approach is to request the data from every police department vis-a-vis a freedom of information request.

We attempted th i s method, but police departments are not obliged to includ e detailed event summaries. In our

experience, the only way t o obtain detailed data is to have c o ntacts within the police department.

The White House launched the Police Data Initiative as a response to the recommendati o n s made by the Task

Fo rc e on 21st Century Policing. The Initiative was created to work with police d ep a rt ments to leverage data on

police-citizen interactio n s (e.g., oﬃcer-involved shootings, use of force, body camera videos and police stops) to

increase transparency and accountability.

Camden and Bost o n each had one OIS during the relevant time frame, so we did not use their data for this

analysis. Camden provided remarkable data o n police-civilian interactions which will be used i n future work.

inside the store. As the vehicle was driving past me I observed the male passenger in

the truck turn around i n the seat, and begin pointing a handgun at me through an

open rear sliding glass window. Whe n I observed this I was still yelling at the femal e

to stop the truck! The male suspect appear ed to be yelling at me, but I could not

hear him. At that point the truck was traveling southbound toward the traﬃc light

on Atlantic Boulevard, and was approximately 30-40 feet away from me. The car had

already passed me so the driver was no longer in my line of ﬁ r e. I could also see my back

drop consisted of a wooded area of tall pine trees. It appeared to me at that time that

his handgun was moving in a similar fashion of bein g ﬁred and goin g th r ough a recoil

process, but I could not hear gunshots. Fearing for my life, the lives of the citizens in

the are a and my fellow oﬃcers I began to ﬁre my riﬂe at the suspect.”

To create a dataset out of these narratives, a team of re sear ch assistants read each summary

and extracted data on 65 pre-determ in ed variables in six categories: (A) suspect characteristics,

(B) suspe ct weapon(s), (C) oﬃcer characteristics, (D ) oﬃcer response reason, (E) other encounter

characteristi cs , and (F) location characteristi c s.

Suspect characteristics include data on suspect

race, age and gender. Suspect weapon variables consist of dummy variables for whether the suspect

used a ﬁrearm, sharp object, vehicle, or other objects as a weapon or did not have a weapon at

all. Oﬃcer characteri st i cs include variables that determine the majority race of the oﬃcer unit,

whether there were any female oﬃcers in the unit, average tenure of the shooting oﬃcer and dummy

variables for whether the oﬃcer was on duty and was accompanied by two or more oﬃcers on the

scene. Oﬃcer response reason vari ab le s determine the reason behind the oﬃcer being present at

the scene. They include dummy variables on whet h er th e oﬃce r was present as a response to a

robbery, a violent disturbance, traﬃc related stop, or was responding to a warrant, any suspicious

activity, a narcotics transaction, a suicide, responding because he was per son all y at t acked or other

reasons. Other encounter characteristics gather inf orm ati on on whether the shooting happened

during the day or night and a variable that is coded 1 if the suspect attacked the oﬃcer or dr ew

a weapon or attempted to draw a weapon on the oﬃcer. The variable is coded 0 if the suspect

only appeared to have a weapon or did not attack th e oﬃcer at all. Finally, location characteristics

Appendix B provides a detailed , step-by-step, a c c o u nt of h ow the O I S dataset was created and was explicitly

designed to allow researchers to replicate our ana ly sis from the original source materi a ls .

include d um mi es to represent the jurisdiction that we collected data from. Appendix B contains

more det ai l s on how the variables were coded.

As a cr u ci al check on data quality, once we coded all OIS d at a from the event summaries, we

wrote Appendix B. We then hired eight new research assistants wh o did not have any i nvolvement

in creating the ﬁrst dataset. We provided them the event summaries, Appendix B, and extremely

minimal instructions – the type of simple clariﬁcation that would be provided to colleagues at-

tempting to repli cat e our work from the source material – and they creat ed a second, independent,

dataset. All results remain qualitatively unchanged with the alternatively coded dataset.

The most obvious advantage of the OIS data is the breadth and speciﬁc ity of information

contained in the event summaries. Descriptions of OIS are typically long and quite detailed relative

to other police data. A se con d advantage is that oﬃcer-involved shootings are non-subjective.

Unlike lower level uses of force, whether or not an oﬃcer discharges a weapon is not open to

interpretat ion . Oﬃcers are also req ui r ed to document anytime they discharge their weapon. Finally,

OIS are subject to internal and often times external review.

The OIS data have several notable limitation s. Taken alone, oﬃcer-involved shootings are the

most extreme and least used f orm of police force and thus, in isolation, may be misl ead i ng. Secon d,

the penalties for wrongfully discharging a lethal weapon in any given situation can be life altering,

thus, the incentive to misrepresent contextual factors on police report s may be large.

Third, we

don’t typically have the suspect’s side of the s t ory and often there are no witnesses. Fourth, it is

impossible to capture all variables of importance at the tim e of a shooting. Thus, what appears to

be d i scr i mi n ati on to some may look like mis-measured contextual factors to others.

A ﬁnal disadvantage, potentially most important for inference, is that all observations in the

OIS data are shootings. In statistical parlance, they don’t contain the “zeros” (e.g., set of police

interactions in which lethal force was justiﬁed bu t not used). To the extent that r aci al bias is

prevalent on the ext en si ve margin – whether or not someone is ever in an oﬃcer-involved shooting

– these data would not capture it.

We address this concer n both directly and indirectly in two ways. First, given the data we

have, we investigate the intensive margin by deﬁning our outcome variable as whether or not the

Thanks to Derek Neal for su g g est i n g this exercise.

Fro m interviews with dozens of current police oﬃcers, we gleaned that in most all police shootings – even when

fully justiﬁed and o b s erved by many – the oﬃcer is taken o↵ active-duty, pending an investigat io n .

oﬃcer shoot s the suspect before being attacked. Second, we collected unprecedented data from

the Hous t on Police Department on all arrest categories in which oﬃcers cou l d have justiﬁably used

lethal force as a way to obtain the “zeros.” These data are described in th e next subsection.

Appendix Table 2C displays summar y statistics for OIS data, divided into four locations and

six categories of data. Column (1) contains obser vations from the full sample – 1,316 shootings

between 2000 and 2015.

Forty-six per ce nt of oﬃcer-involved shootings in our data are blacks,

thirty one percent ar e Hispanic, and twenty three percent are other with the majority in that

category being whites. Given the spate of video evidence on police shootings – all of which are of

blacks – it is a b it surprisi n g that they are less than half of the observations in the data.

Columns (2) and (4) displays data from 508 oﬃcer-involved shootings with ﬁrearms and over

4,000 instances of an oﬃcer-involved shooting with a taser, in Houston, Texas. Most police oﬃcers

in the Houston Police Depart me nt carry Glock 22, Glock 23 or the Smith & Wesson M &P 40 .40

(S&W) caliber semi-automatic handguns on their dominant side, but many carry an X26 taser

on their non-dominant side. We exploit this choice problem to understand how real-time police

decisions may be correlated with suspect race.

Columns (5) through (7) contain OIS data from Austin and Dallas, Texas, six Florida counties

(Brevard, Jacksonville, Lee, Orange, Palm Beach and Pi n el l as) , and Los Angeles County. Panel F

demonstrates that Houston accounts for 39% of all oﬃcer-involved shootings. Austin and Dallas,

combined, provide 20% of the data while Flor i d a provides 26% of the data. Panel G provides t h e

frequency of mis si n g variables.

D. Houst on Police Department Arrests Data

The most comprehensive set of OIS data is from the Houston Police D e par t me nt (HPD). For this

reason, we contacted HPD to help construct a set of police-civilian interactions in which lethal

force may have been justiﬁed. Accordi ng to Chapter 9 of the Texas Penal Code, police oﬃcer s’

use of deadly force is justiﬁed “when and to the degre e the actor r eas onab l y bel i eves the force is

immediately necessary.” Below, we describe the task of implementing this obtuse de ﬁn i t ion in data

We asked for data on all OIS b etween 2000 and 2015 and police departments replied back with years they had

data on. With the exception of LA county, Brevard county, and Jacksonville county that gave us less than 10 years

of data (an average of 5.7 years), the other 7 OIS locations gave us more than 10 years of d a t a (an average of 13.7

years). At the least, we have Jacksonville with 5 years of data (2011-2015) and at the most we have Houston city

and Orange county, with 16 years of data (2000-2 0 1 5 ) .

in an e↵ort to develop a set of police-ci vi l i an i nteractions in which the use of lethal force may have

been justiﬁed by law.

There are approximately 1,000,000 arrests per year in Houston; 16 million total ove r t h e years

we have OIS data. If the data were more systematically collected, the tasks of creating potential

risk sets would be straightforward. Data in HPD is the opposite – most of it is narrative reports

in the form of unstructured blocks of text that one can link to alternative HPD data with uniqu e

case IDs .

We randomly sam pl ed ten percent of case IDs by year from ﬁve arrest categories which are more

likely to contain incidence in which lethal force was justiﬁed: attempt ed capital murder of a public

safety oﬃcer, aggravated assault on a public safety oﬃcer, resistin g arrest, evading arrest, and

interfering in arrest.

This proces s narrowed the set of r el evant arrests to 16,000 total , between

2000 and 2015. Then we randomly sampled ten percent of these ar r est record s by year and manually

coded 290 variables per arrest record. It took between 30 and 45 minutes per record to manually

keypunch and include variables relat e d to speciﬁc locations for calls, incidents, and arrests, suspect

behavior, suspect mental health, suspect injuries, oﬃcer use of force, and oﬃcer injuries resulting

from th e encounter.

These dat a were merged with data on oﬃcer demographics and suspect’s pr ev i ous arrest history

to produce a comprehensive incident-level dataset on interactions between police and civilians in

which lethal force may have been justiﬁed.

We also col l ect e d 4,250 incident reports for all cases in which an oﬃcer discharged their taser.

These data for m another potential risk set. It it important to note: technology allows for HPD t o

centrally monitor the frequency and location of taser discharges.

Appendix Table 2C Colu mn (3) provides descriptive statistics for the Houston Ar r es t Data.

Compared to the oﬃcer-involved shootings dataset, civilians sampled in the arrest dataset carry

far fewer weapons – 95% do not carr y weapons compared to 21% in the OIS dataset. The other

variable that is signiﬁcantly di↵erent between t he two datasets is the fraction of suspects who

In conversations with engineers and data scientists at Google, Microsoft Research, and several o t h ers in A rt iﬁ c ia l

Intelligence and Machine Learning, we were instructed th a t current natural langua g e processing algorithms are not

developed for the level of complexity in our police d a t a . Moreover, one would need a “test sample” (manually coded

data to assess the algorithm’s performance) of several hundred thous a n d to design an algorithm. This is outside the

scope of the current project .

Our original request t o HPD was for a dataset similar to OIS for all arrests between 200 0 and 2015. The response:

“we estimate that it will take 375 years to ful ﬁ ll that request.”

attacked or drew weapon – 56% in the HPD arrest dataset compared to 80% in the OIS dataset.

III. A Note on Potential Sel e ct io n into Police Data Sets

The forthcoming analysis takes t h e four data sets descr i bed above as given and estimates racial

di↵erences in non-lethal and lethal uses of force. But, to the extent that there are racial di↵erence s

in the probability of an interac t i on with police, these data may omit a very important margin. Put

di↵erently, one may discover no di↵erences in police use of force, conditional on an interaction,but

large racial di↵eren ce s in the probability of the types of interactions in which force may be used.

By only concentrating on how and whether force was used in an interaction and ignoring whether

or not an interaction took place, one can misrepresent the total experi en ce with police.

Understanding racial di↵erences in the probability of police interaction is fraught with diﬃculty.

One has to account for di↵erential exposure to police, race-speciﬁc crime par ti c ip at i on rates and

perhaps most import antly, pre-interaction behavior that civili an s exhibit. Ideally, one might set up

a ﬁeld experiment – similar to those used to measure labor market discrimination – that randomly

assigns similar individuals (across all physical dimensions except r ace ) to the vic i ni ty of the same

patrolling oﬃcers in a neighborhood and instruct t h em to behave identically. Conditional on ran-

dom assignment, identic al be havior, and race-speciﬁc crime rates, any di↵erences in the probability

of interaction could be interpreted as racial bias in police stopping behavior.

Without ideal data, researchers often compare the racial distribution of stoppe d civilians t o the

racial distribution of various “at risk” civilians that could potentially be stopped. Determining the

probability of an interaction is essentially a search for th e correct “risk set”.

