NBER WORKING PAPER SERIES

AN EMPIRICAL ANALYSIS OF RACIAL DIFFERENCES IN POLICE USE OF
FORCE
Roland G. Fryer, Jr
Working Paper 22399
http://www.nber.org/papers/w22399

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
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July 2016

This work has benefitted greatly from discussions and debate with Chief William Evans, Chief
Charles McClelland, Chief Martha Montalvo, Sergeant Stephen Morrison, Jon Murad, Lynn
Overmann, Chief Bud Riley, and Chief Scott Thomson. I am grateful to David Card, Kerwin
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
Winship, and seminar participants at Brown University, University of Chicago, London School of
Economics, University College London, and the NBER Summer Institute for helpful comments
and suggestions. Brad Allan, Elijah De La Campa, Tanaya Devi, and William Murdock III
provided truly phenomenal project management and research assistance. Lukas Althoff, Dhruva
Bhat, Samarth Gupta, Julia Lu, Mehak Malik, Beatrice Masters, Ezinne Nwankwo, Charles Adam
Pfander, Sofya Shchukina and Eric Yang provided excellent research assistance. Financial
support from EdLabs Advisory Group and an anonymous donor is gratefully acknowledged.
Correspondence can be addressed to the author by email at rolandfryer@edlabs.harvard.edu. The
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reflect the views of the National Bureau of Economic Research.
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An Empirical Analysis of Racial Differences in Police Use of Force
Roland G. Fryer, Jr
NBER Working Paper No. 22399
July 2016
JEL No. J01,K0
ABSTRACT
This paper explores racial differences 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 most extreme use of force – officerinvolved shootings – we find no racial differences in either the raw data or when contextual
factors are taken into account. We argue that the patterns in the data are consistent with a model
in which police officers are utility maximizers, a fraction of which have a preference for
discrimination, who incur relatively high expected costs of officer-involved shootings.

Roland G. Fryer, Jr
Department of Economics
Harvard University
Littauer Center 208
Cambridge, MA 02138
and NBER
rfryer@fas.harvard.edu

A online appendix is available at http://www.nber.org/data-appendix/w22399

“We can never be satisfied as long as the Negro is the victim of the unspeakable horrors
of police brutality.” Martin 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, high pressure water hoses, and tear gas are an indelible part
of American 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, unarmed, was shot twelve times by a police 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 while attempting to flee. Samuel Du Bose, unarmed, was stopped for failure
to display a front license plate and while trying to drive away was fatally shot once in the head.
Rekia Boyd, unarmed, was killed by a Chicago police officer who fired into a group of people five
times from inside his police car. Zachary Hammond, unarmed, was driving away from a drug deal
sting operation when he was shot to death by a Seneca, South Carolina, police officer. He was
white. And so are 44% of police shooting subjects.1
These incidents, some captured on video and viewed widely, have generated protests in Ferguson,
New York City, Washington, Chicago, Oakland, and several other cities 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, are beginning to issue
body worn cameras, engaging in community policing, and enrolling officers in training in an effort
to purge racial bias from their instinctual decision making. However, for all the eerie similarities

1

Author’s calculations based on ProPublica research that analyzes FBI data between 1980 and 2012.

1

between the current spate of police interactions with African Americans and the historical injustices
which remain unhealed, the current debate is virtually data free. Understanding the extent to which
there are racial differences in police use of force and (if any) whether those differences might be due
to discrimination by police or explained by other factors at the time of the incident is a question
of tremendous social importance, and the subject of this paper.
A primary obstacle to the 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 police narrative accounts of interactions with civilians, it is exceedingly difficult to
extract. Moreover, the task of compiling rich data on officer-involved shootings is burdensome. Until
recently, data on officer-involved shootings were extremely rare and contained little information on
the details surrounding an incident. A simple count of the number of police shootings that occur
does little to explore whether racial differences in the frequency of officer-involved shootings are
due to police malfeasance or differences in suspect behavior.2
In this paper, we estimate the extent of racial differences in police use of force using four
separate datasets – two constructed for the purposes of this study.3 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 question a pedestrian, then can frisk
them for weapons or contraband. The dataset contains roughly five million observations. And,
important for the purposes of this paper, has detailed information on a wide range of uses of force
– from putting hands on civilians to striking them with a baton. The second dataset is the PolicePublic Contact Survey, a triennial survey of a nationally representative sample of civilians, which
contains – from the civilian point of view – a description of interactions with police, which includes
uses of force. Both these datasets are public-use and readily available.4
2

Newspapers such as the Washington Post estimate that there were 965 officer-involved shootings in 2015. Websites such as fatal encounters estimate that the number of annual shootings is approximately 704 between 2000 and
2015.
3
Throughout the text, I depart from custom by using the terms “we,” “our,” and so on. Although this is soleauthored work, it took a large team of talented individuals to collect the data necessary for this project. Using “I”
seems disingenuous.
4
The NYC Stop and Frisk data has been used in Gelman et al. (2012) and Coviello and Persico (2015) to understand 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-

2

The other two datasets were assembled for the purposes of this research. We use event summaries from all incidents in which an officer discharges his weapon at civilians – including both hits
and misses – from three large cities in Texas (Austin, Dallas, Houston), six large Florida counties,
and Los Angeles County, to construct a dataset in which one can investigate racial differences in
officer-involved shootings. Because all individuals in these data have been involved in a police
shooting, analysis of these data alone can only estimate racial differences 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 from
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. Similar to the event studies above, these
data come from arrests narratives that range in length from two to one hundred 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 police officer decides to shoot) and intensive margins.
Further, the Houston arrests data contain almost 3,500 observations in which officers discharged
charged electronic devices (e.g., tasers). This is the second most extreme use of force, and in some
cases, is a substitute for lethal use of force.
The results obtained using these data are informative and, in some cases, startling. Using
data on NYC’s Stop and Frisk program, we demonstrate that on non-lethal uses of force – putting
hands on civilians (which includes slapping or grabbing) or pushing individuals into a wall or onto
the ground, there are large racial differences. In the raw data, blacks and Hispanics are more
than fifty percent more likely to have an interaction with police which involves any use of force.
Accounting for baseline demographics such as age and gender, encounter characteristics such as
whether individuals supplied identification or whether the interaction occurred in a high- or lowcrime area, or civilian behaviors does little to alter the race coefficient. Adding precinct and year
fixed effects, which estimates racial differences in police use of force by restricting to variation
within a given police precinct in a given year reduces the black coefficient by 19.4 percent and the
ogy, to study questions such as whether police treatment of citizens impacts the broader public opinion of the police
(Miller et al., 2004).

3

Hispanic coefficient by 26 percent, though both are still statistically larger than zero. Including
more than 125 controls available in the data, the odds-ratio on black (resp. Hispanic) is 1.173 (resp.
1.120).
Interestingly, as the intensity of force increases (e.g. handcuffing civilians without arrest, drawing 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 racial difference remains surprisingly constant.
For instance, 0.26 percent of interactions between police and civilians involve an officer drawing a
weapon; 0.02 percent involve using a baton. These are rare events. Yet, the results indicate that
they are significantly more rare for whites than blacks. In the raw data, blacks are 21.3 percent
more likely to be involved in an interaction with police in which at least a weapon is drawn than
whites and the difference is statistically significant. Adding our full set of controls reduces the
racial difference to 19.4 percent. Across all non-lethal uses of force, the odds-ratio of the black
coefficient ranges from 1.163 (0.036) to 1.249 (0.129).
Data from the Police-Public Contact Survey are qualitatively similar to the results from Stop
and Frisk data, both in terms of whether or not any force is used and the intensity of force, though
the estimated racial differences is larger. In the raw data, blacks and Hispanics are approximately
two percentage points more likely than whites to report any use of force in a police interaction.
The white mean is 0.8 percent. Thus, the odds ratio is 3.335 for blacks and 2.584 for Hispanics.
As the use of force increases, the racial difference remains roughly constant. Adding controls for
civilian demographics, civilian behavior, contact and officer characteristics, or year does little to
alter the results. The coefficients are virtually unchanged and are all highly significant with the
exception of the highest uses of force for which data is sparse.
There are several potential explanations for the quantitative differences between our estimates
using Stop and Frisk data and those using PPCS data. First, we estimate odds-ratios and the
baseline probability of force in each of the datasets is substantially different. Second, the PPCS is a
nationally representative sample of a broad set of police-civilian interactions. Stop and Frisk data
is from a particularly aggressive form of policing 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 data and unavailable in PPCS. In the end, the “Truth” is likely somewhere in
the middle and, importantly, both bounds are statistically and economically important.
4

In stark contrast to non-lethal uses of force, we find no racial differences in officer-involved
shootings on either the extensive or intensive margins. Using data from Houston, Texas – where
we have both officer-involved shootings and a randomly chosen set of potential interactions with
police where lethal force may have been justified – we find, in the raw data, that blacks are 23.8
percent less likely to be shot at by police relative to whites. Hispanics are 8.5 percent less likely.
Both coefficients are statistically insignificant. Adding controls for civilian demographics, officer
demographics, encounter characteristics, type of weapon civilian was carrying, and year fixed effects,
the black (resp. Hispanic) coefficient is 0.924 (0.417) (resp. 1.256 (0.595)). These coefficients are
remarkably robust across alternative empirical specifications and subsets of the data. Partitioning
the data in myriad ways, we find no evidence of racial discrimination in officer-involved shootings.
Investigating the intensive margin – the timing of shootings or how many bullets were discharged
in the endeavor – there are no detectable racial differences.5
Our results have several important caveats. First, all but one dataset was provided by a select
group of police departments. It is possible that these departments only supplied the data because
they are either enlightened or were not concerned about what the analysis 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 important selection in who was willing
to share their data. The Police-Public contact survey partially sidesteps this issue by including
a nationally representative sample of civilians, but it does not contain data on officer-involved
shootings.
Relatedly, even police departments willing to supply data may contain 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 standard way.6 It is exceedingly difficult to know how prevalent this
type of misreporting bias is (Schneider 1977). Accounting for contextual variables recorded by
police officers who may have an incentive to distort the truth is problematic. Yet, whether or not
we include controls does not alter the basic qualitative conclusions. And, to the extent that there
5

It is important to recognize that there may be racial bias in the likelihood of appearing in the Houston Arrest
Data.
6
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 body camera footage showed no such series of events. In
the Laquan McDonald case in Chicago, the police reported that McDonald lunged at the officer with a knife while
dash-cam footage showed the teenager walking away from the police with a small knife when he was fatally shot 16
times by the officer.

5

are racial differences in underreporting of non-lethal use of force (and police are more likely to not
report force used on blacks), our estimates may be a lower bound. Not reporting officer-involved
shootings seems unlikely.
Third, given the inability to randomly assign race, one can never be confident in the direct
regression approach when interpreting racial disparities. We partially address this in two ways.
First, we build a model of police-civilian interactions that allows for both statistical and tastebased discrimination and use the predictions of the model to help interpret the data. For instance,
if police officers are pure statistical discriminators then as a civilian’s signal to police regarding
their likelihood of compliance becomes increasingly deterministic, racial differences will disappear.
To test this, we investigate racial differences in use of force on a set of police-civilian interactions
in which the police report the civilian was compliant on every measured dimension, was not arrested, and neither weapons nor contraband was found. In contrast to the model’s predictions,
racial differences on this set of interactions is large and statistically significant. Additionally, we
demonstrate that the marginal returns to compliant behavior are the same for blacks and whites,
but the average return to compliance is lower for blacks – suggestive of a taste-based, rather than
statistical, discrimination.
For officer-involved shootings, we employ a simple test 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 suspect versus a white suspect is different
across officer races, then one could reject the null hypothesis of no discrimination. 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, tastebased discrimination among police officers who face convex costs of excessive use of force. Yet, the
data does more to provide a more compelling case that there is no discrimination in officer-involved
shootings than it does to illuminate the reasons behind racial differences 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 uses in the analysis. Section 3 presents estimates of racial differences on non-lethal
uses of force. Section 4 describes a similar analysis for the use of lethal force. Section 5 attempts
6

to reconcile the new facts with a simple model of police-civilian interaction that incorporates both
statistical and taste-based channels of discrimination. The final section concludes. There 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 provides
additional theoretical results.

