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
Cambridge, MA 02138
July 2016, Revised January 2018

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, William Murdock III, and
Hannah Ruebeck 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 usual caveat applies. The views expressed herein are those
of the author and do not necessarily reflect the views of the National Bureau of Economic
Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2016 by Roland G. Fryer, Jr. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including ©
notice, is given to the source.

An Empirical Analysis of Racial Differences in Police Use of Force
Roland G. Fryer, Jr
NBER Working Paper No. 22399
July 2016, Revised January 2018
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
rolandfryer@edlabs.harvard.edu

An 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 five times into a group of
people 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 e↵ort
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 di↵erences in police use of force and (if any) whether those di↵erences 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 di↵erences in the frequency of officer-involved shootings are
due to police malfeasance or di↵erences in suspect behavior.2
In this paper, we estimate the extent of racial di↵erences in police use of force using four separate
datasets – two constructed for the purposes of this study.3 Unless otherwise noted, all results are
conditional on an interaction. Understanding potential selection into police data sets due to bias in
who police interacts with is a difficult endeavor. Section 3 attempts to help get a sense of potential
bias in police interactions. Put simply, if one assumes police simply stop whomever they want for
no particular reason, there seem to be large racial di↵erences. If one assumes they are trying to
prevent violent crimes, then evidence for bias is exceedingly small.
Of the four datasets, 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
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.

2

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 Police-Public 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
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 di↵erences 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 di↵erences 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 arrest 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 4,500 observations in which officers discharged
charged electronic devices (e.g., tasers). This is the second most extreme use of force, and in some
cases, is a substitute for lethal use of force.
The results obtained using these data are informative and, in some cases, startling. Using data
on police interactions from 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 di↵erences. In the raw data, blacks and
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 criminology, to study questions such as whether police treatment of citizens impacts the broader public opinion of the police
(Miller et al., 2004).

3

Hispanics are more than fifty percent more likely to have an interaction with police which involves
any use of force. Accounting for 125 variables that represent baseline characteristics, encounter
characteristics, civilian behavior, precinct and year fixed e↵ects, the odds-ratio on black (resp.
Hispanic) is 1.178 (resp. 1.122).
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 di↵erence 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. With all controls, blacks are 21 percent more likely
than whites to be involved in an interaction with police in which at least a weapon is drawn and
the di↵erence is statistically significant. Across all non-lethal uses of force, the odds-ratio of the
black coefficient ranges from 1.175 (0.036) to 1.275 (0.131).
Data from the Police-Public Contact Survey are qualitatively similar to 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 di↵erences are significantly larger. Blacks and Hispanics are approximately 1.3
percentage points more likely than whites to report any use of force in a police interaction, including
controls for civilian demographice, civilian behavior, contact characteristics, officer characteristics
and year. The white mean is 0.7 percent. Thus, the odds ratio is 2.769 for blacks and 1.818 for
Hispanics.
There are several potential explanations for the quantitative di↵erences between our estimates
using Stop and Frisk data and those using PPCS data. First, we estimate odds-ratios and the
baseline probability of force in each of the datasets is substantially di↵erent. Second, the PPCS
is a nationally representative sample of a broad set of police-civilian interactions. Stop and Frisk
data is from a particular 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 “answer” is likely somewhere in the
middle and, importantly, both bounds are statistically and economically important.
In stark contrast to non-lethal uses of force, we find that, conditional on a police interaction,
there are no racial di↵erences in officer-involved shootings on either the extensive or intensive
4

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, after controlling for suspect demographics, officer demographics, encounter characteristics,
suspect weapon and year fixed e↵ects, that blacks are 27.4 percent less likely to be shot at by police
relative to non-black, non-Hispanics. This coefficient is measured with considerable error and not
statistically significant. This result is 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
di↵erences.
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.5 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
are racial di↵erences 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.
5
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

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 taste-based 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 di↵erences should disappear. To test
this, we investigate racial di↵erences 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 were found. In contrast to the model’s predictions, racial di↵erences 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 Beckarian Outcomes test (Becker 1993) for
discrimination inspired by Knowles, Persico, and Todd (2001) and Anwar and Fang (2006). We
investigate the fraction of white and black suspects, separately, who are armed conditional upon
being involved in an officer-involved shooting. If the ordinal threshold of shooting at a black suspect
versus a white suspect is di↵erent 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 di↵erences in non-lethal uses of force.
The rest of the paper is organized as follows. The next section describes and summarizes the four
data sets used in the analysis. Section 3 describes potential selection into police data sets. Section
4 presents estimates of racial di↵erences on non-lethal uses of force. Section 5 describes a similar
analysis for the use of lethal force. Section 6 attempts 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
6

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
di↵erences in police use of force conditional on an interaction. 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 officer-involved 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 di↵erences 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) handcu↵s,
(4) draw weapon, (5) push to the ground, (6) point a weapon, (7) pepper spray or (8) strike with
a baton.6 Officers are instructed to include as many uses of force as applicable. For instance, if

6

Police officers can also include “other” force as a type of force used against civilians. We exclude “other” forces
from our analysis. Appendix Table 4 calculates racial di↵erences in the use of “other” force and shows that including
these forces does not alter our results.

7

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.7 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.8 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 handcu↵s 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 10 explores the robustness of our results for more disaggregated
clusters – precinctˆtime of day, block-level, and even blockˆtime of day. Our conclusions are
una↵ected by any of these alternative ways to cluster standard errors.
Summary statistics for the Stop and Frisk data are displayed in Appendix Table 2A. There are
7

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.
8
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

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. There is a surprisingly small
number of stops – about three percent – where 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 426,000 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 di↵erences between certain data
in the Uniform Crime Reports (UCR) and the National Crime Victimization Survey (NCVS).9 One
explanation for these di↵erences given in the literature is that individuals are embarrassed or afraid
to report certain crimes to police or believe that reporting such crimes have unclear benefits and
potential costs. Reporting police use of force – in particular for young minority males – may be
9

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 o↵enders.
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

similar.
Another key advantage is that it approximates the universe of potential interactions with police
– rather than limited to arrests or police stops.10 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. There are no geographic indicators. 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 3.28% of them have resisted arrests and only 11.07% of civilians argued when they were
searched despite not being guilty of carrying alcohol, drugs or weapons.
Appendix Table 2B presents summary statistics for PPCS sample with at least one interaction
with police. There are six panels. Panel A contains civilian demographics. Blacks comprise roughly
ten percent of the sample, women are 50 percent. The average age is approximately 13 years older
than the Stop and Frisk data. Over 72 percent of the sample reports being employed in the previous
week – average income category in the sample is 2.09. Income is recorded as a categorical variable
that is 1 for income levels below $20,000, 2 for income levels between 20, 000 and 49, 999, and 3 for
income levels greater than $50,000.
Panel B describes self-reported civilian behavior. According to all PPCS survey respondents,
only 1.93 percent of civilians disobey police orders, try to get away, resist, argue or threaten officers
when they have some interaction with the police.
Panel C of Appendix Table 2B includes summary data on the types of contact and officer
characteristics. Almost half of the interactions between the public and police are traffic stops, 0.35
percent are from street interactions – including the types of street interaction that may not appear
in our Stop and Frisk data – and 44.73 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
10

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

or other anti-crime programs, or being suspected by the police of something or as part of a police
investigation. Panel D contains alternative outcomes and Panel E describes the five uses of force
available in the data. Panel F provides the frequency of 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.11 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.12 Importantly for thinking about the representativeness of the data – many
of these cities were a part of the Obama Administration’s Police Data Initiative.13 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 e↵orts but have not
yet provided data.14 This is likely not a representative set of cities. Appendix Table 17 investigates
di↵erences 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:
“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
11

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.
12
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.
13
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.
14
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

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 of 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.15 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
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
15

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

include dummies to represent the jurisdiction that we collected data from. Appendix B contains
more details on 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.16
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 officer 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.17 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.
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
16

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 o↵ active-duty, pending an investigation.
17

13

officer shoots the suspect before being attacked. Second, we collected unprecedented data from
the Houston Police Department on all arrest categories in which officers could have justifiably used
lethal force as a way to obtain the “zeros.” These data are described in the next subsection.
Appendix Table 2C displays summary statistics for OIS data, divided into four locations and
six categories of data. Column (1) contains observations from the full sample – 1,316 shootings
between 2000 and 2015.18 Forty-six percent of officer-involved shootings in our data are blacks,
thirty one percent are Hispanic, and twenty three percent are other with the majority in that
category being whites. Given the spate of video evidence on police shootings – all of which are of
blacks – it is a bit surprising that they are less than half of the observations in the data.
Columns (2) and (4) displays data from 508 officer-involved shootings with firearms and over
4,000 instances of an officer-involved shooting with a taser, in Houston, Texas. Most police officers
in the Houston Police 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 (5) through (7) 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 39% of all officer-involved shootings. Austin and Dallas,
combined, provide 20% of the data while Florida provides 26% 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
18
We asked for data on all OIS between 2000 and 2015 and police departments replied back with years they had
data on. With the exception of LA county, Brevard county, and Jacksonville county that gave us less than 10 years
of data (an average of 5.7 years), the other 7 OIS locations gave us more than 10 years of data (an average of 13.7
years). At the least, we have Jacksonville with 5 years of data (2011-2015) and at the most we have Houston city
and Orange county, with 16 years of data (2000-2015).