Panel A of Table 1 provides a series of estimates of racial di↵erences in the probability of police

interaction by deﬁning the relevant risk set in various ways. The ﬁrst three col um ns uses NYC Stop

and Frisk data. Column (1) assumes the population at risk of bein g st opped by police as 18-34

year old males. Column (2) assumes the risk s et is arrestees for ten broadly deﬁned felony and

misdemeanor crimes as determined by the New York City Police Department’s Crime Reporting

System. Felonies include murder and non-negligient manslaughter, rape, other felony sex crimes,

robbery, felonious assault, grand larceny, and felony crime mischief. Misdemeanor crimes i nc lu d e

misdemeanor sex crimes, misdemeanor assault, petit l ar ceny, and mi sd em ean or criminal mi schief.

Contents of all broad crime categories are provided in detail in any of the annual Crime and Enforcement Activity

Column ( 3) is similar to column (2) but only includes t h e six felonies.

For each of the 77 precincts, we calculate the average fracti on of stops that are black and the

corresponding fraction for whites. We also calculate the fract i on of blacks in the relevant risk set

and the same fraction for whites, for all precincts. We then regress the fraction of police stops that

are black (resp. white) on the fraction of blacks (res p. white) in the relevant risk set and store

the coeﬃcient. The numbers displayed in each column is the coeﬃcient for blacks div i de d by the

coeﬃcient for whites for the rele vant risk set. A number greater than one indicates a potential bias

against blacks. A number less than one indicates a potential bias in favour of blacks.

A simple – an d often used – method to do t hi s is to compare the fraction of blacks involved

in interactions with police with their proportion in the population, though many soci al scientists

have ar gue d against this approach (Fridell 2004, Ridgeway 2007, Anwar and Fang 2006). Column

(1) demonstr ate s that blacks are almost 4 times more likely to be stopped by police relative to

their population proportion.Yet, this qu antity is diﬃcult to i nterpret. As Fridell 2004 argu es,

“racial/ethnic groups are not equivalent in the nature and extent of their...law violating behavior.”

Column (2) us es incident weighed average (crimes committed more often are more heavily

weighted) for ten felonie s and mis de me anor s. Unfortunately, we do not have racial breakdown of

crime rates for individual precincts. In lieu of this, we calculate the fraction of arrestee s in crimes

for New York City for each year betwee n 2008 and 2013. Conditioning on incident weighted crime

rates reduces the est i mat e of bias in police interactions from 4.23 to 1.43 – a 66.2 percent reduction.

Column (3) conducts a si mi lar exercise using six broad felonies. This method decreases the

estimate of bias in police stopping behavior to 1.03. If one were to use robbery rates rather than all

felonies, the number would be 0.546 implying that blacks are 45.4 percent less likely to be stopped

[not s hown in tabular form].

Column (4) in panel A of Table 1 investigates potential selection into the PPCS dataset. Relative

to NYCs Stop and Frisk data, the PPCS i nvolves a larger set of police interactions and are not the

result of a particular form of aggressive polici ng. Also, the data are from the civilians perspective.

This allows one to analyze the probab i l ity of having an involuntary interact i on with the police

controlling for race and other demographics, for all respondents of the survey. In some ways, this

is closer to the ideal dataset described above though we cannot control for pr e -i nteraction civilian

Reports released by the New York City Police Department.

behavior. Involuntary interacti on is a dummy variable coded to be one if the civilian report ed that

he was involved in an interaction with th e police which was not initiated by him (for example,

traﬃc or parking viol at i on , poli c e asked respon de nt questions et c) . The variable is coded to be 0 if

the civ i li an reported no interaction with police or an interaction that was initiated by himself (for

example, reporting a crime , asking for assistance etc).

We estimat e a logistic regression of involuntary interaction on civilian race, demograp hi c vari -

ables such as gender, age, income categories, the population size of the civilian’s address, a dummy

variable indicating whether the civilian was employed last week or not, an d year, and report the

odds ratio on b lack coeﬃcient. The odds that blacks have an involuntar y interaction with police

is 8 percent less than whites. For comparison we also provide t h e odds ratio for voluntary interac-

tions. Voluntary interactions include all inter act i ons with police that civilians initiated themselves.

Blacks are 21 percent less likely to report a voluntar y interaction with the police than whites.

The ﬁnal three columns in Panel A of Table 1 report estimates from an analysis identical to

the one conducted for the Stop and Frisk dataset, but for Houston Oﬃcer-Involved shootings.

Column (6) demonstrates that blacks are 4.35 times more likely to be involved in an oﬃcer involved

shooting than non-blacks r el at i ve to t he i r proportion in the 18-34 year old male population. This

estimate changes drasticall y to 1.01 – a 76.8 perce nt reduction – when the population deﬁned “at

risk” is the fraction of arrestees in felonies and misdemeanors. The estimate decreas es further to

0.87 when only felony crimes are taken into account.

Panel B of Table 1 reports the results of a series of Beckarian outcomes tests (Becker 1993),

where the outcomes are whether or not a police stop result ed in an arrest or whether contraband

or any weapon was found. Becker (1993), in the context of mortgages, argued that discrimination

in mortgage lending against blacks cannot be found simply by looki n g at the likelihood of getting

a loan for minority versus white applicants who are similar in incomes, credit backgrounds, and

other available characteristics. The correct procedure would be to determine whether loans are

more proﬁtable to blacks (and other minorities) than to whites. Discriminating banks would turn

down marginally proﬁtable black applicants but accept white applicants. This is the spirit behind

the se mi nal work in Knowles, Persico, and Todd (2001).

Potential selection into all OIS locat i o n s by popula ti on weights and Uniform Crime Report coded arrest rates

are presented at the end of A p pendix Table 2C.

For the outcomes test, we estimate a logistic regression of whether the civilian was arrested/was

carrying contraband or weapons on race, civilian demographics, encounter characteristics, civilian

behavior, and suitable ﬁxed e↵ects.

We report the odds ratio on the black coeﬃcient. If the

coeﬃcient is above one – this implies that stops of blacks are more “productive” than whites and

thus, if anything, police should be stopping blacks more at the margin.

Unfortunately, whether or not there seems to be racial bias in police stopping behavior depends

on the outcome tested. When using whether or not the civil ian was arrested as an outcome –

which has the im portant disadvantage of depending both on t h e subsequent behavior of civ il i an s

and police – there seems to be no bias against blacks in police stop pi n g behavior. In other words,

blacks are more likely to be arrested, conditional upon being stopped. When the outcome is whether

or not contraband or a weapon was found, bl ack stops are signi ﬁc antly less productive than whites

and thus is evidence for potential bias.

Taken together, this evidence demonstrates how diﬃcult it is to understand whether ther e is

potential selection into polic e datasets. Estimates range from blacks being 323 percent more likely

to be stopped to 45.4 percent less likely to be stopped. Solving this is outside the scope of this

paper, but the data suggests the following rough rule of thumb – if one assumes that pol ic e are non

strategic in stopping behavior there is bias. Conversely, if one assumes that police are stopping

individuals they are worried will engage in violent crimes, t h e evidence for bias is exceed i ngly small.

IV. Estimating Racial Di↵erences in Non-Lethal Use of Force

NYC’s Stop , Question, and Frisk Data

Table 2 presents a series of estimat es of racial di↵erences in police use of force, conditional on

being stopped, using the St op and Frisk data. We estimate logistic regressions of the foll owing

form:

PrpForce

i,p,t

“ 1q

1 ´ PrpForce

i,p,t

“ 1q

“ Race

↵ ` X

i,t

 ` Z

p,t

µ ` ⌫

` ✏

i,p,t

(1)

where Force

i,p,t

is a measure of police use of for c e on individual i,inprecinctp, at time t.A

full set of race dummie s for civilian s are included in the regressions, with white as the omitted

All controls used are reported in det a il in summary statistics Appendix Table s 2A and 2B.

category. Consequently, the coeﬃcients on race capture the gap between the named racial category

and whites – which is reported as an Odds Rati o.

The vectors of covariates included in the

speciﬁcation, denoted X

i,t

and Z

p,t

, vary between rows in Table 2. As one moves down the table,

the se t of coeﬃcients steadily grows. We caution against a causal interpretation of the coeﬃcients

on the covariates, which are better viewed as proxies for a broad set of environm ental and behavioral

factors at the time of an incident. Standard errors, which appear below each estimate, are clustered

at the precinct level unless otherwise speciﬁed.

Row (a) in Table 2 presents the di↵erences in means for any use of forc e conditional on a police

interaction. These results reﬂect the raw gaps in whether or not a police stop results in any use of

force, by race. Blacks are 53% more likely to experience any use of force relative to a white mean of

15.3 percent. The raw gap for Hispanics is almost identical. Asians are no more likely than whites

to experience use of force. O t h er race – which includes American Indians, Alaskan natives or other

races besides white, black, Hispanic and Asian – is smaller but still considerable.

The raw di↵erence between races is large – perhaps too large – and it seems clear that one needs

to account for at least some contextual factors at the time of a stop in order to better understand,

for example, wheth er racial di↵erences are driven by police response to a given civilian’s behavior

or racial di↵erences in civilian behavior. Yet, it is unclear how to account for context that might

predict how much force is used by police and not include variables which themselves might be

inﬂuenced by biased police.

Row (b) adds baseline civilian characteristics – such as age and gender – all of which ar e

exogenously determined and not strategically chosen as a function of the police interaction. Adding

these variables does almost nothing to alter the odds ratios. Encounter characteristics – whether th e

interaction happe ne d inside , the time of day, whether it occurred in a hi gh or low crime area, and

whether the civilian provided identiﬁcation – are added as controls in row (c). If anything, adding

these variables increases the odds ratios on each race, relative to whites. Surprisingly, accounting

for civ i l i an behavior – row (d) in the table – does little to alter the results.

Row (e) in Table 2 includes both precinct and year ﬁxed e↵ects. This signiﬁcantly changes the

Appendix Tables 3A through 3G runs similar speciﬁcation using ordinary least squares and obtains similar

results. Estimating Probit mode ls provides almo s t identical resu lt s.

The traditional literature in labor economics – beginning wi th Mincer (1958) – dealt with similar issues. O’Neill

(1990) and Neal and Johnson (1996) sidestep this by demonstrating that much o f the racial wage gap can be accounted

for by including only p re- ma rket factors such a s test scores.

magnitude of the coeﬃcients. Blacks are almost ei ghteen percent more likely to incur any use of

force in an interaction, accounting f or all variables we can in the data. Hispanics are roughly twelve

percent mor e l i kely.

Both are statistically signiﬁcant. Asians are slightly less likely, though not

distinguishable from whites. Row (f) interacts p r ec in ct s with year as ﬁxed e↵ects. Results do not

change signiﬁcantly from row (e). Changing ﬁxed e↵ects to be interactions between precinct, year

and month (row (g)) does not alter the results.

These data have two potential takeaway s: precincts matter and, accounting for a large and

diverse set of control variables, black civilians are still more likely to experience police use of force.

Of the 112 variables available in the data, the r e is no linear combination that fully explains the race

coeﬃcients.

From this point forward, we consider the row (e) speciﬁcation, including precinct

and year ﬁxed e↵ects as our main speciﬁcation.

Inferring racial di↵erences in the types of force used in a given interaction is a bit more nuanced.

Police report that in twe nty percent of all st op s, some use of forc e is deployed. Oﬃcers routi ne l y

record more than one use of force. For instance, a stop might result in an oﬃcer putting their

hands on a civilian, who then pushes the oﬃcer and the oﬃcer responds by pushing him to the

ground. This would be recorded as “hands” and “force to ground”. In 85.1% of cases, exactly one

use of force is recorded. Two use of force categories were used in 12.6% of cases, 1.8% report three

use of force categories, and 0.6% of all stop and frisk incide nts in which force is used record more

than t hr e e uses of force.

There ar e several ways to handle this. The simplest is t o code the max force used as “1” and

all the lower level uses of force in that interaction as “0”. In the example above in which an oﬃcer

recorded both “hands” and “forced to t h e ground” as uses of force, one would ignore the use of

hands and code forced to the ground as “1.” The limitation of this approach is that it discards

potentiall y valuable information on lower level uses of force. When anal yz i ng racial di↵erences in

the use of hands by police, one would miss this observation. A similar issue arises if one uses the

Even accounting for eventual outcomes of ea ch stop – which include being let go, being frisked, being searched,

being arrested, being summonsed, and whether or no t a weap o n or so m e form of contraband was found – blacks are

twenty-two percent more likely to experience force and Hispanics are twenty-seven percent more likely. We did not

include these control variables in our main speciﬁcation due to the fear of over-controlling if there is discrimination

in the probability of arrests, conditional on behavior.