II. The Data
We use four sources of data – none ideal – which together paint an empirical portrait of racial
differences in police use of force. The first two data sources – NYC’s Stop and Frisk program and
the Police-Public Contact Survey (PPCS) – provide information on non-lethal force from both the
police and civilian perspectives, respectively. The other two datasets – event summaries of officerinvolved shootings in ten locations across the US, and data on interactions between civilians and
police in Houston, Texas, in which the use of lethal of force may have been justified by law – allow
us to investigate racial differences in officer-involved shootings on both the extensive and intensive
margins.
Below, I briefly discuss each dataset in turn. Appendix A provides further detail.

A. New 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 streets, time of day, inside/outside, high/low crime area), civilian
demographics (race, age, gender, height, weight, build, type of identification provided), whether
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 committed).
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 to a wall, (3) handcuffs,
(4) draw weapon, (5) push to the ground, (6) point a weapon, (7) pepper spray or (8) strike with

7

a baton.7 Officers are instructed to include as many uses of force as apply. For instance, if a stop
results in an officer putting his hands on a civilian and, later within the same interaction, pointing
his weapon, that observation would have both “hands” and “point a weapon” as uses of force.
Unfortunately, officers are not required 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 interactions.8 Between the years 2003 and 2013, the 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 excluding stops that resulted in arrests.9 Unfortunately, even
this robust dataset is incomplete – nowhere is the universe of all police interactions with civilians
– or even all police stops – recorded.
Second, lower level uses of force – such as the use of hands – are both recorded in these data
and more frequently used by law enforcement than more intense uses of force. For instance, if
one were to use arrest data to glean use of force, many lower level uses of force would simply be
considered standard operating procedure. Putting hands on a suspect, pushing them up against a
wall, and putting handcuffs on them are so un-noteworthy in the larger context of an arrest that
they are not recorded in typical arrest descriptions. Yet, because proactive policing is a larger and
less confrontational portion of police work, these actions warrant data entry.
The key limitation of the data is they only capture the police side of the story. There have
been several high-profile cases of police storytelling that is not congruent with video evidence of the
interaction. Another important limitation for inference is that the data do not provide a way to
identify officers or individuals. 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 cluster standard errors at
the precinct level. Appendix table 9 explores the robustness of our results for more disaggregated
clusters – precinct x time of day, block-level, and even block x time of day. Our conclusions are
7

Police officers can also include “other” force as a type of force used against civilians. We exclude “other” forces
from our analysis. Appendix Table 3 calculates racial differences in the use of “other” force and shows that including
these forces does not alter our results.
8
Technically, NYC police are only required to record a stop if some force was used, a civilian was frisked or
searched, was arrested, 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 that legally trigger the requirement to
record the stop.
9
This number was calculated from the Division of Criminal Justice Services’ record of adult arrests by counties
in New York City between 2003 and 2013.

8

unaffected by any of these alternative ways to cluster standard errors.
Summary statistics for the Stop and Frisk data are displayed in table 1A. There are six panels.
Panel A contains baseline characteristics. Fifty eight percent of all stops recorded were of black
civilians. If police were stopping individuals at random, this 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 data 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 stops occur outside after the sun has set in high-crime areas. A surprisingly small number of
stops – about three percent – the police report finding any weapon or contraband. Panel C displays
variables that describe civilian behavior. Approximately 50 percent 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 alternative outcomes such as whether a civilian was frisked, summonsed, or arrested. Panel E provides descriptive statistics for the seven forms of force available
in the data. Panel F provides the frequency of missing variables.

B. The Police-Public Contact Survey
The Police-Public Contact Survey (PPCS) – a nationally representative 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 500,000 observations.
The main advantage of the PPCS data is that, unlike 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 differences between certain data
in the Uniform Crime Reports (UCR) and the National Crime Victimization Survey (NCVS).10
One explanation for these differences given in the literature is that individuals are embarrassed or
10

According to the US Department of Justice, UCR and NCVS measure an overlapping but nonidentical set of
crimes. The UCR Program’s primary objective is to provide a reliable set of criminal justice statistics by compiling
data from monthly law enforcement 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 to provide
previously unavailable information about crime (including crime not reported to police), victims and offenders.
Therefore, there are discrepancies in victimization rates from the two reports like the UCR which reports 89,000
forcible rapes in 2010 while the NCVS reports 203,830 rapes and sexual assaults in 2010.

9

afraid to report certain crimes to police or believe that reporting such crimes have unclear benefits
and potential costs. Police use of force – in particular for young minority males – may be similar.
Another key advantage is that it approximates the universe of potential interactions with police
– rather than limited to arrests or police stops.11 If a police officer is investigating a crime in a
neighborhood and they discuss it with a civilian – this type of interaction would be recorded in the
PPCS. Or, if a police officer used force on a civilian and did not report the 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 individual’s locations is not available
to researchers. Second, the data on contextual factors surrounding the interaction with police or
the officer’s characteristics are limited. Third, the survey omits individuals who are currently in
jail. Fourth, the PPCS only includes the civilian account of the interaction which could be biased
in its own way. In this vein, according to individuals in the PPCS data, only 4.18% of them have
resisted arrests and only 11% of civilians argued when they were searched despite not being guilty
of carrying alcohol, drugs or weapons.
Table 1B presents summary statistics for PPCS data. There are six panels. Panel A contains
civilian demographics. Blacks comprise roughly eleven percent of the sample, women are 53 percent.
The average age is approximately 17 years older than the Stop and Frisk data. Over 60 percent of
the sample reports being employed in the previous week – average income category in the sample
is 1.95. 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 levels greater than $50,000.
Panel B describes self-reported civilian behavior. According to the all PPCS survey respondents,
almost no civilians disobey police orders, try to get away, resist, argue or threaten officers. However,
since these questions were asked in response to why force was used against respondents, if we restrict
the data to civilians who report non-missing use of force from police officers, this percentage rises
to 15.3 percent.
Panel C of table 1B includes summary data on the types of contact and officer characteristics.
Almost half of the interactions between the public and police are traffic stops, eighteen percent
are from street interactions – including the types of street interaction that may not appear in our
11

Contacts exclude encounters with private security guards, police officers seen on a social basis, police officers
related to the survey respondents, or any contacts that occurred outside the United States.

10

Stop and Frisk data – and thirty percent are “other” which include being involved in a traffic
accident, reporting a crime, being provided a service by the police, participating in block watch or
other anti-crime programs, or being suspected by the police of something or as a 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 missing variables.

C. Officer-Involved Shootings
There are no systematic datasets which include officer-involved shootings (OIS) along with demographics, encounter characteristics, and suspect and police behavior.12 For the purposes of this
project, we compile a dataset on officer-involved shootings from ten locations across America.
To begin, fifteen police departments across the country were contacted by the author: Boston,
Camden, NYC, Philadelphia, Austin, Dallas, Houston, Los Angeles, six Florida counties, and
Tacoma, Washington.13 Importantly for thinking about the representativeness of the data – many
of these cities were a part of the Obama Administration’s Police Data Initiative.14 We received
data from all but three of these police departments – NYC, Philadelphia, and Tacoma, Washington
– all of which have indicated a willingness to participate in our data collection efforts but have not
yet provided data.15 This is likely not a representative set of cities. Appendix Table 14 investigates
differences between the cities that provided us data and other Metropolitan Statistical Areas on a
variety of dimensions such as population demographics and crime rates.
In most cases, OIS data begins as event summaries from all incidents in which a police officer
discharged their firearm at civilians (including both hits and misses). These summaries, 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:

12

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.
13
Another approach is to request the data from every police department vis-a-vis a freedom of information request.
We attempted this method, but police departments are not obliged to include detailed event summaries. In our
experience, the only way to obtain detailed data is to have contacts within the police department.
14
The White House launched the Police Data Initiative as a response to the recommendations made by the Task
Force on 21st Century Policing. The Initiative was created to work with police departments to leverage data on
police-citizen interactions (e.g., officer-involved shootings, use of force, body camera videos and police stops) to
increase transparency and accountability.
15
Camden and Boston each had one OIS during the relevant time frame, so we did not use their data for this
analysis. Camden provided remarkable data on police-civilian interactions which will be used in future work.

11

“As I pointed my rifle at the vehicle my primary focus was on the male passenger
based on the information provided by the dispatcher as the person who had been armed
inside the store. As the vehicle was driving past me I observed the male passenger in
the truck turn around in the seat, and begin pointing a handgun at me through an
open rear sliding glass window. When I observed this I was still yelling at the female
to stop the truck! The male suspect appeared 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 fire. 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 being fired and going through a recoil
process, but I could not hear gunshots. Fearing for my life, the lives of the citizens in
the area and my fellow officers I began to fire my rifle at the suspect.”
To create a dataset out of these narratives, a team research assistants read each summary
and extracted data on 65 pre-determined variables in six categories: (A) suspect characteristics,
(B) suspect weapon(s), (C) officer characteristics, (D) officer response reason, (E) other encounter
characteristics, and (F) location characteristics.16 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 characteristics 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 variables determine the reason behind the officer being present at
the scene. They include dummy variables on whether the officer 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 personally attacked or other
reasons. Other encounter characteristics gather information on whether the shooting happened
during the day or night and a variable that is coded 1 if the suspect attacked the officer or drew
16

Appendix B provides a detailed, step-by-step, account of how the OIS dataset was created and was explicitly
designed to allow researchers to replicate our analysis from the original source materials.

12

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 the officer at all. Finally, location characteristics
include dummies to represent the jurisdiction that we collected data from. Appendix B contains
more details of how the variables were coded.
As a crucial check on data quality, once we coded all OIS data from the event summaries, we
wrote Appendix B. We then hired eight new research assistants who did not have any involvement
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 attempting to replicate our work from the source material – and they created a second, independent,
dataset. All results remain qualitatively unchanged with the alternatively coded dataset.17
The most obvious advantage of the OIS data is the breadth and specificity of information
contained in the event summaries. Descriptions of OIS are typically long and quite detailed relative
to other police data. A second advantage is that officer-involved shootings are non-subjective.
Unlike lower level uses of force, whether or not an officers discharges a weapon is not open to
interpretation. Officers are also required to document anytime they discharge their weapon. Finally,
OIS are subject to internal and often times external review.
The OIS data have several notable limitations. Taken alone, officer-involved shootings are the
most extreme and least used form of police force and thus, in isolation, may be misleading. Second,
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 reports may be large.18 Third, we
don’t typically have the suspect’s side of the story and often there are no witnesses. Fourth, it is
impossible to capture all variables of importance at the time of a shooting. Thus, what appears to
be discrimination 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 but not used). To the extent that racial bias is
prevalent on the extensive margin – whether or not someone is ever in an officer-involved shooting
– these data would not capture it.
17

Thanks to Derek Neal for suggesting this exercise.
From interviews with dozens of current police officers, we gleaned that in most all police shootings – even when
fully justified and observed by many – the officer is taken off active-duty, pending an investigation.
18

13

We address this concern 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
officer shoots the suspect before being attacked. Second, we collected unprecedented data from the
Houston Police Department on all arrest categories in which officers may have used justifiable force
as a way to obtain the “zeros.” These data are described in the next subsection.
Table 1C displays summary statistics for OIS data, divided into four locations and six categories
of data. Column (1) contains observations from the full sample – 1,332 shootings between 2000
and 2015. Forty-six percent of officer-involved shootings in our data are blacks, thirty percent are
Hispanic, and twenty-four 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 bit surprising
that they are less than half of the observations in the data.
Columns (2) and (3) displays data from 507 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 Department carry Glock 22, Glock 23 or the Smith & Wesson M&P40 .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 (4) through (6) contain OIS data from Austin and Dallas, Texas, six Florida counties
(Brevard, Jacksonville, Lee, Orange, Palm Beach and Pinellas), and Los Angeles County. Panel F
demonstrates that Houston accounts for 38% of all officer-involved shootings. Austin and Dallas,
combined, provide 20% of the data while Florida provides 27% of the data. Panel G provides the
frequency of missing variables.