14

in an e↵ort to develop a set of police-civilian interactions in which the use of lethal force may have
been justified by law.
There are approximately 1,000,000 arrests per year in Houston; 16 million total 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 randomly sampled ten percent of case IDs by year 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. Then we randomly sampled ten percent of these arrest records by year and manually
coded 290 variables per arrest record. It took between 30 and 45 minutes per record to manually
keypunch and include variables 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 were 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.
Appendix Table 2C Column (3) provides descriptive statistics for the Houston Arrest Data.
Compared to the officer-involved 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 di↵erent between the two datasets is the fraction of suspects who
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

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

III. A Note on Potential Selection into Police Data Sets
The forthcoming analysis takes the four data sets described above as given and estimates racial
di↵erences in non-lethal and lethal uses of force. But, to the extent that there are racial di↵erences
in the probability of an interaction with police, these data may omit a very important margin. Put
di↵erently, one may discover no di↵erences in police use of force, conditional on an interaction, but
large racial di↵erences in the probability of the types of interactions in which force may be used.
By only concentrating on how and whether force was used in an interaction and ignoring whether
or not an interaction took place, one can misrepresent the total experience with police.
Understanding racial di↵erences in the probability of police interaction is fraught with difficulty.
One has to account for di↵erential exposure to police, race-specific crime participation rates and
perhaps most importantly, pre-interaction behavior that civilians exhibit. Ideally, one might set up
a field experiment – similar to those used to measure labor market discrimination – that randomly
assigns similar individuals (across all physical dimensions except race) to the vicinity of the same
patrolling officers in a neighborhood and instruct them to behave identically. Conditional on random assignment, identical behavior, and race-specific crime rates, any di↵erences in the probability
of interaction could be interpreted as racial bias in police stopping behavior.
Without ideal data, researchers often compare the racial distribution of stopped civilians to the
racial distribution of various “at risk” civilians that could potentially be stopped. Determining the
probability of an interaction is essentially a search for the correct “risk set”.
Panel A of Table 1 provides a series of estimates of racial di↵erences in the probability of police
interaction by defining the relevant risk set in various ways. The first three columns uses NYC Stop
and Frisk data. Column (1) assumes the population at risk of being stopped by police as 18-34
year old males. Column (2) assumes the risk set is arrestees for ten broadly defined felony and
misdemeanor crimes as determined by the New York City Police Department’s Crime Reporting
System. Felonies include murder and non-negligient manslaughter, rape, other felony sex crimes,
robbery, felonious assault, grand larceny, and felony crime mischief. Misdemeanor crimes include
misdemeanor sex crimes, misdemeanor assault, petit larceny, and misdemeanor criminal mischief.21
21

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

16

Column (3) is similar to column (2) but only includes the six felonies.
For each of the 77 precincts, we calculate the average fraction of stops that are black and the
corresponding fraction for whites. We also calculate the fraction of blacks in the relevant risk set
and the same fraction for whites, for all precincts. We then regress the fraction of police stops that
are black (resp. white) on the fraction of blacks (resp. white) in the relevant risk set and store
the coefficient. The numbers displayed in each column is the coefficient for blacks divided by the
coefficient for whites for the relevant risk set. A number greater than one indicates a potential bias
against blacks. A number less than one indicates a potential bias in favour of blacks.
A simple – and often used – method to do this is to compare the fraction of blacks involved
in interactions with police with their proportion in the population, though many social scientists
have argued against this approach (Fridell 2004, Ridgeway 2007, Anwar and Fang 2006). Column
(1) demonstrates that blacks are almost 4 times more likely to be stopped by police relative to
their population proportion.Yet, this quantity is difficult to interpret. As Fridell 2004 argues,
“racial/ethnic groups are not equivalent in the nature and extent of their...law violating behavior.”
Column (2) uses incident weighed average (crimes committed more often are more heavily
weighted) for ten felonies and misdemeanors. Unfortunately, we do not have racial breakdown of
crime rates for individual precincts. In lieu of this, we calculate the fraction of arrestees in crimes
for New York City for each year between 2008 and 2013. Conditioning on incident weighted crime
rates reduces the estimate of bias in police interactions from 4.23 to 1.43 – a 66.2 percent reduction.
Column (3) conducts a similar exercise using six broad felonies. This method decreases the
estimate of bias in police stopping behavior to 1.03. If one were to use robbery rates rather than all
felonies, the number would be 0.546 implying that blacks are 45.4 percent less likely to be stopped
[not shown in tabular form].
Column (4) in panel A of Table 1 investigates potential selection into the PPCS dataset. Relative
to NYCs Stop and Frisk data, the PPCS involves a larger set of police interactions and are not the
result of a particular form of aggressive policing. Also, the data are from the civilians perspective.
This allows one to analyze the probability of having an involuntary interaction with the police
controlling for race and other demographics, for all respondents of the survey. In some ways, this
is closer to the ideal dataset described above though we cannot control for pre-interaction civilian
Reports released by the New York City Police Department.

17

behavior. Involuntary interaction is a dummy variable coded to be one if the civilian reported that
he was involved in an interaction with the police which was not initiated by him (for example,
traffic or parking violation, police asked respondent questions etc). The variable is coded to be 0 if
the civilian reported no interaction with police or an interaction that was initiated by himself (for
example, reporting a crime, asking for assistance etc).
We estimate a logistic regression of involuntary interaction on civilian race, demographic variables such as gender, age, income categories, the population size of the civilian’s address, a dummy
variable indicating whether the civilian was employed last week or not, and year, and report the
odds ratio on black coefficient. The odds that blacks have an involuntary interaction with police
is 8 percent less than whites. For comparison we also provide the odds ratio for voluntary interactions. Voluntary interactions include all interactions with police that civilians initiated themselves.
Blacks are 21 percent less likely to report a voluntary interaction with the police than whites.
The final three columns in Panel A of Table 1 report estimates from an analysis identical to
the one conducted for the Stop and Frisk dataset, but for Houston Officer-Involved shootings.22
Column (6) demonstrates that blacks are 4.35 times more likely to be involved in an officer involved
shooting than non-blacks relative to their proportion in the 18-34 year old male population. This
estimate changes drastically to 1.01 – a 76.8 percent reduction – when the population defined “at
risk” is the fraction of arrestees in felonies and misdemeanors. The estimate decreases further to
0.87 when only felony crimes are taken into account.
Panel B of Table 1 reports the results of a series of Beckarian outcomes tests (Becker 1993),
where the outcomes are whether or not a police stop resulted in an arrest or whether contraband
or any weapon was found. Becker (1993), in the context of mortgages, argued that discrimination
in mortgage lending against blacks cannot be found simply by looking at the likelihood of getting
a loan for minority versus white applicants who are similar in incomes, credit backgrounds, and
other available characteristics. The correct procedure would be to determine whether loans are
more profitable to blacks (and other minorities) than to whites. Discriminating banks would turn
down marginally profitable black applicants but accept white applicants. This is the spirit behind
the seminal work in Knowles, Persico, and Todd (2001).
22

Potential selection into all OIS locations by population weights and Uniform Crime Report coded arrest rates
are presented at the end of Appendix Table 2C.

18

For the outcomes test, we estimate a logistic regression of whether the civilian was arrested/was
carrying contraband or weapons on race, civilian demographics, encounter characteristics, civilian
behavior, and suitable fixed e↵ects.23 We report the odds ratio on the black coefficient. If the
coefficient is above one – this implies that stops of blacks are more “productive” than whites and
thus, if anything, police should be stopping blacks more at the margin.
Unfortunately, whether or not there seems to be racial bias in police stopping behavior depends
on the outcome tested. When using whether or not the civilian was arrested as an outcome –
which has the important disadvantage of depending both on the subsequent behavior of civilians
and police – there seems to be no bias against blacks in police stopping behavior. In other words,
blacks are more likely to be arrested, conditional upon being stopped. When the outcome is whether
or not contraband or a weapon was found, black stops are significantly less productive than whites
and thus is evidence for potential bias.
Taken together, this evidence demonstrates how difficult it is to understand whether there is
potential selection into police datasets. Estimates range from blacks being 323 percent more likely
to be stopped to 45.4 percent less likely to be stopped. Solving this is outside the scope of this
paper, but the data suggests the following rough rule of thumb – if one assumes that police are non
strategic in stopping behavior there is bias. Conversely, if one assumes that police are stopping
individuals they are worried will engage in violent crimes, the evidence for bias is exceedingly small.