Using data on geo-spatial coordinates, we also included block-level ﬁxed e↵ects and the results were qualitatively

unchanged.

parallel “min.”

Perhaps a more intuitive way to code the data is to treat each use of force as “at least as much”.

In the example above, both han ds and forced to the ground would be coded as “1” in the raw data.

When analyzing racial di↵erences in the use of h ands by police, this observation would be included.

The interpretation would not be racial di↵erences in the use of hands, per se, but racial di↵erences

in the use of “at least” hands. To be clear, an observation that records only hands would be in

the hands r egr ess i on but not the regression which restricts the sample to observations in which

individuals were at least forced to the ground. This is the method we use throughout.

Results using this method to describe racial di↵erences for each use of force are displayed in

Figure 1. The x-axis contains use of force variables that range from at least hands to at least the

use of pepper spray or b at on. The y-axis measures the odds ratio for blacks (panel A) or Hispanics

(panel B). The solid line is gleaned from regressions with no controls, and the d ash ed line adds all

controls, precinct and year ﬁxed e↵ects (equivalent to row (e) in Table 2).

For blacks, the consistency of the odds ratios are striking. As the use of force increases, the

frequency with which that l e vel of force is used decreases substantially. Ther e are approximately

ﬁve million observations in th e data – 19 percent of them involve the use of hands while 0.04 percent

involve using pepper spray or a baton. The use of high levels of force in these data are r ar e. Yet,

it is consistently r are r for whites relative to blacks. The range in the odds ratios across all levels

of force is between 1.175 (0.036) and 1.275 (0.131).

Interestingly, for Hispanics, once we account for our set of controls, there are small di↵erences

in use of force for the lower level uses of non-lethal force, but the di↵erences converge toward whites

as the use of force increases both in the r aw data and with the inclusion of controls.

One may be concerned that restricting all the coeﬃcient estimates to be identical across the

entire sample may yield misleading results. Regressions on a common support (for e xam pl e , only

on males or only on poli ce stops during the day) provide one means of addressing this con cer n .

Table 3A explores the sensitivity of the estimated racial gaps in police use of force ac ros s a variety

of subsamples of the data. I report only the odds-ratios on black and Hispanic and associated

standard errors. The top row of the tabl e presents baseline results usin g the full (any force) sample

Appendix Tables 9A - 9C demo n s trat e that altering the deﬁnition to be “at most” or using the max/min force

used in any g iven police interaction does not alter the results.

and ou r parsimoni ou s set of controls (corresponding to row (e) in Table 2). The subsequent rows

investigate racial di↵erences in use of force for high/low crime areas, time of d ay, whethe r or not

the oﬃce r was in uniform, indoors/outdoors, gender of civilian, and eventual outcomes.

Most of the coeﬃcients on race do not di↵er signiﬁcantly at the 1% level acr oss these various

subsamples with the exception of ti me of day and eventual outcomes. Black civilians are 8.6 percent

more likely to have any for c e used against them conditional on being arrested. They are 15.6 percent

more likely to have any force used against them condi t i onal on being summonsed and 12.7 percent

more likely conditional on having weapons or contraband found on them. Results are similar for

Hispanics. Additionally, for both blacks and Hispanics, racial di↵erences in use of force are more

pronounced during t h e day relative to night.

To dig deepe r, Panel A in Figure 2 plots the odds ratios of any use of force for black civilians

versus white civilians for every hour of day. Panel B displays the average use of force for black

civilians and white civilians for every hour of day. These ﬁgures s how that force against black

civilians follows approximately the same pattern as white civilians, though the di↵erence between

average force between t h e two races decreases at night.

Police-Public Contact Survey

One of the key limitations of the Stop and Frisk data is that one only gets the police side of

the story, or more acc ur at el y, the police entry of the data. It is plausible that there are large racial

di↵erences that exist that are masked by police misreporting. The Police-Public Contact Survey is

one way to partially address this weakness.

Table 2 Panel B presents a series of estimates of racial di↵erences in police use of force conditional

on an interaction, using the PPCS data. The speciﬁcations estimat ed are of the form:

PrpForce

i,t

“ 1q

1 ´ PrpForce

i,t

“ 1q

“ Race

↵ ` X

i,t

 ` ⌫

` ✏

i,t

where Force

i,t

is a measure of police use of force reported by individual i in year t. A full set of

race dum mi es for individuals and oﬃcers are included in the regressions, with white as the omitted

category. The vectors of covariates included in the speci ﬁ cat i on vary across rows in Table 2 Panel

B. As one moves down the table, the set of coeﬃcients steadily grows. Standard errors, which

appear below each estimate, account for heteroskedastic i ty.

Generally, the data are qualitatively similar to the results using Stop and Frisk – namely, despite

a large and complex set of controls, blacks and Hispanics are more likely to experience some use

of for ce from police. A key di↵erence, however, is that the share of indi v id u als experiencing any

use of force is signiﬁcantly lower. In the Stop and Frisk data, 15.3 p er cent of whites incur some

force in a police interacti on . In the PPCS, this number is 1%. There are a variety of p ot ential

reasons for these stark di↵erences. For instance, the PPCS is a nationally representative sample

of interaction s wi t h police from across the U.S., whereas the Stop and Frisk data is gleaned from

a rather aggressive proactive policing st r at egy in a large urban city. This is important because in

what follows we present odds-rat ios . Odds-ratios are informative, but it is important for the reader

to know that the baseline rate of force is substantially small er in the PPCS.

Blacks are 3.5 times more likely to repor t use of force by police in an interact i on in the raw data.

Hispanics are 2.7 times more likely. Adding controls for demographic and encounter characteristics,

civilian behavior, and year reduces the odds-ratio to roughly 2.8 for blacks and 1.8 for Hispanics.

Di↵erences in q u antitative magnitudes aside, the PPCS paints a si mi l ar portrait – large racial

di↵erences in police use of force that cannot be e xpl ai ne d using a large and varied set of controls.

One important di↵erence between the PPCS and the Stop and Frisk data is in regards to racial

di↵erences on the more extreme uses of non-lethal for ce: using pepper spray or striking with a

baton. Recall, in the Stop and Fr is k data the odds ratios were relat ively consistent as the intensity

of force increased. In the PPCS data, if anything, racial di↵erences on these higher uses of force

disappear. For kicking or using a stun gun or pepper spray, the highest use of force available, the

black coeﬃcient is 1.930 (0.649) and the Hisp ani c co e ﬃci ent is 1.446 (0.490), though because of the

rarity of these cases the coeﬃcients are bar el y statisti cal l y signiﬁcant at the 5% level.

Table 3B explores the heterogeneity in the data by estimating racial di↵ere nc es in police use

of force in PPCS on various subsamples of th e data: oﬃcer race, civilian income, gender, ci vi l i an,

and time of contact . Civilian income is divided into three categories: less than $20,000, between

$20,000 and $50,000, and above $50,000. Strikingly, both the black and Hispanic coeﬃcients are

statistically similar across these income levels – suggesting that higher income minorities do not

price themselves out of police use of force – echoing some of the ideas in C ose (1993). Racial

di↵erences in p oli c e of force does not seem to vary with civilian gender or oﬃcer race especially for

black civilians. Consistent with the results in the Stop and Frisk data, the black coeﬃcient is 3.690

(0.976) for interactions that occur during the day and 1.848 (0.520) for interactions that occur at

night. The p-value on the di↵erence is signiﬁcant but only at the 10% level.

Putting the results from the Stop and Frisk and PPCS datasets together, a pattern emerges.

Relative to whites, blacks and Hispanics seem to have very di↵erent interactions with law en-

forcement – interactions that are consistent with, though deﬁnite ly not proof of, some form of

discrimination. Including myriad controls designed to account for civilian demographics, encounter

characteristi cs , civilian behavior, eventual outcomes of interac t ion and year reduces, but cannot

eliminate, racial di↵erences in non-let h al use of force in either of t he datasets analyzed.

V. Estimating Racial Di↵erences i n Oﬃcer-Involved Shootings

We now focus on racial di↵erences in oﬃcer-involved shootings. We begin with speciﬁcations most

comparable to those used to estimate racial di↵erences in non -l et h al force, using both data from

oﬃcer-involved sho ot i ngs in Houston and data we coded from Houston arrest r ec ord s that contains

interactions with police that might have resulted in the use of lethal force.

Speciﬁcally, we

estimate the fol l owing empirical model:

Prpshooting

i,t

1 ´ Prpshooting

i,t

“ Race

↵ ` X

i,t

 ` ⌫

` ✏

i,t

where shooting

i,t

is a dichotomous variable equal t o one if a police oﬃcer discharged their weapon

at ind i v id u al i in year t. There are no accidental discharges in our data and shootings at canines

have been omitted. A full set of race dummies for individuals and oﬃcers are included in the

regressions, with non-black non-Hispanics as the omitted category for individuals. The vectors of

covariates included in the speciﬁcation vary across rows in Table 4. As one moves down the table,

the set of coeﬃcients steadily grows. As one moves across the columns of the table, t h e comparison

risk set changes .

Presenting t he r es ul t s in this way is meant to under sc ore t h e robustness of the

results to the inclusion of richer sets of controls and to alternative interpretati on s of the risk sets.

Because of this select set of “0s” the non-black, non-Hispanic mean, displayed in column 1, is drastically larger

than a representative samp le of the population – which would be approximately .0001%. 46.1 percent of whites in

our data were involved in an oﬃcer-involved shooting.

Appendix Table 7 investigates the sensitivity of the main re su lt s to more alternative compositions of the risk

sets.

Standard errors, wh i ch appear below each estimate, account for he t er oskedasticity.

Given the stream of video “evidence”, which many take to be i n dicat i ve of structural racism in

police departments across Ameri ca, the ensuing and understandable outr age in black communiti es

across America, and the results from our previous analysis of non-lethal uses of force, the results

displayed in Table 4 are startling.

Blacks are 23.5 percent less likely to be shot by police, relative to whites, in an interaction.

Hispanics are 8.5 percent less likely to be shot but the coeﬃcient is statistically insigniﬁcant.

Rows (b) through (f) add various controls, identical to those in Appendix Table 2C. Acc ount-

ing for basic suspect or oﬃcer demographics, does not signiﬁcantly alter the raw racial di↵erences.

Including encounter characteristics – which one can only accompli s h by hand coding the narratives

embedded in arrest report s – creates more parity between blacks and non-black non-Hispanic sus-

pects, rendering the coeﬃcient closer to 1. Finally, when we include whether or not a suspect was

found with a weapon or year ﬁxed e↵ects, the coeﬃcients st i ll suggest that, if anything, oﬃcers are

less likely to shoot black suspects, ceteri s paribus, though the r aci al di↵erences are not signi ﬁc ant.

Columns (4) and (5) of Table 4 include 4504 incident-suspec t observations from 2005-2015 for

all arrests during which an oﬃcer reported using his taser as a r i sk set, i n addition to all OIS in

Houston from that time period. The empirical question here is whether or not there are racial

di↵erences in the split-second decision as to whether to us e lethal or non-lethal force through the

decision to shoot a pistol or taser.

Consistent with the previous results, the raw racial di↵erence in the decision to employ lethal

force using this taser sample is negative and statistically signiﬁcant. Adding suspect and oﬃcer

demographics, encounter characteristics and year controls does little to change the odds ratios for

black versus non-black suspects. Including all controls available from the tas er sample, Table 4

shows that black civilians are 30.7 percent less likely to be shot with a pistol (rather than a taser)

relative t o non-black suspects. Columns (6) and (7) pool th e sample from hand coded arrest data

and taser data. Results remain qualitatively the same. Control l in g for all characteristics from

incident reports, black suspects are 24.2 percent less likely to be shot than non-black suspects.

To be clear, the empirical thought experiment here is th at a police oﬃcer arrives at a scene

and decides whether or not to use let h al force. Our estimates suggest that this decision is not

correlated with the race of the suspect . This does not, however, rule out the possibility that there

are important racial di↵erences in whether or not thse police-civi li an interactions occur at all.