D. Houston Police Department Arrests Data
The most comprehensive set of OIS data is from the Houston Police Department (HPD). For this
reason, we contacted HPD to help construct a set of police-civilian interactions in which lethal
force may have been justified. According to Chapter 9 of the Texas Penal Code, police officers’
use of deadly force is justified “when and to the degree the actor reasonably believes the force is
immediately necessary.” Below, we describe the task of implementing this obtuse definition in data
in an effort to develop a set of police-civilian interactions in which the use of lethal force may have
14

been justified by law.
There are approximately 100,000 arrests per year in Houston; 1.6 million total over the 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 unique
case IDs.19
We sample case IDs from five arrest categories which are more likely to contain incidence in
which lethal force was justified: attempted capital murder of a public safety officer, aggravated
assault on a public safety officer, resisting arrest, evading arrest, and interfering in arrest.20 This
process narrowed the set of relevant arrests to 16,000 total, between 2000 and 2015. We randomly
sampled five percent of these arrest records and manually coded 290 variables per arrest record. This
process took between 30 and 45 minutes per record to manually keypunch and includes variables
related to specific locations for calls, incidents, and arrests, suspect behavior, suspect mental health,
suspect injuries, officer use of force, and officer injuries resulting from the encounter.
These data are merged with data on officer demographics and suspect’s previous 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 collected 4,250 incident reports for all cases in which an officer discharged their taser.
These data form another potential risk set. It it important to note: technology allows for HPD to
centrally monitor the frequency and location of taser discharges.
Table 1D provides descriptive statistics for the Houston Arrest Data. Compared to the officerinvolved shootings dataset, civilians sampled in the arrest dataset carry far fewer weapons – 95%
do not carry weapons compared to 21% in the OIS dataset. The other variable that is significantly
different between the two datasets is the fraction of suspects who attacked or drew weapon – 56%
in the HPD arrest dataset compared to 80% in the OIS dataset.

19

In conversations with engineers and data scientists at Google, Microsoft Research, and several others in Artificial
Intelligence and Machine Learning, we were instructed that current natural language processing algorithms are not
developed for the level of complexity in our police data. Moreover, one would need a “test sample” (manually coded
data to assess the algorithm’s performance) of several hundred thousand to design an algorithm. This is outside the
scope of the current project.
20
Our original request to HPD was for a dataset similar to OIS for all arrests between 2000 and 2015. The response:
“we estimate that it will take 375 years to fulfill that request.”

15

III. Estimating Racial Differences in Non-Lethal Use of Force
NYC’s Stop, Question, and Frisk Data
Table 2A presents a series of estimates of racial differences in police use of force using the Stop
and Frisk data. We estimate logistic regressions of the following form:

1
1
Forcei,p,t “ Race1i α ` Xi,t
β ` Zp,t
µ ` νt ` ψp ` i,p,t

(1)

where Forcei,p,t is a measure of police use of force on individual i, in precinct p, at time t. A
full set of race dummies for civilians are included in the regressions, with white as the omitted
category. Consequently, the coefficients on race capture the gap between the named racial category
and whites – which is reported as an Odds Ratio.21 The vectors of covariates included in the
1 and Z , vary between rows in table 2A. As one moves down the table,
specification, denoted Xi,t
p,t

the set 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 environmental 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.
The first row in table 2A presents the differences in means for any use of force. 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. Other race – which includes American Indians, Alaskan natives or other races besides white,
black, Hispanic and Asian – is smaller but still considerable.
The raw difference 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, whether racial differences are driven by police response to a given civilian’s behavior
or racial differences 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

21

Appendix Tables 2A through 2G runs similar specification using ordinary least squares and obtains similar
results. Estimating Probit models provides almost identical results.

16

influenced by biased police.22
Row (2) adds baseline civilian characteristics – such as age and gender – all of which are
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
the interaction happened inside, the time of day, whether it occurred in a high or low crime area,
and whether the civilian provided identification – are added as controls in row 3. If anything, adding
these variables increase the odds ratios on each race, relative to whites. Surprisingly, accounting
for civilian behavior – row 4 in the table – does little to alter the results.
The final row in table 2A includes both precinct and year fixed effects. This significantly changes
the magnitude of the coefficients. Blacks are seventeen percent more likely to incur any use of force,
accounting for all variables we can in the data. Hispanics are roughly twelve percent more likely.23
Both are statistically significant. Asians are slightly less likely, though not distinguishable from
whites.
These results have two potential takeaways: 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, there is no linear combination that fully explains the
race coefficients.24 From this point forward, we consider the final specification, including precinct
and year fixed effects as our main specification.
Inferring racial differences in the types of force used in a given interaction is a bit more nuanced.
Police report that in twenty percent of all stops, some use of force is deployed. Officers routinely
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
22

The traditional literature in labor economics – beginning with Mincer (1958) – dealt with similar issues. O’Neill
(1990) and Neal and Johnson (1996) sidestep this by demonstrating that much of the racial wage gap can be accounted
for by including only pre-market factors such as test scores.
23
Even accounting for eventual outcomes of each stop – which include being let go, being frisked, being searched,
being arrested, being summonsed, and whether or not a weapon or some 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.
24
Using data on geo-spatial coordinates, we also included block-level fixed effects and the results were qualitatively
unchanged.

17

use of force categories, and 0.6% of all stop and frisk incidents in which force is used record more
than three uses of force.
There are several ways to handle this. The simplest is to 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 the 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
potentially valuable information on lower level uses of force. When analyzing racial differences in
the use of hands by police, one would miss this observation. A similar issue arises if one uses the
parallel “min.”25
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 hands and forced to the ground would be coded as “1” in the raw data.
When analyzing racial differences in the use of hands by police, this observation would be included.
The interpretation would not be racial differences in the use of hands, per se, but racial differences
in the use of “at least” hands. To be clear, an observation that records only hands would be in
the hands regression 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 differences 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 baton. 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 dashed line adds
precinct and year fixed effects (equivalent to row 5 in table 2A).
For blacks, the consistency of the odds ratios are striking. As the use of force increases, the
frequency with which that level of force is used decreases substantially. There are approximately
five million observations in the 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 rare. Yet,
it is consistently rarer for whites relative to blacks. The range in the odds ratios across all levels
of force is between 1.163 (0.036) and 1.236 (0.058).
Interestingly, for Hispanics, once we account for our set of controls, there are small differences
25

Appendix table 8 demonstrates that altering the definition to be “at most” or using the max/min force used in
any given police interaction does not alter the results.

18

in use of force for the lower level uses of non-lethal force, but the differences converge toward whites
as the use of force increases both in the raw 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 example, only
on males or only on police stops during the day) provide one means of addressing this concern.
Table 3 explores the sensitivity of the estimated racial gaps in police use of force across 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 table presents baseline results using the full (any force) sample
and our parsimonious set of controls (corresponding to row 5 in table 2a). The subsequent rows
investigate racial differences in use of force for high/low crime areas, time of day, whether or not
the officer was in uniform, indoors/outdoors, gender of civilian, and eventual outcomes.
Most of the coefficients on race do not differ significantly across these various subsamples with
the exception of time of day and eventual outcomes. Black civilians are 7 percent more likely to
have any force used against them conditional on being arrested. They are 15 percent more likely
to have any force used against them conditional on being summonsed and 11.1 percent more likely
conditional on having weapons or contraband found on them. Results are similar for Hispanics.
Additionally, for both blacks and Hispanics, racial differences in use of force are more pronounced
during the day relative to night.
To dig deeper, 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 show that force against black
civilians follows approximately the same pattern as white civilians, though the difference between
average force between the 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 accurately, the police entry of the data. It is plausible that there are large racial
differences that exist that are masked by police misreporting. The Police-Public Contact Survey is
one way to partially address this weakness.
Table 2B presents a series of estimates of racial differences in police use of force using the PPCS

19

data. The specifications estimated are of the form:

1
Forcei,t “ Race1i α ` Xi,t
β ` νt ` i,t ,

where Forcei,t is a measure of police use of force reported by individual i in year t. A full set of
race dummies for individuals and officers are included in the regressions, with white as the omitted
category. The vectors of covariates included in the specification vary across rows in table 2B. As
one moves down the table, the set of coefficients steadily grows. Standard errors, which appear
below each estimate, account for heteroskedasticity.
Generally, the data are qualitatively similar to the the results using Stop and Frisk – namely,
despite a large and complex set of controls, blacks and Hispanic are more likely to experience some
use of force from police. A key difference, however, is that the share of individuals experiencing any
use of force is significantly lower. In the Stop and Frisk data, 15.3 percent of whites incur some force
from police. In the PPCS, this number is 1%. There are a variety of potential reasons for these
stark differences. For instance, the PPCS is a nationally representative sample of interactions with
police from across the U.S., whereas the Stop and Frisk data is gleaned from a rather aggressive
proactive policing strategy in a large urban city. This is important because in what follows we
present odds-ratios. Odds-ratios are informative, but it is important for the reader to know that
the baseline rate of force is substantially smaller in the PPCS.
Blacks are three times more likely to report use of force by police in the raw data. Hispanics
are 2.6 times more likely. Adding controls for demographic and encounter characteristics, civilian
behavior, and year fixed effects reduces the odds-ratio to roughly 2.7 for blacks and 1.7 for Hispanics.
Differences in quantitative magnitudes aside, the PPCS paints a similar portrait – large racial
differences in police use of force that cannot be explained using a large and varied set of controls.
One important difference between the PPCS and the Stop and Frisk data is in regards to racial
differences on the more extreme uses of non-lethal force: using pepper spray or striking with a
baton. Recall, in the Stop and Frisk data the odds ratios were relatively consistent as the intensity
of force increased. In the PPCS data, if anything, racial differences 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 1.867 (0.589) and the Hispanic coefficient is 1.228 (0.468), though because of the

20

rarity of these cases the coefficients are barely statistically significant at the 5% level.
Table 4 explores the heterogeneity in the data by estimating racial differences in police use
of force in the PPCS on various subsamples of the data: civilian income, gender, civilian, time of
contact, and officer race. 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 Cose (1993). Racial differences
in police of force does not seem to vary with civilian gender or officer race. Consistent with the
results in the Stop and Frisk data, the black coefficient is 3.17 (0.85) for interactions that occur
during the day and 1.68 (0.48) for interactions that occur at night. The p-value on the difference
is marginally significant.
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 different interactions with law enforcement – interactions that are consistent with, though definitely not proof of, some form of
discrimination. Including myriad controls designed to account for civilian demographics, encounter
characteristics, civilian behavior, eventual outcomes of the interaction and year reduces, but cannot
eliminate, racial differences in non-lethal use of force in either of the datasets analyzed.

IV. Estimating Racial Differences in Officer-Involved Shootings
We now focus on racial differences in officer-involved shootings. We begin with specifications most
comparable to those used to estimate racial differences in non-lethal force, using both data from
officer-involved shootings in Houston and data we coded from Houston arrest records that contains
interactions with police that might have resulted in the use of lethal force.26 Specifically, we
estimate the following empirical model:

1
shootingi,t “ Race1i α ` Xi,t
β ` νt ` i,t ,

26

Because of this select set of “0s” the non-black, non-Hispanic mean, displayed in column 1, is drastically larger
than a representative sample of the population – which would be approximately .0001%. 45.5 percent of whites in
our data were involved in an officer-involved shooting.