IV. Estimating Racial Di↵erences in Non-Lethal Use of Force
NYC’s Stop, Question, and Frisk Data
Table 2 presents a series of estimates of racial di↵erences in police use of force, conditional on
being stopped, using the Stop and Frisk data. We estimate logistic regressions of the following
form:

ln

ˆ

PrpForcei,p,t “ 1q
1 ´ PrpForcei,p,t “ 1q

˙

1
1
“ Race1i ↵ ` Xi,t
` Zp,t
µ ` ⌫t `

p

` ✏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
23

All controls used are reported in detail in summary statistics Appendix Tables 2A and 2B.

19

category. Consequently, the coefficients on race capture the gap between the named racial category
and whites – which is reported as an Odds Ratio.24 The vectors of covariates included in the
1 and Z , vary between rows in Table 2. 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.
Row (a) in Table 2 presents the di↵erences in means for any use of force conditional on a police
interaction. These results reflect the raw gaps in whether or not a police stop results in any use of
force, by race. Blacks are 53% more likely to experience any use of force relative to a white mean of
15.3 percent. The raw gap for Hispanics is almost identical. Asians are no more likely than whites
to experience use of force. Other race – which includes American Indians, Alaskan natives or other
races besides white, black, Hispanic and Asian – is smaller but still considerable.
The raw di↵erence between races is large – perhaps too large – and it seems clear that one needs
to account for at least some contextual factors at the time of a stop in order to better understand,
for example, whether racial di↵erences are driven by police response to a given civilian’s behavior
or racial di↵erences in civilian behavior. Yet, it is unclear how to account for context that might
predict how much force is used by police and not include variables which themselves might be
influenced by biased police.25
Row (b) 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 (c). If anything, adding
these variables increases the odds ratios on each race, relative to whites. Surprisingly, accounting
for civilian behavior – row (d) in the table – does little to alter the results.
Row (e) in Table 2 includes both precinct and year fixed e↵ects. This significantly changes the
24
Appendix Tables 3A through 3G runs similar specification using ordinary least squares and obtains similar
results. Estimating Probit models provides almost identical results.
25
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.

20

magnitude of the coefficients. Blacks are almost eighteen percent more likely to incur any use of
force in an interaction, accounting for all variables we can in the data. Hispanics are roughly twelve
percent more likely.26 Both are statistically significant. Asians are slightly less likely, though not
distinguishable from whites. Row (f) interacts precincts with year as fixed e↵ects. Results do not
change significantly from row (e). Changing fixed e↵ects to be interactions between precinct, year
and month (row (g)) does not alter the results.
These data have two potential 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.27 From this point forward, we consider the row (e) specification, including precinct
and year fixed e↵ects as our main specification.
Inferring racial di↵erences in the types of force used in a given interaction is a bit more nuanced.
Police report that in 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
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 di↵erences in
the use of hands by police, one would miss this observation. A similar issue arises if one uses the

26

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.
27
Using data on geo-spatial coordinates, we also included block-level fixed e↵ects and the results were qualitatively
unchanged.

21

parallel “min.”28
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 di↵erences in the use of hands by police, this observation would be included.
The interpretation would not be racial di↵erences in the use of hands, per se, but racial di↵erences
in the use of “at least” hands. To be clear, an observation that records only hands would be in
the hands 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 di↵erences for each use of force are displayed in
Figure 1. The x-axis contains use of force variables that range from at least hands to at least the
use of pepper spray or 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 all
controls, precinct and year fixed e↵ects (equivalent to row (e) in Table 2).
For blacks, the consistency of the odds ratios are striking. As the use of force increases, the
frequency with which that 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 1.175 (0.036) and 1.275 (0.131).
Interestingly, for Hispanics, once we account for our set of controls, there are small di↵erences
in use of force for the lower level uses of non-lethal force, but the di↵erences converge toward whites
as the use of force increases both in the 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 3A 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
28

Appendix Tables 9A - 9C demonstrate 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.

22

and our parsimonious set of controls (corresponding to row (e) in Table 2). The subsequent rows
investigate racial di↵erences in use of force for high/low crime areas, time of 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 di↵er significantly at the 1% level across these various
subsamples with the exception of time of day and eventual outcomes. Black civilians are 8.6 percent
more likely to have any force used against them conditional on being arrested. They are 15.6 percent
more likely to have any force used against them conditional on being summonsed and 12.7 percent
more likely conditional on having weapons or contraband found on them. Results are similar for
Hispanics. Additionally, for both blacks and Hispanics, racial di↵erences in use of force are more
pronounced during 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 di↵erence 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
di↵erences that exist that are masked by police misreporting. The Police-Public Contact Survey is
one way to partially address this weakness.
Table 2 Panel B presents a series of estimates of racial di↵erences in police use of force conditional
on an interaction, using the PPCS data. The specifications estimated are of the form:

ln

ˆ

PrpForcei,t “ 1q
1 ´ PrpForcei,t “ 1q

˙

1
“ Race1i ↵ ` Xi,t
` ⌫t ` ✏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 2 Panel
B. As one moves down the table, the set of coefficients steadily grows. Standard errors, which

23

appear below each estimate, account for heteroskedasticity.
Generally, the data are qualitatively similar to the results using Stop and Frisk – namely, despite
a large and complex set of controls, blacks and Hispanics are more likely to experience some use
of force from police. A key di↵erence, 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 in a police interaction. In the PPCS, this number is 1%. There are a variety of potential
reasons for these stark di↵erences. 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 3.5 times more likely to report use of force by police in an interaction in the raw data.
Hispanics are 2.7 times more likely. Adding controls for demographic and encounter characteristics,
civilian behavior, and year reduces the odds-ratio to roughly 2.8 for blacks and 1.8 for Hispanics.
Di↵erences in quantitative magnitudes aside, the PPCS paints a similar portrait – large racial
di↵erences in police use of force that cannot be explained using a large and varied set of controls.
One important di↵erence between the PPCS and the Stop and Frisk data is in regards to racial
di↵erences on the more extreme uses of non-lethal 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 di↵erences on these higher uses of force
disappear. For kicking or using a stun gun or pepper spray, the highest use of force available, the
black coefficient is 1.930 (0.649) and the Hispanic coefficient is 1.446 (0.490), though because of the
rarity of these cases the coefficients are barely statistically significant at the 5% level.
Table 3B explores the heterogeneity in the data by estimating racial di↵erences in police use
of force in PPCS on various subsamples of the data: officer race, civilian income, gender, civilian,
and time of contact . Civilian income is divided into three categories: less than $20,000, between
$20,000 and $50,000, and above $50,000. Strikingly, both the black and Hispanic coefficients are
statistically similar across these income levels – suggesting that higher income minorities do not
price themselves out of police use of force – echoing some of the ideas in Cose (1993). Racial
di↵erences in police of force does not seem to vary with civilian gender or officer race especially for
24

black civilians. Consistent with the results in the Stop and Frisk data, the black coefficient is 3.690
(0.976) for interactions that occur during the day and 1.848 (0.520) for interactions that occur at
night. The p-value on the di↵erence is significant but only at the 10% level.
Putting the results from the Stop and Frisk and PPCS datasets together, a pattern emerges.
Relative to whites, blacks and Hispanics seem to have very di↵erent interactions with law 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 interaction and year reduces, but cannot
eliminate, racial di↵erences in non-lethal use of force in either of the datasets analyzed.

V. Estimating Racial Di↵erences in Officer-Involved Shootings
We now focus on racial di↵erences in officer-involved shootings. We begin with specifications most
comparable to those used to estimate racial di↵erences in non-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.29 Specifically, we
estimate the following empirical model:

ln

ˆ

Prpshootingi,t q
1 ´ Prpshootingi,t q

˙

1
“ Race1i ↵ ` Xi,t
` ⌫t ` ✏i,t ,

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 4. 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.30 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.
29
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%. 46.1 percent of whites in
our data were involved in an officer-involved shooting.
30
Appendix Table 7 investigates the sensitivity of the main results to more alternative compositions of the risk
sets.