Appendix Tables 6 and 7 explore the sensitivity of the results for various subsampl e s of the

data: whether the unit that responded was majority black or Hispanic or majority white or Asian,

number of oﬃcers who respond to the scene, whether the suspect clearly drew their weapon versus

appeared to draw their weapon, whether the oﬃcer was on-duty, and the type of call the oﬃcer

was responding to (a partial test of the selection issue described above). Equations identical to (3)

are estimated, but due to the smaller sample sizes inherent in splitting the sample, we estimate

Ordinary Least Squ ar es regression s.

None of the subsamples explored demonstrate much di ↵e re nc e of note. We ﬁnd no di↵erences

in the use of lethal for ce across di↵erent call sl i ps – t he p-value for equality of race coeﬃcient across

di↵erent calls slips is 0.763 for black suspects – suggesting that oﬃcers seeking confrontation in

random street interactions in a way that causes important selection bias into our sample is not

statistically relevant. S u bs ampl i n g on the number and racial composition of the oﬃcer unit also

shows no evidence of racial di↵erences.

Another way to investigate t he robustness of our coeﬃcients is to analyze the odds ratios across

time. These data are dis pl ayed in Figure 4. Racial di↵erences in OIS between 2000 and 2015

are remarkably constant. This inter val is interesting and potentially informative as it is 9 years

after the public beatings of Rodney King and includes the invention of Facebook, the iPhone,

YouTube, and related technology that allows bystanders to capture police-civilian interactions and

make it publicly available at low costs. Crudely, the period between 2000 and 2005 one might think

to be years in which police misconduct could more easily go unnoticed and for which the public

attention was relatively low. Thus, t h e disincentive to misreport was likely lower. After this period,

misreporting costs li kely increased. Yet , as we see from Figure 4, this does not seem to i n ﬂu en ce

racial di↵erences in the use of lethal force.

Are there Racial Di↵erences in the Timing of Lethal Force?

The above results, along with the results on use of force, are about racial di↵erences on the

extensive margin: whether or not an oﬃcer uses a partic ul ar type of force or decides to use lethal

force on a suspect. Because of the richness of our oﬃcer-involved shootings database, we can

also investigate the intensive margin – whether there are r aci al di↵erences in how quickly a police

oﬃcer shoots a suspect in an interaction. In par t ic ul ar , given the narrative accounts, I create a

dichotomous variable that is equal t o one if a police oﬃcer reports th at she (he) shoots a suspect

before they are attacked and zero if they report shooting the suspect after being attacked. These

data are available for Houston as well as the other nine location s where we collected OIS data.

An important caveat to these data is that the sequence of events in a police-civilian interaction is

subject to misreporting by police. Thus, the dependent variable is subjective.

Table 5 presents a series of estimates of racial di↵erences in the timing of police shootings using

the O IS data. The speciﬁcations estimated are of the f or m:

PrpShoot First

i,c,t

1 ´ PrpShoot First

i,c,t

“ Race

↵ ` X

i,t

 ` Z

c,t

T ` ⌫

` ✏

i,c,t

where Shoot First

i,c,t

is a meas ur e of whether a police oﬃcer reports shoot in g indiv i du al i,incityc,

in year t, befor e being attacked. Standard errors, which appear below each estimate, are clustered

at the location level unless otherwise speciﬁed.

The results from these speciﬁcat i ons are consiste nt with our previous results on the exten si ve

margin. Row (a) displays the results from the raw data. Blacks are 4.1% less likely to be shot ﬁrst

by police. Hispanics are slightly more likely. Neither coeﬃcient is statistically sign iﬁ cant. Adding

suspect or oﬃcer demographics does not alter the results.

Row (d) accounts for important context at the time of the shoot i ng. For instance, whether

the shooting happened during day time or night time and whether the s us pect drew weapon or

attacked the oﬃcer. Including these variables decreases the black coeﬃcient to 0.683 (0.094) which

is statistically signiﬁcant. The Hispanic coeﬃcient is similar in size but less p re ci se l y estimated.

Adding whether the suspect was eventually found to have a weapon and its type or including

location and year ﬁxe d e↵ects only stren gt he ns the results in the unexpected direction. Including

all controls available, oﬃcers report that they are 46.6% less likely to discharge their ﬁrearms

before being attacked if the suspect is black. The Hi sp ani c coeﬃc i ent is strikin gl y simil ar (43. 8%

less likely).

Appendix Table 8 explores the heterogen ei ty in the data across various subsamples: the racial

We also estima t e the “intensity” of force used in oﬃcer-involved sho ot i n g s by estimating racial di↵erences in the

total number of bullets used in a given p o li ce shooting. The average number of bullets in oﬃcer-involved shootings

involving blacks is 0.438 (0.805) more relative to shootings that involve non-black non-his p a n ic s. However, this

coeﬃcient is statistically insigniﬁcant [n o t shown in tabular form].

composition of the responding unit, number of oﬃcers who arrive at a scene, whether or not oﬃcer s

report that the suspect clearly drew their weapon or w he t he r they “app e are d” to draw their weapon,

whether t he oﬃcer was on-duty, and the call type. The ﬁnal panel provides results disaggregated

by location.

Estimated race coeﬃcients acr oss call types – wheth er oﬃcers were dispatched because of a

violent crime, robbery, auto crime, or other type of call – are all negative if anything. This is

particularly interesting in light of the potential selection into the sample of OIS cases discussed

earlier. Indee d, t h e majority of police shoot i ngs in our data occur during v iol e nt crimes or robberies

and on these call types, blacks are less likely to be shot at ﬁrst, if anything.

One of the more interesting subsamples is whether or not a suspect “appear e d” to have a weapon

versus an oﬃcer indicat i ng t hat it was clear he had a weapon. This dovetails with many of the

anecdotal reports of police violence and is thought to be a key margin on which implicit bias, and

the resulting discriminatory treatment, occur. Eberhardt et al. (2004) ﬁ nd s that police oﬃcers

detect degraded i mage s of crime related objects faster when they are shown black faces ﬁrst.

Yet our data from the ﬁeld seem to rejec t this lab-based hypothesis, at least as regards oﬃcer-

involved shootings. The coeﬃcient on black for the subsample who police report clearly drew th ei r

weapon ﬁrst is -0.102 (0.023). The same coeﬃcient estimated on the set of interact i on s were police

assumed an individual had a weapon is -0.036 (0.032). The Hispanic coeﬃcients are n ear l y identical.

More generally, the coeﬃcients are uncommonly consist ent across all subsamples of the data.

Of the 5 tests of equality performed in the table, not one is signiﬁcant. We cannot detect racial

di↵erences in oﬃce r -i nvolved shootings on any dimension.

VI. Interpretation

A number of stylized facts emerge from the analysis of the preceding sections. On non-lethal uses

of force, there are racial di↵erences – sometimes quite large – in police use of force, even after

controlling for a large set of controls d es ign ed to acc ount for important contextual and behavioral

factors at the time of th e police-civilian interaction. As the intensity of use of forc e increases from

putting hands on a civilian t o striking them with a baton, the overall probability of such an incident

occurring decreases but the racial di↵erence remains roughly constant. On the most extreme uses

of force, however – oﬃcer-involved shootings with a Taser or lethal weapon – there are no racial

di↵erences in ei t he r the raw data or when acc ounting for controls.

In this section, we explore the extent to which a model of police- ci v i lian interaction that en-

compasses both informati on - and taste-based d i scr i mi n at ion – can successfull y account for this set

of facts . The model is an adaptation of Coate and Loury (1993a, 1993b).

A. A Model of Police-Civilian Interactions

Basic Building Blocks

Imagine a large number of police oﬃce rs and a weakly larger population of civilians. Each

police oﬃcer is randomly matched with civilians from this pop u lat i on . Civilians belong to one of

two identiﬁable groups, B or W . Denote by  the fraction of W ’s in the population. Police oﬃcer s

are assumed to be one of two types: “biased” or “unbiased.” Let  Pp0, 1q denote t h e fraction of

biased police oﬃc e rs .

Nature moves ﬁrst and assigns a cost of compliance to each civilian and a type to each police

oﬃcer. Let c Prc, cs, represent the cost to a civilian of investing in compliance. An alternative way

to think about this assumption is that individuals contain inherent dangerous ne ss an d t hos e who

are dange rou s have higher costs of compliance .

After observing his cost, the civilian makes a dichotomous compliance decision, choosing to

become either a compliant type or a non-compl i ant type with no in-betwee n. Then, based on this

decision, natu r e distributes a signal ✓ Pr✓, ✓s to police oﬃcer s regarding whether or not a civilian

is likely to comply.

Next, the police oﬃcer observes ✓ and decides whether or not to use forc e,

which we denote by h Pt0, 1u.

The distributi on of ✓ depends, in the same way for each race, on whether or not a civilian

has invested in compliance. This signal is meant to captur e the important elements of initial

interactions between poli ce and civilians; clothing, demeanor, attitude, posture, and so on. Let

p✓q [resp. F

p✓q] be the probability that the signal does not exceed ✓, given that a civilian

This mode l is a simpliﬁed version of a more g en era l model in which individuals invest in a “ c o mp l ia n c e identity”

ala Akerlof and Kranton (2000) and then, in any given interaction with police, decide whether to comply or escalate.

Fo r those who have a compliance identity, there is an identity costs of escalation. This model is more intuitive, bu t

delivers the same b a s ic results.

We model the police oﬃcer’s decision as deciding to use force rather than what type of force to use for two

reasons: analytical convenience and for most of our analysis the dependent variable is whether or not to use force.

Extending our analysis to allow for N potential uses of force does not alt er the key predictions of the model.

has invested in compliance (resp. non-compliance) and le t f

p✓q and f

p✓q be the related dens i ty

functions. D eﬁ ne µp✓q”

p✓q

to be the likelihood ratio at ✓. We assume that µp✓q is non-increasing

on r0, 1s, which implies that F

p✓q§F

p✓q for all ✓. Thus, higher values of observed ✓ are more

likely if the civi l ian is c omp liant, and for a gi ven prior , t he posterior l i kelihood that a civilian will

be c ompl i ant is larger if his signal takes a higher value .

Pay o f f s

For the civilian, payo↵s de pend on whe th er or not force is used on him and whether he chose

to invest in compliance. Speciﬁcally, if force is used on the civilian, he receives a payo↵ of ´ ´ c

if he invested i n compliance and ´ if not. If force is not used on the ci v i li an , he receives a payo↵

of ´c if he invests and the payo↵ is nor mal iz ed to zero if he did not invest.

It is assumed that police oﬃcers want to use force on civilians who are non-compliant and prefer

not to use forc e on those that are compl i ant. In addition, we allow for “biased” police oﬃcers to

gain ut i li ty from using force on Bs.

Thus, for police oﬃcers, payo↵s depend on their type, whether or not they use force, and

whether or not t h e civil ian is compliant. We be gi n with unbiased oﬃcers. If force is used, the

oﬃcers payo↵ is ´K ´ 

if the civili an is compliant and 

´ 

if the civili an is non-compliant.

If no force is used, the oﬃcer receives a payo↵ of 0 if the civilian is compliant and ´

if the

civilian is non-compliant. These payo↵s ar e identical for biased oﬃcers when they interact with W

civilians.

When biased police oﬃcers interact with B ci v i li an s they derive psychic pleasure from using

force, independent of whether they are compliant or not. We represent this by ⌧ , a positive term

in the biased oﬃcer’s payo↵ when he us es force on B civilians. Note: This is similar to the taste

parameter pioneered in Becker (1957).

Strategies

A civilian’s strategy is a mapping I : rc, csÑt0, 1u. Without loss of generality, the civili an ’ s

strategy can be represented by a cut-o↵ point, c

, such that the civilian w il l invest in compli anc e

if and only if their cost is below c

. A strategy for the police oﬃcer is a decision of whether or not

to use force, conditional upon what he can observe, h : t0,⌧u

rB, W s

r✓, ✓sÑt0, 1u.