21

where shootingi,t is a dichotomous variable equal to one if a police officer discharged their weapon
at individual 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 5. As one moves down the table,
the set of coefficients steadily grows. As one moves across the columns of the table, the comparison
risk set changes.27 Presenting the results in this way is meant to underscore the robustness of the
results to the inclusion of richer sets of controls and to alternative interpretations of the risk sets.
Standard errors, which appear below each estimate, account for heteroskedasticity.
Given the stream of video “evidence”, which many take to be indicative of structural racism in
police departments across America, the ensuing and understandable outrage in black communities
across America, and the results from our previous analysis of non-lethal uses of force, the results
displayed in Table 5 are startling.
Blacks are 23.8 percent less likely to be shot by police, relative to whites. Hispanics are 8.5
percent less likely to be shot but the coefficient is statistically insignificant.
Rows (2) through (6) add various controls, identical to those in table 1D. Accounting for basic
suspect or officer demographics, does not significantly alter the raw racial differences. Including
encounter characteristics – which one can only accomplish by hand coding the narratives embedded in arrests reports – creates more parity between blacks and non-black non-Hispanic suspects,
rendering the coefficient closer to 1. Finally, when we include whether or not a suspect was found
with a weapon or year fixed effects, the coefficients still suggest that, if anything, officers are less
likely to shoot black suspects, ceteris paribus, though the racial differences are not significant.
Columns (4) and (5) of table 5 include 4504 incident reports from 2005-2015 for all arrests
during which an officer reported using his taser as a risk set, in addition to all OIS in Houston from
that time period. The empirical question here is whether or not there are racial differences in the
split-second decision as to whether to use lethal or non-lethal force through the decision to shoot
a pistol or taser.
Consistent with the previous results, the raw racial difference in the decision to employ lethal
27

Appendix Table 6 investigates the sensitivity of the main results to more alternative compositions of the risk

sets.

22

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 taser sample, table 5
shows that black civilians are 30.9 percent less likely to be shot with a pistol (rather than a taser)
relative to non-black suspects. Columns (6) and (7) pool the sample from hand coded arrest data
and taser data. Results remain qualitatively the same. Controlling for all characteristics from
incident reports, black suspects are 21.6 percent less likely to be shot than non-black suspects.
To be clear, the empirical thought experiment here is that a police officer arrives at a scene
and decides whether or not to use lethal 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 differences in whether or not thse police-civilian interactions occur at all.
Appendix Table 5 explores the sensitivity of the results for various subsamples of the data:
number of officers who respond to the scene, whether the suspect attacked an officer first, whether
the officer was on-duty, whether the unit that responded was majority black or Hispanic or majority
white or Asian, 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 Squares regressions.
None of the subsamples explored demonstrate much difference of note. We find no evidence
that racial differences in the use of lethal force varies in a statistically meaningful way between the
number of officers at an incident. We find no differences in the use of lethal force across different
call slips – the p-value for equality of race coefficient across different calls slips is 0.557 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. Subsampling on the
number and racial composition of the officer unit also shows no evidence of racial differences.
Another way to investigate the robustness of our coefficients is to analyze the odds ratios across
time. These data are displayed in figure 4. Racial differences in OIS between 2000 and 2015 are
remarkably constant. This interval 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
23

to be years in which police misconduct could more easily go unnoticed and for which the public
attention was relatively low. Thus, the disincentive to misreport was likely lower. After this period,
misreporting costs likely increased. Yet, as we see from figure 3, this does not seem to influence
racial differences in the use of lethal force.
Are there Racial Differences in the Timing of Lethal Force?
The above results, along with the results on use of force, are about racial differences on the
extensive margin: whether or not an officer uses a particular type of force or decides to use lethal
force on a suspect. Because of the richness of our officer-involved shooting database, we can also
investigate the intensive margin – whether there are racial differences in how quickly a police officer
shoots a suspect. In particular, given the narrative accounts, I create a dichotomous variable that
is equal to one if a police officer reports that 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 locations 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 6 presents a series of estimates of racial differences in the timing of police shootings using
the OIS data. The specifications estimated are of the form:

1
1
Shoot Firsti,c,t “ Race1i α ` Xi,t
β ` Zc,t
T ` νt ` ψc ` i,c,t ,

where Shoot Firsti,c,t is a measure of whether a police officer reports shooting individual i, in city c,
in year t, before being attacked. Standard errors, which appear below each estimate, are clustered
at the location level unless otherwise specified.
The results from these specifications are consistent with our previous results on the extensive
margin. Row (1) displays the results from the raw data. Blacks are 1.3% less likely to be shot first
by police. Hispanics are slightly more likely. Neither coefficient is statistically significant. Adding
suspect or officer demographics does not alter the results.28
Row (4) accounts for important context at the time of the shooting. For instance, whether
28

We also estimate the “intensity” of force used in officer-involved shootings by estimating racial differences in the
total number of bullets used in a given police shooting. The average number of bullets in officer-involved shootings
involving blacks is 0.256 (0.508) more relative to shootings that involve whites [not shown in tabular form].

24

the shooting happened during day time or night time and whether the suspect drew weapon or
attacked the officer. Including these variables decreases the black coefficient to 0.693 (0.096) which
is statistically significant. The Hispanic coefficient is similar in size but less precisely estimated.
Adding whether the suspect was eventually found to have a weapon and its type or including
location and year fixed effects only strengthens the results in the unexpected direction. Including
all controls available, officers report that they are 47.4% less likely to discharge their firearms
before being attacked if the suspect is black. The Hispanic coefficient is strikingly similar (43.6%
less likely).
Appendix Table 7 explores the heterogeneity in the data across various subsamples: number
of officers who arrive at a scene, whether or not officers report that the suspect clearly drew their
weapon or whether they “appeared” to draw their weapon, whether the officer was on-duty, the
call type, and the racial composition of the responding unit. The final panel provides results
disaggregated by location.
Estimated race coefficients across call types – whether officers were dispatched because of a
violent crime, robbery, auto crime, or other type of call – are statistically identical. This is particularly interesting in light of the potential selection into the sample of OIS cases discussed earlier.
Indeed, the majority of police shootings in our data occur during violent crimes or robberies and
there are no racial differences on these call types.
One of the more interesting subsamples is whether or not a suspect “appeared” to have a weapon
versus an officer indicating that 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) finds that police officers
detect degraded images of crime related objects faster when they are shown black faces first.
Yet our data from the field seem to reject this lab-based hypothesis, at least as regards officerinvolved shootings. The coefficient on black for the subsample who police report clearly drew their
weapon first is -0.105 (0.020). The same coefficient estimated on the set of interactions were police
assumed an individual had a weapon is -0.038 (0.033). The Hispanic coefficients are nearly identical.
More generally, the coefficients are uncommonly consistent across all subsamples of the data.
Of the 5 tests of equality performed in the table, not one is significant. We cannot detect racial
differences in officer-involved shootings on any dimension.
25

V. Interpretation
A number of stylized facts emerge from the analysis of the preceding sections. On non-lethal uses
of force, there are racial differences – sometimes quite large – in police use of force, even after
controlling for a large set of controls designed to account for important contextual and behavioral
factors at the time of the police-civilian interaction. As the intensity of use of force increases from
putting hands on a civilian to striking them with a baton, the overall probability of such an incident
occurring decreases but the racial difference remains roughly constant. On the most extreme uses
of force, however – officer-involved shootings with a Taser or lethal weapon – there are no racial
differences in either the raw data or when accounting for controls.
In this section, we explore the extent to which a model of police-civilian interaction that encompasses both information- and taste-based discrimination – can successfully 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 officers and a weakly larger population of civilians. Each
police officer is randomly matched with civilians from this population. Civilians belong to one of
two identifiable groups, B or W. Denote by λ the fraction of W’s in the population. Police officers
are assumed to be one of two types: “biased” or “unbiased.” Let δ P p0, 1q denote the fraction of
biased police officers.
Nature moves first and assigns a cost of compliance to each civilian and a type to each police
officer. Let c P rc, cs, represent the cost to a civilian of investing in compliance. An alternative way
to think about this assumption is that individuals contain inherent dangerousness and those who
are dangerous 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-compliant type with no in-between. Then, based on this
decision, nature distributes a signal θ P rθ, θs to police officers regarding whether or not a civilian
is likely to comply.29 Next, the police officer observes θ and decides whether or not to use force,
29

This model is a simplified version of a more general model in which individuals invest in a “compliance identity”

26

which we denote h P t0, 1u.30
The distribution of θ depends, in the same way for each race, on whether or not a civilian
has invested in compliance. This signal is meant to capture the important elements of initial
interactions between police and civilians; clothing, demeanor, attitude, posture, and so on. Let
F1 pθq [resp. F0 pθq] be the probability that the signal does not exceed θ, given that a civilian
has invested in compliance (resp. non-compliance) and let f1 pθq and f0 pθq be the related density
functions. Define µpθq ”

f0 pθq
f1 pθq

to be the likelihood ratio at θ. We assume that µpθq is non-increasing

on r0, 1s, which implies that F1 pθq ď F0 pθq for all θ. Thus, higher values of observed θ are more
likely if the civilian is compliant, and for a given prior, the posterior likelihood that a civilian will
be compliant is larger if his signal takes a higher value.
Payoffs
For the civilian, payoffs depend on whether 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 payoff of ´γ ´ c
if he invested in compliance and ´γ if not. If force is not used on the civilian, he receives a payoff
of ´c if he invests and the payoff is normalized 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 force on those that are compliant. In addition, we allow for “biased” police officers to
gain utility from using force on Bs.
Thus, for police officers, payoffs depend on their type, whether or not they use force, and
whether or not the civilian is compliant. We begin with unbiased officers. If force is used, the
officers payoff is ´K ´ φF if the civilian is compliant and χF ´ φF if the civilian is non-compliant.
If no force is used, the officer receives a payoff of 0 if the civilian is compliant and ´χN F if the
civilian is non-compliant. These payoffs are identical for biased officers when they interact with W
civilians.
When biased police officers interact with B civilians they derive psychic pleasure from using
force, independent of whether they are compliant or not. We represent this by, τ a positive term
ala Akerlof and Kranton (2000) and then, in any given interaction with police, decide whether to comply or escalate.
For those who have a compliance identity, there is an identity costs of escalation. This model is more intuitive, but
delivers the same basic results.
30
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 alter the key predictions of the model.

27

in the biased officer’s payoff when he uses 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, cs Ñ t0, 1u. Without loss of generality, the civilian’s
strategy can be represented by a cut-off point, c˚ , such that the civilian will invest in compliance
if and only if their cost is below c˚ . A strategy for the police officer is a decision of whether or not
Ś
Ś
to use force, conditional upon what he can observe, h : t0, τ u rB, W s rθ, θs Ñ t0, 1u.
Expected Payoffs
Let π P r0, 1s denote the officer’s prior belief that a civilian will be compliant. Expected payoffs
for the police officer are functions of her beliefs, her type, and the signal she receives. Given π and
observed signal θ, she formulates a posterior probability (using Bayes’ rule) that the civilian will
be compliant: Ψpπ, θq ”

πf1 pθq
πf1 pθq`p1´πqf0 pθq .

The expected payoff of using force for an unbiased police officer (and, equivalently, a biased
police officer when interacting with Ws) is:

Ψpπ, θqp´K ´ φF q ` p1 ´ Ψpπ, θqqpχF ´ φF q.

(2)

The expected payoff of using force for an biased officer interacting with Bs is:

Ψpπ, θqp´K ´ φF q ` p1 ´ Ψpπ, θqqpχF ´ φF q ` τ.