25

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 4 are startling.
Blacks are 23.5 percent less likely to be shot by police, relative to whites, in an interaction.
Hispanics are 8.5 percent less likely to be shot but the coefficient is statistically insignificant.
Rows (b) through (f) add various controls, identical to those in Appendix Table 2C. Accounting for basic suspect or officer demographics, does not significantly alter the raw racial di↵erences.
Including encounter characteristics – which one can only accomplish by hand coding the narratives
embedded in arrest 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 e↵ects, the coefficients still suggest that, if anything, officers are
less likely to shoot black suspects, ceteris paribus, though the racial di↵erences are not significant.
Columns (4) and (5) of Table 4 include 4504 incident-suspect observations 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
di↵erences 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 di↵erence in the decision to employ lethal
force using this taser sample is negative and statistically significant. Adding suspect and officer
demographics, encounter characteristics and year controls does little to change the odds ratios for
black versus non-black suspects. Including all controls available from the taser sample, Table 4
shows that black civilians are 30.7 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 24.2 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
26

are important racial di↵erences in whether or not thse police-civilian interactions occur at all.
Appendix Tables 6 and 7 explore the sensitivity of the results for various subsamples of the
data: whether the unit that responded was majority black or Hispanic or majority white or Asian,
number of officers who respond to the scene, whether the suspect clearly drew their weapon versus
appeared to draw their weapon, whether the officer was on-duty, and the type of call the officer
was responding to (a partial test of the selection issue described above). Equations identical to (3)
are estimated, but due to the smaller sample sizes inherent in splitting the sample, we estimate
Ordinary Least Squares regressions.
None of the subsamples explored demonstrate much di↵erence of note. We find no di↵erences
in the use of lethal force across di↵erent call slips – the p-value for equality of race coefficient across
di↵erent calls slips is 0.763 for black suspects – suggesting that officers seeking confrontation in
random street interactions in a way that causes important selection bias into our sample is not
statistically relevant. Subsampling on the number and racial composition of the officer unit also
shows no evidence of racial di↵erences.
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 di↵erences 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
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 4, this does not seem to influence
racial di↵erences in the use of lethal force.
Are there Racial Di↵erences in the Timing of Lethal Force?
The above results, along with the results on use of force, are about racial di↵erences on the
extensive margin: whether or not an officer uses a particular type of force or decides to use lethal
force on a suspect. Because of the richness of our officer-involved shootings database, we can
also investigate the intensive margin – whether there are racial di↵erences in how quickly a police

27

officer shoots a suspect in an interaction. 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 5 presents a series of estimates of racial di↵erences in the timing of police shootings using
the OIS data. The specifications estimated are of the form:

ln

ˆ

PrpShoot Firsti,c,t q
1 ´ PrpShoot Firsti,c,t q

˙

1
1
` Zc,t
T ` ⌫t `
“ Race1i ↵ ` Xi,t

c

` ✏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 (a) displays the results from the raw data. Blacks are 4.1% less likely to be shot first
by police. Hispanics are slightly more likely. Neither coefficient is statistically significant. Adding
suspect or officer demographics does not alter the results.31
Row (d) accounts for important context at the time of the shooting. For instance, whether
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 0.683 (0.094) 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 e↵ects only strengthens the results in the unexpected direction. Including
all controls available, officers report that they are 46.6% less likely to discharge their firearms
before being attacked if the suspect is black. The Hispanic coefficient is strikingly similar (43.8%
less likely).
Appendix Table 8 explores the heterogeneity in the data across various subsamples: the racial
31
We also estimate the “intensity” of force used in officer-involved shootings by estimating racial di↵erences in the
total number of bullets used in a given police shooting. The average number of bullets in officer-involved shootings
involving blacks is 0.438 (0.805) more relative to shootings that involve non-black non-hispanics. However, this
coefficient is statistically insignificant [not shown in tabular form].

28

composition of the responding unit, 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, and the call type. 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 all negative if anything. 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 on these call types, blacks are less likely to be shot at first, if anything.
One of the more interesting subsamples is whether or not a suspect “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 -0.102 (0.023). The same coefficient estimated on the set of interactions were police
assumed an individual had a weapon is -0.036 (0.032). 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
di↵erences in officer-involved shootings on any dimension.

VI. Interpretation
A number of stylized facts emerge from the analysis of the preceding sections. On non-lethal uses
of force, there are racial di↵erences – sometimes quite large – in police use of force, even after
controlling for a large set of controls 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 di↵erence remains roughly constant. On the most extreme uses

29

of force, however – officer-involved shootings with a Taser or lethal weapon – there are no racial
di↵erences 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

the fraction of W ’s in the population. Police officers

are assumed to be one of two types: “biased” or “unbiased.” Let

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 ✓ P r✓, ✓s to police officers regarding whether or not a civilian
is likely to comply.32 Next, the police officer observes ✓ and decides whether or not to use force,
which we denote by h P t0, 1u.33
The distribution of ✓ 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 p✓q [resp. F0 p✓q] be the probability that the signal does not exceed ✓, given that a civilian
32

This model is a simplified version of a more general model in which individuals invest in a “compliance identity”
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.
33
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.

30

has invested in compliance (resp. non-compliance) and let f1 p✓q and f0 p✓q be the related density
functions. Define µp✓q ”

f0 p✓q
f1 p✓q

to be the likelihood ratio at ✓. We assume that µp✓q is non-increasing

on r0, 1s, which implies that F1 p✓q § F0 p✓q for all ✓. Thus, higher values of observed ✓ 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, payo↵s 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 payo↵ of ´ ´ c
if he invested in compliance and ´ if not. If force is not used on the civilian, he receives a payo↵
of ´c if he invests and the payo↵ 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, payo↵s 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 payo↵ is ´K ´

F

if the civilian is compliant and

F

´

F

if the civilian is non-compliant.

If no force is used, the officer receives a payo↵ of 0 if the civilian is compliant and ´

NF

if the

civilian is non-compliant. These payo↵s 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 ⌧ , a positive term
in the biased officer’s payo↵ 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-o↵ 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
ë
ë
to use force, conditional upon what he can observe, h : t0, ⌧ u rB, W s r✓, ✓s Ñ t0, 1u.
31

Expected Payoffs
Let ⇡ P r0, 1s denote the officer’s prior belief that a civilian will be compliant. Expected payo↵s
for the police officer are functions of her beliefs, her type, and the signal she receives. Given ⇡ and
observed signal ✓, she formulates a posterior probability (using Bayes’ rule) that the civilian will
be compliant:

p⇡, ✓q ”

⇡f1 p✓q
⇡f1 p✓q`p1´⇡qf0 p✓q .

The expected payo↵ of using force for an unbiased police officer (and, equivalently, a biased
police officer when interacting with Ws) is:
p⇡, ✓qp´K ´

Fq

` p1 ´

p⇡, ✓qqp

F

´

F q.

(2)

The expected payo↵ of using force for a biased officer interacting with Bs is:
p⇡, ✓qp´K ´

Fq

` p1 ´

p⇡, ✓qqp

F

´

Fq

` ⌧.

(3)

Relatedly, the expected payo↵s of not using force, for both types of officers, can be written as:
´p1 ´ p⇡, ✓qqp

N F q.

(4)

Combining equation (2) and equation (4), and using a bit of algebra, an unbiased officer uses
force only if
˚
” mint✓| p⇡, ✓qp´K ´
✓ § ✓ub

Fq

` p1 ´

p⇡, ✓qqp

F

`

NF

´

Fq

° 0u

(5)

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

unbiased officers always use force. Similarly, using the corresponding expected payo↵s for a biased
officer, one can derive ✓b˚ .
Now, consider the civilian’s expected payo↵. W civilians receive F1 p✓˚ ub qp´ q ´ c if they invest

˚ qp´ q if they choose not to invest. When optimizing, a civilian will invest in compliance
and F0 p✓ub

if and only if the cost of compliance is less than the net benefit of compliance. In symbols,
˚
˚
q ´ F1 p✓ub
qu
c § c˚W ” tF0 p✓ub

32

(6)

Similarly, Bs invest if
c § c˚B ”
Note – given we assume

˚
˚
t pF0 p✓ub
q ´ F1 p✓ub
qq ` p1 ´ qpF0 p✓b˚ q ´ F1 p✓b˚ qqu

(7)

° 0 – it follows that c˚B † c˚W .

Definition 1 An equilibrium consists of a pair p✓˚ , ⇡ ˚ 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 (✓) are independent of race, racial disparities
can be produced in this model in two (non-mutually exclusive) ways: di↵erent beliefs or di↵erent
preferences.34 To see this formally, suppose all racial di↵erences were driven by information-based
discrimination and there was no taste-based component. In this case, equation (3) simplifies to (2)
˚ q ´ F p✓ ˚ qu ´ c. Thus,
and both B and W individuals’ net benefit of investment becomes tF0 p✓ub
1 ub

one needs di↵erences in ⇡ to generate discriminatory equilibrium.
In contrast, one can also derive an equilibrium for cases in which we turn o↵ the informationbased channel and only allow di↵erences 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
To better understand whether statistical discrimination might explain some of the patterns in
the data, we investigate two possibilities.35 First, we explore whether racial di↵erences in mean
34
It is also plausible that racial di↵erences arise due to di↵erences in costs of compliance (for instance, through
peer e↵ects) or in the signal distributions. Incorporating these assumptions into the model is a trivial extension.
35
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 14.

