Assessing the County-Level
Structural Covariates
of Police Homicides
Homicide Studies
Volume 12 Number 4
November 2008 350-380
© 2008 Sage Publications
10.1177/1088767908323863
http://hs.sagepub.com
hosted at
http://online.sagepub.com
Robert J. Kaminski
University of South Carolina
Largely paralleling research on general homicides, research on the structural covariates
of murders of police has been carried out at various levels of areal aggregation. However,
although the general homicide research has been extended to counties in the United
States, research on murders of police has yet to follow suit. To begin to fill this gap, this
study extends research on the structural covariates of police homicides to the county level.
Controlling for the number of law enforcement officers at risk, we find that police were
more likely to be murdered in economically depressed counties and in counties with
larger percentages of African Americans, persons aged 25 to 34, and nonsheriff agencies.
Police homicide risk was significantly lower in urbanized counties and in counties located
in the Northeast, whereas the South was no riskier than the West or Midwest. Murders of
police were unrelated to population mobility, divorce, and levels of violent crime.
Keywords:
police; murder; homicide; victimization; counties
W
ith few exceptions, the extant regression-based research on homicides of police
emphasizes the role of adverse structural conditions that generate criminal
motivations or free individuals to engage in crime, a perspective consistent with traditional macrosocial theories developed to explain crime and violence generally
(Merton, 1938; Shaw & McKay, 1969). The implicit assumption in most studies is
that crime and violence in general and violence against the police in particular share
common structural causes, and thus the factors that predict the former should also
predict the latter (Kaminski & Marvell, 2002; Peterson & Bailey, 1988). An examination of the regressors employed in the police homicide literature (discussed later)
shows that they are often the same as those used in studies of general homicides,
with many reflecting various dimensions of the control, strain, or criminal opportunity
theoretic perspectives (Land, McCall, & Cohen, 1990; Parker, McCall, & Land,
Author’s Note: The author thanks Frankie Kelly at the Federal Bureau of Investigation for providing the
data on law enforcement officers killed feloniously in the line of duty and also thank the anonymous
reviewers for their helpful comments on an earlier draft. Correspondence concerning this article should
be addressed to Robert J. Kaminski, Department of Criminology and Criminal Justice, Currell College,
University of South Carolina, Columbia, SC 29208; e-mail: kaminskb@mailbox.sc.edu.
350
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Kaminski / County-Level Covariates of Police Homicides 351
1999). Most commonly, though, these studies include one or more of the core indicators of the social disorganization perspective, that is, population size and density,
racial/ethnic heterogeneity, economic deprivation, population mobility, and family
disintegration (Kornhauser, 1978; Sampson, 1986; Shaw & McKay, 1969). As noted
by Land et al. (1990),
The central hypothesis of the neoclassical community-control theory is that these and
related community-level characteristics . . . directly or indirectly affect informal social
control networks, community attachment, anonymity, and the capacity for surveillance
and guardianship. A weakening of these dimensions of social organization is posited to
lead to increased rates of deviance and crimes such as homicide. (p. 925)
Further examination of the police homicide literature leads to two other observations. First, more than two decades of research on police homicides has failed to
identify virtually any regressor that is statistically significant and of the same sign
across all models or studies (Batton & Wilson, 2006; Kaminski & Marvell, 2002), a
situation similar to that described by Land and his colleagues more than a decade
ago regarding research on general homicides (Land et al., 1990). Thus, additional
research is needed to better understand the social and economic conditions that give
rise to serious violence against the police.
Second, all of the studies attempting to explain the spatial variation in police homicides have been limited to the use of cities or states as units of analysis.1 Although various arguments as to the strengths and weaknesses of these two areal units may be
made, extending the study of structural covariates and police homicides to counties is
important because geographic boundaries are arbitrary with respect to social theory,
and a general theory of how structural conditions affect homicide rates should, therefore, be capable of accommodating all levels of spatial aggregation (Land et al., 1990).
Furthermore, although the appropriateness of the use of large enumeration units such
as counties to study the effects of community structural characteristics derived from
social disorganization theory on crime has been questioned (Bailey, 1984; Petee,
Kowalski, & Duffield, 1994, p. 118), a growing body of research has extended such
analyses to counties (e.g., Baller, Anselin, Messner, Deane, & Hawkins, 2001; Kposowa,
Breault, & Harrison, 1995; Osgood & Chambers, 2000; Weisheit & Wells, 2005;
Wilkinson, 1984). As a first step in extending this line of inquiry to murders of police,
this paper presents a county-level analysis relating police homicides to the structural features of communities specified by social disorganization theory and its extensions.
Explaining Murders of Police
Precisely how structural conditions influence risk of police homicide victimization has not been well explicated in much of the police homicide literature, which
is partly due to several studies that focused on the impact of various crime-control
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352 Homicide Studies
policies on murders of police, with structural measures simply included as controls
(Bailey, 1982; Bailey & Peterson, 1987, 1994; Moody, Marvell, & Kaminski, 2002;
Mustard, 2001). Generally, however, the assumption has been that adverse structural
conditions such as poverty, racial heterogeneity, divorce, and population mobility
generate crime and that these structurally induced opportunities increase the likelihood of police coming into contact with offenders, some of whom are willing to
resist, assault, and murder police officers (Chamlin, 1989, p. 353; Kaminski, 2002,
2004; Peterson & Bailey, 1988). According to this perspective, felonious killings of
police are primarily a byproduct of ordinary criminal violence, with most police
being killed by offenders who wish to avoid apprehension and punishment
(Cardarelli, 1968; Creamer & Robin, 1970; Jacobs & Carmichael, 2002; Kaminski,
2002, 2004; Margarita, 1980b). Support for the traditional structural covariates
examined is mixed, with few consistent findings within or across studies (Table 1).
A second, but related perspective, draws more directly on criminal opportunity
theory to explain areal or temporal variation in violence against police (Fridell,
Faggiani, & Brito, 2004; Kaminski, 2002, 2004). According to this view, variation in
structural conditions affects both motivations for crime and opportunities for crime
(Cohen & Felson, 1979; Hindelang, Gottfredson, & Garofalo, 1978; Miethe &
McDowall, 1993). Criminal opportunity models, for example, commonly measure
proximity to motivated offenders using indicators of adverse structural conditions
(see, for example, Hough, 1987; Miethe & Meier, 1994; Sampson & Wooldredge,
1987). Miethe and McDowall (1993) explained how, from a social disorganization
perspective, criminogenic conditions in areas increase motivations for crime, whereas
from an opportunity perspective they “increase victimization risks by increasing individuals’ exposure to motivated offenders, target attractiveness, and reducing the level
of social control or guardianship” (pp. 747-748). In other words, criminogenic forces
such as population density and heterogeneity, family disruption, residential mobility,
and economic strain “generate a facilitating context for crime by increasing the pool
of potential offenders. The greater one’s proximity to these criminogenic areas, the
greater one’s risk of victimization” (Miethe & Meier, 1994, p. 44).
According to this view, adverse structural conditions facilitate opportunities for
serious and fatal assaults of law enforcement officer by increasing the likelihood of
the convergence in time and place of offenders engaged in serious crime who are
motivated to avoid apprehension and punishment, and law enforcement officers
whose mandate is to intervene in crime and apprehend offenders (Cardarelli, 1968;
Creamer & Robin, 1970; Kaminski, 2002, 2004; Margarita, 1980b). The more
adverse the structural conditions over time or place, the larger the pool of motivated
offenders and the greater the risk of officer victimization, other factors being equal.