(3)

Relatedly, the expected payoffs of not using force, for both types of officers, can be written as:

´p1 ´ Ψpπ, θqqpχN F q.

(4)

Combining equation (2) and equation (4), and using a bit of algebra, an unbiased officer uses
force only if

˚
θ ď θub
” mintθ|Ψpπ, θqp´K ´ φF q ` p1 ´ Ψpπ, θqqpχF ` χN F ´ φF qu ą 0q

28

(5)

˚ , such that for any θ below this threshold
In words, equation (5) provides a threshold, θub

unbiased officers always use force. Similarly, using the corresponding expected payoffs for a biased
officer, one can derive θb˚ .
Now, consider the civilian’s expected payoff. W civilians receive F1 pθ˚ ub qp´γq ´ c if they invest
˚ qp´γq if they choose not to invest. When optimizing, a civilian will invest in compliance
and F0 pθub

if and only if the cost of compliance is less than the net benefit of compliance. In symbols, c ď c˚W ”
˚ q ´ F pθ ˚ qu γ. Similarly, Bs invest if c ď c˚ ” γ tδpF pθ ˚ q ´ F pθ ˚ qq ` p1 ´ δqpF pθ ˚ q ´ F pθ ˚ qqu.
tFnc pθub
c ub
nc ub
c ub
nc b
c b
B

Note – given we assume δ ą 0 – it follows that c˚B ă c˚W .
Definition 1 An equilibrium consists of a pair pθ˚ , π ˚ q such that each is a best response to the
other.

B. Understanding the Data Through the Lens of the Model
Assuming the distribution of costs (c) and the signal (θ) are independent of race, racial disparities
can be produced in this model in two (non-mutually exclusive) ways: different beliefs or different
preferences.31 To see this formally, suppose all racial differences were driven by information-based
discrimination and there was no taste-based component. In this case, equation (3) simplifies to
˚ q ´ F pθ ˚ qu γ ´ c.
(2) and both B and W individuals’ net benefit of investment becomes tFnc pθub
c ub

Thus, one needs differences in π to generate discriminatory equilibrium.
In contrast, one can also derive an equilibrium for cases in which we turn off the informationbased channel and only allow differences through preferences. In this case, police officers observe
investment decisions perfectly. When police officer bias is sufficiently large, any equilibrium will
contain discrimination against Bs.
Distinguishing between these two cases, empirically, is difficult with the available data. In
what follows, we attempt to understand whether the patterns in the data are best explained by an
information-based or taste-based approach to discrimination – recognizing that both channels may
be important.
Statistical Discrimination
31

It is also plausible that racial differences arise due to differences in costs of compliance (for instance, through
peer effects) or in the signal distributions. Incorporating these assumptions into the model is a trivial extension.

29

To better understand whether statistical discrimination might explain some of the patterns in
the data, we investigate two possibilities.32 First, we explore whether racial differences in mean
characteristics across police precincts predicts racial differences in use of force. The key – untestable
– assumption is police officer beliefs about the compliance of a civilian – π in our model – is partly
driven by local variation in variables such as education or income levels.33
Table 7 explores racial differences in any use of force – using the Stop 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 each of these variables, we take the difference between
the white population and black population and rank the precincts by this difference, individually.
We then divide the data into terciles. The first tercile is always the one in which racial differences
between our proxies are the lowest. The third tercile represents precincts in which there are
relatively large racial differences on a given proxy.
Statistically larger racial differences in use of force for the third tercile (first tercile for unemployment), relative to tercile one or two (tercile two or three for unemployment), would be evidence
consistent with statistical discrimination. This would imply that racial differences in use of force
are correlated with racial differences in proxies for dangerousness. Table 7 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.

34

A second prediction of the statistical discrimination model that is testable in our data is how
racial differences in use of force change as signals about civilian compliance become more clear.35
32

Appendix C considers the extent to which discrimination based on categories can explain the results (Fryer and
Jackson 2008). We argue categorical discrimination is inconsistent with the fact that black officers and white officers
interact similarly with black civilians. See Appendix Table 11.
33
Ideally, one might use variables more directly correlated with dangerousness such as racial differences in crime
rates, by precincts. Despite repeated formal Freedom of Information Law requests, the New York Police Department
refused to supply these data.
34
We performed a similar exercise exploiting the variance across space in proxies for dangerousness (see Appendix
Tables 10A-10C for results). We also investigated whether more weight in the bottom quintiles of the distribution of
our proxies predicted 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 statistical discrimination on any of the dimensions tested.
35
Another potential test of statistical discrimination was pioneered by Altonji and Pierret (2001). They investigate
racial differences in wage trajectories, conditional upon being hired. To the extent that statistical discrimination drives
wage differences between racial groups, one would expect the wage trajectory for blacks to be higher than whites
– as employers learn. We performed a similar, though imperfect, test 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

30

If statistical discrimination is the key driver of racial differences in use of force, the model predicts
that as θ becomes perfectly predictive of compliance behavior, there will be no racial differences.
We test this using officer recorded data on the compliance behavior of civilians.
The NYC Stop and Frisk data contains officer recorded information on the compliance of civilians during a stop. These variables include: whether the civilians refused to comply with officers’
directions, whether the civilian verbally threatened an officer, whether they were evasive in their
response to questioning or whether they changed direction at the sight of an officer. If statistical
discrimination is a key driver of racial differences, on the set of interactions in which officers report
perfect compliance (and, to capture potentially important unobservables – the civilian was not
arrested or was not guilty of carrying weapons or contraband) racial differences should be close
to zero. And, on the set of interactions in which civilians engage in questionable behavior, racial
differences should be statistically larger.
Figure 5 shows that even when we take perfectly compliant individuals and control for civilian,
officer, encounter and location variables, black civilians are 21.1 (0.041) percent more likely to
have any force used against them compared to white civilians with 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 differences in use of force. Though our tests have quite limited power, we find no evidence
that statistical discrimination plays an important role.
Taste-Based Models of Discrimination
Similar to any large organization, police departments surely have individuals who hold biased
views toward minority citizens and those views may manifest themselves in biased treatment of
individuals based solely on their race. Yet, as Becker (1957) argued, individual discrimination does
not necessarily equate to market (or systemic) discrimination.
Taste-based discrimination is consistent with the data from the direct regression approach on
non-lethal uses of force if, among those who discriminate, the preference for discrimination is
greater than the expected costs of wrongly using force. In other words, the expected price of
force, blacks and Hispanics are less likely to be arrested conditional upon force being used. As the intensity of force
increases, if anything, minorities are more likely to be arrested conditional upon force being used.

31

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 consistent with the lack
of racial differences in officer-involved shooting if there is a discrete increase in the costs of being
deemed a discriminator, relative to the costs incurred with non-lethal uses of force.36
Below, we explore the extent to which two additional implications of the taste-based channel
of our model are borne out in the data. The first uses the predictions on average versus marginal
returns of compliant behavior. The second is inspired by the seminal work in Knowles, Persico,
and Todd (2001) and Anwar and Fang (2006).
In any equilibrium model 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 returns to compliance may be different across races. We can test this a
bit more directly. One issue in this setting, which does not arise in labor markets, is it’s not obvious
how to aggregate non-compliance into a monotonic index. It may be considered more dangerous
from a police officer perspective that a civilian shouted verbal threats than refusing to comply with
an officer’s directions and being evasive regarding questioning. A simple aggregation of the number
of non-compliant activities is likely misleading.
To sidestep this important potential issue of aggregating non-compliance, 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 regression estimated, then, is whether or not an officer uses
any force – accounting for our full set of controls – and including our measure of non-compliance
interacted with race. Racial differences in the marginal return to non-compliance behavior would
manifest itself in statistically different coefficients on the compliance variable. For a given race,
adding both the race coefficient and the interaction term with compliance 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 differences
in police use of force being driven by taste-based discrimination. Black civilians have statistically
36
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 incident is
complete This is a potentially high cost relative to 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.”

32

similar marginal returns to compliance as white civilians. In other words, the probability of force
being used as θ increases is statistically identical between blacks and whites. Yet, black civilians
always have a higher likelihood of force being used on them compared to white civilians, for all
θ. Further, the net benefit of investment in compliance is lower for blacks relative to whites. This
is precisely what the model predicts if racial animus is an important factor in explaining racial
differences in use 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 described in the previous sections. KPT tests for racist preferences by looking
at officers’ success rate of searches across races. Their model assumes that police maximize the
number of successful searches net of the cost of searching motorists. If racial prejudice exists then
the cost of searching drivers will be different across races. This, in turn, implies that the rate of
successful searches will be different across races.
Anwar and Fang (2001) 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 particular race, across officer races. Under the null hypothesis that none of
the racial groups of officers has racial prejudice, it must be true that the ranking of search rates
for white civilians across officer races is the same as the ranking of search rates for black civilians
across officer races.
We adopt this approach by investigating whether or not a suspect was eventually found to have
a weapon during the interaction with police. In other words, we calculate the probability, for each
race, that a suspect has a weapon conditional upon being involved in an officer-involved shooting.
Given the level of detail in our data, one can perform this test for 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 discrimination in officer-involved shootings. 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 different across suspect races. Second, according to Anwar
and Fang, the null could be rejected if the ranking of “being armed” rates for black suspects across
33

officer races is different from the ranking of being armed rates for white suspects.
Consistent with our direct 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 8. For white officers, the probability that a white suspect who is involved in
officer-involved shooting has a weapon is 85.1% percent. The equivalent probability for blacks is
81%. A difference of 4%, which is not statistically significant. For black officers, the probability
that a white suspect who is involved in an officer-involved shooting has a weapon is surprisingly
lower, 62.5%. The equivalent probability for black suspects is 74%. The only statistically significant
differences by race demonstrate that black officers are more likely to shoot unarmed whites, relative
to white officers.
We perform a similar exercise for non-lethal uses of force, recognizing that as the use of force
gets less extreme the application of that force and whether or not a suspect has a weapon is
more tenuous. For instance, investigating racial differences in whether or not officers use “hands”
on civilians who are unarmed is not a valid test of discrimination as there are myriad legitimate
reasons for police officers to place hands on civilians who are unarmed. Yet, racial differences in
the use of a baton – after accounting for suspect behavior – seem less justifiable. Unfortunately,
where to draw the line on the 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, it does not
seem appropriate.
Table 9 presents these results. Each row is a different 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.
Column (4) displays the number of observations which range from over one million for the use of
hands to 1,745 for the use of pepper spray or baton.
Blacks are 1.3 (0.4) percentage points less likely to have a weapon, conditional upon a police
officer using any force. Hispanics are 0.8 (0.3) less likely to have a weapon. Both are statistically
significant. Interestingly, on all other non-lethal uses of force, the probability that a weapon is
found – conditional upon force being used – is statistically identical across races. Taken at face
value, these data are consistent with discrimination against minorities on the lowest level uses of
non-lethal force.
34

VI. Conclusion
The issue 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 indifference. Yet, very little data
exists to understand whether racial disparities in police use of force exist or might be explained
by situational factors inherent in the complexity of police-civilian interactions. Beyond the lack
of data, the analysis of police behavior is fraught with difficulty including, but not limited to, the
reliability of the data that does exist and the fact that one cannot randomly assign race.
With these caveats in mind, this paper takes first steps into the treacherous terrain of understanding the nature and extent of racial differences in police use of force. On non-lethal uses of
force, there are racial differences – sometimes quite large – in police use of force, even after accounting for a large set of controls designed to account for important contextual and behavioral
factors at the time of the police-civilian interaction. Interestingly, as use of force increases from
putting hands on a civilian to striking them with a baton, the overall probability of such an incident
occurring decreases dramatically but the racial difference remains roughly constant. Even when
officers report civilians have been compliant and no arrest was made, blacks are 21.3 (0.04) percent
more likely to endure some form of force. Yet, on the most extreme use of force – officer-involved
shootings – we are unable to detect any racial differences in either the raw data or when accounting
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 differences in the average returns to compliant
behaviors, the results of our tests of discrimination 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 intensities
of force – even after accounting for a rich set of controls. In the end, however, without randomly
assigning race, we have no definitive proof of discrimination. 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 bias, our
results point to another simple policy experiment: increase the expected price of excessive force

35

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 these tactics.
The appealing feature of this type of policy experiment is that it does not require officers to
change their behavior in extremely high-stakes environments. Many arguments about police reform
fall victim to the “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 differences 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 police and other external forces.
Much more troubling, due to their frequency and potential impact on minority belief formation,
is the possibility that racial differences in police use of non-lethal force have spillovers on myriad
dimensions of racial inequality. If, for instance, blacks use their lived experience with police as
evidence that the world is discriminatory, then it is easy to understand 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.