33

characteristics across police precincts predicts racial di↵erences in use of force. The key – untestable
– assumption is police officer beliefs about the compliance of a civilian – ⇡ in our model – is partly
driven by local variation in variables such as education or income levels.36
Appendix Table 11 explores racial di↵erences 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 di↵erence
between the white population and black population and rank the precincts by this di↵erence,
individually. We then divide the data into terciles. The first tercile is always the one in which
racial di↵erences between our proxies are the lowest. The third tercile represents precincts in which
there are relatively large racial di↵erences on a given proxy.
Statistically larger racial di↵erences 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 di↵erences in use of force
are correlated with racial di↵erences in proxies for dangerousness. Appendix Table 11 demonstrates
no such pattern. The odds-ratio of having any force used on a black civilian versus a white civilian
remains statistically the same across terciles.37
A second prediction of the statistical discrimination model that is testable in our data is how
racial di↵erences in use of force change as signals about civilian compliance become more clear.38
If statistical discrimination is the key driver of racial di↵erences in use of force, the model predicts
that as ✓ becomes perfectly predictive of compliance behavior, there will be no racial di↵erences.
36

Ideally, one might use variables more directly correlated with dangerousness such as racial di↵erences in crime
rates, by precincts. Despite repeated formal Freedom of Information Law requests, the New York Police Department
refused to supply these data.
37
We performed a similar exercise exploiting the variance across space in proxies for dangerousness (see Appendix
Tables 12A-12C 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.
38
Another potential test of statistical discrimination was pioneered by Altonji and Pierret (2001). They investigate
racial di↵erences in wage trajectories, conditional upon being hired. To the extent that statistical discrimination drives
wage di↵erences 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
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.

34

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 di↵erences, 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 di↵erences should be close
to zero. And, on the set of interactions in which civilians engage in questionable behavior, racial
di↵erences 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 21.2 percent more likely to have any
force used against them in an interaction 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 di↵erences 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
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 di↵erences in officer-involved shooting if there is a discrete increase in the costs of being

35

deemed a discriminator, relative to the costs incurred with non-lethal uses of force.39
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 di↵erent across races. We can test this
a bit more directly. One issue in this setting, which does not arise in labor markets, is that it
is not obvious how to aggregate non-compliance into a monotonic index. From a police officer’s
perspective, It may be considered more dangerous if a civilian shouted verbal threats than if he
refused to comply with an officer’s directions or if he was evasive during questioning. A simple
aggregation of the number of non-compliant activities is likely misleading.
To sidestep this important potential issue of aggregating non-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 di↵erences in the marginal return to non-compliance behavior would
manifest itself in statistically di↵erent 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 di↵erences
in police use of force being driven by taste-based discrimination. Black civilians have statistically
similar marginal returns to compliance as white civilians. In other words, the probability of force
being used as ✓ 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
39
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.”

36

✓. 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
di↵erences 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 di↵erent across races. This, in turn, implies that the rate of
successful searches will be di↵erent across races.
Anwar and Fang (2006) build upon the theory of KPT; arguing that the KPT results might not
hold if police officers are non-monolithic in their behavior. They test this by investigating search
rates of civilians of a particular race, across officer races. Under the null hypothesis that none of
the racial groups of officers have relative racial prejudice, it must be true that the ranking of search
rates for white civilians across officer 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 di↵erent 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
officer races is di↵erent 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
37

displayed in Table 6. For white officers, the probability that a white suspect who is involved in
officer-involved shooting has a weapon is 84.2%. The equivalent probability for blacks is 80.9%.
A di↵erence of 4%, which is not 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,
57.1%. The equivalent probability for black suspects is 73.0%. The only statistically significant
di↵erences 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 di↵erences 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 di↵erences 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.
Appendix Table 13 presents these results. Each row is a di↵erent level of force which begins with
“at least hands” and increases in severity of force until “use of pepper spray or Baton.” Column
(1) contains the white mean. Columns (2) and (3) display the coefficient on black and Hispanic,
respectively. 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 1.0 (0.1) percentage points less likely to have a weapon, conditional upon a police
officer using any force. Hispanics are 0.6 (0.1) less likely to have a weapon. Both are statistically
significant. Interestingly, on the two most severe non-lethal uses of force, the 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.

38

VII. 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 indi↵erence. Yet, very little data
exists to understand whether racial disparities in police use of force exist or might be explained
by situational factors 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 di↵erences in police use of force and the probability of
police interaction. On non-lethal uses of force, there are racial di↵erences – 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 di↵erence
remains roughly constant. Even when officers report civilians have been compliant and no arrest
was made, blacks are 21.2 percent more likely to endure some form of force in an interaction. Yet,
on the most extreme use of force – officer-involved shootings – we are unable to detect any racial
di↵erences in 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 di↵erences 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
39

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 di↵erences in lower level uses of force are simply a distraction and movements such as Black
Lives Matter should seek solutions within their own communities rather than changing the behaviors
of police and other external forces.
Much more troubling, due to their frequency and potential impact on minority belief formation,
is the possibility that racial di↵erences in police use of non-lethal force has spillovers on myriad
dimensions of racial inequality. If, for instance, blacks use their lived experience with police as
evidence 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.

40

References
[1] Allport, G.W. 1954. The Nature of Prejudice. Reading, MA: Addison Wesley
[2] Aigner, D.J. and Cain, G.G., 1977. “Statistical theories of discrimination in labor markets.”
Industrial and Labor relations review, pp.175-187.
[3] Altonji, J.G. and Pierret, C.R., 2001. Employer Commitment and Statistical Discrimination.
The Quarterly Journal of Economics, 116.
[4] Anwar, S. and Fang, H., 2006. ”An Alternative Test of Racial Prejudice in Motor Vehicle
Searches: Theory and Evidence.” American Economic Review, 96(1): 127-151.
[5] Becker Gary, S., 1957. The economics of discrimination.
[6] Becker Gary S., 1993. Nobel Lecture: The Economic Way of Looking at Behavior. Journal of
Political Economy, 101(3), pp. 385-409.
[7] Coate, S. and Loury, G.C., 1993a. Will affirmative-action policies eliminate negative stereotypes?. The American Economic Review, pp.1220-1240.
[8] Coate, S. and Loury, G., 1993b. Antidiscrimination enforcement and the problem of patronization. The American Economic Review, 83(2), pp.92-98.
[9] Coviello, D. and Persico, N., 2015. An Economic Analysis of Black-White Disparities in NYPDs
Stop and Frisk Program. Journal of Legal Studies, 44(2), pp. 315-360.
[10] Cose, E., 1993. The rage of a privileged class: Why are middle-class Blacks angry? Why should
America care. New York: HarperPerennial.
[11] Eberhardt, J.L., Go↵, P.A., Purdie, V.J. and Davies, P.G., 2004. Seeing black: race, crime,
and visual processing. Journal of Personality and Social Psychology, 87(6), p.876.
[12] Fiske, S.T. 1998. “Stereotyping, Prejudice, and Discrimination” in D.T. Gilbert, S.T. Fiske
and G. Lindzey, eds, Handbook of Social Psychology, vol 2. New York: Oxford University Press,
357-414.

41

[13] Fridell, L.A., 2004. By the numbers: A guide for analyzing race data from vehicle stops.
Washington, DC: Police Executive Research Forum.
[14] Ridgeway, Greg. 2007. Analysis of Racial Disparities in the New York Police Departments
Stop, Question, and Frisk Practices. Technical report. RAND Corporation, Santa Monica, CA.
[15] Fryer, R. and Jackson, M.O., 2008. “A categorical model of cognition and biased decision
making.” The BE Journal of Theoretical Economics, 8(1).
[16] Gelman, A., Fagan, J. and Kiss, A., 2012. “An analysis of the New York City police department’s stop-and-frisk policy in the context of claims of racial bias.” Journal of the American
Statistical Association.
[17] Go↵, P.A., Jackson, M.C., Di Leone, B.A.L., Culotta, C.M. and DiTomasso, N.A., 2014. “The
essence of innocence: Consequences of dehumanizing Black children.” Journal of Personality
and Social Psychology, 106(4), p.526.
[18] Knowles, J., Persico, N., and Todd, P., 2001. “Racial Bias in Motor-Vehicle Searches: Theory
and Evidence.” Journal of Political Economy, 109(1), pp. 203-29.
[19] Miller, J., Davis, R.C., Henderson, N.J., Markovic, J. and Ortiz, C.W., 2004. Public opinions
of the police: The influence of friends, family and news media. New York: Vera Institute of
Justice.
[20] Mincer, J., 1958. “Investment in human capital and personal income distribution.” The Journal
of Political Economy, pp.281-302.
[21] Neal, D. A., and Johnson, W. R. 1996. “The Role of Premarket Factors in Black White Wage
Di↵erences.” Journal of Political Economy, 104, 869-895.
[22] O’Neill, J. 1990. “The Role of Human Capital in Earnings Di↵erences Between Black and
White Men.” Journal of Economic Perspectives, 4, 25-45.
[23] Ridgeway, G., 2007. Analysis of racial disparities in the New York Police Department’s stop,
question, and frisk practices. Rand Corporation.