Additional opportunity factors that arguably influence police vulnerability and
exposure to offenders include police officer density, arrests, and organizational policies designed to harden officers as targets, such as mandatory vest-wear policies,
(text continues on p. 358)
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353
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56 Cities &
1977-1984 &
1985-1992
Fridell &
Pate, 1995
OLS monthly time series
Welfare
Poverty index
Hispanic
Property crime
ns
ns/–
ns
+/ns
ns
(2/3) +
(1/3) –
(1/3) +
(3/6) +
ns
–
Black
Poverty
Gini
Black
Hispanic
Unemployment
Black
(3/6) +
ns
ns
ns
ns
National
1976-1989
Bailey &
Peterson,
1994
Divorce
(2/8) +
ns
ns
Poverty
Gini
Racial Gini
(2/8) +
ns
Age
OLS cross section regression, Density
2 models
Age
Income
States 1980-1982 OLS & ridge cross section
regressions, 6 models
Chamlin, 1989
Divorce
Urban
(2/11) +
(3/11) +
(2/11) +
(6/12) +
(2/12) –/+
(5/12) –/+
Strain/Deprivation
Poverty
Unemployment
Non-White
(1/12) + Poverty
Black
Sex ratio
ns
+
ns
States 1977-1984 OLS, 8 annual cross
sections
Peterson &
Bailey, 1988
Age
Urban
Informal Social
Control/Disorganization
Divorce
Urban
States 1973-1984 OLS, 12 annual cross
sections
Bailey &
Peterson, 1987
Method
States 1961-1971 OLS, 11 annual cross
sections
Unit/Period
Bailey, 1982
Source
Table 1
Regression-Based Studies of Murders of Police
South
Violent crime
Gun crime
Violent arrests
Property arrests
Assaults of cops
Executions
Executions
in media
South
Violent crime
Property crime
Index crime
Executions
South
Homicide crime
Violent crime
Property crime
Index crime
Index crimes
Index arrests
Sworn cops
Executions
Other
(continued)
ns
+
+/ns
–/ns
+/ns
ns
ns
ns
(2/12) +
ns
ns
ns
ns
ns
ns
ns
ns
ns
(3/6) –
ns
(2/6) –
ns
354
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States, 1984-1996 Weighted & unweighted
fixed effects Tobit and
Poisson pooled
regressions, 16 models
Mustard, 2001
2SLS weighted OLS fixed
effects pooled regression,
2 models
174 Cities 1987,
1990, & 1993
Lott, 2000
OLS annual time series
Method
National
1961-1993
Unit/Period
Southwick, 1998
Source
Age
Population
size
Population
density
Sex (%
female)
nr
nr
nr
nr
Age
nr
Population nr
size
Informal Social
Control/Disorganization
Table 1 (continued)
nr
nr
nr
nr
Unemployment
Income
Income
Income
maintenance
Unemployment
Retirement
compensation
Black
White
Other race
nr
nr
Other race
Male
nr
nr
nr
nr
nr
nr
nr
Black
Hispanic
Strain/Deprivation
Expenditure per
officer
Officer pay
Violent crime
Property crime
Violent crime
arrests
Property crime
arrests
nr
nr
nr
nr
nr
nr
nr
(6/16) –
(3/16) –
ns
ns
ns
+
–
ns/+
–/+
(continued)
No. of sworn cops
Shall issue law
Waiting period
Male cops
Mandatory
vest policy
Gun availability
Male officers
Police wages
Black cops
Minority cops
Other
355
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165 Cities, 1980
190 Cities,
1987-1997
Kaminski,
2002, 2004
Unit/Period
Jacobs &
Carmichael,
2002
Source
Residential ns
stabilitya
Population ns
density
Concentrated
disadvantageb
(8/8) +
ns/+
+
+
Black mayor
Violent crime
Robbery
Murder
Police killings
of Blacks
Black × Pop.
South
Index arrests
Field officer
density
Female officers
ns
ns
(9/10) –
ns
ns
+
Northeast
(10/10) –
(continued)
+
ns
(1/1) +
ns
(9/9) +
(9/9) –
ns
ns
Midwest
(8/8) +
ns
South
Other
(2/10) +
Strain/Deprivation
Population (10/10) + Black
size
Population ns
Black growth
density
Divorce
(10/10) + Black to White
income
Femalens
Gini
headed
Black
family
Femalens
Poverty
headed
White
family
Segregation
Unemployment
Crowding
Informal Social
Control/Disorganization
Generalized estimating
equations, 4-wave Poisson
panel model, 2 models
Poisson & negative
binomial regression,
10 cross section models
Method
Table 1 (continued)
356
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National,
1930-1998
States,
1973-1993
Moody et al.,
2002
Unit/Period
Kaminski &
Marvell, 2002
Source
Fixed-effects Poisson &
negative binomial
regressions, 12 models
OLS & SUR annual time
series; 2 models
Method
nr
nr
ns/+
Divorce
Age
Urban
ns
Age
Informal Social
Control/Disorganization
Table 1 (continued)
ns
Poverty
Unemployment
Income
Black
Inflation
nr
nr
nr
nr
ns/+
Income
–
Consumer prices +/ns
Unemployment
Strain/Deprivation
Firearms trend
Body armor
use trends
Crack trend
Executions
Incarceration
WWII 42-45
WWII 43-44
3-strikes laws
Prison pop
Executions
Shall issue law
Firearm
sentencing
enhancement
ns
ns
–
–
ns
9/12 +
ns
ns
ns
6/12 –
ns
ns
ns
ns
ns
ns
–
ns
ns
ns
(continued)
1-officer patrols
Foot patrol
Semiautos only
authorized
Chemical agents
Police education
Police training
Index arrests ×
Pop. density
interaction term
Trauma systems
Other
357
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National,
1947-1998
Batton &
Wilson, 2006
OLS annual time series,
6 models
Poisson cross section
regression, 2 models
Method
ns
Femalens
headed
families
Intact
ns
families
Population ns
hetereogeneity
Divorce
Population ns
size
Population ns
structure
Divorce
ns
Informal Social
Control/Disorganization
Police killings
of Blacks
Black police
Executions
ns
Murder rate
4/4+
2/2+
Unemployment
Inflation
Nonemploymentd 4/4+
Incarceration
Public assistance 2/2
–
Gini
4/4+
ns
Blacks on city
council
Violent crime
ns
Black to White
income
Economic
deprivationc
Segregation
Black mayor
ns
Black growth
Northeast
+
Other
Black
Strain/Deprivation
4/4+
2/2–
ns
1/1+
+
ns
–
ns
ns
Note: Numbers in parentheses indicate the number of models from the total models estimated in which a regressor was significant at the .05 level when there
were more than two models; ns = not significant; nr = nor reported; + = positive association; – = negative association; –/+ = mixed directional findings;
OLS = ordinary least squares; 2SLS = two-stage least squares; SUR = seemingly unrelated regression.
a. Residential stability is a principal component consisting of residential stability and males 15-29 (inversely related).
b. Concentrated disadvantage is a principal component comprised of poverty, female-headed households with own kids, income, non-Hispanic Black, Black
racial segregation, income inequality, unemployment, and percentage divorced or separated.
c. Economic deprivation is a principal component comprised of poverty, unemployment, and income.
d. Nonemployment refers to persons not in the labor force for legitimate (e.g., retirement) or illegitimate reasons (e.g., underground economy).