36

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38

Table 1A
Summary Statistics for New York City Stop, Question and Frisk, 2003 - 2013
Full Sample
(1)

White
(2)

Black
(3)

Hispanic
(4)

p-val
(2) = (3)

p-val
(2) = (4)

0.10
0.58
0.25
0.03
0.04
28.00
0.93

1.00
0.00
0.00
0.00
0.00
29.25
0.90

0.00
1.00
0.00
0.00
0.00
27.96
0.93

0.00
0.00
1.00
0.00
0.00
27.57
0.93

.
.
.
.
.
0.000
0.000

.
.
.
.
.
0.000
0.000

0.23
0.36
0.56
0.37
0.72
0.53
0.43
0.02
0.02
0.23
0.03

0.16
0.39
0.52
0.36
0.64
0.63
0.34
0.01
0.01
0.30
0.04

0.26
0.35
0.57
0.38
0.73
0.51
0.45
0.03
0.02
0.21
0.03

0.21
0.36
0.55
0.36
0.72
0.54
0.43
0.02
0.01
0.26
0.03

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.931
0.000
0.000
0.000
0.000
0.144
0.000
0.000

0.03
0.17
0.29
0.17
0.04
0.09
0.44
0.08
0.09
0.21

0.04
0.19
0.35
0.20
0.03
0.09
0.37
0.06
0.04
0.21

0.02
0.17
0.27
0.16
0.05
0.10
0.46
0.08
0.10
0.21

0.03
0.17
0.30
0.18
0.04
0.09
0.43
0.09
0.08
0.20

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.162

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.55
0.08
0.06
0.06
0.03

0.43
0.08
0.06
0.06
0.04

0.57
0.08
0.06
0.06
0.03

0.56
0.09
0.06
0.06
0.03

0.000
0.022
0.000
0.010
0.000

0.000
0.000
0.000
0.000
0.000

0.19
0.03
0.04

0.13
0.03
0.04

0.19
0.03
0.04

0.20
0.03
0.03

0.000
0.000
0.085

0.000
0.000
0.019

Panel A: Baseline Characteristics
White
Black
Hispanic
Asian
Other race
Age
Male
Panel B: Encounter Characteristics
Indoors
Daytime
High-crime Area
High-crime Time
Police in Uniform
Photo ID
Verbal ID
Refused ID
Other ID
With Others Who Were Stopped
Wpn or Contraband Fnd
Panel C: Civilian Behavior
Carrying Suspicious Obj
Fit Relevant Descr
Preparing for Crm
Lookout for Crm
Dressed in Crm Attire
Appearance of Drug Tran
Suspicious Mvmnts
Engaging in Vlnt Crm
Concealing Suspicious Obj
Other Suspicious Bhvr
Panel D: Alternative Outcomes
Frisked
Searched
Arrested
Summonsed
Wpn or Contraband Fnd
Panel E: Use of Force
Hands
Push to Wall
Handcuffs

Draw Weapon
Push to Ground
Point Weapon
Pepper Spray/Baton

0.00
0.01
0.00
0.00

0.00
0.01
0.00
0.00

0.00
0.01
0.00
0.00

0.00
0.01
0.00
0.00

0.000
0.000
0.000
0.005

0.077
0.000
0.027
0.385

0.00
0.01
0.03
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.01
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.01
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

.
0.000
0.000
0.000
0.503
.
.
0.132
0.196
0.000
0.164
.
.
.
.
.
.
.
.
.
.

.
0.000
0.000
0.000
0.093
.
.
0.314
0.093
0.000
0.007
.
.
.
.
.
.
.
.
.
.

4,982,426

492,391

2,885,857

1,214,961

Panel F: Missing Variables
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing

Race
Age
Gender
Indoors
Daytime
High-crm Area
High-crm Time
Police Uniform
ID
Others Stopped
Wpn or Contra Fnd
Carry Susp Obj
Relevant Descr
Preparing Crm
Lookout Crm
Crm Attire
Drug Tran
Suspicious Mvmnts
Vlnt Crm
Conceal Susp Obj
Other Susp Bhvr

Observations

Notes: This table reports summary statistics. The sample consists of all NYC stop and frisks from 2003-2013. The first column
includes the entire sample. The second column includes white civilians only. The third column includes black civilians only.
The fourth column includes hispanic civilians only. The fifth column reports p-values for a ttest to see whether the mean for
white civilians is statistically similar to the mean for black civilians. The sixth column reports p-values for a ttest to see whether
the mean for white civilians is statistically similar to the mean for hispanic civilians.

Table 1B
Summary Statistics for Police-Public Contact Survey
Full Sample
(1)

White
(2)

Black
(3)

Hispanic
(4)

p-val
(2) = (3)

p-val
(2) = (4)

0.72
0.11
0.05
0.12
0.47
0.53
45.36
0.61
1.95
1.47

1.00
0.00
0.00
0.00
0.48
0.52
47.19
0.61
2.03
1.31

0.00
1.00
0.00
0.00
0.43
0.57
42.76
0.59
1.64
1.89

0.00
0.00
0.00
1.00
0.49
0.51
38.55
0.63
1.73
1.86

.
.
.
.
0.000
0.000
0.000
0.000
0.000
0.000

.
.
.
.
0.000
0.000
0.000
0.000
0.000
0.000

0.00
0.00
0.00
0.00
0.06
0.02
0.00
0.00

0.00
0.00
0.00
0.00
0.05
0.02
0.00
0.00

0.01
0.00
0.00
0.00
0.07
0.02
0.02
0.00

0.01
0.00
0.00
0.00
0.06
0.02
0.01
0.00

0.013
0.047
0.224
0.057
0.099
0.000
0.000
0.437

0.013
0.364
0.225
0.000
0.697
0.366
0.166
0.436

0.19
0.49
0.32
0.68
0.32
0.09
0.86
0.08
0.05

0.18
0.49
0.32
0.69
0.31
0.06
0.88
0.07
0.04

0.19
0.50
0.31
0.62
0.38
0.11
0.78
0.20
0.06

0.22
0.50
0.28
0.66
0.34
0.25
0.83
0.07
0.09

0.000
0.655
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.349
0.000
0.007
0.007
0.000
0.000
0.201
0.000

0.15
0.64
0.05
0.03
0.17

0.16
0.61
0.04
0.02
0.19

0.12
0.69
0.10
0.05
0.11

0.13
0.66
0.09
0.04
0.16

0.334
0.038
0.000
0.000
0.005

0.483
0.279
0.000
0.000
0.327

0.03
0.01
0.00
0.00

0.02
0.01
0.00
0.00

0.06
0.02
0.00
0.01

0.04
0.01
0.00
0.00

0.000
0.000
0.006
0.000

0.000
0.000
0.079
0.000

Panel A: Civilian Demographics
White
Black
Other Race
Hispanic
Male
Female
Age
Employed last week or not
Income
Population size of Suspect’s Address
Panel B: Civilian Behavior
Disobeyed
Tried to Get Away
Hit Officer
Resisted
Complained
Argued
Threatened Officer
Used Physical Force
Panel C: Contact and Officer Characteristics
Incident type: Street Stop
Incident type: Traffic Stop
Incident type: Other
Time of Contact was Day
Time of Contact was Night
Hispanic
White
Black
Other Race
Panel D: Alternative Outcomes
Civilian
Civilian
Civilian
Civilian
Civilian

injured
perceived excessive force
searched
arrested
guilty of carrying drugs/alcohol/weapon

Panel E: Use of Force
Any use of force
Grab
Kick
Point Gun

Handcuff
Pepper spray/Stungun

0.03
0.00

0.02
0.00

0.06
0.00

0.04
0.00

0.000
0.051

0.000
0.037

0.00
0.00
0.14
0.14
0.28
0.95
0.95
0.95
0.95
0.99
0.95
0.99
0.95
0.42
0.96
0.99
0.96
0.96
0.96

0.00
0.00
0.13
0.14
0.28
0.94
0.94
0.94
0.94
0.99
0.94
0.99
0.94
0.42
0.96
0.99
0.95
0.95
0.95

0.00
0.00
0.16
0.14
0.29
0.95
0.95
0.95
0.95
0.99
0.95
0.99
0.95
0.43
0.96
0.99
0.96
0.96
0.96

0.00
0.00
0.15
0.14
0.29
0.96
0.96
0.96
0.96
0.99
0.96
0.99
0.96
0.43
0.96
0.99
0.96
0.96
0.96

.
.
0.000
0.509
0.000
0.000
0.000
0.000
0.000
0.554
0.000
0.518
0.000
0.000
0.000
0.143
0.000
0.000
0.000

.
.
0.000
0.165
0.000
0.000
0.000
0.000
0.000
0.721
0.000
0.803
0.000
0.000
0.000
0.806
0.000
0.000
0.000

566,674

404,380

62,277

67,660

Panel F: Missing Variables
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing

Gender
Age
Employed last week or not
Income
Population size of Suspect’s Address
Disobeyed
Tried to Get Away
Hit Officer
Resisted
Complained
Argued
Threatened
Used Physical Force
Incident type
Time of Contact
Officer Hispanic
Officer White
Officer Black
Officer Other Race

Observations

Notes: This table reports summary statistics. The sample consists of survey respondents of the Police Public Contact Survey
from 1996 to 2011. The first column includes the entire sample. The second column includes white civilians only. The third
column includes black civilians only. The fourth column includes hispanic civilians only. The fifth column reports p-values for
a ttest to see whether the mean for white civilians is statistically similar to the mean for black civilians. The sixth column
reports p-values for a ttest to see whether the mean for white civilians is statistically similar to the mean for hispanic civilians.

Table 1C
Summary Statistics for Officer Involved Shootings
Full Sample
(1)

Houston
OIS Taser
(2)
(3)

Austin +
Dallas
(4)

Florida

Los Angeles

(5)

(6)

Panel A: Suspect Demographics
Black
Hispanic
Non-Black, Non-Hisp
Male
Age

0.46
0.30
0.24
0.96
30.77

0.52
0.33
0.14
0.96
28.86

0.63
0.03
0.33
0.94
31.39

0.46
0.30
0.23
0.97
32.90

0.47
0.10
0.43
0.97
33.24

0.25
0.60
0.15
0.97
30.56

0.51
0.08
0.15
0.21
0.06

0.52
0.08
0.11
0.24
0.05

.
.
.
.
.