42

[24] Ridgeway, G., and MacDonald, J. M. 2009. Doubly robust internal benchmarking and false
discovery rates for detecting racial bias in police stops. Journal of the American Statistical
Association, 104(486), 661-668.
[25] Schneider, A., 1977. Portland (Or) Forward Record Check of Crime-Victims Final Report,
December 1977. Oregon Research Institute and United States of America, 1977.
[26] Sporer, S. 2001. “Recognizing Faces of Other Ethnic Groups: An Integration of Theories,”
Psychology, Public Policy, and Law, 7, 36-97.

43

Panel A: Potential Selection

Panel B: Outcomes Test

Table 1: Racial Differences in Probability of Interaction and Outcomes Test
NYC Stop and Frisk
PPCS
Population Arrest Rate Felony Arrest
Involuntary
Voluntary
Population
Weighted
Weighted
Weighted
Contact
Contact
Weighted
(1)
(2)
(3)
(4)
(5)
(6)
4.233
1.428
1.026
0.922⇤⇤⇤
0.791⇤⇤⇤
4.347
(0.025)
(0.026)
Civilian
Arrested
(1)
1.080⇤⇤⇤
(0.032)

Contraband/
Weapon Found
(2)
0.777⇤⇤⇤
(0.033)

Civilian
Arrested
(3)
1.814⇤⇤⇤
(0.159)

Houston
Arrest Rate
Weighted
(7)
1.008

Felony Arrest
Weighted
(8)
0.872

Contraband/
Weapon Found
(4)
0.524⇤⇤⇤
(0.118)

This table reports the probability of police interaction and conducts outcomes tests. The sample in NYC Stop and Frisk block consists of all NYC Stop and Frisks from 2003-2013. The sample in
PPCS block consists of all Police Public Contact Survey respondents from 1996-2011. The sample in Houston block consists of all officer involved shootings from Houston between 2000-2015.
All population demographics have been obtained from American Community Survey 2007-2011. Arrest rates for New York City have been obtained from NYC Enforcement Reports 2008-2013.
Arrest rates for Houston have been provided from the Houston Police Department for all arrests in 2015. To obtain the number reported in Panel A, column (1) we go through the following steps
– For each precinct, calculate the fraction of stops that are black and the corresponding fraction for whites; for each precinct, calculate the fraction of 18-34 aged males in the population that are
black and the corresponding fraction for whites; regress the fraction of stops that are black on the fraction of 18-34 aged males that are black (with no constant) for all 77 precincts. The beta
coefficient on the dependent variable shows the representation of “at risk” blacks in stops. Conduct same regression for whites and store that beta coefficient as the representation of “at risk”
whites in stops; finally, divide the beta coefficient for blacks by the beta coefficient for whites. To obtain the numbers in Panel A, columns (2) and (3) we go through the following steps – For each
year, calculate the fraction of stops that are black and the corresponding fraction for whites for New York City; for each year, calculate the fraction of arrestees for the 10 most egregious felonies
and misdemeanors for column (2) and the fraction of arrestees for the 6 most egregious felonies only for column (3) for blacks and whites for New York City; regress the fraction of stops that are
black on the fraction of arrestees that are black (with no constant) for all 6 years of data and store the beta coefficient and do the same regression for whites and store the beta coefficient; finally,
divide the beta coefficient for blacks by the beta coefficient for whites. Panel A columns (4) and (5) report odds ratios on blacks from logistic regressions of involuntary or voluntary interaction
on civilian race, other civilian demographics and year. To obtain the numbers in Panel A columns (6) - (8), we go through the following steps – calculate the fraction of blacks in officer involved
shootings and divide it by the fraction of blacks in the 18-34 aged male population in Houston/ fraction of blacks in all felony and misdemeanor arrests/fraction of balcks in all felony arrests;
calculate the same fraction for non-blacks; and finally divide the black fraction by non-black fraction. For Panel B, we report odds ratios on black dummy from logistic regressions of the outcome
specified on dataset-specific controls. For NYC Stop and Frisk, the controls are civilian demographics (race, gender, quadratic in age), encounter characteristics (stop was indoors or outdoors,
whether the stop took place during the daytime, whether the stop took place in a high crime area, during a high crime time, or in a high crime area at a high crime time, whether the officer was
in uniform, civilian ID type, and whether others were stopped during the interaction), civilian behavior (whether civilian was carrying a suspicious object, if he fit a relevant description, if he was
preparing for a crime, if he was on lookout for a crime, if he was dressed in criminal attire, if there was an appreance of a drug transaction, whether there were any suspicious movements, if he was
engaged in violent crime, if he was concealing a suspicious object, and whether there was any other suspicious behavior), precinct and year fixed effects, and missing indicators for all variables.
For PPCS, the controls are civilian demographics (race, gender, employment last week, income, population size of a civilian’s address, and a quadratic in age), contact and officer characteristics
(time of day of the contact, contact type, and officer race), civilian behavior (civilian disobeyed, tried to get away, resisted, complained, argued, threatened officer, used physical force), year and
missing indicators for all variables.

Table 2: Racial Differences in Non-Lethal Use of Force, Conditional on an Interaction
White Mean
Black
Hispanic Asian Other Race
(1)
(2)
(3)
(4)
(5)
(a)

Panel A: NYC Stop, Question and Frisk
No Controls

(b)

1.534⇤⇤⇤
(0.144)

1.582⇤⇤⇤
(0.149)

1.044
(0.119)

1.392⇤⇤⇤
(0.121)

+ Civilian Demographics

1.480⇤⇤⇤
(0.146)

1.517⇤⇤⇤
(0.146)

1.010
(0.122)

1.346⇤⇤⇤
(0.114)

(c)

+ Encounter Characteristics

1.655⇤⇤⇤
(0.155)

1.641⇤⇤⇤
(0.157)

1.059
(0.133)

1.452⇤⇤⇤
(0.121)

(d)

+ Civilian Behavior

1.462⇤⇤⇤
(0.128)

1.516⇤⇤⇤
(0.136)

1.051
(0.124)

1.372⇤⇤⇤
(0.107)

(e)

+ Precinct FE, Year FE

1.178⇤⇤⇤
(0.034)

1.122⇤⇤⇤
(0.026)

0.953
(0.033)

1.060⇤⇤
(0.028)

(f)

+ Precinct*Year FE

1.171⇤⇤⇤
(0.034)

1.112⇤⇤⇤
(0.025)

0.954
(0.033)

1.066⇤⇤
(0.028)

(g)

+ Precinct*Year*Month FE

1.172⇤⇤⇤
(0.034)

1.112⇤⇤⇤
(0.025)

0.958
(0.032)

1.068⇤⇤
(0.028)

0.153

Observations
(h)

Panel B: Police Public Contact Survey
No Controls

(i)

4,927,962
3.496⇤⇤⇤
(0.364)

2.697⇤⇤⇤
(0.311)

–

1.130
(0.275)

+ Civilian Demographics

2.745⇤⇤⇤
(0.299)

1.716⇤⇤⇤
(0.205)

–

0.792
(0.195)

(j)

+ Encounter Characteristics

2.659⇤⇤⇤
(0.293)

1.695⇤⇤⇤
(0.202)

–

0.811
(0.197)

(k)

+ Civilian Behavior

2.780⇤⇤⇤
(0.330)

1.820⇤⇤⇤
(0.225)

–

0.763
(0.194)

(l)

+ Year

2.769⇤⇤⇤
(0.328)

1.818⇤⇤⇤
(0.225)

–

0.758
(0.193)

Observations

0.007

59,668

Notes: This table reports odds ratios obtained from logistic regressions. The sample in Panel A consists of all NYC Stop and Frisks from
2003-2013 with non-missing use of force data. The dependent variable is an indicator for whether the police reported using any force
during a stop and frisk interaction. The omitted race is white, and the omitted ID type is other. The first column gives the unconditional
average of stop and frisk interactions that reported any force being used for white civilians. Columns (2)-(5) report logistic estimates for
black, Hispanic, Asian, and other race civilians, respectively. Each row corresponds to a different empirical specification. The first row
includes solely racial group dummies. The second row adds controls for gender and a quadratic in age. The third row adds controls for
whether the stop was indoors or outdoors, whether the stop took place during the daytime, whether the stop took place in a high crime
area, during a high crime time, or in a high crime area at a high crime time, whether the officer was in uniform, civilian ID type, and
whether others were stopped during the interaction. The fourth row adds controls for civilian behavior. The fifth row adds precinct and
year fixed effects. The sixth row adds precinct*year fixed effects. The seventh row adds precinct*year*month fixed effects. Each row
includes missings in all variables. Standard errors, clustered at the precinct level, are reported in parentheses. The sample in Panel B
consists of all Police Public Contact Survey respondents from 1996-2011 with non-missing use of force data. The dependent variable is
an indicator for whether the survey respondent reported any force being used in a contact with the police. The omitted race is white. The
first column gices the unconditional average of contacts in which survey respondants reported any force being used for white civilians.
Columns (2)-(4) report logistic estimates for black, Hispanic, and other race civilians, respectively. Each row corresponds to a different
empirical specification. The first row includes solely racial group dummies. The second row adds controls for civilian gender, work,
income, population size of a civilian’s address, and a quadratic in age. The third row adds controls for the time of day of the contact,
contact type, and officer race. The fourth row adds an indicator for civilian behavior. The fifth row adds a control for year. Each row
includes missings in all variables. Standard errors, robust to heteroskedasticity, are reported in parentheses.