190 Cities, 1995
Unit/Period
Kaminski &
Stucky, 2005
Source
Table 1 (continued)
358 Homicide Studies
two-officer patrols, and the replacement of revolvers with semiautomatic sidearms
(Kaminski, 2002, 2004).2 Except for the level of police officer density (proximity)
and aggregate numbers of arrests (exposure), the limited empirical research on organizational opportunity factors has been unable to demonstrate a significant impact on
police victimization risk (Fridell et al., 2004; Kaminski, 2002, 2004).
A third perspective, rooted in conflict theory and the racial threat hypothesis (Eitle,
D’Alessio, & Stolzenberg, 2002; Jackson, 1989), maintains that variation in the rate
of police homicides across enumeration units can be explained in part by political factors, specifically the economic and political subordination of Blacks by the state
(Chamlin, 1989; Jacobs & Carmichael, 2002).3 According to this view, many murders
of police by Blacks are a response to this subordination in the form of inarticulate
protest or primitive rebellion directed against repressive state agents (Jacobs &
Carmichael, 2002). Jacobs and Carmichael (2002) provided the most comprehensive
test of this perspective. Using cities as the unit of analysis, they found that the presence
of a Black mayor—whose presence they consider a direct political explanation—was
consistently significant and inversely related to police killings across many model
specifications. Thus, their study provided strong support for their key theoretical finding and the racial threat hypothesis. However, a reanalysis and extension of Jacobs
and Carmichael found no support for a Black mayor effect (Kaminski & Stucky,
2005). Findings from research that included other measures that may be interpreted
as being consistent with the conflict/racial threat perspective (e.g., percentage Black
and income inequality) have been inconsistent (Table 1).
In summary, the extant research provides little empirical support for any particular theoretical perspective, no less any specific explanatory factor. Testing competing theoretical perspectives is beyond the scope of the present study, suffice to say
that the structural covariates examined here are most closely aligned with social disorganization theory and the neoclassical community-control perspective articulated
by Land et al. (1990).
Extending the Analysis of Structural Conditions to Counties
Social disorganization theory and its extensions have been developed and tested
primarily in urban settings, and there has been some debate in the literature as to
whether or not it is appropriate to extend the analysis of the structural factors specified by social disorganization theory to (largely) nonurban areas such as counties
(Bailey, 1984; Osgood & Chambers, 2000; Petee et al., 1994). However, as Osgood
and Chambers (2000) pointed out, the concept of social disorganization was originally developed by Thomas and Znaniecki (1958) to explain the impacts of migration and industrialization in urban areas in Chicago as well as in rural areas in
Poland. Drawing on the work of Bursik and Grasmick (1993) and others (e.g.,
Wilkinson, 1984), Osgood and Chambers (2000) argued that the private, parochial,
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Kaminski / County-Level Covariates of Police Homicides 359
and public systems of social control are as applicable to crime in rural areas as they
are to urban communities: “The logic by which primary, parochial, and public
spheres would affect social control has everything to do with general principles of
social relations and nothing to do with urban versus rural settings” (p. 85). Similar
sentiments were expressed by Land and colleagues (1990) in their tests of the invariance thesis, and they argued that a general theory of how structural conditions affect
homicide rates should be capable of accommodating all levels of spatial aggregation.
The study by Land et al. (1990) and Osgood and Chambers’ (2000) county-level
analysis of structural factors provided substantial theoretical and empirical support
for the generality of social disorganization theory beyond metropolitan areas. Given
their findings and the growing number of studies examining the impact of structural
conditions on crime at the county level (e.g., Baller et al., 2001; Kposowa et al.,
1995; Weisheit & Wells, 2005), it is important to extend research on structural conditions and police homicides to counties.
Data and Measures
Data for the dependent variable, the number of law enforcement officers murdered
in the line of duty between 1990 and 2000 (N = 544), were obtained by request
directly from the Federal Bureau of Investigation.4 Because we cannot apportion federal or state police to counties, only local law enforcement officer deaths are
included in the analysis (municipal, county, sheriff). Using a common identifier
(ORI code), each felonious killing was matched to data on the victim officer’s
employing agency in the 1996 Directory of Law Enforcement Agencies (Bureau of
Justice Statistics, 1998). Using the appropriate state and county codes in the directory, we then aggregated the number of officers murdered, the number of full-time
equivalent (FTE) sworn employees in 1996, and the number of types of law enforcement agencies in 1996 to counties and county equivalents.5 Because murders of
police are extremely rare events, they are summed over the 11-year period (see, for
example, Jacobs & Carmichael, 2002; Kaminski & Stucky, 2005). Although shorter
temporal aggregations may be possible using larger units of analysis, this simply is
not feasible when using counties.
Summary statistics and definitions for the dependent and independent variables
appear in Table 2. Because felonious killings of police are summed over a decade and
our exposure variable is based on the population of law enforcement officers in 1996,
Census-based variables were calculated by averaging 1990 and 2000 values. Variables
controlling for economic disadvantage are poverty, unemployment, and median
household income. These factors have been linked to higher rates of crime because
conditions that encourage criminal behavior (e.g., need for income, leisure time) are
more pronounced in such areas where social-control mechanisms are weaker and
blocked opportunities generate frustrations that can lead to diffuse hostility and
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360 Homicide Studies
aggression (Brantingham & Brantingham, 1984; Bursik & Grasmick, 1993; Krivo &
Peterson, 1996; Parker & McCall, 1999; Sampson, Morenoff, & Earls, 1999;
Sampson & Raudenbush, 1999; South & Cohen, 1985).
Residential mobility, racial heterogeneity, family disruption, and large and dense
populations are structural features of communities associated with weak formal and
informal social controls and thus higher levels of crime and delinquency (Bursik &
Grasmick, 1993; Kornhauser, 1978; Krivo & Peterson, 1996; Sampson et al., 1999;
Sampson & Raudenbush, 1999; Shaw & McKay, 1969). Residential mobility is a key
theoretical construct of social disorganization theory (Shaw & McKay, 1969), which
argues that high levels of population mobility disrupt a community’s social relations
and control, leading to higher rates of offending (Kornhauser, 1978; Sampson &
Groves, 1989). We use its inverse for the analysis—residential stability—defined as
the percentage of the population residing in the same household as five years earlier.
Consistent with social disorganization theory (Shaw & McKay, 1969), family
breakup is linked to reductions in informal social control as single-parent households
are less able to provide supervision and guardianship for their own children, household
property, and the community generally (Sampson, 1985; Sampson & Groves, 1989).
Family disruption is measured by the percentage of the population that is divorced.
Population size and density are included as measures of population structure.
Large and dense populations are thought to increase crime and delinquency because
they weaken interpersonal ties and inhibit social participation in local affairs, leading
to a weakening of social-control mechanisms (Brantingham & Brantingham, 1984;
Land et al., 1990; Sampson, 1986; Sampson & Groves, 1989). Increases in population size and density are also thought to increase the likelihood of social contact and
interpersonal conflict (Blau & Blau, 1982; Blau & Golden, 1986), proximity to motivated offenders (Cohen, Kluegel, & Land, 1981), and opportunities for the commission of predatory crimes (Felson, 1998). In addition, because counties may consist of
a mix of rural and urban areas, and urbanicity versus rurality has been found to be an
important determinate of crime (Kposowa et al., 1995; Wilkinson, 1984), we also
include the percentage of the county population that resided in an urban area.