0.52
0.07
0.17
0.18
0.06

0.45
0.07
0.24
0.17
0.06

0.54
0.09
0.08
0.25
0.03

0.51
0.09
0.27
0.03
0.09
0.06
0.86
0.29
10.13

0.32
0.14
0.40
0.06
0.08
0.06
0.75
0.22
10.21

0.42
0.15
0.22
0.03
0.18
0.13
.
0.37
9.05

0.53
0.14
0.18
0.04
0.11
0.06
0.90
0.28
8.41

0.80
0.05
0.07
0.01
0.07
0.05
0.94
0.33
9.93

0.28
0.03
0.52
0.03
0.14
0.10
0.95
0.41
12.70

0.20
0.29
0.18
0.04
0.05
0.07
0.06
0.03
0.09

0.26
0.25
0.18
0.07
0.05
0.05
0.05
0.02
0.08

0.07
0.15
0.08
0.00
0.00
0.05
0.05
0.07
0.53

0.23
0.33
0.09
0.02
0.05
0.06
0.07
0.03
0.11

0.15
0.29
0.22
0.01
0.08
0.06
0.06
0.04
0.07

0.08
0.34
0.20
0.04
0.03
0.12
0.04
0.02
0.11

0.37
0.80

0.35
0.79

0.38
.

0.38
0.79

0.43
0.86

0.39
0.75

0.05
0.15

0.00
0.00

.
.

0.25
0.75

0.00
0.00

0.00
0.00

Panel B: Suspect Weapon
Firearm
Sharp Object
Vehicle
None
Other Weapon
Panel C: Officer Characteristics
Officer Unit Majority White
Officer Unit Majority Black
Officer Unit Majority Hisp
Officer Unit Majority Asian/Other
Officer Unit Split Race
Female Officers in Unit
Officer On-duty
Two+ Officers on Scene
Avg Officer Tenure
Panel D: Officer Response Reason
Robbery
Violent Disturbance
Traffic
Personal Attack
Warrant
Suspicious Persons
Narcotics
Suicide
Other Response Reason
Panel E: Other Encounter Characteristics
Daytime
Suspect Attacked or Drew Weapon
Panel F: Location
Austin
Dallas

Houston
Jacksonville
Palm Beach County
Lee County
Brevard County
Pinellas County
Orange County
LA County

0.38
0.03
0.06
0.03
0.03
0.03
0.09
0.15

1.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

1.00
.
.
.
.
.
.
.

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.00
0.11
0.23
0.10
0.09
0.11
0.35
0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.00

0.02
0.02
0.23
0.05
0.16
0.06
0.01
0.03
0.20
0.01
0.36
0.00
0.04

0.04
0.02
0.08
0.03
0.38
0.12
0.00
0.06
0.37
0.00
0.01
0.00
0.03

0.38
0.38
0.38
1.00
0.00
0.00
1.00
1.00
0.00
0.00
0.00
1.00
1.00

0.00
0.00
0.75
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.75
0.00
0.01

0.02
0.01
0.13
0.07
0.06
0.04
0.02
0.03
0.20
0.00
0.75
0.00
0.08

0.00
0.05
0.08
0.08
0.00
0.00
0.06
0.00
0.02
0.07
0.00
0.00
0.00

1,332

507

4,504

269

362

194

Panel G: Missing Variables
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing

Race
Sex
Age
Weapon
Officer Race
Officer Sex
Officer Duty
Num Officers
Officer Tenure
Response Reason
Time of Day
Suspect Behavior
Injury Status

Observations

Notes: This table reports summary statistics. The sample consists of – (1) All officer involved shootings (OIS) between 2000 and
2015 (though exact time frame varies by location) from Austin, Dallas, six large Florida counties, Houston, and Los Angeles,
and (2) Arrests in Houston from 2005 to 2015 during which an officer reported using his or her charged electronic device (taser).
The first column includes the entire OIS sample. The second column includes OIS from Houston only. The third column
includes arrests from Houston where a taser was discharged. The fourth column includes OIS from Austina and Dallas. The
fifth column includes OIS from all Florida counties. The sixth column includes OIS from Los Angeles county.

Table 1D
Summary Statistics for Houston Police Department Arrests Data
Full Sample

Black

Hispanic

p-val

p-val

(1)

Non-Black/
Non-Hispanic
(2)

(3)

(4)

(2) = (3)

(2) = (4)

0.58
0.30
0.12
0.82
26.84

0.00
0.00
1.00
0.79
32.37

1.00
0.00
0.00
0.83
26.85

0.00
1.00
0.00
0.82
24.64

.
.
.
0.325
0.000

.
.
.
0.478
0.000

0.03
0.01
0.00
0.95
0.01

0.04
0.01
0.00
0.94
0.01

0.03
0.02
0.00
0.93
0.01

0.01
0.00
0.00
0.97
0.00

0.880
0.716
0.647
0.855
0.965

0.226
0.488
0.534
0.190
0.488

0.42
0.16
0.19
0.04
0.18
0.10
0.87
0.66
7.62

0.51
0.03
0.13
0.11
0.22
0.14
0.86
0.63
9.19

0.43
0.20
0.17
0.01
0.19
0.10
0.84
0.67
7.20

0.38
0.15
0.27
0.06
0.14
0.08
0.92
0.66
7.44

0.196
0.000
0.460
0.000
0.504
0.246
0.781
0.483
0.006

0.044
0.005
0.013
0.205
0.101
0.171
0.093
0.620
0.035

0.06
0.21
0.16
0.01
0.02
0.25
0.07
0.01
0.22

0.04
0.22
0.14
0.01
0.02
0.24
0.04
0.00
0.29

0.06
0.19
0.12
0.00
0.03
0.30
0.10
0.00
0.19

0.07
0.26
0.23
0.01
0.01
0.16
0.03
0.01
0.23

0.439
0.524
0.617
0.455
0.867
0.255
0.057
0.650
0.046

0.327
0.460
0.121
0.838
0.327
0.104
0.721
0.279
0.291

0.48
0.56

0.47
0.67

0.53
0.50

0.40
0.61

0.427
0.006

0.399
0.339

0.32
0.31

0.00
0.00

0.00
0.00

0.00
0.00

.
.

.
.

Panel A: Suspect Demographics
Black
Hispanic
Non-black/non-hispanic
Male
Age
Panel B: Suspect Weapon
Firearm
Sharp Object
Vehicle
None
Other Weapon
Panel C: Officer Characteristics
Officer Unit Majority White
Officer Unit Majority Black
Officer Unit Majority Hisp
Officer Unit Majority Asian/Other
Officer Unit Split Race
Female Officers in Unit
Officer On-duty
Two+ Officers on Scene
Avg Officer Tenure
Panel D: Officer Response Reason
Robbery
Violent Disturbance
Traffic
Personal Attack
Warrant
Suspicious Persons
Narcotics
Suicide
Other Response Reason
Panel E: Other Encounter Characteristics
Daytime
Suspect Attacked or Drew Weapon
Panel F: Missing Variables
Missing Race
Missing Sex

Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing
Missing

Age
Weapon
Officer Race
Officer Sex
Officer Duty
Num Officers
Officer Tenure
Response Reason
Time of Day
Suspect Behavior

Observations

0.33
0.31
0.35
0.34
0.30
0.30
0.36
0.30
0.63
0.31

0.02
0.02
0.10
0.06
0.01
0.01
0.07
0.01
0.39
0.04

0.01
0.03
0.08
0.06
0.00
0.00
0.09
0.00
0.47
0.02

0.03
0.01
0.07
0.06
0.00
0.00
0.08
0.00
0.46
0.02

1,024

84

402

213

0.562
0.855
0.752
0.927
0.029
0.029
0.640
0.029
0.211
0.475

0.835
0.333
0.473
0.916
0.111
0.111
0.711
0.111
0.295
0.559

Notes: This table reports summary statistics. The sample consists of a random draw of arrests in Houston 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. The first column includes the entire sample. The second column includes nonblack/non-hispanic civilians only. The third column includes black civilians only. The fourth column includes hispanic civilians
only. The fifth column reports p-values for a ttest to see whether the mean for non-black/non-hispanic civilians is statistically
similar to the mean for black civilians. The sixth column reports p-values for a ttest to see whether the mean for non-black/nonhispanic civilians is statistically similar to the mean for hispanic civilians.

1.513∗∗∗
(0.136)
1.120∗∗∗
(0.026)

1.456∗∗∗
(0.128)
1.173∗∗∗
(0.034)

+ Civilian Behavior

+ Fixed Effects
0.951
(0.033)

1.049
(0.124)

1.059
(0.133)

1.010
(0.122)

1.057∗∗
(0.028)

1.368∗∗∗
(0.107)

1.452∗∗∗
(0.121)

1.346∗∗∗
(0.114)

Notes: This table reports odds ratios by running logistic regressions. The sample 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) through (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 or
during 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. Each row includes missings in all
variables. Standard errors clustered at the precinct level are reported in parentheses.

4,927,467

1.641∗∗∗
(0.157)

1.655∗∗∗
(0.155)

+ Encounter Characteristics

Observations

1.517∗∗∗
(0.146)

1.480∗∗∗
(0.146)

+ Baseline Characteristics

Table 2A
Racial Differences in Non-Lethal Use of Force, NYC Stop Question and Frisk,Any Use of Force
White Mean
Black
Hispanic Asian Other Race
(1)
(2)
(3)
(4)
(5)
No Controls
0.153
1.534∗∗∗ 1.582∗∗∗
1.044
1.392∗∗∗
(0.144)
(0.149)
(0.119)
(0.121)

1.763∗∗∗
(0.221)
1.747∗∗∗
(0.226)

2.653∗∗∗
(0.314)
2.697∗∗∗
(0.321)

+ Civilian Behavior

+ Year

0.755
(0.197)

0.758
(0.195)

0.794
(0.198)

0.765
(0.192)

Notes: This table reports odds ratios by running logistic regressions. The sample 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 sixth column gives the unconditional average of
contacts that reported any force being used by white civilians. Columns (1) - (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 dummies.
The second row adds civilian gender, work, income, population size of civilian’s address and a quadratic in age. The third row adds
controls for contact time, contact type and officer race. The fourth row adds a civilian behavior dummy. The fifth row adds a control for
year. Each row includes missing in all variables. Robust standard errors are reported in parentheses.

48,498

1.616∗∗∗
(0.194)

2.582∗∗∗
(0.286)

+ Encounter Characteristics

Observations

1.633∗∗∗
(0.195)

2.609∗∗∗
(0.283)

+ Baseline Characteristics

Table 2B
Racial Differences in Non-Lethal Use of Force, Police Public Contact Survey, Any Use of Force
White Mean
Black
Hispanic Other Race
(1)
(2)
(3)
(4)
No Controls
0.008
3.335∗∗∗ 2.584∗∗∗
1.047
(0.349)
(0.299)
(0.262)

Full Sample

Table 3
Analysis of Subsamples, Any Use of Force, NYC Stop Question and Frisk
White Mean
Coefficient on Black
Coefficient on Hispanic
0.153
1.173∗∗∗
1.120∗∗∗

Panel A: Crime Rate in Area
High Crime

0.143

Low Crime

0.163

p-value
Panel B: Time of Day
Day

0.126

Night

0.170

p-value
Panel C: Officer in Uniform
Uniformed Officer

0.132

Non-Uniformed Officer

0.189

p-value
Panel D: Location
Indoors

0.144

Outdoors

0.154

p-value
Panel E: Civilian Gender
Male

0.160

Female

0.094

p-value
Panel F: Eventual Outcomes
Frisk

0.311

Search

0.411

Arrest

0.327

Summons

0.195

Weapon/Contraband found

0.359

p-value

1.165∗∗∗
(0.035)
1.196∗∗∗
(0.039)

1.115∗∗∗
(0.027)
1.136∗∗∗
(0.029)

0.260

0.321

1.255∗∗∗
(0.035)
1.136∗∗∗
(0.039)

1.162∗∗∗
(0.026)
1.099∗∗∗
(0.029)

0.001

0.020

1.176∗∗∗
(0.047)
1.193∗∗∗
(0.032)

1.124∗∗∗
(0.035)
1.121∗∗∗
(0.023)

0.759

0.923

1.125∗∗∗
(0.044)
1.184∗∗∗
(0.031)

1.092∗∗∗
(0.033)
1.125∗∗∗
(0.025)

0.101

0.252

1.170∗∗∗
(0.034)
1.224∗∗∗
(0.052)

1.120∗∗∗
(0.026)
1.103∗∗∗
(0.040)

0.136

0.614

1.031
(0.024)
1.054
(0.037)
1.073∗∗
(0.034)
1.150∗∗∗
(0.044)
1.111∗∗∗
(0.025)

1.020
(0.021)
1.039
(0.030)
1.038
(0.025)
1.064∗
(0.035)
1.059∗∗∗
(0.024)

0.003

0.394

Observations
4,927,467

2,750,262
2,177,205

1,783,796
3,143,671

3,546,056
1,381,411

1,129,443
3,798,024

4,446,921
480,546

2,699,613
409,255
291,109
304,580
136,894

Notes: This table reports odds ratios by running 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 the 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 or during 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 effects were included in all regressions. Standard errors clustered at the precinct level are reported in parentheses.