Table 3A: Analysis of Subsamples, Any Use of Force (Conditional on an Interaction), NYC Stop Question and Frisk
White Mean Coef. on Black Coef. on Hispanic Observations
(1)
(2)
(3)
(4)
Full Sample

0.153

1.178⇤⇤⇤
(0.034)

1.122⇤⇤⇤
(0.026)

4,927,962

Panel A: Crime Rate in Area
High Crime

0.143

1.170⇤⇤⇤
(0.035)
1.202⇤⇤⇤
(0.039)
0.254

1.118⇤⇤⇤
(0.027)
1.139⇤⇤⇤
(0.029)
0.320

2,750,559

1.260⇤⇤⇤
(0.035)
1.141⇤⇤⇤
(0.039)
0.001

1.164⇤⇤⇤
(0.026)
1.102⇤⇤⇤
(0.029)
0.024

1,783,977

1.180⇤⇤⇤
(0.047)
1.200⇤⇤⇤
(0.033)
0.717

1.126⇤⇤⇤
(0.035)
1.124⇤⇤⇤
(0.023)
0.954

3,546,388

1.143⇤⇤⇤
(0.044)
1.186⇤⇤⇤
(0.031)
0.241

1.105⇤⇤⇤
(0.033)
1.125⇤⇤⇤
(0.025)
0.504

1,129,555

1.175⇤⇤⇤
(0.034)
1.255⇤⇤⇤
(0.055)
0.042

1.122⇤⇤⇤
(0.026)
1.109⇤⇤⇤
(0.043)
0.717

4,447,382

1.036
(0.024)
1.061⇤
(0.038)
1.086⇤⇤⇤
(0.035)
1.156⇤⇤⇤
(0.044)
1.127⇤⇤⇤
(0.026)
0.002

1.022
(0.021)
1.043
(0.031)
1.045⇤
(0.025)
1.068⇤⇤
(0.035)
1.068⇤⇤⇤
(0.024)
0.339

2,725,795

Low Crime

0.163

p-value:
Panel B: Time of Day
Day
Night

0.126
0.170

p-value:
Panel C: Officer in Uniform
Uniformed Officer

0.132

Non-Uniformed Officer

0.189

p-value:
Panel D: Location
Indoors
Outdoors

0.144
0.154

p-value:
Panel E: Civilian Gender
Male
Female

0.160
0.089

p-value:
Panel F: Eventual Outcomes
Frisked

0.312

Searched

0.412

Arrested

0.327

Summonsed

0.195

Weapon/Contraband Found

0.359

p-value:

2,177,403

3,141,371

1,381,074

3,771,939

343,199

415,455
291,166
304,603
136,926

Notes: This table reports odds ratios obtained from logistic regressions. The sample consists of all NYC Stop and Frisks from
2003-2013 in which use of force and reported subgroup variables were non-missing. The dependent variable is whether any force
was used during a stop and frisk interaction, with each panel presenting results from indicated subgroups. We control for gender,
a quadratic in age, civilian behavior, whether the stop was indoors or outdoors, whether the stop took place during the daytime,
whether the stop took place in a high crime area, during a high crime time, or in a high crime area at a high crime time, whether the
officer was in uniform, civilian ID type, whether others were stopped during the interaction, and missings in all variables. Precint
and year fixed effects were included in all regressions. Standard errors, clustered at the precinct level, are reported in parentheses.

Table 3B: Analysis of Subsamples, Any Use of Force (Conditional on an Interaction), Police Public Contact Survey
White Mean Coef. on Black Coef. on Hispanic Observations
(1)
(2)
(3)
(4)
Full Sample

0.007

2.769⇤⇤⇤
(0.328)

1.818⇤⇤⇤
(0.225)

59,668

Panel A: Officer Race
Black/Hispanic

0.005

2.089
(1.336)
2.823⇤⇤⇤
(0.556)
0.653

5.584⇤⇤⇤
(3.048)
1.883⇤⇤⇤
(0.401)
0.064

2,166

2.827⇤⇤⇤
(0.384)
2.588⇤⇤⇤
(0.616)
0.747

1.912⇤⇤⇤
(0.258)
1.433
(0.426)
0.377

3.690⇤⇤⇤
(0.976)
1.848⇤⇤
(0.520)
0.073

2.368⇤⇤⇤
(0.614)
2.332⇤⇤⇤
(0.608)
0.966

16,324

2.944⇤⇤⇤
(0.534)
2.010⇤⇤⇤
(0.491)
3.942⇤⇤⇤
(1.273)
0.220

1.630⇤⇤
(0.334)
1.890⇤⇤⇤
(0.420)
1.761
(0.680)
0.887

15,014

White

0.008

p-value:
Panel B: Civilian Gender
Male
Female

0.011
0.003

p-value:
Panel C: Time of Day
Daytime
Nighttime

0.004
0.012

p-value:
Panel D: Civilian Income
$ 0 - 20,000

0.010

$ 20,000 - 50,000

0.008

$ 50,000+

0.004

p-value:

21,456

30,154
28,835

7,640

14,314
19,246

Notes: This table reports odds ratios by running logistic regressions. The sample consists of all Police Public Contact Survey
respondents between 1996-2011 in which use of force and reported subgroup variables were non-missing. The dependent variable
is whether any force was used during a contact, with each panel presenting results from indicated subgroups. We control for
civilian gender, a quadratic in age, work, income, population size of a civlian’s address, civilian behavior, contact time, contact type,
officer race, year of survey, and missings in all variables. Standard errors, robust to heteroskedasticity, are reported in parentheses.
Significance at the 10%, 5%, and 1% levels is indicated by ***, **, and *, respectively.

Table 4: Racial Differences in Lethal Use of Force (Conditional on an Interaction)
Extensive Margin, Officer Involved Shootings
Approx OIS
Taser
With Narratives
W/O Narratives
Non-Black/
Non-Hispanic Black Hispanic
Non-Black
Black
Mean
Mean
(1)
(2)
(3)
(4)
(5)
0.455
0.765
0.915
0.185
0.636⇤⇤⇤
(0.138)
(0.176)
(0.063)

Full Sample
W/O Narratives
Non-Black
Mean
(6)
0.151

Black
(7)
0.673⇤⇤⇤
(0.065)

(a)

No Controls

(b)

+ Suspect Demographics

0.786
(0.151)

0.969
(0.176)

0.650⇤⇤⇤
(0.066)

0.683⇤⇤⇤
(0.067)

(c)

+ Officer Demographics

0.780
(0.192)

1.115
(0.294)

0.726⇤⇤
(0.094)

0.749⇤⇤
(0.087)

(d)

+ Encounter Characteristics

0.890
(0.252)

0.991
(0.295)

0.687⇤⇤⇤
(0.098)

0.754⇤⇤
(0.097)

(e)

+ Suspect Weapon

0.806
(0.284)

1.333
(0.489)

(-)

(-)

(f)

+ Year

0.726
(0.257)

1.211
(0.457)

0.693⇤⇤
(0.099)

0.758⇤⇤
(0.098)

5,012

5,994

Observations

1,532

Notes: This table reports odds ratios from logistic regressions. The sample for each regression is displayed in the top row. For columns (1)-(3), the sample consists
of all officer involved shootings in Houston from 2000 - 2015, plus a random draw of all arrests for the following offenses, from 2000 - 2015: aggravated assault on
a peace officer, attempted capital murder of a peace officer, resisting arrest, evading arrest, and interfering in an arrest. These arrests contain narratives from police
reports. For columns (4)-(5), the sample consists of all officer involved shootings in Houston from 2000 - 2015, plus a sample of arrests where tasers were used. These
arrests do not contain narratives from police reports. For columns (6)-(7), the sample combines all officer involved shootings in Houston from 2000 - 2015, plus a
random draw of all arrests for the following offenses, from 2000 - 2015: aggravated assault on a peace officer, attempted capital murder of a peace officer, resisting
arrest, evading arrest, and interfering in an arrest, plus arrests where tasers were used. These arrests do not contain narratives from police reports. Data without
narratives have no information on officer duty, civilian’s attack on officer and civilian weapon. The dependent variable is whether the officer fired his gun during the
encounter. The omitted race is non-blacks (with the exception of the sample with narratives where the omitted race is non-black/non-Hispanic). The first column for
each sample gives the unconditional average of contacts that resulted in an officer firing his gun. The second column for each sample reports logistic estimates for
black civilians. Each row corresponds to a different empirical specification. The first row includes solely racial dummies. The second row adds civilian gender and
a quadratic in age. The third row adds controls for the split of races of officers present at the scene, whether any female officers were present, whether officers were
on duty or not, whether multiple officers were present and the average tenure of officers at the scene. The fourth row adds controls for the reason the officers were
responding at the scene, whether the encounter happened during day time, and whether the civilian attacked or drew a weapon. The fifth row adds controls for the
type of weapon the civilian was carrying. The sixth row adds year fixed effects for columns (1)-(2). It adds year as a categorical variable for columns (3)-(8). Each
row includes missing in all variables. For arrest data without narratives missing indicators for officer gender, officer tenure, and number of officers on the scene were
removed to minimize loss of observations in logistic regressions. For all regression, missing indicators for response reason and for whether the civilian attacked or
drew a weapon was removed for the same reason. Standard errors are robust and are reported in parentheses.