High levels of racial/ethnic heterogeneity impede communication, patterns of
interaction, and the ability of residents to achieve consensus and control, thus
increasing the potential for crime and delinquency (Parker et al., 1999; Sampson &
Groves, 1989; Shaw & McKay, 1969).6 However, rather than including a measure of
racial/ethnic heterogeneity, we use the percentage of the population that is (nonHispanic) Black. There are three reasons for choosing this measure. First, relative to
their representation in the population, African Americans are disproportionately represented among felons who murder police. Specifically, Blacks represent about 13%
of the population, but 43% of felons who kill police (Brown & Langan, 2001). (This
disproportionality, of course, increases substantiality if one were to consider that
most felons who kill police are male and neither very old nor very young.) Second,
rates of violent crime tend to be especially high in poor, Black communities (Blau
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Kaminski / County-Level Covariates of Police Homicides 361
Table 2
Summary Statistics for Variables Used in the Analysis
Variable
Min
POLKIL—No. of officers killed
feloniously, 1990-2000
SWORN—No. of FTE sworn officers
in 1996
AGENCY—No. of sheriff’s agencies in
county in 1996
POPULATION—Population size
DENSITY—Population density
URBANICITY—% population residing
in urban area
POVERTY—% population below official
poverty line
UNEMPLOYMENT—% population
unemployed
INCOME—Median household income
DIVORCE—% divorced population
RESTABLE—% in same house as 5 yrs.
earlier
AGE2534—% population aged 25-34
BLACK—% non-Hispanic Black
population
REGION—Region, Census classification
VIOLENT CRIME—Avg. no. of violent
crimes, 1994-1996
Max
Mean
0
26
0.18
1
41,049
0
191
SD
0.92
1,060
100.0
32.3
24.3
9,191,251
25,054
100.0
84,803
193
15.0
303,660
836
30.0
0
57.2
15.2
7.0
0
23.9
5.0
2.1
12,200
1.8
14.4
70,167
16.1
81.3
29,550
8.2
58.8
7,553
1.8
7.7
7.5
0
28.1
86.1
14.9
8.6
87
0.10
0
1
0
4
125,918
2.4
534
1.52
14.4
1.4
3,798
Note: Data on the 544 police killed feloniously in the line of duty 1990-2000 are from the Federal Bureau
of Investigation; data on the number of full-time equivalent (FTE) sworn law enforcement officers are from
the Bureau of Justice Statistics (1998); Census variables are averages of 1990 and 2000 values; violent
crimes are mid-decade estimates based on the average number of violent crimes 1994-1996 (excluding
rape) and are from the FBI’s Uniform Crime Report (UCR; missing data were taken from adjacent years).
& Blau, 1982; Parker, 2001; Wilson, 1987), which arguably increases police risk of
violent victimization. Third, percentage Black has been the most commonly used
measure of race in studies of homicide (Land et al., 1990; Parker et al., 1999) and in
studies of murders of police (Table 1). Using percentage Black, therefore, allows for
a greater number of direct comparisons of the effect of race at the county level to its
effects at other levels of aggregation.
Control Variables
Control variables are measures of age structure, region, violent crime, and
types of law enforcement agencies within counties. Previous studies find virtually no
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362 Homicide Studies
association between age structure and murders of police (Table 1). However, statistics compiled by the FBI show that somewhat older offenders tend to kill police. For
instance, of felons who murdered police between 1988 and 1997, 11.1% were under
18 years of age, 37.0% were aged between 18 and 24 years, and another 51.9% were
aged 25 years or older (table 20 in Federal Bureau of Investigation, 1997, p. 36).
Therefore, we include the percentage of the population aged 25-34 years to control
for the potential effect of differences across counties in age structure (we test alternative age groupings as well).
Indicators of region are included to control regional differences in police homicide
risk. Kaminski et al. (2000) identified significant spatial clustering of homicides of
police in the southeastern United States, and simple tabular analyses adjusting for
levels of violent crime, arrests, population, or the number of law enforcement officers
employed consistently show that police are at greater risk of being murdered in the
South than in other areas (Cardarelli, 1968; Federal Bureau of Investigation, 1997;
Fridell & Pate, 1997; Geller & Scott, 1992). Although substantial theoretical and
empirical work has focused on cultural/subcultural differences for explaining higher
levels of violence among Southerners and other groups (Corzine, Huff-Corzine, &
Whitt, 1999; Ousey, 2000),7 other research suggests structural poverty and economic
inequality account for the higher levels of homicide observed in the South (Blau &
Blau, 1982; Loftin & Hill, 1974; Smith & Parker, 1980; Williams, 1984). Regardless
of the causes, it is important to control for regional differences, and we include indicators of the South, West, and Midwest, with the Northeast serving as the reference
category (Bureau of the Census classification).
Studies of whether police risk of homicide varies by type of law enforcement
agency have not been conducted. We do not hypothesize a direction for the effect of
agency type, but sheriff’s departments and other types of agencies (municipal and
county police departments) can differ in function, geographic coverage, or in other
ways that may affect risk (e.g., training, policies). To control for this possibility, the
percentage of agencies that were sheriff’s offices in 1996 (agency) is included in the
analysis (Bureau of Justice Statistics, 1998). Thus, low values on this measure indicate counties with many municipal agencies, a value of 100% indicates counties in
which the only law enforcement agency is a sheriff’s department (7.9% of counties),
and a zero (7% of counties) represents counties in which there is no sheriff’s agency
(e.g., a county police department has jurisdictional responsibility).
A final variable included in our model, violent crime, is what Kaminski, Jefferis,
and Gu (2003) referred to as propensity for violence. Using Uniform Crime Report
(UCR) data (Federal Bureau of Investigation, 2001), this is the average of the sum
of the number of homicides, aggravated assaults, and robberies per county between
1994 and 1996 (rape is excluded because it is one of the least reliably reported
crimes).8 To reduce collinearity with the other variables in the model, we regress violent crime on three structural factors derived from a principal components analysis
(discussed later), and use the residuals in the regression (Roncek, 1997). The violent
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Kaminski / County-Level Covariates of Police Homicides 363
crime residuals represent the level of violent crime in counties not explained by their
structural characteristics (plus error). Previous research found this measure was positively associated with serious but nonfatal assaults on police at the block-group level
in Boston (Kaminski et al., 2003), and we anticipate that police risk of being murdered will be higher in counties that have a greater propensity for violence, net of
structural conditions and other variables in our model.
Methods
There are three issues that deserve careful attention in the analysis of homicides
of police across enumeration units; these are the rare-event–count nature of police
killings, spatial autocorrelation, and multicollinearity among the regressors. An
additional concern is the presence of within-unit heterogeneity when analyzing large
spatial aggregates, such as states or counties (Bailey, 1984; Osgood & Chambers,
2000). Each issue is discussed in turn.
As displayed in Figure 1, the distribution of the number of murders of police
office across counties and county equivalents over the 11-year period is extremely
skewed. No officers were murdered in 89% (2,776) of the 3,105 counties, one officer was slain in 8.1% (251) of the counties, and in only 2.5% of the counties were
two or more officers murdered.
Two common strategies for dealing with skewed data are to transform the dependent
variable to approximate normality and proceed with linear regression, or to combine all
outcomes greater than zero into a single category and employ binary logistic regression.
Transformations of these data, however, are unable to approximate a normal distribution, and dichotomizing the dependent variable for use with binary logistic regression
results in a loss of efficiency (Cameron & Trivedi, 1998). First recommended by
Kaminski (1997) for analyzing police killings, a now common strategy for analyzing
outcomes with many zeros and large positive skew is the use of count regression models, such as the Poisson, which we employ for the analysis (Cameron & Trivedi, 1998;
Long, 1997).9 Further, to control for unequal exposure, that is, differences in the number
of law enforcement officers at risk across counties, we include the number of FTE
sworn officers in 1996 as an offset in the regression (Long & Freese, 2001).