Expected Payoffs

Let ⇡ Pr0, 1s denote the oﬃcer’s prior b el i ef that a civilian will be compliant. Expected payo↵s

for the police oﬃcer are functions of her be l ie fs , her type, and the signal she rec ei ves. Given ⇡ and

observed signal ✓, she formulates a posterior probability (using Bayes’ rule) that the civilian will

be c ompl i ant: p⇡, ✓q”

⇡f

p✓q

⇡f

p✓q`p1´⇡qf

p✓q

The expected payo↵ of us i ng force for an unbiased police oﬃcer (and, equivalently, a biased

police oﬃcer whe n interacting with Ws) is:

p⇡, ✓qp´K ´ 

q`p1 ´ p⇡, ✓qqp

´ 

q. (2)

The expected payo↵ of using forc e for a biased oﬃcer interac ti n g with Bs is:

p⇡, ✓qp´K ´ 

q`p1 ´ p⇡, ✓qqp

´ 

q`⌧. (3)

Relatedly, the expected payo↵s of not using force, for both types of oﬃcers, can be writ t en as:

´p1 ´ p⇡, ✓qqp

q. (4)

Combining equation (2) and equation (4), and using a bit of algebra, an unbiased oﬃcer uses

force on ly if

✓ § ✓

” mint✓| p⇡, ✓qp´K ´ 

q`p1 ´ p⇡, ✓qqp

` 

´ 

q°0u (5)

In words, equation (5) provides a threshold, ✓

, such t h at for any ✓ below this thresh old

unbiased oﬃcers always use force. Similarly, using the correspondi n g expected payo↵s for a biased

oﬃcer, on e can derive ✓

Now, consider the civilian’s expected payo↵. W civilians receive F

p✓

qp´q´c if they invest

and F

p✓

qp´q if they choose not to invest. When optimizing, a civilian will invest in compliance

if and only if the cost of compliance is less than the net beneﬁt of compliance. In symbols ,

c § c

”tF

p✓

q´F

p✓

qu  (6)

Similarly, Bsinvestif

c § c

”  tpF

p✓

q´F

p✓

qq ` p1 ´ qpF

p✓

q´F

p✓

qqu (7)

Note – given we assume  ° 0 – i t follows that c

† c

Definition 1 An equilibrium consists of a pair p✓

,⇡

q such that each is a best respons e to the

other.

B. Un de rs t and i ng the Data Through the Lens of t he Model

Assuming the d i st r ib u ti on of costs (c) and the signal (✓) are independent of race, racial disparities

can be produced in this model in two (non-mutual ly exclu si ve) ways: di↵erent beliefs or di↵erent

preferences.

To see this formal l y, suppose all rac ial di↵erences were driven by information-based

discrimination and there was no taste-based component. In this case, equation (3) simpliﬁes to (2)

and both B and W individuals’ net be ne ﬁt of investment becomes tF

p✓

q´F

p✓

qu  ´ c.Thus,

one need s di↵erences in ⇡ to generate discriminatory equilibr iu m.

In contrast, one can also derive an equilibrium for cases in which we turn o↵ the information-

based channel and only allow di↵erences t h rou gh preferences. In this case, pol ic e oﬃcers observe

investment decisions perfectly. When police oﬃcer bias is suﬃciently large, any equilibrium will

contain discrimination against Bs.

Distinguishing be tween these two cases, empirically, is diﬃcult with the available data. In

what follows, we attempt to unde rs t and whether the patterns in the data are best explained by an

information-based or taste-based approach to discrimination – recognizing th at both channels may

be i mportant.

Statistical Discrimination

To better understand whether stat is t i cal discrimination might exp l ai n some of the patterns in

the data, we investigate two possi bi l i t ie s.

First, we explore whether racial di↵erences in mean

It is al so plausible tha t racial di↵eren c es arise due to di↵erences in costs of compliance (for instance, through

peer e↵ects) or in th e signal distributions. Incorporati n g these assumptions into the model is a tri via l extension.

Appendix C considers the extent to which discrimination based on categories can explain the resu lt s (Fryer and

Jackson 2008). We argue categorical discri mi n a t io n is i n c o n sis t ent with the fact that black oﬃcers and white oﬃcers

interact similarly with black civilian s. See Appendix Table 14.

characteristi cs across police precincts predicts racial d i ↵er en ce s in use of force. The key – untestable

– assumption is pol ic e oﬃcer beliefs about the compliance of a civilian – ⇡ in our model – is partly

driven by local variat ion in variables such as education or income levels.

Appendix Table 11 explores racial di↵erences in any use of force – using the S top and Frisk

data – for various proxies for “dangerousness” including education, income, and unemployment.

Education is represented by the fraction, by race, in each precinct of individuals with a high school

diploma. Income is measured as median income. Unemployment is measured as the fraction of

civilians in the labor force who are unemployed. For e ach of these variables, we take the di↵erence

between the white population and black population and rank the precincts by this di↵erence,

individually. We then divide the data into terciles. The ﬁrst tercile is always the one in which

racial di↵erences between our proxies are t he lowest. The third tercile rep re se nts precincts in which

there are relati vely large racial di↵erences on a given proxy.

Statistically larger racial di↵erences in use of force for th e third tercile (ﬁrst te rc i le for unem-

ployment), relative to tercile one or two (tercile two or three for unemployment), would be evidence

consistent with statistical discrimination. This would imply that racial di↵erences in use of force

are correlated with racial di↵erences in proxies for dangerousness. Append i x Table 11 demonstrates

no such pattern. The odds-ratio of having any force used on a black civilian versus a white civilian

remains statistically the same across terciles.

A second prediction of the stati st i cal discrimination model th at is testable in our data is how

racial di ↵erences in use of force change as signals about civilian compliance become more clear.

If statistical discrimination is the key driver of racial di ↵e re nc es in use of force, the model predicts

that as ✓ becomes perfectly predictive of compliance behavior, there will be no racial di↵erences.

Ideally, one m ig ht use variables more directly correlated with dangerousness such as racial di↵erences in crime

rates, by precincts. Despite repea ted formal Freedom of Information Law requests, the New York Police Department

refused to supply th ese data.

We performed a similar exercise exploit i n g the variance across space in proxies for dangerousness (see Appen d i x

Tab l es 12A-12C for re su lt s ). We also investigated whether more weight in the bottom quintiles of the distribution of

our proxies pred ic t ed police use of force. These empirical exercises were meant as a partial test of Aigner and Cain

(1977). We ﬁnd no evidence of this sort of stat is ti c a l discrimination on any of the di men s io n s tested.

Another potential test of statistical discrimination was pioneered by Altonji and Pierret (2001). They investigate

racial di↵erenc es in wage trajec to ri es, conditional upon being hired. To the extent that statistical discrimination d rives

wage di↵erences between racial groups, one would expect the wage trajectory for blacks to be higher tha n whites

– as em p loyers learn. We performed a similar, though imperfect, t es t by estimating the probability that a civilian

is arrested, conditional upon force being used. Consistent with a discrimination story, on the lowest level use of

force, blacks and Hispanics are less likely to be arrest ed conditional upon force being used. As the intensity of force

increases, if anything, minorities are more likely to be arrested con d i ti o n a l upon fo rc e being u s ed .

We test this using oﬃcer recorde d data on the compliance behavior of civilians.

The NYC Stop and Frisk data contains oﬃce r recorded information on the compliance of ci v i l -

ians during a stop. These variabl es include: whether the ci v il i an s refused to comply with oﬃcers ’

directions, whether the civilian verbally threatened an oﬃcer, whether they were evasive in thei r

response to questioning or whether t h ey changed direction at the sight of an oﬃcer. If statistical

discrimination is a key driver of racial di↵ere nc es, on the set of interactions in which oﬃcers report

perfect compliance (and, to capture potential l y impor t ant unobservables – the civilian was not

arrested or was not guilty of carrying weapons or contraband) racial di↵erences should be close

to zero. And, on the set of interactions in which civili ans engage in questionable beh avior, racial

di↵erences should be stati s t ic al ly larger.

Figure 5 shows that even when we take per fe ct l y compli ant individuals and control for civilian,

oﬃcer, encounter and location variables, black civilians are 21.2 percent more likely to have any

force used against them in an interaction compared to white c iv i l i ans w it h the same reported

compliance behavior. As the intensity of force increases, the odds ratio for perfectly compliant

individuals decreases.

Ultimately, it is diﬃcult to know if statistical discrimination is an important component of

racial di↵erences in use of f orc e. Though our tests have quite limited power, we ﬁnd no evide nc e

that s t ati s t ic al discrimi nat i on plays an important role.

Taste-Based Models of Discrim in ati on

Similar to any large organization , police departments surely have individuals who hold biased

views toward minori ty citizens and those views may manifest the m se l ves in b i ase d treatment of

individuals based solely on their race. Yet, as Becker (1957) argued, individual discrimination does

not nec es sar il y equate to market (or systemic) discrimination.

Taste-based di s cr i mi nat i on is consistent with t he data from the dir ect regression approach on

non-lethal uses of force if, among those who discrimi n at e, the preference for discriminat ion is

greater than the expected costs of wrongly using force. In other words, the expected price of

discrimination is not large enough – either through low penalties or low probabilities of detection –

to alter behavior of those who have biased preferences. This model is also consiste nt with the lack

of racial di↵erences in oﬃcer-involved shooting if there is a di sc re t e increase in the costs of bei ng

deemed a discrimi nat or , relative to the costs incurred with non-lethal uses of force.

Below, we explore the extent to which two additional implications of the taste-base d channel

of our model are borne out in the data. The ﬁr st uses th e predictions on average versus marginal

returns of compliant behavior. The second is inspired by the seminal work in Knowles, Pers ic o,

and Todd (2001) and Anwar and Fang (2006).

In any equilibrium mode l of discrimination, oﬃcer behavior inﬂuences the incentive to invest

in compliance behavior. This is made explicit in equations (6) and (7). Figure 5 provides some

suggestive evidence that the ret u rn s to compliance may be di↵erent across races. We can test this

a bit more directly. One issue in this setting, which does not arise in l abor markets, is t h at it

is not obvious h ow to aggregate non-compliance into a monot oni c index. From a police oﬃcer’s

perspective, It may be considered more dangerous if a civilian shouted verbal threats than if he

refused to comply wit h an oﬃcer’s directions or if he was evasive during questioning. A simple

aggregation of the number of non-compliant activities is likely misleading.

To sidestep this important potential issue of aggregating non-compl ian ce , we create an index

equal to 1 if a civilian changes direction at the sight of an oﬃcer, 2 if a civilian is non-compliant on

any other, but not all dimensions of measured compliance, and 3 if a civilian is non-compliant on all

four dimensions we can measure. The regressi on estimat e d, t he n, is wheth er or not an oﬃcer uses

any force – accounting for our full set of controls – and in cl ud i ng our measure of non-compl ian ce

interacted with race. Racial di↵erences in the marginal return to non-compliance behavior would

manifest itself i n statistically di↵e r ent coeﬃcients on the compliance variable. For a given race,

adding both the race c oeﬃcient and the interaction term with complianc e behavior provides an

estimate of the net beneﬁt of investment (equations (6) and (7)).

The results of this exercise [not shown in tabular form] are consistent with racial di↵erences

in police use of force being driven by taste-based discrimination. Black civilians have statistically

similar marginal returns to c om pli anc e as white ci v i l ian s. In other words, the probability of force

being used as ✓ increases is statistically identical between blacks and whites. Yet, black civilian s

always have a higher likelihood of force being used on the m compared to white civilians, for all

While purely anecdotal, in police departments across the country, any oﬃcer-involved shooting – no matter how

“justiﬁed” – results in the temporary conﬁscation of the oﬃcer’s weapon until an investigation of the incid ent is

complete This is a potentially high cost relative t o other non-lethal uses of force. Moreover, in informal interviews

with dozens of police oﬃcers in Boston, Cambridge, Camden, and Houston – almost all police oﬃcers described

pulling the trigger of their weapon as a “life altering event.”

✓. Further, the net beneﬁt of invest ment i n com pl i anc e i s lower for blacks relative to whites. This

is precisely what the model predicts if racial animus is an important factor in explaining racial

di↵erences in us e of force.

We conclude our statistical analysis by developing a test for discrimination based on Knowles ,

Persico, and Todd (2001) [hereafter KPT] and Anwar and Fang (2006) to complement the direct

regression approach descri bed in the previous sections. KPT tests for racist preferences by lookin g

at oﬃcers’ s uc ce ss rate of searches across races. Their model assumes that police maximize the

number of successful searches net of the cost of searching motorist s. If racial prejudice exists then

the cost of searching drivers will be di↵erent across races. Th i s, in turn, implies that the rate of

successful searches will be di↵erent across races.