Table 5: Racial Differences in Lethal Use of Force (Conditional on an Interaction)
Intensive Margin, Officer Involved Shootings
Non-Black/
Non-Hispanic
Black
Hispanic
Mean
(1)
(2)
(3)
(a) No Controls
0.542
0.959
1.080
(0.116)
(0.246)
(b)

+ Suspect Demographics

0.933
(0.093)

1.026
(0.263)

(c)

+ Officer Demographics

0.824⇤
(0.089)

0.886
(0.223)

(d)

+ Encounter Characteristics

0.683⇤⇤⇤
(0.094)

0.752
(0.189)

(e)

+ Suspect Weapon

0.568⇤⇤⇤
(0.064)

0.633⇤
(0.153)

(f)

+ Fixed Effects

0.534⇤⇤⇤
(0.043)

0.562⇤⇤
(0.131)

Observations

1,316

Notes: This table reports odds ratios from logistic regressions. The sample consists of
officer involved shootings from Dallas, Austin, six Florida counties, Houston and Los Angeles between 2000 to 2015. The dependent variable is based on who attacked first. It is
coded as 1 if the officer attacked the suspect first and 0 if the suspect attacked the officer
first. The omitted race is non-blacks and non-hispanics. The first column gives the unconditional average of contacts that resulted in an officer firing his gun. The second column
reports logistic estimates for black civilians. Each row corresponds to a different empirical
specification. The first row includes solely racial dummies. The second row adds civilian
gender and a quadratic in age. The third row adds controls for the split of races of officers
present at the scene, whether any female officers were present, whether multiple officers
were present and the average tenure of officers at the scene. The fourth row adds controls
for the reason the officers were responding at the scene, whether the encounter happened
during day time, and whether the civilian attacked or drew a weapon. The fifth row adds
controls for the type of weapon the civilian was carrying. The sixth row adds city and year
fixed effects. Each row includes missing in all variables. Standard errors are clustered at
the police department level and are reported in parentheses.

Table 6: Fraction Weapon Found, Conditional on Being
in an Officer Involved Shooting
Civilian White Civilian Black p-value
(1)
(2)
(3)
Officer White
0.842
0.809
(0.028)
(0.026)
0.388
Officer Black

p-value

0.571
(0.137)

0.730
(0.056)

0.011

0.175

0.246

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. Th third column displays the p-value for equality of means
in columns (1) and (2). The first row presents the fractions when the majority of officers
present during the encounter were white. The second row presents the fractions when
the majority of officers present during the encounter were black.

2

Panel A

Black vs White CI (Full)

6

Black vs White CI (None)

5

Black vs White (Full)

4
Use of Force Rank

Black vs White (None)

3

7

1

2

4
Use of Force Rank

Panel B

Hispanic vs White (Full)

Hispanic vs White (None)

3

6

Hispanic vs White CI (Full)

Hispanic vs White CI (None)

5

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 di↵erent use of force types: 1 is an
indicator for whether the police reported using at least hands or a more severe force on a civilian in a stop and frisk interaction. 2 is for whether
the police reported at least pushing a civilian to a wall or using a more severe force. 3 is for whether the police reported at least using handcu↵s
or a more severe force. 4 is for whether the police reported at least drawing a weapon on a civilian or using a more severe force. 5 is for whether
the police reported at least pushing a civilian to the ground or using a more severe force. 6 is for whether the police reported at least pointing
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 e↵ects were included in
the controlled regression. Standard errors are clustered at the precinct level.

1

Figure 1: Odds Ratios by Use of Force (Conditional on an Interaction), NYC Stop Question and Frisk

1.8

Odds Ratio for Black
1.2
1.4
1.6

1

2
Odds Ratio for Hispanic
1
1.5
.5

Black vs White CI

Panel B

Black
mean_white

White
hi_white/lo_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
Hour

Notes: These figures plot odds ratios with 95% confidence intervals and averages with 95% confidence intervals. For the figure in Panel A, the
y-axis denotes the odds ratio of reporting any use of force for black civilians versus white civilians. For the figure in Panel B, the y-axis denotes
the average fraction of white and black civilians who had any force used against them. For both figures, the x-axis denotes di↵erent hours of the
day. For Panel A, odds ratios are achieved by regressing any use of force on civilian race dummies, civilian gender, a quadratic in age, civilian
behavior, whether the stop was indoors or outdoors, whether the stop took place during the daytime, whether the stop took place in a high crime
area or a high crime time, whether the officer was in uniform, civilian ID type, whether others were stopped during the interaction, and missings
in all variables, for every hour of day. Precinct and year fixed e↵ects were included in all regressions. Standard errors are clustered at the precinct
level.

Panel A

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
Hour

Figure 2: Odds Ratios of Any Use of Force (Conditional on an Interaction) by Time of Day, NYC Stop
Question and Frisk

1.6

Odds Ratio for Black
1.2
1.4

1

.3
Average Use of Force
.15
.2
.25
.1
.05

Panel A

3

Black vs White CI (None)
Black vs White CI (Full)

Use of Force Rank

Black vs White (None)
Black vs White (Full)

2

4
1

Hispanic vs White CI (Full)

Panel B

Hispanic vs White CI (None)

3

Hispanic vs White (Full)

Use of Force Rank
Hispanic vs White (None)

2

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 di↵erent use of force types: 1 is an
indicator for whether the survey respondent report the officer at least grabbing him/her in an interaction. 2 is for whether the respondent reported
the police handcuffing him/her or using a more sever force in an interaction. 3 is for whether the survey respondent reported the 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.

1

Figure 3: Odds Ratios by Use of Force (Conditional on an Interaction), Police Public Contact Survey

8

Odds Ratio for Black
2
4
6

0

5
Odds Ratio for Hispanic
2
3
4
1

1.4

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 o↵enses, from 2000 - 2015: aggravated assault on a peace officer,
attempted capital murder of a peace officer, resisting arrest, evading arrest, and interfering in an arrest ,plus a sample of arrests where tasers
were used. The y-axis denotes odds ratios of an officer shooting at a black civlian versus a white civilian. The x-axis denotes the period of years
for which the odds ratios were calculated. We control for civilian gender, a quadratic in age, officer demographics, encounter characteristics, and
missings in all variables (i.e. all variables included in the final row of Table 4). Year fixed e↵ects are included in all regressions. Robust standard
errors are reported in parentheses.

2000-2005

2006-2010

Figure 4: Odds Ratios for Officer Involved Shootings (Conditional on an Interaction), Extensive Margin, By
Year Categories

Odds Ratio for Black

1.2
1
.8
.6
.4

.4

.6

Odds Ratio for Hispanic
.6
.8
1

Odds Ratio for Black
.8
1
1.2

1.2

1.4

Figure 5: Odds Ratios by Use of Force for Perfectly Compliant Civilians (Conditional on an Interaction),
NYC Stop Question and Frisk

1

2

3

4
Use of Force Rank

Black vs White (Full)

Panel A

5

6

Black vs White CI (Full)

7

1

2

3

4
Use of Force Rank

Hispanic vs White (None)

5

6

7

Hispanic vs White CI (None)

Panel B

Notes: These figures plot odds ratios with 95% confidence intervals from logistic regressions. For the figure on the left, the y-axis denotes the
odds ratio of reporting various uses of force for perfecly compliant black civilians versus perfect compliant white civilians. For the figure on the
right, the y-axis denotes the odds ratio of reporting various uses of force for perfectly compliant hispanic civilians versus perfectly compliant white
civilians. For both figures, the x-axis denotes di↵erent use of force types: 1 is an indicator for whether the police reported using at least hands or
a more severe force on a civilian in a stop and frisk interaction. 2 is for whether the police reported at least pushing a civilian to a wall or using
a more severe force. 3 is for whether the police reported at least using handcu↵s or a more severe force. 4 is for whether the police reported at
least drawing a weapon on a civilian or using a more severe force. 5 is for whether the police reported at least pushing a civilian to the ground or
using a more severe force. 6 is for whether the police reported at least pointing 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 e↵ects were included in all regressions. Standard errors are clustered at the
precinct level.