Full Sample

Table 4
Analysis of Subsamples, Any Use of Force, Police Public Contact Survey
White Mean
Coefficient on Black
Coefficient on Hispanic
0.008
2.697∗∗∗
1.747∗∗∗

Panel A: Civilian Income
0 < 20, 000

0.012

20, 000 < 50, 000

0.010

50, 000+

0.004

p-value
Panel B: Civilian Gender
Male

0.013

Female

0.004

p-value
Panel C: Officer Race
Black/Hispanic

0.011

White

0.008

p-value
Panel D: Time of Day
Day

0.004

Night

0.012

p-value

2.942∗∗∗
(0.532)
1.983∗∗∗
(0.515)
3.989∗∗∗
(1.286)

1.639∗∗
(0.332)
1.779∗∗
(0.411)
1.874∗
(0.708)

0.218

0.937

2.719∗∗∗
(0.373)
2.599∗∗∗
(0.613)

1.815∗∗∗
(0.259)
1.488
(0.453)

0.869

0.555

2.646∗∗
(1.212)
2.790∗∗∗
(0.565)

3.886∗∗∗
(2.040)
1.743∗∗
(0.419)

0.916

0.165

3.169∗∗∗
(0.851)
1.678∗
(0.476)

2.178∗∗∗
(0.598)
2.273∗∗∗
(0.591)

0.104

0.910

Observations
48,498

11,881
11,115
15,849

25,194
23,304

2,272
20,711

16,313
7,656

Notes: This table reports odds ratios by running logistic regressions. The sample consists of all Police Public Contact Survey respondents between
1996 to 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 the indicated subgroups. 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 and reported in parentheses.

1.105
(0.366)
0.973
(0.428)
0.924
(0.417)

+ Encounter Characteristics

+ Suspect Weapon

+ Year

1.256
(0.595)

1.365
(0.600)

0.990
(0.344)

1.113
(0.294)

0.967
(0.176)

5,011

6,035

0.784∗
(0.105)

0.691∗∗
(0.099)

0.782∗
(0.105)

0.686∗∗∗
(0.098)

−
(-)

0.746∗∗
(0.087)

0.728∗∗
(0.094)

−
(-)

0.678∗∗∗
(0.067)

(7)
0.666∗∗∗
(0.065)

Black

0.648∗∗∗
(0.066)

Non-Black
Mean
(6)
0.150

Full Sample
W/O Narratives

Notes: This table reports odds ratios by running 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 omiited race 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 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)-(3). It adds year as a categorical variable for columns (4)-(7). 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 regressions, missing indicator for response reason was removed for the same reason. Standard errors are robust
and are reported in parentheses.

1,531

0.779
(0.191)

+ Officer Demographics

Observations

0.782
(0.150)

+ Suspect Demographics

No Controls

Table 5
Racial Differences in Lethal Use of Force
Extensive Margin, Officer Involved Shootings
Approx OIS
Taser
With Narratives
W/O Narratives
Non-Black/
Non-Hispanic Black Hispanic
Non-Black
Black
Mean
Mean
(1)
(2)
(3)
(4)
(5)
0.455
0.762
0.915
0.185
0.633∗∗∗
(0.137)
(0.176)
(0.062)

Table 6
Racial Differences in Lethal Use of Force
Intensive Margin, Officer Involved Shootings
Non-Black/
Non-Hispanic
Black
Mean
(1)
(2)
No Controls
0.534
0.987
(0.135)

Hispanic
(3)
1.114
(0.257)

+ Civilian Demographics

0.946
(0.103)

1.046
(0.267)

+ Officer Demographics

0.835
(0.094)

0.896
(0.221)

+ Encounter Characteristics

0.693∗∗∗
(0.096)

0.759
(0.191)

+ Civilian Weapon

0.558∗∗∗
(0.066)

0.625∗∗
(0.149)

+ Fixed Effects

0.526∗∗∗
(0.037)

0.564∗∗
(0.131)

Observations

1,332

Notes: This table reports odds ratios by running logistic regressions. The sample consists
of officer involved shootings from Dallas, Austin, six Florida counties, Houston and Los
Angeles between 2000 to 2015. The dependent variable is based on who attacked first.
It is coded as 1 if the officer attacked the civilian first and 0 if the civilian attacked the
officer first. The omitted race is non-blacks and non-hispanics. The first column gives
the unconditional average of non-black/non-hispanic contacts that resulted in an officer
firing his gun. The second column reports logistic estimates for black civilians. The third
column reports logistic estimates for hispanic 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 7
Any Use of Force, NYC Stop Question and Frisk
Education
Income
Unemployment
Terciles
Terciles
Terciles
(1)
(2)
(3)
Tercile 1
1.174∗∗∗
1.194∗∗∗
1.113∗
(0.034)
(0.046)
(0.071)
N
2,275,062
1,941,664
1,472,862
Tercile 2
N
Tercile 3
N

1.172∗∗∗
(0.070)
1,613,725

1.100∗
(0.060)
1,750,137

1.177∗∗∗
(0.044)
1,943,285

1.180∗∗∗
(0.041)
1,030,997

1.259∗∗∗
(0.057)
1,227,983

1.246∗∗∗
(0.043)
1,503,637

Notes: This table reports odds ratios by running logistic regressions, subsampled for precinct demographics. Precinct demographics are calculated by collapsing data across census tracts received from
the American Community Survey 2007-2011. For each column, we take the tract’s white population
demographic minus the black population demographic and collapse the means of the differences over
precinct. We then take terciles in differences and calculate odds ratios for each tercile. Column (1)
shows odds ratios across education terciles. Education is measured as the fraction of high school graduates in every census tract. Column (2) shows odds ratio across income terciles. Incomes is measured
as the median household income. Column (3) shows odds ratios across unemployment terciles. Unemployment is calculated as the total number of unemployed people divided by the total number of people
in the labor force. 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 the 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 or during 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 effects were
included in all regressions. Standard errors clustered at the precinct level are reported in parentheses.

Table 8
Fraction weapon found, conditional on being
in an Officer Involved Shooting
Civilian White Civilian Black p-value
(1)
(2)
(3)
Officer White
0.851
0.810
(0.027)
(0.025)
0.268
Officer Black

p-value

0.625
(0.125)

0.742
(0.054)

0.010

0.115

0.354

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 Shootings (OIS) dataset. The second column presents the fraction of black civilians carrying
weapons in the OIS dataset. The 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.

At Least Hands

Table 9
Weapon Found,
Conditional on Force Used
White Mean Coefficient on Black Coefficient on Hispanic
(1)
(2)
(3)
0.036
−0.013∗∗∗
−0.008∗∗
(0.004)
(0.003)

Observations
(4)
1,028,625

At Least Pushing to Wall

0.036

−0.002
(0.002)

−0.000
(0.002)

253,643

At Least Using Handcuffs

0.040

−0.000
(0.002)

0.000
(0.003)

118,527

At Least Drawing a Weapon

0.053

0.003
(0.004)

0.001
(0.004)

58,443

At Least Pushing to Ground

0.054

0.005
(0.004)

0.002
(0.005)

51,083

At Least Pointing a Weapon

0.083

−0.011
(0.010)

−0.007
(0.010)

19,505

At Least Using Spray/Baton

0.092

−0.013
(0.027)

0.007
(0.033)

1,745

Notes: This table reports OLS estimates. The sample consists of all NYC stop and frisks from 2003-2013 in which use of force
and outcome variable were non-missing. The dependent variable is a binary variable that is coded as 1 whenever a weapon
was found on the civilian and 0 if weapon was not found. Each row looks at the fraction of white civilians carrying weapons
and racial differences in carrying weapons for black civilians versus white civilians and hispanic civilians versus white civlians,
conditional on at least a force level being used. 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 or during 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 effects were included in all regressions. Standard errors
clustered at the precinct level are reported in parentheses.

1

2

4

Panel A

Black vs White CI (Full)

6

Black vs White CI (None)

5

Black vs White (Full)

Use of Force Rank
Black vs White (None)

3

7

1

2

4

Panel B

Hispanic vs White (Full)

5

6

Hispanic vs White CI (Full)

Hispanic vs White CI (None)

Use of Force Rank
Hispanic vs White (None)

3

Figure 1: Odds Ratios by Use of Force, NYC Stop Question and Frisk

Odds Ratio for Hispanic

7

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 different 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 handcuffs
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
a weapon at a civilian or using a more severe force. Finally, 7 is for whether the police reported at least using a pepper 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 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 effects were included in
the controlled regression. Standard errors are clustered at the precinct level.

Odds Ratio for Black

1.8

1.6

1.4

1.2

1

2
1.5
1
.5

Panel A

Black vs White CI

Panel B

Black

White

Hour

Hour
Black vs White

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

At Least Hands

Figure 2: Odds Ratios of Any Use of Force, NYC Stop Question and Frisk

Average Use of Force

Notes: These figures plot odds ratios with 95% confidence intervals from logistic regressions. 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 civlians who had any force used against them. For both figures, the x-axis denotes different 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 effects were included in all regressions. Standard errors are clustered at the precinct level.

Odds Ratio for Black

1.6

1.4

1.2

1

.3
.25
.2
.15
.1

1

Black vs White CI (Full)

Panel A

Black vs White CI (None)

3

Black vs White (Full)

Use of Force Rank
Black vs White (None)

2

4

1

Panel B

Hispanic vs White (Full)

3

Hispanic vs White CI (Full)

Hispanic vs White CI (None)

Use of Force Rank
Hispanic vs White (None)

2

Figure 3: Odds Ratios by Use of Force, Police Public Contact Survey

Odds Ratio for Hispanic

4

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 different 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 police 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 coded 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.

Odds Ratio for Black

8

6

4

2

0

5
4
3
2
1

Black vs Non-Black

Year
Black vs Non-Black CI

2011-2015

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 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 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 5). Year fixed effects are included in all regressions. Robust standard
errors are reported in parentheses.

2000-2005

2006-2010

Figure 4: Odds Ratios for Officer Involved Shootings, Extensive Margin, By Year Categories

Odds Ratio for Black

2
1.5
1
.5

2

4

Panel A

5
Black vs White CI

Use of Force Rank
Black vs White

3

6

7

1

2

4

Panel B

5

6
Hispanic vs White CI

Use of Force Rank
Hispanic vs White

3

7

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 different 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 handcuffs 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 a weapon at a civilian or using a more severe force. Finally, 7 is
for whether the police reported at least using a pepper 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 effects were included in all regressions. Standard errors are clustered at the
precinct level.

1

Odds Ratio for Hispanic

Figure 5: Odds Ratios by Use of Force for Perfectly Compliant Civilians, NYC Stop Question and Frisk

Odds Ratio for Black

1.4

1.2

1

.8

.6

1.2
1
.8
.6
.4