Anwar and Fang (2006) build upon the theory of KPT; arguing that the KPT results might not

hold if police oﬃcers are non-monolithic in their behavior. They test this by investigating search

rates of civilians of a part i cu l ar race, across oﬃcer races. Under the null hypothesis that none of

the racial groups of oﬃcers have relative racial prejudice, it must be true that the ranking of search

rates for white civilians across oﬃcer r ac es is the same as the ranking of search rates for black

civilians across oﬃcer races.

We adopt this app r oach by investigating whether or not a suspect was eventuall y found to have

a weapon during the interact i on with police. In other words, we calculate the probability, for each

race, that a suspect has a weap on condi t i onal upon being involved in an oﬃcer-involved shootin g.

Given the level of detail in our data, one can perform th i s test f or weapons generally – guns, knives

or other cutting objects, or assault weapons – or for guns speciﬁcally, including pistols, riﬂes, or

semi-automatic machine guns, speciﬁcally. Moreover, following the insights in Anwar and Fang

(2006), we disaggregate the data by oﬃcer race.

The null hypothesis is no racial dis cr i mi nat i on in oﬃc er -i nvolved s hootings. The null could

be rejected in several ways . First, according to KPT, the null could be rejected if the fraction of

suspects carrying weapons or ﬁrearms is di↵erent acr oss suspect races. Second, according to Anwar

and Fang, the null could be rejected if the ranking of “being armed” rates for black suspects across

oﬃcer rac es is di↵erent from the ranking of being armed rates for white suspects.

Consistent with our dir ect regression approach and the ﬁndings in Knowles, Persico, and Todd

(2001), and Anwar and Fang (2006), we fail to reject the null of no discrimination. The data are

displayed in Table 6. For white oﬃcers , the probability that a white suspect who is involved in

oﬃcer-involved shooting has a weapon is 84.2%. The equivalent probability for blacks is 80.9%.

A di↵erence of 4%, which is not statistical l y signiﬁcant. For black oﬃcers, the probabi li ty that a

white suspect who is involved in an oﬃcer-involved shooting has a weapon is surprisingly lower,

57.1%. The equivalent probability for black suspects is 73.0%. T he only statistically signiﬁcant

di↵erences by race demonstrate that black oﬃcers are more l i kely to shoot unarmed whites, relative

to whit e oﬃcers.

We perform a si mi l ar exercise for non-lethal uses of force, recognizing that as the use of force

gets less extreme the ap p li c at ion of that force and whether or not a s us pect has a weapon is

more tenuous. For instance, investigating racial di↵erences in wheth er or not oﬃcers use “hands”

on civilians who are unarmed is not a vali d test of discrimination as ther e are myriad legitimate

reasons for police oﬃcers to place hands on civilians who are unarmed. Yet, racial di↵erences in

the use of a baton – after accounting for suspect behavior – seem less justiﬁable . Unfortunately,

where to draw the line on th e continuum of potential uses of force is ad hoc. Thus, we present our

modiﬁed KPT test for all uses of force while acknowledging that for the low level uses, i t does not

seem app rop r iat e .

Appendix Table 13 prese nts these results. Each row is a di↵erent level of force which begins with

“at least hands” and increases in severity of force until “use of pepper spray or Baton.” Column

(1) contains the white mean. Columns (2) and (3) display the coeﬃcient on black and Hispanic,

respectively. Col u mn (4) displays the number of observations which range from over one million

for th e use of hands to 1,745 for the use of pepper spray or baton.

Blacks are 1.0 (0.1) percentage points less likely to have a weapon, conditional upon a police

oﬃcer using any force. Hispanics are 0.6 (0.1) less likely to have a weapon. Both are statistically

signiﬁcant. Interestingly, on the two most severe non-lethal uses of force, the probabili ty that a

weapon is found – conditional upon force being used – is statistically identical across races. Taken

at face value, these data are consistent wi t h discrimination against minorities on the lowest le vel

uses of non-lethal force.

VII. Conclusion

The issu e of police violence and its racial incidence has become one of the most divisive topics in

American discourse. Emotions run the gamut from outrage to indi↵erence. Yet, very little data

exists to understand whether racial disparities in police use of force exist or might be explained

by situational factors inher ent in the complexity of police-civilian interactions. Beyond the lack

of data, the analysis of police behavior is fraught with diﬃculty including, but not l i mi t ed to, the

reliability of th e data that does exist and the fact that one cannot randomly assign race.

With these caveats in mind, this paper takes ﬁrst steps into t he treacherous terrain of under-

standing the nature and extent of racial di↵erences in poli ce use of force and the probab il i ty of

police interaction. On non-lethal uses of force, there are racial di↵er en ce s – sometimes quite large

– in police use of force, even aft er accounting for a large set of c ontrols designed to account for

important contextual and behavioral fact or s at the time of the police-civilian interaction. Interest-

ingly, as use of force increases from putting hands on a ci v i li an to striking them with a baton, the

overall probability of such an incident o cc ur r in g decreases dramatically but the racial di↵erence

remains roughly constant. Even when oﬃcers report civilians have been compliant and no arrest

was made, blacks are 21.2 percent more likely to endure some form of force in an interaction. Yet,

on the most extreme use of force – oﬃcer-involved shootings – we are unable to detect any racial

di↵erences in ei t he r the raw data or when acc ounting for controls.

We argue that these facts are most consistent with a model of taste-based discrimination in

which police oﬃcers face discretely higher costs for oﬃcer-involved shootings relative to non-lethal

uses of force. This model is consistent with racial di↵erences in the average returns to compliant

behaviors, the resul t s of our tests of discriminati on based on Knowles, Persico, and Todd (2001) and

Anwar and Fang (2006), and the fact that the odds-ratio is large and signiﬁcant across all intens i ti e s

of force – even after accounting for a rich set of controls. In the end, however, without ran dom l y

assigning race, we have no deﬁnitive proof of d i sc ri mi n at ion . Our results are also consistent with

mismeasured contextual factors.

As police departments across America consider models of community policing such as the Boston

Ten Point Coalition, body worn cameras, or training designed to purge oﬃcers of implicit bi as, our

results point to another simple pol i cy experiment: i n cr eas e the expected price of excessive force

on lower level uses of force. To date, very few police departments across the country either collect

data on lower level uses of force or explicitly punish oﬃcers for misuse of th es e tactics.

The appealing feature of this type of policy experiment is that it does not re q ui r e oﬃcers to

change their behavior in extremely high-stakes environm ents. Many arguments about police reform

fall victim to t h e “my life versus theirs, us versus them” mantra. Holding oﬃcers accountable for

the misuse of hands or pushing individuals to the ground is not likely a life or death situation and,

as such, may be more amenable to policy change.

****

The importance of our results for racial inequality in America is unclear. It is plausible that

racial di↵erences in lower level uses of force are simply a distraction and movements such as Black

Lives Matter should seek solutions within their own communities rather than changing the behaviors

of pol i ce and other external forces.

Much more troub lin g, due to their frequency and potential impact on minority belief for mat i on,

is the possibility that racial di↵erences in police use of non-lethal force has spillovers on myriad

dimensions of racial inequality. If, for instance, blacks use their lived experience with police as

evidence th at the world is di sc ri mi n at ory, then it is easy to un d er st an d why black youth invest

less in human capital or black adults are more likely to believe discrimination is an important

determinant of economic outcomes. Black Dignity Matters.

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Table 1: Racial Differences in Probability of Interaction and Outcomes Test

NYC Stop and Frisk PPCS Houston

Population Arrest Rate Felony Arrest Involuntary Voluntary Population Arrest Rate Felony Arrest

Weighted Weighted Weighted Contact Contact Weighted Weighted Weighted

(1) (2) (3) (4) (5) (6) (7) (8)

Panel A: Potential Selection 4.233 1.428 1.026 0.922

⇤⇤⇤

0.791

⇤⇤⇤

4.347 1.008 0.872

(0.025) (0.026)

Civilian Contraband/ Civilian Contraband/

Arrested Weapon Found Arrested Weapon Found

(1) (2) (3) (4)

Panel B: Outcomes Test 1.080

⇤⇤⇤

0.777

⇤⇤⇤

1.814

⇤⇤⇤

0.524

⇤⇤⇤

(0.032) (0.033) (0.159) (0.118)

This table reports the probability of police interaction and conducts outcomes tests. The sample in NYC Stop and Frisk block consists of all NYC Stop and Frisks from 2003-2013. The sample in

PPCS block consists of all Police Public Contact Survey respondents from 1996-2011. The sample in Houston block consists of all ofﬁcer involved shootings from Houston between 2000-2015.

All population demographics have been obtained from American Community Survey 2007-2011. Arrest rates for New York City have been obtained from NYC Enforcement Reports 2008-2013.

Arrest rates for Houston have been provided from the Houston Police Department for all arrests in 2015. To obtain the number reported in Panel A, column (1) we go through the following steps

– For each precinct, calculate the fraction of stops that are black and the corresponding fraction for whites; for each precinct, calculate the fraction of 18-34 aged males in the population that are

black and the corresponding fraction for whites; regress the fraction of stops that are black on the fraction of 18-34 aged males that are black (with no constant) for all 77 precincts. The beta

coefﬁcient on the dependent variable shows the representation of “at risk” blacks in stops. Conduct same regression for whites and store that beta coefﬁcient as the representation of “at risk”

whites in stops; ﬁnally, divide the beta coefﬁcient for blacks by the beta coefﬁcient for whites. To obtain the numbers in Panel A, columns (2) and (3) we go through the following steps – For each

year, calculate the fraction of stops that are black and the corresponding fraction for whites for New York City; for each year, calculate the fraction of arrestees for the 10 most egregious felonies

and misdemeanors for column (2) and the fraction of arrestees for the 6 most egregious felonies only for column (3) for blacks and whites for New York City; regress the fraction of stops that are

black on the fraction of arrestees that are black (with no constant) for all 6 years of data and store the beta coefﬁcient and do the same regression for whites and store the beta coefﬁcient; ﬁnally,

divide the beta coefﬁcient for blacks by the beta coefﬁcient for whites. Panel A columns (4) and (5) report odds ratios on blacks from logistic regressions of involuntary or voluntary interaction

on civilian race, other civilian demographics and year. To obtain the numbers in Panel A columns (6) - (8), we go through the following steps – calculate the fraction of blacks in ofﬁcer involved

shootings and divide it by the fraction of blacks in the 18-34 aged male population in Houston/ fraction of blacks in all felony and misdemeanor arrests/fraction of balcks in all felony arrests;

calculate the same fraction for non-blacks; and ﬁnally divide the black fraction by non-black fraction. For Panel B, we report odds ratios on black dummy from logistic regressions of the outcome

speciﬁed on dataset-speciﬁc controls. For NYC Stop and Frisk, the controls are civilian demographics (race, gender, quadratic in age), encounter characteristics (stop was indoors or outdoors,

whether the stop took place during the daytime, whether the stop took place in a high crime area, during a high crime time, or in a high crime area at a high crime time, whether the ofﬁcer was

in uniform, civilian ID type, and whether others were stopped during the interaction), civilian behavior (whether civilian was carrying a suspicious object, if he ﬁt a relevant description, if he was

preparing for a crime, if he was on lookout for a crime, if he was dressed in criminal attire, if there was an appreance of a drug transaction, whether there were any suspicious movements, if he was

engaged in violent crime, if he was concealing a suspicious object, and whether there was any other suspicious behavior), precinct and year ﬁxed effects, and missing indicators for all variables.

For PPCS, the controls are civilian demographics (race, gender, employment last week, income, population size of a civilian’s address, and a quadratic in age), contact and ofﬁcer characteristics

(time of day of the contact, contact type, and ofﬁcer race), civilian behavior (civilian disobeyed, tried to get away, resisted, complained, argued, threatened ofﬁcer, used physical force), year and

missing indicators for all variables.