A second major concern in studies using spatially contiguous units such as counties or states is spatial autocorrelation, which when present can lead to underestimation of standard errors of parameter estimates (Odland, 1988).10 Tests for global and
local spatial autocorrelation on the dependent variable, without regressors, were statistically significant (Anselin, 2003).11 Note, however, that the spatial dependence
may be adequately accounted for with the introduction of regressors (Baller et al.,
2001). Two procedures are used to test for residual spatial dependence following the
introduction of the regressors. First, using the number of FTE sworn officers per
county as the population at risk, we used SatScan’s spatial scan statistic to test for
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364 Homicide Studies
Figure 1
Frequency Distribution of 544 Law Enforcement Officers
Murdered Across 3,105 Counties, 1999-2000
250
Number of Counties
200
150
100
50
1
2
3
4
5
6
7
11
12
14
16
20
26
Number of Officers Murdered
Note: Counties with zero counts excluded.
statically significant clustering of police homicides across counties, with the
assumption that the number of murders in each county is Poisson distributed
(Kulldorff, 1997, 2006). As anticipated (see, for example, Kaminski et al., 2000),
this identified a large statistically significant cluster (p = .001) in the southeastern
United States. Next, to adjust for covariates, we replaced the number of FTE sworn
officers per county with the predicted values from our Poisson regression model.12
No statistically significant clusters were detected with the introduction of the predicted values, suggesting that spatial autocorrelation is no longer problematic once
the regressors are in the model (Kulldorff, 2006).
Anselin’s alternative method was used as a second test for the presence of spatial
dependence (Kubrin & Weitzer, 2003; Land & Deane, 1992). This strategy involves
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Kaminski / County-Level Covariates of Police Homicides 365
a two-stage estimation procedure where the predicted values of the dependent variable from a regression model are multiplied by a spatial weights matrix.13 The resulting product is then included as a variable in the final regression model to adjust for
any remaining spatial dependence. This term was not nearly statistically significant
(p = .62) and its inclusion had virtually no impact on the other included regressors.
Given the negative results of both tests, we conclude that spatial autocorrelation is
not problematic. (Complete results of the tests are available upon request.)
A third major concern is collinearity among the regressors, an apparent common
problem in early general homicide research (Land et al., 1990). Diagnostic tests
were conducted using multiple linear regression, and the results suggested problems
with multicollinearity. Although variance inflation factors were not very high (four
regressors had values greater than 4.0 but less than 6.0), 5 condition indices were
greater than 15 (suggestive of a problem) and 2 were greater than 30 with variance
proportions greater than .50, indicating a serious problem (Belsley, Kuh, & Welsh,
1980; Myers & Well, 2003). Thus, we followed the example of Land et al. (1990)
and conducted a principal components analysis on conceptually similar regressors.
All regressors loaded into interpretable components at .80 or at a higher level. Three
components were extracted, explaining 78.1% of the variance. Component 1 is economic disadvantage, which consists of poverty, unemployment, and income.
Population size and density comprise component 2 (population structure), and component 3 is referred to as instability, which consists of the percentage of the population that is divorced and the percentage of the population still residing in the same
household as 5 years earlier (inversely related).14 Regression diagnostics after substituting these components for the original regressors showed substantial improvement in the collinearity diagnostics (no condition index greater than 30 and only one
variance inflation factor greater than 4.0).
A final concern in the study is that spatially large aggregates such as states or counties is the problem of within-unit heterogeneity (Bailey, 1984; Osgood & Chambers,
2000). Osgood and Chambers (2000) warned, for example, that analysis at the county
level treats a single value of each variable as being characteristic of an entire county,
whereas communities within a county may deviate substantially from the average. This
results in decreased variation in the independent variables, thereby reducing the ability to detect statistical relationships. However, Osgood and Chambers argued, “If a
meaningful level of variation occurs across counties, strong relationships should be
apparent, and any lack of precision would not introduce systematic biases” (p. 90).
Their county-level analysis provided substantial empirical support for their position.
Findings
Table 3 presents the results from four Poisson regression models. Model 1 shows
the initial estimates using all counties and all observations. Model 2 excludes three
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366 Homicide Studies
Table 3
Poisson Regression Models for All Counties, Counties With Populations
> 49,999, and After Removal of Three Influential Counties
Model
1
2
–3 Counties
3
Population
> 49,999
4
Pop. > 49,999 &
–3 Counties
Variable
All Counties
Economic disadvantage
Population structure
Instability
Black
South
West
Midwest
Urban
Age 25-34
Violent crime (residual)
Agency
Sworn (offset)
Constant
McFadden’s Pseudo R2
1.314***
0.961**
0.993
1.010**
1.609*
1.739*
1.574*
0.994***
1.073**
1.008
1.000
2.718
–8.148
0.4570
1.289***
0.999
0.975
1.010**
1.668**
1.717*
1.711**
0.994***
1.067*
1.029
1.001
2.718
–8.097
0.3787
1.186**
0.961*
0.958
1.017***
1.634*
1.986**
1.523*
0.997
1.062*
1.006
0.991*
2.718
–8.207
0.4878
1.159*
0.970
0.919
1.016***
1.703*
2.027*
1.769**
0.997
1.064.097
1.028
0.992.102
2.718
–8.286
0.3907
Note: Coefficients are exponentiated incidence rate ratios; significance tests are based on robust standard
errors; constants are not exponentiated.
*p ≤ .05. **p ≤ .01. ***p ≤ .001.
potentially high-leverage counties (New York, Los Angeles, and Cook counties).15
Model 3 excludes counties with populations less than 50,000 residents to determine
whether the obtained estimates are affected by the extreme variability in county population size (see, for example, Loftin & McDowall, 2003). Finally, Model 4 excludes
both the three high-leverage counties and counties with populations less than 50,000.
To conserve space, only exponentiated coefficients and indicators of statistical significance are presented (the full results are available upon request).
As shown in Model 1, economic disadvantage is strongly associated with
increased risk of police homicide (β = 1.31; p ≤ .000). The model suggests that each
unit increase in the economic disadvantage component is associated with a 31%
increase in the expected mean number of murders of police, controlling for other factors in the model. The impact of economic conditions is nearly identical when New
York, Los Angeles, and Cook Counties are excluded (Model 2). Although the magnitude of the effect is attenuated somewhat when excluding the smaller counties (Model
3), and when both smaller counties and the three outliers are excluded (Model 4), it
remains statistically significant and substantive. Therefore, we conclude that adverse
economic conditions are related to police risk of homicide at the county level.
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Kaminski / County-Level Covariates of Police Homicides 367
Population structure is significant in Model 1 (β = .961; p = .007) and Model 3
(β = .961; p = .022); however, unexpectedly, it is inversely related to killings of
police. Thus, this model suggests that the risk of being killed feloniously in the line
of duty is lower in counties characterized by large and dense populations. However,
population structure is not nearly statistically significant in Model 2 (β = .999; p =
.975) or Model 4 (β = .980; p = .616). Therefore, its impact in Models 1 and 2 is
dependent on the inclusion of Los Angeles, New York, and Cook Counties. This is
not surprising, as these counties have the largest police and civilian populations in
the United States, and New York County/City ranks highest in population density.