Table 2: Racial Differences in Non-Lethal Use of Force, Conditional on an Interaction

White Mean Black Hispanic Asian Other Race

(1) (2) (3) (4) (5)

Panel A: NYC Stop, Question and Frisk

(a) No Controls 0.153 1.534

⇤⇤⇤

1.582

⇤⇤⇤

1.044 1.392

⇤⇤⇤

(0.144) (0.149) (0.119) (0.121)

(b) + Civilian Demographics 1.480

⇤⇤⇤

1.517

⇤⇤⇤

1.010 1.346

⇤⇤⇤

(0.146) (0.146) (0.122) (0.114)

⇤⇤⇤

1.641

⇤⇤⇤

1.059 1.452

⇤⇤⇤

(0.155) (0.157) (0.133) (0.121)

(d) + Civilian Behavior 1.462

⇤⇤⇤

1.516

⇤⇤⇤

1.051 1.372

⇤⇤⇤

(0.128) (0.136) (0.124) (0.107)

(e) + Precinct FE, Year FE 1.178

⇤⇤⇤

1.122

⇤⇤⇤

0.953 1.060

⇤⇤

(0.034) (0.026) (0.033) (0.028)

(f) + Precinct*Year FE 1.171

⇤⇤⇤

1.112

⇤⇤⇤

0.954 1.066

⇤⇤

(0.034) (0.025) (0.033) (0.028)

(g) + Precinct*Year*Month FE 1.172

⇤⇤⇤

1.112

⇤⇤⇤

0.958 1.068

⇤⇤

(0.034) (0.025) (0.032) (0.028)

Observations 4,927,962

Panel B: Police Public Contact Survey

(h) No Controls 0.007 3.496

⇤⇤⇤

2.697

⇤⇤⇤

– 1.130

(0.364) (0.311) (0.275)

(i) + Civilian Demographics 2.745

⇤⇤⇤

1.716

⇤⇤⇤

– 0.792

(0.299) (0.205) (0.195)

(j) + Encounter Characteristics 2.659

⇤⇤⇤

1.695

⇤⇤⇤

– 0.811

(0.293) (0.202) (0.197)

(k) + Civilian Behavior 2.780

⇤⇤⇤

1.820

⇤⇤⇤

– 0.763

(0.330) (0.225) (0.194)

(l) + Year 2.769

⇤⇤⇤

1.818

⇤⇤⇤

– 0.758

(0.328) (0.225) (0.193)

Observations 59,668

Notes: This table reports odds ratios obtained from logistic regressions. The sample in Panel A consists of all NYC Stop and Frisks from

2003-2013 with non-missing use of force data. The dependent variable is an indicator for whether the police reported using any force

during a stop and frisk interaction. The omitted race is white, and the omitted ID type is other. The ﬁrst column gives the unconditional

average of stop and frisk interactions that reported any force being used for white civilians. Columns (2)-(5) report logistic estimates for

black, Hispanic, Asian, and other race civilians, respectively. Each row corresponds to a different empirical speciﬁcation. The ﬁrst row

includes solely racial group dummies. The second row adds controls for gender and a quadratic in age. The third row adds controls for

whether the stop was indoors or outdoors, whether the stop took place during the daytime, whether the stop took place in a high crime

area, during a high crime time, or in a high crime area at a high crime time, whether the ofﬁcer was in uniform, civilian ID type, and

whether others were stopped during the interaction. The fourth row adds controls for civilian behavior. The ﬁfth row adds precinct and

year ﬁxed effects. The sixth row adds precinct*year ﬁxed effects. The seventh row adds precinct*year*month ﬁxed effects. Each row

includes missings in all variables. Standard errors, clustered at the precinct level, are reported in parentheses. The sample in Panel B

consists of all Police Public Contact Survey respondents from 1996-2011 with non-missing use of force data. The dependent variable is

an indicator for whether the survey respondent reported any force being used in a contact with the police. The omitted race is white. The

ﬁrst column gices the unconditional average of contacts in which survey respondants reported any force being used for white civilians.

Columns (2)-(4) report logistic estimates for black, Hispanic, and other race civilians, respectively. Each row corresponds to a different

empirical speciﬁcation. The ﬁrst row includes solely racial group dummies. The second row adds controls for civilian gender, work,

income, population size of a civilian’s address, and a quadratic in age. The third row adds controls for the time of day of the contact,

contact type, and ofﬁcer race. The fourth row adds an indicator for civilian behavior. The ﬁfth row adds a control for year. Each row

includes missings in all variables. Standard errors, robust to heteroskedasticity, are reported in parentheses.

Table 3A: Analysis of Subsamples, Any Use of Force (Conditional on an Interaction), NYC Stop Question and Frisk

White Mean Coef. on Black Coef. on Hispanic Observations

(1) (2) (3) (4)

Full Sample 0.153 1.178

⇤⇤⇤

1.122

⇤⇤⇤

4,927,962

(0.034) (0.026)

Panel A: Crime Rate in Area

High Crime 0.143 1.170

⇤⇤⇤

1.118

⇤⇤⇤

2,750,559

(0.035) (0.027)

Low Crime 0.163 1.202

⇤⇤⇤

1.139

⇤⇤⇤

2,177,403

(0.039) (0.029)

p-value: 0.254 0.320

Panel B: Time of Day

Day 0.126 1.260

⇤⇤⇤

1.164

⇤⇤⇤

1,783,977

(0.035) (0.026)

Night 0.170 1.141

⇤⇤⇤

1.102

⇤⇤⇤

3,141,371

(0.039) (0.029)

p-value: 0.001 0.024

Panel C: Ofﬁcer in Uniform

Uniformed Ofﬁcer 0.132 1.180

⇤⇤⇤

1.126

⇤⇤⇤

3,546,388

(0.047) (0.035)

Non-Uniformed Ofﬁcer 0.189 1.200

⇤⇤⇤

1.124

⇤⇤⇤

1,381,074

(0.033) (0.023)

p-value: 0.717 0.954

Panel D: Location

Indoors 0.144 1.143

⇤⇤⇤

1.105

⇤⇤⇤

1,129,555

(0.044) (0.033)

Outdoors 0.154 1.186

⇤⇤⇤

1.125

⇤⇤⇤

3,771,939

(0.031) (0.025)

p-value: 0.241 0.504

Panel E: Civilian Gender

Male 0.160 1.175

⇤⇤⇤

1.122

⇤⇤⇤

4,447,382

(0.034) (0.026)

Female 0.089 1.255

⇤⇤⇤

1.109

⇤⇤⇤

343,199

(0.055) (0.043)

p-value: 0.042 0.717

Panel F: Eventual Outcomes

Frisked 0.312 1.036 1.022 2,725,795

(0.024) (0.021)

Searched 0.412 1.061

⇤

1.043 415,455

(0.038) (0.031)

Arrested 0.327 1.086

⇤⇤⇤

1.045

⇤

291,166

(0.035) (0.025)

Summonsed 0.195 1.156

⇤⇤⇤

1.068

⇤⇤

304,603

(0.044) (0.035)

Weapon/Contraband Found 0.359 1.127

⇤⇤⇤

1.068

⇤⇤⇤

136,926

(0.026) (0.024)

p-value: 0.002 0.339

Notes: This table reports odds ratios obtained from logistic regressions. The sample consists of all NYC Stop and Frisks from

2003-2013 in which use of force and reported subgroup variables were non-missing. The dependent variable is whether any force

was used during a stop and frisk interaction, with each panel presenting results from indicated subgroups. We control for gender,

a quadratic in age, civilian behavior, whether the stop was indoors or outdoors, whether the stop took place during the daytime,

whether the stop took place in a high crime area, during a high crime time, or in a high crime area at a high crime time, whether the

ofﬁcer was in uniform, civilian ID type, whether others were stopped during the interaction, and missings in all variables. Precint

and year ﬁxed effects were included in all regressions. Standard errors, clustered at the precinct level, are reported in parentheses.

Table 3B: Analysis of Subsamples, Any Use of Force (Conditional on an Interaction), Police Public Contact Survey

White Mean Coef. on Black Coef. on Hispanic Observations

(1) (2) (3) (4)

Full Sample 0.007 2.769

⇤⇤⇤

1.818

⇤⇤⇤

59,668

(0.328) (0.225)

Panel A: Ofﬁcer Race

Black/Hispanic 0.005 2.089 5.584

⇤⇤⇤

2,166

(1.336) (3.048)

White 0.008 2.823

⇤⇤⇤

1.883

⇤⇤⇤

21,456

(0.556) (0.401)

p-value: 0.653 0.064

Panel B: Civilian Gender

Male 0.011 2.827

⇤⇤⇤

1.912

⇤⇤⇤

30,154

(0.384) (0.258)

Female 0.003 2.588

⇤⇤⇤

1.433 28,835

(0.616) (0.426)

p-value: 0.747 0.377

Panel C: Time of Day

Daytime 0.004 3.690

⇤⇤⇤

2.368

⇤⇤⇤

16,324

(0.976) (0.614)

Nighttime 0.012 1.848

⇤⇤

2.332

⇤⇤⇤

7,640

(0.520) (0.608)

p-value: 0.073 0.966

Panel D: Civilian Income

$ 0 - 20,000 0.010 2.944

⇤⇤⇤

1.630

⇤⇤

15,014

(0.534) (0.334)

$ 20,000 - 50,000 0.008 2.010

⇤⇤⇤

1.890

⇤⇤⇤

14,314

(0.491) (0.420)

$ 50,000+ 0.004 3.942

⇤⇤⇤

1.761 19,246

(1.273) (0.680)

p-value: 0.220 0.887

Notes: This table reports odds ratios by running logistic regressions. The sample consists of all Police Public Contact Survey

respondents between 1996-2011 in which use of force and reported subgroup variables were non-missing. The dependent variable

is whether any force was used during a contact, with each panel presenting results from indicated subgroups. We control for

civilian gender, a quadratic in age, work, income, population size of a civlian’s address, civilian behavior, contact time, contact type,

ofﬁcer race, year of survey, and missings in all variables. Standard errors, robust to heteroskedasticity, are reported in parentheses.

Signiﬁcance at the 10%, 5%, and 1% levels is indicated by ***, **, and *, respectively.

Table 4: Racial Differences in Lethal Use of Force (Conditional on an Interaction)

Extensive Margin, Ofﬁcer Involved Shootings

Approx OIS Taser Full Sample

With Narratives W/O Narratives W/O Narratives

Non-Black/

Non-Hispanic Black Hispanic Non-Black Black Non-Black Black

Mean Mean Mean

(1) (2) (3) (4) (5) (6) (7)

(a) No Controls 0.455 0.765 0.915 0.185 0.636

⇤⇤⇤

0.151 0.673

⇤⇤⇤

(0.138) (0.176) (0.063) (0.065)

(b) + Suspect Demographics 0.786 0.969 0.650

⇤⇤⇤

0.683

⇤⇤⇤

(0.151) (0.176) (0.066) (0.067)

⇤⇤

0.749

⇤⇤

(0.192) (0.294) (0.094) (0.087)

(d) + Encounter Characteristics 0.890 0.991 0.687

⇤⇤⇤

0.754

⇤⇤

(0.252) (0.295) (0.098) (0.097)

(e) + Suspect Weapon 0.806 1.333 

(0.284) (0.489) (-) (-)

(f) + Year 0.726 1.211 0.693

⇤⇤

0.758

⇤⇤

(0.257) (0.457) (0.099) (0.098)

Observations 1,532 5,012 5,994

Notes: This table reports odds ratios from logistic regressions. The sample for each regression is displayed in the top row. For columns (1)-(3), the sample consists

of all ofﬁcer involved shootings in Houston from 2000 - 2015, plus a random draw of all arrests for the following offenses, from 2000 - 2015: aggravated assault on

a peace ofﬁcer, attempted capital murder of a peace ofﬁcer, resisting arrest, evading arrest, and interfering in an arrest. These arrests contain narratives from police

reports. For columns (4)-(5), the sample consists of all ofﬁcer involved shootings in Houston from 2000 - 2015, plus a sample of arrests where tasers were used. These

arrests do not contain narratives from police reports. For columns (6)-(7), the sample combines all ofﬁcer involved shootings in Houston from 2000 - 2015, plus a

random draw of all arrests for the following offenses, from 2000 - 2015: aggravated assault on a peace ofﬁcer, attempted capital murder of a peace ofﬁcer, resisting

arrest, evading arrest, and interfering in an arrest, plus arrests where tasers were used. These arrests do not contain narratives from police reports. Data without

narratives have no information on ofﬁcer duty, civilian’s attack on ofﬁcer and civilian weapon. The dependent variable is whether the ofﬁcer ﬁred his gun during the

encounter. The omitted race is non-blacks (with the exception of the sample with narratives where the omitted race is non-black/non-Hispanic). The ﬁrst column for

each sample gives the unconditional average of contacts that resulted in an ofﬁcer ﬁring his gun. The second column for each sample reports logistic estimates for

black civilians. Each row corresponds to a different empirical speciﬁcation. The ﬁrst row includes solely racial dummies. The second row adds civilian gender and

a quadratic in age. The third row adds controls for the split of races of ofﬁcers present at the scene, whether any female ofﬁcers were present, whether ofﬁcers were

on duty or not, whether multiple ofﬁcers were present and the average tenure of ofﬁcers at the scene. The fourth row adds controls for the reason the ofﬁcers were

responding at the scene, whether the encounter happened during day time, and whether the civilian attacked or drew a weapon. The ﬁfth row adds controls for the

type of weapon the civilian was carrying. The sixth row adds year ﬁxed effects for columns (1)-(2). It adds year as a categorical variable for columns (3)-(8). Each

row includes missing in all variables. For arrest data without narratives missing indicators for ofﬁcer gender, ofﬁcer tenure, and number of ofﬁcers on the scene were

removed to minimize loss of observations in logistic regressions. For all regression, missing indicators for response reason and for whether the civilian attacked or

drew a weapon was removed for the same reason. Standard errors are robust and are reported in parentheses.

Table 5: Racial Differences in Lethal Use of Force (Conditional on an Interaction)

Intensive Margin, Ofﬁcer Involved Shootings

Non-Black/

Black HispanicNon-Hispanic

Mean

(1) (2) (3)

(a) No Controls 0.542 0.959 1.080

(0.116) (0.246)

(b) + Suspect Demographics 0.933 1.026

(0.093) (0.263)

⇤

0.886

(0.089) (0.223)

(d) + Encounter Characteristics 0.683

⇤⇤⇤

0.752

(0.094) (0.189)

(e) + Suspect Weapon 0.568

⇤⇤⇤

0.633

⇤

(0.064) (0.153)

(f) + Fixed Effects 0.534

⇤⇤⇤

0.562

⇤⇤

(0.043) (0.131)

Observations 1,316

Notes: This table reports odds ratios from logistic regressions. The sample consists of

ofﬁcer involved shootings from Dallas, Austin, six Florida counties, Houston and Los An-

geles between 2000 to 2015. The dependent variable is based on who attacked ﬁrst. It is

coded as 1 if the ofﬁcer attacked the suspect ﬁrst and 0 if the suspect attacked the ofﬁcer

ﬁrst. The omitted race is non-blacks and non-hispanics. The ﬁrst column gives the uncon-

ditional average of contacts that resulted in an ofﬁcer ﬁring his gun. The second column

reports logistic estimates for black civilians. Each row corresponds to a different empirical

speciﬁcation. The ﬁrst row includes solely racial dummies. The second row adds civilian

gender and a quadratic in age. The third row adds controls for the split of races of ofﬁcers

present at the scene, whether any female ofﬁcers were present, whether multiple ofﬁcers

were present and the average tenure of ofﬁcers at the scene. The fourth row adds controls

for the reason the ofﬁcers were responding at the scene, whether the encounter happened

during day time, and whether the civilian attacked or drew a weapon. The ﬁfth row adds

controls for the type of weapon the civilian was carrying. The sixth row adds city and year

ﬁxed effects. Each row includes missing in all variables. Standard errors are clustered at

the police department level and are reported in parentheses.

Table 6: Fraction Weapon Found, Conditional on Being

in an Oﬃce r Involved Shooting

Civilian White Civilian Black p-value

(1) (2) (3)

Oﬃcer White 0.842 0.809

(0.028) (0.026) 0.388

Oﬃcer Black 0.571 0.730

(0.137) (0.056) 0.246

p-value 0.011 0.175

Notes: This table presents results for Anwar and Fang (2006) test. The ﬁrst column

presents the fraction of white civilians carrying weapons in the Oﬃcer Involved Shoot-

ings (OIS) dataset. The second column presents the f raction of black civilians carrying

weapons in the OIS dataset. Th third column displays the p-value for equality of means

in columns (1) and (2). The ﬁrst row presents the fractions when the majority of oﬃcers

present during the encounter were white. The second row presents the fractions when

the majority of oﬃcers present during the encounter were black.

Figure 1: Odds Ratios by Use of For ce (Conditional on an Interaction), NYC S top Question and Frisk

1 1.2 1.4 1.6 1.8

Odds Ratio for Black

1 2 3 4 5 6 7

Use of Force Rank

Black vs White (None) Black vs White CI (None)

Black vs White (Full) Black vs White CI (Full)

Panel A

.5 1 1.5 2

Odds Ratio for Hispanic

1 2 3 4 5 6 7

Use of Force Rank

Hispanic vs White (None) Hispanic vs White CI (None)

Hispanic vs White (Full) Hispanic vs White CI (Full)

Panel B

Notes: These ﬁgures plot odds ratios with 95% conﬁdence intervals from logistic regressions. For the ﬁgure on the left, the y-axis denotes the odds

ratio of reporting various uses of force for black civilians versus white civilians. For the ﬁgure on the right, the y-axis denotes the odds ratio of

reporting various uses of force for hispanic civilians versus white civilians. For both ﬁgures, the x-axis denotes di↵erent use of force types: 1 is an

indicator for whether the police reported using at least hands or a more severe force on a civilian in a stop and frisk interaction. 2 is for whether

the police reported at least pushing a civilian to a wall or using a more severe force. 3 is for whether the police reported at least using handcu↵s

or a more severe force. 4 is for whether the police reported at least drawing a weapon on a civilian or using a more severe force. 5 is for whether

the police reported at least pushing a civilian to the ground or using a more severe force. 6 is for whether the police reported at least pointing

aweaponatacivilianorusingamoresevereforce. Finally,7isforwhetherthepolicereportedatleastusingapeppersprayorabatonona

civilian. All force indicators are coded as 0 when the police report using no force in a stop and frisk interaction. The line plot with no controls is

achieved by regressing the type of force (described above) on civilian race dummies only. The line plot with full controls is achieved by regressing

the type of force on civilian race dummies, civilian gender, a quadratic in age, civilian behavior, whether the stop was indoors or outdoors, whether

the stop took place during the daytime, whether the stop took place in a high crime area or a high crime time, whether the oﬃcer was in uniform,

civilian ID type, whether others were stopped during the interaction, and missings in all variables. Precinct and year ﬁxed e↵ects were included in

the controlled regression. Standard errors are clustered at the precinct level.

Figure 2: Odds Ratios of Any Use of Force (Con d it ion al on an Interaction) by Time of Day, NYC Stop

Question and Frisk

1 1.2 1.4 1.6

Odds Ratio for Black

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Black vs White Black vs White CI

Panel A

.05 .1 .15 .2 .25 .3

Average Use of Force

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Black White

mean_white hi_white/lo_white

Panel B

Notes: These ﬁgures plot odds ratios with 95% conﬁdence intervals and averages with 95% conﬁdence intervals. For the ﬁgure in Panel A, the

y-axis denotes the odds ratio of reporting any use of force for black civilians versus white civilians. For the ﬁgure in Panel B, the y-axis denotes

the average fraction of white and black civilians who had any force used against them. For both ﬁgures, the x-axis denotes di↵erent hours of the

day. For Panel A, odds ratios are achieved by regressing any use of force on civilian race dummies, civilian gender, a quadratic in age, civilian

behavior, whether the stop was indoors or outdoors, whether the stop took place during the daytime, whether the stop took place in a high crime

area or a high crime time, whether the oﬃcer was in uniform, civilian ID type, whether others were stopped during the interaction, and missings

in all variables, for every hour of day. Precinct and year ﬁxed e↵ects were included in all regressions. Standard errors are clustered at the precinct

level.

Figure 3: Odds Ratios by Use of Force (Conditional on an Interaction), Police Public Contact Survey

0 2 4 6 8

Odds Ratio for Black

1 2 3 4

Use of Force Rank

Black vs White (None) Black vs White CI (None)

Black vs White (Full) Black vs White CI (Full)

Panel A

1 2 3 4 5

Odds Ratio for Hispanic

1 2 3 4

Use of Force Rank

Hispanic vs White (None) Hispanic vs White CI (None)

Hispanic vs White (Full) Hispanic vs White CI (Full)

Panel B

Notes: These ﬁgures plot odds ratios with 95% conﬁdence intervals from logistic regressions. For the ﬁgure on the left, the y-axis denotes the odds

ratio of reporting various uses of force for black civilians versus white civilians. For the ﬁgure on the right, the y-axis denotes the odds ratio of

reporting various uses of force for hispanic civilians versus white civilians. For both ﬁgures, the x-axis denotes di↵erent use of force types: 1 is an

indicator for whether the survey respondent report the oﬃcer at least grabbing him/her in an interaction. 2 is for whether the respondent reported

the police handcuﬃng him/her or using a more sever force in an interaction. 3 is for whether the survey respondent reported the p olice pointing a

gun at him/her or using a more severe force in an interaction. Finally, 4 is for whether the respondent reported the police kicking, using a stun gun

or using a pepper spray on him/her or using a more severe force. All force indicators are c oded as 0 when the respondent reports the police using

no force in an interaction. The line plot with no controls is achieved by regressing the type of force (described above) on civilian race dummies

only. We control for civilian gender, a quadratic in age, work, income, population size of civilian’s address, civilian behavior, contact time, contact

type, oﬃcer race, year of survey and missings in all variables. Standard errors are robust.

Figure 4: Odds Ratios for Oﬃcer Involved Shootings (Conditional on an Interaction), Extensive Margin, By

Year Categories

.4 .6 .8 1 1.2 1.4

Odds Ratio for Black

2000-2005 2006-2010 2011-2015

Yea r

Black vs Non-Black Black vs Non-Black CI

Notes: This ﬁgure plot odds ratios with 95% conﬁdence intervals from logistic regressions. The sample consists of all oﬃcer involved shootings in

Houston from 2000 - 2015, plus a random draw of all arrests for the following o↵enses, from 2000 - 2015: aggravated assault on a peace oﬃcer,

attempted capital murder of a peace oﬃcer, resisting arrest, evading arrest, and interfering in an arrest ,plus a sample of arrests where tasers

were used. The y-axis denotes odds ratios of an oﬃcer shooting at a black civlian versus a white civilian. The x-axis denotes the period of years

for which the odds ratios were calculated. We control for civilian gender, a quadratic in age, oﬃcer demographics, encounter characteristics, and

missings in all variables (i.e. all variables included in the ﬁnal row of Table 4). Year ﬁxed e↵ects are included in all regressions. Robust standard

errors are reported in parentheses.

Figure 5: Odds Ratios by Use of Force for Perfectly Compliant Civilians (Conditional on an Interaction),

NYC Stop Question and Frisk

.6 .8 1 1.2 1.4

Odds Ratio for Black

1 2 3 4 5 6 7

Use of Force Rank

Black vs White (Full) Black vs White CI (Full)

Panel A

.4 .6 .8 1 1.2

Odds Ratio for Hispanic

1 2 3 4 5 6 7

Use of Force Rank

Hispanic vs White (None) Hispanic vs White CI (None)

Panel B

Notes: These ﬁgures plot odds ratios with 95% conﬁdence intervals from logistic regressions. For the ﬁgure on the left, the y-axis denotes the

odds ratio of reporting various uses of force for perfecly compliant black civilians versus perfect compliant white civilians. For the ﬁgure on the

right, the y-axis denotes the odds ratio of reporting various uses of force for perfectly compliant hispanic civilians versus perfectly compliant white

civilians. For both ﬁgures, the x-axis denotes di↵erent use of force types: 1 is an indicator for whether the police reported using at least hands or

amoresevereforceonacivilianinastopandfriskinteraction. 2isforwhetherthepolicereportedatleastpushingaciviliantoawallorusing

amoresevereforce. 3isforwhetherthepolicereportedatleastusinghandcu↵soramoresevereforce. 4isforwhetherthepolicereportedat

least drawing a weapon on a civilian or using a more severe force. 5 is for whether the police reported at least pushing a civilian to the ground or

using a more severe force. 6 is for whether the police reported at least pointing a weapon at a civilian or using a more severe force. Finally, 7 is

for whether the police reported at least using a p epper spray or a baton on a civilian. All force indicators are coded as 0 when the police report

using no force in a stop and frisk interaction. The line plot is achieved by regressing the type of force on civilian race dummies, civilian gender, a

quadratic in age, civilian behavior, whether the stop was indoors or outdoors, whether the stop took place during the daytime, whether the stop

took place in a high crime area or a high crime time, whether the oﬃcer was in uniform, civilian ID type, whether others were stopped during

the interaction, and missings in all variables. Precinct and year ﬁxed e↵ects were included in all regressions. Standard errors are clustered at the

precinct level.