Interestingly, urbanicity affects the risk of police being killed feloniously in the
line of duty independently of population size and density, with the risk being lower
in counties with larger urban populations (β = .994; p ≤ .000). Specifically, each
additional percentage of the population residing in an urban area is associated with
a 6% decrease in the risk of officer homicide. The estimates are virtually identical in
Models 1 and 2; thus, the effect of urbanicity is insensitive to removal of the highleverage counties. However, urbanicity is statistically insignificant in Models 3 and
4, suggesting it is important only when many, largely rural counties are included.16
The third component, residential and family instability, is unrelated to homicides
in Model 1 (β = .993; p = .915), and it remains statistically insignificant in the remaining models. The bivariate analysis described earlier (see Note 14) suggested that percent divorced, but not percent still residing in the same household as 5 years earlier,
was related to murders of police. To assess their independent effects, Models 1-4 were
reestimated using the original variables one at a time in place of the component. In no
instance was either of the variables related to police killings (all p > .15).17
Model 1 suggests that each one unit increase across counties in the percentage of
the population that is non-Hispanic Black is associated with a 1% increase in risk of
police homicide (β = 1.01; p = .002). The effect of race is virtually unchanged with
the removal of New York, Los Angeles, and Cook Counties (Model 2), whereas it
increases somewhat in magnitude in Models 3 and 4 (β = 1.017 and 1.016, respectively). Thus, the risk of police being killed feloniously appears to be higher in counties with larger proportions of Black residents.
The three regional indicators in Model 1 show that the risk of homicide is substantially and significantly lower in the Northeast than in the other three regions.
County location in the South, for example, is associated with a 61% increase in the
expected number of police homicides. To test whether risk in the West and Midwest
regions is significantly different than in the South, we reestimated Model 1 using the
South as the reference category. The results (not displayed) indicate that neither the
West (β = 1.08; p = .621) nor the Midwest (β = 0.98; p = .859) are significantly different from the South regarding police homicide victimization risk. Although we
observe some variation in the magnitudes of the estimates and levels of significance
across the four models, the conclusion remains the same; the risk of homicide is
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368 Homicide Studies
significantly higher in the South, the Midwest, and the West than in the Northeast,
but the South is no riskier than the West or Midwest.
As expected, police risk of being killed feloniously is greater in counties with
larger percentages of persons aged 25-34 years. In Model 1, each one unit increase
in the age variable is associated with 7.3% increase in the expected number of police
homicides (β = 1.073; p = .006). The magnitude of the effect is similar across all
models, but in Model 4 it is statistically significant at the .10 level only (β = 1.06;
p = .097). We find a similar impact when substituting the percentage of persons aged
35-44 years in Model 1 (not shown), but it is significant only at the .10 level
(β = 1.09; p = .081). However, this age group does not approach statistical significance when the high-leverage counties are removed and/or when smaller population
counties are excluded. Estimates for the percentages of persons aged 14-17, 18-24,
and 45-54 years are unrelated to murders of police in all models (results not shown).
In Model 1, the violent crime residuals and the percentage of law enforcement agencies that were sheriff’s offices are unrelated to murders of police (both p > .24). The violent crime residuals remain insignificant in Models 2-4, but the percentage of sheriff’s
agencies is statistically significant in Model 3 (β = 0.991; p = .039), perhaps due to
greater variability in the mix of agency types in the larger counties. Although limited to
larger population counties, this suggests that police homicide risk may be higher in
counties that contain greater proportions of non-sheriff’s agencies. Note, however, that
in Model 4 the effect is not quite significant at the .10 level (β = 0.992; p = .102).
The models explain substantial amounts of the variance (McFadden’s R2 ranges
from .36 to .49). To further assess model fit, deviance residuals were plotted against
observation numbers (Hardin & Hilbe, 2001, p. 43), both before and after removal
of the three high-leverage counties and counties with populations less than 50,000
(see Figure 1A in Appendix). In the top graph, we observe two counties for which
Model 1 does a particularly poor job predicting police homicides. These are
Jennings County, Indiana, (population 25,608; two murders) and Powell County,
Kentucky (population 12,467; two murders). The largest negative residual is for San
Bernardino County, California (population = 1,563,907; zero murders). The pattern
of the residuals improve somewhat with removal of the small population counties
and the three influential cases, but clearly the models have a tendency to underpredict police homicide counts. Generally, however, the residuals appear reasonable.
In summary, the analysis provides strong support for the effects of adverse economic conditions, the percentage of the non-Hispanic Black population, and region
on the geographic patterning of police homicides in the contiguous United States.
There is also substantial support for the impact of urbanicity (when all counties are
included) and the percentage of the population aged 25-34 years. The effect of the
proportion of non-sheriff’s agencies appears to be important only for larger population counties, whereas the effect of population structure is conditional on the inclusion of the three high-leverage counties. We find no evidence that residential
instability, divorce, or the violent crime residuals are related to police homicides.
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Kaminski / County-Level Covariates of Police Homicides 369
Discussion
One of the more robust findings of the analysis is the effect of adverse economic
conditions on police risk of homicide victimization, and we conclude that local police
are significantly more likely to be murdered in counties characterized by low levels of
income and high levels of poverty and unemployment. Economic strains increase
motivations for crime, weaken formal and informal social controls, and generate
frustrations leading to diffuse hostility and aggression (Brantingham & Brantingham,
1984; Bursik & Grasmick, 1993; Krivo & Peterson, 1996; Parker & McCall, 1999;
Sampson et al., 1999; Sampson & Raudenbush, 1999; South & Cohen, 1985), which
arguably increase police officer proximity and exposure to motivated offenders.
Although this finding is consistent with some previous research on police killings
(Batton & Wilson, 2006; Chamlin, 1989; Kaminski, 2002, 2004; Kaminski & Marvell,
2002) and research on serious but nonlethal violence directed against police (Kaminski
et al., 2003), evidence for the impact of economic conditions on officer homicide victimization has largely been mixed (see Table 1). This inconsistency, however, may be
due to methodological shortcomings or other differences among studies. In any case,
this study provides strong support for the effects of economic conditions.
Because residential mobility, family disruption, and large and dense populations
have been associated with weak, formal and informal social controls and higher
levels of crime (Bursik & Grasmick, 1993; Kornhauser, 1978; Krivo & Peterson,
1996; Sampson et al., 1999; Sampson & Raudenbush, 1999; Shaw & McKay, 1969),
we expected these factors to be positively associated with homicides of police.
Residential stability and divorce, whether entered individually or as a combined
component, were unrelated to police homicides. Most studies have not included
measures of population mobility, but the limited evidence to date also suggests that
it is unrelated to murders of police (Kaminski, 2002, 2004). Several previous studies examined the impact of divorce, but with mixed results (Table 1).
Previous research on the effects of urbanicity and population size and density on
police homicide risk almost universally failed to find a relationship (see Table 1).
Interestingly, although we predicted a positive association between these factors and
murders of police, our analysis found that the risk of homicide is actually lower in more
urbanized counties and in counties with large and dense populations (though the impact
of population size/density is dependent on the inclusion of the high-leverage counties).
Although only speculation, a possible explanation may be found in differences in the
availability and quality of emergency trauma care between rural or largely rural counties
and their more urban counterparts (Kaminski et al., 2000; Kaminski & Marvell, 2002).
For example, in urban areas transport times are faster, high patient volume helps maintain provider skills, and greater population density increases local public financing
(Bonnie, Fulco, & Livermore, 1999). Although research shows significant differences
between rural and urban areas in mortality rates from traumatic injury (Bonnie, Fulco, &
Livermore, 1999), research on general homicides and medical resources is less conclusive (Doerner, 1988; Hanke & Gundlach, 1995; Giacopossi, Sparger, & Stein, 1992;
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370 Homicide Studies
Long-Onnen & Cheatwood, 1992). Kaminski and Marvell (2002) tested the effect of the
adoption of statewide trauma care systems on police homicides, but found no evidence
of a relationship. Addressing the role of trauma care is beyond the scope of this study,
but future work should examine its potential impact using improved measures.
The analysis found that police were significantly more likely to be killed feloniously in counties with larger Black populations. One explanation for this finding
is that the high rates of violent crime in Black communities (Blau & Blau, 1982;
Parker, 2001; Wilson, 1987) increase police proximity and exposure to offenders
who are willing to resort to violence to avoid arrest and punishment, including violence against the police (Kaminski, 2002, 2004). If this were true, we would expect
the effect of race to diminish once we controlled for levels of violent crime and other
conditions (e.g., economic deprivation, and residential and family instability).
However, percentage Black remained statistically significant even with these variables in the model. Other recent research also found that the effect of percentage
Black persisted, despite the inclusion of large numbers of regressors (Jacobs &
Carmichael, 2002; Kaminski & Stucky, 2005). Additional research is needed to
explain the persistence of percentage Black in studies of violence against the police.
None of the previous studies using cities or states as the unit of analysis found
strong support for regional differences in police homicide risk (with all but one study
using simple South vs. non-South comparisons), but the regional indicators in our
analysis showed that police risk of being murdered was significantly lower in counties located in the Northeast. Because our models controlled for the number of police
at risk, the types of law enforcement agencies within counties, and a variety of social
and economic conditions, we are unable to explain the persistence of the regional
effects. Interestingly, although the South typically has been characterized as being
particularly risky for police relative to other regions (Kaminski et al., 2000), our
results show that Southern counties were no riskier for police than counties located in
the West or the Midwest, seemingly negating Southern subculture of violence explanations for the high rate of police homicide victimization observed in the South.
We found that police risk of being killed was higher in counties with larger percentages of residents aged 25-34 years. The effect is significant across all models
except for the last (large population counties without outliers), where the effect is
significant at the .10 level. Estimates for older age groups are similar (age range of
35-44 years and 45-54 years), but not statistically significant in most models,
whereas younger-age categories are unrelated to police killings (age ranges of 14-17
years and 18-24 years). Perhaps this finding can be explained by greater police exposure to somewhat older, violent offenders. For example, violent crime index arrest
statistics compiled by the FBI show that the modal age category of arrestees in 1995
was 25-34 years (Federal Bureau of Investigation, 1995: table 39, pp. 218-219).
Although previous studies found virtually no association between age structure and
police killings, our results suggest that it may be premature to dismiss age effects in
macrolevel studies of violence against police.
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Kaminski / County-Level Covariates of Police Homicides 371
The analysis controlled for variation in the types of law enforcement agencies across
counties (percentage of sheriff’s agencies) because the risk of officer victimization may
be related in unknown ways to differences among them (e.g., function, geographical
coverage). The results suggest it may be important to do so in county-level analyses.
Although not statistically significant when small population counties are included, there
is evidence of an effect when analyzing larger population counties. This is probably
because smaller population counties are less likely than larger population counties to
contain many municipal police departments.18 In any case, when restricted to larger
population counties, the analysis suggests that police homicide risk increases with
increases in the proportion of non-sheriff’s agencies. Further study of violence against
police by agency type or function may be an interesting topic for future research.
One previous study found that variation in levels of violent crime was predictive
of serious but nonfatal attacks on police, even when various structural conditions
were controlled (Kaminski et al., 2003). However, despite the use of various measures of violent crime (violent crime residuals, violent crime count, violent crime
rate, violent crime rate residuals, and general homicide rate), we find no evidence of
an effect at the county level. It may be that the propensity for violence measure operates only at a local level of spatial aggregation. Another possible explanation for the
lack of an effect is measurement error associated with county-level UCR data (see
Maltz & Targonski, 2002), and an appropriate assessment of the impact of violent
crime at the county level may need to await corrections to those data.
To summarize, previous studies of homicides of police across enumerations units
have been limited to analyses using cities or states, and we believe our findings
demonstrate the utility of using county-level data to explain the patterning of killings
of police across the contiguous United States. We employed regression models appropriate for the analysis of rare-event counts; controlled the underlying population at
risk; and checked for overdispersion, spatial autocorrelation, multicollinearity, and
the influence of high-leverage counties. The models appear adequate, and the
included regressors explain substantial amounts of the “variance” in police killings.
The results show that police homicide risk is higher in economically depressed
counties, in less urbanized counties, in counties with larger percentages of Black residents, and in counties located in the South, West, and Midwest. Although less consistent, there is some evidence that police homicide risk is higher in counties with larger
percentages of non-sheriff’s agencies and persons aged 25-34 years. Population structure (size and density) was inversely related to murders of police, though its impact is
dependent on the inclusion of three high-leverage counties. We found no evidence that
police killings are related to two traditional measures of social disorganization—
population mobility and divorce rates. Finally, various measures of violent crime were
unrelated to police homicides. Although this study helps explain the patterning of
murders of police across the United States, given the overall lack of consistency of
findings in the extant research, we encourage further study of the causes and correlates
of violence against the police at multiple levels of areal aggregation using additional
and improved measures.
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372 Homicide Studies
Appendix
Figure 1A
Index Plots of Hat Diagonals Before & After Removal
of Los Angeles, New York, & Cook Counties
1.25
hat diagonal
1
NY
LA
.75
Cook
.5
.25
0
0
500
1000
1500
2000
2500
3000
1500
2000
Observation Number
2500
3000
Observation Number
1.25
hat diagonal
1
.75
.5
.25
0
0
500
1000
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Kaminski / County-Level Covariates of Police Homicides 373
Appendix (continued)
Figure 2A
Index Plots of Deviance Residuals Using All Counties, and Minus Los
Angeles, New York, & Cook Counties & Counties With Populations < 50,000
Jennings County, IN; pop = 25,608; 2 killed
4
Powell County, KY; pop = 12,467; 2 killed
3
deviance residual
2
0
–2
San Bernardino County, CA; pop = 1,563,907; 0 killed
–3
0
500
1000
1500
2000
2500
3000
2500
3000
Observation Number
4
3
deviance residual
2
0
–2
–3
0
500
1000
1500
2000
Observation Number
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374 Homicide Studies
Notes
1. One previous study used counties as the unit of analysis to test for statistically significant spatial clustering of police homicides, but that study controlled only for the underlying civilian population to estimate
risk (Kaminski, Jefferis, & Chanhatasilpa, 2000). Because the current study uses multiple regression to
explain the variation of murders of police across the United States, it represents a substantial improvement.
2. Attractiveness also is a major component of opportunity theory and is typically conceptualized as
the symbolic or economic value of targets to offenders (Garofalo, 1987, pp. 38-39; Miethe, Hughes, &
McDowall, 1991, p. 166; Miethe & McDowall, 1993, p. 749). However, the concept of attractiveness as
applied to the victimization of police officers requires substantial redefinition. Although some police officers may be sought out and murdered because of their “symbolic” value (e.g., killed because they are perceived as being representatives of a repressive government), because most officers are murdered by
offenders engaged in serious crime who wish to escape and avoid punishment (Cardarelli, 1968; Creamer
& Robin, 1970; Margarita, 1980b), it is arguable that instrumental rather than expressive motives can be
attributed to most offenders’ decisions to kill police:
The motivation is not to harm police because they are despised or because officers do something
to anger offenders. Rather, most offenders are motivated to kill or seriously injure police because
the potential opportunity costs associated with their current and/or past criminal activities are high
(e.g., safety, loss of freedom, reduced future income). Further, most active criminals wish to avoid
police, and are unlikely to seek officers out as “attractive” targets. (Kaminski, 2004, pp. 23-24)
3. African Americans are vastly overrepresented among those who kill law enforcement officers.
Specifically, though they represent only about 13% of the population, they constitute about 43% of the
felons who kill police (Brown & Langan, 2001).
4. Data on murders of police are considered to be highly reliable and valid (Chapman, 1998, p. 8;
Margarita, 1980a, p. 16), and they do not suffer from data problems typically associated with the Uniform
Crime Report (Maltz & Targonski, 2002). Homicides of police are the most widely publicized events in
law enforcement, and when assailants remain at large all law enforcement agencies are notified, including the FBI, with the hope that the perpetrator will be apprehended. When local police apprehend a suspect, at a minimum the FBI is notified to access the suspect’s criminal history file prior to trial (Chapman,
1998, p. 8; Konstantin, 1984, p. 34). In addition to receiving notification of duty-related deaths directly
from state and local law enforcement agencies, the FBI receives notification from its field divisions and
legal attaché officers, and from the Public Safety Officers’ Benefits Program (administered by the Bureau
of Justice Assistance). Once notification has been made, the FBI obtains additional details concerning the
circumstances surrounding the death from the victim officer’s employing agency. The primary source of
error is the rare incident where the cause of death is not clearly identified (Konstantin, 1984, p. 34).
5. The five New York City Counties (Richmond, Queens, Kings, Bronx, and New York) were merged
into a single polygon and treated as a single entity because the data did not allow for the apportioning of
New York City police officers killed to their respective boroughs. Other adjustments also were made in
merging the county-level data, such as deleting South Boston County, Massachusetts (because of a
merger), counties in Alaska and Hawaii, and Yellowstone National Park. The final number of counties
used in the analysis is 3,105.
6. The subculture-of-violence thesis also has been employed as an explanation for the high Black
crime rates in urban areas (Wolfgang & Ferracuti, 1967), which essentially posits that some subcultures
provide greater normative support for violence in upholding values such as honor, courage, and manliness. Although measurement and design issues leave the debate unsettled, there appears to be more
research support for theoretical perspectives emphasizing structural rather then cultural explanations
(Parker et al., 1999, p. 109).
7. Cultural/subcultural explanations for the observed high levels of homicide in the South essentially
posit that the Southern subculture provides greater normative support for violence in upholding values
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Kaminski / County-Level Covariates of Police Homicides 375
such as honor, courage, and manliness, though not necessarily a culture that condones violence (Corzine
et al., 1999; Gastil, 1971; Hackney, 1969). Cultures more supportive of expressions of physical aggression and combat in response to threats to one’s honor or as a measure of daring and courage increase the
likelihood of violence and homicide (Wolfgang & Ferracuti, 1967).
8. Crime data were not available for 128 counties. Also, we advise readers that county-level crime
data suffer from a number of limitations, and thus caution must be used when interpreting the effects of
this regressor (for details, see Maltz & Targonski, 2002).
9. In practice, count data are frequently overdispersed; that is, the variance is greater than the mean,
which violates the Poisson assumption of equidispersion (the mean and variance of the event counts are
equal). In this case, the Poisson regression model can produce inefficient (though consistent) estimates,
and z tests may overestimate the significance of variables (Long, 1997, p. 230). An alternative to the
Poisson under these conditions is the negative binomial regression model. However, a likelihood-ratio test
of the overdispersion parameter from a negative binomial regression suggests our model is not overdispersed, and a comparison of estimates and standard errors across models shows virtually no differences.
These results are available on request. Note further that given the large number of zero values a zeroinflated Poisson (ZIP) model is arguably more appropriate for the analysis (Long, 1997). We attempted
to estimate a ZIP model, but for reasons unclear we were unable to get the model to converge.
10. Spatial autocorrelation can occur when the enumeration units being analyzed share boundaries
that result in a structure to the data. Units that share physical boundaries or are closer to each other are
likely more similar than units not sharing physical boundaries or those that are farther away from one
another. Thus, geographic data may often fail to meet the assumption that observations are independent.
The consequence is that the errors will not be independent—a condition necessary for valid hypothesis
tests. The consequences of spatial autocorrelation are the same as in temporal autocorrelation, that is, the
standard errors will be biased, and t statistics used to test the null hypothesis may seriously overstate the
statistical significance of an effect. This can lead to the mistaken conclusion that variables are related
when they are not (Odland, 1988).
11. Global Moran’s I = .0907 (p = .0020) with 999 permutations; local Moran statistics indicate significant clustering for 312 observations (p ≤ .05) with 999 permutations.
12. Although SatScan allows the introduction of categorical covariates, it cannot handle continuous
covariates; hence, Kulldorff’s recommendation to use the predicted values from a regression model.
13. Our spatial weights matrix consisted of a first-order spatial lag of the dependent variable using the
queen criterion. All calculations were carried out with GeoDa (version 9.5-i; Anselin, 2003).
14. We examined each individual regressor’s relationship to police killings by entering each into
bivariate Poisson model using the number of full-time equivalent (FTE) sworn officers as the offset.
Poverty, unemployment, and income were all highly significant (all p ≤ .000) and in the expected direction. Percent divorced also was highly significant (p ≤ .000) and positive, but percent still residing in the
same house as 5 years earlier was not significant (p = .902), and it was in the opposite direction expected.
Population size (logged, as the model using the raw metric failed to properly converge) and population
density also were both highly significant (p ≤ .000) but inversely related.
15. Diagonal entries from the regression model’s hat matrix, hii, are useful for detecting influential
observations (Cameron & Trivedi, 1998, p. 150) and are presented in Figure 2A in the Appendix. The top
graph suggests that New York City (all five boroughs combined), Los Angeles County, and Cook County
exert a strong influence on the estimates in Model 1. The bottom graph in Figure 1A in the Appendix
displays the results after removal of these three counties.
16. Counties with populations less than 50,000 had on average only 1.9% of the population residing
within urbanized areas (93% had no residents living in urbanized areas), whereas counties with populations of 50,000 or more had on average 48.7% of the population residing within urbanized areas (23%
had no residents living in urbanized areas).
17. We also tested the effect of an interaction term between the two original variables, but the interaction term did not even approach statistical significance in any model.
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376 Homicide Studies
18. Sheriff’s departments accounted for a third of the agencies in 21.1% of the small population counties (SPCs), for half in 24.5%, and they were the sole local law enforcement agency in 10.7% of the SPCs.
Conversely, sheriff’s departments accounted for a third of agencies in only 7.8% of the large population
counties (LPCs), for half in 5.7%, and they were the sole local agency in only 7 counties (0.8%). Thus,
sheriff’s departments accounted for a third or more of the law enforcement agencies in more than half of
the SPCs (56.3%), but did so in only 14.3% of the LPCs.
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Robert J. Kaminski is an assistant professor in the Department of Criminology and Criminal Justice,
University of South Carolina. His research interests include public perceptions of the police, police use
of force, violence against the police, less lethal technology, crime mapping and spatial analysis, and
applied quantitative methods.
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